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Removing DESpecs directory which deserted to git
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Wed, 29 Nov 2017 16:55:37 +0100
parents 22d6a63640c6
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<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" version="1.0">
  <metadata>
    <dcterms:identifier>ECHO:YHKVZ7B4.xml</dcterms:identifier>
    <dcterms:creator>Alvarus Thomas</dcterms:creator>
    <dcterms:title xml:lang="la">Liber de triplici motu proportionibus annexis magiſtri Aluari Thome Ulixboneñ philoſophicas Suiſeth calculationes ex parte declarans</dcterms:title>
    <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language>
    <dcterms:date xsi:type="dcterms:W3CDTF">1509</dcterms:date>
    <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">
    <div xml:id="N10028" level="1" n="1" type="front">
      <div xml:id="N1002C" level="2" n="1" type="cover">
        <pb file="0001" n="1"/>
        <pb file="0002" n="2"/>
        <figure xml:id="N10036">
          <image file="0002-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0002-01"/>
        </figure>
        <pb file="0003" n="3"/>
        <pb file="0004" n="4"/>
        <figure xml:id="N10040">
          <image file="0004-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0004-01"/>
        </figure>
        <pb file="0005" n="5"/>
      </div>
      <div xml:id="N10047" level="2" n="1" type="dedication">
        <div xml:id="N1004B" level="3" n="1" type="other" type-free="letter">
          <head xml:id="N10050" xml:space="preserve">¶ Illuſtri et magnifico viro domino Petro de meneſes animi non minus <reg norm="quam" type="wordlist">ꝙ̄</reg> ſanguinis gene-<lb/>roſitate perdito liberalium ſimul et ſacrarum litterarum peritiſſimo aſylio <reg norm="protectorique" faithful="protectori" type="simple">protectoriqꝫ</reg> ſuo <lb/>Aluarus Thomas ſalutem plurimam dicit.</head>
          <p xml:id="N10057">
            <s xml:id="N10058" xml:space="preserve">PRodiderunt veteres clauem herculis templi ſui toxibus <reg norm="appenſam" type="context">appēſam</reg> <lb/>procul hinc canes et muſcas ſolo <reg norm="quidem" type="context">quidē</reg> olfactu abigere </s>
            <s xml:id="N1005D" xml:space="preserve"><reg norm="Non" type="context">Nõ</reg> ſecus et <reg norm="omnis" type="wordlist">omīs</reg> <reg norm="litteratorum" type="context">litteratorū</reg> <reg norm="chorus" type="simple">chorꝰ</reg> <lb/>qui ſuis monumentis eternitati <reg norm="commendari" type="context">cõmendari</reg> velint extimat ſuam feturam inſignis <reg norm="cuiuſpiam" type="wordlist">cuiuſpiaꝫ</reg> <lb/>patroni nomine perinde vt claua fretam et ab omnibus oblocutorum aculeis vindicari et auſpicato <lb/>in vulgus exire. </s>
            <s xml:id="N10066" xml:space="preserve">Quos igitur fetus iam dudum parturio nunc pariturus et in lucem emiſſurus (genero­<lb/>ſiſſime petre) tenellos adhuc et implumes tibi deſtino credo <reg norm="commendo" type="context">cõmendo</reg> patiare precor eas tuis ſub alia <lb/>deliteſcere <reg norm="tuique" faithful="tui" type="simple">tuiqꝫ</reg> ſub nominis vmbra recumbere </s>
            <s xml:id="N1006D" xml:space="preserve">Cuius (ſpero) non minus <reg norm="quam" type="wordlist">ꝙ̄</reg> herculee claue olfactu lon-<lb/>ge repellantur canini rictus et oblatratores inuiduli. </s>
            <s xml:id="N10072" xml:space="preserve">Te ſane <reg norm="vnum" type="context">vnū</reg> preceteris mihi <reg norm="patronum" type="context">patronū</reg> eo iuſtius <lb/>elegerim <reg norm="quae" type="wordlist"></reg> et tua ipſius maieſtate familiariter (que tua eſt comitas) quondam vſus ſim et <reg norm="litterarum" type="context">litterarū</reg> ſis <lb/>non minus peritus <reg norm="quam" type="wordlist">ꝙ̄</reg> apperens. </s>
            <s xml:id="N10079" xml:space="preserve">Quis enim illiteratum litterarum <reg norm="defenſorem" type="context">defēſorem</reg>, libidinoſum pudicitie <lb/>et iniuſtum iuſticie putauerit. </s>
            <s xml:id="N1007E" xml:space="preserve">Nempe (ſi chriſtiano poete credas) </s>
            <s xml:id="N10081" xml:space="preserve">Nulla ſub iniuſto virtus eſt principe <lb/>tuta. </s>
            <s xml:id="N10086" xml:space="preserve">Nulla ſub inceſto caſtis eſt gloria rege. </s>
            <s xml:id="N10089" xml:space="preserve">Quis <reg norm="autem" resp="SPT" type="wordlist">aūt</reg> <reg norm="litteratorum(?)" resp="SPT" type="wordlist">litteratuꝫ</reg> te neget qui patriis litteris apprime <lb/>imbutus <reg norm="externarumque" faithful="externarum" type="simple">externarumqꝫ</reg> auidus vltimos gallie ſinus penetraſti non modo viſurus quos ex libris noue­<lb/>ras verum et eos et alios parrhiſtis (vbi <reg norm="frequentem" type="context">frequētem</reg> eruditorum noſti coronam) auditurus. </s>
            <s xml:id="N10090" xml:space="preserve">Sic Pitha­<lb/>goras memphitichos vates (vt cum ieronimo loquar.) </s>
            <s xml:id="N10095" xml:space="preserve">Sic. Plato egiptum et architeu <reg norm="tarentinum" type="context context">tarētinū</reg> <reg norm="eamque" faithful="eam" type="simple">eamqꝫ</reg> <lb/>oram italie (que quondam magna grecia dicebatur) laborioſiſſime peragrauit. </s>
            <s xml:id="N1009A" xml:space="preserve">vt qui athenis magi-<lb/>ſter erat et potens: <reg norm="cuiuſque" faithful="cuiuſ" type="simple">cuiuſqꝫ</reg> dogmata achademie gymnaſia <reg norm="perſonabant" type="context">perſonabãt</reg> fieret peregrinus <reg norm="atque" faithful="at" type="simple">atqꝫ</reg> diſcipu-<lb/>lus malens aliena verecunde diſcere <reg norm="quam" type="wordlist">ꝙ̄</reg> ſua <reg norm="impudenter" type="context">impudēter</reg> ingenere. </s>
            <s xml:id="N100A1" xml:space="preserve">Hac ſane in peregrinatione tua <reg norm="non" type="wordlist">nõ</reg> me­<lb/>diocrem glorie cumulum (vel inimico iudice) aſſequutus es. </s>
            <s xml:id="N100A6" xml:space="preserve">nec <reg norm="minorem" type="context">minorē</reg> <reg norm="quam" type="wordlist">ꝙ̄</reg> illi tui fratres ſtudio rei mili-<lb/>taris: quin et longe (auſim dicere) maiorem. </s>
            <s xml:id="N100AB" xml:space="preserve">Hi enim ex mediis barbariei penetralibus ex efferatis nu­<lb/>midie <reg norm="ethiopieque" faithful="ethiopie" type="simple">ethiopieqꝫ</reg> gentibus ſummamt fateor fortitudinis laudem reportarunt ſed fluxam: ſed <reg norm="caducam" type="simple">caducaꝫ</reg> <lb/></s>
            <s xml:id="N100B1" xml:space="preserve">Tibi vero theſaurum doctrine immarceſſibilem et <reg norm="perpetuum" type="context">perpetuū</reg> nec vetuſtatis cariem: nec euidente: nec <lb/>ipſa <reg norm="denique" faithful="deni" type="simple">deniqꝫ</reg> iouia fulmina reformidantem comparaſſi. </s>
            <s xml:id="N100B6" xml:space="preserve">Sed ne palpo videar et vanus aſſentator vel po­<lb/>tius tuas laudes grauiore tuba decantandas ingenii culpa deteram, audaculum nimis calamum <reg norm="com- peſco" type="context">cõ-<lb/>peſco</reg> </s>
            <s xml:id="N100BD" xml:space="preserve">Noſtros autem liberos (libros intelligo) quo et reliquos omnis ſoles vultu excipe <reg norm="tuoque" faithful="tuo" type="simple">tuoqꝫ</reg> patro-<lb/>cinio non dedignare queſo vale.</s>
          </p>
        </div>
        <div xml:id="N100C2" level="3" n="1" type="other" type-free="poem">
          <cb/>
          <head xml:id="N100C8" xml:space="preserve">Ioannes de haxa argutiſſimo viro domino <lb/><reg norm="hermanno" type="context">hermãno</reg> lethemate de gouda germane natio­<lb/>nis procuratori bene merito. Salutem</head>
          <p xml:id="N100CF">
            <s xml:id="N100D0" xml:space="preserve">Aurea vinaci manat depectore virtus:</s>
          </p>
          <p xml:id="N100D3">
            <s xml:id="N100D4" xml:space="preserve">Pullulat et dexter iam grauitate furor.</s>
          </p>
          <p xml:id="N100D7">
            <s xml:id="N100D8" xml:space="preserve">Soluentur rabidi maturo robore gryphi</s>
          </p>
          <p xml:id="N100DB">
            <s xml:id="N100DC" xml:space="preserve">Surget et exiguis viribus hydra ferox.</s>
          </p>
          <p xml:id="N100DF">
            <s xml:id="N100E0" xml:space="preserve">Nam ſophie aluarus thomas <reg norm="radiantis" type="context">radiãtis</reg> abiſſo</s>
          </p>
          <p xml:id="N100E3">
            <s xml:id="N100E4" xml:space="preserve">Septuplici merſus: condidit arte librum.</s>
          </p>
          <p xml:id="N100E7">
            <s xml:id="N100E8" xml:space="preserve">Hunc tamen arcta tenent mordaci ſcrinia dente</s>
          </p>
          <p xml:id="N100EB">
            <s xml:id="N100EC" xml:space="preserve">Quae tibi non aliis cuncta patere reor.</s>
          </p>
          <p xml:id="N100EF">
            <s xml:id="N100F0" xml:space="preserve">Fac pateat poſco placeat conſire fidelem:</s>
          </p>
          <p xml:id="N100F3">
            <s xml:id="N100F4" xml:space="preserve">Pallados et genti ferre memento pedem</s>
          </p>
          <p xml:id="N100F7">
            <s xml:id="N100F8" xml:space="preserve">Senſa docet ſophiae ſcrutans agioſmata gauro</s>
          </p>
          <cb/>
          <p xml:id="N100FC">
            <s xml:id="N100FD" xml:space="preserve">Grandiſonae ſtudio: maxima quaeque canit.</s>
          </p>
          <p xml:id="N10100">
            <s xml:id="N10101" xml:space="preserve">Uendicet etetra pietas caligine lucem</s>
          </p>
          <p xml:id="N10104">
            <s xml:id="N10105" xml:space="preserve">Suppetat et cunctis membra toroſa viris.</s>
          </p>
        </div>
        <div xml:id="N10108" level="3" n="2" type="other" type-free="poem">
          <head xml:id="N1010D" xml:space="preserve">Dionyſius faber vindocinenſis lectori <lb/>Octoſticon.</head>
          <p xml:id="N10112">
            <s xml:id="N10113" xml:space="preserve"><reg norm="Quiſquis" type="simple">Quiſq̇s</reg> amas phiſicis annexa matemata ſenſis</s>
          </p>
          <p xml:id="N10116">
            <s xml:id="N10117" xml:space="preserve">Et dubio certum figere callepedem</s>
          </p>
          <p xml:id="N1011A">
            <s xml:id="N1011B" xml:space="preserve">Si vacat huic raptum volendo crede libello</s>
          </p>
          <p xml:id="N1011E">
            <s xml:id="N1011F" xml:space="preserve">Exigui minimum temporis articulum.</s>
          </p>
          <p xml:id="N10122">
            <s xml:id="N10123" xml:space="preserve">Grata <reg norm="ſatiſque" faithful="ſatiſ" type="simple">ſatiſqꝫ</reg> tuo noris factura palato</s>
          </p>
          <p xml:id="N10126">
            <s xml:id="N10127" xml:space="preserve">Bis lectum relegas gratia maior erit</s>
          </p>
          <p xml:id="N1012A">
            <s xml:id="N1012B" xml:space="preserve">Nec repetita tibi pariet faſtidia crambe</s>
          </p>
          <p xml:id="N1012E">
            <s xml:id="N1012F" xml:space="preserve">Que ter lecta iuuant ter <reg norm="quoque" faithful="quo" type="simple">quoqꝫ</reg> lecta placent.</s>
          </p>
        </div>
      </div>
    </div>
    <div xml:id="N10132" level="1" n="1" type="body">
      <div xml:id="N10136" level="2" n="1" type="other" type-free="pars">
        <div xml:id="N1013B" level="3" n="1" type="preface">
          <pb chead="Prohemium" file="0006" n="6"/>
          <p xml:id="N10143">
            <s xml:id="N10144" xml:space="preserve">PReclara philonis in libro ſa­<lb/>pientie exſtat ſantentia deum <reg norm="maximum" type="context">maximū</reg> <lb/><reg norm="optimumque" faithful="optimum" type="simple">optimumqꝫ</reg> rerum omnium natura ↄ̨-<lb/>ſtantium opificem, cunctorum <reg norm="ſubſtantiam" type="context">ſubſtãtiam</reg> <reg norm="atque" faithful="at" type="simple">atqꝫ</reg> <reg norm="com- paginem" type="context">cõ-<lb/>paginem</reg> numero, menſura, ac pondere procre-<lb/>aſſe <reg norm="atque" faithful="at" type="simple">atqꝫ</reg> diſpoſuiſſe: cui applaudit illud prophe-<lb/>te qui profert numero ſeculum.             <anchor type="note" xlink:href="note-0006-01" xlink:label="note-0006-01a"/>             </s>
            <s xml:id="N10158" xml:space="preserve">Cui etiam aſtipu-<lb/>latur diuus ille plato in thimeo. magna auctori-<lb/>tate commendans deum numeris mundum fabri­<lb/>caſſe.             <anchor type="note" xlink:href="note-0006-02" xlink:label="note-0006-02a"/>             </s>
            <s xml:id="N10166" xml:space="preserve">Quam <reg norm="ſcententiam" type="context">ſcentētiam</reg>. Aurelius. Auguſtinus <lb/>libro de ciuitate dei <reg norm="commendat" type="context">cõmendat</reg>. </s>
            <s xml:id="N1016B" xml:space="preserve">Quapropter inti­<lb/>ma, <reg norm="ſecretioraque" faithful="ſecretiora" type="simple">ſecretioraqꝫ</reg> nature <reg norm="atque" faithful="at" type="simple">atqꝫ</reg> minerue penetralia, <lb/><reg norm="rerumque" faithful="rerum" type="simple">rerumqꝫ</reg> <reg norm="omnium" type="wordlist">oīm</reg> naturalium reconditas paſſiones, <lb/>ac motus qui numeris <reg norm="conſiſtunt" type="context">cõſiſtunt</reg> <reg norm="perſcrutari" type="simple">ꝑſcrutari</reg> <reg norm="atque" faithful="at" type="simple">atqꝫ</reg> ri-<lb/>mari volentes. </s>
            <s xml:id="N10176" xml:space="preserve">arithmeticam at geometricã aut <lb/>ſaltem harū ſcententiaꝝ quedam requiſita docu-<lb/>mēta neceſſum eſt anteponãt.             <anchor type="note" xlink:href="note-0006-03" xlink:label="note-0006-03a"/>             </s>
            <s xml:id="N10182" xml:space="preserve">Et non abs re quidē <lb/>quoniam non ſolū elementaris hec regio: et natu­<lb/>ralia illa entia: que in ea natura ꝓcreãda cenſuit <lb/>his nuēris et geometricis ponderibus conſtant: <lb/>verumetiam ethereus ille celorum globus (vt inq̇t <lb/>plinius et ariſtoteles) pythagore ſcententia arith­<lb/>meticis ꝓportionibus, muſiciſ tonis circūuolui­<lb/>tur. </s>
            <s xml:id="N10193" xml:space="preserve">Inquit enim ſaturnum dorio moueri, mercu­<lb/>rium pthogo iouem phrygio. </s>
            <s xml:id="N10198" xml:space="preserve">Quantã vim arith­<lb/>metica ſcententia habeant ad philoſophiam vni-<lb/>uerſaſ diſciplinas. </s>
            <s xml:id="N1019F" xml:space="preserve">luculenter in libro de legibꝰ <lb/>diuus plato hoſtendit inquiens Legiſlator ciuibꝰ <lb/>omnibus p̄cipiat ne a numerorum ordine quo ad <lb/>poſſunt diſcedant </s>
            <s xml:id="N101A8" xml:space="preserve">Nã nulla alia diſciplina ad rei <lb/>familiaris gubernationē, ad rē publicã, ad artes <lb/>deni vniuerſas, tãtã hꝫ vim: quantã hmõi nume­<lb/>rorū cognitio. </s>
            <s xml:id="N101B1" xml:space="preserve">Sõnolentos, etiã a natura rudes, <lb/>excitat. </s>
            <s xml:id="N101B6" xml:space="preserve">et dociles, memores, ſolerteſ, facit p̄ter <lb/>naturã ſuã diuīa arte ꝓficientes </s>
            <s xml:id="N101BB" xml:space="preserve">Incõcuſſa em̄ et in­<lb/>uiolata eſt arithmetice at geometrice ſcīa. </s>
            <s xml:id="N101C0" xml:space="preserve">cuiꝰ <lb/>veritati ſacratiſſime ſanctiones auctoritatem pre­<lb/>bēt īquiētes arithmeticã et geometricã in ſe ita­<lb/>tē cõtinere et quãuis pietatis ſcīe non ſint:             <anchor type="note" xlink:href="note-0006-04" xlink:label="note-0006-04a"/>             ſunt tñ <lb/>maxīo admīculo at adiumento ipſi ſcīe pietatis <lb/>vt p̄clare. Aureliꝰ ille Auguſtinꝰ ī libro de doctri­<lb/>na chriſtiana ſacrꝪ ↄ̨probat rõibus. </s>
            <s xml:id="N101D4" xml:space="preserve">Has eī ſapiēs <lb/>ille ſalomõ dicit pediſſeq̈s, at ancillas theolo-<lb/>gie: q̈s iubet vocari ad turrim, et ad menica cinita­<lb/>tis.             <anchor type="note" xlink:href="note-0006-05" xlink:label="note-0006-05a"/>             </s>
            <s xml:id="N101E2" xml:space="preserve">His eī ꝓſtergatis: qui ad theologiſãdū et phi-<lb/>loſophãdū ꝓgredit̄̄ (ſi diuo Seuerino boetio cre­<lb/>dimꝰ) ſuꝑflue conat̄̄. </s>
            <s xml:id="N101E9" xml:space="preserve">Ad philoſophiã vti temere <lb/>his mathemathicis omiſſis documētis accedētes <lb/>phīa ipſa ſacrilogos, ſui minimis īuaſores ve­<lb/>ſtem ſuã in fruſtra lacerantes (teſte boetio) appel-<lb/>lat. </s>
            <s xml:id="N101F4" xml:space="preserve">Et vt verū fatear hinc eſt /  nr̄is tꝑibus ob ha­<lb/>rū diſciplinarū defectū: balbutiens at cõcutiēs <lb/>viſa ē phīa. </s>
            <s xml:id="N101FB" xml:space="preserve">Plurimū em̄ apḋ grecos phīa valuit <lb/>ṗmatū obtinuit: q2 (vt inq̇t cicero) ī ſūmo hono-<lb/>re apud illos geometrica fuit nihil apḋ eos ma­<lb/>thematicis illuſtriꝰ </s>
            <s xml:id="N10204" xml:space="preserve">Nõ ī merito igit̄̄: ſpeculationi­<lb/>bus phyſicis triplicis motus: tractaculū ꝓportio­<lb/>nū ex mathematicis codicibus deprõptū duximꝰ <lb/>p̄ponēdū et quãtū ingenioli nr̄i vires ſupetūt ab-<lb/>ſoluēdū. </s>
            <s xml:id="N1020F" xml:space="preserve">¶ Ad rē ipſaꝫ veniēdo: tractatulus hic ṗn­<lb/>cipaliter tripatient̄̄. </s>
            <s xml:id="N10214" xml:space="preserve">In prīa / em̄ ꝑte prīcipali q̄dã <lb/>cõmunia mathemathicalia cū terminoꝝ declara­<lb/>tionibus ponã. </s>
            <s xml:id="N1021B" xml:space="preserve">In ſecūda / ꝓportionalitatē ꝓpor­<lb/>tionū declarabo. </s>
            <s xml:id="N10220" xml:space="preserve">In tertia / vero parte principali <lb/>ea applicabo ad motus et motuum ꝓportiones.</s>
          </p>
          <div xml:id="N10225" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0006-01a" xlink:label="note-0006-01" xml:id="N10229" xml:space="preserve">plato in <lb/>thimeo.</note>
            <note position="left" xlink:href="note-0006-02a" xlink:label="note-0006-02" xml:id="N10231" xml:space="preserve">Auguſti-<lb/>nꝰ .12. de <lb/>ciuitate. <lb/>c. 18.</note>
            <note position="left" xlink:href="note-0006-03a" xlink:label="note-0006-03" xml:id="N1023D" xml:space="preserve">pliniꝰ ī .2 <lb/>nahiſ. c. <lb/>22.</note>
            <note position="left" xlink:href="note-0006-04a" xlink:label="note-0006-04" xml:id="N10247" xml:space="preserve">auguſti-<lb/>nus .3. de <lb/>doc chriſ</note>
            <note position="left" xlink:href="note-0006-05a" xlink:label="note-0006-05" xml:id="N10251" xml:space="preserve">boetiꝰ ṗ-<lb/>mo de cõ. <lb/>phi. ꝓpri­<lb/>ma.</note>
          </div>
        </div>
        <div xml:id="N1025D" level="3" n="1" type="chapter" type-free="capitulum">
          <cb chead="Incipiunt proportiones"/>
          <head xml:id="N10264" xml:space="preserve">Capitulum primum de <lb/>proportione et eius diuiſione.</head>
          <note position="right" xml:id="N10269" xml:space="preserve">propoſi-<lb/>tio nicho­<lb/>machi.</note>
          <p xml:id="N10271">
            <s xml:id="N10272" xml:space="preserve">OMnis numerus: et ſimiliter <lb/>oīs qunatitas ad alium numerum relatus <lb/>(vt ait nichomachus et boetius in primo <lb/>arithmetice) aut eſt ei equalis: aut inequalis. </s>
            <s xml:id="N1027B" xml:space="preserve">ſi eſt <lb/>equalis: conſtituit ꝓportionem equalitatis: ſi ve-<lb/>ro inequalis: ex eo cū altero inequalitatis propor­<lb/>tio conſurgit. </s>
            <s xml:id="N10284" xml:space="preserve">¶ Unde proportio eſt duorū nume-<lb/>roꝝ: vel duarū quãtitatū: vnius ad alterã certa ha­<lb/>bitudo. </s>
            <s xml:id="N1028B" xml:space="preserve">vt habitudo que eſt inter quatuor et .4. et <lb/>que eſt inter duo et quatuor: et que eſt īter bipeda­<lb/>le et pedale. </s>
            <s xml:id="N10292" xml:space="preserve">Proportio em̄ eſt terminus collecti-<lb/>uus: pro duabus rebus et ſignanter quantis vel ꝓ <lb/>pluribus ſupponens: cõnotando ipſas eſſe equa-<lb/>les: vel vnam alteram aliquo exceſſu excedere. </s>
            <s xml:id="N1029B" xml:space="preserve">Un­<lb/>de iſta conſequentia nichil valet. </s>
            <s xml:id="N102A0" xml:space="preserve">hec proportio eſt <lb/>vna proportio / ergo eſt vnuꝫ ens: quia demonſtra­<lb/>to pedali et bipedali non conſtituentibus vnū de <lb/>illis eſt verum dicere:  ſunt aliqua ꝓportio puta <lb/>dupla: et tamen illa duo non ſunt vnū ens. </s>
            <s xml:id="N102AB" xml:space="preserve">¶ Du-<lb/>plex autē eſt proportio. </s>
            <s xml:id="N102B0" xml:space="preserve">q2 quedã eſt ꝓportio equa­<lb/>litatis: alia vero inequalitatis.             <anchor type="note" xlink:href="note-0006-06" xlink:label="note-0006-06a"/>             </s>
            <s xml:id="N102BA" xml:space="preserve">¶ Proportio eq̈-<lb/>litatis: eſt habitudo duarum quantitatum vel nu­<lb/>merorū equalium. </s>
            <s xml:id="N102C1" xml:space="preserve">vt habitudo q̄ eſt inter .8. et .8. <lb/>pedale et pedale. </s>
            <s xml:id="N102C6" xml:space="preserve">Et ſumat̄̄ hic quãtitas: tã ꝓ quã-<lb/>titate molis: quam pro quantitate virtutis.             <anchor type="note" xlink:href="note-0006-07" xlink:label="note-0006-07a"/>             </s>
            <s xml:id="N102D0" xml:space="preserve">vt ca-<lb/>pit beatus. Auguſtinus quinto de trinitate </s>
            <s xml:id="N102D5" xml:space="preserve">¶ Sed <lb/>proportio inequalitatis eſt duarum quantitatuꝫ <lb/>vel numerorum: vnius ad alterum certa habitudo <lb/>vt ꝓportio que eſt inter .2. et .4. pedale et bipedale <lb/></s>
            <s xml:id="N102DF" xml:space="preserve">¶ Item proportionum inequalitatis: quedam eſt <lb/>maioris inequalitatis: quedam. </s>
            <s xml:id="N102E4" xml:space="preserve">vero minoris.</s>
          </p>
          <div xml:id="N102E7" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0006-06a" xlink:label="note-0006-06" xml:id="N102EB" xml:space="preserve">diuiſio ꝓ­<lb/>portionū</note>
            <note position="right" xlink:href="note-0006-07a" xlink:label="note-0006-07" xml:id="N102F3" xml:space="preserve">auguſti-<lb/>nus .5. de <lb/>trinitate</note>
          </div>
          <note position="right" xml:id="N102FD" xml:space="preserve">diuiſio ꝓ­<lb/>portionū <lb/>īeq̈litatꝪ</note>
          <p xml:id="N10305">
            <s xml:id="N10306" xml:space="preserve">¶ Proportio maioris inequalitatis eſt habitu-<lb/>do maioris quantitatis ad minorem. </s>
            <s xml:id="N1030B" xml:space="preserve">vt habitudo <lb/>que eſt inter .quattuor. et .2. </s>
            <s xml:id="N10310" xml:space="preserve">¶ Sed proportio mi-<lb/>noris inequalitatis: eſt habitudo minoris quan-<lb/>titatis ad maiorē. </s>
            <s xml:id="N10317" xml:space="preserve">vt habitudo duorū ad .4. </s>
            <s xml:id="N1031A" xml:space="preserve">¶ Ex <lb/>quo ſequitur /  pro eiſdem ſupponunt iſti duo ter­<lb/>mini proportio maioris inequalitatis et propor-<lb/>tio minoris inequalitatis. </s>
            <s xml:id="N10323" xml:space="preserve">Connotat tamen <lb/>iſte terminus proportio maioris inequalitatis  <lb/>numerus maior excedat minorem. </s>
            <s xml:id="N1032A" xml:space="preserve">iſte vero termi-<lb/>nus ꝓportio minoris inequalitatis: connotat:  <lb/>numero minor ſiue quantitatis minor exceditur a <lb/>a maiore. </s>
            <s xml:id="N10333" xml:space="preserve">Quando tamen ꝓportio maioris ine­<lb/>qualitatis: non capitur pro aggregato ex nume-<lb/>ris proportionem habentibus inequalitatis: ſed <lb/>pro maiore numero. </s>
            <s xml:id="N1033C" xml:space="preserve">proportio vero minoris ine-<lb/>qualitatis pro minore. </s>
            <s xml:id="N10341" xml:space="preserve">Et iſto modo non ſunt ter­<lb/>mini conuertibiles </s>
            <s xml:id="N10346" xml:space="preserve">Nam iſto modo capiendo ſi .8 <lb/>comparentur ad .4.8. ſunt ꝓportio maioris ine-<lb/>qualitatis .2.4. minoris inequalitatis.             <anchor type="note" xlink:href="note-0006-08" xlink:label="note-0006-08a"/>             </s>
            <s xml:id="N10352" xml:space="preserve">¶ Item ꝓ-<lb/>portio inequalitatis. </s>
            <s xml:id="N10357" xml:space="preserve">eſt duplex. </s>
            <s xml:id="N1035A" xml:space="preserve">quia quedem eſt <lb/>rationalis: et quedam irrationalis. </s>
            <s xml:id="N1035F" xml:space="preserve">¶ Propor-<lb/>tio ratiõalis: eſt illa ꝓportio q̄ īmediate denomi-<lb/>nat̄̄ ab aliq̊ certo nūero vĺ nūeroꝝ fractõe. </s>
            <s xml:id="N10366" xml:space="preserve">vt du-<lb/>pla: ſexq̇altera .etc̈. </s>
            <s xml:id="N1036B" xml:space="preserve">Alio mõ ꝓportio rõalis: ē dua­<lb/>rum quantitatum ſic ſe habentiū:  idem eſt pars <lb/>aliquota vtriuſ idē inquam ad bonum ſenſum. <lb/></s>
            <s xml:id="N10373" xml:space="preserve">¶ Ex quo ſequitur /  cuiuſlibet numeri ad quemli­<lb/>bet alium numerum eſt proportio rationalis. </s>
            <s xml:id="N10378" xml:space="preserve">quo­<lb/>niam cuiuſlibet numeri vnitas eſt pars aliquota. <lb/>             <anchor type="note" xlink:href="note-0006-09" xlink:label="note-0006-09a"/>             </s>
            <s xml:id="N10384" xml:space="preserve">¶ Unde pars aliquota: ē illa que aliquoties ſum-<lb/>pta reddit ſuum totum adequate. </s>
            <s xml:id="N10389" xml:space="preserve">vt vnitas eſt <lb/>pars aliquota numeri quarternarii. </s>
            <s xml:id="N1038E" xml:space="preserve">quoniã vni-             <pb chead="Prime partis" file="0007" n="7"/>             tas ter ſumpta: adequate conſtituit ternarium <lb/>et quater ſumpta: quaternarium. </s>
            <s xml:id="N10398" xml:space="preserve">et dualitas eſt <lb/>pars aliquota numeri octonarii. </s>
            <s xml:id="N1039D" xml:space="preserve">quoniam duali­<lb/>tas quater ſumpta adequate numerū octonariuꝫ <lb/>conſtituit. </s>
            <s xml:id="N103A4" xml:space="preserve">¶ Ex quo patet /  dualitas non eſt ꝑrs <lb/>aliquota numeri ſeptenarii quoniam non aliquo­<lb/>ties ſumpta: reddit illud totum adequate. </s>
            <s xml:id="N103AB" xml:space="preserve">¶ Pro­<lb/>portio autem irrationalis: eſt illa que nõ immedi­<lb/>ate ab aliquo numero denominatur. </s>
            <s xml:id="N103B2" xml:space="preserve">Alio modo <lb/>proportio irrationalis: eſt duarum quantitatum <lb/>ita ſe habentiū:  nulla pars aliquota vnius eſt <lb/>ꝑs aliq̊ta alteriꝰ vt ꝓportio q̄ ē īter diametrū et co­<lb/>ſtã ſui q̈drati. </s>
            <s xml:id="N103BD" xml:space="preserve">nã diameṫ excedit coſtã et nõ aliq̊ties <lb/>nec ꝑ aliquã ꝑtem aliquotã. </s>
            <s xml:id="N103C2" xml:space="preserve">vel per aliq̈s ꝑtes ali­<lb/>quotas. </s>
            <s xml:id="N103C7" xml:space="preserve">vt inferius probabitur in capitulo de ꝓ-<lb/>portione irrationali.             <anchor type="note" xlink:href="note-0007-01" xlink:label="note-0007-01a"/>             </s>
            <s xml:id="N103D1" xml:space="preserve">¶ Proportionum auteꝫ ra-<lb/>tionalium .5. ſunt ſpecies tres ſimplices: et due cõ­<lb/>poſite. </s>
            <s xml:id="N103D8" xml:space="preserve">¶ Simplices ſunt iſte. </s>
            <s xml:id="N103DB" xml:space="preserve">multiplex: ſuperpar­<lb/>ticularis: et ſuprapartiēs. </s>
            <s xml:id="N103E0" xml:space="preserve">¶ Compoſite vero ſunt <lb/>multiplex. </s>
            <s xml:id="N103E5" xml:space="preserve">multiplex ſuperparticularis: mĺtiplex <lb/>ſuprapartiens </s>
            <s xml:id="N103EA" xml:space="preserve">¶ Unde proportio multiplex: eſt ꝓ­<lb/>portio qua maius continet minus aliquoties ta-<lb/>tū vt dupla, tripla .4. enim continent .2. bis. / et .6. <lb/>continent .2. ter tantum </s>
            <s xml:id="N103F3" xml:space="preserve">Et ideo inter illos nume-<lb/>ros eſt ꝓportio multiplex. </s>
            <s xml:id="N103F8" xml:space="preserve">¶ Proportio vero ſu-<lb/>perparticularis. </s>
            <s xml:id="N103FD" xml:space="preserve">eſt proportio qua maius cõtinet <lb/>minus ſemel tãtū: et aliquam partem eius aliquo­<lb/>tã adeq̈te. </s>
            <s xml:id="N10404" xml:space="preserve">vt ꝓportio ſex ad .4. nã .6. cõtinet .4. ſe-<lb/>mel tm̄ et medietatē q̄ eſt pars aliquota ipſoꝝ .4. <lb/></s>
            <s xml:id="N1040A" xml:space="preserve">¶ Proportio autem ſuprapartiēs: eſt proportio <lb/>qua maius continet minus ſemel tantū: et aliquot <lb/>partes eius aliquotas: que ſimul non faciunt ali­<lb/>quam eius partem aliquotam. </s>
            <s xml:id="N10413" xml:space="preserve">vt ꝓportio que eſt <lb/>inter .7. et .5. </s>
            <s xml:id="N10418" xml:space="preserve">Nam .7. continent .5. ſemel tantum: et <lb/>duas partes eius aliquotas: puta duas vnitates <lb/></s>
            <s xml:id="N1041E" xml:space="preserve">¶ Sed proportio multiplex ſuperparticularis eſt <lb/>illa qua maius continet minus aliquotiens: et <lb/>cum hoc aliquam eius partem aliquotam tantuꝫ <lb/>vt proportio que eſt inter nouem et .4. </s>
            <s xml:id="N10427" xml:space="preserve">Nã .9. con-<lb/>tinent .4. bis. / et vnam partem numeri quaternarii <lb/>puta vnitatem. </s>
            <s xml:id="N1042E" xml:space="preserve">¶ Proportio autem multiplex ſu­<lb/>prapartiens: eſt illa qua maius continent minus <lb/>aliquotiens et aliquot partes eiꝰ aliquotas: que <lb/>non faciunt vnam eius partem aliquotam vt pro­<lb/>portio que eſt inter .11. et .4. </s>
            <s xml:id="N10439" xml:space="preserve">Nã .11. continent .4. bis / <lb/>et tres partes aliquotas ipſorum .4. et ille nõ fa-<lb/>ciunt aliquam partem aliquotam ipſorum .4.</s>
          </p>
          <div xml:id="N10440" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0006-08a" xlink:label="note-0006-08" xml:id="N10444" xml:space="preserve">alia diui­<lb/>ſio ꝓpor­<lb/>tionu ieq̈­<lb/>litatis.</note>
            <note position="right" xlink:href="note-0006-09a" xlink:label="note-0006-09" xml:id="N10450" xml:space="preserve">pars ali­<lb/>quota.</note>
            <note position="left" xlink:href="note-0007-01a" xlink:label="note-0007-01" xml:id="N10458" xml:space="preserve">Diuiſio <lb/>ꝓportio­<lb/>nū rõna-<lb/>lium.</note>
          </div>
          <note position="left" xml:id="N10464" xml:space="preserve">Sufficiē-<lb/>cia quī <lb/>numeri ꝓ­<lb/>portiõis <lb/>rõaĺ ma­<lb/>ioris ine­<lb/>q̈litatis.</note>
          <p xml:id="N10474">
            <s xml:id="N10475" xml:space="preserve">¶ Harum autem proportionum: ſiue ſpecierum ꝓ­<lb/>portionum ſufficientia: talis ratione haberi põt <lb/>vt adducit Albertus de ſaxonia ī ſuo tractatu de <lb/>proportionibus poſt alios mathematicos. </s>
            <s xml:id="N1047E" xml:space="preserve">Qm̄ <lb/>oīs numerus: ſiue quantitas ad aliam quantitatē <lb/>habens rationalem proportiouem: aut excedit <lb/>eam: aut exceditur ab illa. </s>
            <s xml:id="N10487" xml:space="preserve">Si excedit eam: aut <lb/>continet ipſam aliquoties. </s>
            <s xml:id="N1048C" xml:space="preserve">aut ſemel tantū: et ali­<lb/>quid vltra. </s>
            <s xml:id="N10491" xml:space="preserve">aut pluries et aliquid vltra. </s>
            <s xml:id="N10494" xml:space="preserve">Si primū / <lb/>tunc erit proportio multiplex </s>
            <s xml:id="N10499" xml:space="preserve">Si ſecūdū / aut illud <lb/>aliquid vltra eſt vna pars eius aliquota adequa-<lb/>te: aut ē plures partes aliquote que nõ faciūt vnã <lb/>partem aliquotam. </s>
            <s xml:id="N104A2" xml:space="preserve">Si primum: ſic eſt ꝓportio ſu­<lb/>perparticularis. </s>
            <s xml:id="N104A7" xml:space="preserve">Si ſecundum / eſt proportio ſuꝑ-<lb/>partiens. </s>
            <s xml:id="N104AC" xml:space="preserve">Si vero maior quantitas continet mi-<lb/>norē pluries. </s>
            <s xml:id="N104B1" xml:space="preserve">et aliquid vltra. </s>
            <s xml:id="N104B4" xml:space="preserve">vel illud quod vltra <lb/>continet eſt pars aliquota adequate aut: plures <lb/>partes aliquote: que non faciunt vnã. </s>
            <s xml:id="N104BB" xml:space="preserve">Si primum / <lb/>ſic eſt proportio multiplex ſuperparticulares. </s>
            <s xml:id="N104C0" xml:space="preserve">Si             <cb chead="Capitulum ſecundum"/>             ſecundum ſic eſt proportio multiplex ſupraparti-<lb/>ens. </s>
            <s xml:id="N104C8" xml:space="preserve">Et quia quantitas maior habens proportio­<lb/>nē rationalem ad quantitatem minorē nõ poteſt <lb/>pluribus modis ad illam referri<gap/> ſiue compara-<lb/>ri. </s>
            <s xml:id="N104D3" xml:space="preserve">quam his quin modis conſequens eſt /  non <lb/>poſſunt eſſe plures ſpecies proportionis rationa­<lb/>lis his .5. </s>
            <s xml:id="N104DA" xml:space="preserve">Quãdoquidem eodem modo venari po­<lb/>teſt minoris inequalitatis proportionum ſuffici­<lb/>entia. </s>
            <s xml:id="N104E1" xml:space="preserve">Sola enim ratione: proportio maioris ine­<lb/>qualitatis: et minoris differunt) </s>
            <s xml:id="N104E6" xml:space="preserve">De irrationali <lb/>autem poſterius dicetur.</s>
          </p>
        </div>
        <div xml:id="N104EB" level="3" n="2" type="chapter" type-free="capitulum">
          <head xml:id="N104F0" xml:space="preserve">Cpitulum ſecundum / in quo agitur de ſpe­<lb/>ciebus horum quin generum proportionū <lb/>et de ipſarum generatione.</head>
          <p xml:id="N104F7">
            <s xml:id="N104F8" xml:space="preserve">OMnis proportio ſiue omne ge­<lb/>nus proportiõis: infinitas habet ſpecies <lb/></s>
            <s xml:id="N104FE" xml:space="preserve">Unde genus multiplicis: habet infinitas <lb/>ſpecies denominatas a naturali ſerie numerorū <lb/>puta duplã denominatã a binario triplã a terna­<lb/>rio: milleculpam a millenario: centuplam a cen-<lb/>tenario. </s>
            <s xml:id="N10509" xml:space="preserve">et ſic in infinitū. </s>
            <s xml:id="N1050C" xml:space="preserve">¶ Proportio em̄ dupla: <lb/>eſt illa qua maius continet minus: bis adequate <lb/>vt .4. cum .2. et tripla qua maius continet minus: <lb/>ter adequate. </s>
            <s xml:id="N10515" xml:space="preserve">et quadrupla quater adequate. </s>
            <s xml:id="N10518" xml:space="preserve">et ſic <lb/>in infinitum. </s>
            <s xml:id="N1051D" xml:space="preserve">¶ Generãtur autem omnes ꝓportio­<lb/>nes duple que infinite ſunt iſto modo. </s>
            <s xml:id="N10522" xml:space="preserve">Diſpona-<lb/>tur / primo ſeries naturalis numeroꝝ in vna linea <lb/>et in alia linea inferiori diſponantur omnes nu-<lb/>meri excedentes ſe binario: incipiendo a binario <lb/>in infinitum. </s>
            <s xml:id="N1052D" xml:space="preserve">Et iſto modo cõparando primum ſu-<lb/>perioris linie primo inferioris: et ſecundū ſecūdo <lb/>et tertiū tertio.             <anchor type="note" xlink:href="note-0007-02" xlink:label="note-0007-02a"/>             </s>
            <s xml:id="N10539" xml:space="preserve">et ſic in infinitum inuenientur infi-<lb/>nite ꝓportiõis duple. </s>
            <s xml:id="N1053E" xml:space="preserve">in preſenti figura clare hoc <lb/>poteris conſpicere.</s>
          </p>
          <div xml:id="N10543" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0007-02a" xlink:label="note-0007-02" xml:id="N10547" xml:space="preserve">gñatio ꝓ­<lb/>portõnū <lb/>duplarū</note>
          </div>
          <xhtml:table xml:id="N10551">
            <xhtml:tr xml:id="N10552">
              <xhtml:td xml:id="N10553" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N10555">
            <s xml:id="N10556" xml:space="preserve">Per naturalem ſeriē numerorum: intelligas ordi­<lb/>ne numerorū incipiēdo ab vnitate nullū numeruꝫ <lb/>omittendo. </s>
            <s xml:id="N1055D" xml:space="preserve">vt .1.2.3.4. etc̈. </s>
            <s xml:id="N10560" xml:space="preserve">¶ Sed infinite ꝓportio-<lb/>nes triple: iſto modo generantur </s>
            <s xml:id="N10565" xml:space="preserve">Diſponatur / oēs <lb/>nūeri ſcḋm ſeriē naturalē nūerorū incipiendo ab <lb/>vnitate ī vna linea et ī linea īferiori diſponãt̄̄ oēs <lb/>nūeri excedētes ſe ṫnario. </s>
            <s xml:id="N1056E" xml:space="preserve">et tūc cõparãdo ṗmū īfe­<lb/>rioris ordinis prīo ſuperioris et ſecūdū ſecūdo et <lb/>tertiū tertio:             <anchor type="note" xlink:href="note-0007-03" xlink:label="note-0007-03a"/>             habebunt̄̄ infinite ꝓportiões triple.</s>
          </p>
          <div xml:id="N1057A" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0007-03a" xlink:label="note-0007-03" xml:id="N1057E" xml:space="preserve">gñatio ꝓ­<lb/>portõnū <lb/>triplarū</note>
          </div>
          <xhtml:table xml:id="N10588">
            <xhtml:tr xml:id="N10589">
              <xhtml:td xml:id="N1058A" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="right" xml:id="N1058C" xml:space="preserve">gñatio ꝓ­<lb/>portõnū <lb/>q̈drupla­<lb/>rum:</note>
          <p xml:id="N10596">
            <s xml:id="N10597" xml:space="preserve">Si vero velis gñare oēs ꝓportiões quadruplas: <lb/>capias nūeros excedentes ſe q̈ternario. </s>
            <s xml:id="N1059C" xml:space="preserve">incipiēdo <lb/>a nūero q̈ternario cū ſerie naturali nūeroꝝ.             <anchor type="note" xlink:href="note-0007-04" xlink:label="note-0007-04a"/>             </s>
            <s xml:id="N105A6" xml:space="preserve">¶ Si <lb/>aūt quītuplã: capias oēs excedētes ſe q̇nario             <anchor type="note" xlink:href="note-0007-05" xlink:label="note-0007-05a"/>             </s>
            <s xml:id="N105B0" xml:space="preserve">¶ Si <lb/>ſextuplã ſenario. </s>
            <s xml:id="N105B5" xml:space="preserve">et ſic in infinitū vt facile eſt vide-<lb/>re in figuris ſequentibus.</s>
          </p>
          <div xml:id="N105BA" level="4" n="3" type="float">
            <note position="right" xlink:href="note-0007-04a" xlink:label="note-0007-04" xml:id="N105BE" xml:space="preserve">Gñatio <lb/>quītupla­<lb/>rum.</note>
            <note position="right" xlink:href="note-0007-05a" xlink:label="note-0007-05" xml:id="N105C8" xml:space="preserve">Gñatio <lb/>ſextupla­<lb/>rum.</note>
          </div>
          <xhtml:table xml:id="N105D2">
            <xhtml:tr xml:id="N105D3">
              <xhtml:td xml:id="N105D4" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N105D6">
            <s xml:id="N105D7" xml:space="preserve">¶ Suꝑparticularis autē ꝓportio etiam infinitas <lb/>habet ſpecies denoīatas a partibus aliquotis: et <lb/>vnitate. </s>
            <s xml:id="N105DE" xml:space="preserve">puta a medietate: a tertia quarta quinta / <lb/>et ſic in infinitū. </s>
            <s xml:id="N105E3" xml:space="preserve">Et ideo prima ſpecies eiꝰ et maxīa <lb/>dicitur ſexquialtera. ſecūda vero ſexquitertia. ſex­             <pb chead="Prime partis" file="0008" n="8"/>             quiquarta. ſexquiquinta. / et ſic in infinitum.</s>
          </p>
          <note position="left" xml:id="N105ED" xml:space="preserve">Seqxui-<lb/>totum.</note>
          <p xml:id="N105F3">
            <s xml:id="N105F4" xml:space="preserve">¶ Unde ſexqui idē eſt quod totū. </s>
            <s xml:id="N105F7" xml:space="preserve">et altera idem eſt <lb/>quod medietas. </s>
            <s xml:id="N105FC" xml:space="preserve">et ſic pportio ſexq̇altera: eſt qua <lb/>maiꝰ cõtinet minus ſemel tantū: et medietatē eius <lb/></s>
            <s xml:id="N10602" xml:space="preserve">Sexquitertia vero eſt qua maius continet minus <lb/>ſemel tantū: et vnã tertiã eiꝰ. </s>
            <s xml:id="N10607" xml:space="preserve">Et ſexquiquarta: qua <lb/>maiꝰ cõtinet minꝰ ſemel tantū: et vnã quartã eius / <lb/>et ſic in infinitū. </s>
            <s xml:id="N1060E" xml:space="preserve">¶ Generantur autē ſpecies huius <lb/>ꝓportionis iſto modo. </s>
            <s xml:id="N10613" xml:space="preserve">Capiatur ordo naturalis <lb/>numerorū incipiendo a binario. </s>
            <s xml:id="N10618" xml:space="preserve">et cõparetur ſecū­<lb/>dus primo: et tertius ſecundo: et quartus tertio: et <lb/>ſic in infinitū. </s>
            <s xml:id="N1061F" xml:space="preserve">et habebūtur oēs ſpecies huiꝰ ꝓpor­<lb/>tionis ſereatim. </s>
            <s xml:id="N10624" xml:space="preserve">¶ Si autē libet infinitas ſexquial­<lb/>teras ꝓcreare: capientur in vna linea oēs numeri <lb/>excedētes ſe binario: et in alia oēs numeri excedē-<lb/>tes ſe ternario: et cõparetur primꝰ īferioris primo <lb/>ſuꝑioris: et ſecūdus ſcḋo / et ſic in infinitū </s>
            <s xml:id="N1062F" xml:space="preserve">¶ Si vero <lb/>in vno ordine ponantur oēs numeri excedentes ſe <lb/>ternario. </s>
            <s xml:id="N10636" xml:space="preserve">et in alio excedētes ſe quaternario: ſcḋa <lb/>ſpecies ꝓducetur. </s>
            <s xml:id="N1063B" xml:space="preserve">puta ſexquitertia. </s>
            <s xml:id="N1063E" xml:space="preserve">¶ Si autē in <lb/>vno ponãtur oēs excedentes ſe quaternario. </s>
            <s xml:id="N10643" xml:space="preserve">et in <lb/>alio quinario ꝓducetur tertia ſpecies: puta ſexq̇-<lb/>quarta. </s>
            <s xml:id="N1064A" xml:space="preserve">et ſic in infinitū in aliis ſpeciebus. </s>
            <s xml:id="N1064D" xml:space="preserve">vt patꝫ <lb/>in figuris ſequentibus.</s>
          </p>
          <note position="left" xml:id="N10652" xml:space="preserve">Genera-<lb/>tio ſpēi <lb/>ſuꝑparti-<lb/>cularis.</note>
          <xhtml:table xml:id="N1065C">
            <xhtml:tr xml:id="N1065D">
              <xhtml:td xml:id="N1065E" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="left" xml:id="N10660" xml:space="preserve">Gñatio <lb/>ſexquial­<lb/>terum.</note>
          <xhtml:table xml:id="N10668">
            <xhtml:tr xml:id="N10669">
              <xhtml:td xml:id="N1066A" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="left" xml:id="N1066C" xml:space="preserve">Genera-<lb/>tio ſexq̇-<lb/>tertiarū.</note>
          <xhtml:table xml:id="N10674">
            <xhtml:tr xml:id="N10675">
              <xhtml:td xml:id="N10676" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N10678">
            <s xml:id="N10679" xml:space="preserve">¶ Proportio ſuprapartiens infinitas habet ſpe­<lb/>cies: videlicet ſuꝑbipartiēs tertias: ſuꝑbipartiēs <lb/>quītas: ſuꝑtripartiens quartas: et ſic in infinitum <lb/></s>
            <s xml:id="N10681" xml:space="preserve">¶ Unde ꝓportio ſuꝑbipartiēs tertias eſt qua ma­<lb/>ius continet minus ſemel tantū: et duas tertias mi­<lb/>noris. </s>
            <s xml:id="N10688" xml:space="preserve">Unde in quolibet noīe huiꝰ ſpeciei ponūtur <lb/>duo numeri. </s>
            <s xml:id="N1068D" xml:space="preserve">Primus numerus denotat numerū <lb/>partiū aliquotaꝝ. </s>
            <s xml:id="N10692" xml:space="preserve">Et ſecūdus denotat denoīatio­<lb/>nes illaꝝ. </s>
            <s xml:id="N10697" xml:space="preserve">vt cū dicimus ſuꝑbipartiens tertias. ly <lb/>bi. dicit numeꝝ partiū aliquotarū. </s>
            <s xml:id="N1069C" xml:space="preserve">quas dicit eſſe <lb/>duas. </s>
            <s xml:id="N106A1" xml:space="preserve">et ly tertias dicit / illas eſſe tertias partes nu­<lb/>meri mīoris. </s>
            <s xml:id="N106A6" xml:space="preserve">et ſic exēplifica in aliis. </s>
            <s xml:id="N106A9" xml:space="preserve">¶ Generãtur <lb/>autē infinite ſpecies huius ꝓportionis iſto modo <lb/></s>
            <s xml:id="N106AF" xml:space="preserve">Capiatur in vna ſerie naturalis ordo numeroruꝫ <lb/>incipiēdo a ternario. </s>
            <s xml:id="N106B4" xml:space="preserve">et in alia oēs impares īcipiē­<lb/>do a quinario. </s>
            <s xml:id="N106B9" xml:space="preserve">et ↄ̨paret̄̄ primꝰ vniꝰ ordinis ṗmo <lb/>alteriꝰ.             <anchor type="note" xlink:href="note-0008-01" xlink:label="note-0008-01a"/>             </s>
            <s xml:id="N106C3" xml:space="preserve">et ſecundus ſecūdo et ſic in īfinitū et habebū­<lb/>tur īfinite ſpecies huiꝰ ꝓportiõis. </s>
            <s xml:id="N106C8" xml:space="preserve">vt ptꝫ in figura</s>
          </p>
          <div xml:id="N106CB" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0008-01a" xlink:label="note-0008-01" xml:id="N106CF" xml:space="preserve">Genera-<lb/>tio ſpeci­<lb/>ei ſupra-<lb/>partietꝪ.</note>
          </div>
          <xhtml:table xml:id="N106DB">
            <xhtml:tr xml:id="N106DC">
              <xhtml:td xml:id="N106DD" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N106DF">
            <s xml:id="N106E0" xml:space="preserve">¶ Proportio auteꝫ multiplex ſuperparticularis <lb/>multas habet ſpecies. </s>
            <s xml:id="N106E5" xml:space="preserve">puta duplã ſexquialteram <lb/>duplã ſexquitertiã, triplã ſexquialterã, triplã ſex­<lb/>quitertiã, et ſic in infinitū: quartū ſpecierū diffini­<lb/>tiones patent ex dictis.             <anchor type="note" xlink:href="note-0008-02" xlink:label="note-0008-02a"/>             </s>
            <s xml:id="N106F3" xml:space="preserve">¶ Generantur autē īfinite <lb/>ſpecies eiꝰ hoc modo. </s>
            <s xml:id="N106F8" xml:space="preserve">Capiatur in vno ordine na­<lb/>turalis ſeries numeroꝝ incipiendo a binario. </s>
            <s xml:id="N106FD" xml:space="preserve">et in <lb/>alio ordine capiãtur oēs nūeri excedentes ſe q̇na-<lb/>rio: a q̇nario exordiendo. </s>
            <s xml:id="N10704" xml:space="preserve">et cõparãdo primū vniꝰ <lb/>ordinis. </s>
            <s xml:id="N10709" xml:space="preserve">primo alteriꝰ: cõſtabitur prima ſpecies. </s>
            <s xml:id="N1070C" xml:space="preserve">et <lb/>referendo ſecundum ſecundo. / educetur ſecunda. / et <lb/>ſic in infinitum. </s>
            <s xml:id="N10713" xml:space="preserve">vt patet in figura.</s>
          </p>
          <div xml:id="N10716" level="4" n="5" type="float">
            <note position="left" xlink:href="note-0008-02a" xlink:label="note-0008-02" xml:id="N1071A" xml:space="preserve">Genera-<lb/>tio ſpēi <lb/>multipli­<lb/>cis ſuper­<lb/>particu-<lb/>laris.</note>
          </div>
          <xhtml:table xml:id="N1072A">
            <xhtml:tr xml:id="N1072B">
              <xhtml:td xml:id="N1072C" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <cb chead="Capitulū ſecundū."/>
          <p xml:id="N10730">
            <s xml:id="N10731" xml:space="preserve">¶ Proportio vero multiplex ſuꝑparticularis īfi­<lb/>nitas habet ſpecies: quarū q̄libet in infinitas etiã <lb/>patit̄̄ ſpecies. </s>
            <s xml:id="N10738" xml:space="preserve">puta duplã ſuꝑparticularē: triplaꝫ <lb/>ſuꝑparticularē quadruplã ſuꝑparticularē: et ſic in <lb/>infinitū. </s>
            <s xml:id="N1073F" xml:space="preserve">¶ Unde ad ꝓcreandas infinitas duplas <lb/>ſuꝑparticularis: capiant̄̄ due ſeries numerorū. </s>
            <s xml:id="N10744" xml:space="preserve">et <lb/>in prima ponat̄̄ naturalis ſeries numeroꝝ incipi­<lb/>endo a binario. </s>
            <s xml:id="N1074B" xml:space="preserve">in alia vero ponãtur oēs numeri <lb/>impares a quīario inchoãdo. </s>
            <s xml:id="N10750" xml:space="preserve">et tūc referēdo primū <lb/>inferioris ṗmo ſuperioris: et ſcḋm inferioris: ſcḋo <lb/>ſuperioris: et ſic cõſequēter: habebūtur infinite ſpe­<lb/>cies huiꝰ duple ſuꝑparticularis. </s>
            <s xml:id="N10759" xml:space="preserve">¶ Sed ad ꝓducē­<lb/>das īfinitas triplas ſuꝑparticulares: cõſtituat̄̄ in <lb/>ṗma ſerie naturalis ordo nūeroꝝ ſemota vnitate <lb/>et in ſcḋa capiant̄̄ oēs nūeri excedētes ſe ternario <lb/>incipiēdo a ſeptenario: tūc modo iã ſepiꝰ dicto: re­<lb/>ferendo nūeros: infinitas triplas ſuperparticula­<lb/>res educes. </s>
            <s xml:id="N10768" xml:space="preserve">¶ A generandas vero īfinitas quadru­<lb/>plas ſuperparticulares: ↄ̨ſtituat̄̄ naturalis ſeries <lb/>numeroꝝ a ṗmo nūero īchoãdo in linea ſuperiori <lb/>in īferiori vero ordinet̄̄ quedã ſeries numeroꝝ: cõ­<lb/>tinue excedētiū ſe q̈ternario īchoãdo a nouenario <lb/></s>
            <s xml:id="N10774" xml:space="preserve">¶ Ad generandã autē ſequentē ſpeciē: puta quītu­<lb/>plã ſuperparticularē: capias ꝓ primo ordine na-<lb/>turale ſeriē numerorū: ꝙ̄ ꝓ qualibet ſpecie debes <lb/>capere. </s>
            <s xml:id="N1077D" xml:space="preserve">et ꝓ ſcḋo oēs numeros excedētes ſe q̇nario <lb/>incipiēdo ab vndenario. </s>
            <s xml:id="N10782" xml:space="preserve">et pro ſequēti ſpecie puta <lb/>ſextupla ſuperparticulari: capiant̄̄ oēs numeri ex­<lb/>cedētes ſe ſenario: incipiēdo a tridenario numero <lb/>ꝓ alia excedētes ſe ſeptenario: īchoãdo a quīdena­<lb/>rio. </s>
            <s xml:id="N1078D" xml:space="preserve">et ſic in īfinitū. </s>
            <s xml:id="N10790" xml:space="preserve">vt ptꝫ in figuris ſequentibus.</s>
          </p>
          <note position="right" xml:id="N10793" xml:space="preserve">Gñatio <lb/>duplarū <lb/>ſuꝑparti­<lb/>culariuꝫ.</note>
          <xhtml:table xml:id="N1079D">
            <xhtml:tr xml:id="N1079E">
              <xhtml:td xml:id="N1079F" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="right" xml:id="N107A1" xml:space="preserve">Triplaꝝ <lb/>ſuꝑparti­<lb/>culariū.</note>
          <xhtml:table xml:id="N107A9">
            <xhtml:tr xml:id="N107AA">
              <xhtml:td xml:id="N107AB" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="right" xml:id="N107AD" xml:space="preserve">Qua­<lb/>druplaꝝ <lb/>ſuꝑparti­<lb/>culariuꝫ.</note>
          <xhtml:table xml:id="N107B7">
            <xhtml:tr xml:id="N107B8">
              <xhtml:td xml:id="N107B9" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N107BB">
            <s xml:id="N107BC" xml:space="preserve">¶ Proportio vero multiplex ſuprapartiēs infini­<lb/>tas habet ſpecies: vt dupla ſuprabipartiēs ṫcias <lb/>tripla ſuprabipartiēs tertias: et ſic in īfinitū. </s>
            <s xml:id="N107C3" xml:space="preserve">coa-<lb/>dunãdo oēs ſpecies ꝓportiõis multiplicis cū q̈li-<lb/>bet ſuprapartiēte. </s>
            <s xml:id="N107CA" xml:space="preserve">et ecõuerſo. </s>
            <s xml:id="N107CD" xml:space="preserve">Et īfinitas ſimiliter <lb/>habet ſpecies: quaꝝ q̄libet in infinitas etiã partit̄̄ <lb/>ſpecies: vt puta dupla ſuprapartiēs: in duplã ſu-<lb/>prabipartientē tertias: in duplã ſuprabipartiētē <lb/>quītas: in duplã ſuprabipartientē quartas. </s>
            <s xml:id="N107D8" xml:space="preserve">et ſic <lb/>in īfinitū. </s>
            <s xml:id="N107DD" xml:space="preserve">¶ Generant̄̄ aūt dupla ſuperpartiēs iſto <lb/>modo. </s>
            <s xml:id="N107E2" xml:space="preserve">Cõſtituat̄̄ naturalis ſeries nūeroꝝ īcipiēdo <lb/>a ternario: q̄ ſemꝑ debet eſſe ṗma in q̈libet ſpecie <lb/>tali: et in linea īferiori ponant̄̄ oēs nūeri: excedētes <lb/>ſe ternario inchoãdo ab octonario. </s>
            <s xml:id="N107EB" xml:space="preserve">¶ Pro gene-<lb/>ratiõe vero triple ſuprapartiētis: in ſcḋa ſerie po­<lb/>nant̄̄ oēs nūeri excedētes ſe q̈ternario īcipiēdo ab <lb/>vndenario. </s>
            <s xml:id="N107F4" xml:space="preserve">¶ Pro generatiõe aūt q̈druple ſupra­<lb/>pariētꝪ: ponãtur in ſcḋa ſerie oēs nūeri. </s>
            <s xml:id="N107F9" xml:space="preserve">excedētes <lb/>ſe q̇nario: īcipiēdo a q̈tuordecim. </s>
            <s xml:id="N107FE" xml:space="preserve">Et ꝓ ſequēti ſpe-<lb/>cie: capiant̄̄ oēs excedētes ſe ſenario. </s>
            <s xml:id="N10803" xml:space="preserve">et ꝓ alia ſepte­<lb/>nario. </s>
            <s xml:id="N10808" xml:space="preserve">et ſic in īfinitū. </s>
            <s xml:id="N1080B" xml:space="preserve">vt ptꝫ in figuris ſequentibus</s>
          </p>
          <note position="right" xml:id="N1080E" xml:space="preserve">Gñatio <lb/>duplarū <lb/>ſupraꝑ-<lb/>tientiū.</note>
          <xhtml:table xml:id="N10818">
            <xhtml:tr xml:id="N10819">
              <xhtml:td xml:id="N1081A" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <note position="right" xml:id="N1081C" xml:space="preserve">Gñatio <lb/>triplarū <lb/>ſupraꝑti-<lb/>entium.</note>
          <xhtml:table xml:id="N10826">
            <xhtml:tr xml:id="N10827">
              <xhtml:td xml:id="N10828" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
        </div>
        <div xml:id="N1082A" level="3" n="3" type="chapter" type-free="capitulum">
          <pb chead="Prime partis" file="0009" n="9"/>
          <head xml:id="N10833" xml:space="preserve">Capitulū tertiū / in quo oſtenditur: et de­<lb/>mõſtratur: proportionem irrationalem <lb/>eſſe ponendam.</head>
          <p xml:id="N1083A">
            <s xml:id="N1083B" xml:space="preserve">AD demonſtrandum inter a-<lb/>liquas magnitudines ꝓportionē irra­<lb/>tionalem inueniri: que nullo pacto ſit <lb/>ſicut numeri ad numerum.</s>
          </p>
          <p xml:id="N10844">
            <s xml:id="N10845" xml:space="preserve">Suppono primo /  proportio qua-<lb/>dratorum ſuperficialium: eſt proportio coſtarum <lb/>dublicata. </s>
            <s xml:id="N1084C" xml:space="preserve">Hoc eſt ſi inter coſtas duorum quadra­<lb/>torum ſuperficialium: ſit aliqua proportio maio-<lb/>ris inequalitatis: inter quadrata erit proportio <lb/>dupla: ad illã: que eſt inter coſtas ſignatorū qua-<lb/>dratorū: vt ſi inter coſtas duorū quadratorū ine-<lb/>qualiū ſuperficialiū: fuerit proportio dupla: inter <lb/>quadrata erit proportio q̈drupla </s>
            <s xml:id="N1085B" xml:space="preserve">Hec ſuppoſitio <lb/>clare ꝓbatur: et demõſtratur: inferiꝰ. in tertia ꝑte <lb/>tractatu ſecūdo: capitulo .2. </s>
            <s xml:id="N10862" xml:space="preserve">Uideas eã ibi.</s>
          </p>
          <p xml:id="N10865">
            <s xml:id="N10866" xml:space="preserve">Secunda ſuppoſitio. </s>
            <s xml:id="N10869" xml:space="preserve">Quadratum <lb/>diametri: ſe hꝫ ad q̈dratū coſte in ꝓportiõe dupla <lb/></s>
            <s xml:id="N1086F" xml:space="preserve">Hoc eſt q̈dratū cuiꝰ q̈libet coſta. </s>
            <s xml:id="N10872" xml:space="preserve">eſt eq̈lis diametro <lb/>alicuiꝰ q̈drati ſe hꝫ in ꝓportiõe dupla: ad illud q̈-<lb/>dratū. </s>
            <s xml:id="N10879" xml:space="preserve">Probat̄̄ hec ſuppoſitio: et ſit vnū q̈dratum <lb/>magnū: cuiꝰ latꝰ ſit .d.c. et diameṫ ſit a.c. ſit aliḋ <lb/>paruū cū iſto cõicans cuiꝰ coſta ſit .c.f. et diameter <lb/>ſit .d.c et diuidat̄̄ q̈dratū maiꝰ: ꝑ duos diametros <lb/>in quatuor triãgulos equales: vt ptꝫ in hac figura / <lb/>             <anchor type="figure" xlink:href="fig-0009-01" xlink:label="fig-0009-01a"/>             quo poſito argr̄ ſic / ma-<lb/>gnū q̈dratū ē duplū <lb/>ad paruū q̈dratū et <lb/>ipſū magnū q̈dratū <lb/>eſt quadratū diame­<lb/>tri ipſius parui qua­<lb/>drati. </s>
            <s xml:id="N10897" xml:space="preserve">vt ptꝫ manife­<lb/>ſte / igit̄̄ quadratū di­<lb/>ametti: ſe hꝫ ad q̈dra­<lb/>tū coſte: in ꝓportiõe <lb/>dupla. </s>
            <s xml:id="N108A2" xml:space="preserve">Cõſeq̄ntia ptꝫ <lb/>cū mīore. </s>
            <s xml:id="N108A7" xml:space="preserve">et argr̄ maior. </s>
            <s xml:id="N108AA" xml:space="preserve">q2 q̈dratū magnū: cõtinet <lb/>q̈termedietatē parui q̈drati. </s>
            <s xml:id="N108AF" xml:space="preserve">adeq̈te igr̄ ipſū ma-<lb/>gnū q̈dratū: cõtinet bis adeq̈te: paruū q̈dratū. </s>
            <s xml:id="N108B4" xml:space="preserve">Cõ­<lb/>ſequentia ptꝫ ex ſe: et ꝓbat̄̄ añs. </s>
            <s xml:id="N108B9" xml:space="preserve">q2 q̈dratū magnū <lb/>q̈ter ↄ̨tinet tm̄: ſicut ē triãgulꝰ .d.e.c. / vt ptꝫ. </s>
            <s xml:id="N108BE" xml:space="preserve">et ille tri­<lb/>angulꝰ eſt medietas parui quadrati: vt manifeſte <lb/>ptꝫ in figura. </s>
            <s xml:id="N108C5" xml:space="preserve">igit̄̄ magnū quadratū: quater conti-<lb/>net adequate: mediante parui / qḋ fuit ꝓbandum.</s>
          </p>
          <div xml:id="N108CA" level="4" n="1" type="float">
            <figure xlink:href="fig-0009-01a" xlink:label="fig-0009-01" xml:id="N108CE">
              <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0009-01"/>
            </figure>
          </div>
          <p xml:id="N108D4">
            <s xml:id="N108D5" xml:space="preserve">Terita ſuppoſitio. </s>
            <s xml:id="N108D8" xml:space="preserve">diametri ad coſtã <lb/>eſt ꝓportio: que eſt medietas duple. </s>
            <s xml:id="N108DD" xml:space="preserve">Probatur / q2 <lb/>quadrati diametri ad quadratū coſte eſt ꝓportio <lb/>dupla: vt ptꝫ ex ſcḋa ſuppoſitione. </s>
            <s xml:id="N108E4" xml:space="preserve">ergo diametri <lb/>ad coſtã: eſt ꝓportio ſubdupla ad duplã. </s>
            <s xml:id="N108E9" xml:space="preserve">et ꝑ conſe­<lb/>quēs medietas duple. </s>
            <s xml:id="N108EE" xml:space="preserve">Patet cõſequētia ex prima <lb/>ſuppoſitione. </s>
            <s xml:id="N108F3" xml:space="preserve">Qm̄ ſemꝑ ꝓportio quadratorū: eſt <lb/>dupla ad ꝓportionē coſtaꝝ. </s>
            <s xml:id="N108F8" xml:space="preserve">Et ſic ꝓportio coſtaꝝ <lb/>eſt medietas ꝓportionis quadratoꝝ. </s>
            <s xml:id="N108FD" xml:space="preserve">Cum igitur <lb/>proportio quadratoruꝫ fuerit dupla: coſtaꝝ pro-<lb/>portio erit medietas duple.</s>
          </p>
          <note position="left" xml:id="N10904" xml:space="preserve">Numeri <lb/>primi.</note>
          <p xml:id="N1090A">
            <s xml:id="N1090B" xml:space="preserve">Quarta ſuppoſitio cuinſlibet ꝓpor­<lb/>tionis ſuprapartientis alter primorū numeroruꝫ <lb/>eſt impar. </s>
            <s xml:id="N10912" xml:space="preserve">Sunt autē primi numeri alicuius ꝓpor­<lb/>tionis: qui in ea ꝓportiõe ſunt numeri: vt tria et .2. <lb/>ſunt primi numeri ꝓportionis ſexquialtere: quia <lb/>in naturali ſerie numeroruꝫ: inter nullos minores             <cb chead="Capitulum tertiū."/>             ꝓportio ſexquialtera inuenit̄̄: </s>
            <s xml:id="N1091E" xml:space="preserve">Probatur ſuppoſi­<lb/>tio. </s>
            <s xml:id="N10923" xml:space="preserve">q2 ſi non: detur oppoſitū. </s>
            <s xml:id="N10926" xml:space="preserve">videlicet /  vter ſit <lb/>numerus par. </s>
            <s xml:id="N1092B" xml:space="preserve">et arguitur ſic. </s>
            <s xml:id="N1092E" xml:space="preserve">vter iſtorꝝ eſt nume­<lb/>rus par. </s>
            <s xml:id="N10933" xml:space="preserve">ergo ſequitur /  vter illoꝝ eſt medietas / <lb/>vt patet ex diffinitione numeri paris: et proportio <lb/>medietatū: eſt eadē cū ꝓportione totoꝝ: vt conſtat <lb/>et inferius ꝓbabis: igitur illi non erant primi nu-<lb/>meri talis ꝓportiõis. </s>
            <s xml:id="N1093E" xml:space="preserve">q2 nõ erant minimi illiꝰ pro­<lb/>portionis: cū ſue medietates ſint numeri minores <lb/>et ꝑ ↄ̨ñs: nõ dediſti ṗmos nūeros: talis ꝓpoſitiõis</s>
          </p>
          <p xml:id="N10945">
            <s xml:id="N10946" xml:space="preserve">Quīta ſuppoſitio. </s>
            <s xml:id="N10949" xml:space="preserve">Omne quadratū <lb/>numeri īparis: eſt īpar. </s>
            <s xml:id="N1094E" xml:space="preserve">Probatur: q2 oē quadra-<lb/>tum numeri īparis: eſt ille numerꝰ: qui reſultat ex <lb/>ductu numeri īparis: in ſeipſum ſemel. </s>
            <s xml:id="N10955" xml:space="preserve">vt patet ex <lb/>ſcḋo arithmetice nichomachi. </s>
            <s xml:id="N1095A" xml:space="preserve">ſed oīs numerꝰ: re-<lb/>ſultãs ex ductu numeri īparis in ſeipſum: eſt īpar / <lb/>igitur oē quadratū numeri īparis: eſt īpar. </s>
            <s xml:id="N10961" xml:space="preserve">Pro-<lb/>batur minor: q2 ſi numerꝰ īpar: multiplicetur per <lb/>numeꝝ parē immediate precedentē ipſum vt .5. per <lb/>4. / tunc reſultaret numerꝰ par: ſed quãdo multipli­<lb/>catur per ſeipſum: ſiue dicetur ī ſeipſum ſemel (qḋ­<lb/>ideꝫ ē) adhuc illi nūero pari: qui reſultabat ex mul­<lb/>tiplicatione numeri paris: immediate preceden-<lb/>tis: additur numerꝰ īpar: vt patet intelligenti. </s>
            <s xml:id="N10972" xml:space="preserve">igr̄ <lb/>totū reſultans: erit nūerꝰ īpar. </s>
            <s xml:id="N10977" xml:space="preserve">Patet cõſequētia: <lb/>qm̄ ſi numerꝰ īpar: addatur numero pari: reſulta­<lb/>bit numerꝰ īpar. </s>
            <s xml:id="N1097E" xml:space="preserve">Exemplū / vt ſi ternariꝰ: multipli­<lb/>cetur per numeꝝ parem: īmediate precedentē: puta <lb/>binariū: reſultabit numerꝰ par: puta ſenariꝰ. </s>
            <s xml:id="N10985" xml:space="preserve">et ſi <lb/>vlteriꝰ addatur numerꝰ teruariꝰ: ſupra ſenariū re­<lb/>ſultabit nouenarius: qui eſt numerꝰ īpar reſultãs <lb/>ex ductu ternarii in ſeipſum ſemel.</s>
          </p>
          <p xml:id="N1098E">
            <s xml:id="N1098F" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N10992" xml:space="preserve">nullus numerus <lb/>impar: eſt duplas ad aliquē numerū. </s>
            <s xml:id="N10997" xml:space="preserve">Probatur: <lb/>q2 ſi eſſet duplus ad aliquē numerū: iã ille numerꝰ <lb/>eſſet ſua medietas adequate: et ſic diuideret̄̄ in du-<lb/>as medietates: et ꝑ cõſequēs nõ eſſet impar.</s>
          </p>
          <p xml:id="N109A0">
            <s xml:id="N109A1" xml:space="preserve">Hīs iactis ſuppoſitiõibus: ſit prima <lb/>cõcluſio. </s>
            <s xml:id="N109A6" xml:space="preserve">Nulla ꝓportio diametri ad coſtã: ē mĺti­<lb/>plex, aut mĺtiplex ſuꝑparticularis: aut multiplex <lb/>ſuprapartiēs. </s>
            <s xml:id="N109AD" xml:space="preserve">Probat̄̄ hec cõcluſio: oīs ꝓportio <lb/>mĺtiplex, aut mĺtiplex ſuꝑparticĺaris, aut mĺti-<lb/>plex ſuprapartiēs eſt dupla aut maior dupla: ſed <lb/>nulla ꝓportio diametri ad coſtã: ē dupla aut ma-<lb/>ior dupla: igit̄̄ nulla ꝓportio diametri ad coſtam <lb/>eſt mĺtiplex: aut mĺtiplex ſuꝑparticularꝪ, aut mĺ-<lb/>tiplex ſuprapartiēs. </s>
            <s xml:id="N109BC" xml:space="preserve">Ptꝫ ↄ̨ña in ſcḋo ſcḋe et maior <lb/>ſimiliter: q2 oīs proportio multiplex: eſt dupla: vĺ <lb/>mior: et oīs ꝓportio multiplex ſuperparticularis <lb/>aut multiplex ſuprapartiens: eſt maior dupla: vt <lb/>patebit ex cſḋa parte: igitur oīs proportio multi­<lb/>plex: aut multiplex ſuꝑparticularis: aut mĺtiplex <lb/>ſuprapartiens: eſt dupla: vel maior dupla. </s>
            <s xml:id="N109CB" xml:space="preserve">Iã ꝓ-<lb/>batur minor. </s>
            <s xml:id="N109D0" xml:space="preserve">q2 oīs proportio diametri ad coſtã: <lb/>eſt medietas duple: ſiue ſubdupla ad duplã (quod <lb/>idē eſt) adequate: ergo nulla proportio diametri <lb/>ad coſtã: eſt ipſa tota dupla: vel maior dupla </s>
            <s xml:id="N109D9" xml:space="preserve">Pa­<lb/>tet antecedēs. </s>
            <s xml:id="N109DE" xml:space="preserve">ex tertia ſuppoſitione: et probat̄̄ cõ­<lb/>ſequētia. </s>
            <s xml:id="N109E3" xml:space="preserve">q2 alias medietas eſſet equalis ſuo toti: <lb/>vel maior. </s>
            <s xml:id="N109E8" xml:space="preserve">quod nõ eſt poſibile: deductis ſophiſta­<lb/>rum quiſquiliis.</s>
          </p>
          <p xml:id="N109ED">
            <s xml:id="N109EE" xml:space="preserve">Secunda concluſio. </s>
            <s xml:id="N109F1" xml:space="preserve">nulla proportio <lb/>diametri ad coſtã: eſt aliqua proportio ſuꝑparti-<lb/>cularis. </s>
            <s xml:id="N109F8" xml:space="preserve">Probatur: q2 oīs proportio ſuꝑparticu-             <pb chead="Prime partis" file="0010" n="10"/>             laris: eſt ſexquialtera: vel ſexquitertia: vel minor <lb/>ſexquitertia: et nulla proportio diametri ad coſtã <lb/>eſt ſexquialtera: vel ſexquitertia vel minor ſexq̇ter­<lb/>tia. / ergo nulla proportio diametri ad coſtã: eſt ſu-<lb/>perparticularis. </s>
            <s xml:id="N10A08" xml:space="preserve">Cõſequētia ptꝫ cū maiore mani-<lb/>feſte: et probatur minor. </s>
            <s xml:id="N10A0D" xml:space="preserve">qm̄ oīs proportio ſexqui-<lb/>altera: vel ſexquitertia: vel minor ſexquitertia. eſt <lb/>maior vel minor: medietate duple. et nulla propor­<lb/>tio diametri ad coſtã: eſt maior vel minor medieta­<lb/>te duple. q2 eſt equalis medietati duple. / vt patꝫ ex <lb/>tertia ſuppoſitiõe. </s>
            <s xml:id="N10A1A" xml:space="preserve">igitur nulla ꝓportio diametri <lb/>ad coſtã: eſt ſexquialtera. vel ſexq̇tertia: vel minor <lb/>ſexquitertia. </s>
            <s xml:id="N10A21" xml:space="preserve">Cõſequētia patet cū minore: et maior <lb/>probatur: q2 ſexquialtera eſt maior quã medietas <lb/>duple. et ſexquitertia minor quã medietas duple / et <lb/>ex cõſequēti: ꝑ locū a maiori: quelibet minor ſexq̇-<lb/>tertia: eſt minor quã medietas duple. / ergo oīs pro­<lb/>portio ſexquialtera. vel ſexquitertia: vĺ minor ſex­<lb/>quitertia: eſt maior: vel minor: medietate duple. <lb/></s>
            <s xml:id="N10A31" xml:space="preserve">Probatur tamē ãtecedēs. </s>
            <s xml:id="N10A34" xml:space="preserve">q2 dupla. cõponit̄̄ ade-<lb/>quate ex ſexquialtera: et ſexquitertia. / vt patet ex <lb/>ſecūda parte. </s>
            <s xml:id="N10A3B" xml:space="preserve">et ſexquialtera eſt maior. </s>
            <s xml:id="N10A3E" xml:space="preserve">et ſexquiter­<lb/>tia mīor. </s>
            <s xml:id="N10A43" xml:space="preserve">igitur ſexquialtera eſt maior quã medie­<lb/>tas duple. et ſexquitertia minor quã medietas du­<lb/>ple. </s>
            <s xml:id="N10A4A" xml:space="preserve">Patet conſequētia ex ſexta ſuppoſitione q̈rti <lb/>capitis ſecūde partis.</s>
          </p>
          <p xml:id="N10A4F">
            <s xml:id="N10A50" xml:space="preserve">Tertia concluſio. </s>
            <s xml:id="N10A53" xml:space="preserve">Nulla proportio <lb/>diametri ad coſtã eſt aliqua proportio ſuprapar-<lb/>tiens. </s>
            <s xml:id="N10A5A" xml:space="preserve">Probatur. </s>
            <s xml:id="N10A5D" xml:space="preserve">q2 oīs proportio ſuprapartiēs: <lb/>reperibilis eſt inter duos numeros: quoꝝ alter eſt <lb/>impar. </s>
            <s xml:id="N10A64" xml:space="preserve">et nulla proportio diametri ad coſtã: repe­<lb/>ribilis eſt inter duos numeros: quoꝝ alter eſt īpar / <lb/>ergo nulla proporito diametri ad coſtã: eſt aliqua <lb/>proportio ſuprapartiens </s>
            <s xml:id="N10A6D" xml:space="preserve">Patet conſequentia in <lb/>ſcḋo ſcḋe vt prius. </s>
            <s xml:id="N10A72" xml:space="preserve">et maior ex quarta ſuppoſitiõe <lb/>et minor probat̄̄. </s>
            <s xml:id="N10A77" xml:space="preserve">q2 ſi nõ detur oppoſitū. </s>
            <s xml:id="N10A7A" xml:space="preserve">videlicet / <lb/> proportio diametri ad coſtã: reperitur inter du­<lb/>os numeros: quoꝝ alter eſt impar. </s>
            <s xml:id="N10A81" xml:space="preserve">ita  diameter <lb/>et coſta: ſe habere poſſūt vt duo nūeri: quoꝝ alter <lb/>eſt impar. </s>
            <s xml:id="N10A88" xml:space="preserve">vel igitur diameter erit numerꝰ impar: <lb/>vel coſta ſi diameter: ſequitur /  quadratū ipſius <lb/>diametri: erit numerꝰ impar. </s>
            <s xml:id="N10A8F" xml:space="preserve">Patet cõſequētia ex <lb/>quinta ſuppoſitione. </s>
            <s xml:id="N10A94" xml:space="preserve">et vltra quadratū diametri: <lb/>eſt numerꝰ impar. </s>
            <s xml:id="N10A99" xml:space="preserve">ergo quadratū diametri: nõ eſt <lb/>duplū ad quadratū coſte. </s>
            <s xml:id="N10A9E" xml:space="preserve">Patet conſequentia ex <lb/>ſexta ſuppoſitione. </s>
            <s xml:id="N10AA3" xml:space="preserve">et cõſequēs eſt falſum: vt patet <lb/>ex ſecūda ſuppoſitione. </s>
            <s xml:id="N10AA8" xml:space="preserve">igitur et antecedens: </s>
            <s xml:id="N10AAB" xml:space="preserve">Non <lb/>eſt igitur dicendū /  diameter eſt numerus impar <lb/>reſpectu coſte. </s>
            <s xml:id="N10AB2" xml:space="preserve">ſi vero coſta ſit nūerꝰ īpar reſpectu <lb/>diametri: ſequit̄̄ /  quadratū eiꝰ erit numerꝰ īpar <lb/>ſed quadratū eiꝰ: eſt etiã quadratū diametri. </s>
            <s xml:id="N10AB9" xml:space="preserve">qm̄ <lb/>ipſa coſta: eſt diameter mīoris quadrati. </s>
            <s xml:id="N10ABE" xml:space="preserve">vt patet <lb/>in ſuperiori figura. </s>
            <s xml:id="N10AC3" xml:space="preserve">Igit̄̄ quadratū diametri: eſt <lb/>numerꝰ impar. </s>
            <s xml:id="N10AC8" xml:space="preserve">Patet cõſequētia ex quinta ſuppo­<lb/>ſitione. </s>
            <s xml:id="N10ACD" xml:space="preserve">et per cõſequēs quadratū diametri: nõ eſt <lb/>duplū ad q̈dratū coſte. </s>
            <s xml:id="N10AD2" xml:space="preserve">Patet cõſequētia ex ſexta <lb/>ſuppoſitione. </s>
            <s xml:id="N10AD7" xml:space="preserve">et cõſequēs eſt falſum. </s>
            <s xml:id="N10ADA" xml:space="preserve">vt patet ex ſe­<lb/>cūda ſuppoſitione: igitur et ãtecedēs. </s>
            <s xml:id="N10ADF" xml:space="preserve">Et ſic patet: <lb/> nec diameter ſe habet ſicut nūerꝰ īpar: nec coſta <lb/>             <anchor type="note" xlink:href="note-0010-01" xlink:label="note-0010-01a"/>             </s>
            <s xml:id="N10AEB" xml:space="preserve">¶ Aliquam autem quantitatem: ſe habere vt nu-<lb/>merus impar reſpectu alterius: eſt ipſam diuidi <lb/>ſaltē ad ymaginationē: in partes equales denoīa­<lb/>tas a numero impari. </s>
            <s xml:id="N10AF4" xml:space="preserve">vt in tres tertias: in quin <lb/>quītas in ſeptem ſeptimas / et ſic cõſequēter. </s>
            <s xml:id="N10AF9" xml:space="preserve">et hoc <lb/>reſpectu alterius quãtitatis: diuiſe in partes illis             <cb chead="Capitulū quartū."/>             equales. </s>
            <s xml:id="N10B01" xml:space="preserve">vt ſi pedale diuidatur in tres tertias et bi­<lb/>pedale in ſexſexas quarum ſextarum quelibet eſt <lb/>equalis vni tertie pedalis: tūc dico:  pedale ſe hꝫ <lb/>vt nūerꝰ impar: reſpectu bipedalis. </s>
            <s xml:id="N10B0A" xml:space="preserve">Tu tamē ad-<lb/>uerte  etiã poteſt ſe habere vt nūerꝰ par: reſpectu <lb/>bipedalis. </s>
            <s xml:id="N10B11" xml:space="preserve">tamē ſemꝑ īter pedale et bipedale erit <lb/>ꝓportio dupla. </s>
            <s xml:id="N10B16" xml:space="preserve">Diameter autē et coſta: nū̄ ſic ſe <lb/>poſſunt habere:  diameter ſe habeat vt numerus <lb/>impar reſpectu coſte: vel econtra / vt ꝓbatū eſt.</s>
          </p>
          <div xml:id="N10B1D" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0010-01a" xlink:label="note-0010-01" xml:id="N10B21" xml:space="preserve">Quid ſit <lb/>quãtita-<lb/>tē ſe hr̄e <lb/>vt nūerꝰ.</note>
          </div>
          <p xml:id="N10B2D">
            <s xml:id="N10B2E" xml:space="preserve">Quarta cõcluſio. </s>
            <s xml:id="N10B31" xml:space="preserve">Omnis proportio <lb/>diametri ad coſtã: eſt irrationalis </s>
            <s xml:id="N10B36" xml:space="preserve">Probatur hec <lb/>cõcluſio. </s>
            <s xml:id="N10B3B" xml:space="preserve">q2 oīs ꝓportio rationalis: eſt multiplex: <lb/>aut multiplex ſuꝑparticularis, aut multiplex ſu-<lb/>prapartiens, aut ſuꝑparticularis, aut ſuprapar­<lb/>tiens, et nulla ꝓportio diametri ad coſtã: eſt mul-<lb/>tiplex, aut multiplex ſuperparticularis, aut mul-<lb/>tiplex ſuprapartiēs. </s>
            <s xml:id="N10B48" xml:space="preserve">vt patet ex prima cõcluſione <lb/>aut ſuꝑparticularis. </s>
            <s xml:id="N10B4D" xml:space="preserve">vt ptꝫ ex ſcḋa: aut ſuprapar-<lb/>tiens: vt patet ex tertia. / igitur nulla ꝓportio dia­<lb/>metri ad coſtã: eſt rationalis. </s>
            <s xml:id="N10B54" xml:space="preserve">Cõſequētia patet vt <lb/>ſupra: et maior ex fine primi capitis. </s>
            <s xml:id="N10B59" xml:space="preserve">Illa enim eſt <lb/>ſūma diuiſio ꝓportiõis rationalis: et vltra nulla <lb/>ꝓportio diametri ad coſtã: eſt ratiõalis. </s>
            <s xml:id="N10B60" xml:space="preserve">et eſt pro­<lb/>portio: igitur eſt proportio irrationalis. </s>
            <s xml:id="N10B65" xml:space="preserve">Patet <lb/>cõſequentia a ſufficienti diuiſione.</s>
          </p>
        </div>
        <div xml:id="N10B6A" level="3" n="4" type="chapter" type-free="capitulum">
          <head xml:id="N10B6F" xml:space="preserve">Capitulum quartum / in quo agitur de <lb/>infinitis ſpeciebus proportionis irratio­<lb/>nalis: et de earum procreatione.</head>
          <p xml:id="N10B76">
            <s xml:id="N10B77" xml:space="preserve">PRoportio irrationalis: per-<lb/>inde at rationalis: in infinitas di-<lb/>ſtribuitur ſpecies </s>
            <s xml:id="N10B7E" xml:space="preserve">Ad quod mathema­<lb/>tica induſtria inferendū: ponūtur alique ſuppões</s>
          </p>
          <p xml:id="N10B83">
            <s xml:id="N10B84" xml:space="preserve">Prima ſuppoſitio. </s>
            <s xml:id="N10B87" xml:space="preserve">Si due quantita­<lb/>tes: ſe habent vt duo numeri: aggregatū ex eis: ſe <lb/>habebit vt vnꝰ numerꝰ. </s>
            <s xml:id="N10B8E" xml:space="preserve">Probatur. </s>
            <s xml:id="N10B91" xml:space="preserve">q2 ſemꝑ ex ad­<lb/>ditiõe numeri ad numerū: reſultat numerꝰ maior</s>
          </p>
          <p xml:id="N10B96">
            <s xml:id="N10B97" xml:space="preserve">Secūda ſuppoſitio </s>
            <s xml:id="N10B9A" xml:space="preserve">Si alique quan­<lb/>titates. </s>
            <s xml:id="N10B9F" xml:space="preserve">ſe habeant in ꝓportione rationali: ille ſe <lb/>habebunt: vt duo numeri: et econtra. </s>
            <s xml:id="N10BA4" xml:space="preserve">Patet ſup-<lb/>poſitio hec ex diffinitione ꝓportiõis ratioalis: cū <lb/>ſuo correlario: primo capite poſita.</s>
          </p>
          <p xml:id="N10BAB">
            <s xml:id="N10BAC" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N10BAF" xml:space="preserve">Si due quantita­<lb/>tes ſe habeant in ꝓportione ratiõali: aggregatū <lb/>ex eis: ſe habet in ꝓportione ratiõali: ad quãlibet <lb/>illaꝝ quantitatū. </s>
            <s xml:id="N10BB8" xml:space="preserve">Probatur hec ſuppoſitio. </s>
            <s xml:id="N10BBB" xml:space="preserve">qm̄ ſi <lb/>ſe habent in ꝓportione rationali: iã quelib3 illaꝝ <lb/>ſe habet vt numerꝰ: vt patet ex ſecūda ſuppoſitõe <lb/>et ſi quelibet illaꝝ ſe habet vt uūerꝰ: ſe aggregatū <lb/>ex eis: ſe habet vt nūerꝰ. </s>
            <s xml:id="N10BC6" xml:space="preserve">vt patet ex prima ſuppo­<lb/>ſitiõe. </s>
            <s xml:id="N10BCB" xml:space="preserve">et ꝑ cõſequens illiꝰ agggregati: quod ſe ha­<lb/>bet vt numerꝰ: ad vtrã illarū quantitatū: que ſe <lb/>habent vt numeri: erit ꝓportio rationalis. </s>
            <s xml:id="N10BD2" xml:space="preserve">vt ptꝫ <lb/>ex ſecūda ſuppoſitione: quod fuit ꝓbandum.</s>
          </p>
          <p xml:id="N10BD7">
            <s xml:id="N10BD8" xml:space="preserve">Qurata ſuppoſitio. </s>
            <s xml:id="N10BDB" xml:space="preserve">Coſte: ad exceſſū <lb/>quo diameter excedit coſtã: ꝓportio irrationalis <lb/></s>
            <s xml:id="N10BE1" xml:space="preserve">Probatur. </s>
            <s xml:id="N10BE4" xml:space="preserve">q2 ſi eſſet rationalis: iã ſe haberent vt <lb/>duo numeri. </s>
            <s xml:id="N10BE9" xml:space="preserve">vt patet ex ſecūda ſuppoſitiõe. </s>
            <s xml:id="N10BEC" xml:space="preserve">et ſi ſe <lb/>haberēt vt duo numeri: aggregatū ex eis: qḋ ade­<lb/>q̈te eſt diameter haberet ſe in ꝓportione ratiõali <lb/>ad vtrū illoꝝ. </s>
            <s xml:id="N10BF5" xml:space="preserve">et ꝑ cõſequēs ad coſtam. </s>
            <s xml:id="N10BF8" xml:space="preserve">vt patet ex <lb/>tertia ſuppoſitione: et ſic diametri ad coſtam: eſſet <lb/>rationalis proportio. </s>
            <s xml:id="N10BFF" xml:space="preserve">quod eſt contra quratã cõ­<lb/>cluſionem precedentis capitis.</s>
          </p>
          <pb chead="Prime partis" file="0011" n="11"/>
          <p xml:id="N10C08">
            <s xml:id="N10C09" xml:space="preserve">Quinta ſuppoſitio. </s>
            <s xml:id="N10C0C" xml:space="preserve">Si quantitatis <lb/>moioris ad aliquã partē aliquota quãtitatis mi-<lb/>noris ſit proportio rationalis: eiuſdē quãtitatis <lb/>maioris ad totã quantitatē minorē erit ꝓportio-<lb/>rationalis. </s>
            <s xml:id="N10C17" xml:space="preserve">Probatur. </s>
            <s xml:id="N10C1A" xml:space="preserve">q2 ſi quantitatis maioris <lb/>ad partē aliquotã quantitatis minoris eſt ꝓpor-<lb/>tio rationalis: iam quantitas maior: et pars ali-<lb/>quota minoris quantitatis ſe habent vt duo nu-<lb/>meri. </s>
            <s xml:id="N10C25" xml:space="preserve">et ꝑ cõſequens pars aliquota minoris quati­<lb/>tatis ſe habet vt numerus. </s>
            <s xml:id="N10C2A" xml:space="preserve">et cū nõ ſit maior ratio <lb/>de vna parte aliquota quã de qualibet tanta: ſe-<lb/>quitur /  quelibet tanta: ſe habet vt numerꝰ. </s>
            <s xml:id="N10C31" xml:space="preserve">et per <lb/>ↄ̨ñs aggregatū ex oībus partibꝰ aliquotꝪ ipſius <lb/>mīoris: ſe habet vt nūerꝰ. </s>
            <s xml:id="N10C38" xml:space="preserve">vt ptꝫ ex ṗma ſuppoſiti­<lb/>one: et illud aggregatū eſt ipſa mīor quãtitas: igr̄ <lb/>tp̄a mīor quãtitas ſe hꝫ vt numerꝰ: ad maiorē et ſic <lb/>inter illas eſt ꝓportio rõnalis. </s>
            <s xml:id="N10C41" xml:space="preserve">et ſic ptꝫ ſuppoſitio</s>
          </p>
          <p xml:id="N10C44">
            <s xml:id="N10C45" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N10C48" xml:space="preserve">Si due quantita­<lb/>tes inequales ſe habeant in ꝓportione rationali. <lb/></s>
            <s xml:id="N10C4E" xml:space="preserve">vtra illaꝝ ſe habet ad exceſſum quo maior exce-<lb/>dit minorē in ꝓportione rationali: vĺ equalitatis <lb/></s>
            <s xml:id="N10C54" xml:space="preserve">Probatur hec ſuppoſitio. </s>
            <s xml:id="N10C57" xml:space="preserve">qm̄ ſi ille quantitates: <lb/>ſe habent in ꝓportione rationali: ſe habēt vt duo <lb/>numeri. </s>
            <s xml:id="N10C5E" xml:space="preserve">et vltra ſe habent vt duo numeri: ergo ex-<lb/>ceſſus quo vna excedit alterã eſt numerꝰ. </s>
            <s xml:id="N10C63" xml:space="preserve">qm̄ ſemꝑ <lb/>numerꝰ excedit numerū ꝑ numerū. </s>
            <s xml:id="N10C68" xml:space="preserve">et vltra exceſſus <lb/>eſt numerꝰ: et quelibet aliarū ſe habet vt numerus <lb/>reſpectu illiꝰ exceſſus. </s>
            <s xml:id="N10C6F" xml:space="preserve">igr̄ inter illū exceſſū et quãli­<lb/>bet illarum quantitatem eſt proportio ratiõalis <lb/>vel equalitatis: quod fuit probandum.</s>
          </p>
          <p xml:id="N10C76">
            <s xml:id="N10C77" xml:space="preserve">His ſuppoſitionibus poſitis: ſit pri-<lb/>ma cõcluſio </s>
            <s xml:id="N10C7C" xml:space="preserve">Infinite ſunt ſpecies ꝓportionis irra­<lb/>tionalis minores dupla: et illarū in īfinitū parua <lb/>eſt aliqua. </s>
            <s xml:id="N10C83" xml:space="preserve">Probatur prima pars huiꝰ cõcluſiõis / <lb/>et capio coſtã vniꝰ quadrati: et ſuã diametrū. </s>
            <s xml:id="N10C88" xml:space="preserve">et vo­<lb/>lo /  vniformiter in hora diminuat̄̄ exceſſus quo <lb/>diameter excedit coſtã ad nõ quantū. </s>
            <s xml:id="N10C8F" xml:space="preserve">ita  in fine <lb/>diameter et coſta erūt equalia. </s>
            <s xml:id="N10C94" xml:space="preserve">quo poſito ſic argr̄ <lb/></s>
            <s xml:id="N10C98" xml:space="preserve">Inter diametrū que ſic diminuitur et coſtaꝫ erunt <lb/>infinite ꝓportiones irratiõales cõtinuo minores <lb/>dupla: igitur infinite ſunt ſpecies ꝓportiõis irra-<lb/>tionalis minores dupla. </s>
            <s xml:id="N10CA1" xml:space="preserve">Probatur ãtecedēs. </s>
            <s xml:id="N10CA4" xml:space="preserve">qm̄ <lb/>quãdo exceſſus: quo diameter excedit coſtã ꝑdide-<lb/>rit medietatē ſui / tūc aggregatū ex alia medietate <lb/>et coſta ſe habebit ad coſtã in ꝓportiõe irratiõali <lb/>minori dupla. / et quãdo exceſſus diametri fuerit di­<lb/>minutꝰ ad vnã quartã ſui: tūc aggregati ex coſta <lb/>et illa quarta exceſſus diametri ad coſtã erit ꝓpor­<lb/>tio irrationalis. </s>
            <s xml:id="N10CB5" xml:space="preserve">et ſic cõſequēter ſemꝑ aggregatū <lb/>ex coſta: et aliqua parte aliquota exceſſus ſe habe­<lb/>bit ad coſtã in ꝓportione irratiõali mīori dupla: <lb/>et infinita ſunt talia aggregata ex coſta et aliqua <lb/>parte aliquota exceſſus: igitur infinite erūt ꝓpor­<lb/>tiones irrationales cõtinuo minores dupla. </s>
            <s xml:id="N10CC2" xml:space="preserve">Ptꝫ <lb/>cõſequētia. </s>
            <s xml:id="N10CC7" xml:space="preserve">et arguit̄̄ maior videlicet /  aggregatū <lb/>ex coſta et medietate exceſſus diametri: ſe habet in <lb/>ꝓportione irrationali ad coſtã: q2 ſi nõ. </s>
            <s xml:id="N10CCE" xml:space="preserve">ſed ſe ba-<lb/>bent in ꝓportione rationali. </s>
            <s xml:id="N10CD3" xml:space="preserve">ſequitur:  vtra il­<lb/>laꝝ: ſe habet ad exceſſum quo maior excedit mino­<lb/>rem in ꝓportione rationali vel equalitatis. </s>
            <s xml:id="N10CDA" xml:space="preserve">Ptꝫ <lb/>ↄ̨ña ex ſexta ſuppoſitione. </s>
            <s xml:id="N10CDF" xml:space="preserve">et cõſequēs eſt falſū. </s>
            <s xml:id="N10CE2" xml:space="preserve">qm̄ <lb/>ſi vtra illarū ſe haberet ad exceſſum quo diame­<lb/>ter excedit coſtã: in ꝓportione rationali .etc̈. cū al-<lb/>tera illarum ſit coſta: et exceſſus quo maior excedit <lb/>minorē ſit medietas exceſſus diametri: ſequitur /              <cb chead="Capitulum quartū."/>             coſte ad medietatē exceſſus diametri erit ꝓportio <lb/>rationalis. </s>
            <s xml:id="N10CF2" xml:space="preserve">Patet hec cõſequētia ex ſe. </s>
            <s xml:id="N10CF5" xml:space="preserve">et vltra ſe-<lb/>quitur /  coſte: ad exceſſum diametri erit ꝓportio <lb/>rationalis. </s>
            <s xml:id="N10CFC" xml:space="preserve">Patet cõſequētia ex quīta ſuppoſitio­<lb/>ne. </s>
            <s xml:id="N10D01" xml:space="preserve">hoc addito /  medietas exceſſus eſt pars aliq̊ta <lb/>illius: cõſequēs eſt falſum: vt patet ex quarta igit̄̄ <lb/>et ãtecedēs. </s>
            <s xml:id="N10D08" xml:space="preserve">Et ſic ꝓbabis. </s>
            <s xml:id="N10D0B" xml:space="preserve"> aggregatū ex coſta et <lb/>quarta parte exceſſus diametri ſe habet in ꝓpor-<lb/>tione irratiõali ad coſtã: et ſimiliter  aggregatū <lb/>ex coſta et octaua parte exceſſus / et ſic cõſequenter. <lb/></s>
            <s xml:id="N10D15" xml:space="preserve">Quod autē ille ꝓportiones cõtinuo ſint minores <lb/>dupla: patet. </s>
            <s xml:id="N10D1A" xml:space="preserve">q2 a principio ꝓportio diametri ad <lb/>coſtã erat minor dupla. cū eſſet medietas duple: et <lb/>cõtinuo diminuet̄̄ vſ ad nõ gradū: vt ptꝫ ex ſcḋa <lb/>parte. </s>
            <s xml:id="N10D23" xml:space="preserve">igr̄ cõtinuo erit minor dupla. </s>
            <s xml:id="N10D26" xml:space="preserve">Itē continuo <lb/>exceſſus erit minor et minor reſpectu eiuſdē quãti-<lb/>tatis: ergo cõtinuo ꝓportio erit minor et mīor. </s>
            <s xml:id="N10D2D" xml:space="preserve">Et <lb/>ex hoc ptꝫ ſcḋa pars cõclſionis. </s>
            <s xml:id="N10D32" xml:space="preserve">q2 in infinitū mo-<lb/>dicus erit exceſſus quãtitatis maioris ad quãtita­<lb/>tē minorē: et ipſa quãtitas minor cõtinuo manebit <lb/>equalis et īuariata. </s>
            <s xml:id="N10D3B" xml:space="preserve">igitur infinite modica erit ꝓ-<lb/>portio maioris ad quantitatem minorem. </s>
            <s xml:id="N10D40" xml:space="preserve">Conſe­<lb/>quentia patet ex ſecūda parte. </s>
            <s xml:id="N10D45" xml:space="preserve">Et ſic patet prima <lb/>concluſio.              <anchor type="note" xlink:href="note-0011-01" xlink:label="note-0011-01a"/>             </s>
            <s xml:id="N10D4F" xml:space="preserve">¶ Ex hac concluſione ſequitur:  infini-<lb/>tis modis poſſunt generari infinite ſpecies mino­<lb/>res dupla irrationalis ꝓportiõis: vtpote ſi exceſ-<lb/>ſus diametri diminuatur per partes ꝓportiona-<lb/>les ꝓportione dupla: </s>
            <s xml:id="N10D5A" xml:space="preserve">Alio modo ꝓportiõe tripla <lb/>alio quadrupla. alio ſexquialtera. / et ſic in infinitū <lb/></s>
            <s xml:id="N10D60" xml:space="preserve">Patet correlariū intelligēti ꝓbationē cõculſiõis</s>
          </p>
          <div xml:id="N10D63" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0011-01a" xlink:label="note-0011-01" xml:id="N10D67">
              <s xml:id="N10D6B" xml:space="preserve">Correla-<lb/>rium. <lb/></s>
              <s xml:id="N10D71" xml:space="preserve">Gñatio <lb/>infinitoꝝ <lb/>ſpecierū <lb/>ꝓportio-<lb/>nis irra-<lb/>tionalis.</s>
            </note>
          </div>
          <p xml:id="N10D7E">
            <s xml:id="N10D7F" xml:space="preserve">Secūda cõcluſio. </s>
            <s xml:id="N10D82" xml:space="preserve">Infinite ſunt ſpe-<lb/>cies ꝓportionis irratiõalis maioris dupla: et illa­<lb/>rū infinite magna eſt aliqua. </s>
            <s xml:id="N10D89" xml:space="preserve">Probatur hec con-<lb/>cluſio: et pono /  exceſſus quo diameter excedit co-<lb/>ſtam: diminuatur vniformiter in hora vſ ad nõ <lb/>quantū. </s>
            <s xml:id="N10D92" xml:space="preserve">et capio ꝓportionē que eſt coſte ad exceſſū <lb/>diametri: et arguo ſic. </s>
            <s xml:id="N10D97" xml:space="preserve">Illa ꝓportio eſt maior du-<lb/>pla irrationalis. </s>
            <s xml:id="N10D9C" xml:space="preserve">et ꝓportio coſte ad medietatē il-<lb/>lius exceſſus eſt etiã irratiõalis maior: et ꝓ-<lb/>portio coſte ad quartã eſt etiã irrationalis maior <lb/>dupla: et ſic in infinitū quelibet ꝓportio coſte ad <lb/>aliquã partē aliquotã exceſſus eſt ꝓportio irrati-<lb/>onalis et ſunt īfinite partes aliquote cõtinuo mi-<lb/>nores et minores / ergo īfinite ſunt ꝓportiões irra­<lb/>tiõales minores dupla. </s>
            <s xml:id="N10DAD" xml:space="preserve">Probat̄̄ maior. </s>
            <s xml:id="N10DB0" xml:space="preserve">qm̄ coſte <lb/>ad exceſſū q̊ diameṫ excedit coſtã eſt ꝓportio irra-<lb/>tionalis: ex q̈rta ſuppoſitiõe maior dupla: vt con-<lb/>ſtat. </s>
            <s xml:id="N10DB9" xml:space="preserve">qm̄ ille exceſſus eſt minor quã medietas coſte. <lb/></s>
            <s xml:id="N10DBD" xml:space="preserve">qm̄ ſi eſſet medietas coſte aut moior: iam ibi eſſet <lb/>ꝓportio ſexq̇altera īter diametrū et coſtã: vel ma-<lb/>ior ſexquialtera: quod eſt falſum. </s>
            <s xml:id="N10DC4" xml:space="preserve">vt ptꝫ ex pcedēti <lb/>capite. </s>
            <s xml:id="N10DC9" xml:space="preserve">ergo q̄libet ꝓportio coſte ad aliquã partē <lb/>aliquotã exceſſus quo diameter excedit coſtam eſt <lb/>ꝓportio irratiõalis maior dupla: qḋ fuit ꝓbãdū. <lb/></s>
            <s xml:id="N10DD1" xml:space="preserve">Patet cõſequētia ex quīta ſuppoſitiõe. </s>
            <s xml:id="N10DD4" xml:space="preserve">qm̄ ex illa <lb/>ſuppoſitione. </s>
            <s xml:id="N10DD9" xml:space="preserve">ſi coſta ad aliquã partē aliquotã ex-<lb/>ceſſus quo diameter excedit coſtã ſe habet in pro-<lb/>portione ratiõali: ipſius coſte ad totū illū exceſſū <lb/>erit ꝓportio rationalis: ſed nõ ipſiꝰ coſte ad totū <lb/>illū exceſſū quo diameter excedit coſtã eſt ꝓportio <lb/>rationalis. </s>
            <s xml:id="N10DE6" xml:space="preserve">vt ptꝫ ex quarta ſuppoſitiõe. </s>
            <s xml:id="N10DE9" xml:space="preserve">igitur nõ <lb/>coſta ad aliquã partē aliquotã exceſſus quo dia-<lb/>meter excedit coſtã: ſe habet in ꝓportiõe ratiõali. <lb/></s>
            <s xml:id="N10DF1" xml:space="preserve">Patet cõſequētia ꝑ ſyllogiſmū hypotheticum: a <lb/>tota cõditionali cū deſtructiõe cõſequētis .etc̈. / et ſic <lb/>patet prima pars. </s>
            <s xml:id="N10DF8" xml:space="preserve">Et ſcḋa ꝓbatur facile. </s>
            <s xml:id="N10DFB" xml:space="preserve">q2 in īfi-             <pb chead="Prime partis" file="0012" n="12"/>             nitū magnꝰ erit exceſſus quo quantitas maior ex­<lb/>cedet minorē. </s>
            <s xml:id="N10E05" xml:space="preserve">igitur in infinitū magna erit ꝓpor-<lb/>tio quãtitatis maior ad minorē: et per cõſequens <lb/>illarū infinitarū proportionū in infinitū magna <lb/>erit aliqua: quod fuit probandū. </s>
            <s xml:id="N10E0E" xml:space="preserve">Et ſic patet con-<lb/>cluſio. </s>
            <s xml:id="N10E13" xml:space="preserve">¶ Simile correlariū: correlario ṗme cõclu-<lb/>ſiõis: hic poteris inferre de gñatione huiuſmodi <lb/>proportionū irrationaliū. </s>
            <s xml:id="N10E1A" xml:space="preserve">¶ Plures adieciſſem <lb/>cõcluſiones et correlaria: niſi obſtaret hanc mate­<lb/>riã ex ſecunda parte in vniuerſum dependere. </s>
            <s xml:id="N10E21" xml:space="preserve">Nec <lb/>mirari oportet: ſi plurimū in his duobus capitibꝰ <lb/>cõtra morē et ordinē mathematicū: ſequētibꝰ vſus <lb/>fuerim. </s>
            <s xml:id="N10E2A" xml:space="preserve">Non em̄ potuit hec materia alio mõ īduci</s>
          </p>
        </div>
        <div xml:id="N10E2D" level="3" n="5" type="chapter" type-free="capitulum">
          <head xml:id="N10E32" xml:space="preserve">Capitulū quintū / in quo agit̄̄ de diuiſione <lb/>corporis in partes proportionales qua pro­<lb/>portione rationali quis voluerit.</head>
          <p xml:id="N10E39">
            <s xml:id="N10E3A" xml:space="preserve">QUoniam plerū in materia <lb/>triplicis motus occurūt pleri caſus: <lb/>in quibus oportet vti multiplici ſpecie <lb/>diuiſionis corporis in partes ſuas proportiona­<lb/>les variis et diuerſis ꝓportionibus rationalibus <lb/>ideo ad vniuerſalē methodū inueniendam ſit.</s>
          </p>
          <p xml:id="N10E47">
            <s xml:id="N10E48" xml:space="preserve">Prīa ſuppõ. </s>
            <s xml:id="N10E4B" xml:space="preserve">Nõ oēs ꝑtes alicuiꝰ cor­<lb/>poris ī q̈s idē corpꝰ diuidit̄̄ ↄ̨tinuo ſe hñtes ī eadē <lb/>ꝓportiõe: gr̄a exēpli a. ſūt oēs ꝑtes ꝓportionales <lb/>eiuſdē corꝑis eadē ꝓportiõe a. </s>
            <s xml:id="N10E54" xml:space="preserve">Probat̄̄ / q2 poſſibi­<lb/>le eſt /  vna medietas alicuiꝰ corꝑis diuidat̄̄ in oēs <lb/>partes ſuas ꝓportione tripla: et omēs ille partes <lb/>ſunt partes illiꝰ corporis totalis. </s>
            <s xml:id="N10E5D" xml:space="preserve">in q̈s idē corpꝰ <lb/>diuidit̄̄ hñtes ſe cõtinuo in ꝓportiõe tripla: 2. et tñ <lb/>nõ ſunt oēs partes ꝓportionales illius corporis <lb/>proportione tripla. </s>
            <s xml:id="N10E66" xml:space="preserve">Et capio in ſuppoſitiõe ly oēs <lb/>collectiue in primo loco et in ſecundo.</s>
          </p>
          <p xml:id="N10E6B">
            <s xml:id="N10E6C" xml:space="preserve">Secūda ſuppoſitio. </s>
            <s xml:id="N10E6F" xml:space="preserve">Oēs partes ali­<lb/>cuius corporis innuite continue ſe habētes aliq̈ <lb/>ꝓportione: puta a. et abſoluentes totū corpꝰ: ſunt <lb/>oēs partes ꝓportionales eiuſdē corporis propor­<lb/>tione a. </s>
            <s xml:id="N10E7A" xml:space="preserve">Et volo dicere /  ſi aliquod corpꝰ diuidat̄̄ <lb/>in infinitas partes continuo ſe habentes in ꝓpor­<lb/>tione a. et abſoluētes totū corpus: ille ſimul ſunt <lb/>oēs partes proportionales proportione a. </s>
            <s xml:id="N10E83" xml:space="preserve">Patꝫ <lb/>hec ſuppoſitio: q2 ſic diuidere corpus eſt diuidere <lb/>ipſū in oēs partes ꝓportionales proportione a. <lb/></s>
            <s xml:id="N10E8B" xml:space="preserve">Patet hoc ex deſcriptione termini.</s>
          </p>
          <p xml:id="N10E8E">
            <s xml:id="N10E8F" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N10E92" xml:space="preserve">Quãdocun ali­<lb/>qua cõtinuo ꝓportionãtur aliqua ꝓportione geo­<lb/>metrica: qualis eſt ꝓportio inter proportionata: <lb/>talis eſt inter ſuas differētias ſiue exceſſeus: quod <lb/>idem eſt: vt q2 .3. ad .4. ſe habet in ꝓportiõe dupla <lb/>et ſimiliter .4. ad 2. / et cõtinuo proportionant̄̄ eadē <lb/>proportione: ideo differentia ſiue exceſſus inter .8 <lb/>et .4. ſe habet ad differãtiã ſiue exceſſum inter .4. et <lb/>2. in proportiõe dupla. </s>
            <s xml:id="N10EA5" xml:space="preserve">Patet hec ſuppoſitio ex <lb/>quīta proprietate proportionalitatis ſiue medie­<lb/>tatis geometrice ex ſecūda parte capitulo ſecūdo</s>
          </p>
          <p xml:id="N10EAC">
            <s xml:id="N10EAD" xml:space="preserve">Quarta ſuppoſitio. </s>
            <s xml:id="N10EB0" xml:space="preserve">Si aliquod cor­<lb/>pus diuidatur in infinitas partes: et deperdendo <lb/>primã illarū perdit aliquã ꝓportionē puta a. / hoc <lb/>eſt efficitur in a. ꝓportione minꝰ: et ꝑdendo ſcḋam <lb/>poſt primã iterum efficitur in a. minus: et ꝑdendo <lb/>tertiam poſt ſecūdã iterum efficitur in a. minus. </s>
            <s xml:id="N10EBD" xml:space="preserve">et <lb/>ſic conſequenter ille partes ſunt oēs partes ꝓpor­<lb/>tionales illius corporis ꝓportione a. / ſi vero ꝑden­<lb/>do primã illarū non perdit vnam proportionē a. /             <cb chead="Capitulum quintū."/>             et ꝑdendo ſecundã poſt primã: vnã alteram, ꝑden-<lb/>do tertiã poſt ſecundã vnã alteram ꝓportionē a. / <lb/>et ſic cõſequenter: tales partes nõ ſunt oēs partes <lb/>ꝓportionales talis corporis ꝓportione a. </s>
            <s xml:id="N10ECF" xml:space="preserve">Pro-<lb/>batur prima pars / q2 ſi nõ: detur oppoſitū: videli­<lb/>cet /  aliquod corpus diuiditur in aliquas partes <lb/>iufinitas: et ꝑdēdo primã illarum ꝑdit ꝓportionē <lb/>a. etc̈. et tamen nõ ſunt ille oēs partes ꝓportiona-<lb/>les illius corporis ꝓportiõe a. et ſic tale corpus b. / <lb/>et arguitur ſic / b. eſt diuiſum in infinitas partes: et <lb/>ꝑdendo primã illarū in prima parte ꝓportionali <lb/>hore exempli gratia: in fine illius partis eſt in a. <lb/>ꝓportiõe minꝰ: et ꝑdendo ſecundã partē in ſecūda <lb/>parte ꝓportionali tēporis: iterum efficitur in fine <lb/>eiuſdem partis in a. proportione minꝰ quaꝫ erat <lb/>in principio eiuſdē partis: et in tertia parte ꝓpor­<lb/>tionali ꝑdēdo terntiã ip̄m efficitur minꝰ / quã erat <lb/>in principio eiuſdē ꝑtis in a. ꝓportione: et ſic con­<lb/>ſequēter. </s>
            <s xml:id="N10EF0" xml:space="preserve">igitur in partibus ꝓportionabilibꝰ illiꝰ <lb/>hore ſunt infinita corpora cõtinuo ſe habentia in <lb/>ꝓportione a. </s>
            <s xml:id="N10EF7" xml:space="preserve">Patet / q2 corpus qḋ eſt in principio <lb/>p̄me partis ꝓportionalis: ſe habet in ꝓportione <lb/>a. ad illud quod eſt in prīcipio ſecunde et illud qḋ <lb/>eſt in p̄ncipio ſecunde ſe habet in ꝓportione a. ad <lb/>illud quod eſt in principio tertie: et ſic cõſequēter / <lb/>igitur illa infinta corpora continuo ſe habet in <lb/>ꝓportiõe a. / et ex cõſequēti ſequit̄̄ /  exceſſus inter <lb/>illa corpora cõtinuo ſe habēt in ꝓportiõe a. / puta <lb/>exceſſus quo corpus in p̄ncipio ṗme partis ꝓpor­<lb/>tionalis excedit corpus in p̄ncipio ſecunde: ſe ha­<lb/>bet in ꝓportione a. / ad exceſſum quo corpus in p̄n­<lb/>cipio ſecūde excedit corpus in p̄ncipio tertie: et ſic <lb/>cõſequēter. </s>
            <s xml:id="N10F12" xml:space="preserve">Patet hec cõſequētia ex p̄cedenti ſup­<lb/>poſitione: et illi exceſſus ſunt ille partes que deper­<lb/>dūtur in partibus ꝓportionalibus tēporis: ergo <lb/>ille ꝑtes que deꝑduntur in illis partibus propor-<lb/>tionalibus tēporis ſe habent cõtinuo in ꝓportõe <lb/>a. </s>
            <s xml:id="N10F1F" xml:space="preserve">Conſequētia patet: et ꝓbatur antecedens: quia <lb/>corpus in principio p̄me partis ꝓportionalis tē-<lb/>poris: exedit corpus in principio ſecunde ꝑ illud <lb/>quod deꝑdit in ip̄a p̄ma parte ꝓportionali tēpo-<lb/>ris: et illud eſt p̄ma illarum partiū in quas diuidi­<lb/>tur corpus ex caſu: igitur aſſumptum verum </s>
            <s xml:id="N10F2C" xml:space="preserve">Qm̄ <lb/>ſic ꝓbabis de quocū alio exceſſu. </s>
            <s xml:id="N10F31" xml:space="preserve">et vltra ille par­<lb/>tes in quas diuiditur illud corpus b. ſunt infinite <lb/>cõtinuo ſe habentes in ꝓportione a. / et abſoluūt to­<lb/>tum corpus: igitur ille ſunt oēs partes ꝓportiona­<lb/>les illius corporis ꝓportione a. / quod fuit negatū <lb/></s>
            <s xml:id="N10F3D" xml:space="preserve">Patet hec conſequentia ex ſecunda ſuppoſitione. <lb/></s>
            <s xml:id="N10F41" xml:space="preserve">Quod vero ille partes abſoluant totum corpus <lb/>patet / quia per deperditionem illarū perditur to­<lb/>tum corpus ad nõ quantum: cum deperdat infini­<lb/>tam latitudinem proportionis: vt conſtat: igitur. <lb/></s>
            <s xml:id="N10F4B" xml:space="preserve">Secūda pars patet facile / quia bene ſequitur de-<lb/>perdendo illas partes continuo: tale corpus non <lb/>continuo efficitur minus in proportione a. / ergo <lb/>ſequitur /  non ſunt ibi in tali diminutione infini­<lb/>ta corpora continuo ſe habentia in proportione <lb/>a. modo ſuperius expoſito: ergo ſequitur /  exceſ­<lb/>ſus illorum corporum non continuo ſe habent in <lb/>proportione a. </s>
            <s xml:id="N10F5C" xml:space="preserve">Patet conſequentia ex tertia ſup­<lb/>poſitione: et illi exceſſus ſunt partes in quas diui­<lb/>debatur ipſum corpus b. / igitur ipſe non ſunt par­<lb/>tes proportionales corporis b. proportione a. / et <lb/>per conſequens de primo ad vltimum ſequitur il­<lb/>la ſecunda pars ſuppoſitionis.</s>
          </p>
          <pb chead="Prime partis" file="0013" n="13"/>
          <p xml:id="N10F6D">
            <s xml:id="N10F6E" xml:space="preserve">His poſitis ſit prima cõcluſio. </s>
            <s xml:id="N10F71" xml:space="preserve">Quã­<lb/>docun aliquod corpus diuiditur quouis genere <lb/>proportionis: totū corpus ſe debet habere ad ag­<lb/>gregatum ex omnibus partibus proportionalibꝰ <lb/>ſequentibus primam: in ea proportione qua cor­<lb/>pus diuiditur. </s>
            <s xml:id="N10F7E" xml:space="preserve">Exemplum / vt ſi corpus diuidatur <lb/>proportione ſexquialtera: oportet /  illud corpus <lb/>ſe habeat ad aggregatum ex omnibus partibus <lb/>proportionabilibꝰ. </s>
            <s xml:id="N10F87" xml:space="preserve">ſequentibus primam: in pro­<lb/>portione ſexquialtera. </s>
            <s xml:id="N10F8C" xml:space="preserve">Probatur hec concluſio: et <lb/>volo /  b. corpꝰ diuidatur in partes proportiona­<lb/>les proportione a. in infinitum: et arguo ſic / b. cor-<lb/>pus diuiditur in partes proportionales propor­<lb/>tione .a. in infinitum: igitur deperdendo primam <lb/>partem proportionalem proportione a. ipſum ef­<lb/>ficitur in a. proportione minus: patet conſequētia <lb/>ex ſecunda parte quarte ſuppoſitionis: et vltra il­<lb/>lud corpus b. deperdendo primã partem propor-<lb/>tionalem a. efficitur ſiue manet in a. proportione <lb/>minus et non manet niſi aggregatum ex omībus <lb/>ſequentibus primam partem proportionalē: igi­<lb/>tur illud corpus b. ſe habet ad aggregatum ex om­<lb/>nibus partibus proportionabilibus ſequentibus <lb/>primam eius partem proportionalem proportio­<lb/>ne a. in eadem proportione a. / quod fuit ꝓbanduꝫ. <lb/></s>
            <s xml:id="N10FAE" xml:space="preserve">Patet hec conſequentia: quia ſi illud aggregatū <lb/>ex omnibus ſequentibus primã. etc̈. eſt minus ipſo <lb/>b. corpore in a proportione: ſequitur /  ipſum b. <lb/>corpus eſt maius illo aggregato ex omnibus ſe-<lb/>quentibus primam in a. proportione.</s>
          </p>
          <p xml:id="N10FB9">
            <s xml:id="N10FBA" xml:space="preserve">Secunda cõcluſio. </s>
            <s xml:id="N10FBD" xml:space="preserve">Ad inueniendū <lb/>reſiduū a prima parte ꝓportionali quauis ꝓpor­<lb/>tione rationali corpus diuidatur: capiãtur primi <lb/>numeri talis ꝓportionis: et diuidat̄̄ corpus in tot <lb/>vnitates quotus eſt numerꝰ maior illius propor­<lb/>tionis: et ex illis partibꝰ ꝓ reſiduo a prima parte <lb/>capiantur tot: quotus eſt numerus minor talis ꝓ-<lb/>portionis. </s>
            <s xml:id="N10FCE" xml:space="preserve">Exēplum / vt ſi vis diuidere corpꝰ ꝓpor-<lb/>tione ſexquitertia: et videre quid reſtabit pro reſi-<lb/>duo a prima parte proportionali: capias .4. et .3. <lb/>primos numeros ꝓportionis ſexquitertie: et diui­<lb/>das totū corpus in quatuor partes equales: quia <lb/>numerus maior eſt quaternarius: et pro reſiduo a <lb/>prima ꝑte ꝓportionali capias tres partes ex illis <lb/>q2 numerus minor eſt ternarius. </s>
            <s xml:id="N10FDF" xml:space="preserve">Probat̄̄ hec con­<lb/>cluſio et volo /  b. corpus diuidatur proportione <lb/>a. cuius proportionis primi numeri ſint c. maior <lb/>numerus et d. minor / et arguo ſic. </s>
            <s xml:id="N10FE8" xml:space="preserve">Iſtud corpus eſt <lb/>diuiſum per partes ꝓportionales proportione a / <lb/>ergo totū iſtud b. corpus ſe habet ad aggregatuꝫ <lb/>ex oībus partibus ꝓportionabilibus ꝓportione <lb/>a. ſequētibus primã in proportione a. </s>
            <s xml:id="N10FF3" xml:space="preserve">Patet ↄ̨ña <lb/>ex priori concluſione: et vltra totum b. ſe habet ad <lb/>aggregatum .etc̈. in ꝓportione a. / ergo ſequitur /  <lb/>ipſuꝫ b. ſe habet ad illud aggregatū ſicut c. nume­<lb/>reus ad d. numerū / vt cõſtat et d. numerꝰ eſt nume­<lb/>rus minor: ergo ſequitur /  aggregatū ex omībꝰ <lb/>partibus ꝓportionalibꝰ proportione a. ſequē-<lb/>tibus primã ſe habet vt numerus mīor primorum <lb/>numerorū proportionis a. reſpectu maioris nu-<lb/>meri: et nõ poteſt ſic ſe habere: niſi fiat diuiſio ta-<lb/>lis corporis modo dicto in concluſione vel equiua­<lb/>lenti / vt conſtat: igitur ſequitur concluſio.</s>
          </p>
          <p xml:id="N1100C">
            <s xml:id="N1100D" xml:space="preserve">Tertia cõcluſio. </s>
            <s xml:id="N11010" xml:space="preserve">Ad diuidendū cor-<lb/>pus per partes proportionales qua vis ꝓportõe             <cb chead="Capitulum quintū"/>             multiplici capiēda eſt pro reſiduo a prima parte <lb/>proportionali vna pars aliquota denoīata a nu­<lb/>mero talē proportionē multiplicem denominante <lb/>vt in diuiſione dupla proportione capiēda eſt vna <lb/>medietas pro reſiduo a prima parte ꝓportionali <lb/>et proportione tripla vna tertia et quadrupla vna <lb/>quarta quintupla vero vna quinta et ſic ī infinitū <lb/></s>
            <s xml:id="N11025" xml:space="preserve">Probatur hec cõcluſio: qm̄ ſemper corpus diuiſū <lb/>per partes proportionales aliqua proportione ſe <lb/>debet habere ad reſiduū a prima parte ꝓportio-<lb/>nali in eadeꝫ ꝓportione qua diuiditur: vt patet ex <lb/>prima concluſione: ſed quodlibet corpus ſe hab3 <lb/>ad ſuã medietatē in proportiõe dupla et quodlib3 <lb/>ad ſuã tertiã in tripla: ad quartã in quadrupla: et <lb/>ſic conſequēter: ergo in qualibet diuiſione corpo-<lb/>ris ꝓportione dupla debet capi ꝓ reſiduo a pri-<lb/>ma parte proportionali medietas. </s>
            <s xml:id="N1103A" xml:space="preserve">et proportione <lb/>tripla vna tertia: et q̈drupla vna quarta et quintu­<lb/>pla vna quīta. </s>
            <s xml:id="N11041" xml:space="preserve">et ſic in infinituꝫ: quod fuit ꝓbandū <lb/>             <anchor type="note" xlink:href="note-0013-01" xlink:label="note-0013-01a"/>             </s>
            <s xml:id="N1104B" xml:space="preserve">¶ Ex hac cõcluſione ſequitur primo:  diuidendo <lb/>corpus proportiõe dupla prima pars erit medie­<lb/>tas, et ſecūda medietas reſidui: et tertia medietas <lb/>reſidui, et ſic cõſequenter. </s>
            <s xml:id="N11054" xml:space="preserve">ꝓportione tripla prima <lb/>pars eſt due tertie totius: et ſecūda due tertie reſi-<lb/>dui, et tertia due tertie reſidui a prima et ſecunda: <lb/>et ſic ſine termino. </s>
            <s xml:id="N1105D" xml:space="preserve">ꝓportione vero quadrupla pri­<lb/>ma pars eſt tres quarte, et ſecunda tres quarte re­<lb/>ſidui. </s>
            <s xml:id="N11064" xml:space="preserve">ꝓportiõe vero quītupla prima pars eſt qua­<lb/>tuor quinte. </s>
            <s xml:id="N11069" xml:space="preserve">et ſextupla quin ſexte et ſeptupla ſex <lb/>ſeptime: et ſic ſine termino. </s>
            <s xml:id="N1106E" xml:space="preserve">Probatur hoc correla­<lb/>riū: quia diuidendo proportione dupla: totum re­<lb/>ſiduū a prima parte ꝓportõali eſt vna medietas / <lb/>vt patet ex cõcluſione: igitur prima pars erit vna <lb/>medietas </s>
            <s xml:id="N11079" xml:space="preserve">Patet cõſequētia ex ſecūda ſuppoſitio­<lb/>ne / qm̄ omnes partes proportionales totū corpꝰ <lb/>abſoluūt. </s>
            <s xml:id="N11080" xml:space="preserve">Item diuidendo ꝓportione tripla reſi­<lb/>duū a prima parte ꝓportionali eſt vna tertia / igit̄̄ <lb/>prima erit due tertie. </s>
            <s xml:id="N11087" xml:space="preserve">Itē diuidēdo quadrupla re­<lb/>ſiduū a ṗma eſt vna quarta / igit̄̄ prima eſt 3 quar-<lb/>te. </s>
            <s xml:id="N1108E" xml:space="preserve">Quītupla vero eſt vna quīta / igitur prima erit <lb/>quatuor quinte. </s>
            <s xml:id="N11093" xml:space="preserve">Et ſimiliter arguēdū eſt de ꝓpor­<lb/>tione ſextupla ſeptupla / et ſic cõſequenter. </s>
            <s xml:id="N11098" xml:space="preserve">igit̄̄ cor-<lb/>relarium verū. </s>
            <s xml:id="N1109D" xml:space="preserve">Antecedentia harū cõſequētiarum <lb/>patēt ex ꝓxima concluſione et ipſe conſequentie ex <lb/>ſecunda ſuppoſitione.             <anchor type="note" xlink:href="note-0013-02" xlink:label="note-0013-02a"/>             </s>
            <s xml:id="N110A9" xml:space="preserve">¶ Sequitur ſecūdo /  diui­<lb/>dēdo corpus per partes proportionales ꝓportõe <lb/>dupla: reſiduum a prima eſt equale prime parti: et <lb/>ꝓportione tripla eſt ſubduplū ad ṗmã: et quadru­<lb/>pla ſubtriplū: et quītupla ſubquadruplū: et ſextu-<lb/>pla ſubquintuplū: et ſic ſine termīo. </s>
            <s xml:id="N110B6" xml:space="preserve">Patet hec cor­<lb/>relariū facile ex priori et concluſione. </s>
            <s xml:id="N110BB" xml:space="preserve">Si em̄ diui-<lb/>dendo ꝓportione tripla prima pars eſt due tertie <lb/>et reſiduū vna tertia cū vna tertia ſit ſubduplū ad <lb/>duas tertias reſiduū a prima diuidēdo ꝓportiõe <lb/>tripla erit ſubduplū ad primã. </s>
            <s xml:id="N110C6" xml:space="preserve">Item cū diuidēdo <lb/>corpus ꝓportione quadrupla prima pars ſit tres <lb/>quarte et reſiduuꝫ a prima vna quarta vna: autem <lb/>quarta eſt ſubtripla ad tres quartas: igitur reſi-<lb/>duū a prima parte diuidendo proportõe quadru­<lb/>pla eſt ſubtriplum ad primã partem. </s>
            <s xml:id="N110D3" xml:space="preserve">Et hoc mo-<lb/>do de aliis probabis.</s>
          </p>
          <div xml:id="N110D8" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0013-01a" xlink:label="note-0013-01" xml:id="N110DC" xml:space="preserve">Correla­<lb/>riū ṗmū.</note>
            <note position="right" xlink:href="note-0013-02a" xlink:label="note-0013-02" xml:id="N110E4" xml:space="preserve">Corelari­<lb/>riū ſcḋm</note>
          </div>
          <p xml:id="N110EC">
            <s xml:id="N110ED" xml:space="preserve">Quarta cõcluſio. </s>
            <s xml:id="N110F0" xml:space="preserve">Ad diuidendū cor­<lb/>pus qua vis ꝓportione ſuperparticulari: capiēda <lb/>eſt ꝓ ṗma parte ꝓportionali vna pars aliquota <lb/>denoīata a maiori numero ṗmorū numeroꝝ talis <lb/>ꝓportionis. </s>
            <s xml:id="N110FB" xml:space="preserve">puta diuidendo ꝓportione ſexquial-             <pb chead="Prime partis" file="0014" n="14"/>             tera: capienda eſt vna tertia pro ṗma parte: et ſex­<lb/>quitertia. / vna quarta et ſexquiquarta vna quinta <lb/>et ſexquiquīta vna ſexta: et ſic cõſequēter. </s>
            <s xml:id="N11107" xml:space="preserve">Probat̄̄ / <lb/>qm̄ ad diuidēdum corpus aliqua ꝓportione: pro <lb/>prima parte capiēdus eſt exceſſus quo numerꝰ ma­<lb/>ior et primus talis ꝓportionis excedit numerū mi­<lb/>norē eiuſdē ꝓportiõis: vt facile educitur ex prima <lb/>cõcluſione adiūcta ſcḋa ſuppoſitione: ſed primus <lb/>numerꝰ et maior ꝓportionis ſuperparticularis ex­<lb/>cedit numeꝝ minorē ſemꝑ vna parte aliquota ſui <lb/>denoīta a numero maiore: vt primꝰ numerꝰ et ma­<lb/>ior ꝓportionis ſexq̇altere excedit minorē per vnã <lb/>tertiã ſui: et primꝰ numerꝰ et maior ꝓportiõis ſex-<lb/>quitertie excedit minorē. </s>
            <s xml:id="N11120" xml:space="preserve">per vnã quartã ſui primꝰ <lb/>vero numerꝰ et maior ꝓportiões ſexquiquarte ex­<lb/>cedit minorē per vnã quintaꝫ ſui: vt ptꝫ ex genera-<lb/>tione ſpecierū ꝓportionis ſuperparticularis ca-<lb/>pite ſecūdo huius partis: igitur diuidendo ꝓpor­<lb/>tione ſexquialtera debet capi vna tertia ꝓ prima <lb/>parte: et ſexquitertia vna quarta: et ſic conſequen­<lb/>ter. </s>
            <s xml:id="N11131" xml:space="preserve">Patet igitur concluſio.             <anchor type="note" xlink:href="note-0014-01" xlink:label="note-0014-01a"/>             </s>
            <s xml:id="N11139" xml:space="preserve">¶ Ex hac concluſione <lb/>ſequitur /  diuiſo corpore per partes ꝓportiona­<lb/>les proportiõe ſexquialtera reſiduū a prima par­<lb/>te eſt duplum ad primū: et ſexquitertia triplū: et ſex­<lb/>quiquarta quadruplã: et ſexquiquinta. / quintuplū <lb/>et ſic in infinitū. </s>
            <s xml:id="N11146" xml:space="preserve">oppoſito modo ad ſpecies ꝓpor-<lb/>tionis multiplicis incipiēdo a tripla. </s>
            <s xml:id="N1114B" xml:space="preserve">Probatur <lb/>hoc correlariū. </s>
            <s xml:id="N11150" xml:space="preserve">qm̄ diuiſo corpore proportiõe ſex­<lb/>quialtera prima pars eſt vna tertia. / vt ptꝫ ex pre­<lb/>cedēti concluſione: ergo reſiduum a prima eſt due <lb/>tertie. </s>
            <s xml:id="N11159" xml:space="preserve">Modo due tertie ſunt duplum ad vnã. </s>
            <s xml:id="N1115C" xml:space="preserve">Iteꝫ <lb/>diuiſo corpore ꝓportiõe ſexquitertia prima pars <lb/>corporis ē vna quarta: igit̄̄ reſiduū a prima eſt .3. <lb/>quarte ſed triū quartarū ad vnã quartam eſt pro­<lb/>portio tripla: igitur. </s>
            <s xml:id="N11167" xml:space="preserve">Iteꝫ diuiſo corpore ꝓportio­<lb/>ne ſexquiquarta prima pars eſt vna quinta / vt ptꝫ <lb/>ex prima concluſione: igit̄̄ totū reſiduū eſt .4. quin­<lb/>te. </s>
            <s xml:id="N11170" xml:space="preserve">Modo .4. quītarum ad vnã quintam eſt pro-<lb/>portio quadrupla et ſic de qualibet alia ꝓbabis <lb/></s>
            <s xml:id="N11176" xml:space="preserve">Patet iſte conſequētie ex ſecunda ſuppoſitione.</s>
          </p>
          <div xml:id="N11179" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0014-01a" xlink:label="note-0014-01" xml:id="N1117D" xml:space="preserve">Correla­<lb/>rium.</note>
          </div>
          <p xml:id="N11185">
            <s xml:id="N11186" xml:space="preserve">Quinta concluſio. </s>
            <s xml:id="N11189" xml:space="preserve">Ad diuidendum <lb/>corpus qua placuerit ꝓportiõe ſuprapartiēti ge-<lb/>nerentur ſpecies huiꝰ ꝓportionis ſereatim modo <lb/>poſito in ſecundo capite huiꝰ partis: et diuidatur <lb/>corpus in tot partes quotus eſt nūerus inferioris <lb/>ordinis: et ex illis partibus capiantur tot pro re-<lb/>ſiduo a prima parte ꝓportionali quotꝰ eſt nume­<lb/>rus ſuperior: et reſiduū erit prima pars ꝓportio-<lb/>nalis: </s>
            <s xml:id="N1119C" xml:space="preserve">Exemplū / vt cõſtituatur naturalis ſeries nu­<lb/>meroꝝ incipiendo a ternario: et cõſtituatur inferꝰ <lb/>ſeries omnium numerorum impariuꝫ incipiēdo a <lb/>quinario / vt patet in figura.</s>
          </p>
          <xhtml:table xml:id="N111A5">
            <xhtml:tr xml:id="N111A6">
              <xhtml:td xml:id="N111A7" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N111A9">
            <s xml:id="N111AA" xml:space="preserve">Tunc ſi vis diuidere aliquod corpus in ꝓportiõe <lb/>ſuprabipartiente tertias: q2 numerus inferior in <lb/>illa ſpecie eſt quinariꝰ diuidas totū corpꝰ ī quī <lb/>quintas: et q2 nūerus ſuperior eſt ternariꝰ: capias <lb/>ꝓ reſiduo a ṗma parte ꝓportionali tres quītas et <lb/>manebūt due quīte: et ille due quīte ſunt ṗma pars <lb/>ꝓportiõalis ꝓportiõe ſuprabipartiēte tertias. </s>
            <s xml:id="N111B9" xml:space="preserve">Et <lb/>iſto modo in oībus aliis ſpecieꝰ operaberis. </s>
            <s xml:id="N111BE" xml:space="preserve">Et <lb/>qm̄ in capite ſcḋo vbi generant̄̄ ſpecies huiꝰ ꝓpor­<lb/>tionis nõ oēs generant̄̄ quãuis generent̄̄ infinite <lb/></s>
            <s xml:id="N111C6" xml:space="preserve">Ideo ad diuidendū corpꝰ qua volueris ꝓportiõe <lb/>ſuprapartiēte vtaris doctrina ſecūde cõcluſionis             <cb chead="Capitulum quintū."/>             </s>
            <s xml:id="N111CE" xml:space="preserve">Patet hec cõcluſio facile ex cõcluſiõe ſecūda. </s>
            <s xml:id="N111D1" xml:space="preserve">¶ Ex <lb/>hac cõcluſione ſequit̄̄ /  in diuiſiõe corporis ṗma <lb/>ſpecie ꝓportiõis ſuprapartientis ſignate inferiꝰ <lb/>reſiduū a prima parte ꝓportiõali eſt ſexquialteꝝ <lb/>ad primã: et in ſecūda ſpecie reſiduū a prima eſt ſex­<lb/>quitertiū ad primã: et in tertia ſpecie eſt ſexquiq̈r­<lb/>tū ad primã: et in q̈rta reſiduū a prima erit ſexqui­<lb/>quītū ad primã: et ſic in īfinitū ꝓcedēdo ꝑ ſpecies <lb/>ꝓportionis ſuꝑparticularis. </s>
            <s xml:id="N111E4" xml:space="preserve">Probat̄̄ hoc corre-<lb/>lariū / qm̄ in prima ſpecie illaꝝ ſpecieꝝ generataꝝ <lb/>in figura ꝓ reſiduo a prima parte ꝓportionali ca­<lb/>piūtur tres quīte: et ꝓ prima parte manēt due quī­<lb/>te / vt ptꝫ ex concluſione precedēti: ſed triū quītarū <lb/>ad duas quītas eſt ꝓportio ſexquialtera: igr̄. </s>
            <s xml:id="N111F1" xml:space="preserve">Itē <lb/>in ſcḋa ſpecie ꝓ reſiduo a prima parte ꝓportõali <lb/>capiunt̄̄ quatuor ſeptime: et ꝓ prima tres ſeptime <lb/>ſed quatuor ſeptimaꝝ ad tres ſeptimas in ꝓpor-<lb/>tio ſexq̇tertia: igr̄. </s>
            <s xml:id="N111FC" xml:space="preserve">In tertia / vero ſpecie ꝓ reſiduo <lb/>a prima capiūtur quī none: et pro prima reſidue <lb/>q̈ttuor none: ſed q̇n nonaꝝ ad quattuor nonas <lb/>eſt ꝓportio ſexquiq̈rta igit̄̄. </s>
            <s xml:id="N11205" xml:space="preserve">Et ſic ꝓbabis de qua­<lb/>libet alia ſpecie illiꝰ figure. </s>
            <s xml:id="N1120A" xml:space="preserve">Ptꝫ igit̄̄ correlarium <lb/></s>
            <s xml:id="N1120E" xml:space="preserve">¶ Sed ad īueniēdã ꝓportionē reſidui a ṗma par­<lb/>te proportiõali ad ipſam primam in reſiduis ſpe­<lb/>ciebus conſulas ſecundam concluſionem.</s>
          </p>
          <p xml:id="N11215">
            <s xml:id="N11216" xml:space="preserve">Sexta concluſio. </s>
            <s xml:id="N11219" xml:space="preserve">Ad diuidendū cor­<lb/>pus qua volueris ꝓportione multiplici ſuꝑparti­<lb/>culari: generent̄̄ in nūeris ſpecies huiꝰ ꝓportiõis <lb/>modo poſito in ſecūdo capite huiꝰ partis: et diui­<lb/>datur corpus in tot partes quotꝰ eſt numerꝰ infe­<lb/>rioris ordinis: et ex illis partibꝰ capiant̄̄ tot ꝓ re­<lb/>ſiduo a prima parte ꝓportionali quotus eſt nume­<lb/>rus ſuperior: et reſiduū erit prima pars ꝓportiõa­<lb/>lis. </s>
            <s xml:id="N1122C" xml:space="preserve">Et eodē modo fiat diuidēdo ꝓportõe multipli­<lb/>ci ſuprapartiēte: vt ad diuidendū corpꝰ ꝓportiõe <lb/>dupla ſexquialtera: q2 numerꝰ maior ī illa ſpecie <lb/>eſt quinariꝰ: diuidat̄̄ corpus in quī quītas: et q2 <lb/>numerꝰ minor eſt binariꝰ capiant̄̄ due quīte ꝓ re-<lb/>ſiduo a prima parte ꝓportiõali: et tres quīte erūt <lb/>ṗma pars ꝓportionalis: et tres quīte reſidui ſcḋa <lb/>et iteꝝ tres quinte reſidui a prima et ſcḋa, tertia: et <lb/>ſic ſine termīo. </s>
            <s xml:id="N1123F" xml:space="preserve">Itē ſi vis diuidere corpꝰ ꝓportione <lb/>dupla ſuprabipartiēte tertias diuidas corpus in <lb/>octo octauas: q2 nūerꝰ octonariꝰ eſt nūerꝰ maior <lb/>illius ꝓportiõis: et capias ꝓ reſiduo a ṗma parte <lb/>proportiõali tres octauas: et reſidue quī octaue <lb/>erūt prima pars ꝓportiõalis: et quī octaue reſi <lb/>dui erūt ſcḋa pars proportiõalis: et ſic cõſequēter <lb/></s>
            <s xml:id="N1124F" xml:space="preserve">Ptꝫ hec cõcluſio ex ſcḋa cõcluſiõe             <anchor type="note" xlink:href="note-0014-02" xlink:label="note-0014-02a"/>             </s>
            <s xml:id="N11257" xml:space="preserve">¶ Ex quo ſequit̄̄ / <lb/> in oībus ſpeciebꝰ ꝓportiõis multiplicis ſuꝑpar­<lb/>ticularis aut multiplicis ſuprapartiētis: et etiã in <lb/>oībus aliis reſiduū a prima parte ꝓportionali hꝫ <lb/>ſe ad primã partē ꝓportiõalē in ea proportõe qua <lb/>ſe habēt nūeri ſuperiores in figuris ſuaꝝ genera-<lb/>tionū ad nūeros ꝑ quos īferiores excedūt ſuperio­<lb/>res: vt in proportiõe dupla ſexquialtera q2 nūerꝰ <lb/>ſuperior eſt binariꝰ et nūerus īferior quinarius: et <lb/>quinariꝰ excedit binariū ꝑ ternariū. </s>
            <s xml:id="N1126C" xml:space="preserve">reſiduū a pri­<lb/>ma parte ꝓportionali in tali proportiõe ſe habet <lb/>ad primã partē proportionalē ſicut duo ad tria et <lb/>q2 in proportiõe dupla ſuprabipartiente tertias <lb/>nūerus ſuperior eſt ternariꝰ: et inferior octonariꝰ <lb/>et octonariꝰ excedit ternariū ꝑ quīariū. </s>
            <s xml:id="N11279" xml:space="preserve">ideo in ta­<lb/>lis proportionis diuiſione reſiduū a prima parte <lb/>proportiõali ſe hꝫ ad primã ſicut q̇nariꝰ ad terna­<lb/>riū. </s>
            <s xml:id="N11282" xml:space="preserve">Probat̄̄ hoc correlariū ex ſecūda cõcluſione:             <pb chead="Prime partis" file="0015" n="15"/>             qm̄ iuxta illam cõcluſionē reſiduū a prima parte <lb/>ꝓportionali quauis ꝓportione rationali debet ſe <lb/>habere vt numerꝰ minor talis ꝓportionis: et ꝑ cõ­<lb/>ſequēs manebit ꝓ prima parte ꝓportiõali nume­<lb/>rus ille quo numerꝰ maior talis ꝓportionis exce-<lb/>dit minorē. </s>
            <s xml:id="N11294" xml:space="preserve">Patet hec cõſequētia / q2 ſemꝑ corpus <lb/>debet diuidi in tot partes quotus eſt numerꝰ ma-<lb/>ior et primus ꝓportiõis qua debet fieri diuiſio: vt <lb/>patet ex ſecūda cõcluſione: et pro reſiduo a prima <lb/>debent capi tot partes ex illis quotus eſt numerꝰ <lb/>minor vt dictum eſt. </s>
            <s xml:id="N112A1" xml:space="preserve">igitur relique partes remanē­<lb/>tes erunt prima pars. </s>
            <s xml:id="N112A6" xml:space="preserve">Patet cõſequētia ex prima <lb/>ſuppoſitione: et ille partes remanentes ſunt nume­<lb/>rus quo numerus maior excedit minorē, vt patet: <lb/>igitur prima pars ꝓportionalis eſt numerus quo <lb/>maior numerꝰ et primꝰ proportionis qua ſit diui­<lb/>ſio excedit minorē. </s>
            <s xml:id="N112B3" xml:space="preserve">Habet ſe / igitur totū reſiduū a <lb/>prima parte proportionali ad primã partē pro-<lb/>portionalē in ea proportione qua numerꝰ minor <lb/>et primus talis proportionis ſe habet ad numerū <lb/>quo maior et primus eiuſdem proportiõis excedit <lb/>minorem. </s>
            <s xml:id="N112C0" xml:space="preserve">quod fuit probandum </s>
            <s xml:id="N112C3" xml:space="preserve">¶ Ad habendam <lb/>autē praxim huius correlarii in cõpoſitis propor­<lb/>tionibus conſtituētur alique figure: quibus facile <lb/>iudicabitur in qua proportiõe ſe habet reſiduū a <lb/>prima parte ꝓportionali ad primã partē ꝓpor-<lb/>tionalē. </s>
            <s xml:id="N112D0" xml:space="preserve">Ad quod facile inſpiciendū in ꝓportioni­<lb/>bus duplis ſuperparticularibus conſtituatur na­<lb/>turalis ſeries numeroꝝ incipiēdo a binario in īfe­<lb/>riori linea: et in ſuperiori linea conſtituatur natu­<lb/>ralis ordo numerorū incipiendo a ternario: tunc <lb/>referendo primum inferioris ordinis. </s>
            <s xml:id="N112DD" xml:space="preserve">primo ſu-<lb/>periois: habebis in qua ꝓportione ſe habet reſi-<lb/>duū a prima parte proportiõali ad primã diuidē­<lb/>do corpus prima ſpecie ꝓportionis duple ſuper-<lb/>particularis: et referendo ſecundū inferioris ordi­<lb/>nis ſecundo ſuperioris habebis illud idem in ſe-<lb/>cunda ſpecie ꝓportionis duple ſuperparticula­<lb/>ris. </s>
            <s xml:id="N112EE" xml:space="preserve">et ſic conſequenter vt patet in figura.</s>
          </p>
          <div xml:id="N112F1" level="4" n="3" type="float">
            <note position="right" xlink:href="note-0014-02a" xlink:label="note-0014-02" xml:id="N112F5" xml:space="preserve">Correla-<lb/>rium.</note>
          </div>
          <xhtml:table xml:id="N112FD">
            <xhtml:tr xml:id="N112FE">
              <xhtml:td xml:id="N112FF" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N11301">
            <s xml:id="N11302" xml:space="preserve">Sed ad praxim huiꝰ negocii in ſpeciebus ꝓporti­<lb/>onis triple ſuꝑparticularis cõſtituatur in inferio­<lb/>ri ſerie naturalis ordo numerorū incipiendo a bi­<lb/>nario: et in ſuperiori conſtituãtur oēs numeri īpa­<lb/>res incipiendo a quinario: et tunc referēdo primū <lb/>inferioris ordinis primo ſuperioris: et ſecundū in­<lb/>ferioris ſecūdo ſuperioris: et tertiū inferioris ter-<lb/>tio ſuperioris: et ſic conſequenter. </s>
            <s xml:id="N11313" xml:space="preserve">cõſpicies in qua <lb/>ꝓportione ſe habet reſiduum a prima parte pro­<lb/>portionali ad primã diuiſione corporis facto pro­<lb/>portione tripla ſuperparticulari: vt ptꝫ in figura</s>
          </p>
          <xhtml:table xml:id="N1131C">
            <xhtml:tr xml:id="N1131D">
              <xhtml:td xml:id="N1131E" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N11320">
            <s xml:id="N11321" xml:space="preserve">Ad praticandū autē ita in ſpeciebus quadruple <lb/>ſuꝑparticularis quintuple ſuꝑparticularis .etc̈. / cõ­<lb/>ſtituatur naturalis ſeries numerorū incipiendo a <lb/>binario in linea inferiori: et in ſuperiori oēs nume­<lb/>ros excedentes ſe continuo ternario incipiendo a <lb/>ſeptenario: et ſic habebis quod queris in ſpeciebꝰ <lb/>ꝓportionis quadruple ſuꝑparticularis </s>
            <s xml:id="N11330" xml:space="preserve">Ad quod <lb/>inueniēdū in ſpeciebus ꝓportionis quītuple ſuꝑ­<lb/>particularis cõſtituas in ſuperiori ordine oēs nu­<lb/>meros excedentes ſe quaternario incipiendo a nu­<lb/>mero nouenario: et in ſpecie ſequeuti coſtituas in <lb/>ſuperiori ordine oēs numeros excedentes ſe qui­             <cb chead="Capitulum ſextū."/>             nario incipiendo a numero vndenario: et ſic conſe­<lb/>quenter in aliis ſpeciebus operaberis </s>
            <s xml:id="N11342" xml:space="preserve">Patet hoc <lb/>in figuris ſequentibus.</s>
          </p>
          <xhtml:table xml:id="N11347">
            <xhtml:tr xml:id="N11348">
              <xhtml:td xml:id="N11349" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N1134B">
            <s xml:id="N1134C" xml:space="preserve">¶ Sed ad exercitiū huiꝰ vltimi correlarii in ſpecie­<lb/>bus multipliciū ſuprapartientiū quedã etiaꝫ con-<lb/>ſtituentur figuere. </s>
            <s xml:id="N11353" xml:space="preserve">Unde ac facile īueniendã ꝓpor­<lb/>tionē reſidui a prima parte ꝓportionali ad ipſaꝫ <lb/>primã in ſpeciebus ꝓportionis duple ſupraparti­<lb/>entis cõſtituatur naturalis ſeries incipiēdo a ter­<lb/>nario inferiori linea: in ſuperiori vero cõſtituan-<lb/>tur oēs numeri īpares incipiēdo a quinario: et tūc <lb/>referēdo primū inferioris ordinis primo ſuperio­<lb/>ris: et ſcḋm ſcḋo: et tertiū tertio id quod queris fa-<lb/>cile reperies / vt patet in figura ſequenti.</s>
          </p>
          <xhtml:table xml:id="N11366">
            <xhtml:tr xml:id="N11367">
              <xhtml:td xml:id="N11368" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N1136A">
            <s xml:id="N1136B" xml:space="preserve">¶ Ad īueniendã autē proportionē reſidui a prima <lb/>parte ꝓportionali ad ipſam primã diuiſione cor­<lb/>poris facta ꝓportione tripla ſuprapartiente con­<lb/>ſtituatur ſupra naturalē ſeriē numeroꝝ incipiēdo <lb/>a ternario vna ſeries omnium numerorum conti-<lb/>nuo excedentium ſe ternario incipiendo ab octo-<lb/>nario numero: vt patet in figura.</s>
          </p>
          <xhtml:table xml:id="N1137A">
            <xhtml:tr xml:id="N1137B">
              <xhtml:td xml:id="N1137C" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N1137E">
            <s xml:id="N1137F" xml:space="preserve">¶ Ad īueniendū autē ꝓpoſitū in ſpeciebus ꝓpor-<lb/>tionis quadruple ſuprapartiētis ſupra naturalē <lb/>ſeriē numeroꝝ incipiendo a ternario conſtituatur <lb/>ſeries numeroꝝ ↄ̨tinuo excedentiū ſe quaternario <lb/>incipiendo ab vndeuario: et ſic cõſequenter ſupra <lb/>eandē naturalē ſeriē numeroꝝ incipiendo a terna­<lb/>rio cõſtituatur ſeries numeroꝝ cõtinuo exedentiū <lb/>ſe numero quinario īcipiēdo a numero quarto de­<lb/>cimo: et ſic cõſequenter operaberis in aliis. </s>
            <s xml:id="N11392" xml:space="preserve">Et hec <lb/>de diuiſione corpoꝝ ꝓportione rationali.</s>
          </p>
        </div>
        <div xml:id="N11397" level="3" n="6" type="chapter" type-free="capitulum">
          <head xml:id="N1139C" xml:space="preserve">Capitulū ſextū / ī quo datur modus di­<lb/>uidendi corpus in partes proportiona-<lb/>les proportione irrationali.</head>
          <p xml:id="N113A3">
            <s xml:id="N113A4" xml:space="preserve">QUemadmodū quodlibet cor-<lb/>pus diuidi poteſt ꝓportione rationali <lb/>infinitiſ ſpeciebus eius / vt caput prece­<lb/>dens oſtendit: ita etiã ꝓportione irrationali infi-<lb/>nitiſ ſpeciebus eiꝰ quodlibet corpꝰ diuidi poteſt <lb/></s>
            <s xml:id="N113B0" xml:space="preserve">Pro cuius diuiſionis noticia ſit</s>
          </p>
          <p xml:id="N113B3">
            <s xml:id="N113B4" xml:space="preserve">Prima concluſio </s>
            <s xml:id="N113B7" xml:space="preserve">Quodlibet corpus <lb/>diuiſū aliqua ꝓportione irrationali ſe debet ha­<lb/>bere ad aggregatū ex oībus partibus ꝓportiona­<lb/>bilibus tali ꝓportione ſequētibus primam in ea <lb/>proportione qua totum diuidatur. </s>
            <s xml:id="N113C2" xml:space="preserve">Hec concluſio <lb/>claram et euidentem ex prima precedentis capitis <lb/>demonſtrationem ſortitur.</s>
          </p>
          <p xml:id="N113C9">
            <s xml:id="N113CA" xml:space="preserve">Secunda cõcluſio. </s>
            <s xml:id="N113CD" xml:space="preserve">Ad diuidendum <lb/>corpus infinitis ꝓportionibꝰ irrationabilibꝰ mi­<lb/>noribus dupla: vt puta ꝓportione diametri ad co­<lb/>ſtam: aggregati ex medietate exceſſus quo diame­<lb/>ter excedit coſtã et ipſa coſta ipſammet coſtam:             <pb chead="Prime partis" file="0016" n="16"/>             et ſic cõſequenter / vt capite quarto oſtenſum eſt: de­<lb/>bet ꝓ prima parte capi exceſſus quo maior quan-<lb/>titas excedit minorem ita  reſiduum a prima ſit <lb/>minor quantitas et totum corpus ſit maior quan-<lb/>titas talis proportionis. </s>
            <s xml:id="N113E5" xml:space="preserve">Probatur hec cõcluſio <lb/>ex precedenti / quoniam totū corpus diuiſum pro-<lb/>portiõe aliqua irrationali ſe debet habere ad ag­<lb/>gregatum ex omnibus ſequentibus primam tali <lb/>diuiſione: in ea proportione qua ipſum corpus di­<lb/>uiditur: igitur oportet /  totum corpus ſe habeat <lb/>vt maior quantitas talis proportionis: et aggre-<lb/>gatum ex omnibus ſequentibus primam vt minor <lb/>quantitas: et per conſequens exceſſus / quo totum <lb/>corpus excedit aggregatum ex omnibus ſequen-<lb/>tibus primã erit prima pars proportionalis tali <lb/>proportione. </s>
            <s xml:id="N113FE" xml:space="preserve">Patet conſequentia / quia reſiduum <lb/>eſt aggregatū ex omnibus aliis a prima: ille igit̄̄ <lb/>exceſſus erit prima / quod fuit probandū.             <anchor type="note" xlink:href="note-0016-01" xlink:label="note-0016-01a"/>             </s>
            <s xml:id="N1140A" xml:space="preserve">¶ Ex hac <lb/>concluſione ſequitur primo /  ad diuidendum cor­<lb/>pus proportione irrationali diametri ad coſtam <lb/>oportet / pro prima parte proportionali capere ex­<lb/>ceſſum quo diameter excedit coſtam: et pro ſecūda <lb/>capere etiam exceſſum / quo illa coſta cum eſt dia-<lb/>meter quadrati excedit coſtam illius quadrati / et <lb/>ſic conſequenter: et addandam primã partem pro­<lb/>portionale proportionis irrationalis / que eſt ag-<lb/>gregati ex coſta et medietate exceſſus diametri ad <lb/>ipſam coſtam capiatur pro prima parte propor-<lb/>tionali illa medietas exceſſus: et pro ſecūda parte <lb/>proportiõali capiatur tanta pars reſidui ad quã <lb/>prima habeat illam proportionem / que eſt totius <lb/>corporis ad aggregatum ex omnibus ſequen-<lb/>tibus primam: et iterum in reſiduo a prima parte <lb/>et ſecunda, pro tertia parte capiatur tanta pars <lb/>ad quam ſecunda habeat illam proportionē quã <lb/>prima habet ad ipſam: et ſic cõſequenter. </s>
            <s xml:id="N11431" xml:space="preserve">Et ſimili <lb/>modo operandum eſſet / ſi diuideretur corpus pro­<lb/>portione irrationali / que eſt aggregati ex coſta et <lb/>q̈rta parte, vel octaua, vel decimaſexta exceſſus / q̇ <lb/>diameter excedit coſtã ad ipſã coſtã. </s>
            <s xml:id="N1143C" xml:space="preserve">Ptꝫ correla-<lb/>riū ex cõcluſione addita ſuppoſitiõe ſecunda pre­<lb/>cedētis capitis: ille enim partes infinite continue <lb/>ſe habent in proportione diuiſionis et totum ab-<lb/>ſoluūt.             <anchor type="note" xlink:href="note-0016-02" xlink:label="note-0016-02a"/>             </s>
            <s xml:id="N1144C" xml:space="preserve">¶ Sequitur ſecundo /  diuiſo corpore per <lb/>partes proportionales proportione irrationali / <lb/>que eſt diametri ad coſtam: omnes partes impa-<lb/>res continuo ſe habent in proportione dupla: et <lb/>omnes pares ſimiliter: et oēs due inter quas me-<lb/>diant due ſe habent continuo in proportione ſex-<lb/>quialtera ad duplam: et omnes inter quas mediãt <lb/>tres ſe habent in proportione quadrupla: et ſic cõ­<lb/>ſequenter. </s>
            <s xml:id="N1145F" xml:space="preserve">Probatur / quia proportio que eſt pri-<lb/>me partis proportionalis ad tertiam componi-<lb/>tur ex duabus proportionibus equalibus quarū <lb/>vtra eſt medietas duple: ergo ſequitur /  illa eſt <lb/>dupla. </s>
            <s xml:id="N1146A" xml:space="preserve">Patet conſequentia: et probatur antece-<lb/>dens: quia componitur illa proportio ex propor-<lb/>tione prime partis ad ſecundam que eſt medietas <lb/>duple: et ex proportione ſecunde ad tertiã que etiã <lb/>eſt medietas duple: quoniam proportio diametri <lb/>ad coſtã eſt medietas duple: vt patet ex tertia ſup­<lb/>poſitione tertii capitꝪ. </s>
            <s xml:id="N11479" xml:space="preserve">Et ſic probabis de quibuſ-<lb/>cun duabus partibus paribus īmediatis: et etiã <lb/>īparibus. </s>
            <s xml:id="N11480" xml:space="preserve">Sed iam probo partes inter quas me-<lb/>diant due ſe habere in proportione ſexquialtera <lb/>ad duplam quia proportio inter tales partes cõ-             <cb chead="Capitulum ſextū."/>             ponitur ex proportione prime ad ſecundam: et ſe-<lb/>cunde ad tertiam: et tertie ad quartam: ſed pro-<lb/>portio prime ad tertiam eſt dupla: vt patet ex pro­<lb/>batione precedentis partis: et proportio tertie ad <lb/>quartam eſt proportio que eſt medietas duple: vt <lb/>conſtat: ergo proportio prime ad quartam con-<lb/>tinet duplam et medietateꝫ duple adequate: et per <lb/>conſequēs talis proportio que eſt prime ad quar-<lb/>tam eſt ſexquialtera ad duplam. </s>
            <s xml:id="N1149A" xml:space="preserve">Patet hec conſe­<lb/>quentia ex diffinitione ſexquialtere. </s>
            <s xml:id="N1149F" xml:space="preserve">Et ſic proba-<lb/>bis de aliis huiuſcemodi partibus. </s>
            <s xml:id="N114A4" xml:space="preserve">Sed iam ꝓbo <lb/>tertiam parteꝫ / quia proportio partiū inter quas <lb/>manent tres cuiuſmodi eſt proportio prime par-<lb/>tis ad quintaꝫ cõponitur ex duabus duplis: puta <lb/>ex proportione que eſt prime ad tertiaꝫ et tertie ad <lb/>quintam que ſunt duple: vt patet ex prima parte <lb/>huius correlarii: et per conſequens talis propor-<lb/>tio prime ad quintam eſt dupla ad duplam cū con­<lb/>tineat ipſam duplam bis: et per conſequens qua-<lb/>drupla. </s>
            <s xml:id="N114B9" xml:space="preserve">Patet conſequētia ex diffinitione duple <lb/>et ſecunda parte. </s>
            <s xml:id="N114BE" xml:space="preserve">Et hoc modo probabis de omni­<lb/>bus ſimilibus. </s>
            <s xml:id="N114C3" xml:space="preserve">Patet hoc correlarium ſenſui in fi­<lb/>gura ſequēti / in qua prima pars eſt diameter qua­<lb/>drati maioris ibidem poſiti: et ſecunda eſt coſta <lb/>eiuſdem quadrati: et tertia eſt coſta quadrati ſe-<lb/>quentis: et tertia eſt coſta tertii quadrati: et diame­<lb/>ter quarti: et quarta eſt coſta quarti quadrati: et <lb/>diametri quinti: et quinta eſt coſta ipſius quinti <lb/>quadrati: et ſic in infinitum poteris procedere ibi <lb/>n. conſpicies /  prime ad tertiã eſt proportio du-<lb/>pla et ſecunde ad quartam etiam dupla: et prime <lb/>ad quintam eſt quadrupla.</s>
          </p>
          <div xml:id="N114DA" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0016-01a" xlink:label="note-0016-01" xml:id="N114DE" xml:space="preserve">Primuꝫ <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0016-02a" xlink:label="note-0016-02" xml:id="N114E8" xml:space="preserve">Secūduꝫ <lb/>correlar̄.</note>
          </div>
          <figure xml:id="N114F0">
            <image file="0016-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0016-01"/>
          </figure>
          <note position="right" xml:id="N114F4" xml:space="preserve">Tertium <lb/>correlar̄.</note>
          <p xml:id="N114FA">
            <s xml:id="N114FB" xml:space="preserve">¶ Ex quo ſequitur tertio /  in tali diuiſiõe aggre-<lb/>gatuꝫ ex oībus īparibus a prima īpari eſt equale <lb/>ṗme: et aggregatū ex oībus paribꝰ a ſecunda q̄ eſt <lb/>prima par eſt equale ſecunde: et aggregatum ex <lb/>oībus imparibus ſe habet ad aggregatum ex om­<lb/>nibus paribus in proportione que eſt medietas <lb/>duple. </s>
            <s xml:id="N1150A" xml:space="preserve">Probatur prima pars huius correlarii / <lb/>quia partes impares continuo ſe habent in pro-<lb/>portione dupla / vt patet ex proximo correlario: <lb/>igitur reſiduum ex omnibus īparibus ſequētibus <lb/>primã imparem eſt equale prime impari. </s>
            <s xml:id="N11515" xml:space="preserve">Patet <lb/>conſequentia ex ſecundo correlario tertie conclu-<lb/>ſionis quinti capitis. </s>
            <s xml:id="N1151C" xml:space="preserve">Et eodem modo probabis <lb/>ſecundam partem. </s>
            <s xml:id="N11521" xml:space="preserve">Sed iam probatur tertia / quo-<lb/>niam medietas aggregati ex omnibus impari-<lb/>bus ſe habet ad medietatem aggregati ex omni-<lb/>bus paribus in proportione que eſt medietas du-<lb/>ple: ergo totum aggregatum imparium ſe habet <lb/>ad totum aggregatuꝫ parium in proportione du-<lb/>pla. </s>
            <s xml:id="N11530" xml:space="preserve">Patet conſequentia / per hanc regulam in <lb/>quacun proportione ſe habent partes aliquote <lb/>aliquarum quantitatum eiuſdem denominatio-<lb/>nis in eadem ſe habent et ille quantitates totales / <lb/>et per conſequens in proportione qua ſe habent <lb/>due medietates aliquoꝝ in eadē ſe hñt tota illarū <lb/>medietatū. </s>
            <s xml:id="N1153F" xml:space="preserve">Sed ꝓbat̄̄ añs / q2 prima pars ꝓporti-<lb/>onalis īpar ſe habet ad ṗmã parē: que eſt ſecūda. <lb/></s>
            <s xml:id="N11545" xml:space="preserve"><pb chead="Prime partis" file="0017" n="17"/>             in proportione que eſt medietas duple vt conſtat: <lb/>quia illa eſt proportio diuiſionis: et prima pars <lb/>proportionalis impar eſt medietas totius aggre­<lb/>gati ex omnibus imparibus: et prima par que eſt <lb/>ſecunda eſt medietas aggregati ex omnibus pa-<lb/>ribus: vt patet ex duabus primis partibus corre-<lb/>larii: ergo medietas omnium imparium ſe habet <lb/>ad medietatem omnium parium in proportione <lb/>que eſt medietas duple: quod fuit probandum.</s>
          </p>
          <note position="left" xml:id="N1155C" xml:space="preserve">Quartū <lb/>correlar̄.</note>
          <p xml:id="N11562">
            <s xml:id="N11563" xml:space="preserve">¶ Sequitur quarto /  diuiſo corpore per partes <lb/>proportionales proportione irrationali que eſt <lb/>medietas triple: omnes partes impares talis di-<lb/>uiſionis ſe habent in proportione tripla: et etiam <lb/>omēs pares: et omnes inter quas mediant tres in <lb/>proportione nouocupla: et aggregatum ex omni-<lb/>bus imparibus ſe habet ad aggregatum ex omni­<lb/>bus paribus in proportione que eſt medietas tri-<lb/>ple. </s>
            <s xml:id="N11576" xml:space="preserve">Hoc correlarium cum precedenti ſimilem de-<lb/>monſtrationem admittit.</s>
          </p>
          <p xml:id="N1157B">
            <s xml:id="N1157C" xml:space="preserve">Tertia concluſio: </s>
            <s xml:id="N1157F" xml:space="preserve">Ad diuidendū cor­<lb/>pus in partes proportionales infinitis ſpeciebus <lb/>proportionis irrationalis maioris dupla: vt pu-<lb/>ta proportione que eſt totius diametri ad exceſſū <lb/>quo ipſa diameter excedit coſtam et totius diame­<lb/>tri cum medietate exceſſus quo excedit coſtam vel <lb/>ad quarta in vel ad quintã vel ad ſextã vt ſuperiꝰ <lb/>dictum eſt: pro prima parte proportionali capi-<lb/>endus eſt exceſſus quo quãtitas maior excedit mi­<lb/>norem in tali proportione: et quãtitas miuor pro <lb/>reſiduo vt ſi velis partiri corpꝰ in partes propor­<lb/>tionales proportione que eſt totius diametri ad <lb/>exceſſum quo diameter excedit coſtam: capienda <lb/>eſt coſta quadrati cuius illud corpus diuidendum <lb/>eſt diameter pro prima parte proportionali: et ſic <lb/>pro reſiduis maneat exceſſus que eſt quãtitas mi-<lb/>nor talis proportionis: et pro ſecunda capien-<lb/>da eſt coſta quadrati cuius totum aggregatum ex <lb/>omnibus ſequentibus primam eſt diameter: et ad­<lb/>dandam tertiam capiatur coſta quadrati cuius <lb/>eſt diameter aggregatum ex omnibus ſequenti-<lb/>bus primam et ſecundam. </s>
            <s xml:id="N115AC" xml:space="preserve">Et ad diuidendum ali-<lb/>quod corpus proportione que eſt totius diametri <lb/>ad medietatē exceſſus quo excedit coſtaꝫ, pro pri-<lb/>ma parte ꝓportionali capiendus eſt exceſſus quo <lb/>maior quantitas excedit minorem tali proporti-<lb/>one. </s>
            <s xml:id="N115B9" xml:space="preserve">Conſtituendum .n. eſt totum corpus diameter <lb/>alicuius quadrati / et tunc pro prima parte propor­<lb/>tionali capienda eſt tanta pars illius corporis  <lb/>pro omnibus ſequentibus non maneat niſi medie­<lb/>tas exceſſus quo tale corpus exiſtens diameter ex­<lb/>cedit coſtam eiuſdem quadrati: et addandam ſe-<lb/>cundam partem proportionalem conſtituatur to­<lb/>tum / quod ſequitur primã diameter alicuius qua-<lb/>drati: et pro ſecūda parte capiatur tantum /  pro <lb/>ſequentibus non maneat niſi medietas exceſſus <lb/>quo talis diameter excedit ſuam coſtam / et ſic con­<lb/>ſequenter. </s>
            <s xml:id="N115D2" xml:space="preserve">Patet hec concluſio eo modo quo ſe-<lb/>cūda huius capitis. </s>
            <s xml:id="N115D7" xml:space="preserve">Hic poteris multa correlaria <lb/>inferre ſed iam ad ea inferenda ex predictis faci-<lb/>lem haberes aditum. </s>
            <s xml:id="N115DE" xml:space="preserve">Et hec de proportione irra-<lb/>tionali: et de diuiſione corporum eadem irratio-<lb/>nali proportione: de qua non eſt facile cum rotio-<lb/>ne loqui.</s>
          </p>
        </div>
        <div xml:id="N115E7" level="3" n="7" type="chapter" type-free="capitulum">
          <head xml:id="N115EC" xml:space="preserve">Capitulum ſeptimum / in quo agi­<lb/>tur de proportione ordinum par-           <cb chead="Capitulū ſeptimū."/>           tium proportionalium interſcala-<lb/>riter ſe habentium.</head>
          <p xml:id="N115F6">
            <s xml:id="N115F7" xml:space="preserve">OCcurrit nonnūquam in mate-<lb/>teria de motu locali quo ad effectū et mo-<lb/>tu augmentationis comparatio alicuius <lb/>ordinis aliquarum partium proportionalium in­<lb/>terſcalariter ſe habentiū ad alium ordinem par-<lb/>tium proportionalium: vt cum volumus compara­<lb/>re totum ordinem partium imparium toti ordini <lb/>partium parium: vt iam ex parte tangebatur in <lb/>precedēti capite: ideo non abs re pro noticia huiꝰ <lb/>pono aliquas concluſiones.</s>
          </p>
          <p xml:id="N1160C">
            <s xml:id="N1160D" xml:space="preserve">Prima cõcluſio. </s>
            <s xml:id="N11610" xml:space="preserve">Diuiſo corpore per <lb/>partes proportionales quauis proportione: et ca­<lb/>ptis certis ordinibus partium proportionalium <lb/>interſcalariter ſe habentium: totum corpus ab-<lb/>ſoluentibus: tunc illi ordines ſe habent continuo <lb/>in proportione diuiſionis: vt ſi corpus diuidatur <lb/>proportione dupla: et capiantur oēs partes inter <lb/>quas mediant due pro primo ordine puta prima <lb/>quarta, ſeptima, decima, tridecima .etc̈ / et deinde <lb/>pro ſecundo ordine ſecunda, quinta, octaua, vn-<lb/>decima, decima quarta, et ſic cõſequenter. </s>
            <s xml:id="N11627" xml:space="preserve">et demū <lb/>pro tertio ordine capiantur tertia, ſexta, nona, <lb/>duodecima, quindecima, et ſic deinceps. </s>
            <s xml:id="N1162E" xml:space="preserve">Dico /  <lb/>primus ordo ſe habet ad ſecundū in ꝓportiõe du-<lb/>pla: et etiam ſecundus ad tertium in proportione <lb/>dupla. </s>
            <s xml:id="N11637" xml:space="preserve">Et eſto /  centum ordines caperes illi etiaꝫ <lb/>in proportione dupla continuo ſe haberent. </s>
            <s xml:id="N1163C" xml:space="preserve">Pa-<lb/>tet hoc / quoniam cuiuſlibet illorum ordinum con-<lb/>tinuo partes correſpõdentes ſe habent in eadem <lb/>proportione: igitur in quacū proportione ſe ha­<lb/>bent continuo prime partes illorum ordinum in <lb/>eadem proportione continuo ſe habent ille ordi-<lb/>nes: ſed prime partes ſe habent in proportione di­<lb/>uiſionis / vt conſtat: igitur et illi ordines. </s>
            <s xml:id="N1164D" xml:space="preserve">Proba-<lb/>tur tamen cõſequētia per hanc regulam. </s>
            <s xml:id="N11652" xml:space="preserve">Quado-<lb/>cū aliqua diuiduntur equali ꝓportione in qua-<lb/>cū proportione ſe habent prime partes propor­<lb/>tionales in eadem proportione ſe habent et ipſa <lb/>tota: quoniam ſunt partes aliquote eiuſdē deno-<lb/>minationis. </s>
            <s xml:id="N1165F" xml:space="preserve">Modo in quacū proportione ſe ha­<lb/>bent partes aliquote eiuſdem denominationis in <lb/>eadem ſe habent et ipſa tota quorum ſunt partes <lb/>aliquote / vt poſtea demonſtrabitur igitur.</s>
          </p>
          <p xml:id="N11668">
            <s xml:id="N11669" xml:space="preserve">Secunda concluſio per modum do-<lb/>cumenti poſita. </s>
            <s xml:id="N1166E" xml:space="preserve">Ad ſciendū quota pars vel quote <lb/>partes aliquote eſt quilibet illorum ordinum vi-<lb/>dendum eſt quot ſint ordines: et tunc cõſtituantur <lb/>in numeris tot proportiões diuiſionis quot ſunt <lb/>illi ordinis dempta vna: et coadunētur omnes ter­<lb/>mini illarum proportionum: et diuidatur totū in <lb/>tot partes aliquotas quotꝰ eſt numerus reſultãs <lb/>et dentur primo ordini tot ex illis partibas qnotꝰ <lb/>eſt maximus numerus in illis proportionibus: et <lb/>ſecundo ordini tot quotus eſt ſecundus numerus: <lb/>et ſic conſequenter. </s>
            <s xml:id="N11685" xml:space="preserve">Et ſic videbis quot partes ali-<lb/>quotas et cuiꝰ denominationis continet primꝰ or­<lb/>do: et ſecundus, et tertius, et ſic conſequenter. </s>
            <s xml:id="N1168C" xml:space="preserve">Exē-<lb/>plum / vt ſi pedale fuerit diuiſum in partes propor­<lb/>tionales proportione dupla conſtituantur tres <lb/>ordines / vt paulo ãte exēplo expreſſimꝰ / q2 ibi tres <lb/>ſunt ordines conſtituti: et proportio diuiſionis eſt <lb/>dupla: conſtituas in numeris duas proportiones             <pb chead="Prime partis" file="0018" n="18"/>             duplas: puta quattuor ad duo: et duo ad vnum: <lb/>tunc coacerua illos numeros puta quaternarium <lb/>binarum et vnitatem et inuenies .7. </s>
            <s xml:id="N116A2" xml:space="preserve">Diuidas igi-<lb/>tur corpus in ſeptem ſeptimas: et pro primo ordi­<lb/>ne capias quattuor ſeptimas: et pro ſecundo du-<lb/>as ſeptimas: et pro vltimo vnam ſeptimam: et ſic <lb/>comperies quot partes aliquotas continet quili-<lb/>bet illorum ordinū. </s>
            <s xml:id="N116AF" xml:space="preserve">Et iſto modo in qualibet pro­<lb/>portione operaberis facile autem hoc demonſtra­<lb/>tur ex prima concluſione quoniam ſicut illi tres <lb/>ordines cõtinuo ſe habent in proportione dupla <lb/>et ſunt partes illius corporis: ita oprtet capere ꝑ­<lb/>tes continuo ſe habentes in proportiõe dupla to­<lb/>tum corpus abſoluētes eo  oꝑati ſumꝰ artificio</s>
          </p>
          <p xml:id="N116BE">
            <s xml:id="N116BF" xml:space="preserve">Tertia concluſio. </s>
            <s xml:id="N116C2" xml:space="preserve">Alicuius cõtinui <lb/>partes aliquota proportionem aliquam rationa­<lb/>lem acquirente: proportionē acquiſitam toti inue­<lb/>nire. </s>
            <s xml:id="N116CB" xml:space="preserve">vt diuiſio corpore in quin partes aliquo-<lb/>tas putas in .5. quintas vna illarum quintarum <lb/>acquirente proportionem duplam: inuenire quan­<lb/>tam proportionem totum illud corpus proportio­<lb/>nē acquirat. </s>
            <s xml:id="N116D6" xml:space="preserve">In illo em̄ caſu illud corpus propor-<lb/>tionem ſexquiquintam acquirit: cum acquirat ſu­<lb/>pra ſe vnã quintam: hoc eſt tantuꝫ quanta eſt vna <lb/>eius quinta. </s>
            <s xml:id="N116DF" xml:space="preserve">Probaemtur hec concluſio / et diuidatur / <lb/>a pedale in aliquot partes aliquotas gratia exē-<lb/>pli in .7. / et acquirat vna illarum aliquam propor­<lb/>tionem rationalem: tunc vel illa proportio acqui­<lb/>ſita alicui illarum partium eſt multiplex vel non <lb/>multiplex: ſi multiplex tunc aliquotiens vel ſemel <lb/>acquirit ſupra ſe tantum quanta ipſa pars eſt. </s>
            <s xml:id="N116EE" xml:space="preserve">et <lb/>tot partes equales ſibi quot acquirit ſupra ſe tot <lb/>acq̇rit ſupra oēs illas .7. partes aliquotas ī quas <lb/>corpus erat diuiſum: et quelibet talis pars acqui­<lb/>ſita illi parti eſt equalis cuilibet illarum partium <lb/>aliquotarū in quas corpus eſt diuiſum: igitur ille <lb/>partes acquiſite vel pars acquiſita eſt vel ſūt eiuſ­<lb/>dem denominationis cū parte cui acquiruntur vĺ <lb/>acquiritur: et ita ſi ille partes ī quas corpus diui­<lb/>debatur ſunt ſeptime: et ille partes acquiſite ſunt <lb/>due vel tres vel quattuor / et ſic cõſequenter: totum <lb/>illud corpus acquiſiuit duas vel tres vel quatuor <lb/>ſeptimas vel ſi eſt vna totum illud corpus acqui-<lb/>ſiuit vnam ſeptimam: quo ad inuento: iam patet <lb/>quãtam proportionē illud corpus acquiſiuit. </s>
            <s xml:id="N1170D" xml:space="preserve">Si <lb/>em̄ acquiſiuit tres tales partes et ille ſūt ſeptime <lb/>iam acquiſiuit totum proportionem ſupratripar­<lb/>tientem ſeptimas / et ſic habetur propoſitum vbi <lb/>pars aliquota proportionem multiplicē acquirit <lb/></s>
            <s xml:id="N11719" xml:space="preserve">Si autem acquirit rationalem nõ multiplicē ma-<lb/>nifeſtum eſt /  illa denominatur ab aliqua parte <lb/>aliquota vel ab aliquibꝰ partibꝰ aliquotis ade-<lb/>quate vel inadequate (non eſt modo cura) ſicut du­<lb/>pla ſexquitertia denominatur a numero binario <lb/>cum tertia: et ſuprabipartiens tertias ab vnitate <lb/>cum duabus tertiis. </s>
            <s xml:id="N11728" xml:space="preserve">Dato igitur /  aliquam talē <lb/>proportionem rationalem non multiplicē aliqua <lb/>talium partium aliquotarum acquiſiuerit: ad in-<lb/>uendiendum quam proportionem acquirit totum <lb/>diuidatur quelibet pars aliquota in partes ali-<lb/>quotas a quibus denominatur talis proportio / et <lb/>tunc coaceruentur omnes ille partes aliquote: et <lb/>numerus reſultans indicabit quota pars aliquo­<lb/>ta totius eſt aliqua īmo quelibet illarum. </s>
            <s xml:id="N1173B" xml:space="preserve">deinde <lb/>illis omnibus addantur ille partes aliquote ac-<lb/>quiſite equales eis. </s>
            <s xml:id="N11742" xml:space="preserve">et ſic inuenies quot partes ali­             <cb chead="Capitulum octauū."/>             quotas acquiſiuit totum: et per conſequens qua-<lb/>lem proportionem vt ſi in exemplo poſito vna il-<lb/>larum ſeptimarum acquirat proportionē ſupra­<lb/>bipartientem tertias: et quoniam illa proportio <lb/>denominatur ab vno cum duabus tertiis diuida­<lb/>tur quelibet ſeptima in tres tertias: et multipliciē­<lb/>tur .7. per tria / et reſultabunt .12. et iam ille nume-<lb/>rus indicat tibi quamlibet illarum partium eſſe <lb/>vnam viceſimam primam: et partes acquiſite ſunt <lb/>equales illis quia ſunt tertie vnius ſeptime: et ſūt <lb/>due. </s>
            <s xml:id="N1175C" xml:space="preserve">ergo acquiſiuit duas viceſimas primas et ſic <lb/>ꝓportionē ſuprabipartiētē viceſimas ṗmas totū <lb/>acq̇ſiuit. </s>
            <s xml:id="N11763" xml:space="preserve">Si autē vna illarum ſeptimarū acquirat <lb/>duplam ſexquitertiam: diuidas quamlibet ſepti­<lb/>mam etiam in tertias: et multiplica ſeptē per tria <lb/>et reperies / vt dictum eſt viginti vnum / et quia vna <lb/>ſeptima acquiſiuit tantum quanta ipſa eſt puta <lb/>vnam ſeptimam totius cuꝫ vna tertia illius ſepti­<lb/>me: diuidas etiam illam ſeptimam acquiſitam in <lb/>tres partes: et ille tres partes erunt tres viceſime <lb/>prime totius / vt conſtat: et totum acquiſiuit illas <lb/>tres et cum hoc vnam. </s>
            <s xml:id="N11778" xml:space="preserve">Acquiſiuit igitur quattuor <lb/>viceſimas primas: et per conſequens proportionē <lb/>ſupraquadripartiētem viceſimas primas. </s>
            <s xml:id="N1177F" xml:space="preserve">Et iſto <lb/>modo in omni alia ſpecie proportionis operabe­<lb/>ris. </s>
            <s xml:id="N11786" xml:space="preserve">Et ex hoc poteris inuenire proportionem quã <lb/>acquirit totum duabus partibus eius aliquotis <lb/>nequalibus: ſiue duabus non facientibus vnam: <lb/>ſiue pluribus acquirentibus equalem proportio­<lb/>nem vel etiam inequalem. </s>
            <s xml:id="N11791" xml:space="preserve">Et conſimiliter cogno­<lb/>ſces quam proportionem deperdit totum aliqua <lb/>parte eius vel aliquibus partibus aliquotis oli-<lb/>quam vel aliquas proportiēes deperdente vel de­<lb/>perdentibus.</s>
          </p>
        </div>
        <div xml:id="N1179C" level="3" n="8" type="chapter" type-free="capitulum">
          <head xml:id="N117A1" xml:space="preserve">Capitulum octauum / in quo agi-<lb/>tur de inuentione proportionis mi-<lb/>noris inequalitatis et etiam maio-<lb/>ris reſpectu cuiuſcū numeri ex re-<lb/>bus diuiſibilibus compoſiti.</head>
          <p xml:id="N117AC">
            <s xml:id="N117AD" xml:space="preserve">PLerum contingit tam in <lb/>materia nitenionis difformis quã ꝓ­<lb/>portiõis motuum querere proportio­<lb/>nem ſubſequialteram vel ſubduplam vel aliquã-<lb/>aliam minoris inequalitatis vel etiam maioris <lb/>inequalitatis reſpectu numeri non habentis illaꝫ <lb/>ſine fratione id eſt diuiſione vnitatis vel vnitatū <lb/>talis numeri. </s>
            <s xml:id="N117BE" xml:space="preserve">vt ſi ponat̄̄ /  aliquod mobile per-<lb/>tranſeat tripedale ſpacium in hora / tunc mouēs <lb/>ſubdupla velocitate tranſit ſubduplum ſpacium <lb/>ad tripedale in eodem tēpore. </s>
            <s xml:id="N117C7" xml:space="preserve">Modo non eſt poſ-<lb/>ſibile dare ſubduplum ad tripedale ſine fractiõe <lb/>vnitatis: quoniam bipedale cum dimidio eſt ſub-<lb/>duplum tripedalis. </s>
            <s xml:id="N117D0" xml:space="preserve">Item contingit non nunquaꝫ <lb/>querere ſexquialterum reſpectu numeri quinarii: <lb/>et illud non poteſt dari ſine fractione vnitatis .7. <lb/>enim cum dimidio ad .5. eſt proportio ſexquialte-<lb/>ra. </s>
            <s xml:id="N117DB" xml:space="preserve">Quare pro inuentione talis proportionis ma­<lb/>ioris aut minoris inequalitatis cum fractione.</s>
          </p>
          <p xml:id="N117E0">
            <s xml:id="N117E1" xml:space="preserve">Suppono primo /  duplex eſt nume­<lb/>rus vt ad propoſitum ſufficit quidaꝫ eſt compoſi-<lb/>tus ex vnitatibꝰ diuiſibilibꝰ .i. cuius quelibet vni­<lb/>tas eſt res diuiſibilis: vt numerus trium pedaliū <lb/>quattuor qualitatū .etc̈. alius vero numerus eſt cõ­             <pb chead="Prime partis" file="0019" n="19"/>             poſitus ex vnitatibus indiuiſibilibus vt numerus <lb/>5. punctorū .5. intelligentiarum et .10. animarū ra­<lb/>tionalium. </s>
            <s xml:id="N117F5" xml:space="preserve">Hec ſuppoſitio ex ſe patet.</s>
          </p>
          <p xml:id="N117F8">
            <s xml:id="N117F9" xml:space="preserve">Secunda ſuppoſitio. </s>
            <s xml:id="N117FC" xml:space="preserve">Nõ oīs nume­<lb/>rus habet ſubduplū. </s>
            <s xml:id="N11801" xml:space="preserve">nec oīs habet ſubtriplum: et <lb/>ſic conſequenter. </s>
            <s xml:id="N11806" xml:space="preserve">Probatur / quoniã aliquis nume­<lb/>rus puta rerum indiuiſibiliū cuiuſmodi: eſt nūerꝰ <lb/>ternarius angelorū nõ poteſt diuidi in duo equa-<lb/>lia: igitur nõ habet ſubduplū: nec in quatuor par­<lb/>tes equales: et ſic non habet ſubquadruplum: et ſic <lb/>probatur de aliis / igitur ſuppoſitio vera.</s>
          </p>
          <p xml:id="N11813">
            <s xml:id="N11814" xml:space="preserve">Tertia ſuppoſitio </s>
            <s xml:id="N11817" xml:space="preserve">Oīs numerus re­<lb/>rum diuiſibiliū habet ſubduplū ſubtriplū: et vni-<lb/>uerſaliter oēm proportioneꝫ minoris inequalita-<lb/>tis: et etiaꝫ maioris aut habere poteſt. </s>
            <s xml:id="N11820" xml:space="preserve">Probatio <lb/>huius ſuppoſitionis: quia talis numerus poteſt <lb/>diuidi in duo equalia cū ſit numerus rerū diuiſi-<lb/>bilium et tria equalia et in .4. et in 5. / et ſic in infini-<lb/>tum </s>
            <s xml:id="N1182B" xml:space="preserve">Quare dabitur quilibet numerus habēs pro­<lb/>portionē minoris inequalitatis ad ipſum: et etiaꝫ <lb/>maioris. </s>
            <s xml:id="N11832" xml:space="preserve">Nam ad ſui medietatē habebit propor­<lb/>tionem duplã: ad tertiam triplã: ad duas tertias <lb/>ſexquialteram: et ſic in infinitum.</s>
          </p>
          <p xml:id="N11839">
            <s xml:id="N1183A" xml:space="preserve">Quarta ſuppoſitio </s>
            <s xml:id="N1183D" xml:space="preserve">Ad diuidendum <lb/>numerū aliquem per alterum ſiue maiorē, ſiue mi­<lb/>norem, ſiue equalem, ſiue oporteat vti fractione, <lb/>ſiue nõ: diuidenda eſt quelibet vnitas numeri diui­<lb/>dendi in tot partes aliquotas quotus eſt numerꝰ <lb/>per quem fit diuiſio: et dande ſunt tot partes illa­<lb/>rum cuilibet vnitati numeri ꝑ quē fit diuiſio quo-<lb/>tus eſt numerus diuidendus: et ſic quelibet vnitas <lb/>habebit equaliter. </s>
            <s xml:id="N11850" xml:space="preserve">Exemplū / vt ſi velis diuidere nu­<lb/>merū quinariū per numeꝝ ternariū: vt puta quī <lb/>gradus in tres partes equales: vel quin denari­<lb/>os per tres homines: diuidas quãlibet vnitatem <lb/>numeri quinarii ī tres partes aliquotas: puta in <lb/>tres tertias quia numerus per quem fit diuiſio eſt <lb/>ternarius: deinde da quin tertias culibet vnita­<lb/>ti ternarii: quia numerus diuidēdus eſt quinariꝰ <lb/></s>
            <s xml:id="N11862" xml:space="preserve">Item ſi velis diuidere tria per quin: q2 numerus <lb/>per quē fit diuiſio eſt quinarius: diuidas quãlibet <lb/>vnitatē numeri ternarii diuidēdi in quī partes <lb/>equales. </s>
            <s xml:id="N1186B" xml:space="preserve">puta in quī quītas et q2 numerus diui-<lb/>dendus eſt ternarius: da cuilibet tres quintas: et <lb/>quilibet illorū quī habebit equaliter. </s>
            <s xml:id="N11872" xml:space="preserve">Probat̄̄ <lb/>hec ſuppoſitio / qm̄ ſic diuendo cuilibet equaliter <lb/>datur / vt patet ex ſe et nichil manet: ergo illa diui­<lb/>ſio eſt cõpleta: et modus diuidendi ſufficiens: et per <lb/>cõſequens ſuppoſitio vera. </s>
            <s xml:id="N1187D" xml:space="preserve">Probatur minor / qm̄ <lb/>quando tria diuiditur per quin gratia exempli <lb/>oportet iuxta tenorē ſuppoſitionis diuidere quã­<lb/>libet vnitatē numeri ternarii in quī partes equa­<lb/>les. </s>
            <s xml:id="N11888" xml:space="preserve">et ſic erunt partes ille, ter, quin: et per conſe­<lb/>quēs quīquies tres partes adequate / vt patꝫ: erūt <lb/>igitur ibi quī ternarii illarū partiū adequate et <lb/>datur cuilibet vnitati quinarii numeri vnꝰ terna­<lb/>rius: igitur nullus ternarius manet / qm̄ illi terna­<lb/>rii et vnitates numeri quinarii ſunt numero equa­<lb/>les: igitur tunc nichil manet diuidendū. </s>
            <s xml:id="N11897" xml:space="preserve">Et ſic pro­<lb/>babis de quibuſcū aliis numeris quorum vnus <lb/>per alterum diuiditur: ſequitur igitur ſuppoſitio</s>
          </p>
          <p xml:id="N1189E">
            <s xml:id="N1189F" xml:space="preserve">His ſuppoſitis pono talem regulam <lb/></s>
            <s xml:id="N118A3" xml:space="preserve">Ad diuidendum numerum ſe habentem in qua vo­             <cb chead="Capitulum octauū."/>             lueris proportione minoris inequalitatis ad quē­<lb/>cū numerum volueris capias in numeris duos <lb/>numeros ſe habentes in tali proportione: et diui-<lb/>das numerum reſpectu cuiꝰ queris numerū ſe ha-<lb/>bentem in proportione minoris inequalitatis in <lb/>tot partes equales quotus eſt numerus maior ta­<lb/>lis proportionis: et ex his capias tot illarū par­<lb/>tium quotus eſt numerus minor dicte proportio-<lb/>nis. </s>
            <s xml:id="N118B9" xml:space="preserve">Et ſic inuenies propoſitum. </s>
            <s xml:id="N118BC" xml:space="preserve">Hoc facili mõſtra­<lb/>tur exemplo: vt ſi vis inuenire numerū ſe habentē <lb/>in proportione ſubſexquitertia reſpectu numeri <lb/>quinarii in rebus diuiſibilibus (quoniã in indiui­<lb/>ſibilibus nõ eſt poſſibile / vt patet ex primis duabꝰ <lb/>ſuppoſitionibus) capias in nūeris .4. et .3. qui ſūt <lb/>numeri ſe habentes in proporſitione ſexquitertia <lb/>et numerus maior eſt quaternariꝰ: diuidas nume-<lb/>rum quinariū reſpectu cuius queris ſubſexquiter­<lb/>tium numerum in quattuor partes equales: et hãc <lb/>diuiſionem facies per quarte ſuppoſionis docu­<lb/>mentū: et q2 nūerus mīor eſt ternariꝰ capias tres <lb/>quartas quinarii: et illarum trium quartarū ad <lb/>illum numerum quinarium qui componitur ade-<lb/>quate ex quattuor talibꝰ eſt proportio ſubſexqui­<lb/>tertia. </s>
            <s xml:id="N118DD" xml:space="preserve">Et iſto modo in omībus aliis operaberis <lb/></s>
            <s xml:id="N118E1" xml:space="preserve">Patet hec regula quoniã / tunc talis numerus ſe <lb/>habebit ad illas ſuas partes aliquotas ſicut ſe <lb/>habent nūeri proportionis queſite / vt conſtat: igit̄̄ <lb/>illo modo oportet operari ad inueniēdū id quod <lb/>docet regula: et per cõſequens regula vera.</s>
          </p>
          <p xml:id="N118EC">
            <s xml:id="N118ED" xml:space="preserve">Secunda regula. </s>
            <s xml:id="N118F0" xml:space="preserve">Ad inueniendum <lb/>numerū ſe habentem in proportione maioris ine­<lb/>qualitatis ad quem volueris numerū: et in quacū­<lb/> libuerit proportione: capias in numeris duos <lb/>numeros ſe habentes in tali proportione: et diui­<lb/>das numerū reſpectu cuius queris numerū ſe ha-<lb/>bentē in illa proportione maioris inequalitatis <lb/>in tot partes equales quotus eſt numerus minor <lb/>talis proportionis: et tunc illi numero minori ſic <lb/>diuiſio addas tot equales partes partibus diui­<lb/>ſionis quot ſunt per quas numerus maior talis <lb/>proportionis excedit minorē. </s>
            <s xml:id="N11909" xml:space="preserve">et tunc numerus re-<lb/>ſultans ex nnmero minori et illa additione eſt nu­<lb/>merus ſe habens ad numerū ſic diuiſuꝫ in prppor­<lb/>tione data maioris inequalitatis. </s>
            <s xml:id="N11912" xml:space="preserve">Hoc facile de-<lb/>clarabit exemplū </s>
            <s xml:id="N11917" xml:space="preserve">Si em̄ velis īuenire numeꝝ ſex­<lb/>quialterū ad numerū quinariū in rebus diuiſibi-<lb/>libus (in īdiuiſibilibus em̄ id nequit fieri / vt dictū <lb/>eſt) capias in numeris duos numeros ſe habētes <lb/>in proportione ſexquialtera: vt puta .2. et .3: et q2 <lb/>numerus minor eſt binarius diuidas numeꝝ qui­<lb/>narium reſpectu cuius queris numerum ſexquial­<lb/>terum in duas partes equales quod fiet ſecūdum <lb/>documentum quarte ſuppoſitionis. </s>
            <s xml:id="N1192A" xml:space="preserve">Oportt em̄ <lb/>tunc diuidere .5. per .2. et quia ternarius numerus <lb/>maior talis proportionis excedit numerum bina­<lb/>rium minorem numerum talis proportionis per <lb/>vnam vnitatem adequate: addas ſupra numeruꝫ <lb/>quinariū vnam de illis partibus duabus in quas <lb/>iam diuiſus eſt quinarius puta medietateꝫ ipſius <lb/>quinarii: tūc aggregatum ex quinario et illa par­<lb/>te ſe habet ad quinarium in proportione data pu­<lb/>ta ſexquialtera. </s>
            <s xml:id="N1193F" xml:space="preserve">Patet hec regula ſicut ſuperior <lb/></s>
            <s xml:id="N11943" xml:space="preserve">Applica probationem. </s>
            <s xml:id="N11946" xml:space="preserve">Et hec breuiter de prima <lb/>parte huius operis introductionis gratia dicta <lb/>ſufficiant.</s>
          </p>
        </div>
      </div>
      <div xml:id="N1194D" level="2" n="2" type="other" type-free="pars">
        <pb chead="Secunde partis" file="0020" n="20"/>
        <p xml:id="N11956">
          <s xml:id="N11957" xml:space="preserve">¶ Sequitur ſecunda pars de pro-<lb/>portionalitatibus et de quibuſdam <lb/>proportionum et proportionalita­<lb/>tum proprietatibus et accidentiis.</s>
        </p>
        <div xml:id="N11960" level="3" n="1" type="chapter" type-free="capitulum">
          <head xml:id="N11965" xml:space="preserve">Capitulum primum in quo a: <lb/>gitur de diffinitione et diuiſione <lb/>proportionalitatum.</head>
          <note position="left" xml:id="N1196C" xml:space="preserve">Nicho-<lb/>machus.</note>
          <p xml:id="N11972">
            <s xml:id="N11973" xml:space="preserve">pRoportionalitas iux­<lb/>ta nichomachi ſententiam <lb/>plurimum ad aſtrologiam <lb/>muſicam, veterum lectio-<lb/>nes intelligendas confert. <lb/></s>
            <s xml:id="N1197F" xml:space="preserve">Sed profecto ad phiſicam <lb/>phiſicaſ calculatões nõ mi­<lb/>nꝰ cõducit </s>
            <s xml:id="N11986" xml:space="preserve">Ad cuiꝰ ītelligēti­<lb/>am aduertēdū eſt differētiã eſſe inter ꝓportionē et <lb/>ꝓportionalitatē.             <anchor type="note" xlink:href="note-0020-01" xlink:label="note-0020-01a"/>             </s>
            <s xml:id="N11992" xml:space="preserve">¶ Proportio em̄ / vt dictum eſt <lb/>habitudo eſt duarū quantitatū ad inuicē cõpara-<lb/>tarū. </s>
            <s xml:id="N11999" xml:space="preserve">De qua ſuperius dictū eſt.             <anchor type="note" xlink:href="note-0020-02" xlink:label="note-0020-02a"/>             </s>
            <s xml:id="N119A1" xml:space="preserve">¶ Sed ꝓportiõa­<lb/>litas eſt duarū ꝓportionū vel pluriū vnius ad al­<lb/>teram certa habitudo. </s>
            <s xml:id="N119A8" xml:space="preserve">Ita vt ꝓportio: habitudo <lb/>ſit numerorū ſiue quantitatū: ꝓportionalitas ve­<lb/>ro proportionū collatio exiſtat. </s>
            <s xml:id="N119AF" xml:space="preserve">Sicut em̄ numeri <lb/>ad inuicē cõparãtur in maioritate et in minoritate <lb/>ita ꝓportiones ad inuiceꝫ in maioritate et minori­<lb/>tate referūtur. </s>
            <s xml:id="N119B8" xml:space="preserve">¶ Naſcitur hinc oēm ꝓportionali­<lb/>tatem ꝓportionē eſſe: quãuis nõ omīs ꝓportio ꝓ-<lb/>portionalitas exiſtat.             <anchor type="note" xlink:href="note-0020-03" xlink:label="note-0020-03a"/>             </s>
            <s xml:id="N119C4" xml:space="preserve">Patet hoc correlariū ex ſe <lb/></s>
            <s xml:id="N119C8" xml:space="preserve">Nam ꝓportio, aut genus, aut loco generis ſe ha-<lb/>bet cū huic termino ꝓportionalitas comparatur <lb/></s>
            <s xml:id="N119CE" xml:space="preserve">Et aduerte /  in ꝓpoſito idem eſt medietas equa-<lb/>litas et ꝓportionalitas: et eodē modo diffiniūtur. <lb/>             <anchor type="note" xlink:href="note-0020-04" xlink:label="note-0020-04a"/>             </s>
            <s xml:id="N119DA" xml:space="preserve">Medietas em̄ eſt duarum vel pluriū ꝓportionum <lb/>vnius ad alterã certa habitudo: vt habitudo que <lb/>eſt inter ꝓportionē duplã et quadrupã.             <anchor type="note" xlink:href="note-0020-05" xlink:label="note-0020-05a"/>             </s>
            <s xml:id="N119E6" xml:space="preserve">¶ Poſita <lb/>diffintione ꝓportionalitatis ponēda eſt diuiſio. <lb/>             <anchor type="note" xlink:href="note-0020-06" xlink:label="note-0020-06a"/>             </s>
            <s xml:id="N119F2" xml:space="preserve">Apud recentiores mathematicos vndecim ſunt <lb/>ꝓportionalitates ſiue medietates: quarū vltima <lb/>perfectiſſima eſt: qm̄ in ea oēs conſonãtie muſica­<lb/>les ſimplices reperiūtur. </s>
            <s xml:id="N119FB" xml:space="preserve">Sed apud ãtiquos tres <lb/>ꝓportionalitates famate reperiūtur: videlicet a-<lb/>rithmetica, geometrica, et muſica ſiue harmonica <lb/>             <anchor type="note" xlink:href="note-0020-07" xlink:label="note-0020-07a"/>             </s>
            <s xml:id="N11A09" xml:space="preserve">¶ Unde ꝓportionalitas arithmetica eſt quando <lb/>diſpoſitis tribus quattuor vel pluribus terminis <lb/>inter eos eedem differētie: ſed nõ eedem ꝓportio-<lb/>nes reperiūtur. </s>
            <s xml:id="N11A12" xml:space="preserve">Exemplū / vt diſpoſitis his tribus <lb/>terminis ſine numeris .1.3.5. inter quos nõ eadem <lb/>ꝓportio reperitur: ſed bene eadē differētia. </s>
            <s xml:id="N11A19" xml:space="preserve">Uniꝰ <lb/>em̄ ad .3. eſt ꝓpotio ſubtripla: et triū ad .5. eſt pro-<lb/>portio ſubſuꝑbipartiēs tertias. </s>
            <s xml:id="N11A20" xml:space="preserve">Modo ille pro-<lb/>portiones nõ ſunt ſimiles. </s>
            <s xml:id="N11A25" xml:space="preserve">Differentia tamen. </s>
            <s xml:id="N11A28" xml:space="preserve">i ex­<lb/>ceſſus quo ſecūdus numerꝰ excedit primū eſt equa­<lb/>lis differentie qua tertius excedit ſecundum: quia <lb/>vtra dr̄a eſt binarius. </s>
            <s xml:id="N11A31" xml:space="preserve">In ꝓpoſito em̄ / hoc eſt in <lb/>data diffinitione per terminos intelligas nume-<lb/>ros ſereatim poſitos vel ea que ſe habēt vt nume­<lb/>ri ſereatim poſiti:             <anchor type="note" xlink:href="note-0020-08" xlink:label="note-0020-08a"/>             et ꝑ differētias ītelligas exceſſū <lb/>quo vnus numerus excedit alterū. </s>
            <s xml:id="N11A41" xml:space="preserve">Reperies autē / <lb/>hanc ꝓportionalitatē in naturali ſerie numerorū <lb/>capiendo .6.7.8. comperies inter illos terminos <lb/>diuerſas ꝓportiones: quoniã primi ad ſecundum <lb/>eſt ꝓportio ſubſexquitertia / et ſecundi ad tertiū eſt <lb/>ꝓportio ſubſexq̇ſeptīa et eſt equalis differētia in-             <cb chead="Capitulum primū."/>             tes illos terminos. </s>
            <s xml:id="N11A51" xml:space="preserve">Quare in illis terminis repe­<lb/>ritur ꝓportionalitas arithmetica. </s>
            <s xml:id="N11A56" xml:space="preserve">Sunt enim illi <lb/>termini continuo proportionabiles arithmetice. <lb/>             <anchor type="note" xlink:href="note-0020-09" xlink:label="note-0020-09a"/>             </s>
            <s xml:id="N11A62" xml:space="preserve">¶ Unde termini continuo proportionabiles pro-<lb/>portionalitate arithmetica ſunt illi inter quos cõ-<lb/>tinuo eſt equalis exceſſus ita  ſicut primus exce-<lb/>dit ſecundum aliquo exceſſu: ita ſecundus excedat <lb/>tertium equali exceſſu: et tertius quartum / et ſic con­<lb/>ſequenter: vel econtra ſi incipias a minoribus.</s>
          </p>
          <div xml:id="N11A6F" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0020-01a" xlink:label="note-0020-01" xml:id="N11A73" xml:space="preserve">ꝓportio.</note>
            <note position="left" xlink:href="note-0020-02a" xlink:label="note-0020-02" xml:id="N11A79" xml:space="preserve">Propor­<lb/>tiõalitaſ</note>
            <note position="left" xlink:href="note-0020-03a" xlink:label="note-0020-03" xml:id="N11A81" xml:space="preserve">Correla­<lb/>riū ṗmū</note>
            <note position="left" xlink:href="note-0020-04a" xlink:label="note-0020-04" xml:id="N11A89" xml:space="preserve">medietaſ</note>
            <note position="left" xlink:href="note-0020-05a" xlink:label="note-0020-05" xml:id="N11A8F" xml:space="preserve">Diuiſio <lb/>ꝓportio­<lb/>nalitate.</note>
            <note position="left" xlink:href="note-0020-06a" xlink:label="note-0020-06" xml:id="N11A99" xml:space="preserve">Undecim <lb/>medieta­<lb/>tes.</note>
            <note position="left" xlink:href="note-0020-07a" xlink:label="note-0020-07" xml:id="N11AA3" xml:space="preserve">ꝓportio­<lb/>nalitas <lb/>arithme­<lb/>tica.</note>
            <note position="left" xlink:href="note-0020-08a" xlink:label="note-0020-08" xml:id="N11AAF" xml:space="preserve">Differen­<lb/>tia.</note>
            <note position="right" xlink:href="note-0020-09a" xlink:label="note-0020-09" xml:id="N11AB7">
              <s xml:id="N11ABB" xml:space="preserve">Tertimini <lb/>ↄ̨tinuo ꝓ-<lb/>portiõa-<lb/>les ꝓpor­<lb/>tõalitate <lb/>aritithme <lb/>tica. <lb/></s>
              <s xml:id="N11ACB" xml:space="preserve">Corrrela­<lb/>riū ſcḋm</s>
            </note>
          </div>
          <p xml:id="N11AD0">
            <s xml:id="N11AD1" xml:space="preserve">¶ Ex quo elicitur omēs numeros in naturali ſerie <lb/>numerorum eſſe terminos continuo proportiona­<lb/>biles proportionalitate arithmetica: quoniã con­<lb/>tinuo ſe excedunt equali exceſſu puta vnitate</s>
          </p>
          <note position="right" xml:id="N11ADA" xml:space="preserve">Correla-<lb/>riū ṫciū.</note>
          <p xml:id="N11AE0">
            <s xml:id="N11AE1" xml:space="preserve">¶ Sequitur vlterius proportiones duplam qua-<lb/>druplam, octuplam, ſexdecuplam, trigecuplam <lb/>ſecundam / et ſic conſequenter aſcēdendo per nume­<lb/>ros pariter pares: eſſe terminos continuo propor­<lb/>tionabiles arithmetice. </s>
            <s xml:id="N11AEC" xml:space="preserve">quoniã continuo ille pro-<lb/>portiones ſe excedūt per equalem proportionem: <lb/>puta duplam </s>
            <s xml:id="N11AF3" xml:space="preserve">Nam quadrupla excedit duplã per <lb/>duplam: et octupla excedit quadruplam etiam per <lb/>duplam: et ſimiliter ſexdecupla excedit octuplam <lb/>per duplã: igitur ille proportiones continuo ſūt <lb/>proportionabiles arithmetice. </s>
            <s xml:id="N11AFE" xml:space="preserve">Antecedens patet / <lb/>quia addendo duplam ſupraduplã efficitur qua-<lb/>drupla: et addendo duplam ſupraquadruplã effi­<lb/>citur octupla: et ſic conſequenter. </s>
            <s xml:id="N11B07" xml:space="preserve">Et ille proporti-<lb/>ones continuo per illa additamenta ſe excedūt: et <lb/>illa additamenta cõtinuo ſunt proportiones du-<lb/>ple / igitur cõtinuo ſe excedunt per proportionem <lb/>dulam: quod fuit probandum. </s>
            <s xml:id="N11B12" xml:space="preserve">Huius medietatis <lb/>proprietates in ſequenti capite patebunt.             <anchor type="note" xlink:href="note-0020-10" xlink:label="note-0020-10a"/>             </s>
            <s xml:id="N11B1C" xml:space="preserve"><gap/> Geo-<lb/>metrica autem medietas ſiue ꝓportionalitas eſt <lb/>quotienſcun tribus diſpoſitis terminis: aut plu­<lb/>ribus inter eos eedem proportiones reperiuntur <lb/>eedeꝫ vero differētie nequa̄. </s>
            <s xml:id="N11B28" xml:space="preserve">Et per eaſdē ꝓpor-<lb/>tiones in propoſitio ītelligas proportiones equa­<lb/>les. </s>
            <s xml:id="N11B2F" xml:space="preserve">Et per equales proportiones intelligas pro-<lb/>portiones eiuſdem denominationis. </s>
            <s xml:id="N11B34" xml:space="preserve">Cuiuſmodi <lb/>ſunt proportio .4. ad .2. et 12. ad .6. </s>
            <s xml:id="N11B39" xml:space="preserve">Sunt em̄ eiuſ-<lb/>dem denominationis: eſt enim vtra illarum du-<lb/>pla: vt conſtat ex priori parte. </s>
            <s xml:id="N11B40" xml:space="preserve">Unde omnes duple <lb/>ſunt equales: oēs ſexquialtere, et oēs ſuprabipar-<lb/>tientes tertias. </s>
            <s xml:id="N11B47" xml:space="preserve">Exemplū / huius medietatis in his <lb/>terminis .2:4.8. reperitur: quoniã qualis eſt pro-<lb/>portio primi ad ſecūdum talis eſt proportio ſecū­<lb/>di ad tertium: vtrobi enim ſubdupla proportio <lb/>inuenitur: ſed non ſunt eedem differentie: quoniã <lb/>tertius terminus ſecundum numero quaternario <lb/>excedit: ſecūdus vero primum binario dumtaxat <lb/>             <anchor type="note" xlink:href="note-0020-11" xlink:label="note-0020-11a"/>             </s>
            <s xml:id="N11B5D" xml:space="preserve">¶ Educitur ex dictis omnes numeros pariter pa-<lb/>res cõtinuo geometrice proportionari. </s>
            <s xml:id="N11B62" xml:space="preserve">Inter eas <lb/>enim cõtinuo proportio dupla eſt: vt patet in his <lb/>terminis. 2 4 8 16</s>
          </p>
          <div xml:id="N11B69" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0020-10a" xlink:label="note-0020-10" xml:id="N11B6D" xml:space="preserve">Geome-<lb/>trica me-<lb/>dietas.</note>
            <note position="right" xlink:href="note-0020-11a" xlink:label="note-0020-11" xml:id="N11B77" xml:space="preserve">Correla­<lb/>riū q̈rtū.</note>
          </div>
          <note position="right" xml:id="N11B7F" xml:space="preserve">Correla­<lb/>riū quītã</note>
          <p xml:id="N11B85">
            <s xml:id="N11B86" xml:space="preserve">¶ Sequitur ſecundo omnes numeros impares cõ­<lb/>tinuo ſe triplantes incipiendo a ternario conti-<lb/>nuo proportionari geometrice. </s>
            <s xml:id="N11B8D" xml:space="preserve">Nam ſi continuo <lb/>ſe triplant: continuo ſe habent in proportione tri­<lb/>pla: ex quo quilibet ſequens immediate preceden­<lb/>tem ter continet: vt patet in his terminis .3.9.2.7. <lb/>             <anchor type="note" xlink:href="note-0020-12" xlink:label="note-0020-12a"/>             </s>
            <s xml:id="N11B9D" xml:space="preserve">¶ Elicitur tertio omnes proportiones denomi-<lb/>natas a numeris pariter paribus relinquendo <lb/>poſt ſecundum numerum pariter parem vnum nu­<lb/>merum: poſt quartum duos poſt ſeptimum quat­<lb/>tuor: et ſic conſequenter duplando continuo nu-<lb/>meros intermiſſos: eſſe terminos             <pb chead="Prime partis" file="0021" n="21"/>             continuo ꝓportionabiles geometrice: vt ꝓportio <lb/>dupla, q̈drupla, ſexdecupla, cētecupla vicecupla, <lb/>octupla / et ſic ↄ̨ñter: quoue reperiūtur in his ṫmīs</s>
          </p>
          <div xml:id="N11BB3" level="4" n="3" type="float">
            <note position="right" xlink:href="note-0020-12a" xlink:label="note-0020-12" xml:id="N11BB7" xml:space="preserve">Correla­<lb/>riū ſextã</note>
          </div>
          <xhtml:table xml:id="N11BBF">
            <xhtml:tr xml:id="N11BC0">
              <xhtml:td xml:id="N11BC1" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N11BC3">
            <s xml:id="N11BC4" xml:space="preserve">¶ Hoc correlariū magis liquide patebit ex ſequē­<lb/>tibus. </s>
            <s xml:id="N11BC9" xml:space="preserve">Proprietates huiꝰ medietas in ſequēti ca­<lb/>pite ponētur.             <anchor type="note" xlink:href="note-0021-01" xlink:label="note-0021-01a"/>             </s>
            <s xml:id="N11BD3" xml:space="preserve">¶ Harmonica autē muſicave medie­<lb/>tas ſiue ꝓportionalitas eſt quotienſcū diſpoſi-<lb/>tis tribus termīs vel pluribus inter ipſos nec ſūt <lb/>eedē ꝓportiones: nec differentie: ſed ſicut ſe habet <lb/>maximꝰ terminꝰ ad minimū. </s>
            <s xml:id="N11BDE" xml:space="preserve">ita ſe hꝫ differentia <lb/>maiorū ad differentiã minoꝝ vt diſpoſitis his tri­<lb/>bus terminis .6.4.3. inter eos non reperiunt̄̄ eedē <lb/>ꝓportiões: nec eedē differētie: ſed ſicut ſe hꝫ maxi-<lb/>mus eoꝝ ad minimū: ita differētie maximi ad me­<lb/>diū et medii ad minimū ſeſe habēt: vt cõſtat. </s>
            <s xml:id="N11BEB" xml:space="preserve">Aliq̄ <lb/>ꝓprietates ſignantur huic hermonice medietati: <lb/>ſed ille in poſterū oſtendent̄̄             <anchor type="note" xlink:href="note-0021-02" xlink:label="note-0021-02a"/>             </s>
            <s xml:id="N11BF7" xml:space="preserve">¶ Addit nichomachꝰ <lb/>his tribus antiquis et famatis medietatibus ſiue <lb/>ꝓportionalitatibus .7. recentiores proportiona-<lb/>litates: vt cõpleretur numerus denariꝰ: qui apud <lb/>antiquos pluris habebat̄̄:             <anchor type="note" xlink:href="note-0021-03" xlink:label="note-0021-03a"/>             vt patꝫ ꝑ philoſophū <lb/>decima quīta particula ꝓblematū: ſed has videre <lb/>poteris apud Seuerinū boetiū in calce ſue arith­<lb/>metice: et apud alios recentes mathematicos: </s>
            <s xml:id="N11C0D" xml:space="preserve">Nõ <lb/>em̄ huic operi ſunt interſerēde. </s>
            <s xml:id="N11C12" xml:space="preserve">qm̄ philoſophan-<lb/>tes nequa̄ eis in ſuis phiſicis calculationibꝰ vtū­<lb/>tur.             <anchor type="note" xlink:href="note-0021-04" xlink:label="note-0021-04a"/>             </s>
            <s xml:id="N11C1E" xml:space="preserve">¶ Hic tamē aduertendū eſt /  duplex eſt ꝓpor-<lb/>tionalitas quedã cõiuncta: quedã vero diſiiuncta. <lb/>             <anchor type="note" xlink:href="note-0021-05" xlink:label="note-0021-05a"/>             </s>
            <s xml:id="N11C2A" xml:space="preserve">¶ Cõiuncta ꝓportionalitas eſt illa / q̄ in tribus vel <lb/>pluribus termīs cõſiſtit cõtinue: vt ꝓportiõalitas <lb/>reꝑta in his tribus termīs .3.6.12. </s>
            <s xml:id="N11C31" xml:space="preserve">Et huic medie­<lb/>tati ꝓpriū eſt eſſe duarū ꝓportionū inter tres ter­<lb/>minos ad minꝰ. </s>
            <s xml:id="N11C38" xml:space="preserve">Inter tres terminos vti ſolum <lb/>due ꝓportiones reperiuntur: nec poſſunt reperiri <lb/>plures vtendo illis terminis et nõ aliis niſi cõpa-<lb/>retur primus ad vltimum. </s>
            <s xml:id="N11C41" xml:space="preserve">Sed tunc omnes termi­<lb/>ni bis capiuntur. </s>
            <s xml:id="N11C46" xml:space="preserve">Quare notandum eſt /  quando <lb/>dicimus /  inter tres terminos reperiuntur dum­<lb/>taxat due ꝓportiões vel ad ſummū tres: ſi vltimꝰ <lb/>comparetur ad primū ītelligendū eſt dūmodo nõ <lb/>vtamur niſi illis tribꝰ termīs: et nõ aliquibꝰ aliis <lb/>virtualiter intermediis. </s>
            <s xml:id="N11C53" xml:space="preserve">Inter .6. em̄ et .12. multe <lb/>reperiuntur ꝓportiones dūmodo vtamur termīs <lb/>intermediis puta octonario, nouenario, denario <lb/>et vndenario.             <anchor type="note" xlink:href="note-0021-06" xlink:label="note-0021-06a"/>             </s>
            <s xml:id="N11C61" xml:space="preserve">¶ Sed proportionalitas diuiſa ſiue <lb/>diſiūcta eſt illa que cõſiſtit in .4. terminis aut plu­<lb/>ribus diſcõtinue: vt ꝓportionalitas que eſt in his <lb/>quattuor termīs: 1.2.6.12. eſt ꝓportiõalitas diſiū­<lb/>ta </s>
            <s xml:id="N11C6C" xml:space="preserve">Et huic ꝓpriū eſt ī quattuor termīs ad mininꝰ <lb/>cõſiſtere diſcõtinue ꝓportionabilibus: ita  non <lb/>eadem ſit proportio primi ad ſecundum et ſecundi <lb/>ad tertium. </s>
            <s xml:id="N11C75" xml:space="preserve">Hoc patet in exemplo dato.             <anchor type="note" xlink:href="note-0021-07" xlink:label="note-0021-07a"/>             </s>
            <s xml:id="N11C7D" xml:space="preserve">¶ His <lb/>tribus medietatibus addenda eſt quedam medie-<lb/>tas ſiue ꝓportionalitas que a mathematicis ma­<lb/>xima et perfectiſſima dicitur. </s>
            <s xml:id="N11C86" xml:space="preserve">Unde medietas per­<lb/>fectiſſima eſt illa que in quattuor terminis et tribꝰ <lb/>interuallis cõſiſtit: in qua alie famate ꝓportiona­<lb/>litates reperiri poſſunt: vt in iſtis quatuor termīs <lb/>6.8.9.12.             <anchor type="note" xlink:href="note-0021-08" xlink:label="note-0021-08a"/>             </s>
            <s xml:id="N11C96" xml:space="preserve">Ibi em̄ eſt maxima et perfectiſſima pro-<lb/>portionalitas. </s>
            <s xml:id="N11C9B" xml:space="preserve">Per interuallū intellige propor-<lb/>tionē que eſt inter duos terminos īmediatos. </s>
            <s xml:id="N11CA0" xml:space="preserve">Et <lb/>ſic intelligēdo reperies dumtaxat inter quattuor <lb/>terminos tria interualla: hoc eſt tres ꝓportiones <lb/>ſereatim ſe habētes: vt in datis terminis reperies <lb/>ꝓportiones .6. ad .8. et 8. ad .9. et .9. ad .12. </s>
            <s xml:id="N11CAB" xml:space="preserve">¶ Iſta <lb/>medietas multas habet proprietates. </s>
            <s xml:id="N11CB0" xml:space="preserve">¶ Prima             <cb chead="Capitulum primū."/>             proprietas eſt /  ſi cõparetur tertius ad primū, et <lb/>quartus ad tertium: reperitur proportionalitas <lb/>arithmetica: quoniã reperiūtur eedem differentie <lb/>et nõ eedem proportiones. </s>
            <s xml:id="N11CBC" xml:space="preserve">¶ Secūda proprietas <lb/></s>
            <s xml:id="N11CC0" xml:space="preserve">Si comparetur quartus ad ſecūduꝫ, et tertius ad <lb/>primū, reperietur proportionalitas geometrica / <lb/>qm̄ vtrobi eſt ibi ſexq̇altera ꝓportio: differētie <lb/>vero nõ vtrobi eedē: qm̄ vna differētia eſt nūerꝰ <lb/>quaternariꝰ: alia vero ternariꝰ: igitur ibi eſt geo­<lb/>metrice medietas. </s>
            <s xml:id="N11CCD" xml:space="preserve">Patet ↄ̨ña ex diffinitione geo-<lb/>metrica medietatis. </s>
            <s xml:id="N11CD2" xml:space="preserve">¶ Tertia proprietas. </s>
            <s xml:id="N11CD5" xml:space="preserve">Si cū-<lb/>paretur numerus quartus ad ſcḋm, et ſecūdus ad <lb/>primū, reperies harmonicam, ꝓportionalitatem <lb/></s>
            <s xml:id="N11CDD" xml:space="preserve">¶ Quarta ꝓprietas. </s>
            <s xml:id="N11CE0" xml:space="preserve">In iſta medietate perfectiſſi­<lb/>ma oēs cõſonantie ſimplices compariūtur.             <anchor type="note" xlink:href="note-0021-09" xlink:label="note-0021-09a"/>             </s>
            <s xml:id="N11CEA" xml:space="preserve">Qua­<lb/>tuor em̄ ſunt muſice cõſonãtie ſimplices: videlicet <lb/>tonus, diapente, diateſſeron, et diapaſon </s>
            <s xml:id="N11CF1" xml:space="preserve">¶ Unde <lb/>tonus eſt duarū vocū quarum vna eleuatur ſuper <lb/>alterã in ꝓportione ſexquioctaua vniꝰ ad alteran <lb/>harmonica ↄ̨ſonãtia. </s>
            <s xml:id="N11CFA" xml:space="preserve">vt inṫ duas voces quaꝝ vna <lb/>ſe habet vt .8. et alia vt nouē: vel quaꝝ vna ſe ha-<lb/>bet vt .16. et alia vt .18.             <anchor type="note" xlink:href="note-0021-10" xlink:label="note-0021-10a"/>             </s>
            <s xml:id="N11D06" xml:space="preserve">¶ Sed diateſſero eſt duarū <lb/>vocum: quarum vna eleuatur ſuper alteram in ꝓ-<lb/>portione ſexquitertia muſica conſonantia: vt in-<lb/>ter duas voces ſe habentes vt .4. et .3.             <anchor type="note" xlink:href="note-0021-11" xlink:label="note-0021-11a"/>             </s>
            <s xml:id="N11D14" xml:space="preserve">¶ Diapente <lb/>vero eſt hermonica cõſonãtia duarū vocum: qua-<lb/>rum vna eleuatur ſuper alterã in ꝓportõe ſexqui­<lb/>altera. </s>
            <s xml:id="N11D1D" xml:space="preserve">vt inter duas voces ſe habentes vt .12. et .8 <lb/>vt .3. et .2.             <anchor type="note" xlink:href="note-0021-12" xlink:label="note-0021-12a"/>             </s>
            <s xml:id="N11D27" xml:space="preserve">¶ Diapaſon vero eſt conſonãtia harmo­<lb/>nica duarum vocum vel ſonorum (quod in preſen­<lb/>tiarum pro eodem capio) quarū vna eleuatur ſu-<lb/>pra alteram in ꝓportione dupla. / vt conſonatia <lb/>illa harmonica que eſt inter duas voces ſe haben­<lb/>tes ſicut .12. ad .6. eſt muſica conſonantia: que dia­<lb/>paſon vocitatur.             <anchor type="note" xlink:href="note-0021-13" xlink:label="note-0021-13a"/>             </s>
            <s xml:id="N11D3B" xml:space="preserve">¶ Ex quo ſequitur /  inter omēs <lb/>harmonicas ſimplices cõſonantias diapaſon eſt <lb/>maxima. </s>
            <s xml:id="N11D42" xml:space="preserve">Probatur / quia alie ſunt partes eius: <lb/>igit̄̄ ſūt ea minores: </s>
            <s xml:id="N11D47" xml:space="preserve">Arguitur añs / q2 componitur <lb/>diapaſon ex tono, diateſſeron, et diapente, igitur <lb/></s>
            <s xml:id="N11D4D" xml:space="preserve">Probatur antecedens / qm̄ .12. ad .6. eſt diapaſon <lb/>conſonantia: et talis conſonantia componitur ex <lb/>cõſonantia .8. ad .6. que eſt diateſſeron: et ex conſo­<lb/>nantia .9. ad .8. que eſt tonus: et ex conſonantia .12 <lb/>ad .8. que eſt diapēte: igitur diapaſon ex aliis tri­<lb/>bus ſimplicibus concentibus conſtruitur ſiue con­<lb/>ponitur. </s>
            <s xml:id="N11D5C" xml:space="preserve">Quare ſequitur diapaſon eſſe maximã <lb/>muſicã cõſonantiã inter ſimplices.             <anchor type="note" xlink:href="note-0021-14" xlink:label="note-0021-14a"/>             </s>
            <s xml:id="N11D66" xml:space="preserve">Dico inter ſim­<lb/>plices / qm̄ multe ſunt cõpoſite conſonantie: vt di-<lb/>tonus, ſemitonus, tritonus, bis diateſſeron, bis <lb/>diapēte, bis diapaſon, et ter, et quater diapaſon / <lb/>et ſic conſequenter.             <anchor type="note" xlink:href="note-0021-15" xlink:label="note-0021-15a"/>             </s>
            <s xml:id="N11D76" xml:space="preserve">Sed cum difficultate maior cõ­<lb/>ſonantia bis diapaſon reperitur in voce humana <lb/>niſi ſtētor ab inferis rediret cuiꝰ mire vocis et ho-<lb/>merus et philoſophus ſeptimo politicorū capite <lb/>quarto meminit. </s>
            <s xml:id="N11D81" xml:space="preserve">Si tamen vox humana in aſcen­<lb/>dendo in infinitū augmētaretur ſiue intenderetur <lb/>vel aliquod inſtrumentū harmonicū: in infinitum <lb/>duplicarentur harmonice conſonantie: et ſemper <lb/>harmonicam ꝓportionalitatem ſeruarent </s>
            <s xml:id="N11D8C" xml:space="preserve">¶ Sed <lb/>de his hactenus. </s>
            <s xml:id="N11D91" xml:space="preserve">Parum em̄ philoſophie deſer-<lb/>uiūt: ſed introducuntur omnia iſta vt clare inſpi-<lb/>ciat phiſicus rerum naturalium indagator velo-<lb/>citatem motuū non penes harmonicas conſonan­<lb/>tias: aut muſicas equalitates ſiue proportionali-<lb/>tates attendi debere: que vti concluſio niſi ter-<lb/>minos predictos intelligeret ei perſpicua nõ eſſet <lb/>             <anchor type="note" xlink:href="note-0021-16" xlink:label="note-0021-16a"/>             </s>
            <s xml:id="N11DA7" xml:space="preserve">¶ Patet ſecundo ex dictis hanc medietatem / quã             <pb chead="Prime partis" file="0022" n="22"/>             tertio adiecimus merito perfectiſſimam vocitari <lb/></s>
            <s xml:id="N11DB0" xml:space="preserve">Cuiꝰ probatio eſt / qm̄ in dicta medietate tres fa-<lb/>mate ꝓportionalitates reperiuntur arithmetica <lb/>geometrica, et harmonica. </s>
            <s xml:id="N11DB7" xml:space="preserve">In iſta etiã medietate <lb/>oēs ſimplices harmonice cõſonantie reperiuntur <lb/>             <anchor type="note" xlink:href="note-0022-01" xlink:label="note-0022-01a"/>             </s>
            <s xml:id="N11DC3" xml:space="preserve">¶ Ex his omnibus demū infero oēm ſcientiã aliã <lb/>oēm artem: philoſophie inſeruire. </s>
            <s xml:id="N11DC8" xml:space="preserve">ei ancillari <lb/>at famulari. </s>
            <s xml:id="N11DCD" xml:space="preserve">vt facile ex his que dicta ſunt ꝑſpi­<lb/>ci poteſt: et ſignanter inſeruirent iſta philoſophie. <lb/>             <anchor type="note" xlink:href="note-0022-02" xlink:label="note-0022-02a"/>             </s>
            <s xml:id="N11DD9" xml:space="preserve">Pythagore qui aſtruxit celos corpora illa ſempi <lb/>terna perpetuo harmonicis cõſonantiis circūuo-<lb/>lui teſte philoſopho ſecūdo celi et mundi: et plinio <lb/>ſecundo naturalis hiſtorie.</s>
          </p>
          <div xml:id="N11DE2" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0021-01a" xlink:label="note-0021-01" xml:id="N11DE6" xml:space="preserve">Muſica <lb/>medietaſ</note>
            <note position="left" xlink:href="note-0021-02a" xlink:label="note-0021-02" xml:id="N11DEE" xml:space="preserve">Nicho-<lb/>machus.</note>
            <note position="left" xlink:href="note-0021-03a" xlink:label="note-0021-03" xml:id="N11DF6" xml:space="preserve">phūs .5. <lb/>ꝑti: ꝓble­<lb/>matum.</note>
            <note position="left" xlink:href="note-0021-04a" xlink:label="note-0021-04" xml:id="N11E00" xml:space="preserve">Alia di-<lb/>uſio me-<lb/>dietatuꝫ.</note>
            <note position="left" xlink:href="note-0021-05a" xlink:label="note-0021-05" xml:id="N11E0A" xml:space="preserve">Cõiūcta <lb/>medietaſ</note>
            <note position="left" xlink:href="note-0021-06a" xlink:label="note-0021-06" xml:id="N11E12" xml:space="preserve">Propor­<lb/>tiõalitas <lb/>diuiſa.</note>
            <note position="left" xlink:href="note-0021-07a" xlink:label="note-0021-07" xml:id="N11E1C" xml:space="preserve">maxima <lb/>medietaſ</note>
            <note position="left" xlink:href="note-0021-08a" xlink:label="note-0021-08" xml:id="N11E24" xml:space="preserve">ꝓp̄etateſ <lb/>medietaſ­<lb/>tis perfe­<lb/>ctiſſime.</note>
            <note position="right" xlink:href="note-0021-09a" xlink:label="note-0021-09" xml:id="N11E30" xml:space="preserve">quatuor <lb/>muſice cõ­<lb/>ſonãtie.</note>
            <note position="right" xlink:href="note-0021-10a" xlink:label="note-0021-10" xml:id="N11E3A" xml:space="preserve">Diateſſe­<lb/>ron.</note>
            <note position="right" xlink:href="note-0021-11a" xlink:label="note-0021-11" xml:id="N11E42" xml:space="preserve">Diapēte</note>
            <note position="right" xlink:href="note-0021-12a" xlink:label="note-0021-12" xml:id="N11E48" xml:space="preserve">diapaſõ</note>
            <note position="right" xlink:href="note-0021-13a" xlink:label="note-0021-13" xml:id="N11E4E" xml:space="preserve">Correla­<lb/>riū ṗmū.</note>
            <note position="right" xlink:href="note-0021-14a" xlink:label="note-0021-14" xml:id="N11E56" xml:space="preserve">cõpoſite. <lb/>ↄ̨ſonãtie</note>
            <note position="right" xlink:href="note-0021-15a" xlink:label="note-0021-15" xml:id="N11E5E" xml:space="preserve">Stentoꝝ</note>
            <note position="right" xlink:href="note-0021-16a" xlink:label="note-0021-16" xml:id="N11E64" xml:space="preserve">Correla-<lb/>riū ſcḋm</note>
            <note position="left" xlink:href="note-0022-01a" xlink:label="note-0022-01" xml:id="N11E6C" xml:space="preserve">tertium. <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0022-02a" xlink:label="note-0022-02" xml:id="N11E76">
              <s xml:id="N11E7A" xml:space="preserve">pythago­<lb/>ras. <lb/></s>
              <s xml:id="N11E80" xml:space="preserve">phūs <lb/>plinius.</s>
            </note>
          </div>
        </div>
        <div xml:id="N11E85" level="3" n="2" type="chapter" type-free="capitulum">
          <head xml:id="N11E8A" xml:space="preserve">Capitulum ſecundum / in quo ꝓbantur <lb/>alique proprietates predictarum ꝓpor-<lb/>tionalitatem ſiue medietatum.</head>
          <p xml:id="N11E91">
            <s xml:id="N11E92" xml:space="preserve">AD inducendas mathemathi­<lb/>co ordine aliquas ꝓprietates predicta­<lb/>rum medietatum: ponende ſunt alique <lb/>ſuppoſitiones: quarū alique erunt diffinitiones: <lb/>et alique petentur ꝓpter earuꝫ euidentē noticiam: <lb/>alique vero probabuntur ſit igitur.</s>
          </p>
          <p xml:id="N11E9F">
            <s xml:id="N11EA0" xml:space="preserve">Prima ſuppoſitio / que et difinitio. <lb/></s>
            <s xml:id="N11EA4" xml:space="preserve">Medium eſt quod equali inter capidine diſtat ab <lb/>vtro extemorum. </s>
            <s xml:id="N11EA9" xml:space="preserve">vt numerus ternarius eſt medi­<lb/>um inter quaternarium et binarium. </s>
            <s xml:id="N11EAE" xml:space="preserve">quia equali <lb/>exceſſu ſiue equali differentia ab vtro illoruꝫ di­<lb/>ſtat: puta vnitate.</s>
          </p>
          <p xml:id="N11EB5">
            <s xml:id="N11EB6" xml:space="preserve">Secunda ſuppoſitio / que et difinitio <lb/></s>
            <s xml:id="N11EBA" xml:space="preserve">Partes aliquote eiuſdem denominationis ſunt <lb/>ille q̄ ab eodē numero denominãtur vt medietates <lb/>a binario: tertie. a ternario. </s>
            <s xml:id="N11EC1" xml:space="preserve">q̈rte a q̈ternario .etc̈.</s>
          </p>
          <p xml:id="N11EC4">
            <s xml:id="N11EC5" xml:space="preserve">Tertia ſuppoſitio / que etiam difini-<lb/>tio eſt </s>
            <s xml:id="N11ECA" xml:space="preserve">Aliquã quãtitatē continere aliquod equa-<lb/>le in aliqua ꝓportione pluries adequate quã alia <lb/>quantitas idem equale contineat: eſt illam quãti­<lb/>tatem in eadem ꝓportione ſe habere ad alteram <lb/>vt ſi aliqua quantitas contineat in ꝓportione ſex­<lb/>quialtera adequate plura pedalia quã vna altera <lb/>minor talis quantitas ſe habet ad minorem in ꝓ-<lb/>portione ſexquialtera.</s>
          </p>
          <p xml:id="N11EDB">
            <s xml:id="N11EDC" xml:space="preserve">Quarta ſuppoſitio </s>
            <s xml:id="N11EDF" xml:space="preserve">Si aliqua quan­<lb/>titas vel numerus contineat tota vice ſecūdum nu­<lb/>merum: quota vice tertius numerus cõtinet quar­<lb/>tum vel tota vice et aliquã vel aliquot partes ali-<lb/>quotas eiuſdem denominationis quota tertiꝰ cõ­<lb/>tinet quartum et aliquam partem vel aliquot par­<lb/>tes aliquotas eius adequate: qualis ē proportio <lb/>inter primū et ſecundum talis eſt inter tertiū et q̈r­<lb/>tum. </s>
            <s xml:id="N11EF2" xml:space="preserve">Patet hec ſuppoſitio ex diffinitione nume-<lb/>rorum habentium ad reliquos eandeꝫ proportio-<lb/>nem. </s>
            <s xml:id="N11EF9" xml:space="preserve">Sic eī tales numeri debent definiri vt cõſtat.</s>
          </p>
          <p xml:id="N11EFC">
            <s xml:id="N11EFD" xml:space="preserve">Quinta ſuppoſitio </s>
            <s xml:id="N11F00" xml:space="preserve">Si duo numeri <lb/>vel quantitates diuidantur in partes aliquotas <lb/>eiuſdem denominationis: quot partes illiꝰ deno­<lb/>minationis ſunt in vno tot ſunt in altero. </s>
            <s xml:id="N11F09" xml:space="preserve">Patet / <lb/>quia ſi ſunt eiuſdem denominationis: ab eodē nu-<lb/>mero denominantur: vt patet ex ſecunda ſuppoſi­<lb/>tione / et per conſequēs ſunt equales numero. </s>
            <s xml:id="N11F12" xml:space="preserve">Tūc <lb/>enim alique partes aliquote alicuius quantitatis <lb/>denominantur ab aliquo numero: quando talis <lb/>quãtitas diuiditur in tot partes equales quot ſūt <lb/>vnitates in tali numero:</s>
          </p>
          <cb chead="Capitulum ſecundum"/>
          <p xml:id="N11F1F">
            <s xml:id="N11F20" xml:space="preserve">Sexta ſuppoſitio </s>
            <s xml:id="N11F23" xml:space="preserve">Si duo numeri <lb/>vel quantitates diuidantur in partes aliquotas <lb/>eiuſdem denominationis: et perdit aliquam vel <lb/>aliquod partes aliquotas ex illa vter illorū re-<lb/>manentibus aliquibus: reſidue erunt eiuſdē deno­<lb/>minationis. </s>
            <s xml:id="N11F30" xml:space="preserve">vt ſi bipedale diuidatur in .5. quin-<lb/>tas et pedale ſimiliter: et perdit bipedale duas q̇n­<lb/>tas ex eis: et pedale ſimiliter: reſidue partes erunt <lb/>eiuſdē denominatiõis: puta tertie: vt patet </s>
            <s xml:id="N11F39" xml:space="preserve">Pro­<lb/>batur / quia in principio decremēti ille partes ali-<lb/>quote illarum quantitatum ſunt equales numero <lb/>et equales numero deperdentur ab vtra illaruꝫ <lb/>quantitatum / vt ponitur remanentibus aliquibus <lb/>ex illis: ergo remantes manebunt equales nu-<lb/>mero. </s>
            <s xml:id="N11F48" xml:space="preserve">Patet conſequentia / q2 ſi ab equalibus nu-<lb/>meris equales demas .etc̈. / et ꝑ conſequens ſemper <lb/>denominabuntur ab equali numero: quare ſemꝑ <lb/>erunt eiuſdem denominationis / vt patet ex diffini­<lb/>tione.</s>
          </p>
          <p xml:id="N11F53">
            <s xml:id="N11F54" xml:space="preserve">Septima ſuppoſitio </s>
            <s xml:id="N11F57" xml:space="preserve">Qualis eſt pro­<lb/>portio alicuius ad aliquam eius partem aliquo-<lb/>tam: talis eſt cuiuſlibet alteriꝰ ad partē aliquotã <lb/>eius conſiĺis denominationis. </s>
            <s xml:id="N11F60" xml:space="preserve">vt qualis eſt ꝓpor­<lb/>tio alicuius quãtitatis ad ſuã medietatē tertiam <lb/>quartam .etc̈. talis eſt cuiuſlibet alterius ad ſuã me­<lb/>dietatem tertiã quartã .etc̈. </s>
            <s xml:id="N11F69" xml:space="preserve">Patet hec ex q̈rta ſup­<lb/>poſitõe / hoc adito /  q̊ties aliq̈ quãtitas ↄ̨tinet ali­<lb/>quam ſui partem aliquotaꝫ: toties quelibet alia <lb/>quantitas continet partem ſui aliquotam cõſimi­<lb/>lis denominationis: cum ſemper partes aliquote <lb/>eiuſdem denominationis ſint equales numero / vt <lb/>patet ex quinta ſuppoſitione:</s>
          </p>
          <p xml:id="N11F78">
            <s xml:id="N11F79" xml:space="preserve">Octaua ſuppoſitio </s>
            <s xml:id="N11F7C" xml:space="preserve">Si aliqui duo nu­<lb/>meri ſiue quantitates diuidantur in duas partes <lb/>equales: cuiuſlibet illorum numerorum ad alterã <lb/>illarum ſuarum partium eſt eadem ꝓportio. </s>
            <s xml:id="N11F85" xml:space="preserve">Et ſi <lb/>vter duorum numerorum diuidatur in plures ꝑ­<lb/>tes aliquotas eiuſdem denominationis quaꝫ ſint <lb/>due: talis eſt ꝓportio vnius illorum numerorū ad <lb/>aggregatū ex omnibus talibus partibus aliquo­<lb/>tis dempta vna: qualis eſt alterius ad aggrega-<lb/>tum ex omnibus dempta ſimiliter vna. / vt diuiſo <lb/>ſenario in tres partes aliquotas: et ſimiliter ter­<lb/>nario: talis eſt ꝓportio ipſius ſenarii ad aggre-<lb/>gatum ex duabus tertiis eius qualis ē ternarii ad <lb/>aggregatum ex duabus tertiis eius. </s>
            <s xml:id="N11F9C" xml:space="preserve">vt conſtat.</s>
          </p>
          <p xml:id="N11F9F">
            <s xml:id="N11FA0" xml:space="preserve">Probatur ſuppoſitio. </s>
            <s xml:id="N11FA3" xml:space="preserve">ſint duo numeri ſiue equa­<lb/>les ſiue inequales. </s>
            <s xml:id="N11FA8" xml:space="preserve">primus .a.b. ſecundus .c.d. diui­<lb/>ſi in partes aliquotas eiuſdem denominationis <lb/>et ſit primi numeri vna illarum partium .a. et reſi­<lb/>due .b. ſecundi vero numeri ſit conſimilis pars ali­<lb/>quota .c. et reſidue partes eiuſdem numeri .d. / et di­<lb/>co /  talis ē proportio a.b. ad .b. qualis eſt .c.d. ad <lb/>d. </s>
            <s xml:id="N11FB7" xml:space="preserve">Quod probatur ſic / quia quota vice .a.b. conti-<lb/>net .b. et aliquam partem aliquotam ipſius .b. to-<lb/>ta vice .c.d. continet .d. quia ſemel / vt conſtat et vnã <lb/>partem eius aliquotam euſdem denominationis <lb/>cum parte aliquota ipſius .b. quam coutinet .a.b / <lb/>igitur qualis eſt proportio .a.b. ad b. talis eſt pro­<lb/>portio .c.d. ad .d. / quod fuit probãdū </s>
            <s xml:id="N11FC6" xml:space="preserve">Patet hec cõ­<lb/>ſequentia clare ex quarta ſuppoſitione. </s>
            <s xml:id="N11FCB" xml:space="preserve"> autem .c. <lb/>ſit pars aliquota ipſius .d. eiuſdem denominatio­<lb/>nis cuius .a. eſt pars aliquota ipſius .b. / probatur / <lb/>quia ſi .a.b. numerus perdat .a. et .c.d. ꝑdat .c. / tunc <lb/>reſidue partes manebunt partes eiuſdem denomi­             <pb chead="Prime partis" file="0023" n="23"/>             uatiõis puta partes aliquote .b. et partes aliquo­<lb/>te .d. / vt patet ex ſexta ſuppoſitione: et qualibet illa­<lb/>rum in .b. equalis erit ipſi .a. quia antea erat equa­<lb/>lis: ēt quelibet in .d. et equalis ipſi .c. eadē ratione / <lb/>igitur .c. eſt pars aliquota .d. illius denominatio-<lb/>nis cuius .a. eſt pars aliquota .b. / quod fuit probã-<lb/>dum. </s>
            <s xml:id="N11FE7" xml:space="preserve">Et ſic patet: ſecunda pars ſuppoſitionis: et <lb/>prima patet de ſe: quia vter talium numerorum <lb/>habet ad talem partem aliquotam ſui ꝓportionē <lb/>duplam q2 eſt ſua medietas </s>
            <s xml:id="N11FF0" xml:space="preserve">Continet eteuim eam <lb/>bis: igitur ad eam habet proportionem duplam. <lb/></s>
            <s xml:id="N11FF6" xml:space="preserve">¶ Ex iſta ſuppoſitione ſequitur:  ſi vtra illaruꝫ <lb/>quantitatum ſiue numerorum ſit diuiſorum in ꝑ-<lb/>tes aliquotas eiuſdem denominationis ꝑdat vnã <lb/>talē partē aliquotã adequate: eq̈le proportionem <lb/>deꝑdit </s>
            <s xml:id="N12001" xml:space="preserve">Patꝫ / q2 eq̈lē ꝓportionē vter hab3 ad ag­<lb/>gregatū ex oībꝰ dēpta vna / vt ptꝫ ex .8. ſuppoſitiõe <lb/>et illam deperdit / vt conſtat igitur. </s>
            <s xml:id="N12008" xml:space="preserve">¶ Sequitur ſe­<lb/>cundo /  ſi vter duorum numerorum ſit diuiſus <lb/>in ꝑtes aliquotas eiuſdē denominatiõs: et acq̇rat <lb/>vnã illarum partiū ſupra ſe p̄ciſe eq̈le ꝓportionē <lb/>acquirit vter </s>
            <s xml:id="N12013" xml:space="preserve">Patet ex priori correlario. </s>
            <s xml:id="N12016" xml:space="preserve">q2 quã­<lb/>do vter illorum illam partem deperdit equalem <lb/>ꝓportionē deperdit / ergo quando acquirit equa-<lb/>lem acquirit: igitur.</s>
          </p>
          <p xml:id="N1201F">
            <s xml:id="N12020" xml:space="preserve">Nona ſuppoſitio </s>
            <s xml:id="N12023" xml:space="preserve">Si duo numeri in­<lb/>equales ſiue quantitates ſe habeant in aliqua ꝓ-<lb/>portione: et maior illorum deperdat aliquam pro­<lb/>portionem ſtante minori inuariato: tunc ꝓportio <lb/>inter maiorē et minorē deꝑdit illã ꝓportionē quã <lb/>deꝑdit maior adeq̈te. </s>
            <s xml:id="N12030" xml:space="preserve">dūmõ minor ſēꝑ maneat mi­<lb/>nor. </s>
            <s xml:id="N12035" xml:space="preserve">vt ſi ꝓportionis q̄ eſt inter .8. et .4. maior nūe­<lb/>rus puta octonariꝰ ꝑdat ꝓportionē ſexquitertiaꝫ <lb/>que eſt octo ad ſex illam ꝓportionem deperdit ꝓ-<lb/>portio que eſt inter octo et quattuor. </s>
            <s xml:id="N1203E" xml:space="preserve">Probatur / et <lb/>ſint .a.b. numerus maior et .c. numerus minor in-<lb/>ter quos ſit proportio .g. ſit .b. numerus maior <lb/>c. / et manifeſtum eſt /  ꝓportio .a.b. ad .c. componi-<lb/>tur ex proportione .a.b. ad .b et .b. ad .c. vt poſtea vi­<lb/>debitur. </s>
            <s xml:id="N1204B" xml:space="preserve">Deperdat igitur numerus maior ꝓpor-<lb/>tioneꝫ que eſt .a.b. ad .b. / et arguitur ſic / ꝓportio .g. <lb/>componebatur antea ex proportione .a.b. ad .b. <lb/>et .b. ad .c. modo non manet niſi proportio .b. ad .c. / <lb/>igitur proportio .g. ꝑdit ꝓportionē ab. ad .b. et illã <lb/>deperdat numerus maior / igitur.</s>
          </p>
          <p xml:id="N12058">
            <s xml:id="N12059" xml:space="preserve">Decima ſuppoſitio </s>
            <s xml:id="N1205C" xml:space="preserve">Si duo numeri <lb/>ſiue quantitates inequales ſe habeant in aliqua <lb/>proportione: et minor deperdat aliquam propor­<lb/>tionem ſtante moiore: illam proportionem acqui­<lb/>rit proportio que eſt inter maiorem quantitatem <lb/>et minorem. </s>
            <s xml:id="N12069" xml:space="preserve">et ſi tantam proportionem deperdat <lb/>quantitas maior ſicut minor: tunc proportio in-<lb/>ter maiorem et minorem nec augetur nec diminui­<lb/>tur: ſed ſemper manet equalis extremis manenti-<lb/>bus quãtitatis. </s>
            <s xml:id="N12074" xml:space="preserve">vt ſi proportionis que eſt inter .8. <lb/>et .quattuor. minor numerus perdat proportionē <lb/>duplam ſtante maiore proportio inter maiorem <lb/>et minorem acquirit proportionem duplaꝫ: et ſi qñ <lb/>numerus minor perdit duplã etiaꝫ maior perdat <lb/>duplã: illi numeri manebūt in eadem proportiõe <lb/>in qua antea ſe habebant. </s>
            <s xml:id="N12083" xml:space="preserve">Erunt enim tn fine <lb/>4. et .2. </s>
            <s xml:id="N12088" xml:space="preserve">Probatur prima pars ſuppoſitionis. </s>
            <s xml:id="N1208B" xml:space="preserve">et <lb/>ſint .a. numerus maior et .b.c. numerus minor īter <lb/>quos ſit proportio .g. et īuariato .a. perdat nume-<lb/>rus minor proportionē que eſt .b.c. ad .c. / et manife­             <cb chead="Capitulum ſecundum"/>             ſtum eſt /  in fine proportio īter illos numeros cõ-<lb/>ponetur ex proportione .a. ad .b.c. et .b.c. ad .c. et an­<lb/>tea proportio illa inter illos numeros puta .g. e-<lb/>rat preciſe proportio .a. ad .b.c: et modo ꝓportio <lb/>inter illos numeros cõponitur ex illa ꝓportione <lb/>g. que eſt .a. ad .b.c. et ex proportione .b.c. ad .c. / ergo <lb/>acquiſiuit ꝓportionē que eſt .b.c. ad .c. et illam de-<lb/>perdit quantitas minor .b.c. / igitur ꝓpoſitū. </s>
            <s xml:id="N120A5" xml:space="preserve">Se-<lb/>cunda pars facile deducitur ex prima et penultīa <lb/>ſuppoſitione: quoniam quantam ꝓportionem de­<lb/>perdit quantitas minor tantam acquirit ꝓportio <lb/>inter maiorem et minorem ſtante maiore: vt patet <lb/>ex priori parte iſtius ſuppoſitionis: et quantam ꝓ­<lb/>portionem deperdit quantitas maior tantam de­<lb/>perdit proportio inter ipſam et minorē quantita­<lb/>tem ſtante minore: vt patet ex penultima: igitur ſi <lb/>tantam ꝓportionem deꝑdat maior quantitas ſi-<lb/>cut deperdit minor quantitas: proportio illa in­<lb/>ter maiorē et minorem nullã proportionē acquirit <lb/>nec deperdit: et ſic in illas quantitates manet <lb/>eadem proportio. </s>
            <s xml:id="N120C2" xml:space="preserve">¶ Ex quo ſequitur /  ſi tantam <lb/>proportioneꝫ adequate acquirat quãtitas minor <lb/>quantam acquirit quãtitas maior: ſemper mane­<lb/>bit eadem proportio. </s>
            <s xml:id="N120CB" xml:space="preserve">Probatur / quia ſi ille quan­<lb/>titates illas proportiones equales quas acquiſi-<lb/>uerunt deperdant manebunt in eadem proportio­<lb/>ne in qua modo ſe habent: et illa eſt proportio in <lb/>qua ſe habebant ante acquiſitionem illarum pro­<lb/>portionum equaliū: igitur quando quãtitates ac­<lb/>quirunt ꝓpportiones equales ipſe manet in eadē <lb/>proportione in qua ſe habebant antea.</s>
          </p>
          <p xml:id="N120DC">
            <s xml:id="N120DD" xml:space="preserve">Undecima ſuppoſitio. </s>
            <s xml:id="N120E0" xml:space="preserve">Quecū pro­<lb/>portio eſt inter aliquos numeros ſiue quãtitates <lb/>talis eſt inter partes aliquotas conſimilis deno-<lb/>minationis. </s>
            <s xml:id="N120E9" xml:space="preserve">vt qualis eſt proportio inter .8. et .4. <lb/>talis eſt intermedietatē .8. et medietateꝫ .4. et quar­<lb/>tam .8. et quartam .4. </s>
            <s xml:id="N120F0" xml:space="preserve">Probatur / ſint duo numeri <lb/>primus .a.b.c. ſecundus .d.e.f. diuiſi in partes ali-<lb/>quotas eiuſedem denominationis puta primus in <lb/>a.b.c. et ſecundus in .d.e. et .f. / tunc dico /  qualis eſt <lb/>proportio .a.b.c. ad .d.e.f. talis eſt .c. ad .f. </s>
            <s xml:id="N120FB" xml:space="preserve">Quod ꝓ­<lb/>batur ſic. </s>
            <s xml:id="N12100" xml:space="preserve">et ſit inter illos numeros ſiue quantita­<lb/>tes .g. ꝓportio: et deperdat numerus maior .a. per­<lb/>tem aliquotam et minor .d. partem aliquotam cõ­<lb/>ſimilis denominationis: et manifeſtum eſt /  quã­<lb/>tam proportionem deperdit numerus maior tan­<lb/>tam deperdit numerus minor / vt patet ex prīo cor­<lb/>relario octaue ſuppoſitionis / ergo reſidui numeri <lb/>adhuc manent in eadē proportione puta .g. </s>
            <s xml:id="N12111" xml:space="preserve">Pa-<lb/>tet conſequentia ex ſeunda parte decime ſuppoſi­<lb/>tionis: et reſidui numeri puta .b.c. et .e.f. adhuc ma­<lb/>nent diuiſi in partes aliquotas eiuſdem denomi-<lb/>nationis / vt patet ex ſexta ſuppoſitiõe: perdat igi­<lb/>tur numerus maior .b. partem aliquotam et nume­<lb/>rus minor .e. partem aliquotam: et ſequitur /  eq̈­<lb/>lē ꝓportionē deperdit nūerꝰ maior et nūerꝰ minor / <lb/>vt iã argutū eſt: ergo reſidui numeri manent in ca­<lb/>dem proportione in qua antea ſe habebant puta <lb/>g. / vt patet ex ſecunda parte decime ſuppoſitionis <lb/>et reſidui numeri ſunt .c. et .f. / ergo c. et .f. ſe habent <lb/>in .g. proportione et .c. et .f. ſunt ꝑtes aliquote eiuſ­<lb/>dem denominationis datorum numerorum ſe ha­<lb/>bentium in .g. proportione: igitur in quacun por­<lb/>portione ſe habent alique quantitaters in eadem <lb/>ſe habent ſue partes aliquote eiuſdem denomina­<lb/>tionis / quod fuit probandum. </s>
            <s xml:id="N12136" xml:space="preserve">¶ Et hac ſuppoſi-             <pb chead="Secūde partis" file="0024" n="24"/>             tione ſequitur /  ſi duo numeri ſe habentes in ali­<lb/>qua proportione acquirãt ↄ̨tinuo partes aliquo­<lb/>tas eiuſdem denominationis: ſemper manebunt <lb/>in eadem proportione. </s>
            <s xml:id="N12144" xml:space="preserve">Patet / q2 vter illorū eq̈­<lb/>lem proportionem acquirit. </s>
            <s xml:id="N12149" xml:space="preserve">Patet / quia ſi vter <lb/>illorum numerorum illas partes aliquotas eiuſ-<lb/>dem denominationis deperderet eq̈lē ꝓportionē <lb/>deꝑderet / vt patet ex ſuppoſitione: igitur quando <lb/>acquirit equalem acquirit.</s>
          </p>
          <p xml:id="N12154">
            <s xml:id="N12155" xml:space="preserve">Duodecima ſuppoſitio. </s>
            <s xml:id="N12158" xml:space="preserve">Si aliquid <lb/>componitur ex duobus ſiue equalibus ſiue īequa­<lb/>libus: et quantum deperdit vnum illorum tantuꝫ <lb/>acquirit reliquum: compoſitum ex illis nichil ac-<lb/>quirit vel deperdit ſed ſemper manet equale. </s>
            <s xml:id="N12163" xml:space="preserve">Et <lb/>hanc peto quia nota eſt ex ſe.</s>
          </p>
          <note position="left" xml:id="N12168" xml:space="preserve">cal. de in­<lb/>duc. gra-<lb/>ſum et de <lb/>mo. 10.</note>
          <p xml:id="N12172">
            <s xml:id="N12173" xml:space="preserve">Prima concluſio </s>
            <s xml:id="N12176" xml:space="preserve">Omne compoſitū <lb/>ex duobus inequalibus inter que eſt mediuꝫ eſt du­<lb/>plum ad medium inter illa vt compoſitum ex .4. et <lb/>2. eſt duplum ad ternarium numerum qui mediat <lb/>inter illos </s>
            <s xml:id="N12181" xml:space="preserve">Probatur / ſint a.c. duo īequalia .a ma­<lb/>ius et .c. minus et ſit .b. medium inter .a.c. compoſi­<lb/>tum ex a.c. ſit .d. / tunc dico /  .d. eſt duplum ad .b. <lb/></s>
            <s xml:id="N12189" xml:space="preserve">Quod ſic probo / quia cū .b. ſit medium: equali dif­<lb/>ferentia diſtat ab extremis ex prima ſuppoſitiõe / <lb/>capio igitur illam differentiã ſiue exceſſum qua .a <lb/>excedit b. / et addo illam .c. / et manifeſtum eſt /  .a. et <lb/>b. manēt equalia: et ſimiliter .c. et .b. quia ipſi .c. ad <lb/>dictus eſt exceſſꝰ / quo excedebatur a.b. / igitur ag-<lb/>gregatum ex .a. et .c. componitur ex duobus equa­<lb/>lidus .b. adequate. </s>
            <s xml:id="N1219A" xml:space="preserve">igitur tale aggregatum eſt du­<lb/>plum ad .b. et tale aggregatum eſt .d. / igitur d. eſt <lb/>duplum ad .b. et .d. eſt in tantum quantum erat añ <lb/>variationem .a.c. / vt patet ex vltima ſuppoſitione / <lb/>igitut .d. ante variationem a.c. eſt duplum ad .b. / <lb/>quod fuit probandum.             <anchor type="note" xlink:href="note-0024-01" xlink:label="note-0024-01a"/>             </s>
            <s xml:id="N121AC" xml:space="preserve">¶ Ex hac concluſione ſequi­<lb/>tur:  mediū inter duo inequalia eſt medietas ag­<lb/>gregati ex eis. </s>
            <s xml:id="N121B3" xml:space="preserve">Patet / quia eſt ſubdupluꝫ / ergo me­<lb/>dietas.             <anchor type="note" xlink:href="note-0024-02" xlink:label="note-0024-02a"/>             </s>
            <s xml:id="N121BD" xml:space="preserve">¶ Sequitur ſecūdo /  medietas aggrega­<lb/>ti ex duobus inequalibus inter que eſt mediuꝫ: eq̈­<lb/>liter ab vtro illorum diſtat. </s>
            <s xml:id="N121C4" xml:space="preserve">Probatur / q2 medi­<lb/>etas illorum eſt equalis medio inter illa / vt patet <lb/>ex precedenti correlario: ergo ſequitur /  equali-<lb/>ter diſtat ab vtro. </s>
            <s xml:id="N121CD" xml:space="preserve">cum mediuꝫ ſit /  equaliter di­<lb/>ſtat ab extremis / vt patet ex prima ſuppoſitione. <lb/>             <anchor type="note" xlink:href="note-0024-03" xlink:label="note-0024-03a"/>             ¶ Sequitur tertio /  omnis numerus circū ſe poſi­<lb/>torum numerorum et equaliter ab eo diſtantium <lb/>eſt medietas. </s>
            <s xml:id="N121DD" xml:space="preserve">Quod ſi eoruꝫ fuerit medietas illos <lb/>ab eo eque diſtare conueniet. </s>
            <s xml:id="N121E2" xml:space="preserve">Probatur / ſint .a.c. <lb/>duo numeri inter quos mediat .b. ſit aggregatū <lb/>ex .a.c.d. / tunc .b. eſt medietas ipſius .d. / vt patet ex <lb/>ṗmo correlario et ſi .b. eſt medietas aggregati .a.c. <lb/>equaliter diſtat ab .a. et .c. / vt patet ex ſecundo cor-<lb/>relario / ergo .a.c. equaliter diſtant .a.b.             <anchor type="note" xlink:href="note-0024-04" xlink:label="note-0024-04a"/>             </s>
            <s xml:id="N121F4" xml:space="preserve">¶ Sequi-<lb/>tur quarto /  cõiuncte arithmetice medietatis me­<lb/>diis terminus extremorum ſimul iunctorum ē me­<lb/>dietas: vt captis his terminis .a.bc. continuo ꝓ-<lb/>portionabilibꝰ arithmetice .b. medius terminus <lb/>eſt medietas aggregati ex .a.c. </s>
            <s xml:id="N12201" xml:space="preserve">Patꝫ ex primo cor­<lb/>relario             <anchor type="note" xlink:href="note-0024-05" xlink:label="note-0024-05a"/>             </s>
            <s xml:id="N1220B" xml:space="preserve">Et hec ſit prima ꝓprietas arithmetice me­<lb/>dietatis </s>
            <s xml:id="N12210" xml:space="preserve">Et intelligas hanc proprietatem quan-<lb/>do tales termini continuo proportionaabiles hac ꝓ­<lb/>portionalitate fuerint impares: vel quantitates <lb/>continue. </s>
            <s xml:id="N12219" xml:space="preserve">Alias plerū non inuenires medium in­<lb/>ter tales terminos. </s>
            <s xml:id="N1221E" xml:space="preserve">ſicut inter .2.3.4.5             <anchor type="note" xlink:href="note-0024-06" xlink:label="note-0024-06a"/>             </s>
            <s xml:id="N12226" xml:space="preserve">¶ Sequitur <lb/>quinto /  diſpoſitis .3. terminis continuo ꝓportio­             <cb chead="Capitulum ſecundum"/>             nabilibꝰ arithmetice: aggregatū ex maxīo termīo <lb/>et mīmo ē due tertie aggregati ex illis tribꝰ termi­<lb/>nis: et diſpoſitis .5. continuo proportionalibus <lb/>arithmetice aggregatum ex maximo et minimo ē <lb/>due quinte:             <anchor type="note" xlink:href="note-0024-07" xlink:label="note-0024-07a"/>             et etiam aggregatum ex ſecūdo termi­<lb/>no et quarto eſt due quinte: et poſitis .7. aggrega­<lb/>tum ex maximo et minimo eſt due ſeptime ſimili-<lb/>ter aggregatum ex ſecundo et ſexto et ex tertio et <lb/>quinto. </s>
            <s xml:id="N12243" xml:space="preserve">et vniuerſaliter vbicū plures termini in <lb/>numero impari arithmetice continuo proportio­<lb/>nantur ſemper aggregatum ex quibuſcū duo-<lb/>bus equaliter diſtantibus a medio eſt due partes <lb/>aliquote. </s>
            <s xml:id="N1224E" xml:space="preserve">aggregati ex omnibus illis quarū par­<lb/>tium aliquotarum vtra denominatur a numero <lb/>impari a quo denominantur illi termini. </s>
            <s xml:id="N12255" xml:space="preserve">vt ſi ter­<lb/>mini ſint vndeci3 denominabuntur due vndecime <lb/>et ſi .13. due tridecime. </s>
            <s xml:id="N1225C" xml:space="preserve">Probatur hoc correlarium / <lb/>et ſigno tres terminos .a.b.c. / et arguo ſic / aggrega­<lb/>tum ex .a.c. eſt duplum ad .b. quia .b. eſt terminꝰ me­<lb/>dius inter .a.c. ſed aggregatum ex a.b.c. componi­<lb/>tur adeq̈te ex .b. et aggregato ex .a.c. duplo ad .b. / <lb/>vt patet ex concluſione: ergo b. eſt vna tertia totiꝰ <lb/>aggregati cum ter in illo contineatur adequate et <lb/>per conſequens aggregatum ex .a.c. due tertie / qḋ <lb/>fuit probandum. </s>
            <s xml:id="N1226F" xml:space="preserve">Item poſitis quin trrminis .a <lb/>b.c.d.e. aggregatum ex .a. et .e. eſt duplum ad ter-<lb/>minum medium .c. et ſimiliter aggregatum ex .b. et <lb/>d. / vt patet ex concluſioīe et totum aggregatum ex <lb/>illis quin terminis componitur adequate ex c. et <lb/>ex aggregato .a. et .e. et aggregato ex .b. et .d. et vtrū­<lb/> illorum aggregatorum eſt duplum ad .c. / vt pro­<lb/>batum eſt: ergo .c. eſt vna quinta totius aggrega-<lb/>ti ex illis quin terminis: cum quīquies in illo ag­<lb/>gregato contineatur: et per conſequens aggrega­<lb/>tum ex .a. et .e. eſt due quinte: et ſimiliter aggrega-<lb/>tum ex .b.d. cum ſit duplum ad .c </s>
            <s xml:id="N12288" xml:space="preserve">Et iſto modo pro­<lb/>babis capiendo quotcū alios terminos īpares <lb/>continuo arithmetice ꝓportionabiles. </s>
            <s xml:id="N1228F" xml:space="preserve">Et iſta ſit <lb/>ſecunda proprietas medietatis arithmetice.</s>
          </p>
          <div xml:id="N12294" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0024-01a" xlink:label="note-0024-01" xml:id="N12298" xml:space="preserve">p̄mū cor-<lb/>relarium</note>
            <note position="left" xlink:href="note-0024-02a" xlink:label="note-0024-02" xml:id="N122A0" xml:space="preserve">Secūduꝫ <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0024-03a" xlink:label="note-0024-03" xml:id="N122AA" xml:space="preserve">Tercium <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0024-04a" xlink:label="note-0024-04" xml:id="N122B4" xml:space="preserve">Quartū <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0024-05a" xlink:label="note-0024-05" xml:id="N122BE" xml:space="preserve">prima ꝓ­<lb/>prietas <lb/>medieta-<lb/>tis arith­<lb/>metice.</note>
            <note position="left" xlink:href="note-0024-06a" xlink:label="note-0024-06" xml:id="N122CC" xml:space="preserve">Quintū <lb/>correlari­<lb/>um.</note>
            <note position="right" xlink:href="note-0024-07a" xlink:label="note-0024-07" xml:id="N122D6" xml:space="preserve">Secūda <lb/>ꝓprietas <lb/>medietaſ <lb/>arithme-<lb/>tice.</note>
          </div>
          <p xml:id="N122E4">
            <s xml:id="N122E5" xml:space="preserve">Secunda concluſio </s>
            <s xml:id="N122E8" xml:space="preserve">Si duo nume-<lb/>ri a duobus numeris circum ſe poſitis equaliṫ di­<lb/>ſtent: illis coniunctis erunt equales. </s>
            <s xml:id="N122EF" xml:space="preserve">Quod ſi eis <lb/>equales fuerint: ab eis equidiſtare neceſſe eſt vt ca­<lb/>ptis his terminis .2.3.4.5. numerus quinarus et <lb/>binarius circunſtantes quaternarium et ternariū <lb/>equaliter ſimul iuncti equantur quaternario et ter­<lb/>nario ſimul iunctis et quia quinarius et binariꝰ <lb/>ſimul iuncti equales ſunt quaternario et binario <lb/>ſimul iuncti: ideo neceſſario ab illis equaliter di-<lb/>ſtant. </s>
            <s xml:id="N12302" xml:space="preserve">Probatur concluſio / et ſint .a.b.c.d.a.d. cir-<lb/>cunſtantes reliqui vero intermedii: et diſtat .a. ab <lb/>b.g. dnr̄a ita  .a. ſit maior numerus et eadem .g <lb/>dnr̄ia excedat .c. ipſum .d. / tunc dico /  aggregatū <lb/>ex .a.d. extremis numeris eſt equale aggregato ex <lb/>b.c. intermediis a quibus alii equaliter diſtant.</s>
          </p>
          <p xml:id="N1230F">
            <s xml:id="N12310" xml:space="preserve">Quod probatur ſic / et volo /  .a. perdat .g. dnr̄iaꝫ / <lb/>ita  fiat equale b. et .d. acquirat illam ita  fiat <lb/>equale .c. / et arguo ſic / facta tali variatione in a.d. <lb/>aggregatū ex .a.d. ↄ̨ponit̄̄ adeq̈te ex duobꝰ eq̈libꝰ <lb/>aliis duobus ex quibus adequate cõponitur ag-<lb/>gretatum ex .b.c. / igitur facta tali variatiõe in .a. <lb/>d. aggregatum ex .a.d. eſt equale aggregato ex .b <lb/>c. et illud aggregatum ex .a.d. facta tali variatio­<lb/>ne eſt equale aggregato .a.d. ante talem variatio­<lb/>nem / vt patet ex vltima ſuppoſitione: igitur aggre­<lb/>gatum ex .a.c. ante talem variationem eſt equale             <pb chead="Secūde partis" file="0025" n="25"/>             aggregato ex .b.c. / quod fuit probandum </s>
            <s xml:id="N1232C" xml:space="preserve">Sed iam <lb/>probo /  facta tali variatione aggregatum ex .a. <lb/>d. componitur ex duobus equalibus adequate il-<lb/>lis duobus ex quibus adequate componitur ag-<lb/>gregatum ex .b.c. / quia facta tali variatione .a. ef-<lb/>ficit̄̄ eq̈le ipſi b. et d. efficit̄̄ eq̈le ipſi .c. / vt ↄ̨ſtat: igit̄̄ <lb/>facta tali variatiõe aggregatū ex a.d. ↄ̨ponit̄̄ ade­<lb/>te ex duobus aqualibus illis duobus puta .b.c. ex <lb/>quibus componitur adequate aggregatum ex .b. <lb/>c. / quod fuit oſtendēdum. </s>
            <s xml:id="N12341" xml:space="preserve">Et ſic patet prima pars <lb/></s>
            <s xml:id="N12345" xml:space="preserve">Secūda pars probatur: et ſint a.b.c.d. quattuor <lb/>numeri a.d. circūſtantes .b. vero et .c. intermedii et <lb/>diſtet .a. ab .b.g. differētia et .c. excedat .d. / tunc dico / <lb/> ſi aggregatū ex .b.c. eſt equale aggregato ex .a. <lb/>d.b.c. equaliter diſtant ab .a.d. </s>
            <s xml:id="N12350" xml:space="preserve">Quod ſic proba-<lb/>tur / quia .a diſtat a.b.g. differentia: et .c.a.d. diſtat <lb/>eadē differētia. </s>
            <s xml:id="N12357" xml:space="preserve">igitur illi intermedii equaliter di­<lb/>ſtãt ab illis extremis. </s>
            <s xml:id="N1235C" xml:space="preserve">Probatur minor / quia ſi .c. <lb/>non eadem differentia diſtat a.d. ſicut a. ab .b. ca-<lb/>pio / igitur vnum terminū qui ſit .f. a quo .c. diſtet <lb/>eadē differentia qua .a. diſtat ab .b. / et tunc ex prio­<lb/>ri parte aggregatuꝫ ex a. et .f. eſt equale aggrega­<lb/>to ex .b.c. et per te aggregatum ex .a.d. eſt ēt equa-<lb/>le aggregato ex .b.c: igitur aggregatum ex .a.f. eſt <lb/>equale aggregato ex .a.d. / patet conſequentia ꝑ il­<lb/>laꝫ dignitatē que eidē tertio equantur inter ſe ſūt <lb/>equalia. </s>
            <s xml:id="N12371" xml:space="preserve">et vltra aggregatum ex .a.f. eſt equale ag­<lb/>gregato ex .a.d. / ergo ſequitur /  eodeꝫ cõmuni dē­<lb/>pto puta a. reſidua manebunt equalia videlicet .f. <lb/>et .d. et .c. diſtat .g. differētia qua a. diſtat ab .b. ab <lb/>ipſo .f. / ergo .c. diſtat .g. differentia ab ipſo .d. / et ſic <lb/>b.c. equaliter diſtant ab .a.d. numeris circunſtan-<lb/>tibus / quod fuit probandum. </s>
            <s xml:id="N12380" xml:space="preserve">Patet tamen conſe­<lb/>quentia / quia que ſunt equalia qualiter diſtant a <lb/>quouis tertio             <anchor type="note" xlink:href="note-0025-01" xlink:label="note-0025-01a"/>             </s>
            <s xml:id="N1238C" xml:space="preserve"><gap/> Hec cõcluſio in propria forma in­<lb/>ſtantiam patitur: ſed ſic poſita eſt / quia ita poni­<lb/>tur a iordano primo elementorum. </s>
            <s xml:id="N12394" xml:space="preserve">Nam iſti nu-<lb/>meri .8.8. equaliter diſtãt ab his duobus .4.4. in <lb/>iſta ſerie .4.8.8.4. / et tamen extrema coniūcta nõ <lb/>equantur mediis. </s>
            <s xml:id="N1239D" xml:space="preserve">Item iſti duo numeri .4.1. equa­<lb/>liter diſtant ab his duobus extremis .8.5. in iſta <lb/>ſeries .8.4.1.5. / et tamen medii iuncti non equãtur <lb/>extremis coniunctis / vt conſtat. </s>
            <s xml:id="N123A6" xml:space="preserve">Item illi numeri . <lb/>4. et .4. coniuncti equantur his numeris ſimul iun­<lb/>ctis .4. et .4. / et tamen duo intermedii non equali­<lb/>ter diſtant a duobus extremis: quia non diſtant. <lb/>             <anchor type="note" xlink:href="note-0025-02" xlink:label="note-0025-02a"/>             </s>
            <s xml:id="N123B6" xml:space="preserve">¶ Intellige igitur concluſionē in ſenſu in quo ma­<lb/>thematici eam intelligunt. </s>
            <s xml:id="N123BB" xml:space="preserve">puta /  ſi duo nume-<lb/>ri equaliter diſtēt a duobus numeris extrimis ita­<lb/> primus excedat ſecundum eadē differentia qua <lb/>tertius quartum: vel primus excedatur a ſecundo <lb/>ea differentia qua tertius exceditur a quarto illi <lb/>intermedii ſimul iuncti extremis copulatis equã-<lb/>tur. </s>
            <s xml:id="N123CA" xml:space="preserve"> ſi intermedii ab extremis diſtãtes ſimul iū­<lb/>cti extremis equantur ab extremis eos equidiſta­<lb/>re neceſſe eſt.             <anchor type="note" xlink:href="note-0025-03" xlink:label="note-0025-03a"/>             </s>
            <s xml:id="N123D6" xml:space="preserve">¶ Ex hac concluſione ſequitur arith­<lb/>metice medietatis diſiūcte quattuor terminis ab­<lb/>ſolute extrema ſimul iuncta collectis medii equa­<lb/>ri.             <anchor type="note" xlink:href="note-0025-04" xlink:label="note-0025-04a"/>             </s>
            <s xml:id="N123E4" xml:space="preserve">Et hec eſt tertia ꝓprietas mediedatis arithme­<lb/>tice. </s>
            <s xml:id="N123E9" xml:space="preserve">Patet hoc correlarium facile ex precedēti cõ­<lb/>cluſione </s>
            <s xml:id="N123EE" xml:space="preserve">Nam ſi quattuor termini proportionen­<lb/>tur arithmetice et diſiiuncte ea differētia que erit <lb/>inter primū et ſecundum. erit inter tertium et quar­<lb/>tū </s>
            <s xml:id="N123F7" xml:space="preserve">Quare medii equaliter diſtabunt ab extremis <lb/>coniunctis / igitur mediis equabuntur externa col­<lb/>lecta iuxta doctrinam concluſionis. </s>
            <s xml:id="N123FE" xml:space="preserve">Et dixi notã-             <cb chead="Capitulum ſecundum"/>             ter in correlario. </s>
            <s xml:id="N12404" xml:space="preserve">quattuor terminis quia ſi ponã­<lb/>tur plures termini non oportet illud verificari.</s>
          </p>
          <div xml:id="N12409" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0025-01a" xlink:label="note-0025-01" xml:id="N1240D" xml:space="preserve">īueſtigat̄̄ <lb/>itas ſe­<lb/>cūde con­<lb/>cluſionis <lb/>Iordanꝰ <lb/>.1. ele.</note>
            <note position="left" xlink:href="note-0025-02a" xlink:label="note-0025-02" xml:id="N1241D" xml:space="preserve">Senſus <lb/>ſecūde cõ­<lb/>cluſionis</note>
            <note position="left" xlink:href="note-0025-03a" xlink:label="note-0025-03" xml:id="N12427" xml:space="preserve">Primu <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0025-04a" xlink:label="note-0025-04" xml:id="N12431" xml:space="preserve">tertia ꝓ-<lb/>prietas <lb/>medieta­<lb/>tis arith­<lb/>metice.</note>
          </div>
          <p xml:id="N1243F">
            <s xml:id="N12440" xml:space="preserve">Quare inconſiderate aliqui illam proprietatem <lb/>abſolute ponūt. </s>
            <s xml:id="N12445" xml:space="preserve">Patet enim inſtantia in his ter­<lb/>minis .2.5.7.11.1.4. manifeſtum eſt enim /  aggre­<lb/>gatum ex extremis minus eſt aggregato ex inter-<lb/>mediis. </s>
            <s xml:id="N1244E" xml:space="preserve">Imo implicat aggregatum ex extremis <lb/>equari omnibus itermediis ſimul ſumptis cum <lb/>ſunt plures termini quattuor: quoniam ſuper ag­<lb/>gregatum ex extermis puta ex primo et vltimo ad­<lb/>dequatur aggregato ex ſecūdo et penultimo. </s>
            <s xml:id="N12459" xml:space="preserve">ergo <lb/>non aggregato ex omnibus intermediis quia il-<lb/>lud erit maiꝰ. </s>
            <s xml:id="N12460" xml:space="preserve">Si autem velis dicere ꝓprietatē il-<lb/>lam intelligi /  aggregatum ex ṗmo et vltimo ade­<lb/>quatur aggregato ex ſecūdo et penultimo: et etiã <lb/>equatur aggregato ex tertio et ante penultimo .etc̈ / <lb/>patet hoc eſſe falſum in datis terminis. </s>
            <s xml:id="N1246B" xml:space="preserve">Nã in il-<lb/>lis duo et .14. conſtituunt .1.6. tertius tñ et ante pe­<lb/>nultimus puta .7. et .10. conſtituunt .1.7. / igitur.</s>
          </p>
          <note position="right" xml:id="N12472" xml:space="preserve">Secūduꝫ <lb/>correlari­<lb/>um.</note>
          <p xml:id="N1247A">
            <s xml:id="N1247B" xml:space="preserve">¶ Sequitur ſecundo /  poſitis quattuor terminis <lb/>proportionabilibus arithmetice ſiue cõiuncte ſi-<lb/>ue diſiuncte aggregatum ex primo et vltimo ē me­<lb/>dietas aggregati ex omnibus ſimul et etiam ag-<lb/>gregatum ex ſecūdo. </s>
            <s xml:id="N12486" xml:space="preserve">et tertio eſt medietas totius <lb/>aggregati ex omnibus ſimul. </s>
            <s xml:id="N1248B" xml:space="preserve">Patet / quia illa ag­<lb/>gregata ſunt eq̈lia ex cõcluſione et adequate com­<lb/>ponunt aggregatū ex omnibus illis quattuor ter­<lb/>minis: igitur vtrum illorū aggregatum eſt me-<lb/>dietas aggregati ex omnibus illis terminis ſimĺ <lb/>ſumptis / quod fuit probãdum.             <anchor type="note" xlink:href="note-0025-05" xlink:label="note-0025-05a"/>             </s>
            <s xml:id="N1249D" xml:space="preserve">¶ Sequitur tertio / <lb/> poſitis ſex terminis ſi octo.             <anchor type="note" xlink:href="note-0025-06" xlink:label="note-0025-06a"/>             </s>
            <s xml:id="N124A7" xml:space="preserve">ſiue .10. et in quo-<lb/>cun numero pari cõtinuo proportionabilibus <lb/>arithmetice. </s>
            <s xml:id="N124AE" xml:space="preserve">aggregatum ex primo et vltimo et ag­<lb/>gregatum ex ſecundo et penultimo et aggregatū <lb/>ex tertio et ante penultimo / et ſic conſequenter eſt <lb/>pars aliquota aggregati ex omnibus illis ter-<lb/>minis denominata a numero ſubduplo ad nume-<lb/>rum parem in quo conſtituuntur tales termini. </s>
            <s xml:id="N124BB" xml:space="preserve">vt <lb/>ſi ſint ſex termini aggregatum ex primo et ſexto et <lb/>etiam aggregatum ex ſecundo et quinto et ex ter-<lb/>tio et quarto eſt vna tertia aggregati ex omnibus <lb/>illis ſex terminis: et ſi fuerint octo talia aggrega­<lb/>ta erunt quarte / q2 quarta denominatur a nume-<lb/>ro ſubduplo ad numerum octonarium. </s>
            <s xml:id="N124CA" xml:space="preserve">Proba-<lb/>tur hoc / et ſint ſex termini .a.b.d.c.e.f. ↄ̨tinuo arith­<lb/>metice proportionabiles. </s>
            <s xml:id="N124D1" xml:space="preserve">et arguitur ſic / aggrega­<lb/>tum ex a.f. eſt equale aggregato ex .b.e. / vt patet ex <lb/>concluſione / quia illa extrema equaliter diſtãt ab <lb/>illis mediis et eadem ratione aggregatum ex .c.d <lb/>eſt equale aggregato ex b.e. / igitur ibi ſūt tria ag­<lb/>gregata omnino equalia: et illa componunt ag-<lb/>gregatum ex omnibus illis .6. adequate: igitur qḋ­<lb/>libet illorum aggregatorum eſt vna tertia totius <lb/></s>
            <s xml:id="N124E3" xml:space="preserve">Et iſto modo probabis quando fuerint octo ter-<lb/>mini / quia inuenies ibi quattuor aggregata equa­<lb/>lia: et quando decem inuenies quin. </s>
            <s xml:id="N124EA" xml:space="preserve">Et ſic dein-<lb/>ceps inuenies talia aggregata equalia in ſubdu­<lb/>plo numero ad numerum terminorum: quoniam <lb/>ſemper pro quolibet tali aggregato capis duos <lb/>terminos / et per conſequens dualitatem illorum <lb/>terminorum. </s>
            <s xml:id="N124F7" xml:space="preserve">Modo in quolibet numero pari in <lb/>duplo pauciores dualitates reperiūtur quam vni­<lb/>tates. </s>
            <s xml:id="N124FE" xml:space="preserve">Et ſic patet correlarium.             <anchor type="note" xlink:href="note-0025-07" xlink:label="note-0025-07a"/>             </s>
            <s xml:id="N12506" xml:space="preserve">¶ Sequitur quar­<lb/>to /  ſint quattuor termini non continuo propor-<lb/>tionabiles arithmetice continuo tamen minores <lb/>et minores continuo ſe excedētes minori et mino-             <pb chead="Secunde partis." file="0026" n="26"/>             ri differentia: aggregatum ex extremis eſt maius <lb/>aggregato ex mediis: et eſt maius quaꝫ medietas <lb/>aggregati ex illis quatnor terminis.             <anchor type="note" xlink:href="note-0026-01" xlink:label="note-0026-01a"/>             </s>
            <s xml:id="N1251D" xml:space="preserve">vt captꝪ his <lb/>terminis: 12.9.7.6. dico /  aggregatum ex .12. et. 6 <lb/>eſt maius aggregato ex .9. et .7. et eſt maius quam <lb/>medietas illorum quatuor terminorum coniūcto­<lb/>rum. </s>
            <s xml:id="N12528" xml:space="preserve">Probatur / ſint quatuor termini a.b.c.d. con­<lb/>tinuo minores et minores continuo minori et mi­<lb/>nori differentia ſeſe excedentes: et dico /  aggre-<lb/>gatum ex a. et .d. eſt maius aggregato ex .b. et .c.</s>
          </p>
          <div xml:id="N12531" level="4" n="3" type="float">
            <note position="right" xlink:href="note-0025-05a" xlink:label="note-0025-05" xml:id="N12535" xml:space="preserve">Tertium <lb/>correlari­<lb/>um.</note>
            <note position="right" xlink:href="note-0025-06a" xlink:label="note-0025-06" xml:id="N1253F" xml:space="preserve">Cal. ḋ 10 <lb/>ele.</note>
            <note position="right" xlink:href="note-0025-07a" xlink:label="note-0025-07" xml:id="N12547" xml:space="preserve">Quartū <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0026-01a" xlink:label="note-0026-01" xml:id="N12551" xml:space="preserve">calcu. de <lb/>10. ele. cir­<lb/>ca prin.</note>
          </div>
          <p xml:id="N1255B">
            <s xml:id="N1255C" xml:space="preserve">Quod ſic probatur / quia ſi c. excederet d. tãta dif-<lb/>ferentia quanta a. excedit .b. / tunc aggregatum ex <lb/>a. et d. eſſet equalis aggregato ex b.c. / vt patet ex <lb/>concluſione: ſed modo c. excedit d. minori exceſſu / <lb/>igitur d. eſt maius quam eſſet tunc et a. eſt equale: <lb/>igitur aggregatum ex a.d. eſt maius quã eſſet tūc <lb/>quia componitur ex vno tanto ex quanto / tunc cõ­<lb/>poneretur et ex vno altero maiore quã tunc et hoc <lb/>adequate: igitur modo eſt maius quam tunc: ſed <lb/>tunc eſſet equale aggregato ex b. et c. / ergo modo ē <lb/>maius aggregato ex b. et c. / quod fuit probandum <lb/></s>
            <s xml:id="N12574" xml:space="preserve">Et ex hoc patet ſecunda pars correlarii / quoniam <lb/>aggregatum ex omnibus illis terminis componi­<lb/>tur ex duobus inequalibus adequate puta ex ag-<lb/>gregato ex a. et d. et aggregato ex b. et c. et aggre­<lb/>gatum ex a. et d. eſt maius aggregato ex b. et c. / igi­<lb/>tur aggregatum ex a. et d. eſt maius quam medie-<lb/>tas totius aggreti ex illis quatuor terminis </s>
            <s xml:id="N12583" xml:space="preserve">Pa­<lb/>tet hec conſequētia / q2 qñcun aliquid componi-<lb/>tur ex duobus inequalibus adequate maius illo-<lb/>rum eſt magis quam medietas totius / vt facile de­<lb/>monſtrabitur.             <anchor type="note" xlink:href="note-0026-02" xlink:label="note-0026-02a"/>             </s>
            <s xml:id="N12593" xml:space="preserve">¶ Sequitur quinto /  ſi ſint ſex ter­<lb/>mini continuo minores minori exceſſu ſeſe con-<lb/>tinuo excedentes aut .8. aut .10. aut in quouis nu-<lb/>mero pari: aggregatuꝫ ex primo et vltimo eſt ma­<lb/>ius quam pars aliquota denominata a numero <lb/>ſubduplo ad numerum illorum terminorum: et ag­<lb/>gregatum ex duobus terminis mediis et īmedia-<lb/>tis eſt minus quam talis pars aliquota totius ag­<lb/>gregati ex omnibus illis terminis. </s>
            <s xml:id="N125A6" xml:space="preserve">vt .19.14.10.7. <lb/>5.4. captis aggregatum ex .19. et .4. eſt maius quã <lb/>vna tertia aggregati ex omnibus illis ſex termīs <lb/>et aggregatum ex .10. et .7. eſt minus / vt patet cal-<lb/>culanti </s>
            <s xml:id="N125B1" xml:space="preserve">Probatur correlarium / ſint ſex termini a <lb/>b.c.d.e.f. continuo minori et minori differentia ſe­<lb/>ſe excedentes. </s>
            <s xml:id="N125B8" xml:space="preserve">et dico /  aggregatuꝫ ex a. et f. ē ma­<lb/>ius quam tertia aggregati ex omnibus illis ter-<lb/>minis et aggregatum ex c.d. terminis mediis et ī-<lb/>mediatis eſt minus quam tertia totius aggrega-<lb/>ti ex omnibus ſex. </s>
            <s xml:id="N125C3" xml:space="preserve">Probatur / quia totum illud ag­<lb/>gregatum ex omnibus illis ſex componixur ex tri­<lb/>bus inequalibus adequate quorum primum ē ma­<lb/>ius ſecundo et ſecundum maius tertio / igitur pri-<lb/>mum eſt maius quam tertia totius: et tertium mi-<lb/>nus quam tertia: </s>
            <s xml:id="N125D0" xml:space="preserve">Patet hec conſequentia quoni-<lb/>am ſi primuꝫ eſſet vna tertia oporteret /  alia duo <lb/>eſſent due tertie / et ſic non eēt vtrū alioꝝ duorum <lb/>minus primo: et ſi primum eſſet minus qnaꝫ tertia <lb/>oporteret /  aliquod aliorū eſſet maius primo: q2 <lb/>alias illa tria non facerent tres tertias illius to-<lb/>tius: et ſic nõ adequate componerēt totū. </s>
            <s xml:id="N125DF" xml:space="preserve">Et eodē <lb/>modo patet /  tertium eſt minus quam tertia to-<lb/>tius quia ſi eſſet tertia vel maius tertia oporteret / <lb/> vel reliqua duo eſſent due tertie vel aliquod illo­<lb/>rum minus eo quod tameu eſt falſum. </s>
            <s xml:id="N125EA" xml:space="preserve">Et ex conſe­<lb/>quenti arguitur: primum illorum eſt maius quam             <cb chead="Capitulum ſecundū."/>             tertia totius et tertium minus quam tertia ſed pri­<lb/>mum illormm eſt aggregatum ex a. et f. et tertium <lb/>eſt aggregatum ex c.d. / igitur aggregatum ex a.f: <lb/>eſt maius quam tertia illius totius et aggregatū <lb/>ex c.d. minus. </s>
            <s xml:id="N125FA" xml:space="preserve">Couſequentia patet ex ſe </s>
            <s xml:id="N125FD" xml:space="preserve">Sed reſtat <lb/>ſimul probare aggregatum ex omnibus illis ſex <lb/>terminis cõponi ex tribus inequalibus quoruꝫ pri­<lb/>mum eſt maius ſecundo 2. ſecundū maius tertio et <lb/> primum illorum eſt aggregatū ex a. et f. et ſccun­<lb/>dū aggregatū ex b. et e. etc̈. quia aggregatum ex il­<lb/>lis ſex terminis cõponitur adequate ex aggregato <lb/>ex a. et f. et aggregato ex b. et e. et aggregato ex c. et <lb/>d. / que ſunt tria aggregata partialia / vt conſtat: et <lb/>aggregatum ex a. et .f. eſt maius aggregato ex b. et <lb/>e. etc̈. / igitur propoſitū. </s>
            <s xml:id="N12614" xml:space="preserve">Arguitur minor / quia ſi per <lb/>tantã dnr̄aꝫ ſiue tantū exceſſū e. excederet f. ſicut a. <lb/>excedit b. / tunc aggregatum ex a. et f. eēt equale ag­<lb/>gregato ex b. et e. / vt patet ex ſecunda concluſione: <lb/>ſed modo aggregatum ex a. et f. eſt maius / quã tūc <lb/>quia vna pars eius v3 f. eſt maior / quam tunc et re-<lb/>liqua equalis puta a. quia per minus exceditur f. <lb/>ab vno tertio / quam tunc ab eodem / igitur aggre-<lb/>gatum ex a. et f. eſt maius aggregato ex b. et e. / et ea­<lb/>dem ratione probabitur /  aggregatum ex b. et e <lb/>eſt maius aggregato ex c.d. / quod fuit ꝓbandum. <lb/></s>
            <s xml:id="N1262C" xml:space="preserve">Et equali ratione probabis /  cuꝫ dantur octo ter­<lb/>mini continuo per minus et minus ſe excedentes: <lb/>et continuo minores et minores:  tunc aggrega­<lb/>tum ex primo et vltimo eſt maius ꝙ̄ quarta aggre­<lb/>gati ex omnibus: et aggregatum ex quarto et quī­<lb/>to eſt minus quam quarta. </s>
            <s xml:id="N12639" xml:space="preserve">Et ſi ſint decem aggre­<lb/>gatum ex primo et vltimo eſt maius quaꝫ vna quī­<lb/>ta totius: et aggregatum ex quinto et ſexto eſt mi­<lb/>nus quam quinta totius: et ſic conſequenter: quia <lb/>tale aggregatum ex octo talibus terminis cõpo-<lb/>nitur ex quatuor quorum quodlibet eſt cuilibet al­<lb/>teri inequale. </s>
            <s xml:id="N12648" xml:space="preserve">puta primū maius ſecundo et ſecun­<lb/>dū maius tertio / et ſic ↄ̨ſequenter: et primū illoꝝ eſt <lb/>aggregatū ex primo et vltimo et ſecundū ex ſecun­<lb/>do et ſeptimo. </s>
            <s xml:id="N12651" xml:space="preserve">et tertiū ex tertio et ſexto et quartum <lb/>ex quarto et quinto. </s>
            <s xml:id="N12656" xml:space="preserve">igitur maximū illorum puta <lb/>aggregatū ex primo et vltimo eſt maius quã q̈r-<lb/>ta et minimū puta aggregatū eſt quarto et quinto <lb/>eſt minus quã quarta: </s>
            <s xml:id="N1265F" xml:space="preserve">Et ſic in omnibus aliis oꝑa­<lb/>beris. </s>
            <s xml:id="N12664" xml:space="preserve">Patet ergo correlariū.             <anchor type="note" xlink:href="note-0026-03" xlink:label="note-0026-03a"/>             </s>
            <s xml:id="N1266C" xml:space="preserve">¶ Sexto ſequitur /  <lb/>ſi ſint plures termini in numero pari conſtituti cõ­<lb/>tinuo maiores et maiores continuo maiori et ma­<lb/>iori exceſſu ſe excedentes: aggregatum ex primo et <lb/>vltimo eſt maius quã pars aliquota denoīata a <lb/>numero ſubduplo ad numerū in quo illi termini <lb/>conſtituuntur et aggregatū ex duobus mediis ī-<lb/>mediatis equaliter diſtantibus ab extremis: mi-<lb/>nus quam pars aliquota denoīata ab eodem nu­<lb/>mero ſubduplo. vt .4.5.7.10.14.19. captis: aggre-<lb/>gatum ex extremis puta ex .4. et .19. eſt maius quã <lb/>tertia totius aggregati ex omnibus illis: et aggre­<lb/>gatum ex .7. et .10. eſt minus quã tertia totius. </s>
            <s xml:id="N12687" xml:space="preserve">Hoc <lb/>correlariuꝫ ex p̄cedenti ſuã ſortitur demonſtratio­<lb/>nē et quidē euidenter quoniã in eiſdē terminis de­<lb/>monſtratur ordine prepoſtero ſe habentibus: pu-<lb/>ta in iſto incipiendo a minoribus in precedenti ve­<lb/>ro a maioribus.             <anchor type="note" xlink:href="note-0026-04" xlink:label="note-0026-04a"/>             </s>
            <s xml:id="N12699" xml:space="preserve">¶ Sequitur ſeptimo /  ſi ſint plu­<lb/>res termini numero pari conſtituti continuo mi-<lb/>nores et minores maiori et maiori exceſſu ſeſe cõ-<lb/>tinuo excedenter: aggregatuꝫ ex primo et vltimo <lb/>erit minor pars aliquota totius aggregati ex oī-             <pb chead="Secūde partis" file="0027" n="27"/>             bus quã ſit pars aliquota denoīata a numero ſub­<lb/>duplo ad numerum parem in quo ſunt conſtituti <lb/>dati termini: et aggregatum ex duobus mediis <lb/>immediatis equaliter diſtantibus ab extremis <lb/>eſt maius quaꝫ talis pars aliquota. </s>
            <s xml:id="N126B1" xml:space="preserve">vt captis his <lb/>terminis .12.11.9.6. aggregatum ex .12. et ſex. eſt <lb/>minus quam medietas aggregati oīm illorū me­<lb/>dietas denomīatur a numero binario qui eſt ſub­<lb/>duplus ad numerū quaternariū in quo illi termi-<lb/>ni ſunt conſtituti: et aggregatum ex .11. et .9. eſt ma­<lb/>ius quã medietas. </s>
            <s xml:id="N126C0" xml:space="preserve">Probatur: et ſint a.b.c.d.e.f.6. <lb/>termini continuo minores et minores maiori con­<lb/>tinuo dnr̄ia ſeſe excedentes: et q2 illi ſunt conſtitu­<lb/>ti in numero ſenario dico /  aggregatū ex primo <lb/>et vltimo eſt minor pars totius ꝙ̄ pars aliquota <lb/>eiuſdem totius denoīata a numero ſubduplo ad <lb/>ſenarium que eſt vna tertia. / et aggregatū ex duo­<lb/>bus intermediis īmediatis equaliter diſtantibus <lb/>ab extremis puta c.d. eſt maius quã talis pars ali­<lb/>quota totius puta quã tertia. </s>
            <s xml:id="N126D5" xml:space="preserve">Probat̄̄ / q2 tale ag­<lb/>gregatū cõponitur ex tribus partialibus aggre­<lb/>gatis adequate puta ex aggregato ex a. et f. et ex <lb/>aggregato ex b. et e. et aggregato et c. et d. et ag-<lb/>gregatū ex a. et f. eſt minus ſecundo aggregato et <lb/>ſecundū minus tertio. </s>
            <s xml:id="N126E2" xml:space="preserve">igitur aggregatū ex a. et f. <lb/>eſt minus quaꝫ tertia totius: et aggregatū ex c.d. <lb/>maius quã tertia totius. </s>
            <s xml:id="N126E9" xml:space="preserve">Patet hec conſequentia / <lb/>quia quando aliquid cõponitur ex tribus quoruꝫ <lb/>quodlibet cuilibet alteri eſt inequale: maius illoꝝ <lb/>eſt maius quã tertia: et ſic dices quando cõponitur <lb/>ex quatuor adequate quorū quodlibet cuilibet al­<lb/>teri eſt īequale: et ex .5. et ex .6. / et ſic deinceps vt po­<lb/>ſtea oſtendetur. </s>
            <s xml:id="N126F8" xml:space="preserve">Iam probo minorem videlicet /  <lb/>aggregatū ex a. et f. eſt minus ſecundo aggrega-<lb/>to puta ex b. et e. / q2 ſi tanto exceſſu. </s>
            <s xml:id="N126FF" xml:space="preserve">et dnr̄a a exce-<lb/>deret b. quanta e. excedit f. / tunc aggregatū ex a. et <lb/>f. eſſet equale aggregato ex b. et e. / vt patet ex ſecū­<lb/>da concluſione: ſed modo aggregatū ex a.f. eſt mi­<lb/>nus quã tunc: quia a. eſt tãtum ſicut tunc et f. eſt mi­<lb/>nus quã tunc: quia maiori dnr̄ia exceditur modo <lb/>quã tunc ab eodē puta e. / igitur aggregatū ex a. et <lb/>f. eſt minus quã aggregatū ex b. et e. / et eadē ratio­<lb/>ne ꝓbabis /  aggregatū ex b. et e. eſt minus aggre­<lb/>gato ex c. et d. / et ſic patet minor et totū correlariū / <lb/>quoniã et ſi iſta ſit particularis demonſtratio tñ <lb/>dat formã vniuerſaliter ꝓbandi quibuſcū ter-<lb/>minis paribus conſtitutis. </s>
            <s xml:id="N1271A" xml:space="preserve">¶ Similia correlaria <lb/>poteris inferre q̇buſcun termīs īpari nūero cõ­<lb/>ſtitutis ſiue continuo maioribus et maioribus ma­<lb/>iori continuo dnr̄a ſe excedentibus: ſiue eocontra <lb/>etc. / que omnia predictorum auxilio facile monſtra­<lb/>ri poſſunt.</s>
          </p>
          <div xml:id="N12727" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0026-02a" xlink:label="note-0026-02" xml:id="N1272B" xml:space="preserve">5. correla­<lb/>riū.</note>
            <note position="right" xlink:href="note-0026-03a" xlink:label="note-0026-03" xml:id="N12733" xml:space="preserve">6. corre-<lb/>lariū</note>
            <note position="right" xlink:href="note-0026-04a" xlink:label="note-0026-04" xml:id="N1273B" xml:space="preserve">7. corre-<lb/>lariū</note>
          </div>
          <note position="left" xml:id="N12743" xml:space="preserve">1. ele. ior. <lb/>3. con. <lb/>4. ꝓprie­<lb/>tas arith­<lb/>metice <lb/>medieta­<lb/>tis.</note>
          <p xml:id="N12753">
            <s xml:id="N12754" xml:space="preserve">Tertia concluſio in hac medietate <lb/>arithmetica / quod ſub extremis continetur cum q̈­<lb/>drato differentie. </s>
            <s xml:id="N1275B" xml:space="preserve">equale eſt quadrato medii. </s>
            <s xml:id="N1275E" xml:space="preserve">Hec <lb/>concluſio eſt tertia decimi elementorum iordani et <lb/>breuitatis cauſa hic non demonſtratur / quia eius <lb/>demõſtratio prolixa eſt eo  dependet ex decima <lb/>quarta et decima nona primi elementorum eiuſ-<lb/>dem iordani. </s>
            <s xml:id="N1276B" xml:space="preserve">¶ Aduerte tamen pro intelli­<lb/>gentia contextus ipſius concluſionis /  illud dici­<lb/>tur contineri. </s>
            <s xml:id="N12772" xml:space="preserve">ſub extremis arithmetice ꝓportio-<lb/>nalitatis quod reſultat ex ductu vnius extremi in <lb/>alterum: vt numerus octonarius continetur ſub <lb/>extremis huius ꝓportionalitatis .4.3.2. quia du-<lb/>cendo .4. per .2. reſultant octo. </s>
            <s xml:id="N1277D" xml:space="preserve">Bis em̄ .4. ſūt octo             <cb chead="Capitulum ſecundum"/>             </s>
            <s xml:id="N12783" xml:space="preserve">Item .32. continētur ſub extremis huius ꝓportio­<lb/>nalitatis arithmetice .8.7.4. qm̄ ducendo .8. per . <lb/>4. reſultant: 32. </s>
            <s xml:id="N1278A" xml:space="preserve">Quater enim octo ſunt .32.             <anchor type="note" xlink:href="note-0027-01" xlink:label="note-0027-01a"/>             </s>
            <s xml:id="N12792" xml:space="preserve">¶ Ad­<lb/>uerte vlterius /  quadratū medii termini eſt illud <lb/>quod reſultat ex ductu medii termini in ſeipſuꝫ:             <anchor type="note" xlink:href="note-0027-02" xlink:label="note-0027-02a"/>             vt <lb/>numerus nouenarius eſt quadratum medii in hac <lb/>arithmetica proportionalitate .4.3.2. quia reſul-<lb/>tat ex ductu numeri ternarii in ſeipſum. </s>
            <s xml:id="N127A4" xml:space="preserve">Nam ter <lb/>tria ſunt nouē. </s>
            <s xml:id="N127A9" xml:space="preserve">¶ Quadratū autē differentie eſt il­<lb/>lud quod reſultat ex ductu differentie in ſeipſum: <lb/>vt in hac arithmetica medietate .8.6.4. numerus <lb/>quaternarius eſt quadratū dnr̄e. </s>
            <s xml:id="N127B2" xml:space="preserve">Nã differentia <lb/>eſt numerus binarius / vt conſtat. </s>
            <s xml:id="N127B7" xml:space="preserve">Binarius enim <lb/>ductus in ſeipſum quaternarium educit / vt cõſtat. <lb/></s>
            <s xml:id="N127BD" xml:space="preserve">¶ His dictis ſenſus concluſionis eſt talis. </s>
            <s xml:id="N127C0" xml:space="preserve">Nume-<lb/>rus reſultans ex ductu vnius extremi in alterū in <lb/>medietate arithmetica continua cum numero re-<lb/>ſultante ex ductu differentie in ſeipſam eſt equalis <lb/>numero qui fit ex ductu medii in ſeipſū: vt in hac <lb/>medietate .8. que fiunt ex ductu vnius extremi in al­<lb/>terum iuncto quaternario numero qui fit ex dictu <lb/>differentie in ſeipſaꝫ ſunt equalia .36. que fiunt ex <lb/>ductu ſenarii medii termini in ſeipſum.</s>
          </p>
          <div xml:id="N127D3" level="4" n="5" type="float">
            <note position="right" xlink:href="note-0027-01a" xlink:label="note-0027-01" xml:id="N127D7" xml:space="preserve">quadra-<lb/>tū medii</note>
            <note position="right" xlink:href="note-0027-02a" xlink:label="note-0027-02" xml:id="N127DF" xml:space="preserve">q̈dratuꝫ <lb/>dnr̄ie.</note>
          </div>
          <note position="right" xml:id="N127E7" xml:space="preserve">4. cõclu-<lb/>ſio prīa <lb/>ꝓprietaſ <lb/>medieta­<lb/>tis geo-<lb/>metrice.</note>
          <p xml:id="N127F5">
            <s xml:id="N127F6" xml:space="preserve">Quarta concluſio in medietate geo-<lb/>metrica q̈tuor terminis conſtituta ſi primus ad ſe­<lb/>cundū ſicut tertius ad quartum: ita primus ad ter­<lb/>tiū ſicut tertius ad quartū ſe habeat neceſſe eſt: vt <lb/>quia ſicut ſe habent octo ad quatuor ita ſe habēt <lb/>ſex. ad .tria. / conſequens eſt /  ſicut ſe habent .octo <lb/>ad .ſex. ita quatuor ad tria. </s>
            <s xml:id="N12805" xml:space="preserve">Probatur / ſint a.b. <lb/>c.d. quatuor termini in medietate geometrica: et <lb/>habeat ſe a. ad .b. ſicut c. ad d. / tūc dico /  ſicut ſe hꝫ <lb/>a. ad .c. ita b. ad d. </s>
            <s xml:id="N1280E" xml:space="preserve">Qḋ ſic ꝓbat̄̄ et ṗmo ī nūerꝪ / q2 ſi <lb/>ſicut ſe habet a. ad b. ita .c. ad .d.b. eſt pars vel par­<lb/>tes aliquote reſpectu a. eiuſdem denoīationis ſi-<lb/>cut d. ipſius c. et vltra b. eſt pars aliquota vel par­<lb/>tes aliq̊te eiuſdē denoīationis reſpectu a. ſicut d. <lb/>reſpectu c. / ergo ſicut ſe habet a. ad c. ita b. ad d. / qḋ <lb/>fuit probandū. </s>
            <s xml:id="N1281D" xml:space="preserve">Secunda conſequētia patet ex vn-<lb/>decima ſuppoſitione huius capitis: et prima ptꝫ <lb/>ex hoc / quod inferius probabitur. </s>
            <s xml:id="N12824" xml:space="preserve">Si aliqui duo <lb/>numeri maiores habent ↄ̨ſimiles proportiones <lb/>ad duos minores: illi minores numeri ſūt partes <lb/>aliquote maiorū conſimilis denoīationis. </s>
            <s xml:id="N1282D" xml:space="preserve">Et ſit <lb/>hec prima proprietas geometrice medietatis.</s>
          </p>
          <p xml:id="N12832">
            <s xml:id="N12833" xml:space="preserve">Probatur iaꝫ vniuerſaliter / ſint a.b.c.d. quatuor <lb/>termini in hac medietate geometrica conſtituti ſi­<lb/>ue continuo ꝓportionabiles, ſiue diſcontinue, ſi-<lb/>ue proportione rationali, ſiue irrationali. </s>
            <s xml:id="N1283C" xml:space="preserve">et ipſi-<lb/>us a. ad b. ſit f. proportio: et ſimiliter ipſius c. ad <lb/>ipſum d. ſit f. proportio: et ſit a. ad .c.g. ꝓportio. </s>
            <s xml:id="N12843" xml:space="preserve">et <lb/>tunc dico /  etiam b. ad d. eſt g. proportio. </s>
            <s xml:id="N12848" xml:space="preserve">Quod <lb/>probatur ſic / et capio ꝓportionem g. / que eſt a. ad <lb/>c. / et volo /  a deperdat ꝓportioneꝫ f. quam habet <lb/>ad b. ita  in fine maneat equale ipſi b. / vt oportet <lb/>et c. perdat eandem proportionem f. quam ex hy-<lb/>potheſi habet ad ipſum d. ita  in fine maneat eq̈­<lb/>le ipſi d. / et arguo ſic. </s>
            <s xml:id="N12857" xml:space="preserve">huius ꝓportionis g. que eſt a <lb/>ad c. equalem omnino ꝓportionē deperdit termi-<lb/>nus maior ſicut minor: quia vter f. proportioneꝫ / <lb/>vt patet ex hypotheſi: igitur facta tali diminutio­<lb/>ne adhuc manet inter reſiduum maioris termini et <lb/>minoris. </s>
            <s xml:id="N12864" xml:space="preserve">eadem proportio g. / vt patet ex ſecunda <lb/>parte decime ſuppoſitionis ſecundi capitis ſecun­<lb/>de partis ſed reſiduū maioris termini eſt b. et reſi­<lb/>duū mīoris d. / vt pꝫ ex hypotheſi: igit̄̄ b. ad d. ē g. ꝓ­             <pb chead="Secūde partis" file="0028" n="28"/>             portio / qḋ fuit ꝓbãdū. </s>
            <s xml:id="N12872" xml:space="preserve">Et ſic ptꝫ ↄ̨cluſio gñaliter.</s>
          </p>
          <note position="left" xml:id="N12875" xml:space="preserve">1. correl. <lb/>ſcḋa ꝓṗe­<lb/>tas medi­<lb/>etatꝪ gro­<lb/>trice.</note>
          <p xml:id="N12881">
            <s xml:id="N12882" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  conſtitu-<lb/>tis quatuor terminis in hac medietate ſicut ag-<lb/>gregatum ex primo et ſecundo ad ſecundū ita ag­<lb/>gregatū ex tertio et quarto ad quartū vt conſtitu­<lb/>tis his quatuor terminis .8.4.6.3. ſicut ſe habent <lb/>8. et .4. ad .4. ita .6. et .3. ad .3. </s>
            <s xml:id="N1288F" xml:space="preserve">Probatur / et ſint q̈-<lb/>tuor termini in hac medietate geometrica ꝓpor-<lb/>tionabiles a.b.c.d. / dico /  qualis eſt ꝓportio .ab. <lb/>ad b. talis eſt .cd. ad d. </s>
            <s xml:id="N12898" xml:space="preserve">Quod probatur ſic et vo­<lb/>lo /  b. addatur ipſi a. et d. ipſi c. / et arguo ſic / ſicut <lb/>ſe habet a. ad b. ita c. ad .d. / ergo b. eſt talis pars ali­<lb/>quota vel partes aliquote et eiuſdem denomina-<lb/>tionis reſpectu a. qualis eſt d. reſpectu c. (et proce­<lb/>das a maioribus verſus minores) et b. additur ip­<lb/>ſi a. et d. ipſi .c. / igitur equalem ꝓportionem acqui­<lb/>rit a. ſupra ſe ſicut c. ſupra ſe </s>
            <s xml:id="N128A9" xml:space="preserve">Patet conſequentia <lb/>ex correlario vndecime ſuppoſitionis: et eandeꝫ ꝓ­<lb/>portionē quã acquiſiuit a. ſupra ſe acquiſiuit pro­<lb/>portio ipſius a. ad b. et ſimiliter eam quam acqui­<lb/>ſiuit c. ſupra ſe acquiſiuit ꝓportio ipſius c. ad d. / <lb/>vt patet ex probatione none ſuppoſitionis / igitur <lb/>facta tali acquiſitione qualis eſt proportio .ab. <lb/>ad b. talis eſt .cd. ad d. / quod fuit ꝓbandum </s>
            <s xml:id="N128BA" xml:space="preserve">Pa-<lb/>tet conſequentia / quia ꝓportio a. ad b. eſt equa-<lb/>lis proportioni c. ad d. et equalem ꝓportionem ac­<lb/>quirunt ille due proportiones / igitur ī fine manēt <lb/>eq̈les / q2 ſi equalibus eq̈lia addas etc. ſꝫ in fine vna <lb/>illaꝝ ꝓportionū ē .ab. ad .b. et alia ē .cd. ad d. / er-<lb/>go proportio .ab. ad .b. eſt equalis ꝓportioni .cd. <lb/>ad d. </s>
            <s xml:id="N128CB" xml:space="preserve">Eodē mõ ꝓbabis / ſi procedas ad minoribus <lb/>ad maiores termīos in ꝓportiõe mīoris īeq̈litatꝪ <lb/></s>
            <s xml:id="N128D1" xml:space="preserve">Sed eadē hypotheſi retēta gñaliter probat̄̄ corre­<lb/>lariū ſic: et volo /  a. diminuat̄̄ ad eq̈litatē b. et c. ad <lb/>equalitatē d. / et ſic ꝑdēt eq̈les ꝓportiones ex hypo­<lb/>theſi: deiñ reſiduū ipſius a. acq̇rat ſupra ſeipſū b. <lb/>et reſiduū c. aq̇rat ipſū d. / et manifeſtum eſt /  ag-<lb/>gregati ex reſiduo a. et ipſo b. ad ipſū b. et aggre­<lb/>gati ex reſiduo ipſiꝰ c. et ipſo d. ad ipſū d: eſt eq̈lis <lb/>ꝓportio puta dupla: volo igit̄̄ /  aggregatum ex <lb/>reſiduo ipſius a. et ipſo b. acq̇rat illa quãtitatem <lb/>quã deꝑdidit a. ita  maneat aggregatū ex a. et b. <lb/>et aggregatū ex reſiduo ipſius c. et ipſo d. acq̇rat <lb/>quãtitatē quã deꝑdidit ipſū c. ita  maneat in fi-<lb/>ne aggregatū ex c. et d. / et tunc ſeq̇tur /  aggregati <lb/>ex a. et b. ad ip̄m b. et aggregati ex c. et d. ad ipſum <lb/>d. ē eadē ꝓportio / qḋ fuit ꝓbãdū. </s>
            <s xml:id="N128F0" xml:space="preserve">Probat̄̄ ↄ̨ña. </s>
            <s xml:id="N128F3" xml:space="preserve">q2 <lb/>illi termini añ acq̇ſitionē quãtitatū deꝑditaꝝ ab <lb/>ipſo a. et ipſo c. / ſe hēbaut in eadē ꝓportione puta <lb/>dupla / vt dictū ē: et acq̇ſiuerunt eq̈les ꝓportiones <lb/>termini maiores illaꝝ ꝓportionū: igit̄̄ iter datos <lb/>terminos manet eq̈lis ꝓportio: q2 ſi eq̈libꝰ eq̈lia <lb/>addas etc </s>
            <s xml:id="N12902" xml:space="preserve">Probatur minor: q2 medietates illorū <lb/>terminorū maiorū eq̈les ꝓportiões acq̇ſiuer̄t: igi­<lb/>tur et ipſi termini maiores eq̈les proportiões acq̇­<lb/>ſinerūt / vt ptꝫ ex tertia cõcluſione ſeptimi capitꝪ ṗ­<lb/>me ꝑtis: et p ↄ̨ñs proportiões quas hñt ad mīores <lb/>terminos eq̈les proportiones acq̇ſiuerūt / vt ptꝫ ex <lb/>ſuppoſitione huiꝰ.              <anchor type="note" xlink:href="note-0028-01" xlink:label="note-0028-01a"/>             </s>
            <s xml:id="N12916" xml:space="preserve">Et ſic ptꝫ correlariū / qḋ ſit medi­<lb/>etatis geometrice ſcḋa proṗetas </s>
            <s xml:id="N1291B" xml:space="preserve">¶ Seq̇tur ſeḋo /  <lb/>in hac medietate cõſtitutis .4. termīs q̈lis ē ꝓpor-<lb/>tio ṗmi ad m talis ē ꝓportio aggregati ex ṗmo et <lb/>tertio ad aggregatū ex ſcḋo. et .4. vt cõſtitutis his <lb/>terīs .12.6.4.2. q̈ĺ ē ꝓportio .12. ad .6. taĺ ē ꝓportõ <lb/>12. et .4: ad .6. et .2. </s>
            <s xml:id="N12928" xml:space="preserve">Probat̄̄ / ſint .4: terī ī hac medie­<lb/>tate a.b.c.d. / et dico /  ſic̈ a. ad b. ita aggregatū ex <lb/>a. et c. ad aggregatū ex b. et d. </s>
            <s xml:id="N1292F" xml:space="preserve">Qḋ ſic oñdit̄̄ / et .1. ī nū­<lb/>ris / et volo /  a. acq̇rat c. et b. acq̇rat d. (et ꝓcedo a <lb/>maioribꝰ) / et arguit̄̄ ſic ſicut ſe hꝫ a. ad b. ita c. ad d / <lb/>igr̄ ꝑmutatī ex .4. ↄ̨cĺoe ſicut ſe hꝫ a. ad c. ita b. ad d / <lb/>et ex ↄ̨ñti ſeq̇r̄ /  c. ē ꝑs aliq̊ta vĺ ꝑtes reſpectu a. eiuſ­             <cb chead="Capitulum ſecundum"/>             dē denoīatiõis ſicut d. reſpectu b. vel eoↄ̈ ſi ꝓpor-<lb/>tio a. ad c. ſit mīorꝪ īeq̈litatꝪ: et a. aq̇rit c. et b. aq̇rit d / <lb/>igr̄ q̀lē ꝓportionē aq̇rit nūerꝰ maior hꝰ ꝓportõis q̄ <lb/>ē a. ad b. talē acq̇rit nūerꝰ mīor. </s>
            <s xml:id="N12943" xml:space="preserve">Cõſequētia / ptꝫ ex <lb/>ſcḋo correlario octaue ſuppõis: g̊ ī fine facta tali <lb/>acq̇ſitiõe manet eadē ꝓportio ſiue eq̈lis illi q̄ ē īter <lb/>a: et b. / vt ptꝫ ex correlario decime ſuppõnis / et in fi­<lb/>ne manet proportio .ac. ad bd. / g̊ proportio .ac. ad <lb/>.bd. ē equalis ꝓportioni a. ad b. / qḋ fuit probandū <lb/></s>
            <s xml:id="N12951" xml:space="preserve">Sed eadē hypotheſi retēta probo gñaliter /  ſicut <lb/>ſe hꝫ c. ad d. / ita ſe hꝫ aggregatū ex .ac. ad aggrega­<lb/>tū ex .bd. </s>
            <s xml:id="N12958" xml:space="preserve">Et arguo / ſic ſicut ſe hꝫ a. ad b. ita c. ad d. / g̊ <lb/>ex ↄ̨cluſione ſicut ſe hꝫ a. ad c. ita b. ad d. diminuat̄̄ / <lb/>igr̄ a. ad equalitatē c. et b. ad equalitatē d. / et ſic ma­<lb/>nifeſtū ē /  equalē ꝓportionē deꝑdūt a. et b. </s>
            <s xml:id="N12961" xml:space="preserve">Uolo <lb/>igr̄ /  reſiduū ex a. acq̇rat ſupra ſeipſū c. et reſiduū <lb/>ex b. ipſū d. et tūc aggregati ex reſiduo a. et ipſo c. <lb/>ad ipſū c. ē illa proportio q̄ ē aggregati ex r̄ſiduo <lb/>b. et ipſo d. q2 dupla / vt ↄ̨ſtat: acq̇rat g̊ aggregatū <lb/>ex reſiduo a. et ip̄o c. quãtitatē quã ꝑdidit a. et ag-<lb/>gregatū ex reſiduo b: et ip̄o d. quãtitatē quã deꝑdi­<lb/>dit b. et tūc manifeſtū ē /  ꝓportio aggregati ex re­<lb/>ſiduo a. et ip̄o c. ad ipſū c. et ꝓportio aggregati ex <lb/>reſiduo b. et ipſo d. ad ipſū d. eq̈les ꝓportiones ac­<lb/>q̇rūt q2 medietates maioꝝ termīoꝝ equales ꝓpor­<lb/>tiões acq̇rūt puta illas quas antea pdiderūt et ſic <lb/>maiores termī illaꝝ ꝓportionū eq̈les ꝓportiões <lb/>acq̇r̄t / vt pꝫ ex tertia ↄ̨cĺoe ſeptī capitis ṗme ꝑtꝪ: igr̄ <lb/>īter illos termīos q̇ ſūt iã .ac. et c. et .bd. et b. manet <lb/>adhuc eq̈lis ꝓportio: et ꝑ ↄ̨ñs ſicut ſe hꝫ aggrega-<lb/>tū ex a. et c. ad ipſū c. ita ſe hꝫ aggregatū ex b. et d. <lb/>ad ip̄m d. / igr̄ ex ↄ̨cluſione ſicut ſe hꝫ aggregatū ex <lb/>a. et c. ad aggregatū ex b. et d. ita ſe hꝫ c. ad d. / quod <lb/>fuit ꝓbandū. </s>
            <s xml:id="N1298A" xml:space="preserve">Et ſolēt antiq̇ geometre et ſignanter <lb/>calculator vti hoc correlario ſub his rermīs             <anchor type="note" xlink:href="note-0028-02" xlink:label="note-0028-02a"/>             </s>
            <s xml:id="N12994" xml:space="preserve">Qua­<lb/>lis ē ꝓportio diuiſoꝝ talis ē ↄ̨iūctoꝝ: vt ſi ſint due <lb/>ꝓportiões duple: et cõpulet̄̄ terminꝰ maior vniꝰ cū <lb/>termīo maiore vlteriꝰ: et mīor vniꝰ cū mīore alteri­<lb/>us īter illos termīos ſic ↄ̨iūctos manebit ꝓportio <lb/>dupla.             <anchor type="note" xlink:href="note-0028-03" xlink:label="note-0028-03a"/>             </s>
            <s xml:id="N129A6" xml:space="preserve">¶ Seq̇tur .3. /  .4. termīs in hac medietate ↄ̨­<lb/>ſtitutis: q̈lis ē ꝓportio ſcḋi ad ṗmū talis ē quarti <lb/>ad tertiū vt ↄ̨ſtitutis. </s>
            <s xml:id="N129AD" xml:space="preserve">his 4: termīs .8.4.6.3. q̈lis ē <lb/>ꝓportio .4. ad .8. talis ē .3. ad 6. </s>
            <s xml:id="N129B2" xml:space="preserve">Ptꝫ hoc coreela-<lb/>riū facile / qm̄ ſꝑ ꝓportiões mīoris īeq̈litatis ſunt <lb/>eq̈les īter ſe cū ꝓportiões maioris īeq̈litatis q̇bus <lb/>corrñdent īter ſe ſūt equales: et eoↄ̈. </s>
            <s xml:id="N129BB" xml:space="preserve">Sicut eī oēs <lb/>duple ſūt equales: ita oēs ſubduple ſūt equales: et <lb/>ſic̈ oēs ſubtriple ſṫ eq̈les: ita oēs triple igr̄ vĺr ſi ta­<lb/>lis ꝓportio fuerit a. ad b. maioris īeq̈litatꝪ q̈lis ē <lb/>c. ad d. ↄ̨ñs ē  ꝓportio mīoris īeq̈litatꝪ d. ad c. et <lb/>b. ad a ſint eq̈les. </s>
            <s xml:id="N129C8" xml:space="preserve">Et ita ēt ꝓbaſſes ſi a. ad .b. fuiſſꝫ <lb/>ꝓportio mīoris īeq̈litatꝪ. </s>
            <s xml:id="N129CD" xml:space="preserve">Et hec ſit .4. ꝓṗetas geo­<lb/>metrice medietatꝪ. </s>
            <s xml:id="N129D2" xml:space="preserve">¶ Seq̇t̄̄ .4. /  diſpoſitis .4. ter-<lb/>mīs ſicut ṗmꝰ et ſcḋs ad m et tertiꝰ et quartꝰ ad q̈r <lb/>ita ṗmꝰ ad m et tertiꝰ ad q̈rtū / vt ↄ̨ſtitutis his .4. <lb/>termīs .8.4.2.1. / q2 .8. et 4. ad .4. ē talis ꝓportio q̈­<lb/>lis ē .2. et .1. ad .1. / vt pꝫ ex ṗmo correlario huiꝰ ↄ̨clu­<lb/>ſionis. </s>
            <s xml:id="N129DF" xml:space="preserve">Iõ q̈lis ē ꝓportio ṗmi ad m talis ē terti ad <lb/>.4. / vt ↄ̨ſtat. </s>
            <s xml:id="N129E4" xml:space="preserve">Probat̄̄ ṗmo / ī nūeris ſint .4. nūeri a. <lb/>b.c.d. et ſicut .ab.. ad .b. ita c. ad .cd. / tūc ḋt correĺm / <lb/> ſicut a. ad b. ita c. ad d. et ſit .a maiꝰ b. et c. maiꝰ d. <lb/>et deꝑdat .ab:b. et .cd.d. / et arguit̄̄ ſic ſicut ſe hꝫ .ab. <lb/>ad b. ita c.d. ad d. / igr̄ b. ē talis ꝑs aliq̊ta vel ꝑtes <lb/>aliq̊te et eiuſdē denoīatiõis reſpectu ipſiꝰ .ab. / q̈lis <lb/>ē d. reſpectu .cd. et .ab. ꝑdit b. et .cd. ꝑdit d. / g̊ illi duo <lb/>nūeri maiores puta .ab. et .cd. ꝑdūt eq̈les ꝓportio­<lb/>nes / vt pꝫ ex .1. correĺ. 8. ſuppõis / g̊ ſeq̇t̄̄ /  quãtã ꝓ­<lb/>portionē adeq̈te ꝑdit ꝓportio ab. ad b. tãtã ade­<lb/>q̈te ꝑdit ꝓportio .cd. ad d. / vt pꝫ ex nona ſuppoſiti­<lb/>one: et ille ꝓportões ante erãt equales / vt ponitur <lb/>igitur mõ manēt equales: q2 ſi ab equalibus equa­             <pb chead="Secunde partis" file="0029" n="29"/>             lia demas etc. ſed modo manet proportio a. ad b. <lb/>et c. ad .d. / ergo ille ſunt equales / quod fuit ꝓbãduꝫ <lb/></s>
            <s xml:id="N12A07" xml:space="preserve">Sꝫ vniuerſaliter probatur /  ſi ſicut ſe hꝫ a.b. ad b. <lb/>ita .cd. ad d. / tūc ſic̈ ſe hꝫ a. ad b. ita c. ad .d. </s>
            <s xml:id="N12A0C" xml:space="preserve">Qḋ ſic <lb/>probatur / qr. ſicut ſe hꝫ a.b. ad b. ita c.d. ad d. / ergo <lb/>ſicut ſe habet a.b. ad c.d. ita b. ad .d. / vt patet ex cõ­<lb/>cluſione. </s>
            <s xml:id="N12A15" xml:space="preserve">Uolo igit̄̄ /  a.b. ꝑdat .b. et c.d. ꝑdat d. ita­<lb/> maneãt a. et c. / et tūc arguo ſic / a.b. et c.d. ſe habēt <lb/>in ea proportione in qua ſe habent b. et d. q̄ ſit f. <lb/>gr̄a argumenti: et a.b. terminus maior deperdit <lb/>d. et c.d. terminꝰ minor deperdit d. / ergo inter de-<lb/>perditum a maiori termino et deꝑditū a minori ē <lb/>ꝓportio f. puta īter b. et d. et talis ꝓportio puta f. <lb/>eſt īter a.b. et c.d. / vt ꝓbatū eſt: igit̄̄ facta tali deꝑ-<lb/>ditione vel diminutione inter reſiduū ex a.b. et re-<lb/>ſiduū ex c.d. manet ꝓportio f. / vt ptꝫ ex ſeptīo cor-<lb/>relario quarte cõcluſionis octaui capitis huiꝰ par­<lb/>tis: et reſiduū ex a.b. ē a: et reſiduū ex c.d. eſt c. / igit̄̄ <lb/>īter a. et c. eſt f. ꝓportio ſicut inter .b. et d. et ꝑ ↄ̨ñs ſi­<lb/>cut ſe hꝫ a. ad c. ita b. ad d. puta in f. ꝓportione: et <lb/>ex cõſequēti ſeq̇tur ex cõcluſione /  ſicut ſe habet a <lb/>ad b. ita c. ad d. / qḋ fuit probandū. </s>
            <s xml:id="N12A36" xml:space="preserve">Et eodē mõ pro­<lb/>bares ſi a. eēt terminꝰ minor et b. maior. </s>
            <s xml:id="N12A3B" xml:space="preserve">et ēt c. mi­<lb/>nor et d. maior.             <anchor type="note" xlink:href="note-0029-01" xlink:label="note-0029-01a"/>             </s>
            <s xml:id="N12A45" xml:space="preserve">¶ Seq̇tur quīto /  diſpoſitis ī hac <lb/>medietate q̈tuor terminis: ſicut aggregatū ex q̈r-<lb/>to et tertio ad tertiū ita aggregatum ex ſecūdo et <lb/>prīo ad primū vt diſpoſitis his termīs .8.4.6.3. ſi­<lb/>cut ſe hñt 3. et .6. ad .6 ita .4. et .8. ad .8. </s>
            <s xml:id="N12A50" xml:space="preserve">Probat̄̄ / <lb/>ſint 4 ṫmini ī hac medietate ↄ̨ſtituti a.b.c.d. / tūc <lb/>ſicut ſe habet d.c. ad c. ita b.a. ad a. </s>
            <s xml:id="N12A57" xml:space="preserve">Qḋ ſic probat̄̄ / <lb/>q2 bñ ſeq̇tur ſicut ſe habet a. ad b. ita c. ad d. / igitur <lb/>ſicut ſe habet a.b. ad b. ita ſe habet c.d. ad d. / vt ptꝫ <lb/>ex ṗmo correlario huiꝰ concluſionis: et vltra ſicut <lb/>ſe habet a.b. ad b. ita c.d. ad d. / igit̄̄ ſicut ſe hꝫ d. ad <lb/>d.c. ita b. ad b.a. / quod fuit ꝓbandū. </s>
            <s xml:id="N12A64" xml:space="preserve">Ptꝫ hec cõſe-<lb/>quētia ex ꝓbatione tertii correlarii huius ↄ̨cluſio­<lb/>nis. </s>
            <s xml:id="N12A6B" xml:space="preserve">Et ſic patet correlariū.             <anchor type="note" xlink:href="note-0029-02" xlink:label="note-0029-02a"/>             </s>
            <s xml:id="N12A73" xml:space="preserve">¶ Sequitur ſexto /  diſ­<lb/>poſitis .3. terminis cõtinuo ꝓportionabilibus hac <lb/>medietate: et aliis tribus etiã cõtinuo ꝓportiona-<lb/>bilibꝰ eadē medietate: et eadē ꝓportione qua tres <lb/>priores cõtinuo proportionant̄̄: ſicut ſe habēt ex-<lb/>trema ṗmi ternarii: ita ſe habēt extrema ſecundi. <lb/></s>
            <s xml:id="N12A81" xml:space="preserve">vt cõſtitutis .4. et .1.21.6.3. ſicut ſe habēt .4. ad .1. ita <lb/>21. ad .3. </s>
            <s xml:id="N12A86" xml:space="preserve">Sint ſex termini a.b.c.d.e.f. et continuo <lb/>ꝓportionētur tres primi termini ꝓportione g. / et <lb/>eadē ꝓportione cõtinuo ꝓportionent̄̄ alii tres pu­<lb/>ta d.e.f. / et ſit ꝓportio cõpoſita adequate ex dupli­<lb/>ci g.h. / tūc dico /  eadē eſt ꝓportio a. ad c. q̄ eſt d. ad <lb/>f. </s>
            <s xml:id="N12A93" xml:space="preserve">Quod ſic oñditur. </s>
            <s xml:id="N12A96" xml:space="preserve">q2 ꝓportio a. ad .c. eſt .h. et ea-<lb/>dē eſt d. ad .f. / igit̄̄ eadē eſt proportio a. ad c. q̄ eſt d. <lb/>ad f. / qḋ fuit ꝓbãdū. </s>
            <s xml:id="N12A9D" xml:space="preserve">q2 vtrobi h. proportio </s>
            <s xml:id="N12AA0" xml:space="preserve">Pro­<lb/>batur maior: quia proportio a. ad c. cõponitur ex <lb/>duplici g. proportione adeq̈te puta ex proportio-<lb/>ne que eſt a. ad b. q̄ eſt g. et b. ad .c. q̄ etiã eſt g. / igitur <lb/>illa proportio a. ad c. eſt h. </s>
            <s xml:id="N12AAB" xml:space="preserve">Patet conſequētia / q2 <lb/>proportio h. vt ponit̄̄ cõponitur ex duplici g. ade-<lb/>quate. </s>
            <s xml:id="N12AB2" xml:space="preserve">Et iſto mõ probabis minorē: qm̄ proportio <lb/>d. ad f. componitur ex duplici g. puta ex proportio­<lb/>ne g. q̄ eſt d. ad e. et ex proportione g. que eſt e. ad f. <lb/>adequate. </s>
            <s xml:id="N12ABB" xml:space="preserve">Et ſic patet correlariū. </s>
            <s xml:id="N12ABE" xml:space="preserve">Et pari demon-<lb/>ſtratione oſtendes:  conſtitutis tribus quaterna­<lb/>riis continuo proportionabilibus eadem propor­<lb/>tione: et quin quinariis: et in quo volueris nūe-<lb/>ro: in quacun proportione ſe habent extrema <lb/>vniꝰ in eadē ſe habent extrema cuiuſuis alterius.</s>
          </p>
          <div xml:id="N12ACB" level="4" n="6" type="float">
            <note position="left" xlink:href="note-0028-01a" xlink:label="note-0028-01" xml:id="N12ACF">
              <s xml:id="N12AD3" xml:space="preserve">2. correl. <lb/></s>
              <s xml:id="N12AD7" xml:space="preserve">3. ꝓṗetaſ <lb/>medieta­<lb/>tꝪ geome­<lb/>trice.</s>
            </note>
            <note position="right" xlink:href="note-0028-02a" xlink:label="note-0028-02" xml:id="N12AE0" xml:space="preserve">eadē ē ꝓ-<lb/>portio di­<lb/>uiſoꝝ et ↄ̨­<lb/>iūctoruꝫ.</note>
            <note position="right" xlink:href="note-0028-03a" xlink:label="note-0028-03" xml:id="N12AEC" xml:space="preserve">4. ꝓprie­<lb/>tas medi­<lb/>etatꝪ geo­<lb/>metrice</note>
            <note position="left" xlink:href="note-0029-01a" xlink:label="note-0029-01" xml:id="N12AF8" xml:space="preserve">5. correĺ.</note>
            <note position="left" xlink:href="note-0029-02a" xlink:label="note-0029-02" xml:id="N12AFE" xml:space="preserve">6. correl.</note>
          </div>
          <note position="left" xml:id="N12B04" xml:space="preserve">5. ꝓp̄etaſ <lb/>medieta­<lb/>tis geo-<lb/>metrice.</note>
          <p xml:id="N12B0E">
            <s xml:id="N12B0F" xml:space="preserve">Quinta concluſio </s>
            <s xml:id="N12B12" xml:space="preserve">Quotlibet in hac <lb/>medietate geometrica terminis conſtitutis conti­<lb/>nuo proportionabilibus:: qualis eſt illoruꝫ termi­<lb/>norū cõtinuo ꝓportio: talis eſt inter eorū differen­             <cb chead="Capitulum tertiū."/>             tias ſiue exceſſns. </s>
            <s xml:id="N12B1E" xml:space="preserve">vt conſtitutis his terminis .16.8 <lb/>4.2.1. qualis eſt ꝓportio .6. ad .8. talis eſt exceſſus <lb/>quo .16. excedunt .8. ad exceſſum quo .8. excedūt .4. <lb/>et exceſſus quo .4. excedunt .2. ad exceſſum quo duo <lb/>excedunt vnum / vt patet. </s>
            <s xml:id="N12B29" xml:space="preserve">Eſt enim inter illos exceſ-<lb/>ſus proportio dupla quēadmodū īter terīos </s>
            <s xml:id="N12B2E" xml:space="preserve">Pro­<lb/>bat̄̄ / ſint .3. ṫmini cõtinuo ꝓportionabiles .f. ꝓpor-<lb/>tione puta .ab.cd.e. et exceſſus quo primus excedit <lb/>ſecunduꝫ ſit a: et exceſſus quo ſecundus excedit ter­<lb/>tium ſit c. / tūc dico /  ſicut f. ꝓportio eſt inter illos <lb/>terminos: vcꝫ īter primum et ſecundum et inter ſe-<lb/>cundum et tertium. </s>
            <s xml:id="N12B3D" xml:space="preserve">ita etiã eſt f. proportio inter a. <lb/>et c. exceſſus ita  a. ad c. eſt proportio f. </s>
            <s xml:id="N12B42" xml:space="preserve">Quod ſic <lb/>oſtendit̄̄ / q2 b. ad d. eſt ꝓportio f. et a. ad .c. eſt eadeꝫ <lb/>proportio / igitur a. ad c. eſt f. proportio / quod fuit <lb/>ꝓbandū. </s>
            <s xml:id="N12B4B" xml:space="preserve">Probatur maior / quia b. eſt equale c.d. <lb/>q2 a.b: excedebat preciſe per a. ipſum .cd. et ſic re-<lb/>moto exceſſu .b. manebit equale c.d. et d. eſt equale <lb/>e. eadem rõne: et inter .cd. et e. eſt f. proportio / vt po­<lb/>nitur: ergo inter b: et d. eſt eadem f. proportio </s>
            <s xml:id="N12B56" xml:space="preserve">Pa­<lb/>tet conſequentia / q2 oīm equaliū eſt eadem ꝓpor-<lb/>tio </s>
            <s xml:id="N12B5D" xml:space="preserve">Minor ꝓbatur / et capio vnū terminū ad quem <lb/>a. habeat ꝓportionē f. qui ſit g. / et arguo ſic / ſicut ſe <lb/>habet b. ad d. ita ſe habet a. ad g. puta in f. propor­<lb/>tione: ergo ſicut ſe habet b. ad d: puta in f. ꝓportio­<lb/>ne ita ſe habet a.b. ad g.d. puta in f. proportione. <lb/></s>
            <s xml:id="N12B69" xml:space="preserve">Patet hec conſequentia ex ſecundo correlario q̈r­<lb/>te concluſionis: et .ab. etiam ad .cd. eſt proportio <lb/>f. / vt ponitur igitur g.d. et c.d. ſunt equalia. </s>
            <s xml:id="N12B70" xml:space="preserve">Patet <lb/>conſequentia / quia idem tertium eandē ꝓportiõeꝫ <lb/>hꝫ ad vtrum illoꝝ: et vltra .gd. et c.d. ſūt eq̈lia: g̊ <lb/>eodē cõi dēpto puta d. r̄ſidua manebūt eq̈lia / ſꝫ re­<lb/>ſidua ſunt g. et c. / g̊ g. et c. ſunt eq̈lia et a. ad g. eſt f. <lb/>proportio / vt poſitū eſt / ergo a. ad c. eſt f. proportio / <lb/>quod fuit ꝓbandum </s>
            <s xml:id="N12B7F" xml:space="preserve">Patet hec conſequētia / quia <lb/>eiuſdē tertii ad vtrū duorū equaliū eſt eadem ꝓ­<lb/>portio. </s>
            <s xml:id="N12B86" xml:space="preserve">Et ſic ptꝫ concluſio </s>
            <s xml:id="N12B89" xml:space="preserve">Qm̄ eo modo quo pro­<lb/>batū eſt in illis tribus terminis probabitur quot­<lb/>cnn diſpoſitis cõtinuo proportionabilibus hac <lb/>medietate. </s>
            <s xml:id="N12B92" xml:space="preserve">Et hec ſit quinta proprietas medieta-<lb/>tis geometrice.             <anchor type="note" xlink:href="note-0029-03" xlink:label="note-0029-03a"/>             </s>
            <s xml:id="N12B9C" xml:space="preserve">¶ Ex hac concluſione ſequitur pri-<lb/>mo /  ſi duo numeri inequales continuo diminuã­<lb/>tur continuo in eadem ꝓportione manentes: con-<lb/>tinno deperditū maiori numero ſe habet in eadeꝫ <lb/>ꝓportione ad deperditū minori numero in qua cõ­<lb/>tinuo ſe habent illi numeri qui diminuuntur. </s>
            <s xml:id="N12BA9" xml:space="preserve">vt ſi <lb/>numerus octonarius et quaternarius continuo di­<lb/>minuantur continuo manētes in ꝓportiõe dnpla: <lb/>continuo deperditum ab octonario ſe habebit in <lb/>ꝓportione dupla ad deperditum a quaternario. <lb/></s>
            <s xml:id="N12BB5" xml:space="preserve">Hoc correlarium facile ex demonſtratione conclu­<lb/>ſionis probatur.             <anchor type="note" xlink:href="note-0029-04" xlink:label="note-0029-04a"/>             </s>
            <s xml:id="N12BBF" xml:space="preserve">¶ Sequit̄̄ ſecundo /  ſi nõ conti-<lb/>nuo deperditum maiori numero ſe habeat ad de­<lb/>perditum a minori numero in eadem proportiõe: <lb/>in qua continuo ſe habent illi numeri q̇ diminuun­<lb/>tur: illi duo numeri inequales q̇ cõtinuo diminuū­<lb/>tur non ſe habent in eadem ꝓportione etc. </s>
            <s xml:id="N12BCC" xml:space="preserve">Patet <lb/>hoc correlarium ex priori / qm̄ p̄cedens correlariū <lb/>eſt vna conditionalis a: igitur ex oppoſito ↄ̨ñtis <lb/>eius ſequit̄̄ oppoſitum añcedentis: et ꝑ conſequēs <lb/>conditionalis in qua arguitur ex oppoſito conſe­<lb/>quentis illius ad oppoſitum añtis eſt vera: et ta-<lb/>lis eſt correlarium / igitur correlarium verum.</s>
          </p>
          <div xml:id="N12BDB" level="4" n="7" type="float">
            <note position="right" xlink:href="note-0029-03a" xlink:label="note-0029-03" xml:id="N12BDF" xml:space="preserve">1. correĺ.</note>
            <note position="right" xlink:href="note-0029-04a" xlink:label="note-0029-04" xml:id="N12BE5" xml:space="preserve">2. correĺ.</note>
          </div>
          <note position="right" xml:id="N12BEB" xml:space="preserve">3. correĺ.</note>
          <p xml:id="N12BEF">
            <s xml:id="N12BF0" xml:space="preserve">¶ Sequitur tertio /  ſi continuo deperdita a duo­<lb/>bus numeris inequalibus manent in eadem pro-<lb/>portione in qua ſe habent illi numeri in principio <lb/>deperditionis: numeri remanētes cõtinuo manēt <lb/>in eadem ꝓportione. </s>
            <s xml:id="N12BFB" xml:space="preserve">vt ſi numerus duodenarius <lb/>et ſenarius diminuantur: et continuo deperdituꝫ             <pb chead="Secūde partis" file="0030" n="30"/>             a duodenario ſe habeat in proportio dupla a <lb/>ſenario: continuo illud quod remanet ex duode-<lb/>nario ſe habet in proportione dupla ad illud qḋ <lb/>remanet a numero ſenario. </s>
            <s xml:id="N12C0B" xml:space="preserve">Et ſub tenore huiꝰ exē­<lb/>pli ego intelligo correlarium </s>
            <s xml:id="N12C10" xml:space="preserve">Non enī in iſtis exa­<lb/>ctꝰ ſenſus dialecticus ex expetendus ſed ipſa ma­<lb/>thematica ſententia eſt efflagitanda. </s>
            <s xml:id="N12C17" xml:space="preserve">Hoc correla­<lb/>rium perinde at primum demonſtrationem con­<lb/>cluſionis exquirit. </s>
            <s xml:id="N12C1E" xml:space="preserve">Applica vt vales.</s>
          </p>
          <note position="left" xml:id="N12C21" xml:space="preserve">4. correĺ.</note>
          <p xml:id="N12C25">
            <s xml:id="N12C26" xml:space="preserve">¶ Sequitur quarto /  quandocun duo numeri ī­<lb/>equales continuo creſcunt: et continuo ſe habent <lb/>in eadem proportione: oportet /  continuo acqui­<lb/>ſitū maiori numero ſe habeat in eadeꝫ proportio­<lb/>ne ad acquiſitum minori in qua ſe habent illi nūe­<lb/>ri creſcentes. </s>
            <s xml:id="N12C33" xml:space="preserve">vt ſi numerus quaternarius et ſena-<lb/>rius continuo creſcant et continuo manent in pro­<lb/>portione ſexquialtera: oportet /  continuo acqui­<lb/>ſitum ſenario ſe habeat in proportione ſexquial-<lb/>tera ad acquiſitum quaternario. </s>
            <s xml:id="N12C3E" xml:space="preserve">Hoc correlariuꝫ <lb/>eadem cum precedentibus demonſtratione oſten-<lb/>ditur. </s>
            <s xml:id="N12C45" xml:space="preserve">¶ Sequitur quinto /  datis quibuſcun <lb/>duobus numeris inequalibus ſe habentibus ī ali­<lb/>q̄ ꝓportiõe et ī ea ꝓportiõe ī q̄ mīor excedit̄̄ a maio­<lb/>re ī eadē cõtinuo tardiꝰ creſcat maiore: cõtinuo ta­<lb/>les numeri manent in eadem proportione. </s>
            <s xml:id="N12C50" xml:space="preserve">vt da-<lb/>tis: 4. et .6. ſe habentibus in proportione ſexqui-<lb/>altera: ſi quando ſex acquiſiuerint aliquod cremē­<lb/>tum. </s>
            <s xml:id="N12C59" xml:space="preserve">quatuor acquirant in ſexquialtero minus: ip­<lb/>ſi continuo manent in proportione ſexquialtera. <lb/></s>
            <s xml:id="N12C5F" xml:space="preserve">Probatur hoc correlarium / quoniam ſi in eadem <lb/>proportione in qua numerꝰ maior ſe habet ad mi­<lb/>norem velocius creſcat quaꝫ minor: ſequitur /  cõ­<lb/>tinuo inter acquiſitum minori numero eſt eadem <lb/>proportio que eſt inter illos numeros. </s>
            <s xml:id="N12C6A" xml:space="preserve">vt patet ex <lb/>probatioue concluſionis: et per conſequens con-<lb/>tinuo tales numeri manent in eadem proportione <lb/></s>
            <s xml:id="N12C72" xml:space="preserve">Et ſic patet correlarium</s>
          </p>
          <p xml:id="N12C75">
            <s xml:id="N12C76" xml:space="preserve">Sexta concluſio </s>
            <s xml:id="N12C79" xml:space="preserve">Datis tribus nu-<lb/>meris in hac medietate conſtitutis: quod fit ex du­<lb/>ctu extremi in extremum equale eſt quadrato me-<lb/>dii: hoc eſt illi numero qui reſultat ex ductu medii <lb/>termiui in ſeipſum. </s>
            <s xml:id="N12C84" xml:space="preserve">vt conſtitutis his tribus termi­<lb/>nis .8.4.2. numerus ſexdenarius reſultans ex du-<lb/>ctu octonarii in binarium eſt equalis numero qui <lb/>fit ex ductu quaternarii in ſeipſū / vt conſtat. </s>
            <s xml:id="N12C8D" xml:space="preserve">Pro­<lb/>batur hec concluſio / ſint tres numeri a.b.c. in hac <lb/>medietate conſtituti continuo ꝓportionabiles .g. <lb/>ꝓportione: et ſit d. numerus reſultãs ex ductu a. in <lb/>b. et e. ſit numerus reſultãs ex ductu b. in idē b. et f. <lb/>numerus reſultans ex ductu a. in c. / tunc dico /  e. et <lb/>f. ſunt equales. </s>
            <s xml:id="N12C9C" xml:space="preserve">Qḋ ſic ꝓbatur: qm̄ d. ad e. eſt ꝓpor­<lb/>tio g. et d. ad f. eſt eadē ꝓportio g. / ergo e. et f. ſunt <lb/>equalia / quod fuit ꝓbandū. </s>
            <s xml:id="N12CA3" xml:space="preserve">Patet conſequētia et <lb/>maior oſtenditur. </s>
            <s xml:id="N12CA8" xml:space="preserve">quia ſicut ſe hꝫ d. ad a. ita ſe ha-<lb/>bet e. ad .b. q2 toties adeq̈te a. cõtinet̄̄ in d. quoties <lb/>eſt vnitas in b. et toties continetur b. in e. quoties <lb/>eſt vnitas in b. cum d. fiat ex ductu a in b. et e. ex du­<lb/>ctu b. in b. / igit̄̄ ſicut ſe habet d. ad a. ita e. ad b. </s>
            <s xml:id="N12CB3" xml:space="preserve">Con­<lb/>ſequētia claret ex tertia ſuppoſitione huius capi-<lb/>tis: et ex conſequēti ſicut ſe hꝫ d. ad a. ita e. ad b: er­<lb/>go ſicut ſe habet d. ad e. ita ſe habet a. ad b. ſed a. <lb/>ad b. eſt g. proportio / ergo .d. ad e. eſt g. ꝓportio / qḋ <lb/>fuit ꝓbandū. </s>
            <s xml:id="N12CC0" xml:space="preserve">Patet igitur maior. </s>
            <s xml:id="N12CC3" xml:space="preserve">Iã probat̄̄ mi-<lb/>nor. </s>
            <s xml:id="N12CC8" xml:space="preserve">q2 d. in g. ꝓportione pluries cõtinet a. quaꝫ f. <lb/>contineat idē a. adeq̈te: ergo d. ſe habet ad f. in g. <lb/>ꝓportione </s>
            <s xml:id="N12CCF" xml:space="preserve">Patet conſequentia ex tertia ſuppoſi­<lb/>ctione p̄allegata. </s>
            <s xml:id="N12CD4" xml:space="preserve">Probatur antexedens / q2 d. toti­<lb/>es continet a. quoties eſt vnitas in b. cuꝫ a. in b. du­<lb/>catur et inde reſultat d. et f. toties continet a quo             <cb chead="Capitulum ſecundum"/>             ties eſt vnitas in c. eadē rõue: ſꝫ in g. ꝓportiõe plu­<lb/>ries continetnr vnitas in b. quã in c. cū b. et c. ſe ha­<lb/>beant in g. ꝓportione: ergo in g. ꝓportione pluri­<lb/>es cõtinetur a. in d. quã in f. / qḋ fuerat oñdendū. </s>
            <s xml:id="N12CE4" xml:space="preserve">Et <lb/>ſic patet cõclnſio q̄ ꝓfecto pulchra eſt et induſtria q̄ <lb/>ſit huius medietatis. </s>
            <s xml:id="N12CEB" xml:space="preserve">ſexta proprietas.             <anchor type="note" xlink:href="note-0030-01" xlink:label="note-0030-01a"/>             </s>
            <s xml:id="N12CF3" xml:space="preserve">¶ Ex hac <lb/>concluſione ſeq̇tur ṗmo /  ī hac medietate id quod <lb/>fit ex ductu vnius extremi ad triū termīorū alterū <lb/>extremū eſt numerꝰ quadratꝰ: </s>
            <s xml:id="N12CFC" xml:space="preserve">Probatur / q2 talis <lb/>numerus eſt equalis quadrato medii termini / g̊ eſt <lb/>numerus quadratus </s>
            <s xml:id="N12D03" xml:space="preserve">Cõſequētia patet de ſe et añ­<lb/>cedens ex concluſione.             <anchor type="note" xlink:href="note-0030-02" xlink:label="note-0030-02a"/>             </s>
            <s xml:id="N12D0D" xml:space="preserve">¶ Sequitur ſecundo /  ſi cõ­<lb/>ſtitutis duobus numeris ſe habentibus in aliqua <lb/>ꝓportione maioris ineqnalitatis rationali. </s>
            <s xml:id="N12D14" xml:space="preserve">nūe-<lb/>rus q̇ fit ex ductu vnius extremi in alterū non eſt q̈­<lb/>dratꝰ: inter tales termīos nõ eſt medium ꝓportio­<lb/>nabile ꝓportione rationali: ita  ṗmi ad illḋ me-<lb/>diū ſit eadē ꝓportio rationalis que eſt illius me-<lb/>dii ad tertiuꝫ. </s>
            <s xml:id="N12D21" xml:space="preserve">Probatur hoc correlarium / qnia ſi <lb/>inter tales numeros reperiatur mediū ꝓportiõa-<lb/>bile ꝓportione rationali: puta aliquis numerus <lb/>medio loco proportionabilis: iam ſequitur /  ibi­<lb/>dē reperiuntur tres numeri cõtinuo ꝓportionabi­<lb/>les hac medietate: et ꝑ cõſequēs numerꝰ q̇ fit ex du­<lb/>ctu extremi in extremum eſt equalis quadrato me­<lb/>dii / vt patet ex coucluſione: igitur talis numerus ē <lb/>quadratus / vt patet ex primo correlario / quod eſt <lb/>oppoſitū añcedetis correlari ꝓbãdi. </s>
            <s xml:id="N12D36" xml:space="preserve">īfert igir̄ cor­<lb/>relarii oppoſitū conſequentis oppoſitū añceden-<lb/>tis / et ꝑ conſequēs correlarium verum.             <anchor type="note" xlink:href="note-0030-03" xlink:label="note-0030-03a"/>             </s>
            <s xml:id="N12D42" xml:space="preserve">¶ Sequitur <lb/>tertio /  ſi medium proportionabile īter duos nu­<lb/>meros ſe habētes in proportione maioris inequa­<lb/>litatis nõ ſit latus numeri contenti ſub extremis: <lb/>tunc numerus qui fit ex ductu vnius extremi in al-<lb/>terū nõ eſt quadratus. </s>
            <s xml:id="N12D4F" xml:space="preserve">Probatur / ſint a.c. duo nu­<lb/>meri ſe habentes in proportione maioris inequa­<lb/>litatis a. maior c. minor: et numerus qui fit ex du­<lb/>ctu a. in c. ſit d. et e. ſit medium ꝓpõrtionale inter a <lb/>et c. / tunc dico /  ſi e. non ſit latus ipſius d: d. nõ eſt <lb/>numerus quadratus. </s>
            <s xml:id="N12D5C" xml:space="preserve">Quod ſic oñditur: q2 ſi d: ſit <lb/>numerus quadratus ſequitur /  eius latus eſt e. / <lb/>igitur ex oppoſito ſequitur oppoſitum: et per con­<lb/>ſequens correlarium verum. </s>
            <s xml:id="N12D65" xml:space="preserve">Probatur antece-<lb/>dens / quia ſi d. eſt numerus quadratus cum nõ ſit <lb/>quadratus a. nec quadratus ipſius c. / vt conſtat: <lb/>qm̄ quando duo numeri inequales in ſeipſos du­<lb/>cuntur quod inde ſit neutrius illoꝝ eſt quadratuꝫ: <lb/>ſed eſt alicuius numeri minoris maiore illorum et <lb/>maioris minore: ſit igitur talis numerus b. cuius <lb/>d. eſt quadratum / et ſequitur /  a. ad b. eſt aliqua ꝓ­<lb/>portio: conſtituo igitur tres terminos continuo ꝓ­<lb/>portionabiles illa proportione a. ad b. que ſint a. <lb/>b.h. / et ſequitur ex cõcluſione /  numerus qui fit ex <lb/>ductu a. in h. eſt equalis ipſi d. et per te numerꝰ qui <lb/>fit ex ductu a. in c. eſt equalis ipſi d. </s>
            <s xml:id="N12D80" xml:space="preserve">Imo eſt ipſum <lb/>d. / igitur h. et c: ſunt numeri equales. </s>
            <s xml:id="N12D85" xml:space="preserve">Patet hec cõ­<lb/>ſequentia / q2 ex ductu vuius tertii in vtrū illorū <lb/>reſultat idem numerus. </s>
            <s xml:id="N12D8C" xml:space="preserve">et ſic tot vnitates continet <lb/>c. ſicut h. / et per conſequens ſunt equales. </s>
            <s xml:id="N12D91" xml:space="preserve">ſed inter <lb/>a. et h. eſt mediū ꝓportionale quod eſt latus qua-<lb/>drati quod fit ex ductu a. in h. quod latus eſt b. / igi­<lb/>tur inter a. et c. eſt mediū ꝓportionale quod eſt la-<lb/>tus quadrati quod fit ex ductu a. in h. / et per conſe­<lb/>quens medium e. inter a. et c. eſt latus numeri d. q̇ <lb/>fit ex ductu a. in c. / quod fuit probandum. </s>
            <s xml:id="N12DA0" xml:space="preserve">Et ſic pa­<lb/>tet correlarium.             <anchor type="note" xlink:href="note-0030-04" xlink:label="note-0030-04a"/>             </s>
            <s xml:id="N12DAA" xml:space="preserve">¶ Sequitur quarto /  conſtitutis <lb/>duobus terminis ſe habentibus in aliqua ꝓpor-<lb/>tione maioris inequalitatis rationali ſi numerus <lb/>qui fit ex ductu vnius extremi in alterum ſit qua-             <pb chead="Secunde partis" file="0031" n="31"/>             dratus: inter tales numeros reperitur medium ꝓ­<lb/>portionabile ꝓportione rationali ita  primi ad <lb/>ipſum ſit ea proportio rationalis que eſt ipſiꝰ ad <lb/>tertium. </s>
            <s xml:id="N12DBE" xml:space="preserve">et illius numeri quadrati tale medium eſt <lb/>vnum latus. </s>
            <s xml:id="N12DC3" xml:space="preserve">Probatur prima pars huius corre-<lb/>larii / quia illa pars eſt vna cõditionalis ex cuiꝰ op­<lb/>poſito conſequentis / ſequitur oppoſitum antece-<lb/>dentis: vt patet ex ſecundo correlario: igitur illa <lb/>pars vera. </s>
            <s xml:id="N12DCE" xml:space="preserve">Secunda probatur ex correlario īme-<lb/>diate precendenti. </s>
            <s xml:id="N12DD3" xml:space="preserve">¶ Sequitur quīto /  inter ṗmos <lb/>numeros ꝓportionis duple: triple: octuple: ſexq̇-<lb/>altere etc̈. non inuenitur medium ꝓportionabile ꝓ­<lb/>portione rationali </s>
            <s xml:id="N12DDC" xml:space="preserve">Probatur primo de dupla / q̄ <lb/>eſt inter iſtos terminos .4.2. quoniam numerus q̇ <lb/>fit ex ductu vnius extremi in alterum puta .4. in .2. <lb/>non eſt quadratus / igitur inter illa extrema non ī­<lb/>uenitur medium ꝓportionabile proportione ra-<lb/>tionali </s>
            <s xml:id="N12DE9" xml:space="preserve">Añs patet intelligenti diffinitionem nu-<lb/>meri quadrati. </s>
            <s xml:id="N12DEE" xml:space="preserve">et conſequentia patet ex ſecundo <lb/>correlario. </s>
            <s xml:id="N12DF3" xml:space="preserve">Et eodē modo ꝓbabis reliquas ꝑtes. <lb/></s>
            <s xml:id="N12DF7" xml:space="preserve">¶ Et ex hoc habes pulchrū documentuꝫ ab cogno­<lb/>ſcendū quãdo aliqua ꝓportio īeq̈litatꝪ habet ſub­<lb/>duplam proportionem ad eam rationalem. </s>
            <s xml:id="N12DFE" xml:space="preserve">Quã­<lb/>do enim numerus reſultans ex ductu vnius extre-<lb/>mi in alterum non eſt quadratus / tunc talis ꝓpor­<lb/>tio non habet ꝓportionem rationalem ſubduplã <lb/>ad illam cum non habeat medium ꝓportionabile <lb/>ꝓportione rationali. </s>
            <s xml:id="N12E0B" xml:space="preserve">et ſic tale medium inter ter-<lb/>minos illius ꝓportionis non ſe habet vt numerꝰ <lb/>reſpectu alicuius extremi illius ꝓportionis. </s>
            <s xml:id="N12E12" xml:space="preserve">Si eī <lb/>ſe haberet vt numerus: maioris extremi ad ipſum <lb/>eſſet aliqua ꝓportio rationalis: et ipſius ad mini­<lb/>mum extremum eſſet eadem ꝓportio rationalis: et <lb/>ſic iam ibi eſſent tres numeri continuo ꝓportiona­<lb/>biles in hac medietate geometrica: et ſic numerus <lb/>qui fit ex ductu extremi in extremū eſſet quadratꝰ / <lb/>vt patet ex primo correlario / quod eſt oppoſitū da­<lb/>ti.             <anchor type="note" xlink:href="note-0031-01" xlink:label="note-0031-01a"/>             </s>
            <s xml:id="N12E2A" xml:space="preserve">Et ex hoc facile elicitur ꝓportionem irrationa-<lb/>lem neceſſario ponendã eſſe: quod nota.</s>
          </p>
          <div xml:id="N12E2F" level="4" n="8" type="float">
            <note position="right" xlink:href="note-0030-01a" xlink:label="note-0030-01" xml:id="N12E33" xml:space="preserve">1. correĺ.</note>
            <note position="right" xlink:href="note-0030-02a" xlink:label="note-0030-02" xml:id="N12E39" xml:space="preserve">2. correĺ.</note>
            <note position="right" xlink:href="note-0030-03a" xlink:label="note-0030-03" xml:id="N12E3F" xml:space="preserve">3. correĺ.</note>
            <note position="right" xlink:href="note-0030-04a" xlink:label="note-0030-04" xml:id="N12E45" xml:space="preserve">4. correĺ.</note>
            <note position="left" xlink:href="note-0031-01a" xlink:label="note-0031-01" xml:id="N12E4B" xml:space="preserve">irrõnaliſ <lb/>ꝓportio <lb/>alio mõ <lb/>ponenda <lb/>oñditur.</note>
          </div>
          <p xml:id="N12E59">
            <s xml:id="N12E5A" xml:space="preserve">Gratia ordinis obſeruandi medieta­<lb/>tis harmonice aliquas proprietates ponã quas <lb/>non intendo demonſtrare: quia huic operi paruꝫ <lb/>conducunt.             <anchor type="note" xlink:href="note-0031-02" xlink:label="note-0031-02a"/>             </s>
            <s xml:id="N12E68" xml:space="preserve">¶ Prima proprietas </s>
            <s xml:id="N12E6B" xml:space="preserve">Medietas har-<lb/>monica in maioribus terminis maiorem ſeruat ꝓ­<lb/>portionē quam in minoribus. </s>
            <s xml:id="N12E72" xml:space="preserve">Hoc eſt dicere /  ca­<lb/>ptis tribus terminis hac medietate ꝓportionabi­<lb/>libus: maior eſt proportio maximi ad mediū: quã <lb/>medii ad minimū. </s>
            <s xml:id="N12E7B" xml:space="preserve">vt conſtitutis his terminis .12.8 <lb/>6. maior eſt proportio .12. ad .8. que eſt ſexquialte­<lb/>ra quã .8. ad .6. que eſt ſexquitertia.             <anchor type="note" xlink:href="note-0031-03" xlink:label="note-0031-03a"/>             </s>
            <s xml:id="N12E87" xml:space="preserve">¶ Secunda ꝓ-<lb/>prietas. </s>
            <s xml:id="N12E8C" xml:space="preserve">tribus terminis in hac medietate conſtitu­<lb/>tis medius terminus in collectas extremitates du­<lb/>ctus dupluꝫ numero qui fit ex extremo in extremū <lb/>ꝓducit. </s>
            <s xml:id="N12E95" xml:space="preserve">vt conſtitutis predictis terminis .12.8.6. et <lb/>collectis extremis puta .6. et .12. que .18. conſtituūt <lb/>numerus qui fit ex ductu medii puta octonarii in <lb/>collectas extremitates puta ī .18. eſt duplus ad nu­<lb/>merum qui fit ex ductu extremorum .12. ſcilicet ī .6 <lb/></s>
            <s xml:id="N12EA1" xml:space="preserve">Quod patet / quia ille eſt .144. hic vero .72. mõ con­<lb/>ſtat illū eſſe dupluꝫ ad hunc.             <anchor type="note" xlink:href="note-0031-04" xlink:label="note-0031-04a"/>             </s>
            <s xml:id="N12EAB" xml:space="preserve">¶ Tertia proprietas <lb/>in hac medietate determinatis extremis medius <lb/>terminus reperitur ſi per extremorum coniuncto-<lb/>rum numerum: numerus qui ex differentia extre-<lb/>morum in minimū conſurgit diuiditur. </s>
            <s xml:id="N12EB6" xml:space="preserve">iſ qui <lb/>ex diuiſiõe relinquit̄̄ accipiat̄̄: at minimo extre-<lb/>mo aggregatur. </s>
            <s xml:id="N12EBD" xml:space="preserve">vt determinatis his terminis .6. <lb/>et .3. / ſi vis inuenire medium harmonicum inter il-<lb/>los addas extremū extrēo puta .3. ip̄is .6 et erūt 9. / <lb/>deiñ ducas dnr̄aꝫ inter .6. et .3. in .3. mīmū extremū:             <cb chead="Capitulum tertiū."/>             et quia illa differentia eſt .3. ex ductu eius in .3. fi-<lb/>unt .9. diuidas / igitur .9. per .9. et relictū ex diuiſio­<lb/>ne erit vnitas: addas igitur vnitatem ternario: et <lb/>aggregatum ex illa vnitate et ternario eſt mediuꝫ <lb/>harmonicum inter ſex. et tria: eſt enim aggregatū <lb/>illud quaternarius numerus. </s>
            <s xml:id="N12ED3" xml:space="preserve">Modo .6.4.3: ꝓpor­<lb/>tionantur harmonice. </s>
            <s xml:id="N12ED8" xml:space="preserve">¶ Et hic aduerte /  quibuſ-<lb/>cū duobus numeris inequalibus cõſtitutis hac <lb/>doctrina mediante reperies medium terminū in-<lb/>ter eos: et hoc cum fractione aut ſine inter .4. enim <lb/>et .3. medium harmonicū eſt .3. cuꝫ tribus ſeptimis <lb/></s>
            <s xml:id="N12EE4" xml:space="preserve">Quomodo autem inueniatur medium geometri-<lb/>cum partim ex his / que dicta ſunt / patet et comple­<lb/>te in poſterum dicetur.</s>
          </p>
          <div xml:id="N12EEB" level="4" n="9" type="float">
            <note position="left" xlink:href="note-0031-02a" xlink:label="note-0031-02" xml:id="N12EEF" xml:space="preserve">ṗma ꝓṗe­<lb/>tas medi­<lb/>etatꝪ har­<lb/>monice.</note>
            <note position="left" xlink:href="note-0031-03a" xlink:label="note-0031-03" xml:id="N12EFB" xml:space="preserve">ſcḋa ꝓṗe­<lb/>tas medi­<lb/>etatꝪ har­<lb/>monice.</note>
            <note position="left" xlink:href="note-0031-04a" xlink:label="note-0031-04" xml:id="N12F07" xml:space="preserve">3. ꝓṗetas <lb/>medieta­<lb/>tis har-<lb/>monice.</note>
          </div>
        </div>
        <div xml:id="N12F13" level="3" n="3" type="chapter" type-free="capitulum">
          <head xml:id="N12F18" xml:space="preserve">Capitulum tertium / in quo <lb/>agitur de quibuſdam propor­<lb/>tionalitatibus et modis argu­<lb/>endi in eis.</head>
          <p xml:id="N12F21">
            <s xml:id="N12F22" xml:space="preserve">SEx modos argumentandi pro­<lb/>portionabiliter ſiue in ꝓportionalitati-<lb/>bus quibus nonun̄. </s>
            <s xml:id="N12F29" xml:space="preserve">et philoſophi et cal­<lb/>culatores phiſici vtūtur ponit Euclides ſexto ele-<lb/>mentorum et recentiores mathematici poſt eum. <lb/></s>
            <s xml:id="N12F31" xml:space="preserve">¶ Iſtarum autem argumentationum prima dici-<lb/>tur conuerſa: ſecunda permutata: tertia coniun-<lb/>cta. </s>
            <s xml:id="N12F38" xml:space="preserve">quarta diſiuncta. </s>
            <s xml:id="N12F3B" xml:space="preserve">quinta euerſa: et ſexta equa. <lb/></s>
            <s xml:id="N12F3F" xml:space="preserve">¶ Pro intelligentia primi modi arguendi aduer­<lb/>tendum eſt /  in propoſito antecedens alicuius ꝓ­<lb/>portionis dicitur terminus / qui ad alterum com-<lb/>paratur et conſequens terminus cui aliquis com­<lb/>paratur / vt cum dicitur quatuor ad duo ille termi­<lb/>nus quatuor eſt antecedens et duo conſequens / et <lb/>ſi dicamus duo ad quatuor duo dicuntur antece-<lb/>dens et quatuor conſequens             <anchor type="note" xlink:href="note-0031-05" xlink:label="note-0031-05a"/>             </s>
            <s xml:id="N12F55" xml:space="preserve">¶ Iſto ſuppoſito pro­<lb/>portionalitas conuerſa eſt quando ex anteceden-<lb/>tibus fiunt conſequētia: et eocontra. </s>
            <s xml:id="N12F5C" xml:space="preserve">Uel aliter eſt <lb/>proportionalis illatio in qua ex proportionibus <lb/>maioris inequalitatis concluduntur proportio-<lb/>nes minoris ineq̈litatis eis correſpondentes. </s>
            <s xml:id="N12F65" xml:space="preserve">ſic <lb/>arguendo ſicut ſe habet octo ad quatuor ita duo a­<lb/>d vnum / igitur ſicut ſe habet vnum ad duo ita qua­<lb/>tuor ad octo. </s>
            <s xml:id="N12F6E" xml:space="preserve">Et etiã econuerſo cõcludēdo ex pro­<lb/>portionibus minoris inequalitatis ꝓportiones <lb/>maioris īeq̈litatꝪ eis correſpõdētes.             <anchor type="note" xlink:href="note-0031-06" xlink:label="note-0031-06a"/>             </s>
            <s xml:id="N12F7A" xml:space="preserve">¶ Permuta-<lb/>ta ꝓportiõalitas dicit̄̄ / cū ex ãtecedēte ſcḋe ꝓporti-<lb/>onis ſit ↄ̨ñs prime et ex ↄ̨ñti prime ſit añs ſcḋe. </s>
            <s xml:id="N12F81" xml:space="preserve">Uel <lb/>aliter eſt diſpoſitis quatuor terminis geometri-<lb/>ce proportionalibus primi ad tertium. </s>
            <s xml:id="N12F88" xml:space="preserve">et ſecundi <lb/>ad quartum proportionalis illatio ſic arguendo <lb/>ſicut ſe habet .8. ad .4. ita .2. ad .1. / igitur ſicut ſe ha­<lb/>bent .8. ad .2. ita .4. ad vnū. </s>
            <s xml:id="N12F91" xml:space="preserve">Et iſto modo arguen-<lb/>endi vtitur philoſophus in pleriſ locis vt in fi-<lb/>ne ſecundi perihermenias: in tertio topi. </s>
            <s xml:id="N12F98" xml:space="preserve">et in pri­<lb/>mo celi et mundi in tractatu de infinito.             <anchor type="note" xlink:href="note-0031-07" xlink:label="note-0031-07a"/>             </s>
            <s xml:id="N12FA2" xml:space="preserve">¶ Coniun­<lb/>cta proportionalitas eſt a diſiunctis terminis geo­<lb/>meteice proportionabilibus ad coniunctos pro-<lb/>portionalis illatio. </s>
            <s xml:id="N12FAB" xml:space="preserve">tali modo arguendo: ſicut ſe <lb/>habent .8. ad .4. ita .2. ad .1. / igitur ſicut ſe habent. <lb/></s>
            <s xml:id="N12FB1" xml:space="preserve">octo et quatuor ad quatuor ita duo et vnū ad vnū <lb/>             <anchor type="note" xlink:href="note-0031-08" xlink:label="note-0031-08a"/>             </s>
            <s xml:id="N12FBB" xml:space="preserve">¶ Diſiuncta proportionalitas eſt a cõiunctis ter-<lb/>minis geometrice proportionabilibus ad diſiun­<lb/>ctos proportionalis illatio. </s>
            <s xml:id="N12FC2" xml:space="preserve">tali modo arguendo / <lb/>ſicut ſe habent 8. et .4. ad .4. ita duo et vnū ad vnū / <lb/>igitur ſicut ſe habent octo ad quatuor ita duo ad <lb/>vnum.             <anchor type="note" xlink:href="note-0031-09" xlink:label="note-0031-09a"/>             </s>
            <s xml:id="N12FD0" xml:space="preserve">¶ Euerſa ꝓportionalitas eſt a diuiſis ter-<lb/>minis geometrice proportionabilibus ad coniun­<lb/>ctos ordine conuerſo ad coniunctam proportio-             <pb chead="Secunde partis" file="0032" n="32"/>             nalis illatio. </s>
            <s xml:id="N12FDC" xml:space="preserve">iſto modo arguendo ſicut ſe ha-<lb/>bent octo ad quatuor ita duo ad vnū. </s>
            <s xml:id="N12FE1" xml:space="preserve">igitur ſicut <lb/>ſe habēt vnū et duo ad duo ita quatuor et octo ad <lb/>octo. </s>
            <s xml:id="N12FE8" xml:space="preserve">Et differt iſte modus arguendi a tertio / quia <lb/>in conſequente tertii inferuntur ꝓportiones ma-<lb/>ioris inequalitatis in iſto autem inferuntur ꝓpor­<lb/>tiones minoris inequalitatis.             <anchor type="note" xlink:href="note-0032-01" xlink:label="note-0032-01a"/>             </s>
            <s xml:id="N12FF6" xml:space="preserve">¶ Equa aūt ꝓpor-<lb/>tionalitas eſt duabus multitudinibus quantita-<lb/>tum aut numerorū datis numero equalibus: et ꝓ-<lb/>portionabilibus continuo eadem proportione: ex­<lb/>cluſis mediis extremorum ꝓportionalis illatio. <lb/></s>
            <s xml:id="N13002" xml:space="preserve">Iſto modo arguendo ſicut ſe habent .1.2.4. ita .4. <lb/>8.16. / igitur ſicut ſe habent .4. ad .16. ita .1. ad 4.</s>
          </p>
          <div xml:id="N13007" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0031-05a" xlink:label="note-0031-05" xml:id="N1300B" xml:space="preserve">ꝓportõa­<lb/>litas con­<lb/>uerſa</note>
            <note position="right" xlink:href="note-0031-06a" xlink:label="note-0031-06" xml:id="N13015" xml:space="preserve">ꝑmutata</note>
            <note position="right" xlink:href="note-0031-07a" xlink:label="note-0031-07" xml:id="N1301B" xml:space="preserve">Cõiūcta.</note>
            <note position="right" xlink:href="note-0031-08a" xlink:label="note-0031-08" xml:id="N13021" xml:space="preserve">diſiūcta.</note>
            <note position="right" xlink:href="note-0031-09a" xlink:label="note-0031-09" xml:id="N13027" xml:space="preserve">Euerſa.</note>
            <note position="left" xlink:href="note-0032-01a" xlink:label="note-0032-01" xml:id="N1302D" xml:space="preserve">Equa ꝓ-<lb/>portiõa-<lb/>litas.</note>
          </div>
          <p xml:id="N13037">
            <s xml:id="N13038" xml:space="preserve">Poteris etiã exēplificare in aliis generibus pro-<lb/>portionū addendo in qualibet illarū duarū mul-<lb/>titudinū quotcun terminos volueris dūmõ ſint <lb/>continuo ꝓportionabiles: et tot in vna multitudīe <lb/>quot in altera. </s>
            <s xml:id="N13043" xml:space="preserve">¶ Et aduerte /  illa particula ſicut <lb/>ſe habent que ponitur in oībus his modis arguē-<lb/>di: denotat ſimilitudinē ſpecificã ꝓportionum.             <anchor type="note" xlink:href="note-0032-02" xlink:label="note-0032-02a"/>             </s>
            <s xml:id="N1304F" xml:space="preserve">Et <lb/>intelligitur ſic ſicut ſe habēt .1.2.4. ita .3.6.12. hoc <lb/>eſt quacun ꝓportione ꝓportionantur ſereatim <lb/>1.2.4. / eadē ꝓportione ſpecifice ꝓportionant̄̄: 3.6. <lb/>12. </s>
            <s xml:id="N1305A" xml:space="preserve">¶ Sed qm̄ hi ſex modi argumētandi in ꝓpor-<lb/>tionalitatibus ſunt plurimū vſitati: et apud phi-<lb/>loſophantes calculatores et apud primores ma-<lb/>thematicoꝝ celebres habentur quibus magnam <lb/>ſue doctrine partē demõſtrant: ideo nõ abs re eos <lb/>arguendi modos in preſentiaꝝ duxi demonſtran­<lb/>dos: qm̄ hoꝝ modoꝝ arguendi demõſtrationes ex <lb/>precedenti capite eliciūtur facile. </s>
            <s xml:id="N1306B" xml:space="preserve">Sit igitur.</s>
          </p>
          <div xml:id="N1306E" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0032-02a" xlink:label="note-0032-02" xml:id="N13072" xml:space="preserve">Denota-<lb/>tio illius <lb/>ꝑticule ſi­<lb/>cut ſe hꝫ:</note>
          </div>
          <p xml:id="N1307E">
            <s xml:id="N1307F" xml:space="preserve">Prima concluſio. </s>
            <s xml:id="N13082" xml:space="preserve">Argumentatio a <lb/>cõuerſa ꝓportiõalitate eſt neceſſariū argumentū. <lb/></s>
            <s xml:id="N13088" xml:space="preserve">Hec concluſio ſuã demonſtrationē ex tertio corre-<lb/>lario quarte cõcluſionis precedentis capitis ſorti­<lb/>tur: qm̄ illud correlariū principaliter oſtēdit hūc <lb/>modū arguēdi ꝓportiõalitate cõuerſa eſſe validū</s>
          </p>
          <p xml:id="N13091">
            <s xml:id="N13092" xml:space="preserve">Secunda concluſio modus ratioci-<lb/>nandi a ꝓportionalitate permutata ſiue cõmuta-<lb/>ta infallibilis eſt. </s>
            <s xml:id="N13099" xml:space="preserve">Probatur hec cõcluſio manife-<lb/>ſte ex quarta precedentis capitis. </s>
            <s xml:id="N1309E" xml:space="preserve">Idem enim hec <lb/>et illa intendunt.</s>
          </p>
          <p xml:id="N130A3">
            <s xml:id="N130A4" xml:space="preserve">Tertia cõcluſio </s>
            <s xml:id="N130A7" xml:space="preserve">Deductio illa et mo­<lb/>dus arguendi qui ꝓportionalitati cõiuncte īnitit̄̄ <lb/>omni exceptione eſt maior. </s>
            <s xml:id="N130AE" xml:space="preserve">Patet hec cõcluſio de-<lb/>monſtratione euidenti ex primo correlario eiuſdē <lb/>quarte concluſionis.</s>
          </p>
          <p xml:id="N130B5">
            <s xml:id="N130B6" xml:space="preserve">Quarta concluſio </s>
            <s xml:id="N130B9" xml:space="preserve">Forma ratiocinã­<lb/>di a diſiūcta ꝓportiõalitate oēm exuperat inſtan-<lb/>tiam. </s>
            <s xml:id="N130C0" xml:space="preserve">Semꝑ prauū excipio intellectū. </s>
            <s xml:id="N130C3" xml:space="preserve">Hec conclu-<lb/>ſio patrocinante quarto correlario quarte cõclu-<lb/>ſionis predicte manifeſta euadet.</s>
          </p>
          <p xml:id="N130CA">
            <s xml:id="N130CB" xml:space="preserve">Quinta concluſio </s>
            <s xml:id="N130CE" xml:space="preserve">Conſequentia il­<lb/>la que ꝓportionalitas euerſa nūcupat̄̄ omne du-<lb/>bietatis telū euertit facile: et inconcuſſa permanet <lb/></s>
            <s xml:id="N130D6" xml:space="preserve">Hec etiã cõcluſio quīti correlarii auxilio mõſtrat̄̄.</s>
          </p>
          <p xml:id="N130D9">
            <s xml:id="N130DA" xml:space="preserve">Sexta concluſio </s>
            <s xml:id="N130DD" xml:space="preserve">Equa argumenta­<lb/>tio ita equitatis mediū ſureat: vt nullo inſtantie <lb/>vicio in eã adducto ab equitatꝪ et rectitudinis tra­<lb/>mite declinet. </s>
            <s xml:id="N130E6" xml:space="preserve">Huiꝰ concluſionis inconcuſſa equi-<lb/>tas at īuiolata veritas clipeis et armis ſexti cor­<lb/>relarii eiuſdē concluſionis munitur et defenſatur <lb/></s>
            <s xml:id="N130EE" xml:space="preserve">Et hec ad demõſtrandos predictos arguendi mo­<lb/>dos dixiſſe ſufficiat / qm̄ illoꝝ correlarioꝝ demon-<lb/>ſtratio harum cõcluſionum eſt euidens probatio.</s>
          </p>
          <cb chead="Capitulum quartū."/>
        </div>
        <div xml:id="N130F7" level="3" n="4" type="chapter" type-free="capitulum">
          <head xml:id="N130FC" xml:space="preserve">Capitulum quartum / in quo agitur de ex-<lb/>ceſſu cõpoſitione et diuiſione ꝓportionū.</head>
          <p xml:id="N13101">
            <s xml:id="N13102" xml:space="preserve">AD inueſtigandum paucis ex <lb/>quibus ꝓportionibus ꝓportio aliqua <lb/>cõponitur: in quas reſoluitur: et qua vĺ <lb/>quibus minorē excedit: pono aliquas ſuppoſitio-<lb/>nes quarum alique ſunt diffinitiones: et petitio-<lb/>nes: alie vero demonſtrabuntur.</s>
          </p>
          <p xml:id="N1310F">
            <s xml:id="N13110" xml:space="preserve">Prima ſuppoſitio. </s>
            <s xml:id="N13113" xml:space="preserve">Primi termini a-<lb/>licuius ꝓportionis ſunt illi qui in ſua ꝓportione <lb/>ſunt minimi.             <anchor type="note" xlink:href="note-0032-03" xlink:label="note-0032-03a"/>             </s>
            <s xml:id="N1311F" xml:space="preserve">Minimi autē termini alicuiꝰ ꝓporti-<lb/>onis (et loquor tam in quantitate continua quam <lb/>diſcreta) ſunt quorū minor denominatur ab vni-<lb/>tate: maior vero a numero vel numero cū fractiõe <lb/>vel vnitate cū fractione. </s>
            <s xml:id="N1312A" xml:space="preserve">Hec nõ ꝓbatur / q2 diffini­<lb/>tio eſt ſed exēplo explicatur binarius em̄ et vnitas <lb/>ſunt primi termini ꝓportionis duple: ternarius et <lb/>vnitas triple: quaternarius et vnitas quadruple: <lb/>et ſic cõſequenter. </s>
            <s xml:id="N13135" xml:space="preserve">Unitas et vnitas cū medietate: et <lb/>vnitas cū vnitate et tertia. </s>
            <s xml:id="N1313A" xml:space="preserve">Itē vnitas cū quarta et <lb/>vnitas / et ſic cõſequenter ſunt primi termini ſuper-<lb/>particulariū proportionum. </s>
            <s xml:id="N13141" xml:space="preserve">Unitatis .n. cum me-<lb/>dietate ad vnitatem eſt ſexquialtera: et vnitatis <lb/>cum tertia ad vnitatem ſexquitertia: vnitatis cum <lb/>quarta ſexquiquarta: et ſic conſequēter. </s>
            <s xml:id="N1314A" xml:space="preserve">Et iſto mo­<lb/>do exēplificabis in aliis generibus proportionis.</s>
          </p>
          <div xml:id="N1314F" level="4" n="1" type="float">
            <note position="right" xlink:href="note-0032-03a" xlink:label="note-0032-03" xml:id="N13153" xml:space="preserve">Minimi <lb/>termini.</note>
          </div>
          <p xml:id="N1315B">
            <s xml:id="N1315C" xml:space="preserve">Secunda ſuppoſitio. </s>
            <s xml:id="N1315F" xml:space="preserve">Denominatio <lb/>alicuius ꝓportionis eſt illa que ſumitur a maiori <lb/>primoꝝ terminoꝝ talis ꝓportionis. </s>
            <s xml:id="N13166" xml:space="preserve">vt denomina­<lb/>tio duple ſumitur a binario qui eſt maior termi-<lb/>norū primoꝝ proportionis duple: et denominatio <lb/>ſexquialtere ab vnitate cū dimidio.             <anchor type="note" xlink:href="note-0032-04" xlink:label="note-0032-04a"/>             </s>
            <s xml:id="N13174" xml:space="preserve">¶ Ex quo ſe-<lb/>quitur /  ſpecies ꝓportionis multiplicis denomi­<lb/>nãtur cõſequenter a naturali ſerie numeroꝝ. </s>
            <s xml:id="N1317B" xml:space="preserve">Ptꝫ / <lb/>q2 maior terminus primoꝝ terminoꝝ ꝓportionis <lb/>duple eſt binariꝰ, triple, ternariꝰ, quadruple qua­<lb/>ternarius: et ſic conſequēter ꝓcedendo per natura­<lb/>lē ſeriē numeroꝝ referendo numeros ad vnitatem / <lb/>igitur ex ſecūda ſuppoſitione tales ſpecies deno-<lb/>minantur a naturali ſerie.             <anchor type="note" xlink:href="note-0032-05" xlink:label="note-0032-05a"/>             </s>
            <s xml:id="N1318F" xml:space="preserve">¶ Sequitur ſecundo /  <lb/>ſpecies ꝓportionis ſuperparticularis denominã­<lb/>tur ab vnitate cū aliqua parte aliquota. </s>
            <s xml:id="N13196" xml:space="preserve">Probat̄̄ / <lb/>q2 maior terminus primoꝝ numeroꝝ ꝓportionis <lb/>ſexquialtere eſt vnitas cū dimidio: et ſexquitertie <lb/>vnitas cū tertia: et ſexquiquarta cū quarta / et ſex-<lb/>quiquinta cū quinta: et ſic conſequenter deſcendē-<lb/>do per partes aliquotas denominatas continuo <lb/>a naturali ſerie numeroꝝ: igitur ſpecies ꝓportio-<lb/>nis ſuperparticularis denominantur ab vnitate <lb/>cū parte aliquota.             <anchor type="note" xlink:href="note-0032-06" xlink:label="note-0032-06a"/>             </s>
            <s xml:id="N131AE" xml:space="preserve">¶ Sequitur tertio /  oēs ſpeci-<lb/>es ꝓportionis ſuprapartientis denominantur ab <lb/>vnitate cū aliquot partibus aliquotis nõ facien-<lb/>tibus vnã. </s>
            <s xml:id="N131B7" xml:space="preserve">Probatur / q2 maior primoꝝ terminoꝝ <lb/>ꝓportionis ſuprabipartientis tertias eſt vnitas <lb/>cū duabus tertiis: et ſuprapartiētis quītas vni-<lb/>tas cū duabus quintis: et ſuprabipartientis ſepti­<lb/>mas vnitas cū duabus ſeptimis: et ſic conſequen-<lb/>ter: diſcurrēdo per duas partes aliquotas nume-<lb/>ri imparis. </s>
            <s xml:id="N131C6" xml:space="preserve">Item diſcurrendo per tres partes ali­<lb/>quotas nõ facientes vnã. / per quatuor. / per quin / <lb/>et ſic conſequenter: igitur ſpecies ꝓportionis ſu-<lb/>prapartiētis denominãtur ab vnitate cū aliquot <lb/>partibus aliquotis nõ facientibus vnã             <anchor type="note" xlink:href="note-0032-07" xlink:label="note-0032-07a"/>             </s>
            <s xml:id="N131D6" xml:space="preserve">¶ Sequit̄̄ <lb/>quarto /  ꝓportiones cõpoſite denominãtur a nu­<lb/>mero cū fractione partis aliquote vel partiū ali-<lb/>quotarū nõ facientiū vnã. </s>
            <s xml:id="N131DF" xml:space="preserve">Oſtendas hoc correla-<lb/>riū ſicut precedentia.</s>
          </p>
          <div xml:id="N131E4" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0032-04a" xlink:label="note-0032-04" xml:id="N131E8" xml:space="preserve">1. correla­<lb/>rium.</note>
            <note position="right" xlink:href="note-0032-05a" xlink:label="note-0032-05" xml:id="N131F0" xml:space="preserve">2. correĺ.</note>
            <note position="right" xlink:href="note-0032-06a" xlink:label="note-0032-06" xml:id="N131F6" xml:space="preserve">3. correĺ.</note>
            <note position="right" xlink:href="note-0032-07a" xlink:label="note-0032-07" xml:id="N131FC" xml:space="preserve">4. correĺ.</note>
          </div>
          <pb chead="Prime partis" file="0033" n="33"/>
          <p xml:id="N13206">
            <s xml:id="N13207" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N1320A" xml:space="preserve">Oēs proportiões <lb/>ſūt eq̈les quarū denoīationes ſunt eq̈les et illa ma­<lb/>ior cuiꝰ denoīatio ē maior: et illa mīor: cuiꝰ denoīa­<lb/>tio mīor. </s>
            <s xml:id="N13213" xml:space="preserve">Illa autem denoīatio dicitur maior / que <lb/>ſumitur a maiori numero cū fractione vel ſine: vel <lb/>ab vnitate cū maiori fractione.             <anchor type="note" xlink:href="note-0033-01" xlink:label="note-0033-01a"/>             </s>
            <s xml:id="N1321F" xml:space="preserve">Hec nõ demõſtra-<lb/>tur / q2 diffinitio eſt / et a iordauo petitur in princi-<lb/>pio ſecūdi elemētoꝝ. </s>
            <s xml:id="N13226" xml:space="preserve">Exemplū / vt ꝓportio que eſt <lb/>8. ad .4. eſt equalis ꝓportioni que eſt .2. ad .1. quia <lb/>vtra illarū denominatur dupla. </s>
            <s xml:id="N1322D" xml:space="preserve">Sexquialtera <lb/>autē maior eſt ſexquitertia: q2 denominatio eius <lb/>maior eſt: denominatur em̄ ab vnitate cū medieta­<lb/>te: altera vero ab vnitate cum tertia. </s>
            <s xml:id="N13236" xml:space="preserve">Modo plus <lb/>eſt vnitas cū medietate quã cū tertia.</s>
          </p>
          <div xml:id="N1323B" level="4" n="3" type="float">
            <note position="left" xlink:href="note-0033-01a" xlink:label="note-0033-01" xml:id="N1323F" xml:space="preserve">Ior. ſcḋo <lb/>ele.</note>
          </div>
          <p xml:id="N13247">
            <s xml:id="N13248" xml:space="preserve">Quarta ſuppoſitio. </s>
            <s xml:id="N1324B" xml:space="preserve">Omne totum ex <lb/>quantolibet minori eo cõponitur: et diſtribuat ly <lb/>quãtolibet pro generibus ſingnloꝝ. </s>
            <s xml:id="N13252" xml:space="preserve">Probat̄̄ hec <lb/>ſuppoſitio / q2 quãtūlibet minus aliquo maiori eo <lb/>eſt pars illius: ergo ex quãtolibet tali cõponitur. <lb/></s>
            <s xml:id="N1325A" xml:space="preserve">Probatur antecedens / q2 capto vno pedali: quã-<lb/>talibet mīor quãtitas pedali eſt ꝑs eiꝰ / vt ptꝫ ex ſe.</s>
          </p>
          <p xml:id="N1325F">
            <s xml:id="N13260" xml:space="preserve">Quinta ſuppoſitio. </s>
            <s xml:id="N13263" xml:space="preserve">Omne cõpoſitū <lb/>ex duobus equalibus adequate: eſt preciſe duplū <lb/>ad vtrū illoꝝ: et omne cõpoſitū ex tribus equali-<lb/>bus adequate eſt triplum ad quodlibet illoꝝ: et ex <lb/>quattuor quadruplū: et ex quin quintuplum .etc̈. <lb/></s>
            <s xml:id="N1326F" xml:space="preserve">Patet hec ſuppoſitio ex diffinitione dupli, tripli <lb/>quadrupli, et ſic ſine termino.</s>
          </p>
          <p xml:id="N13274">
            <s xml:id="N13275" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N13278" xml:space="preserve">Omne cõpoſituꝫ <lb/>ex duobus inequalibus eſt maius quã duplum ad <lb/>minꝰ illoꝝ: et minus quã duplū ad maius illoꝝ: et <lb/>ſi cõponatur ex tribus inequalibus: eſt maius quã <lb/>triplū ad minimū illoꝝ: et minꝰ quã triplū ad ma-<lb/>ximū: et ſi ex quattuor eſt maius quã quadruplum <lb/>ad minimū illoꝝ: et minus quã quadruplū ad ma­<lb/>ximū: et ſic conſequēter: ſi cõponatur ex quin, ex <lb/>ſex .etc̈. </s>
            <s xml:id="N1328B" xml:space="preserve">Probatur prima pars: q2 illud cõpoſitum <lb/>continet minus illorū duorū bis: et aliquid vltra: <lb/>ergo eſt maius quã duplū ad illud. </s>
            <s xml:id="N13292" xml:space="preserve">Cõſequētia eſt <lb/>nota: et antecedens ꝓbatur: q2 ſi ↄ̨tineret minꝰ bis <lb/>adequate iam illud eſſet ſua medietas: et per con-<lb/>ſequens reſiduū etiã eſſet medietas: et ſic illa duo <lb/>eſſent equalia / quod eſt contra hypotheſim. </s>
            <s xml:id="N1329D" xml:space="preserve">Alia <lb/>pars huius partis ſimiliter ꝓbatur / q2 ſi eſſet du-<lb/>plū ad maius illoꝝ / iã illud eſſet ſua medietas / qḋ <lb/>modo eſt īpugnatū. </s>
            <s xml:id="N132A6" xml:space="preserve">Secūda pars probatur / quia <lb/>illud cõpoſitū continet minimū illoꝝ triū ter et a-<lb/>liquid vltra: ergo eſt pluſquã triplū ad illud. </s>
            <s xml:id="N132AD" xml:space="preserve">Con­<lb/>ſequētia patet et antecedens ꝓbatur / q2 ſi cõtineret <lb/>eū ter adequate iã illud eſſet vna tertia eius / vt ptꝫ <lb/>ex ſe et ꝑ cõſequēs alie due partes eſſent due tertie / <lb/>et ſic aggregatū ex eis eſſet dupluꝫ ad illud mini-<lb/>mū: ſed hoc eſt falſum: q2 alterū illoꝝ duoꝝ eſt ma­<lb/>ius iſto minimo: et aliud equale vel maius / vt con-<lb/>ſtat: igitur aggregatū ex iſtis duobꝰ eſt maiꝰ quã <lb/>duplū ad illud minimū. </s>
            <s xml:id="N132C0" xml:space="preserve">Alia pars huius partis <lb/>ꝓbatur / q2 maximū illoꝝ triū eſt maius quã tertia / <lb/>ergo cõpoſitū ex illis eſt minꝰ quã triplū ad illud. <lb/></s>
            <s xml:id="N132C8" xml:space="preserve">Cõſequentia patet et antecedens ꝓbatur / q2 ſi eſſet <lb/>adeq̈te tertia iã alie due ꝑtes eſſent due tertie: et ſic <lb/>aggregatū ex eis eſſet duplū ad illud / qḋ eſt falſuꝫ / <lb/>q2 aggregatū ex aliis duobus componitur ex vno <lb/>minori illo: et alio equali vel minori: igitur aggre­<lb/>gatū ex eis nõ eſt duplū ad illud. </s>
            <s xml:id="N132D5" xml:space="preserve">Et ſic ꝓbabis ali­<lb/>as partes. </s>
            <s xml:id="N132DA" xml:space="preserve">Patet igitur ſuppoſitio.</s>
          </p>
          <p xml:id="N132DD">
            <s xml:id="N132DE" xml:space="preserve">Septima ſuppoſitio. </s>
            <s xml:id="N132E1" xml:space="preserve">Quãdo aliqua <lb/>latitudo ſiue exceſſus additur alicui maiorē ꝓpor­             <cb chead="Capitulū ſequartū."/>             tionē acquirit quã quãdo eidē additur minor ex-<lb/>ceſſus ſiue latitudo: vt quando quaternario addi­<lb/>tur quaternarius maiorē ꝓportionē acquirit quã <lb/>quando ei additur binarius: </s>
            <s xml:id="N132EF" xml:space="preserve">Et ex conſequenti ſe-<lb/>quitur /  quãdo aliq̇d deperdit aliquã latitudinē <lb/>ſiue quantitatē maiorē ꝓportionē deperdit quaꝫ <lb/>quando deperdit minorē latitudinē. </s>
            <s xml:id="N132F8" xml:space="preserve">Hec ſuppoſi­<lb/>tio cū ſuo correlario propter ſui euidentiã nõ pro­<lb/>batur: ſed ſimpliciter petitur.</s>
          </p>
          <p xml:id="N132FF">
            <s xml:id="N13300" xml:space="preserve">Octaua ſuppoſitio. </s>
            <s xml:id="N13303" xml:space="preserve">Quãdocū idē <lb/>exceſſus ſiue latitudo additur maiori et mīori: ma­<lb/>iorē ꝓportionē acquirit minꝰ quã maius. </s>
            <s xml:id="N1330A" xml:space="preserve">Et cum <lb/>maius et minus deperdūt eandē latitudinē ſiue ex­<lb/>ceſſum maiorē ꝓportionē deperdit minus quã ma­<lb/>ius: vt ſi quaternarius et octonarius perdant bi-<lb/>nariū maiorē ꝓportionē deperdit quaternarius <lb/>quã octonarius. </s>
            <s xml:id="N13317" xml:space="preserve">Quaternarius em̄ perdit ꝓpor-<lb/>tionē duplã: octonarius vero ſexquitertiã: vt con-<lb/>ſtat. </s>
            <s xml:id="N1331E" xml:space="preserve">Et ſi binarius et ſenarius binariū acquirant <lb/>binariꝰ eadē ratione maiorē ꝓportionē acquirit <lb/>quam ſenarius: vt cõſtat. </s>
            <s xml:id="N13325" xml:space="preserve">Probatur / ſint a.b. due <lb/>quantitates ſine numeri ſiue que vis alie latitudi-<lb/>nes a. maior et b. minor que ſe habeant in ꝓporti-<lb/>one f. et acquirat tam a. quã b.d. exceſſum ſiue lati-<lb/>tudinē: tunc dico /  b. maiorē ꝓportionē acquirit <lb/>quã a. </s>
            <s xml:id="N13332" xml:space="preserve">Quod ſic ꝓbatur: et volo /  quãdo a. acqui-<lb/>rit d. antea quã b. acquirat ipſum d. acquirat vnã <lb/>quantitatē ad quã d. ſe habet in ꝓportione f. et ſit <lb/>illa quantitas e. / et arguitur ſic / a. et b. ſe habent in <lb/>ꝓportione f. et quantitas acquiſita ipſi a ſe habet <lb/>etiã in eadē ꝓportione ad quantitatē acquiſitam <lb/>ipſi b. / ergo continuo a. et b. manent in eadē ꝓpor-<lb/>tione f. in qua ſe habebant ante talē acquiſitionē. <lb/></s>
            <s xml:id="N13344" xml:space="preserve">Patet hec cõſequentia ex quīto correlario quīte <lb/>concluſionis ſecūdi capitis huiꝰ: et per cõſequens <lb/>tantã ꝓportionē acquiſiuit b. ſupra ſe quantam a <lb/>ſupra ſe. </s>
            <s xml:id="N1334D" xml:space="preserve">Si em̄ b. acquiſiuiſſet minorē iã ꝓportio <lb/>inter a. et b. fuiſſet augmentata: et ſi maiorem iam <lb/>fuiſſet diminuta: qm̄ quantã ꝓportionē acquirit <lb/>numerus minor vltra numeꝝ maiorē tantã deꝑdit <lb/>ꝓportio inter illos numeros: et quantã numerus <lb/>maior acquirit vltra minorē tãtã acq̇rit ꝓportio <lb/>inṫ illos nūeros ſiue q̄uis alia latitudo: vt ↄ̨ſtat ex <lb/>ſuꝑioribꝰ et ex ↄ̨ñti quantã ꝓportionē acq̇ſiuit b. ꝑ <lb/>acquiſitionē e. latitudinis tantã adequate acqui-<lb/>ſiuit a. per additionē d. latitudinis et eocõtra. </s>
            <s xml:id="N13362" xml:space="preserve">igit̄̄ <lb/>quando b. acquirit d. maiorē latitudinē quã ſit e. <lb/>maiorē ꝓportionē acquirit: et per cõſequens ma-<lb/>iorē ꝓportionē acquirit b: acquirendo d. quam a. <lb/>acquirendo d. / quod fuit probandū. </s>
            <s xml:id="N1336D" xml:space="preserve">Patet tamen <lb/>conſequentia ex ſeptima ſuppoſitione huiꝰ capi-<lb/>tis. </s>
            <s xml:id="N13374" xml:space="preserve">Et ſic patet prima pars: et ſecunda facile ꝓba-<lb/>tur / qm̄ ſi quando a. et b. acquirūt d. latitudinē ma­<lb/>iorē ꝓportionē acquirit b. quã a. / ſequitur /  cū de­<lb/>perdunt eandē d. latitudinē maiorē ꝓportionem <lb/>deperdit b. quã a. </s>
            <s xml:id="N1337F" xml:space="preserve">Nam adequate perdit illã quã <lb/>acquiſiuit et maiorē acquiſiuit: ergo maiorem de-<lb/>perdit. </s>
            <s xml:id="N13386" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
          </p>
          <p xml:id="N13389">
            <s xml:id="N1338A" xml:space="preserve">His iactis fundamentis ſit prima cõ­<lb/>cluſio. </s>
            <s xml:id="N1338F" xml:space="preserve">Oīs ꝓportio multiplex, multiplex ſuꝑpar-<lb/>ticularis, vel multiplex ſuprapartiens eſt maior <lb/>ꝓportione ſuperparticulari vel ſuprapartiente. <lb/></s>
            <s xml:id="N13397" xml:space="preserve">Probatur: q2 cuiuſlibet ꝓportionis multiplicis, <lb/>multiplicis ſuꝑparticularis, vel multiplicis ſu-<lb/>prapartiens, denominatio eſt maior quã alicu-<lb/>ius ſuperparticularis vel ſuprapartientis: igitur <lb/>quelibet ꝓportio multiplex, aut multiplex ſuper-<lb/>particularis, aut multiplex ſuprapartiēs, eſt ma­             <pb chead="Secunde partis" file="0034" n="34"/>             ior ꝓportione ſuꝑparticulari aut ſuprapartiente <lb/></s>
            <s xml:id="N133AA" xml:space="preserve">Conſequētia eſt nota ex tertia ſuppoſitione et an-<lb/>tecedēs ꝓbatur: q2 denominationes illaꝝ ꝓpor-<lb/>tionum multiplicis, multiplicis ſuꝑparticularis, <lb/>et multiplicis ſuprapartientis, ſumūtur a nūero <lb/>vel numero cum fractione: denominationis vero <lb/>ſuꝑparticularis, aut ſuprapartientis, ſumuntur <lb/>ab vnitate cū fractione: vt patet ex correlariis ſe-<lb/>cunde ſuppoſitionis huiꝰ capitis: igitur denomi-<lb/>nationes illaꝝ puta multiplicis: multiplicis .etc̈. <lb/>ſunt maiores quã ſuꝑparticularis aut ſuprapar-<lb/>tientis. </s>
            <s xml:id="N133C1" xml:space="preserve">Et ſic patet cõcluſio.             <anchor type="note" xlink:href="note-0034-01" xlink:label="note-0034-01a"/>             </s>
            <s xml:id="N133C9" xml:space="preserve">¶ Ex qua ſequitur pri­<lb/>mo:  ꝓportiones multiplices ſuꝑparticulares: et <lb/>multiplices ſuprapartientes ſunt maiores ꝓpor-<lb/>tionibꝰ multiplicibꝰ: ita  quelibet multiplex <lb/>ſuꝑparticĺaris, aut ſuprapartiēs, qualibet mul-<lb/>tiplici ab eodē numero denominata eſt maior: vt <lb/>dupla ſexquialtera eſt maior dupla: tripla ſexqui­<lb/>quarta maior tripla: tripla em̄ et tripla ſexquiq̈r­<lb/>ta ab eodē numero denominantur: ſed nõ adequa­<lb/>te. </s>
            <s xml:id="N133DE" xml:space="preserve">Patet hoc correlariū eo modo quo concluſio. <lb/>             <anchor type="note" xlink:href="note-0034-02" xlink:label="note-0034-02a"/>             </s>
            <s xml:id="N133E8" xml:space="preserve">¶ Sequitur ſecūdo:  ex dictis faciliter eſt inueni­<lb/>re modū cognoſcendi ꝓpoſitis ꝓportiõe ſuꝑpar-<lb/>ticulari et ſuprapartiēte: que illaꝝ ſit maior. </s>
            <s xml:id="N133EF" xml:space="preserve">Pro­<lb/>batur: et ꝓponantur due ꝓportiones a. ſuꝑparti-<lb/>cularis et b. ſuprapartiēs: et cū quelibet ſuprapar­<lb/>tiens denominetur ab vnitate cū fratione partiū <lb/>aliquotaꝝ nõ facientiū vnã: et quelibet ſuꝑparti-<lb/>cularis ab vnitate cū fractiõe partis aliquote: vt <lb/>dictū eſt: et omne aggregatū ex partibus aliquotꝪ <lb/>alicuiꝰ nõ facientibus vnã eſt qualibet parte ali-<lb/>quota eiuſdē maius vel minꝰ: vel igitur illud ag-<lb/>gregatū partiū aliquotaꝝ a quo denoīatur ꝓpor­<lb/>tio b. ſuprapartiens eſt maius parte aliquota a <lb/>qua denomīatur ꝓportio a. ſuꝑparticularis: aut <lb/>minus: ſi maius tūc ꝓportio ſuprapartiēs eſt ma-<lb/>ior data ꝓportione ſuꝑparticulari a. </s>
            <s xml:id="N1340C" xml:space="preserve">Sin minus <lb/>tunc ꝓportio ſuꝑparticularis eſt maior data ꝓ-<lb/>portiõe b. ſuprapartiente: qm̄ denomīatur ab vni­<lb/>tate cū maiori fractione.</s>
          </p>
          <div xml:id="N13415" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0034-01a" xlink:label="note-0034-01" xml:id="N13419" xml:space="preserve">1. correla­<lb/>rium.</note>
            <note position="left" xlink:href="note-0034-02a" xlink:label="note-0034-02" xml:id="N13421" xml:space="preserve">2. correĺ.</note>
          </div>
          <p xml:id="N13427">
            <s xml:id="N13428" xml:space="preserve">Secunda concluſio. </s>
            <s xml:id="N1342B" xml:space="preserve">Oīs proportio <lb/>extremi ad extremū cõponitur ex qualibet minori <lb/>ꝓportiõe illa: vt ꝓportio dupla cõponitur ex qua­<lb/>libet ꝓportione ſuprapartiente: et qualibet ſuper­<lb/>particulari. </s>
            <s xml:id="N13436" xml:space="preserve">Et diſtribuat ly qualibet pro generi-<lb/>bus ſinguloꝝ. </s>
            <s xml:id="N1343B" xml:space="preserve">Probatur hec cõcluſio oſtenſiue ex <lb/>quarta ſuppoſitione: qm̄ ſi omne cõpoſitū ex quã­<lb/>tolibet minori eo cõponitur: et oīs ꝓportio eſt cõ-<lb/>poſita ex aliquibus ꝓportionibus / vt ſupponitur <lb/>cõſequens eſt /  oīs ꝓportio ex qualibet mīori ea <lb/>cõponatur / quod fuit ꝓbandū.             <anchor type="note" xlink:href="note-0034-03" xlink:label="note-0034-03a"/>             </s>
            <s xml:id="N1344D" xml:space="preserve">¶ Ex hac cõcluſiõe <lb/>ſequitur primo:  quelibet ꝓportio cõponitur ex <lb/>qualibet ꝓportione medioꝝ ad īuicē: et mediorum <lb/>ad extrema. </s>
            <s xml:id="N13456" xml:space="preserve">vt ꝓportio dupla que eſt inter .8. et .4. <lb/>cõponitur ex ꝓportione .7. ad .6. et .6. ad .5. que ſūt <lb/>ꝓportiones medioꝝ: et ex ꝓportione .8. ad .7. et .5. <lb/>ad .4. que ſunt extremi ad mediū et medii ad extre­<lb/>mū. </s>
            <s xml:id="N13461" xml:space="preserve">Probatur correlariū: q2 quelibet talis pro-<lb/>portio eſt pars illius ꝓportiõis extremi ad extre-<lb/>mū cū cõponat eã: et eſt minor illa vt patet ex ṗma <lb/>cõcluſione: igitur cõponitur ex qualibet ꝓportiõe <lb/>medioꝝ: et medioꝝ ad extrema.             <anchor type="note" xlink:href="note-0034-04" xlink:label="note-0034-04a"/>             </s>
            <s xml:id="N13471" xml:space="preserve">¶ Sequitur ſecūdo / <lb/> oīs ꝓportio ex infinitis ꝓportionibus cõponit̄̄ <lb/></s>
            <s xml:id="N13477" xml:space="preserve">Probatur / qm̄ ex qualibet minore ea cõponitur: <lb/>vt ptꝫ ex cõcluſione: ſed qualibet data infinite ſunt <lb/>minores: ergo quelibet ex infinitis cõponit̄̄. </s>
            <s xml:id="N1347E" xml:space="preserve">Pro-<lb/>batur minor / q2 ymaginor quãlibet proportionē <lb/>inequalitatis eſſe latitudinē in infinitū diuiſibilē <lb/>q2 alias nõ poſſet augeri nec ad nõ gradū ꝓpor-             <cb chead="Capitulum quartū."/>             tionis inequalitatis ſucceſſiue diminui.             <anchor type="note" xlink:href="note-0034-05" xlink:label="note-0034-05a"/>             </s>
            <s xml:id="N1348F" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio:  oīs ꝓportio poteſt in infinitas ꝓportio-<lb/>nes diuidi: que ꝓportiones ſe habebūt vt partes <lb/>ꝓportionales illiꝰ: et hoc qua volueris ꝓportiõe. <lb/></s>
            <s xml:id="N13499" xml:space="preserve">Patet: q2 cū quelibet ꝓportio ſit latitudo quedã: <lb/>ipſa habet medietatē, tertiã, quartã, ſextam, et ſic <lb/>deinceps: et ꝑ cõſequens quauis ꝓportione diuiſi­<lb/>bilis eſt in infinitas ꝓportiones que ſunt partes <lb/>ꝓportionales eius. </s>
            <s xml:id="N134A4" xml:space="preserve">¶ Sequit̄̄ quarto:  ſi aliqua <lb/>ꝓportio maioris inequalitatis diminuatur vſ <lb/>ad ꝓportionē equalitatis neceſſe eſt ipſam conti-<lb/>nuo ſucceſſiue tranſire per īfinitas ꝓportiones mi­<lb/>nores ea: vt ſi ꝓportio .8. ad .4. deueniat ad ꝓpor­<lb/>tioneꝫ equalitatis per diminutionem ipſorum .8. <lb/>vſ ad .4. neceſſe eſt eã tranſire per oēs ꝓportiões <lb/>ex quibus cõponitur talis ꝓportio .8. ad .4. et ille <lb/>ſunt infinte vt dicit ſecundū correlariū: igit̄̄. </s>
            <s xml:id="N134B7" xml:space="preserve">Ma­<lb/>ior patet / q2 cū cõtinuo aliquid diminuitur vſ ad <lb/>certã quantitatē per infinitas minores quantita­<lb/>tes tranſit: vt notū eſt. </s>
            <s xml:id="N134C0" xml:space="preserve">Et ſic ſimiliter eſt de quali-<lb/>bet latitudine que continuo ſucceſſiue diminuitur <lb/>ſed ꝓportio .8. ad .4. eſt latitudo que continuo ſuc­<lb/>ceſſiue diminuitur (vt pono) igitur. </s>
            <s xml:id="N134C9" xml:space="preserve">et ſic patet cor-<lb/>relariū: qm̄ eo modo ꝓbabis de quauis alia.</s>
          </p>
          <div xml:id="N134CE" level="4" n="5" type="float">
            <note position="left" xlink:href="note-0034-03a" xlink:label="note-0034-03" xml:id="N134D2" xml:space="preserve">1: correĺ.</note>
            <note position="left" xlink:href="note-0034-04a" xlink:label="note-0034-04" xml:id="N134D8" xml:space="preserve">2. correĺ.</note>
            <note position="right" xlink:href="note-0034-05a" xlink:label="note-0034-05" xml:id="N134DE" xml:space="preserve">3. correĺ.</note>
          </div>
          <p xml:id="N134E4">
            <s xml:id="N134E5" xml:space="preserve">Tertia concluſio. </s>
            <s xml:id="N134E8" xml:space="preserve">Quãlibet propor-<lb/>tionē in duas equales ꝓportiões ſecare: vt capta <lb/>ꝓportione que eſt .8. ad .4. ipſa in duas inequales <lb/>diuidetur inuento numero ſine termino equaliter <lb/>diſtante ab vtro extremoꝝ: puta īuento numero <lb/>ſenario .8. em̄ ad .6. eſt ꝓportio ſexquitertia: et .6. <lb/>ad .4. proportio ſexquialtera: et hec maior eſt illa. <lb/></s>
            <s xml:id="N134F8" xml:space="preserve">Probatur hec concluſio: q2 aut talis ꝓportio da­<lb/>tur inter duas quantitates cõtinuas: aut inter du­<lb/>os numeros: ſi inter duas quantitates cõtinuas: <lb/>ille erunt inequales: qm̄ de ꝓportione maioris in­<lb/>equalitatis loquimur: capiatur igitur quantitas <lb/>media inter illas que equaliter diſtat ab vtra il­<lb/>larū: et tunc manifeſtū eſt /  maioris illaꝝ quanti-<lb/>tatū ad quãtitatē mediã eſt vna ꝓportio: et medie <lb/>quantitatis ad minimã illaꝝ eſt vna alia ꝓportio <lb/>et illa ꝓportio que eſt inter illas quantitates di-<lb/>uiditur in illas duas ꝓportiones ītermedias, q2 <lb/>ex illis cõponitur / vt patet ex primo correlario ſe-<lb/>cunde concluſionis: et prima illaꝝ que videlicet eſt <lb/>maioris quantitatis ad mediã minor eſt illa que <lb/>eſt medie ad alterū extremū minꝰ: igitur talis ꝓ-<lb/>portio diuiditur in duas proportiões inequales / <lb/>quod fuit ꝓbandū. </s>
            <s xml:id="N1351B" xml:space="preserve">Minor ꝓbatur: q2 illa quãti-<lb/>tas media ꝑ tantū excedit minus extremū: ꝑ quan­<lb/>tū adequate maius extremū excedit illã: igit̄̄ ma-<lb/>ior eſt ꝓportio illius quantitatis medie ad minus <lb/>extremū: quã alteriꝰ extremi puta maioris ad me­<lb/>diã. </s>
            <s xml:id="N13528" xml:space="preserve">Patet hec cõſequentia ex octaua ſuppoſitiõe <lb/>huiꝰ capitis. </s>
            <s xml:id="N1352D" xml:space="preserve">Sin autē talis ꝓportio eſt inter nu-<lb/>meros puta inter a. et c. quoꝝ a. eſt maior et c. mīor / <lb/>vel igit̄̄ illi nūeri ſunt pares: vĺ nõ pares ſi pares <lb/>manifeſtū eſt /  aggregatū ex eis eſt nūerus par: <lb/>et ꝑ cõſequens hꝫ medietatē: et illa medietas eſt me­<lb/>diū inter illos duos numeros a.c. / vt patet ex ṗmo <lb/>correlario prime cõcluſionis ſecūdi capitis huiꝰ: <lb/>ſit igitur illud mediū b. / et ſequit̄̄ /  a. ad b. eſt vna <lb/>ꝓportio: et b. ad c. eſt vna altera: et ex illis cõponit̄̄ <lb/>ꝓportio a. ad b. / vt ptꝫ ex primo correlario ſecūde <lb/>cõcluſionis huiꝰ: et prima illaꝝ que videlicet eſt a. <lb/>ad b. eſt minor quã illa que eſt b. ad .c. / quod ptꝫ vt <lb/>ſupra: igitur ꝓportio a. ad c. in duas ꝓportiones <lb/>inequales ſecatur. </s>
            <s xml:id="N1354A" xml:space="preserve">Sin nõ pares creſcat vter il-<lb/>loꝝ duoꝝ numeroꝝ ad ſuū duplū: et ſequitur /  eq̈­<lb/>lem ꝓportionē acquirit maior illoꝝ et minor puta             <pb chead="Prime partis" file="0035" n="35"/>             duplã: manent igitur in eadē ꝓportione / vt ptꝫ ex <lb/>correlario decime ſuppoſitiõis ſecūdi capitꝪ huiꝰ <lb/>īueniatur / igitur mediū inter illos duos numeros <lb/>et īueniētur due ꝓportiones tnequales in quas di­<lb/>uiditur ꝓportio inter illos duos numeros / vt pre-<lb/>oſtenſum eſt. </s>
            <s xml:id="N13560" xml:space="preserve">Patet igitur vniuerſaliter concluſio <lb/>             <anchor type="note" xlink:href="note-0035-01" xlink:label="note-0035-01a"/>             </s>
            <s xml:id="N1356A" xml:space="preserve">¶ Ex qua ſequitur primo /  quelibet proportio in <lb/>infinitas ꝓportiones ſecari valet in numeris ſine <lb/>vnitatis fractione: et capio ly infinitas ſyncathe-<lb/>goreumatice. </s>
            <s xml:id="N13573" xml:space="preserve">Probatur / qm̄ capta ꝓportione a. <lb/>in numeris manifeſtū eſt /  illi numeri ſaltē ꝑ vni-<lb/>tatē diſtabūt / hoc eſt ſaltē maior excedit minorē ꝑ <lb/>vnitatē que vnitas eſt pars aliquota minoris: du­<lb/>pletur igitur vter illoꝝ numeroꝝ: et ſequitur /  <lb/>adhuc inter illos numeros duplatos manet ꝓpor­<lb/>tio a. / vt paulo ãte deductū eſt: igitur iam exceſſus <lb/>erit in duplo maior: q2 erit pars aliquota eiuſdē <lb/>denomīationis numeri in duplo maioris: igitur <lb/>iam ibi inter illos duos numeros reperietur vnꝰ <lb/>numerus medius vt ſuperiꝰ oſtenſum eſt: et ꝑ cõſe-<lb/>quens due ꝓportiones inequales in quas diuidit̄̄ <lb/>talis ꝓportio. </s>
            <s xml:id="N1358E" xml:space="preserve">Iteꝝ duplent̄̄ illi numeri īter quos <lb/>eſt ꝓportio a. et iam inter eos īuenientur tres nu-<lb/>meri intermedii et ſic erūt quatuor ꝓportiões in-<lb/>termedie. </s>
            <s xml:id="N13597" xml:space="preserve">Et ſi tertio duplentur illi numeri īueni-<lb/>entur ſeptē numeri intermedii: et ſic erūt .8. ꝓpor-<lb/>tiones: et ſic in infinitū duplando ſemꝑ numeros. <lb/></s>
            <s xml:id="N1359F" xml:space="preserve">Data igit̄̄ quã volueris ꝓportione ipſa vel ſibi e-<lb/>qualis (quod ꝓ eodē reputo) in infinitas ꝓportio-<lb/>nes ſecari valet: quod fuit oſtendendū. </s>
            <s xml:id="N135A6" xml:space="preserve">Et ſicut ꝓ-<lb/>batur in numeris: ita et facilius ꝓbabitur in quã-<lb/>titatibus. </s>
            <s xml:id="N135AD" xml:space="preserve">Et ſicut ꝓbatur capiēdo primos nume-<lb/>ros excedentes ſe vnitate: ita per locū a maiori ꝓ-<lb/>babitur capiendo numeros excedētes ſe numero: <lb/>vt ſatis conſtat. </s>
            <s xml:id="N135B6" xml:space="preserve">Patet igit̄̄ correlariū.             <anchor type="note" xlink:href="note-0035-02" xlink:label="note-0035-02a"/>             </s>
            <s xml:id="N135BE" xml:space="preserve">¶ Sequit̄̄ <lb/>ſecūdo /  capitis tribꝰ terminis cõtinuo ꝓportio-<lb/>nabilibus arithmetice: et captis aliis tribus ſic ſe <lb/>habentibꝰ /  qualis eſt ꝓportio inter duos maio-<lb/>res primi ternarii: talis ſit inter duos maiores ſe­<lb/>cūdi ternarii: et qualis inter duos numeros primi <lb/>ternarii: talis etiã ſit inter duos minores ſecundi <lb/>ternarii: tūc termini ſecūdi ternarii ſunt ꝓportio-<lb/>nabiles arithmetice: ſicut et termini ṗmi ternarii: <lb/>vt captis his tribus terminis .4.3.2. qui ſunt pro-<lb/>portiõabiles arithmetice: dico /  iſti .3. termini .8. <lb/>6.4. ſunt etiã arithmetice proportionabiles: qm̄ <lb/>qualis eſt ꝓportio inter .4. et .3. talis eſt inter .8. et <lb/>6. et qualis inter .3. et .2. talis inter .6. et .4. / vt patꝫ <lb/></s>
            <s xml:id="N135DC" xml:space="preserve">Probatur / ſint tres termini a.b.c. ꝓportiõabiles <lb/>arithmetice: et ſint alii trrs d.e.f. et ſit inter d. et e. <lb/>talis ꝓportio qualis inter a. et b. et inter e. et f. q̈lis <lb/>inter b. et c. </s>
            <s xml:id="N135E5" xml:space="preserve">Et tunc dico /  d.e.f. ſunt tres termini <lb/>ꝓportionabiles arithmetice: </s>
            <s xml:id="N135EA" xml:space="preserve">Ad quod probandū <lb/>volo /  exceſſus quo a. excedit b. ſit g. et quo b. exce­<lb/>dit c. ſit h. equalis g. / vt oportet: et exceſſus q̊ d. exce­<lb/>dit e. ſit i. et quo e. excedit f. ſit k. / et manifeſtū eſt /  g. <lb/>eſt tota pars aliquota ipſiꝰ b. vel tote partes q̊ta <lb/>vel quote i. eſt ipſiꝰ e. et eiuſdē denominationis: et <lb/>h. eſt tota pars vel tote partes aliquote et eiuſdeꝫ <lb/>denomīationis reſpectu c. ſicut k. reſpectu f. / vt ptꝫ <lb/>ex probatione quarte ſuppoſitionis ſecūdi capi-<lb/>tis huiꝰ. </s>
            <s xml:id="N135FF" xml:space="preserve">Quo ſuppoſito arguit̄̄ ſic / i. quod eſt ex-<lb/>ceſſus inter d. et e. eſt equale ipſi k. / quod eſt exceſſus <lb/>inter e. et f. / igit̄̄ illi tres termini d.e.f. ſunt ꝓporti-<lb/>onabiles arithmetice. </s>
            <s xml:id="N13608" xml:space="preserve">Cõſequentia ptꝫ manifeſte: <lb/>et arguit̄̄ antecedens: q2 ſicut ſe habet b. ad .c. ita e. <lb/>ad f. / igit̄̄ ſicut ſe habet b. ad e. ita c. ad f. </s>
            <s xml:id="N1360F" xml:space="preserve">Patet cõ-<lb/>ſequentia ex ſecūda cõcluſione tertii capitis huiꝰ: <lb/>et ex ↄ̨ſequenti ſicut ſe habet b. ad e. ita c. ad f. puta             <cb chead="Capitulū quartū."/>             in l. ꝓportione / igitur g. ſe habet ad i. in l. ꝓporti-<lb/>one et h. ad k. etiã in l. ꝓportione. </s>
            <s xml:id="N1361B" xml:space="preserve">Patet cõſequen­<lb/>tia ex vndecima ſuppoſitione ſecūdi capitis huiꝰ: <lb/>ille em̄ ſunt partes aliquote eiuſdē denoīationis <lb/>numeroꝝ ſe habentiū in l. ꝓportione: et vltra g. ſe <lb/>habet ad i. in l. ꝓportiõe: et h. ad k. etiã in l. pro-<lb/>portione: igit̄̄ ſicut ſe habet g. ad h. ita i. ad k. </s>
            <s xml:id="N13628" xml:space="preserve">Ptꝫ <lb/>per locū a. ꝑmutata proportione: ſed g. et h. ſe ha-<lb/>bent in proportione equalitatis: igit̄̄ i. et k. / qḋ fuit <lb/>probandñ. </s>
            <s xml:id="N13631" xml:space="preserve">Probatur aliter correlariū tam in nu­<lb/>meris quã in quãtitatibus cõtinuis: et retēta eadē <lb/>hypotheſi: manifeſtū eſt /  ipſiꝰ a. ad d. et ipſiꝰ b. <lb/>ad c. et ipſius c. ad f. eſt eadē ꝓportio: que ſit l. / qm̄ <lb/>ex hypotheſi ſicut ſe habet a. ad b. ita ſe habet d. <lb/>ad e. / ergo per locū a. permutata proportiõe ſicut <lb/>ſe habet a. ad d. ita b. ad e. et vltra ſicut ſe habet b <lb/>ad c. ita e. ad f. ex hypotheſi: ergo ꝑmutatim: ſicut <lb/>ſe habet b. ad e. ita c. ad f. et a. ad d. eſt etiã ꝓportio <lb/>illa que eſt b. ad c. / igit̄̄ eadē proportio eſt a. ad d. et <lb/>b. ad e. et c. ad f. puta l. </s>
            <s xml:id="N13648" xml:space="preserve">Quo ſuppoſito: probatur <lb/>correlariū: q2 i. et k. ſūt equales: igit̄̄ .d.e.f. ſunt ter­<lb/>mini cõtinuo proportionabiles arithmetice. </s>
            <s xml:id="N1364F" xml:space="preserve">Ptꝫ <lb/>cõſequentia ex hypotheſi: iūcta diffinitione ꝓpor­<lb/>tionalitatis arithmetice. </s>
            <s xml:id="N13656" xml:space="preserve">Probat̄̄ antecedens: q2 <lb/>ſicut ſe habet g. ad h. ita ſe habet i. ad k. ſed g et h. <lb/>ſe habent in proportiõe equalitatis / vt ptꝫ ex hy-<lb/>potheſi: igit̄̄ i. et k. ſe habent in proportione equa-<lb/>litatis: et ſic ſunt equalia igit̄̄. </s>
            <s xml:id="N13661" xml:space="preserve">Probat̄̄ antecedēs / <lb/>q2 ſicut ſe habet g. ad i. ita h. ad k. / ergo ꝑmutatim <lb/>ſicut ſe habet g. ad h. ita i. ad k. / qḋ fuit probandū. <lb/></s>
            <s xml:id="N13669" xml:space="preserve">Probatur antecedens: q2 g. ſe habet ad i. in l. ꝓ-<lb/>portione: et h. ſe habet ad k. in eadē l. proportione / <lb/>igitur intentū. </s>
            <s xml:id="N13670" xml:space="preserve">Probat̄̄ maior / q2 g. ſe hꝫ ad i. ſicut <lb/>a. ſe hꝫ ad d. / igitur ſe hꝫ in l. ꝓportione. </s>
            <s xml:id="N13675" xml:space="preserve">Patꝫ ↄ̨ña <lb/>ex hypotheſi. </s>
            <s xml:id="N1367A" xml:space="preserve">Probat̄̄ antecedēs: et volo /  a. dimi­<lb/>nuatur ad equalitatē b. ꝑdendo g. differentiã per <lb/>quã excedit ipſum b. ex hypotheſi: et d. diminuatur <lb/>ad equalitatē c. ꝑdendo i. differentiã ꝑ quã excedit <lb/>e. ex hypotheſi: et manifeſtū eſt /  reſidui ex ipſo a. / <lb/>qḋ eſt b. ad reſiduū ex ipſo d. / qḋ eſt e. adhuc eſt l. ꝓ­<lb/>portio: vt ptꝫ ex hypotheſi: g̊ inṫ deꝑditū ab ip̄o a <lb/>et deꝑditū ab ip̄o d. eſt etiã l. ꝓportio: et deꝑditū ab <lb/>ip̄o a eſt g. et deꝑditū ab ipſo d. eſt i. / g̊ g. ſe hꝫ ad i. <lb/>ſicut a. ad d. puta in l. ꝓportione. </s>
            <s xml:id="N1368F" xml:space="preserve">Ptꝫ tamen ↄ̨ña <lb/>ex primo correlario quinte cõcluſionis ſecūdi ca-<lb/>pitis huiꝰ partis. </s>
            <s xml:id="N13696" xml:space="preserve">Et ſic ptꝫ maior. </s>
            <s xml:id="N13699" xml:space="preserve">Iam ꝓbo mi-<lb/>norē / q2 h. ſe hꝫ ad k. ſicut b. ſi ſe hꝫ ad e. / igr̄ ꝓpoſitū <lb/></s>
            <s xml:id="N1369F" xml:space="preserve">Probat̄̄ ãtecedēs: et volo /  b. diminuat̄̄ ad equa-<lb/>litatē c: perdendo h. differentiã: et e. diminuat̄̄ ad <lb/>equalitatē f. perdendo k. differentiã: et manifeſtuꝫ <lb/>eſt /  reſidui ex ipſo b. / qḋ eſt c. ad reſiduū ex ipſo e. <lb/>qḋ eſt f. eſt adhuc l. ꝓportio: vt patet ex hypotheſi: <lb/>igitur inter h. deperditū a b. termino maiori, et <lb/>k. deꝑditū ab c. ṫmīo minori eſt ēt l ꝓportio: vt ſu-<lb/>pra argutū eſt / igr̄ h. ſe hꝫ ad k. ſicut b. ad e. puta in <lb/>l. ꝓportione: qḋ fuit probandū. </s>
            <s xml:id="N136B2" xml:space="preserve">Et ſic ptꝫ correla-<lb/>riū.             <anchor type="note" xlink:href="note-0035-03" xlink:label="note-0035-03a"/>             </s>
            <s xml:id="N136BC" xml:space="preserve">Et hec ē ſuppoſitio quã calculator ponit ī ca-<lb/>pitulo de inductione gradus ſummi circa princi-<lb/>piū ſub iſta forma. </s>
            <s xml:id="N136C3" xml:space="preserve">Si ſint tria cõtinuo ꝓportio-<lb/>nabilia ꝓportione arithmetica: et ſint alia tria cõ­<lb/>ſimiliter ꝓportionabilia proportiõe geometrica <lb/>ſicut prima tria: illa etiã ſunt cãtinuo ꝓportiõabi­<lb/>lia proportiõe arithmetica.             <anchor type="note" xlink:href="note-0035-04" xlink:label="note-0035-04a"/>             </s>
            <s xml:id="N136D3" xml:space="preserve">¶ Sequit̄̄ ex hoc ter-<lb/>tio /  ſi ſint tres termini arithmetice proportiõa-<lb/>biles: et quilibet illoꝝ dupletur, aut tripletur, aut <lb/>ſexquialteretur .etc̈. ſemꝑ ꝓportio extremi ad ex-<lb/>tremū manet equalis: et cõtinuo manebūt illi tres <lb/>termini arithmetice ꝓportiõabiles: et in ea ꝓpor-<lb/>tiõe in qua termini augmētant̄̄ exceſſus augmētat̄̄ <lb/></s>
            <s xml:id="N136E3" xml:space="preserve"><pb chead="Secunde partis" file="0036" n="36"/>             Probatur prima pars: quia ſemper vter extre-<lb/>morum acquirit equalē proportionē: igitur con-<lb/>tinuo inter ea manet eadem proportio. </s>
            <s xml:id="N136EE" xml:space="preserve">Secunda <lb/>pars probatur: quia continuo manet eadem pro-<lb/>portio inter medium et tertium continuo etiam <lb/>manet eadem roportio que antea erat inter ſecun­<lb/>dum et tertium eadem ratione qua inter extrema <lb/>manet eadem proportio: igttur continuo illi ter-<lb/>mini manent proportionabiles arithmetice.</s>
          </p>
          <div xml:id="N136FD" level="4" n="6" type="float">
            <note position="left" xlink:href="note-0035-01a" xlink:label="note-0035-01" xml:id="N13701" xml:space="preserve">Primuꝫ <lb/>correlari­<lb/>um.</note>
            <note position="left" xlink:href="note-0035-02a" xlink:label="note-0035-02" xml:id="N1370B" xml:space="preserve">Secūduꝫ <lb/>correlar̄.</note>
            <note position="right" xlink:href="note-0035-03a" xlink:label="note-0035-03" xml:id="N13713" xml:space="preserve">Calcu. de <lb/>īduc. gra­<lb/>dus ſūmi</note>
            <note position="right" xlink:href="note-0035-04a" xlink:label="note-0035-04" xml:id="N1371D" xml:space="preserve">Tertium <lb/>correlar̄.</note>
          </div>
          <p xml:id="N13725">
            <s xml:id="N13726" xml:space="preserve">Patet conſequentia ex precedenti correlario. <lb/></s>
            <s xml:id="N1372A" xml:space="preserve">Tertia autem ſic probatur: quia ſemper illi ex-<lb/>ceſſus cõtinuo manent partes aliquote cõſimilis <lb/>denominationis ſuorū numerorū: igitur in ea ꝓ-<lb/>portione qua numeri fiunt maiores et illi exceſſus <lb/>etiã fiūt maiores: quia ſunt partes aliquote illoꝝ <lb/>numerorū eiuſdē denominationis. </s>
            <s xml:id="N13737" xml:space="preserve">Et ſic patet cor­<lb/>relariū.             <anchor type="note" xlink:href="note-0036-01" xlink:label="note-0036-01a"/>             </s>
            <s xml:id="N13741" xml:space="preserve">¶ Sequitur quarto:  ſi ſint tres termini <lb/>arithmetice ꝓportionabiles: et ſtante maximo il-<lb/>lorū īuariato deſcreſcat minimus illoꝝ ſucceſſiue: <lb/>ita  cõtinue illi tres maneant arithmetice ꝓpor-<lb/>tionabiles: neceſſe eſt mediū in duplo tardius cõ-<lb/>tinuo decreſcere minimo: neceſſe quo eſt ꝓporti-<lb/>onē extremi ad extremū continuo augeri: vt datis <lb/>his tribus terminis .12.8.4. et ſtantibus .12. decre­<lb/>ſcant .4. perdendo binariū: ſi illi tres termini de-<lb/>beant cõtinuo manere arithmetice ꝓportionabi-<lb/>les: neceſſe eſt numerū mediū perdere vnitatē: et ſic <lb/>manebunt arithmetice ꝓportiõabiles. </s>
            <s xml:id="N1375A" xml:space="preserve">Manebūt <lb/>em̄ .12.7.2. et manebit maior ꝓportio quã erat an­<lb/>tea inter extrema. </s>
            <s xml:id="N13761" xml:space="preserve">Probatur / et ſint a.b.c. tres ter-<lb/>mini arithmetice ꝓportionabiles a. maximus c. <lb/>vero minimus: et perdat c. vnã partē ſui que ſit d. <lb/>et medietas d. ſit e. / et tunc dico /  cum c. perdit d.b. <lb/>perdit e. adequate. </s>
            <s xml:id="N1376C" xml:space="preserve">Quod ſic ꝓbatur: quoniã illi <lb/>tres termini cõtinuo manēt ꝓportiõabiles arith-<lb/>metice: igitur medium inter extrema eſt medietas <lb/>aggregati et extremis vt ex ſuperioribus conſtat: <lb/>ſed facta tali diminutiõe aggregatū ex extremis <lb/>eſt minus per d. latitudinē quã antea: quia illam <lb/>perdit adequate: igitur medietas illius aggrega­<lb/>ti effecta eſt minor per medietatē illius quod per-<lb/>dit totū puta per medietatē ipſiꝰ d: ſed medietas <lb/>ipſius d. eſt e. / igitur medietas illius aggregati fa­<lb/>cta eſt minor per e. adeq̈te: et illa medietas eſt me-<lb/>diū inter illa extrema: igitur medietas inter illa <lb/>extrema perdidit e. / quod fuit probandū. </s>
            <s xml:id="N13787" xml:space="preserve">Secūda <lb/>vero pars patet ex priori parte decime ſuppoſiti-<lb/>onis ſecundi capitis huius: quoniã numerus mi-<lb/>nor creſcit ſtante maiore. </s>
            <s xml:id="N13790" xml:space="preserve">Et hec eſt quedã ſuppo-<lb/>ſitio quã ponit: et aliter probat calculator in prin­<lb/>cipio capituli de intenſione elementi.             <anchor type="note" xlink:href="note-0036-02" xlink:label="note-0036-02a"/>             </s>
            <s xml:id="N1379C" xml:space="preserve">¶ Sequitur <lb/>quinto /  oīs ꝓportio cõponitur ex duabus pro-<lb/>tionibus puta maximi termini ad mediū: et medii <lb/>ad minimū: et proportio maximi ad mediū minor <lb/>eſt quã ſubdupla ad ipſam que eſt extremi ad ex-<lb/>tremū: et proportio medii termini ad minimū ma­<lb/>ior eſt quam ſubdupla: vt proportio ſexquialtera <lb/>que eſt .6. ad .4. cõponitur ex proportione .6. ad .5 <lb/>et .5. ad .4. et proportio .6. ad .5. minor eſt quã ſub-<lb/>dupla: et .5. ad .4. maior eſt quã ſubdupla ad ſex-<lb/>quialterã. </s>
            <s xml:id="N137B3" xml:space="preserve">Prima pars huius patet ex concluſiõe / <lb/>et ſecūda probatur: quia omne cõpoſitū adequate <lb/>ex duobus inequalibus eſt maius quam duplum <lb/>ad minus illorum: et minus quam duplum ad ma­<lb/>ius illorum / vt patet ex ſexta ſuppoſitione huius <lb/>ſed omnis proportio componitur ex duabus pro­<lb/>portionibus inequalibus quarum minor eſt ma-             <cb chead="Capitulū quartū"/>             oris extremi ad medium: et maior medii ad mini-<lb/>mum extremum: vt patet ex eadem cõcluſione: igi-<lb/>tur omnis proportio eſt maior quãdupla ad pro-<lb/>portionem que eſt maioris extremi ad medium: et <lb/>minor quam dupla ad proportionem quē eſt me-<lb/>dii termini ad minimum extremum. </s>
            <s xml:id="N137CF" xml:space="preserve">Patet conſe­<lb/>quentia in primo prime: et ſic patet correlarium. <lb/>             <anchor type="note" xlink:href="note-0036-03" xlink:label="note-0036-03a"/>             </s>
            <s xml:id="N137DB" xml:space="preserve">¶ Sequitur ſexto:  omnis proportio ſuperpar-<lb/>ticularis componitur ex duabus quarum vna eſt <lb/>maximi termini ad medium: et alia eſt medii ad mi­<lb/>nus extremum: et vtra illarum eſt ſuperparticu-<lb/>laris: et proportio medii ad minimum demonina-<lb/>tur a parte aliquota denominata a numero du-<lb/>plo ad numerū a quo denominatur pars aliquo-<lb/>ta a qua denoīatur ꝓportio maximi ad minimū: <lb/>et ꝓportio maximi termini ad medium denoīatur <lb/>a parte aliquota denominata a numero īmedia-<lb/>te ſequente numerum illum duplum: vt proportio <lb/>ſexquialtera que eſt .6. ad .4. cõponitur ex duabꝰ <lb/>inequalibus / vt dictum eſt: et vtra illarum eſt ſu-<lb/>perparticularis. </s>
            <s xml:id="N137F8" xml:space="preserve">Nam proportio .6. ad .5. eſt ſu-<lb/>perparticularis et .5. ad .4. ſimiliter: et proportio <lb/>que eſt .5. ad .4. denomīatur a quarta que eſt pars <lb/>aliquota denominata a numero in duplo maiore <lb/>quam ſit numerus a quo denominatur medietas <lb/>a qua medietate denominatur ſexquialtera. </s>
            <s xml:id="N13805" xml:space="preserve">De-<lb/>nominatur enim medietas a binario, et quarta a <lb/>quaternario, et quinta denominatur a quinario <lb/>qui eſt numerus ſequens immediate quaternariū <lb/></s>
            <s xml:id="N1380F" xml:space="preserve">Probatur prima pars huius ex correlario imme­<lb/>diate precedenti: et ſecunda probatur / et quia om-<lb/>nis proportio ſuperparticularis reperitur inter <lb/>duos numeros immediatos: vt patet ex eius gene­<lb/>ratione poſita in prima parte: capio igitur vnam <lb/>proportionem ſuperparticularem que ſit f. et du-<lb/>os terminos eius in numeris immediatos: puta <lb/>a. maiorem: et c. minorem: et tunc dico /  propor-<lb/>tio ſuperparticularis inter illos duos numeros <lb/>immediatos cõponitur adequate ex duabus pro-<lb/>portionibus ſuperparticularibus: ex vna videli-<lb/>cet que eſt maximi ad medium: et altera que eſt me­<lb/>dii ad extremum. </s>
            <s xml:id="N1382A" xml:space="preserve">Probatur quoniam cum a. et c. <lb/>ſunt nnmeri immediati: et a. maior: ſequitur /  a. <lb/>excedit c. per vnitatem: dupletur igitur tam c. quã <lb/>a. / et manifeſtum eſt /  inter illos duos numeros <lb/>duplatos manet eadeꝫ proportio que erat antea <lb/>puta f. / vt patet ex correlario decime ſuppoſitio-<lb/>nis ſecundi capitis huius: igitur exceſſus maioris <lb/>termini. </s>
            <s xml:id="N1383B" xml:space="preserve">ſic duplati ad minorem etiam ſit dupla-<lb/>tum erit in duplo maior: vt patet ex tertio corre-<lb/>lario huius concluſionis: et antea erat vnitas / er-<lb/>go modo eſt dualitas: et per conſequens inter nu­<lb/>merum maiorem ipſius proportionis f. et nume-<lb/>rum minorem mediat numerus excedens minimū <lb/>illorum per vnitatem: et qui exceditur maximo <lb/>illorum per vnitatem. </s>
            <s xml:id="N1384C" xml:space="preserve">Patet hec conſequentia / <lb/>quia omnis numerus excedens alterum per dua-<lb/>litatem diſtat ab eo per vnum numerum tantum <lb/>in naturali ſerie numerorum / vt ſatis conſtat: ſit <lb/>igitur talis numerus medius b. / et ſequitur /  ma-<lb/>ximi termini illius proportionis f. ſuperparticu-<lb/>laris date ad ipſum b. eſt proportio ſuperparti-<lb/>cularis: et ipſius b. ad minimum extremum eiuſ-<lb/>dem proportionis f. eſt etiam proportio ſuper-<lb/>particularis: quia illi tres numeri ſunt imme-<lb/>diati / igitur illa proportio f. ſuperparticularis             <pb chead="Secunde partis" file="0037" n="37"/>             cõponitur ex duabus proportionibus ſuperpar-<lb/>ticularibus quarum vna eſt maximi ad medium: et <lb/>altera medii ad minimū extremum / quod fuit pro­<lb/>bandum. </s>
            <s xml:id="N1386E" xml:space="preserve">Patet tamen conſequentia / quia omnis <lb/>proportio que reperitur inter duos numeros im-<lb/>mediatos eſt ſuperparticularis / vt patet ex gene-<lb/>ratione ſuperparticulariū. </s>
            <s xml:id="N13877" xml:space="preserve">Sed tertia pars pro-<lb/>batur / quia duplato ſic a. et c. numero vt ſupra: iã <lb/>a. numerus ſic duplatus excedit c. ſic duplatū per <lb/>dualitatem: et illa dualitas erit pars aliquota e-<lb/>iuſdem denominationis ipſius c. ſicut antea erat <lb/>vnitas quia adhuc manet proportio f. inter illos <lb/>terminos: igitur adhuc maior illorum terminorū <lb/>excedit minorem mediante eadem parte aliquota <lb/>minoris: diuiſa igitur illa parte aliquota a mino-<lb/>ris que eſt dualitas in duas partes equales / puta <lb/>in duas vnitates manifeſtum eſt /  quelibet illarū <lb/>partium in quas diuiditur eſt pars aliquota mi-<lb/>noris denominata a numero in duplo maiori / vt <lb/>conſtat: igitur numerus continens numerum mi-<lb/>norem et talem partē aliquotam adequate ſe ha-<lb/>bebit ad minorem numerum in proportione ſu-<lb/>perparticulari denominata a parte aliquota que <lb/>denominatur a numero duplo a quo denomina-<lb/>tur tota illa pars aliquota continens illas duas <lb/>vnitates: et talis numerus qui videlicet cõtinet nu­<lb/>merum minorem et medietatem illius partis ali-<lb/>quote ſic diuiſe eſt numerus medius inter extrema <lb/>date proportionis ſuperparticularis: igitur pro­<lb/>portio medii termini inter terminos proportiõis <lb/>ſuperparticularis ad minimum extremum deno-<lb/>minatur a parte aliquota denominata a numero <lb/>in duplo maiore quaꝫ ſit numerus a quo denomi-<lb/>natur pars aliquota a qua denominatur totalis <lb/>illa proportio data ſuperparticularis. </s>
            <s xml:id="N138B2" xml:space="preserve">Conſe-<lb/>quētia patet: et minor probatur: quia ſemper me-<lb/>dius numerus inter duos excedit minorē per me-<lb/>dietatem exceſſus quo maior excedit minorē quia <lb/>alias nõ eſſet medius. </s>
            <s xml:id="N138BD" xml:space="preserve">Et ſic patet tertia pars cor­<lb/>relari. </s>
            <s xml:id="N138C2" xml:space="preserve">Et quarta probatur / quia ad īuento medio <lb/>inter terminos proportionis ſuperparticularis <lb/>quod per ſolam vnitatem excedit numerum mino­<lb/>rem: et per ſolam vuitatē exceditur a maiore vt eſt <lb/>in propoſito: ibi reperiuntur tres numeri īmedia­<lb/>ti in naturali ſerie numerorum / igitur proportio <lb/>maximi eorum ad medium denominatur a parte <lb/>aliquota denominata a numero īmediate ſequē-<lb/>te numerū a quo denominatur pars aliquota de-<lb/>nominans proportionem medii numeri ad mino­<lb/>rem / vt patet ex prima parte aſpicienti generatio-<lb/>nem ſuperparticularium in naturali ſerie nume-<lb/>rorum. </s>
            <s xml:id="N138DD" xml:space="preserve">Et ſic patet correlarium quadripartitum / <lb/>quod difficile apparet propter longitudinem ter­<lb/>minorum quibus vtitur inprobatione.             <anchor type="note" xlink:href="note-0037-01" xlink:label="note-0037-01a"/>             </s>
            <s xml:id="N138E9" xml:space="preserve">Et ideo de <lb/>cetero cum voluero dicere /  aliqua proportio ſu-<lb/>perparticularis denomīatur ab aliqua parte a-<lb/>liquota denominata ab aliquo certo numero: di-<lb/>cã /  talis proportio ſuperparticularis denomi-<lb/>natur a tali numero gratia breuitatis: quia nulla <lb/>ſuperparticularis denominatur a numero: ſed a <lb/>parte aliquota et vnitate: et cū dico /  denomina-<lb/>tur a parte aliquota intelligo inadequate quod <lb/>ad propoſitum ſufficit.             <anchor type="note" xlink:href="note-0037-02" xlink:label="note-0037-02a"/>             </s>
            <s xml:id="N13903" xml:space="preserve">¶ Sequitur ſeptimo /  in <lb/>omni proportiõe ſuperparticulari capta propor­<lb/>tione que eſt medii termini ad infimum: illa etiam <lb/>componitur ex duabus ſuperparticularibus qua­<lb/>rum vna ſimiliter eſt medii termini ad infimum: <lb/>et illa denominatur a numero quadruplo ad nu-<lb/>merum a quo denominatur illa ſuperparticula-             <cb chead="Capitulum quintū."/>             ris proportio data: vt in proportione ſexquiquar­<lb/>ta que eſt .20. ad .16. capta proportione que eſt in-<lb/>ter .18. et .16. puta medii numeri ad īfimū: illa etiã <lb/>cõponitur ex proportione medii termini eius pu-<lb/>ta .17. ad .16. / et illa proportio denominatur a nu-<lb/>mero quadruplo ad numerū a quo denominatur <lb/>proportio ſexquiquarta: quia ꝓportio que eſt .17. <lb/>ad .16. denominatus a numero ſexdecimo: et pro-<lb/>portio .20: ad .16. a numero quaternario hoc eſt a <lb/>parte aliquota denominata ab illo puta quater­<lb/>nario (ſemper ſic intelligo) </s>
            <s xml:id="N13929" xml:space="preserve">Modo ſexdecimus nu­<lb/>merus eſt quadruplus ad quaternarium. </s>
            <s xml:id="N1392E" xml:space="preserve">Proba­<lb/>tur: et capio vnam proportionem ſuperparticula­<lb/>rem f. que ſit a. ad d. et medius numerus inter illa <lb/>extrema ſit b. / tunc dico /  proportio b. ad d. com-<lb/>ponitur ex duabus proportionibus ſuperparti-<lb/>cularibus quaruꝫ vna eſt medii termini ad infimū <lb/>qui medius terminus inter b. et d. ſit c. et illa puta <lb/>c. ad d. denominatur a numero quadruplo ad nu-<lb/>merū a quo denominatur proportio a. ad .d. </s>
            <s xml:id="N13941" xml:space="preserve">Pri­<lb/>ma pars videlicet /  ꝓportio que eſt b. ad d. com-<lb/>ponitur ex duabus ſuperparticularibꝰ .etc̈. / patet <lb/>ex īmediate precedenti: et ſecunda probatur / quia <lb/>proportio b. ad d. denominatur a numero duplo <lb/>ad numerum a quo denominatur f. ꝓportio a. ad <lb/>d. / vt patet ex precedenti correlario: et proportio c. <lb/>ad d. eadē ratione denominatur a numero duplo <lb/>ad numerū a quo denominatur proportio b. ad d / <lb/>vt patet ex eodem correlario: igitur proportio c. <lb/>ad d. denomīatur a numero quadruplo ad nume­<lb/>merū a quo denominatur ꝓportio f.a. ad d. / quod <lb/>fuit probandū. </s>
            <s xml:id="N1395C" xml:space="preserve">Patet hec conſequentia: quia nu-<lb/>merus duplus ad duplū alicuiꝰ certi dati eſt qua-<lb/>druplus ad illum certum datum / vt conſtat: ſed nu­<lb/>merus a quo denomīatur proportio c. ad d. eſt du­<lb/>plus ad numerum a quo denominatur proportio <lb/>b. ad d. et ille iterum eſt duplus ad numeruꝫ a quo <lb/>denominatur proportio f.a. ad d. / igitur numerus <lb/>a quo denominatur proportio c. ad d. eſt quadru-<lb/>plus ad numerum a quo denominatnr proportio <lb/>f. que eſt a. ad d. / quod fuit probandū.             <anchor type="note" xlink:href="note-0037-03" xlink:label="note-0037-03a"/>             </s>
            <s xml:id="N13976" xml:space="preserve">¶ Sequitur <lb/>octauo /  quacun proportione ſuperparticula-<lb/>ri data denomīata ab aliquo certo numero: oīs <lb/>proportio ſuperparticularis denominata a ma-<lb/>iori numero vſ ad duplū incluſiue eſt maior quã <lb/>medietas illius proportionis ſuperparticularis <lb/>date: vt data proportione ſexquiquarta oīs pro-<lb/>portio ſuperparticularis denominata ab olique <lb/>numero a quaternario vſ ad octonarium inclu-<lb/>ſiue qui eſt numerus duplus ad quaternarium eſt <lb/>maior quam ſubdupla ad ſexquiquartã et ſic ſex-<lb/>quiquarta, ſexquiſexta, ſexquiſeptima, ſexq̇octa-<lb/>ua, eſt maior quam ſubdupla ad ſexquiquartam. <lb/></s>
            <s xml:id="N13992" xml:space="preserve">Probatur / quoniã quacun tali ſuperparticula-<lb/>ri data ab aliquo numero denominata: propor-<lb/>tio ſuperparticularis denominata a numero in <lb/>duplo maiore eſt maior quam ſubdupla ad illam <lb/>quia talis eſt medii termini ad infimū / vt patet ex <lb/>quinto et ſexto correlario cõiunctis: igitur omnis <lb/>ꝓportio ſuperparticularis denominata a nume-<lb/>ro minori quã duplo ad numerū a quo denomina­<lb/>tur data ꝓportio ſuꝑparticularis eſt maior quã <lb/>ſubdupla ad illam datã ſuperparticularē. </s>
            <s xml:id="N139A7" xml:space="preserve">Patet <lb/>hec cõſequentia per hoc /  oīs ſuperparticularis <lb/>que denomīatur a minori numero eſt maior: quia <lb/>talis denomīatur a maiori parte aliquota: et hoc <lb/>auxiliante loco a maiori: et per conſequens pro-<lb/>portione ſuperparticulari data denominata ab <lb/>aliquo certo nūero: oīs ꝓportio ſuꝑparticularis             <pb chead="Secunde partis" file="0038" n="38"/>             denominata a maiori numero vſ ad dupluꝫ in-<lb/>īcluſiue eſt maior quam ſubdupla ad illam ſuper-<lb/>particularem datam. </s>
            <s xml:id="N139BF" xml:space="preserve">Patet igitur correlarium. <lb/>             <anchor type="note" xlink:href="note-0038-01" xlink:label="note-0038-01a"/>             </s>
            <s xml:id="N139C9" xml:space="preserve">¶ Sequitur nono /  in omni proportione ſuper-<lb/>particulari proportio maximi extremi eiꝰ ad me-<lb/>dium eſt maior quam ſubdupla ad proportioneꝫ <lb/>medii ad minimū extremum: vt data proportione <lb/>ſexquitertia que eſt .8. ad .6. proportio .8. ad .7. eſt <lb/>maior quam ſubdupla ad proportionem .7. ad .6. <lb/></s>
            <s xml:id="N139D7" xml:space="preserve">Probatur / quia ꝓportio maximi extremi ad me-<lb/>dium in proportione ſuperparticulari quecun <lb/>fuerit illa denominatur a numero ſuperparticu-<lb/>ri īmediate ſequenti numerum a quo denomina-<lb/>tur proportio medii ad minimū extremum / vt patꝫ <lb/>ex quarta parte ſexti correlarii: et ſic denomīatur <lb/>a numero minori duplo ad numeruꝫ a quo deno-<lb/>minatur proportio medii ad minimū extremum: <lb/>igitur talis proportio maximi ad medium eſt ma­<lb/>ior quam ſubdupla ad proportionē medii ad mi-<lb/>nimuꝫ extremum. </s>
            <s xml:id="N139EE" xml:space="preserve">Patet conſequentia ex octauo <lb/>correlario.             <anchor type="note" xlink:href="note-0038-02" xlink:label="note-0038-02a"/>             </s>
            <s xml:id="N139F8" xml:space="preserve">¶ Sequitur decimo /  in omni propor­<lb/>tione ſuperparticulari ꝓportio maximi extremi <lb/>ad medium eſt maior quam ſubtripla ad illã pro-<lb/>portionem ſuperparticularem. </s>
            <s xml:id="N13A01" xml:space="preserve">Probatur / quia <lb/>dato oppoſito puta /  ſit ſubtripla aut mīor ſub-<lb/>tripla: ſequeretur /  ipſa eſſet ſubdupla adequate <lb/>ad proportionem medii ad minimū extremū, vel <lb/>minor quam ſubdupla: ſed conſequens eſt falſum / <lb/>vt patet ex nono correlario: igitur illud ex quo ſe-<lb/>quitur: et per conſequens correlarium verū / quod <lb/>fuit probandum. </s>
            <s xml:id="N13A12" xml:space="preserve">Sequela tamen probatur / quia <lb/>quando aliquid componitur ex duobus inequali­<lb/>bus adequate: et minus illornm eſt ſubtriplū eius <lb/>puta vna tertia illud minus eſt ſubduplum ad re-<lb/>ſiduū puta ad duas tertias: et ſi illud ſit minꝰ quã <lb/>tertia illius totius illud eſt minus quã ſubdupluꝫ <lb/>ad totū reſiduū: ſed ſic eſt in propoſito per te igi-<lb/>tur intentum.             <anchor type="note" xlink:href="note-0038-03" xlink:label="note-0038-03a"/>             </s>
            <s xml:id="N13A28" xml:space="preserve">¶ Sequitur vndecimo /  data qua-<lb/>cun proportione ſuperparticulari denominata <lb/>ab aliquo numero: omnis proportio ſuperparti-<lb/>cularis denominata a numero excedente illū per <lb/>vnitatem adequate eſt maior quã medietas illius <lb/>proportionis date. </s>
            <s xml:id="N13A35" xml:space="preserve">Patet hoc correlariū ex octa­<lb/>uo correlario: quia omnis talis denoīatur nu-<lb/>mero minori quam duplo ad numerū a quo deno­<lb/>minatur data ſuperparticularis.             <anchor type="note" xlink:href="note-0038-04" xlink:label="note-0038-04a"/>             </s>
            <s xml:id="N13A43" xml:space="preserve">¶ Sequit̄̄ duo-<lb/>decimo /  data naturali ſerie proportionum ſu-<lb/>perticulariū puta ſexquialtera, ſexquitertia, ſex-<lb/>quiquarta, et ſic deinceps: quelibet proportio ſu-<lb/>perparticularis que denomīatur ab altero duo-<lb/>rum numerorum īmediate ſequentium numerū a <lb/>quo denominatur ſexquialtera eſt maior quã me-<lb/>dietas ſexquialtere: et quelibet denominata ab a-<lb/>liquo trium numerorum īmediate ſequentium nu­<lb/>meruꝫ a quo denominatur ſexquitertia eſt maior <lb/>quã medietas ſexquitertie: et quelibet denomina-<lb/>ta ab aliquo quatuor numerorū īmediate ſequē-<lb/>tium numerū a quo denomīatur ſexquiquarta eſt <lb/>maior quam medietas eius: et ſic in infinitū ſemꝑ <lb/>addendo vnū. </s>
            <s xml:id="N13A62" xml:space="preserve">Patet hoc correlariū / quoniã que-<lb/>libet talis denominatur a numero duplo vel mi-<lb/>nori duplo ad numerū a quo denominatur data <lb/>proportio ſuꝑparticularis / vt patet intuenti: igi-<lb/>tur quelibet talis eſt maior quam medietas date <lb/>proportionis ſuperparticularis. </s>
            <s xml:id="N13A6F" xml:space="preserve">Patet conſe-<lb/>quentia ex octauo correlario.</s>
          </p>
          <div xml:id="N13A74" level="4" n="7" type="float">
            <note position="left" xlink:href="note-0036-01a" xlink:label="note-0036-01" xml:id="N13A78" xml:space="preserve">4. correĺ <lb/>Calcu. in <lb/>prīcipio <lb/>de ītē. ele.</note>
            <note position="left" xlink:href="note-0036-02a" xlink:label="note-0036-02" xml:id="N13A84" xml:space="preserve">5. correĺ.</note>
            <note position="right" xlink:href="note-0036-03a" xlink:label="note-0036-03" xml:id="N13A8A" xml:space="preserve">6. correĺ.</note>
            <note position="left" xlink:href="note-0037-01a" xlink:label="note-0037-01" xml:id="N13A90" xml:space="preserve">Documē­<lb/>tū nõ pre­<lb/>tereundū</note>
            <note position="left" xlink:href="note-0037-02a" xlink:label="note-0037-02" xml:id="N13A9A" xml:space="preserve">7. correĺ.</note>
            <note position="right" xlink:href="note-0037-03a" xlink:label="note-0037-03" xml:id="N13AA0" xml:space="preserve">8. correĺ.</note>
            <note position="left" xlink:href="note-0038-01a" xlink:label="note-0038-01" xml:id="N13AA6" xml:space="preserve">9. correĺ.</note>
            <note position="left" xlink:href="note-0038-02a" xlink:label="note-0038-02" xml:id="N13AAC" xml:space="preserve">10. correĺ</note>
            <note position="left" xlink:href="note-0038-03a" xlink:label="note-0038-03" xml:id="N13AB2" xml:space="preserve">11. correĺ.</note>
            <note position="left" xlink:href="note-0038-04a" xlink:label="note-0038-04" xml:id="N13AB8" xml:space="preserve">12. correĺ.</note>
          </div>
          <p xml:id="N13ABE">
            <s xml:id="N13ABF" xml:space="preserve">Quarta concluſio. </s>
            <s xml:id="N13AC2" xml:space="preserve">Quibuſcū dua­<lb/>bus ꝓportiõibus inequalibus propoſitis: maior             <cb chead="Capitulū quintū."/>             illarū minorem per proportionē que eſt inter de-<lb/>nominationes earum excedit: vt captis quadru-<lb/>pla et tripla: quadrupla que eſt maior excedit tri-<lb/>plam per proportionem que eſt inter .4. et .3. que <lb/>eſt ſexquitertia. </s>
            <s xml:id="N13AD2" xml:space="preserve">Et hoc ideo / quia tripla denomi-<lb/>natur a ternario quadrupla vero a quaternario <lb/>             <anchor type="note" xlink:href="note-0038-05" xlink:label="note-0038-05a"/>             </s>
            <s xml:id="N13ADE" xml:space="preserve">Et hic aduerte /  aliud eſt dicere proportio qua-<lb/>drupla excedit triplam per proportionem ſexqui­<lb/>tertiam: et ſe habet ad triplam in proportione ſex­<lb/>quitertia. </s>
            <s xml:id="N13AE7" xml:space="preserve">Nam ſexdecupla excedit octuplam per <lb/>proportionem duplam: et ſe habet ad illã in pro-<lb/>portione ſexquitertia / vt poſtea patebit. </s>
            <s xml:id="N13AEE" xml:space="preserve">Et hoc do­<lb/>cumentum debes memorie cõmendare ſi vis calcu­<lb/>latorem intelligere in capitulo ſcḋo de medio nõ <lb/>reſiſtēte / qḋ ego voco de medio vniformiter diffor­<lb/>miter reſiſtente. </s>
            <s xml:id="N13AF9" xml:space="preserve">Probatur concluſio ſupponēdo <lb/>primū vnū manifeſtum / quod probatione non in-<lb/>diget: videlicet  quacun quantitate continua <lb/>ſignata ad eã poteſt dari omnis proportio poſſi-<lb/>bilis capiendo maiorē quantitatem: quo ſuppo-<lb/>ſito capio duas proportiones f. maiorem et g. mi-<lb/>norem: et vtriuſ illarum proportionum minimū <lb/>extremum ſit c. quantitas continua: et aliud ex-<lb/>tremū f. proportionis ſit a. et aliud g. proportiõis <lb/>ſit b. / ita  proportio f. ſit a. ad c. et proportio g. ſit <lb/>b. ad c. / et ſint illi primi termini illarum proporti-<lb/>onū gratia argumenti: et tunc dico /  proportio f. <lb/>maior excedit proportionem g. per proportioneꝫ / <lb/>que eſt inter denominationes illaruꝫ / hoc eſt inter <lb/>terminos a quibus ille proportiones denominã-<lb/>tur puta inter a. et .b. </s>
            <s xml:id="N13B1A" xml:space="preserve">Quod ſic probatur / q2 f. pro-<lb/>portio a. ad .c. maior componitur adequate ex ꝓ-<lb/>portione a. ad b. et ex proportione b. ad c. que eſt g / <lb/>vt patet ex ſecunda concluſione huius: igitur pro-<lb/>portio a. ad c. continet adequate proportioneꝫ b. <lb/>ad c. et vltra proportionē que eſt a. ad b. / igitur ꝓ-<lb/>portio f. que eſt a. ad c. excedit proportionē g. que <lb/>eſt b. ad c. per ꝓportionē que eſt a. ad b. / quod fuit <lb/>probandum. </s>
            <s xml:id="N13B2D" xml:space="preserve">Illa eni3 eſt proportio inter primos <lb/>terminos illarum proportionū a quibus ille pro­<lb/>portiones f. et g. denominantur.             <anchor type="note" xlink:href="note-0038-06" xlink:label="note-0038-06a"/>             </s>
            <s xml:id="N13B39" xml:space="preserve">¶ Ex hac conclu-<lb/>ſione ſequitur primo /  capto vno termino habē-<lb/>te duas proportiones maioris inequalitatis ad <lb/>duos terminos minores inequales / vt oportet: ꝓ-<lb/>portio inter illos duos minores terminos eſt illa <lb/>per quam maior proportio excedit minorē: vt ca-<lb/>pto octonario numero habente proportioneꝫ ad <lb/>ternariū et quaternariū: dico /  ꝓportio octona-<lb/>rii ad ternariū que eſt maior excedit proportionē <lb/>octonarii ad quaternariū minorē per ꝓportionē <lb/>que eſt inter quaternariū et ternariū. </s>
            <s xml:id="N13B50" xml:space="preserve">Probatur / <lb/>ſint due ꝓportiones puta f. ꝓportio que ſit a. ad <lb/>c. et g. ꝓportio minor que ſit a. ad b. / et tūc ego dico / <lb/> ꝓportio b. ad c. eſt illa per quã ꝓportio f. exce-<lb/>dit ꝓportionē g. </s>
            <s xml:id="N13B5B" xml:space="preserve">Probatur / q2 ꝓportio f. cõponi-<lb/>tur adequate ex ꝓportione a. ad b. et ex ꝓportione <lb/>b. ad c. / vt patet ex ſecūda concluſione: igitur ꝓpor­<lb/>tio f. que eſt a. ad c. addit adequate ſupra ꝓportio­<lb/>nē g. que eſt a. ad b. ꝓportionē b. ad c. / et per conſe-<lb/>quens f. ꝓportio excedit ꝓportionē g. ꝑ ꝓportio-<lb/>nē b. ad c. adequate cū illaꝫ adequate addat vltra <lb/>alteraꝫ / et illa videlicet b. ad c. eſt proportio que eſt <lb/>inter terminos minores illarum duarum propor­<lb/>tionum inequalium / igitur correlarium verum.</s>
          </p>
          <div xml:id="N13B70" level="4" n="8" type="float">
            <note position="right" xlink:href="note-0038-05a" xlink:label="note-0038-05" xml:id="N13B74" xml:space="preserve">Documē­<lb/>tum.</note>
            <note position="right" xlink:href="note-0038-06a" xlink:label="note-0038-06" xml:id="N13B7C" xml:space="preserve">1. correĺ.</note>
          </div>
          <note position="right" xml:id="N13B82" xml:space="preserve">2. correĺ.</note>
          <p xml:id="N13B86">
            <s xml:id="N13B87" xml:space="preserve">¶ Sequitur ſecundo /  ſi duo numeri ſiue quanti-<lb/>tates ſe habent in proportione tripla ſubquadru­<lb/>plum maioris eſt ſubſexquitertium minoris: et ſi <lb/>duo numeri ſe habēt in ꝓportiõe dupla ſubq̈dru-<lb/>plū maioris eſt ſubduplū minoris: quēadmodum             <pb chead="Secunde partis" file="0039" n="39"/>             duobꝰ numeris ſe habētibus in proportione ſex-<lb/>quialtera ſubduplum maioris eſt ſubſexquiterti-<lb/>um minoris. </s>
            <s xml:id="N13B9B" xml:space="preserve">Probatur prima pars / quia in caſu <lb/>illius idē numerus habet duas proportiones ma­<lb/>ioris inequalitatis ad duos numeros minores <lb/>īequales puta triplam ad ſuū ſubtriplum et qua-<lb/>druplam ad ſuum ſubquadruplum / vt conſtat: igi­<lb/>tur proportio per quaꝫ quadrupla excedit triplã <lb/>eſt proportio inter illos numeros minores puta <lb/>ſubtriplum et ſubquadruplum / vt patet ex prece-<lb/>denti: et proportio per quã quadrupla excedit tri-<lb/>plam eſt ſexquitertia que eſt inter numerus deno­<lb/>minantes illas / vt patet ex concluſione: igitur in-<lb/>ter illos duos numeros minores puta ſubtriplū <lb/>et ſubquadrupluꝫ eſt proportio ſexquitertia / quod <lb/>fuit probandum. </s>
            <s xml:id="N13BB8" xml:space="preserve">Et eodem modo probabis reli-<lb/>quas partes et infinita talia correlaria.             <anchor type="note" xlink:href="note-0039-01" xlink:label="note-0039-01a"/>             </s>
            <s xml:id="N13BC2" xml:space="preserve">¶ Sequi-<lb/>tur tertio /  vniuerſaliter talis eſt proportio inter <lb/>duas partes aliquotas inequales alicuius quan­<lb/>titatis: qualis eſt inter numeros a quibus deno-<lb/>minantur tales partes aliquote: vt capta quarta <lb/>alicuius et etiam tertia eiuſdem: dico /  inter ter-<lb/>tiam et quartam talis eſt proportio qualis eſt in-<lb/>ter .4. et .3. puta ſexquitertia. </s>
            <s xml:id="N13BD3" xml:space="preserve">Ad quod probanduꝫ <lb/>peto primo /  quelibet pars aliquota alicuius de­<lb/>nominatur a certo numero vt medietas a binario <lb/>tertia a ternario: quarta a quaternario: quīta a <lb/>quinario .etc̈. </s>
            <s xml:id="N13BDE" xml:space="preserve">Peto ſecundo /  cuiuſlibet quanti-<lb/>tatis ad quamlibet ſui partem aliquotam eſt pro­<lb/>portio mĺtiplex denominata a numero a quo de-<lb/>nominatur talis pars aliquota: vt cuiuſlibet quã­<lb/>titatis ad ſuam quartam eſt proportio quadru-<lb/>pla denominata a numero quaternario a quo <lb/>denominatur quarta, et ad ſuam tertiã eſt tripla <lb/>denominata a numero ternario a quo denomina­<lb/>tur tertia: et ſic cõſequenter. </s>
            <s xml:id="N13BF1" xml:space="preserve">Quibus baſibus ſup­<lb/>poſitis oſtenditur correlarium: et ſit a. vna quan-<lb/>titas: et ſit h. vna pars eius aliquota: et c. alia mi-<lb/>nor pars aliquota eiuſdem a. et ſit a. ad .c.f. ꝓpor-<lb/>tio: et a. ad b.g. proportio minor / vt oportet / et ſit d. <lb/>numerus a quo denominatur b. pars aliquota: et <lb/>e. a quo denominatur c. pars aliquota: et tūc dico / <lb/> tales eſt proportio inter b. et c. qualis inter d. <lb/>et e. </s>
            <s xml:id="N13C04" xml:space="preserve">Quod ſic oſtenditur / quia proportio f. que eſt <lb/>a. ad c. excedit proportionem g. que eſt a. ad b. per <lb/>proportioneꝫ b. ad c. / vt patet ex primo correlario / <lb/>et proportio per quã proportio f. excedit propor-<lb/>tionem g. eſt illa que eſt inter denominatiões ſiue <lb/>inter termininos a. quibus denominãtur f. et g. pro-<lb/>portiones / vt patet ex concluſione: igitur propor-<lb/>tio b. ad c. eſt proportio que eſt inter terminos a <lb/>quibus denominatur f. et g. proportiões: et f. et g. <lb/>proportiones denominantur a d. et e. numeris a <lb/>quibus denominantur b.c. partes aliquote ipſiꝰ <lb/>a. / vt patet ex ſecunda petitione igitur: talis eſt ꝓ-<lb/>portio inter b. et c. qualis eſt inter d. et e. / quod fuit <lb/>probandum. </s>
            <s xml:id="N13C21" xml:space="preserve">Et ſic patet correlariuꝫ.             <anchor type="note" xlink:href="note-0039-02" xlink:label="note-0039-02a"/>             </s>
            <s xml:id="N13C29" xml:space="preserve">¶ Sequitur <lb/>quarto /  conſtituta naturali ſerie proportionuꝫ <lb/>multipliciū: et conſtituta etiam naturali ſerie pro­<lb/>portionum ſuperparticularium: ſecunda ſpecies <lb/>proportionis multiplicis excedit primam ſpecieꝫ <lb/>per primam ſpeciem proportionis ſuperparticu-<lb/>laris puta per ſexquialterã: et tertia ſpecies mul-<lb/>tiplicis excedit ſecundã: per ſecundam ſpeciem ꝓ-<lb/>portionis ſuperparticularis: et quarta multipli-<lb/>cis excedit tertiam: per tertiaꝫ ſuperparticularis / <lb/>et ſic in infinitum. </s>
            <s xml:id="N13C40" xml:space="preserve">Probatur / quia captis primis <lb/>duabus ſpeciebus ꝓportionis multiplicis puta <lb/>dupla et tripla ille denominantur a. numero bina­             <cb chead="Capitulum quintū."/>             rio et ternario / vt conſtat: et tripla excedit duplam <lb/>per proportioneꝫ que eſt inter illos numeros ter-<lb/>narium videlicet et binarium / vt patet in concluſi-<lb/>one: et inter illos eſt prima ſpecies proportionis <lb/>ſuperparticularis / vt patet ex ſecundo capite pri-<lb/>me partis vbi generantur infinite ſpecies propor­<lb/>tionis ſuperparticularis ſereatim in naturali ſe­<lb/>rie numerorum igitur. </s>
            <s xml:id="N13C58" xml:space="preserve">Item captis tripla et qua-<lb/>drupla multiplicibus ille excedunt ſe: per propor­<lb/>tionem que eſt .4. ad .3. / vt patet ex concluſiõe: et in-<lb/>ter illos numeros eſt ſecunda ſpecies proportio-<lb/>nis ſuperparticularis / puta ſexquitertia / vt patet <lb/>ex loco preallegato: igit̄̄ correlariū verum quoniã <lb/>eodem modo probabis de aliis.             <anchor type="note" xlink:href="note-0039-03" xlink:label="note-0039-03a"/>             </s>
            <s xml:id="N13C6C" xml:space="preserve">¶ Sequitur quin­<lb/>to /  per tot proportiones ſuperparticulares cõ-<lb/>ſequenter / et ſereatim aſſumptas excedit quelibet <lb/>ſpecies multiplicis proportiõis diſtans a. prima <lb/>primã ſpeciem multiplicis: per quot vnitates nu-<lb/>merus a quo denominatur illa ſpecies diſtat a <lb/>numero a quo denomīatur prima ſpecies propor­<lb/>tionis multiplicis puta dupla. </s>
            <s xml:id="N13C7D" xml:space="preserve">Et ſic etiam dicen-<lb/>dum eſt de qualibet alia ſpecie mĺtiplici a qua di-<lb/>ſtat per aliquot ſpecies vt proportio quintupla <lb/>excedit proportionē duplam per tres ſpecies pro­<lb/>portionis ſuperparticulares ſereatim ſumptas <lb/>videlicet per proportionem ſexquialteram que eſt <lb/>3. ad .2. et ſexquitertiam que eſt .4. ad .3. et ſexqui-<lb/>quartam que eſt .5. ad .4. </s>
            <s xml:id="N13C8E" xml:space="preserve">Patet hoc correlarium <lb/>facile ex anteriori.             <anchor type="note" xlink:href="note-0039-04" xlink:label="note-0039-04a"/>             </s>
            <s xml:id="N13C98" xml:space="preserve">¶ Sequitur ſexto /  vniuerſa-<lb/>lis ſeries proportionum ſuperparticularium in-<lb/>finitam latitudinē proportionis conſtituit. </s>
            <s xml:id="N13C9F" xml:space="preserve">Pro-<lb/>batur / quia conſtituit infinite magnam proporti-<lb/>onem multiplicem cum proportione dupla: igitur <lb/>talis ſeries in infinitum magna latitudo eſt pro-<lb/>portionis. </s>
            <s xml:id="N13CAA" xml:space="preserve">Item talis ſeries proportionum ſuper­<lb/>particularium eſt naturalis ſeries numerorum in­<lb/>cipiendo a binario: ſed in infinitum magna pro-<lb/>portio eſt alicuius numeri a binarium: igitur infi-<lb/>nitum magna latitudo proportionis eſt natura-<lb/>lis ſeries proportionum ſuperparticularium. </s>
            <s xml:id="N13CB7" xml:space="preserve">Et <lb/>hoc nota ad capitulum de augmentatione.</s>
          </p>
          <div xml:id="N13CBC" level="4" n="9" type="float">
            <note position="left" xlink:href="note-0039-01a" xlink:label="note-0039-01" xml:id="N13CC0" xml:space="preserve">Tertium <lb/>correlar̄.</note>
            <note position="left" xlink:href="note-0039-02a" xlink:label="note-0039-02" xml:id="N13CC8" xml:space="preserve">4. correĺ.</note>
            <note position="right" xlink:href="note-0039-03a" xlink:label="note-0039-03" xml:id="N13CCE" xml:space="preserve">5. correĺ.</note>
            <note position="right" xlink:href="note-0039-04a" xlink:label="note-0039-04" xml:id="N13CD4" xml:space="preserve">6. correĺ.</note>
          </div>
        </div>
        <div xml:id="N13CDA" level="3" n="5" type="chapter" type-free="capitulum">
          <head xml:id="N13CDF" xml:space="preserve">Capitulum quintum / in quo reci-<lb/>tatur paucis et impugnatur opinio <lb/>baſani politi de proportione ſiue <lb/>cõmenſurabilitate proportionum.</head>
          <p xml:id="N13CE8">
            <s xml:id="N13CE9" xml:space="preserve">COnſueuerunt veteres  ſi-<lb/>gnanter paripathetici philoſophan-<lb/>tes amputare at reſecare contrari-<lb/>as opinationes: et deinde veras interſerere. </s>
            <s xml:id="N13CF2" xml:space="preserve">Ideo <lb/>baſani politi opinionem in materia proportio-<lb/>nalitatum ceteris mathematicis aduerſam pre-<lb/>ſenti duximus expugnandam.</s>
          </p>
          <p xml:id="N13CFB">
            <s xml:id="N13CFC" xml:space="preserve">Sit igit̄̄ capitalis ſuppoſitio. </s>
            <s xml:id="N13CFF" xml:space="preserve">Quod­<lb/>libet habens ſubduplum eſt duplum ad ſuam me-<lb/>dietatem et ſi ipſum eſt duplum ipſum continet ſu­<lb/>am medietatem bis adequate. </s>
            <s xml:id="N13D08" xml:space="preserve">Hec petitio nec <lb/>iuuat eam demonſtrare.</s>
          </p>
          <p xml:id="N13D0D">
            <s xml:id="N13D0E" xml:space="preserve">Secunda ſuppoſitio ſiue petitio. <lb/></s>
            <s xml:id="N13D12" xml:space="preserve">Omne duplum ad aliquod continet ipſum vel e-<lb/>quale ei bis tantum: et ſi contineat ipſum pluſquã <lb/>bis eſt pluſquam duplum ad illud.</s>
          </p>
          <p xml:id="N13D19">
            <s xml:id="N13D1A" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N13D1D" xml:space="preserve">Si aliquid effici-<lb/>tur in duplo minus ipſum perdit adequate medi-<lb/>etatem ſui.</s>
          </p>
          <pb chead="Secunde partis" file="0040" n="40"/>
          <p xml:id="N13D28">
            <s xml:id="N13D29" xml:space="preserve">Quarta ſuppoſitio ſiue petitio. </s>
            <s xml:id="N13D2C" xml:space="preserve">Oē <lb/>quod ſucceſſiue diminuitur vſ ad non gradū eſt <lb/>latitudo diuiſibilis: et in duas medietates: et ī tres <lb/>tertias, et in quatuor quartas, et ſic conſequenter <lb/></s>
            <s xml:id="N13D36" xml:space="preserve">Diminuitur enim ad ſubduplum, ad ſubtriplum, <lb/>ad ſubquadruplum: et ſic deinceps.</s>
          </p>
          <p xml:id="N13D3B">
            <s xml:id="N13D3C" xml:space="preserve">Quīta ſuppoſitio. </s>
            <s xml:id="N13D3F" xml:space="preserve">Latitudo propor-<lb/>tionis maiores inequalitatis eſt ſucceſſiue dimi-<lb/>nuibilis vſ ad nõ gradum. </s>
            <s xml:id="N13D46" xml:space="preserve">Probatur tum pri-<lb/>mo / quia maius extremum proportionis maioris <lb/>īequalitatis ſucceſſiue valet diminui vſ ad equa­<lb/>litatē minoris extremi: et in tali diminutione pro-<lb/>portio maioris inequalitatis ſucceſſiue diminui-<lb/>tur ad non gradum / vt conſtat: igitur in tali di-<lb/>minutione quelibet proportio minor illa ſignata <lb/>dabitur. </s>
            <s xml:id="N13D57" xml:space="preserve">Tum ſecundo / q2 vt baſanus concedit ve­<lb/>locitas motus correſpondet magnitudini ꝓpor-<lb/>tionis quo ad equalitatē: ſed ipſa velocitas mo-<lb/>tus eſt diminuibilis continuo ſucceſſiue vſ ad nõ <lb/>gradū: igitur et latitudo proportionis ſibi corre-<lb/>ſpondens inequalitate. </s>
            <s xml:id="N13D64" xml:space="preserve">¶ Ex hac ſequitur /  que-<lb/>libet latitudo proportionis maioris inequalita-<lb/>tis diuidi poteſt in duas medietates, in tres ter-<lb/>tias, in quatuor quartas, et ſic deinceps. </s>
            <s xml:id="N13D6D" xml:space="preserve">Patet <lb/>hoc correlariū ex priore auxiliante quarta.</s>
          </p>
          <p xml:id="N13D72">
            <s xml:id="N13D73" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N13D76" xml:space="preserve">Omne quod effi-<lb/>citur ſubduplū ad id quod erat antea perdit me-<lb/>dietatem ſui: et id quod remanet eſt tantū quantuꝫ <lb/>eſt id quod perdidit / qm̄ perdidit aliã medietatem <lb/>et cuiuſlibet quanti medietates ſunt equales.</s>
          </p>
          <p xml:id="N13D81">
            <s xml:id="N13D82" xml:space="preserve">His ſuppoſitis aduertendū eſt /  ba-<lb/>ſanus volens defenſare quãlibet proportionalē ra-<lb/>tionalē cuilibet alteri eſſe cõmenſurabilē aſtruxit <lb/>proportionū cõmenſurabilitatē ſiue ꝓportioneꝫ <lb/>aſſumendã eſſe ex denominationū ꝓportionibus <lb/>ponens talem concluſionē. </s>
            <s xml:id="N13D8F" xml:space="preserve">Proportionū propor­<lb/>tio eſt earū denominationū proportio: vt quadru­<lb/>pla eſt dupla ad duplã: q2 inter earum denomina­<lb/>tiones ſiue numeros a quibus denominantur eſt <lb/>proportio dupla, a binario enim dupla: et a qua-<lb/>ternario quadrupla denomīatur. </s>
            <s xml:id="N13D9C" xml:space="preserve">Item dupla eſt <lb/>ſexquitertia ad ſexquialteram: q2 dupla a bina-<lb/>rio ſexquialtera vero ab vnitate cū dimidio deno­<lb/>minatur. </s>
            <s xml:id="N13DA5" xml:space="preserve">Conſtat autem binarii ad vnitatem cum <lb/>dimidio proportionem ſexquitertiam eſſe.</s>
          </p>
          <note position="left" xml:id="N13DAA" xml:space="preserve">Contra <lb/>baſanū <lb/>primo.</note>
          <p xml:id="N13DB2">
            <s xml:id="N13DB3" xml:space="preserve">Sed contra hanc opinationem mea <lb/>ſententia mathemathicis principiis derogantē et <lb/>contrariã: arguitur primo ſic. </s>
            <s xml:id="N13DBA" xml:space="preserve">Ex hac opinione ſe­<lb/>quitur octuplam eſſe duplaꝫ ad quadruplam: ſed <lb/>conſequens eſt manifeſte falſū: igitur illud ex quo <lb/>ſequitur. </s>
            <s xml:id="N13DC3" xml:space="preserve">Sequela probatur / q2 illarū proportio-<lb/>onū octuple videlicet et quadruple denominatio-<lb/>nes ſiue numeros a quibus denominãtur, duple <lb/>ꝓportiõis rationē habere conſtat .8. em̄ ad .4. du­<lb/>pla ꝓportio eſt: igitur expoſitiõe octupla dupla <lb/>eſt ad quadruplã. </s>
            <s xml:id="N13DD0" xml:space="preserve">Iã falſitatē cõſequentis oſten-<lb/>damus ſuꝑeſt: qm̄ ſi octupla eſt dupla ad quadru-<lb/>plã: ſequitur /  quadrupla eſt medietas ipſiꝰ octu­<lb/>ple: vt ptꝫ ex prima ſuppoſitione: ſed cõſequēs eſt <lb/>falſum: igitur illud ex quo ſequitur: q2 tūc ſeque-<lb/>retur /  octupla cõtineret quadruplã bis adequa­<lb/>te: ſed hoc eſt falſuꝫ / q2 cõtinet quadruplã et duplã <lb/>adequate / vt ptꝫ in his terminis .8. ad .4. et .4. ad .1. <lb/></s>
            <s xml:id="N13DE2" xml:space="preserve">Patet hec conſequentia ex ſecunda parte eiuſdē <lb/>ſuppoſitionis.             <anchor type="note" xlink:href="note-0040-01" xlink:label="note-0040-01a"/>             </s>
            <s xml:id="N13DEC" xml:space="preserve">¶ Et confirmatur / q2 omne dupluꝫ <lb/>ad aliquod continet ipſum vel equale ei bis tantū             <cb chead="Capitulū quintū."/>             ſed octupla eſt dupla ad quadruplã per te / igitur <lb/>continet ipſum bis tantū: ſed cõſequens eſt falſuꝫ / <lb/>q2 ſexdecupla cõtinet quadruplã bis tantū. </s>
            <s xml:id="N13DF8" xml:space="preserve">Cõſe-<lb/>quentia ptꝫ ex ſe: et minor eſt prima pars ſecunde <lb/>ſuppoſitionis.             <anchor type="note" xlink:href="note-0040-02" xlink:label="note-0040-02a"/>             </s>
            <s xml:id="N13E04" xml:space="preserve">¶ Confirmatur ſecundo / q2 ſi poſi-<lb/>tio eſſet vera / ſequeretur /  dupla eſſet medietas <lb/>octuple: ſed hoc eſt falſum: igitur illud ex quo ſe-<lb/>quitur: q2 ſecundū iſtã opinionē octupla eſt qua-<lb/>drupla ad duplã / vt ptꝫ ex ꝓportione denoīationū <lb/>duple et octuple: et ſi octupla eſt quadrupla ad du­<lb/>plã iam ſequitur /  ipſa dupla eſt quarta octuple <lb/>et nõ medietas. </s>
            <s xml:id="N13E15" xml:space="preserve">Quodlibet em̄ eſt quadruplū ad <lb/>ſui quartã: cum eã contineat quater adequate. </s>
            <s xml:id="N13E1A" xml:space="preserve">Iã <lb/>probatur ſequela: et capio ꝓportionē octuplam: et <lb/>volo /  diminuatur quouſ fiat quadrupla ade-<lb/>quate: vt poſito /  octo diminuãtur vſ ad quatu­<lb/>or: et arguitur ſic: ipſa proportio octupla efficitur <lb/>in duplo minor vĺ cõcedit poſitio. </s>
            <s xml:id="N13E27" xml:space="preserve">Efficitur enim <lb/>q̈drupla que eſt ſubdupla ad octuplã: igitur ipſa <lb/>proportio octupla perdit adequate medietatem <lb/>ſui / vt ptꝫ ex tertia ſuppoſitione: et non perdit niſi <lb/>duplã adequate / vt conſtat / igitur dupla eſt medie­<lb/>tas octuple / qḋ fuit inferendū.             <anchor type="note" xlink:href="note-0040-03" xlink:label="note-0040-03a"/>             </s>
            <s xml:id="N13E39" xml:space="preserve">¶ Et ↄ̨firmat̄̄ tertio / <lb/>q2 ſi iſta poſitio eſſet vera / ſeq̄ret̄̄ /  dupla eſſet eq̈-<lb/>lis quadruple. </s>
            <s xml:id="N13E40" xml:space="preserve">Cõſequēs eſt falſum et cõtra opi-<lb/>nantem / igitur illud ex quo ſequitur. </s>
            <s xml:id="N13E45" xml:space="preserve">Sequela ar-<lb/>guitur / et volo /  potentia vt octo moueat reſiſten­<lb/>tiam vt vnum velocitate vt quatuor exempli gra-<lb/>tia / deinde volo /  potētia ſtante reſiſtentia: dimi-<lb/>nuatur vſ ad ſubduplū: et arguo ſic / ille motꝰ ſiue <lb/>velocitas vt quatuor diminuetur ad ſubduplum: <lb/>igitur perdit medietatē ſui. </s>
            <s xml:id="N13E54" xml:space="preserve">Patet cõſequentia ex <lb/>ſuppoſitione tertia: et per cõſequens nõ manebit <lb/>niſi velocitas vt duo: et deperdet̄̄ velocitas vt duo / <lb/>igitur tanta ꝓportio deperdita eſt quanta manet <lb/></s>
            <s xml:id="N13E5E" xml:space="preserve">Patet hec cõſequētia / q2 ab equalibꝰ ꝓportioni-<lb/>bus equales latitudines motuū ꝓueniūt: ſed ma-<lb/>net quadrupla / ergo deperdita eſt ei equalis: ſed <lb/>deperdita eſt dūtaxat ꝓportio dupla: ergo dupla <lb/>eſt equalis quadruple: quod fuit inferendum.</s>
          </p>
          <div xml:id="N13E69" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0040-01a" xlink:label="note-0040-01" xml:id="N13E6D" xml:space="preserve">Cõfirma­<lb/>tio ṗma.</note>
            <note position="right" xlink:href="note-0040-02a" xlink:label="note-0040-02" xml:id="N13E75" xml:space="preserve">Cõfirma­<lb/>tio ſcḋa</note>
            <note position="right" xlink:href="note-0040-03a" xlink:label="note-0040-03" xml:id="N13E7D" xml:space="preserve">3. confir-<lb/>matio</note>
          </div>
          <p xml:id="N13E85">
            <s xml:id="N13E86" xml:space="preserve">Secundo arguitur ſic / ſi illa poſitio <lb/>eſſet vera / ſequeretur /  quarta alicuiꝰ et ſua medie­<lb/>tas eſſent equales ſed cõſequens eſt falſum: igitur <lb/>illud ex quo ſequitur. </s>
            <s xml:id="N13E8F" xml:space="preserve">Sequela ꝓbatur / q2 dupla <lb/>eſt quarta pars octuple et medietas octuple ꝑ po-<lb/>ſitionē: igitur propoſitū. </s>
            <s xml:id="N13E96" xml:space="preserve">Maior probatur / q2 du­<lb/>pla eſt quarta pars ipſius octuple cū octuple ad <lb/>duplam ſit proportio quadrupla / vt patet ex po-<lb/>ſitiõe. </s>
            <s xml:id="N13E9F" xml:space="preserve">Minor probatur: et volo /  octupla perdat <lb/>ꝓportionē duplã adequate: et manifeſtū eſt /  effi-<lb/>citur quadrupla: et per cõſequens ſubdupla ad id <lb/>quod erat antea / vt patet ex poſitione: igitur ꝑdit <lb/>medietatē ſui. </s>
            <s xml:id="N13EAA" xml:space="preserve">Patet cõſequentia ex tertia et ſexta <lb/>ſuppoſitionibus: et non perdit niſi duplam: ergo <lb/>dupla eſt medietas octuple / quod fuit probandū. <lb/>             <anchor type="note" xlink:href="note-0040-04" xlink:label="note-0040-04a"/>             </s>
            <s xml:id="N13EB8" xml:space="preserve">¶ Et confirmatur / quia ſi poſitio eſſet vera / ſeque-<lb/>retur /  aliquid contineret alterum bis adequate <lb/>et tamen non eſſet duplum ad illud: ſed minꝰ quaꝫ <lb/>duplum: conſequens eſt manifeſte falſuꝫ et contra <lb/>diffinitionem proportionis duple: igitur. </s>
            <s xml:id="N13EC3" xml:space="preserve">Seque­<lb/>la probatur: quia proportio dupla ſexquiquar-<lb/>ta bis adequate continet ſexquialteram: patet <lb/>in his terminis .9.6.4. </s>
            <s xml:id="N13ECC" xml:space="preserve">Nouem enim ad quatuor <lb/>eſt proportio dupla ſexquiquarta: et componitur <lb/>adequate ex proportione .9. ad .6. et .6. ad .4. qua­<lb/>rum vtra eſt ſexquialtera: et tamen ipſa propor­<lb/>tio dupla ſexquiquarta eſt minor quam dupla <lb/>ad ſexquialteram: igitur propoſitum.</s>
          </p>
          <div xml:id="N13ED9" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0040-04a" xlink:label="note-0040-04" xml:id="N13EDD" xml:space="preserve">Cõfirma­<lb/>tio ṗma.</note>
          </div>
          <pb chead="Secunde partis" file="0041" n="41"/>
          <p xml:id="N13EE9">
            <s xml:id="N13EEA" xml:space="preserve">Probatur minor / q2 tripla eſt dupla ad ſequial-<lb/>terã: et dupla ſexquiquarta eſt minor tripla / ergo <lb/>dupla ſexquiquarta eſt minor quã dupla ad ſex-<lb/>quialterã. </s>
            <s xml:id="N13EF3" xml:space="preserve">Cõſequentia eſt nota cū minore: et ꝓbat̄̄ <lb/>maior / qm̄ denominatiõis triple ad denoīationē <lb/>ſexquialtere eſt proportio dupla. </s>
            <s xml:id="N13EFA" xml:space="preserve">Triū em̄ ad vnū <lb/>cū dimidio eſt proportio dupla: igitur tripla eſt <lb/>dupla ad ſexquialterã. </s>
            <s xml:id="N13F01" xml:space="preserve">Patet cõſequētia ex opi-<lb/>nione.             <anchor type="note" xlink:href="note-0041-01" xlink:label="note-0041-01a"/>             </s>
            <s xml:id="N13F0B" xml:space="preserve">¶ Cõfirmatur ſecūdo / q2 ſi poſitio eſſet vera / <lb/>ſequeretur /  aliquid cõtineret alteꝝ pluſ̄ bis: et <lb/>tamen eſſet adequate dnplū ad illud quod cõtinet <lb/>adequate bis: et aliquid cõtineret alteꝝ minus quã <lb/>bis hoc eſt contineret ipſum ſemel et medietatē eiꝰ <lb/>p̄ciſe et eſſet duplū ad illud et nõ ſexquialteꝝ. </s>
            <s xml:id="N13F18" xml:space="preserve">Oīa <lb/>iſta cõſequentia ſunt cõtra diffinitiões et prīcipia <lb/>mathematica / igitur et poſitio. </s>
            <s xml:id="N13F1F" xml:space="preserve">Sūt em̄ cõtra diffi­<lb/>nitiones ſexquialtere et duple / vt cõſtat. </s>
            <s xml:id="N13F24" xml:space="preserve">Iã ꝓbatur <lb/>ſequela / q2 tripla eſt dupla ad ſexq̇alterã: et tamē <lb/>cõtinet bis ſexquialterã: et aliquid vltra puta ſex-<lb/>quitertiã: vt ptꝫ in his terminis .12.9.6.4:12. em̄ <lb/>ad .9. eſt proportio ſexquitertia et .9. ad .6. eſt vna <lb/>proportio ſexquialtera et .6. ad 4. vna altera .12. <lb/>vero ad .4. eſt tripla ex illis duabus ſexquialteris <lb/>et vna ſexquitertia cõpoſita. </s>
            <s xml:id="N13F35" xml:space="preserve">Et ſic ptꝫ ſequela quo <lb/>ad primã partē. </s>
            <s xml:id="N13F3A" xml:space="preserve">Secūda pars patet de octupla et <lb/>quadrupla: octupla em̄ nõ cõtinet bis quadruplã <lb/>et tamen eſt dupla ad illam / vt patet ex poſitione. <lb/></s>
            <s xml:id="N13F42" xml:space="preserve">¶ Multa ſimilia poſſunt inferri / que manifeſte ſūt <lb/>cõtra dignitates, petitiones, et diffinitiones ma-<lb/>thematicas, qui debent ſupponi tan̄ principia <lb/>ſcientie mathematice. </s>
            <s xml:id="N13F4B" xml:space="preserve">¶ Sed oīa hec argumenta <lb/>facile (quãuis proterue et abſ ratione) reſcindit <lb/>baſanus negando illas petitiones et diffinitiões: <lb/>eas dūtaxat ad numeros ſiue quantitates conti-<lb/>nuas reſtringendo ſiue limitando. </s>
            <s xml:id="N13F56" xml:space="preserve">Sed ꝓfecto et <lb/>diminute loquit̄̄ et cõtra rationē: diminute quidē <lb/>et inſufficienter, q2 nõ aſſignat diffinitionē ꝓpor-<lb/>tions duple, quadruple, aut alterius ſufficienter <lb/>que cuilibet cõtento ſub diffinito cõueniat: et cõtra <lb/>rationē, qm̄ ſicut ipſe aſtruxit illas diffinitiones <lb/>duple, quadruple .etc̈. cõuenire quantitatibꝰ dūta­<lb/>xat et nūmeris: pari ꝓteruia quilibet poſſet defen­<lb/>ſare at aſſeuerare illas diffinitiones dumtaxat <lb/>cõuenire numeris cõpoſitis ex vnitatibus indiui-<lb/>ſibilibus puta intelligentiaꝝ aut punctoꝝ: et nul-<lb/>lis aliis. </s>
            <s xml:id="N13F6F" xml:space="preserve">Sicut em̄ ipſe negat hanc cõſequentiam <lb/>ꝓportio dupla ſexquiquarta cõtinet bis adequa-<lb/>te ſexquialterã / ergo eſt dupla ad illã: pari teme-<lb/>rario auſu poſſet quilibet hanc cõſequentiã nega­<lb/>re bipedale cõtinet bis adequate pedale / ergo eſt <lb/>duplū ad pedale: et oī dubio ꝓcul cõtra eū nõ eſſet <lb/>diſputandū ſi philoſopho primo phiſicoꝝ credat̄̄ <lb/></s>
            <s xml:id="N13F7F" xml:space="preserve">Sed q2 ipſe diceret ſe nõ negare prīcipia mathe-<lb/>matica: ſed ea coartare ſiue limitare: qm̄ illa non <lb/>ſunt intelligenda in proportionibus.</s>
          </p>
          <div xml:id="N13F86" level="4" n="3" type="float">
            <note position="left" xlink:href="note-0041-01a" xlink:label="note-0041-01" xml:id="N13F8A" xml:space="preserve">Scḋa cõ-<lb/>firmatio.</note>
          </div>
          <note position="left" xml:id="N13F92" xml:space="preserve">3. arguit̄̄</note>
          <p xml:id="N13F96">
            <s xml:id="N13F97" xml:space="preserve">Idco cõtra eū tertio arguo ex prīci-<lb/>piis iã limitatis ad ꝓportiones et hoc ſic ꝓportio <lb/>ſexdecupla eſt dupla ad q̈druplã: et octupla tripla <lb/>ad duplã vt deducã ex mathematicis prīcipiis: et <lb/>ſecundū eum proportio ſexdecupla eſt quadrupla <lb/>ad quadruplam vt ſuadet proportionū denomi-<lb/>natio. </s>
            <s xml:id="N13FA6" xml:space="preserve">Item ſecunduꝫ eum octupla eſt quadrupla <lb/>ad duplam / vt denominationes duple et octuple <lb/>oſtendunt: igitur ſua poſitio principiis mathema­<lb/>ticis ad proportiones limitatis contrariatur / et ꝑ <lb/>conſequens falſa. </s>
            <s xml:id="N13FB1" xml:space="preserve">Conſequentia eſt nota cū mino­<lb/>re / et maior probatur primo quantum ad priorem <lb/>partem / quia capta proportione ſexdecupla inter <lb/>16. et .1. ibi reperiūtur .3. termini continuo propor-             <cb chead="Capitulum quintū."/>             <anchor type="note" xlink:href="note-0041-02" xlink:label="note-0041-02a"/>             tionabiles proportione quadrupla vtpote .16.4: <lb/>1. / igitur extremi ad extremū puta .16. ad .1. eſt du-<lb/>pla proportio ad proportionē primi ad ſecundū <lb/>puta .16. ad .4. / vt patet ex decima diffinitione quī­<lb/>ti elementorum euclidis expreſſe: et ex quinta diffi­<lb/>nitione ſecundi elementorum iordani.             <anchor type="note" xlink:href="note-0041-03" xlink:label="note-0041-03a"/>             </s>
            <s xml:id="N13FD1" xml:space="preserve">Secunda <lb/>pars maioris probatur / quoniã capta proporti-<lb/>one octupla octo ad vnum: ibi reperiuntur quatu­<lb/>or termini cõtinuo proportionabiles proportiõe <lb/>dupla videlicet .8.4.2.1. / igit̄̄ extremi ad extremuꝫ <lb/>puta .8. ad .1. eſt proportio tripla ad proportionē <lb/>8. ad .4. que eſt dupla. </s>
            <s xml:id="N13FE0" xml:space="preserve">Patet conſequentia ex ea-<lb/>dem decima diffinitione quinti elementoꝝ euclu-<lb/>dis: et quinta ſecundi elementoꝝ iordani: </s>
            <s xml:id="N13FE7" xml:space="preserve">Nec ba-<lb/>ſanus poſſet hoc argumentū diſſoluere niſi prin-<lb/>cipia arithmetica in eum adducta neget.</s>
          </p>
          <div xml:id="N13FEE" level="4" n="4" type="float">
            <note position="right" xlink:href="note-0041-02a" xlink:label="note-0041-02" xml:id="N13FF2" xml:space="preserve">Eu. 5. ele.</note>
            <note position="right" xlink:href="note-0041-03a" xlink:label="note-0041-03" xml:id="N13FF8" xml:space="preserve">Iorda. 2 <lb/>ele.</note>
          </div>
          <p xml:id="N14000">
            <s xml:id="N14001" xml:space="preserve">Quarto  ad opinãtē argr̄ / qm̄ vt ip̄e <lb/>ꝓfitet̄̄ in ſui operis ex ordio ſuarū ꝓportionū tra-<lb/>ctatus introductorius eſt ad ſuiſethicas calcula-<lb/>tiones: ſed ipſe calculator ſuiſeth longe aliter ſen­<lb/>tit: et plurimū ab eo diſcrepat in materia de pro-<lb/>portione proportionū vt ex quam plurimis locis <lb/>eius percipere poſſumus: igitur nec calculatoris <lb/>mentem intellexit nec eius tractatus ad eum intel­<lb/>ligendum introducit: īmo potius extraducit. </s>
            <s xml:id="N14014" xml:space="preserve">Pro­<lb/>bat̄̄ minor.             <anchor type="note" xlink:href="note-0041-04" xlink:label="note-0041-04a"/>             </s>
            <s xml:id="N1401E" xml:space="preserve">Tū primo / quoniã calculator in quīta <lb/>concluſione prime opinionis de augmentatione <lb/>dicit /  ſi aliquid augeatur in duplo velocius al-<lb/>tero: et illud acquirat vnam proportionē f. in ali-<lb/>quo tēpore neceſſe eſt in eodeꝫ tempore illud quod <lb/>in duplo velocius augetur proportionem compo­<lb/>ſitam ex duplici f. acquirere: cum in caſu calcula-<lb/>toris ibidem illud quod in duplo velocius auge-<lb/>tur continuo in duplo velocius augetur: ſed illa <lb/>conſequentia nichil penitus valeret ſi baſani po-<lb/>ſitio eſſet vera. </s>
            <s xml:id="N14035" xml:space="preserve">qm̄ quando a. acquireret propor-<lb/>tionem quadruplam et b. in eodem tempore in du­<lb/>plo velocius augeretur adequate non eſſet neceſſe <lb/> b. in eodem tempore acquireret proportionem <lb/>compoſitam ex duabus quadruplis: īmo neceſſe <lb/>eſſet /  non acquireret tantum: ſed acquireret cõ-<lb/>poſitã ex quadrupla et dupla que eſt octupla que <lb/>ſecundū baſanū eſt dupla ad quadruplam.             <anchor type="note" xlink:href="note-0041-05" xlink:label="note-0041-05a"/>             </s>
            <s xml:id="N1404B" xml:space="preserve">Tum <lb/>ſecundo / quia idem calculator in capitulo de diffi­<lb/>cultate actionis in primo argumento quo impu-<lb/>gnat tertiam poſitiouem aſſumit potentiam mo-<lb/>uentem a proportione ſexquialtera in aliquo me-<lb/>dio: et dicit /  ſi illa potētia augeatur ad ſexquial­<lb/>terum preciſe ſtante reſiſtentia medii  ipſa po-<lb/>tentia mouebitur in duplo velocius adequate: ex <lb/>quo immediate ſequitur /  proportio potentie ad <lb/>reſiſtentiã fuit effecta in duplo maior. </s>
            <s xml:id="N14060" xml:space="preserve">Patet con­<lb/>ſequentia / quoniã ſecundū eum velocitas motuum <lb/>ꝓportionū ꝓportionē inſequit̄̄ / vt ptꝫ ex principio <lb/>capituli de motu locali: ſed cū potētia illa, habēs <lb/>ꝓportionē ſexquialterã ad ſuã reſiſtētiã acquirit <lb/>ſupra ſe proportionem ſexquialteram tota pro-<lb/>portio componitur adequate ex duabus ſexquial­<lb/>teris et efficitur dupla ſexquiquarta qualis eſt .9 <lb/>ad .4. / igitur dupla ſexquiquarta ſecundum calcu­<lb/>latorem eſt dupla ad ſexquialteram: et ſecundum <lb/>baſanum tripla eſt dupla ad ſexquialteram: igi-<lb/>tur ſua poſitio, ſuuſ ſuarum proportionuꝫ tra-<lb/>ctatus non ad intelligendam calculatoris ſenten­<lb/>tiam introducit ſed ei aduerſatur.             <anchor type="note" xlink:href="note-0041-06" xlink:label="note-0041-06a"/>             </s>
            <s xml:id="N14082" xml:space="preserve">Tum tertio / q2 <lb/>idem calculator in vltimo capitulo de medio non <lb/>reſiſtente concluſione octaua dicit expreſſe in pro­<lb/>batione illius concluſionis /  ſexdecupla eſt du-<lb/>pla ad quadruplã: et ſi ſic non eſſet. </s>
            <s xml:id="N1408D" xml:space="preserve">concluſio eſſet             <pb chead="Secunde partis" file="0042" n="42"/>             falſa et probatio nulla. </s>
            <s xml:id="N14095" xml:space="preserve">et ſecundumm baſanum ē <lb/>quadrupla ad quadruplam: igitur dicta baſani <lb/>et calculatoris non coherent. </s>
            <s xml:id="N1409C" xml:space="preserve">¶ Hoc idem ex mul-<lb/>tis aliis locis calculatoris euidenter deprehēde-<lb/>re potes. </s>
            <s xml:id="N140A3" xml:space="preserve">ſed hii loci ſufficiant. </s>
            <s xml:id="N140A6" xml:space="preserve">Et ſic relinquo po-<lb/>ſitionem eius confutatam et exploſam: que tamē <lb/>proterue defenſari poteſt: ſed nõ conſequenter ad <lb/>mathemathica prīcipia vt dictū eſt.             <anchor type="note" xlink:href="note-0042-01" xlink:label="note-0042-01a"/>             </s>
            <s xml:id="N140B4" xml:space="preserve">¶ Ex his igit̄̄ <lb/>abunde apparet /  proportio proportionū nõ eſt <lb/>ſicut proportio denominationum.</s>
          </p>
          <div xml:id="N140BB" level="4" n="5" type="float">
            <note position="right" xlink:href="note-0041-04a" xlink:label="note-0041-04" xml:id="N140BF" xml:space="preserve">Cal. ca. <lb/>de aug.</note>
            <note position="right" xlink:href="note-0041-05a" xlink:label="note-0041-05" xml:id="N140C7" xml:space="preserve">Cal. de <lb/>diffi. ac.</note>
            <note position="right" xlink:href="note-0041-06a" xlink:label="note-0041-06" xml:id="N140CF" xml:space="preserve">Calcu. de <lb/>me. nõ re­<lb/>ſiſ. capite <lb/>ſecūdo.</note>
            <note position="left" xlink:href="note-0042-01a" xlink:label="note-0042-01" xml:id="N140DB" xml:space="preserve">correĺm.</note>
          </div>
        </div>
        <div xml:id="N140E1" level="3" n="6" type="chapter" type-free="capitulum">
          <head xml:id="N140E6" xml:space="preserve">Capitulū ſextū / in quo agitur de pro-<lb/>portionū proportione: cõmenſurabilita­<lb/>te earūdem, et incõmenſurabilitate.</head>
          <p xml:id="N140ED">
            <s xml:id="N140EE" xml:space="preserve">PRo ſpecialiori noticia propor­<lb/>tionis ꝓportionū habenda ſit.</s>
          </p>
          <p xml:id="N140F3">
            <s xml:id="N140F4" xml:space="preserve">Prima ſuppoſitio. </s>
            <s xml:id="N140F7" xml:space="preserve">Cõmenſurabilia <lb/>ſiue in ꝓportione rationali ſe habentia ſunt illa <lb/>quorū idem eſt pars aliquota vt .4. et .2. pedale et <lb/>bipedale. </s>
            <s xml:id="N14100" xml:space="preserve">Unitas em̄ eſt pars aliquota et duorū et <lb/>quatuor: et medietas pedalis eſt pars aliquota et <lb/>pedalis et bipedalis.             <anchor type="note" xlink:href="note-0042-02" xlink:label="note-0042-02a"/>             </s>
            <s xml:id="N1410C" xml:space="preserve">Hec eſt diffinitio cõmenſura­<lb/>biliū in principio decimi elementoꝝ euclidis.</s>
          </p>
          <div xml:id="N14111" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0042-02a" xlink:label="note-0042-02" xml:id="N14115" xml:space="preserve">eu. 10. ele.</note>
          </div>
          <p xml:id="N1411B">
            <s xml:id="N1411C" xml:space="preserve">Secunda ſuppoſitio. </s>
            <s xml:id="N1411F" xml:space="preserve">Ille proportio­<lb/>nes dicūtur cõmenſurabiles quarum eadem pro-<lb/>portio eſt pars aliquota. </s>
            <s xml:id="N14126" xml:space="preserve">Patet ex priori.</s>
          </p>
          <p xml:id="N14129">
            <s xml:id="N1412A" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N1412D" xml:space="preserve">Quando aliqua <lb/>ꝓportio cõponitur ex aliquot ꝓportionibus ade-<lb/>quate ſemꝑ altera illarū eſt ꝓportio que eſt alicu-<lb/>ius termini intermedii ad minimū extremū: vt ꝓ-<lb/>portio quatuor ad duo componitur ex proportio­<lb/>ne .4. ad .3. et trium ad duo que eſt alicuius termi-<lb/>ni intermedii ad minimum extremum. </s>
            <s xml:id="N1413C" xml:space="preserve">Patet hec <lb/>ſatis ex his que dicta ſunt in quarto capite huius <lb/>partis.</s>
          </p>
          <p xml:id="N14143">
            <s xml:id="N14144" xml:space="preserve">Quarta ſuppoſitio </s>
            <s xml:id="N14147" xml:space="preserve">Quilibet nume-<lb/>rus eſt multiplex ad vnitatem </s>
            <s xml:id="N1414C" xml:space="preserve">Patet ex his que <lb/>dicta ſunt in quarto capite: </s>
            <s xml:id="N14151" xml:space="preserve">Et rurſns quia omīs <lb/>numerus aut componitur ex duabus vnitatibus: <lb/>et ſic eſt duplus ad vnitatem. </s>
            <s xml:id="N14158" xml:space="preserve">vel ex tribus / et ſic eſt <lb/>triplus, vel ex quatuor / et ſic eſt quadruplus: et ſic <lb/>in infinitum. </s>
            <s xml:id="N1415F" xml:space="preserve">¶ Ex hac ſequitur.</s>
          </p>
          <p xml:id="N14162">
            <s xml:id="N14163" xml:space="preserve">Quinta ſuppoſitio </s>
            <s xml:id="N14166" xml:space="preserve">Cuiuſlibet pro-<lb/>portionis multiplicis vnitas eſt minimum extre-<lb/>mum.</s>
          </p>
          <p xml:id="N1416D">
            <s xml:id="N1416E" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N14171" xml:space="preserve">Nullus numerus <lb/>eſt ſuprapartiēs, aut ſuperparticularis: aut mul­<lb/>tiplex ſuprapartiens, aut multiplex ſuperparti-<lb/>cularis ad vnitatem. </s>
            <s xml:id="N1417A" xml:space="preserve">Probatur / quoniã quilibet <lb/>numerus adequate eſt multiplex ad vnitatem / vt <lb/>patet ex quarta: igitur nullꝰ eſt ſuprapartiēs aut <lb/>ſuperparticularis: aut multiplex etc. ad vnitatem</s>
          </p>
          <p xml:id="N14183">
            <s xml:id="N14184" xml:space="preserve">His ſuppoſitis ſit </s>
            <s xml:id="N14187" xml:space="preserve">Prima concluſio <lb/></s>
            <s xml:id="N1418B" xml:space="preserve">Nulla proportio multiplex eſt pars aliquota ali­<lb/>cuius proportionis non multiplicis. </s>
            <s xml:id="N14190" xml:space="preserve">Probatur / <lb/>quoniaꝫ multiplex nullius proportionis ſuperꝑ-<lb/>ticularis aut ſuprapartientis eſt pars: cum quali­<lb/>bet tali ſit maior: nec etiam alicuius non multipli­<lb/>cis alterius: quia ſi ſic detur illa proportio et ſit a. / <lb/>et multiplex pars aliquota eius ſit b. inter d. et e. <lb/>terminos primos / et arguitur ſic b. proportio mul­<lb/>tiplex eſt pars aliquota ipſius a. / igitur a. eſt pro-<lb/>portio multiplex / quod eſt oppoſitum dati. </s>
            <s xml:id="N141A3" xml:space="preserve">Pro-<lb/>batur conſequentia / quia ſi b. eſt pars aliquota ip­<lb/>ſius a. / ſequitur /  ipſa b. proportio multiplex ali-             <cb chead="Capitulum ſextum"/>             quoties ſumpta reddit et componit ipſam a. pro-<lb/>portionem: cõponat igitur c. vicibus ſumpta ade­<lb/>quate: et tūc capio proportionem b. inter primos <lb/>numeros eius ſiue terminos d. videlicet maiorem <lb/>et e. minorem: et manifeſtum eſt /  e. eſt vnitas vt <lb/>patet ex quinta ſuppoſitione: capio igitur / tūc vnū <lb/>alium numerum que ſe habeat in proportione b. <lb/>ad ipſum d. qui ſit f. et iterum vnum alterum qui <lb/>ſe habeat in proportione b. ad f: et ſic c. vicibus: et <lb/>ſit vltimus numerus ſic ſumptus g. / et manifeſtum <lb/>eſt /  g. ad e. erit proportio compoſita ex b. ꝓpro-<lb/>tione c. vicibus adequate: et illa proportio g. ad e. <lb/>eſt multiplex quia eſt inter g. numerum et e. vnita-<lb/>tem. </s>
            <s xml:id="N141C7" xml:space="preserve">Conſequentia patet ex quarta ſuppoſitione <lb/>et ſexta: et illa eſt a. proportio per te / ergo a. ē mul <lb/>multiplex / quod fuit probandum. </s>
            <s xml:id="N141CE" xml:space="preserve">Et ſic patet con-<lb/>cluſio. </s>
            <s xml:id="N141D3" xml:space="preserve">¶ Ex qua ſequitur /  nulla proportio non <lb/>multiplex eſt dupla, quadrupla, aut aliqua alia <lb/>de genere multiplici, ad aliquam multiplicem.</s>
          </p>
          <p xml:id="N141DA">
            <s xml:id="N141DB" xml:space="preserve">Probatur facile ex concluſione: quia ſi ſic: iã mul­<lb/>tiplex eſſet pars aliquota illius nõ multiplicis / vt <lb/>conſtat / quod eſt contra concluſionem.</s>
          </p>
          <p xml:id="N141E2">
            <s xml:id="N141E3" xml:space="preserve">Secunda concluſio </s>
            <s xml:id="N141E6" xml:space="preserve">Nulla propor-<lb/>tio multiplex eſt cõmenſurabilis alicui proportio­<lb/>ni ſuperparticulari aut ſuprapartienti. </s>
            <s xml:id="N141ED" xml:space="preserve">Proba-<lb/>tur / quoniam cuiuſlibet proportionis multiplicis <lb/>vnitas eſt minimum extremum: igitur nulla ꝓpor­<lb/>tio multiplex eſt cõmenſurabilis alicui proportio­<lb/>ni ſuperparticulari aut ſuprapartienti. </s>
            <s xml:id="N141F8" xml:space="preserve">Antece-<lb/>dens patet ex quinta ſuppoſitione: et conſequen-<lb/>tia probatur / quia detur oppoſitum conſequētis: <lb/>et ſit illa proportio ſuperparticularis aut ſuper-<lb/>partiens b. et multiplex et commenſurabilis a. / et <lb/>ſequitur /  aliqua proportio eſt pars aliquota ip­<lb/>ſius b. et ipſius a. / vt patet ex ſecunda ſuppoſitio-<lb/>ne: ſit igitur illa proportio que eſt pars aliquota <lb/>c. / et arguit̄̄ ſic / c. ē pars aliq̊ta ipſius a. / igr̄ a. ex ali­<lb/>quot c. proportionibus adequate componitur.</s>
          </p>
          <p xml:id="N1420D">
            <s xml:id="N1420E" xml:space="preserve">Patet hec conſequentia ex definitione partis ali­<lb/>quote: et vltra ex aliquot proportionibus c. ade-<lb/>quate componitur: ergo altera illarum c. propor­<lb/>tionum eſt alicuius termini ītermedii ad minimū <lb/>extremum ipſius proportionis a. </s>
            <s xml:id="N14219" xml:space="preserve">Patet hec con­<lb/>ſequentia ex tertia ſuppoſitione. </s>
            <s xml:id="N1421E" xml:space="preserve">et c. non eſt ꝓpor­<lb/>tio multiplex / vt conſtat: cum ſit pars aliquota ꝓ-<lb/>portionis qualibet multiplice minoris. </s>
            <s xml:id="N14225" xml:space="preserve">ergo ſeq̇-<lb/>tur /  minimum extremum talis ꝓportionis c. nõ <lb/>eſt vnitas: et illud minimum extremum proportio­<lb/>nis .c. eſt minimum extremum proportionis a. / igi­<lb/>tur illud minimum extremum proportionis a. nõ <lb/>eſt vnitas: et a. eſt multiplex per te: ergo non cuiuſ­<lb/>libet multiplicis vnitas eſt minimum extremum / <lb/>quod eſt oppoſitum antecedentis conſequentie ꝓ­<lb/>bande et quinte ſuppoſitionis.</s>
          </p>
          <p xml:id="N14238">
            <s xml:id="N14239" xml:space="preserve">Tertia concluſio. </s>
            <s xml:id="N1423C" xml:space="preserve">Nulla proportio <lb/>multiplex eſt commenſurabilis alicui multiplici <lb/>ſuperparticulari aut multiplici ſuprapartienti.</s>
          </p>
          <p xml:id="N14243">
            <s xml:id="N14244" xml:space="preserve">Probatur: quia ſi aliqua proportio multiplex <lb/>ſit commenſurabilis alicui proportioni multipli­<lb/>ci ſuperparticulari: aut ſuprapartienti: aliqua ꝓ­<lb/>portio eſſet pars aliquota vtriuſ puta multipli­<lb/>cis, et multiplicis ſuperparticularis, vel multipli­<lb/>cis ſuprapartientis que ſit c. / et arguo ſic / c. non eſt <lb/>proportio multiplex / vt patet ex prima concluſio-<lb/>ne huius: nec eſt ſuperparticularis: aut ſuprapar­<lb/>tiens vt patet ex ſecunda: igitur erit multiplex ſu­<lb/>perparticularis, aut multiplex ſuprapartiens: ſꝫ <lb/>hoc eſt falſum / igitur c. non eſt pars aliquota pro­             <pb chead="Secūde partis" file="0043" n="43"/>             portionis multiplicis vel multiplicis ſuperparti­<lb/>cularis, vel multiplicis ſuprapartientis. </s>
            <s xml:id="N14262" xml:space="preserve">Falſitas <lb/>conſequentis probatur: quoniam ſi c. eſt pars ali­<lb/>quota multiplicis ꝓportionis: capio talem ꝓpor­<lb/>tionem multiplicem inter primos terminos eius: <lb/>et arguo ſic: c: proportio multiplex ſuperparticu-<lb/>laris, aut multiplex ſnpraꝑtiens, eſt pars aliquo­<lb/>ta alicuius ꝓportionis multiplicis: igitur ex ali-<lb/>quot c. illa proportio multiplex componitur. </s>
            <s xml:id="N14273" xml:space="preserve">igi-<lb/>tur ex conſequenti ſequitur /  alicuius termini in-<lb/>termedii ad minimum extremū ipſius proportio-<lb/>nis mĺtiplicis / qḋ minimū externū ē vnitas ē ꝓpor­<lb/>tio c. / vt patet ex tertia ſuppoſitione: et illa ꝓpor-<lb/>tio c. eſt multiplex ſuꝑparticularis, aut multiplex <lb/>ſuꝑperpartiens: igitur alicuius numeri ad vnita-<lb/>tem eſt ꝓportio multiplex ſuprapartiens aut mul­<lb/>tiplex ſuperparticularis quod eſt oppoſitum ſex-<lb/>te ſuppoſitionis: et per conſequens falſum: et ex <lb/>conſequenti illud ex quo ſequitur videlicet /  c. eſt <lb/>ꝓportio multiplex ſuperparticularis, aut multi-<lb/>plex ſuprapartiens. </s>
            <s xml:id="N1428E" xml:space="preserve">Et ſic patet concluſio.</s>
          </p>
          <p xml:id="N14291">
            <s xml:id="N14292" xml:space="preserve">Quarta concluſio. </s>
            <s xml:id="N14295" xml:space="preserve">Nulla proportio <lb/>multiplex eſt commenſurabilis alicui proportio-<lb/>ni rationali non multiplici. </s>
            <s xml:id="N1429C" xml:space="preserve">Probatur: quia nul­<lb/>la ꝓportio multiplex eſt commenſurabilis alicui <lb/>ſuperparticulari, aut ſuprapartienti / vt patet ex <lb/>ſecunda, nec alicui multiplici ſuꝑparticulari, aut <lb/>multiplici ſuprapartienti / vt ptꝫ ex tertia, igit̄̄ nul­<lb/>la ꝓportio multiplex ↄ̨menſurabilis eſt alicui ꝓ-<lb/>portioni rationali non multiplici. </s>
            <s xml:id="N142AB" xml:space="preserve">Et ſic patet cõ­<lb/>cluſio.</s>
          </p>
          <p xml:id="N142B0">
            <s xml:id="N142B1" xml:space="preserve">Quinta concluſio </s>
            <s xml:id="N142B4" xml:space="preserve">Nulla proportio <lb/>ſuperparticularis eſt commenſurabilis alicui ꝓ-<lb/>portioni ſuperparticulari. </s>
            <s xml:id="N142BB" xml:space="preserve">Probatur ſupponen­<lb/>do /  inter cuiuſlibet ꝓportionis ſuperparticula­<lb/>ris primos numeros nullus numerus mediat vt <lb/>viſum eſt in prima parte vbi agebatur de genera­<lb/>tione ꝓportionum ſuperparticularium. </s>
            <s xml:id="N142C6" xml:space="preserve">quo ſup­<lb/>poſito arguitur ſic: inter cuiuſlibet ꝓportionis ſu­<lb/>perparticularis primos numeros nullus mediat <lb/>numerus: igitur nulla talis ex aliquot ītermediis <lb/>ꝓportionibus adequate componitur. </s>
            <s xml:id="N142D1" xml:space="preserve">Patet con­<lb/>ſequentia / quia nulla eſt ꝓportio intermedia niſi <lb/>ſit numerus intermedius: et vltra ex nullis ꝓpor-<lb/>tionibus componitur. </s>
            <s xml:id="N142DA" xml:space="preserve">igitur nulla ꝓportio ē pars <lb/>aliquota eius: et per conſequens ipſa non eſt com­<lb/>menſurabilis alicui proportioni ſuperparticula­<lb/>ri. </s>
            <s xml:id="N142E3" xml:space="preserve">Patet conſequentia / quia alias aliquid eſſet <lb/>pars aliquota vtriuſ. </s>
            <s xml:id="N142E8" xml:space="preserve">Et ſic patet concluſio.</s>
          </p>
          <note position="left" xml:id="N142EB" xml:space="preserve">obiectio.</note>
          <p xml:id="N142EF">
            <s xml:id="N142F0" xml:space="preserve">¶ Sed tu dices /  hec ꝓbatio eſt inefficax: quoniã <lb/>concedit /  aliqua proportio ex nullis ꝓportioni­<lb/>bus componitur quod eſt contra ea que dicta ſūt <lb/>capite quarto huius partis. </s>
            <s xml:id="N142F9" xml:space="preserve">imo ꝓbatio nihil ali­<lb/>ud probat niſi /  ex nullis ꝓportionibus equalibꝰ <lb/>rationalibus componitur que ſint partes aliquo­<lb/>te illius: cum hoc tamen ſtat /  aliqua ꝓportio ir-<lb/>rationalis eſt pars aliquota duarum ꝓportionū <lb/>ſuperparticularium: et ſic erunt commenſurabi-<lb/>les.             <anchor type="note" xlink:href="note-0043-01" xlink:label="note-0043-01a"/>             </s>
            <s xml:id="N1430D" xml:space="preserve">¶ Sed hoc non obſtat / quia nulla ꝓportio ſuꝑ­<lb/>particularis componitur ex alia ſuperparticula­<lb/>ri et vna irrationali: ſicut nec aliq̄ rationalis cõ-<lb/>ponitur ex vna rationali et altera irrationali a-<lb/>dequate / vt probãt mathemathici. </s>
            <s xml:id="N14318" xml:space="preserve">igitur nulla ſu­<lb/>ꝑparticularis continet alteram ſuꝑparticularem <lb/>ſemel aut aliquoties et vnam partem aliquotam <lb/>eius que ſit ꝓportio irrationalis: quia tunc com-<lb/>poneretur ex rationali et irrationali adequate: <lb/>nec aliqua ſuꝑparticularis continet alteram ſe-             <cb chead="Capitulum ſextum"/>             mel vel aliquoties et aliquot partes eius aliquo-<lb/>tas que ſint proportiones irrationales: quia tunc <lb/>iam ille proportiones irrationales componerent <lb/>vnam rationalem: quia alias componeretur illa <lb/>ſuperparticularis ex rationali et irrationali: et ſi <lb/>ille partes aliquote faciant vnam rationalem iaꝫ <lb/>inter terminos illius ꝓportionis ſuꝑparticularis <lb/>reperientur aliquot ꝓportiones rationales equa­<lb/>les / vt patet intuenti: quod tamen eſt falſum cum <lb/>non reperiantur inter primos numeros alicuius <lb/>ꝓportionis ſuꝑparticularis.</s>
          </p>
          <div xml:id="N1433C" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0043-01a" xlink:label="note-0043-01" xml:id="N14340" xml:space="preserve">reiicitur <lb/>obiectio.</note>
          </div>
          <p xml:id="N14348">
            <s xml:id="N14349" xml:space="preserve">Sexta concluſio </s>
            <s xml:id="N1434C" xml:space="preserve">Inter rationales. <lb/></s>
            <s xml:id="N14350" xml:space="preserve">tantum ꝓportio multiplex commenſuratur ꝓpor­<lb/>tioni multiplici. </s>
            <s xml:id="N14355" xml:space="preserve">Probatur / quia proportio multi­<lb/>plex eſt commenſurabilis ꝓportioni multiplici / vt <lb/>patet de quadrupla reſpectu duple: et inter ratio-<lb/>nales nulla non multiplex eſt cõmenſurabilis ali­<lb/>cui ꝓportioni multiplici / vt patet ex quarta cõclu­<lb/>ſione / igitur propoſitum. </s>
            <s xml:id="N14362" xml:space="preserve">Conſequentia patet ex <lb/>dialectica.</s>
          </p>
          <p xml:id="N14367">
            <s xml:id="N14368" xml:space="preserve">Septima concluſio </s>
            <s xml:id="N1436B" xml:space="preserve">Omēs propor-<lb/>tiones multiplices quarum denominationes ſunt <lb/>de numero numerorum ſunt inter ſe cõmenſurabi­<lb/>les.             <anchor type="note" xlink:href="note-0043-02" xlink:label="note-0043-02a"/>             </s>
            <s xml:id="N14379" xml:space="preserve">Hanc concluſionem ponit Nicholaus horen <lb/>ſub forma dicta: ſed pono eam ſub alia forma cla­<lb/>riori. </s>
            <s xml:id="N14380" xml:space="preserve">Omnes ꝓportiones multiplices ꝓcedentes <lb/>ſemper ſecundum dendminationem prime illarū <lb/>ſunt cõmenſurabiles: ita  ſi prima illarum ſit du­<lb/>pla. </s>
            <s xml:id="N14389" xml:space="preserve">ſecunda immediate ſequens ſit etiam dupla: <lb/>et ſic conſequenter tales ſunt cõmenſurabiles. </s>
            <s xml:id="N1438E" xml:space="preserve">Et <lb/>vt paucis abſoluam omnes ꝓportiones quarum <lb/>quelibet īmediate ſequētes ſunt eiuſdem denomi­<lb/>nationis cum prima ſunt commenſurabiles </s>
            <s xml:id="N14397" xml:space="preserve">Pa-<lb/>tet hec concluſio / quoniam omnes tales ita ſe ha-<lb/>bent  aliquid eſt pars aliquota vtriuſ / igitur. <lb/></s>
            <s xml:id="N1439F" xml:space="preserve">Et ad hoc videndum diſponatur vna ſeries nūe-<lb/>rorum incipiendo ab vnitate ſemper duplando et <lb/>vna alia ſemper triplando, et alia quadruplan-<lb/>do, et alia quintuplando, et ſic in infinitum. </s>
            <s xml:id="N143A8" xml:space="preserve">et tunc <lb/>dico /  omnes ꝓportiones primi ordinis ſunt cõ-<lb/>menſurabiles inter ſe. </s>
            <s xml:id="N143AF" xml:space="preserve">et quelibet cuilibet alteri il­<lb/>lius ordines: </s>
            <s xml:id="N143B4" xml:space="preserve">Et ſic etiam dicendum eſt de ꝓportio­<lb/>nibus alioruꝫ ordinum. </s>
            <s xml:id="N143B9" xml:space="preserve">Patet hoc in his figuris</s>
          </p>
          <div xml:id="N143BC" level="4" n="3" type="float">
            <note position="right" xlink:href="note-0043-02a" xlink:label="note-0043-02" xml:id="N143C0" xml:space="preserve">nicholaꝰ <lb/>horen.</note>
          </div>
          <xhtml:table xml:id="N143C8">
            <xhtml:tr xml:id="N143C9">
              <xhtml:td xml:id="N143CA" xml:space="preserve"/>
            </xhtml:tr>
          </xhtml:table>
          <p xml:id="N143CC">
            <s xml:id="N143CD" xml:space="preserve">Et ſic etiam conſtitues ordines multarum ſuper-<lb/>particularium et ſuprapartientium etc. </s>
            <s xml:id="N143D2" xml:space="preserve">Quod au­<lb/>tem iſte ſunt commenſurabiles probatur / quoniã <lb/>quelibet illius ordinis eſt equalis prime aut com­<lb/>ponitur ex aliquot equalibus illi: igitur. </s>
            <s xml:id="N143DB" xml:space="preserve">¶ Iſte <lb/>concluſiones dempta prima et ſexta ſunt Nicho-<lb/>lai horen cum ſuis probationibus ſaltem virtu-<lb/>tes probationum et fundamenta ſunt ex ipſo.</s>
          </p>
          <note position="right" xml:id="N143E4" xml:space="preserve">cõtra ni-<lb/>cholauꝫ <lb/>horen.</note>
          <p xml:id="N143EC">
            <s xml:id="N143ED" xml:space="preserve">¶ Sed videntur mihi ille probationes inefficaces <lb/></s>
            <s xml:id="N143F1" xml:space="preserve">Fundatur enim principaliter probatio ſecūde ter­<lb/>tie et quarte in hac ſuppoſitione cuiuſlibet ꝓpor­<lb/>tionis multiplicis vnitas eſt minimum extremum <lb/></s>
            <s xml:id="N143F9" xml:space="preserve">Modo illa ſuppoſitio falſa eſt / quoniam octo ad <lb/>quatuor eſt proportio multiplex: tamen neutrum <lb/>extremorum eius eſt vnitas: </s>
            <s xml:id="N14400" xml:space="preserve">Sed diceret Nicho-<lb/>laus horen et bene /  illa ſuppoſitio et ſi nõ ſit ve-<lb/>ra diſtribuendo pro ſingulis generum. </s>
            <s xml:id="N14407" xml:space="preserve">eſt tamen <lb/>vera diſtribuendo pro generibus ſingulorum: et ī             <pb chead="Secunde partis." file="0044" n="44"/>             tali ſenſu capitur / vt patet intuenti.</s>
          </p>
          <p xml:id="N14411">
            <s xml:id="N14412" xml:space="preserve">Sꝫ contra / q2 in tali ſenſu capiendo <lb/>eã non cõcluditur propoſitum ſed ſolum concludi­<lb/>tur /  de qualibet ſpecie proportionis multipli-<lb/>cis aliquod indiuiduum eiuſdem ſpeciei non ē cõ-<lb/>menſurabile alicui ſuperparticulari, aut ſupraꝑ­<lb/>tienti etc. / et adhuc vix id poteſt haberi contra pro­<lb/>teruum. </s>
            <s xml:id="N14421" xml:space="preserve">¶ Sed diceret nicholaus /  ſatis ei ē ha-<lb/>bere /  vna proportio dupla non eſt commenſura­<lb/>bilis alicui proportioni non multiplici rationali / <lb/>quoniam cuꝫ omnes duple ſint equales. </s>
            <s xml:id="N1442A" xml:space="preserve">quicquid <lb/>non eſt commenſurabile vni certe non eſt commē-<lb/>ſurabile alteri. </s>
            <s xml:id="N14431" xml:space="preserve">Et certo credo /  in hoc fundatur <lb/>principaliter deductio illarum concluſionū qua-<lb/>rum fundamenta ſumuntur ex euclide ſeptimo et <lb/>octauo elementorum. </s>
            <s xml:id="N1443A" xml:space="preserve">Notum eni3 eſt /  ſi aliquid <lb/>eſt īcommenſurabile vni equalium etiam cuilibet <lb/>erit incommenſurabile: quoniam omnia equalia <lb/>ex equalibus adequate componuntur.</s>
          </p>
          <p xml:id="N14443">
            <s xml:id="N14444" xml:space="preserve">Sed contra diceret proteruus / quia <lb/>dabiles ſunt due proportiones equales et tamen <lb/>aliqua proportio eſt pars vnius: et nec illa nec ali­<lb/>qua equalis ei eſt pars alterius: igitur non eſt in-<lb/>conueniens aliquas duas proportiones eſſe equa­<lb/>les: et aliquid eſſe partem vnius et nec illud nec tã­<lb/>tum eſſe partem alterius: et per conſequens pari <lb/>ratione poſſet dici /  quamuis omnes duple ſint <lb/>equales: aliquid tamen eſt pars aliquota vnius / <lb/>quod non eſt pars aliquota alterius nec tantum: <lb/>quemadmodum aliqua proportio eſt pars alicu-<lb/>ius proportionis duple: et tamen nec illa. </s>
            <s xml:id="N1445D" xml:space="preserve">nec ei eq̈­<lb/>lia eſt pars alterius duple. </s>
            <s xml:id="N14462" xml:space="preserve">Probatur aſſumptuꝫ <lb/>de his duabus duplis quarum vna eſt .8. ad .4. et <lb/>altera .2. ad .1. </s>
            <s xml:id="N14469" xml:space="preserve">Nam illa que eſt .8. ad .4. componi-<lb/>tur ex ꝓportione ſexquialtera et ſexquitertia que <lb/>mediant inter ſua extrema: illa vero que eſt duoꝝ <lb/>ad vnum ex nulla ſexquialtera aut ſexquitertia cõ­<lb/>ponitur: quoniam nullus numerus mediat inter <lb/>extrema illius. </s>
            <s xml:id="N14476" xml:space="preserve">Nec valet dicere /  quamius nõ me­<lb/>diat numerus mediat tamen vnitas cum fractio-<lb/>ne aliqua: et illud ſufficit: quoniam vnitatis cum <lb/>dimidio ad vnitatem eſt proportio ſexquialtera: <lb/></s>
            <s xml:id="N14480" xml:space="preserve">Quoniaꝫ iam tunc haberem /  alicuius ꝓportio-<lb/>nis ſexquialtere vnitas eſt alterum extremum / qḋ <lb/>ipſe negare videtur. </s>
            <s xml:id="N14487" xml:space="preserve">Et etiam habito illo: iam de-<lb/>ſtruitur totus modus procedendi et ꝓbandi illas <lb/>concluſiones et etiam quintã. </s>
            <s xml:id="N1448E" xml:space="preserve">Fundatur enim pro­<lb/>batio illius quinte concluſionis in hoc:  īter nu­<lb/>lius proportionis ſuperparticularis primos nu-<lb/>meros reperitur aliqua ꝓportio rationalis que <lb/>ſit pars eius. </s>
            <s xml:id="N14499" xml:space="preserve">Modo illud eſt falſum vtendo fra-<lb/>ctione vnitatis: inter .5. eī et .6. mediant .5. cū dimi­<lb/>dio. </s>
            <s xml:id="N144A0" xml:space="preserve">Item eſto /  inter primos numeros ꝓportio-<lb/>nis ſuperparticularis non mediat aliquis nume­<lb/>rus mediat tamen inter non primos: et diceret ꝓ-<lb/>teruus /  proportio ſuperparticularis inter non <lb/>primos numeros componitur ex aliquot rationa­<lb/>libus quibus eſt commenſurabilis: et tamen ipſa <lb/>proportio inter primos numeros conſtituta non <lb/>componitur ex talibus. </s>
            <s xml:id="N144B1" xml:space="preserve">Nec valet dicere /  non eſt <lb/>imaginabile /  aliqua duo ſint equalia: et tamen <lb/>aliquid ſit pars aliquota vnius et nullum tantuꝫ <lb/>ſit pars aliquota alterius. </s>
            <s xml:id="N144BA" xml:space="preserve">quoniam diceret ꝓter­<lb/>uus illud non eſſe imaginabile in quantitatibus <lb/>continuis: ſed bene eſſe imaginabile in ꝓportioni­<lb/>bus quoniam impoſſibile eſt dare duas quantita­<lb/>tes cõtinuas equales: et  aliquid ſit pars vnius <lb/>ſiue aliquota ſiue non. </s>
            <s xml:id="N144C7" xml:space="preserve">et  nullum tantuꝫ ſit pars             <cb chead="Capitulum ſextum"/>             alterius: et tamen illud datur in proportionibus <lb/></s>
            <s xml:id="N144CE" xml:space="preserve">Duarum enim intelligentiarum ad vnam intelli-<lb/>gentiam eſt proportio dupla que non componi-<lb/>tur ex ſexquialtera et ſexquitertia nec cum fractio­<lb/>ne nec ſine. </s>
            <s xml:id="N144D7" xml:space="preserve">et tamen proportio dupla ei equalis .4. <lb/>ad duo componitur ex ſexquialtera et ſexquiter-<lb/>tia / vt patet.             <anchor type="note" xlink:href="note-0044-01" xlink:label="note-0044-01a"/>             </s>
            <s xml:id="N144E3" xml:space="preserve">¶ Hic tamen tu aduerte /  hee conclu­<lb/>ſiones cum demonſtrationibus ſuis dependēt ex <lb/>octaua propoſitione octaui elementorum euclidis <lb/>que dependet ex .35. ſeptimi, et .14. et .18. et .21. ſepti­<lb/>mi et tertia octaui. </s>
            <s xml:id="N144EE" xml:space="preserve">Et ideo difficilis eſt demonſtra­<lb/>tio harum concluſionum: quia ex multis depēdēt <lb/>             <anchor type="note" xlink:href="note-0044-02" xlink:label="note-0044-02a"/>             </s>
            <s xml:id="N144FA" xml:space="preserve">Dicit tamen euclides in propoſitione allegata  <lb/>ſi inter aliquos numeros non primos alicuius ꝓ­<lb/>portionis reperiuntur aliqui numeri cõtinuo pro­<lb/>portionabiles: totidē inter primos numeros eiuſ­<lb/>dem proportionis reperiuntur. </s>
            <s xml:id="N14505" xml:space="preserve">Et ideo tu ipſe ef-<lb/>ficatiores demonſtrationes inquire.</s>
          </p>
          <div xml:id="N1450A" level="4" n="4" type="float">
            <note position="right" xlink:href="note-0044-01a" xlink:label="note-0044-01" xml:id="N1450E" xml:space="preserve">Aduerte</note>
            <note position="right" xlink:href="note-0044-02a" xlink:label="note-0044-02" xml:id="N14514" xml:space="preserve">eu. 8. ele.</note>
          </div>
          <p xml:id="N1451A">
            <s xml:id="N1451B" xml:space="preserve">Octaua concluſio. </s>
            <s xml:id="N1451E" xml:space="preserve">Si fuerint tres <lb/>termini continuo proportionabiles geometri-<lb/>ce erit proportio extremi ad extremum dupla ad <lb/>vtrã intermediam. </s>
            <s xml:id="N14527" xml:space="preserve">et ſi fuerint .4. tripla, ſi .5. q̈-<lb/>drupla: et ſic in infinitum. </s>
            <s xml:id="N1452C" xml:space="preserve">ſemper vno minus. </s>
            <s xml:id="N1452F" xml:space="preserve">hoc <lb/>eſt ſi fuerint decem termini non erit ꝓportio decu­<lb/>pla extremi ad extremum: ſed noncupla. </s>
            <s xml:id="N14536" xml:space="preserve">Proba-<lb/>tur: quoniam ſi ſunt tres termini continuo ꝓpor-<lb/>tionabiles: reperientur ibi due ꝓportiones equa­<lb/>les ex quibus adequate componitur ꝓportio ex-<lb/>tremi ad extremum: et ſi quatuor tres. </s>
            <s xml:id="N14541" xml:space="preserve">et ſi quin <lb/>quatuor / et ſic conſequenter. </s>
            <s xml:id="N14546" xml:space="preserve">Modo omne compo-<lb/>ſitum ex duobus equalibus adequate eſt duplum <lb/>ad quodlibet illorum, et ex tribus tripluꝫ, et ſic cõ­<lb/>ſequenter / vt patet ex quinta ſuppoſitione quarti <lb/>capitis huius partis: igitur cõcluſio vera:              <anchor type="note" xlink:href="note-0044-03" xlink:label="note-0044-03a"/>             </s>
            <s xml:id="N14556" xml:space="preserve">¶ Et hec <lb/>eſt decima diffinitio quinti elementorum euclidis <lb/>et quinta diffinitio ſecundi elementorum iordani <lb/></s>
            <s xml:id="N1455E" xml:space="preserve">¶ Et aduerte /  quotienſcun allego euclidē: ſem­<lb/>per vtor noua traductione. Bartholomei3 am-<lb/>berti.</s>
          </p>
          <div xml:id="N14565" level="4" n="5" type="float">
            <note position="right" xlink:href="note-0044-03a" xlink:label="note-0044-03" xml:id="N14569">
              <s xml:id="N1456D" xml:space="preserve">eu. 5. ele. <lb/></s>
              <s xml:id="N14571" xml:space="preserve">ior. 2. ele. <lb/></s>
              <s xml:id="N14575" xml:space="preserve">Ne hoc <lb/>p̄tereas.</s>
            </note>
          </div>
          <p xml:id="N1457A">
            <s xml:id="N1457B" xml:space="preserve">Nona concluſio </s>
            <s xml:id="N1457E" xml:space="preserve">Nulla proportio ra­<lb/>tionalis habet ſubduplam rationalem. </s>
            <s xml:id="N14583" xml:space="preserve">niſi habe­<lb/>at numerū mediū ꝓportionabilem inter ſua extre­<lb/>ma: et ſi non habet talem numerum non habet ſub­<lb/>quadruplam proportionem rationalem, nec ſub­<lb/>octuplam: nec ſubſexdecuplam: et ſic in infinitum <lb/>procedendo per numeros pariter. </s>
            <s xml:id="N14590" xml:space="preserve">Proba­<lb/>tur prima pars huius concluſionis: quia ſi nõ de-<lb/>tur oppoſitum videlicet /  aliqua proportio ha-<lb/>beat ſubduplam rationaleꝫ que non habet nume­<lb/>rum medium ꝓportionabilem inter ſua extrema: <lb/>et ſit illa a. / et arguo ſic / a. proportio habet ꝓpor-<lb/>tionem ſubduplam rationalem que ſit f. gratia ex­<lb/>empli: igitur a. proportio componitur ex duplici <lb/>f: adequate et per conſequēs vna illaruꝫ f. erit ma­<lb/>ioris extremi ipſius a. ad aliquem numerum inter­<lb/>medium: et altera eiuſdem numeri intermedii ad <lb/>aliud extremum minus eiuſdem a. ꝓportionis: et <lb/>per conſequens ille numerus intermedius erit me­<lb/>dio loco proportionabilis / vt patet ex diffinitiõe <lb/>numeri medio loco proportionabilis / quod eſt op­<lb/>poſitum dati. </s>
            <s xml:id="N145B1" xml:space="preserve">Iam probatur ſecunda pars: quo-<lb/>niam ſi inter terminos date ꝓportionis rationa­<lb/>lis non fuerit numerus qui ſit medium proportio­<lb/>nale: iam ibi non reperiuntur quin numeri cõti-<lb/>nuo proportionabiles geometrice: et ſi non ſunt <lb/>ibi quin numeri cõtinuo proportionabiles geo­<lb/>metrice: iam extremi ad extremum non erit ꝓpor-<lb/>tio quadrupla ad aliquam proportionem ratio-             <pb chead="Secūde partis" file="0045" n="45"/>             nalem intermediam: et per conſequens iam nõ ha­<lb/>bet ſubquadruplam rationalem. </s>
            <s xml:id="N145C9" xml:space="preserve">Patet hec con-<lb/>ſequentia / quia ex oppoſito ſequitur oppoſituꝫ / vt <lb/>patet ex decima diffinitione quinti elementorum <lb/>euclidis. </s>
            <s xml:id="N145D2" xml:space="preserve">Iam probo priorem conſequentiam vi-<lb/>delicet /  ſi inter terminos date proportionis non <lb/>fuerit numerus qui ſit medium proportionabile: <lb/>non reperiuntur ibi .5. numeri cõtinuo proportio­<lb/>nabiles. </s>
            <s xml:id="N145DD" xml:space="preserve">Que probatur ſic: q2 ex oppoſito conſe-<lb/>quentis ſequitur oppoſitum ãtecedentis: q2 ſi ſūt <lb/>ibi quin numeri continuo ꝓportionabiles iam <lb/>ibi tertius numerus eſt medio loco ꝓportionabi-<lb/>lis: quia primi ad ipſum eſt ea proportio que ē ip­<lb/>ſius ad quintum / vt conſtat: quia ex equalibus cõ-<lb/>ponuntur ille ꝓportiones adequate. </s>
            <s xml:id="N145EC" xml:space="preserve">Et ſic proba­<lb/>bis alias partes.             <anchor type="note" xlink:href="note-0045-01" xlink:label="note-0045-01a"/>             </s>
            <s xml:id="N145F6" xml:space="preserve">¶ Ex hac concluſione ſequitur /  <lb/>ſi inter terminos alicuius proportionis fuerit nu­<lb/>merus qui ſit medium proportionabile ipſa ha-<lb/>bet ſubduplam rationalem et ſi ipſius numeri me­<lb/>dii proportio ad aliud extremuꝫ minus date pro-<lb/>portionis haberit numerum qui ſit medium pro-<lb/>portionabile: tunc tota proportio habet ſubqua­<lb/>druplam rationalem: et ſi iteruꝫ illius numeri me­<lb/>dii proportio ad minus extremum date ꝓportio-<lb/>nis habuerit numerum qui ſit medium ꝓportio-<lb/>nabile: iam data proportio habebit ſuboctuplaꝫ <lb/>rationalem / et ſic in infinitum. </s>
            <s xml:id="N1460F" xml:space="preserve">Patet hoc correla­<lb/>rium ex concluſione et eius ꝓbatione: auxilianti-<lb/>bus correlariis ſexte concluſionis ſecūdi capitis</s>
          </p>
          <div xml:id="N14616" level="4" n="6" type="float">
            <note position="left" xlink:href="note-0045-01a" xlink:label="note-0045-01" xml:id="N1461A" xml:space="preserve">correĺm.</note>
          </div>
          <p xml:id="N14620">
            <s xml:id="N14621" xml:space="preserve">Decima concluſio notanda. </s>
            <s xml:id="N14624" xml:space="preserve">Propo­<lb/>ſita quauis proportione rationali an habeat ſub­<lb/>duplam rationalem inueſtigare. </s>
            <s xml:id="N1462B" xml:space="preserve">vt propoſita du­<lb/>pla aut tripla volo īueſtigare et ſcire ex predictis <lb/>an habeat ſubduplã rationalem. </s>
            <s xml:id="N14632" xml:space="preserve">Sit propoſita <lb/>proportio rationalis f. inter a. numerū maiorem <lb/>et b. numerum minoreꝫ. </s>
            <s xml:id="N14639" xml:space="preserve">et volo inueſtigare vtrum <lb/>f. ꝓportio habeat ſubduplã rationalem: tunc du-<lb/>cam maiorem numerum in minorem / hoc eſt multi­<lb/>plicabo a. per b. et ſi numerus inde ꝓueniens fue-<lb/>rit quadratus: dico /  habet ſubduplam rationa­<lb/>lem. </s>
            <s xml:id="N14646" xml:space="preserve">ſin minus non habet ſubduplam rationalem <lb/></s>
            <s xml:id="N1464A" xml:space="preserve">Probatur prima pars videlicet /  ſi numerus qui <lb/>fit ex ductu ipſius a. in b. ſit quadratus: tunc ha-<lb/>bet ſubduplam rationalem. </s>
            <s xml:id="N14651" xml:space="preserve">quia ſit talis numerꝰ <lb/>eſt quadratus: tunc inter a. et b. eſt medius nume-<lb/>rus proportionabilis / vt patet ex quarto correla­<lb/>rio ſexte concluſionis ſecundi capitis huius par-<lb/>tis: et ſi ſit numerus qui ſit medium ꝓportionabi­<lb/>le inter a. et b. / ſequitur /  illa proportio habet ſub­<lb/>duplam rationalem. </s>
            <s xml:id="N14660" xml:space="preserve">Patet conſequentia ex cor-<lb/>relario precedentis. </s>
            <s xml:id="N14665" xml:space="preserve">Iam probatur ſecunda pars / <lb/>quia ſi numerus qui fit ex ductu a. in b. non ſit qua­<lb/>dratus: iam inter a. et b. non eſt numerus qui ē me­<lb/>dio loco proportionabilis / vt patet ex ſecundo cor­<lb/>relario ſexte concluſionis ſecundi capitis huius: <lb/>et ſi non eſt numerus qui eſt medio loco proportio­<lb/>nabilis inter a. et b. iam ille non habet ſubduplaꝫ <lb/>rationalem / vt patet ex concluſione nona huius.</s>
          </p>
          <p xml:id="N14676">
            <s xml:id="N14677" xml:space="preserve">Patet igitur concluſio.             <anchor type="note" xlink:href="note-0045-02" xlink:label="note-0045-02a"/>             </s>
            <s xml:id="N1467F" xml:space="preserve">¶ Ex hac ſequitur /  du-<lb/>pla non habet ſubduplam rationalem, nec tripla <lb/>nec octupla, nec aliqua ſuperparticularis. </s>
            <s xml:id="N14686" xml:space="preserve">Pro-<lb/>batur / quoniam ducendo quatuor per duo reſul-<lb/>tat numerus octonarius qui non eſt quadratus / vt <lb/>conſtat: et ducendo .6. per duo: reſultat numerus <lb/>duodenarius qui etiam non eſt quadratus: et du­<lb/>cendo .16. per duo conſurgit numerus .32. qui non <lb/>eſt quadratus vt apparet intelligenti. </s>
            <s xml:id="N14695" xml:space="preserve">Item ducē­<lb/>do .3: per duo producuntur .6. qui non ſunt nume-<lb/>rus quadratus: et ſic probabis de qualibet alia ꝓ­             <cb chead="Capitulum ſextum"/>             portione ſuperparticulari.             <anchor type="note" xlink:href="note-0045-03" xlink:label="note-0045-03a"/>             </s>
            <s xml:id="N146A4" xml:space="preserve">¶ Sequitur ſecundo / <lb/> propoſita qua volueris ꝓportione rationali. </s>
            <s xml:id="N146A9" xml:space="preserve">ī­<lb/>ueſtigare poterimus vtrum habeat ſubquadru-<lb/>plam rationalē ſuboctuplaꝫ, ſubſexdecuplam, et <lb/>ſic in infinitum procedendo per numeros pariter <lb/>pares. </s>
            <s xml:id="N146B4" xml:space="preserve">vt propoſita proportione ſexdecupla: vo-<lb/>lo inueſtigare: vtrum habeat ſubquadruplam ra­<lb/>tionalem, ſuboctuplam, ſubſexdecuplam, et ſic in <lb/>infinitum. </s>
            <s xml:id="N146BD" xml:space="preserve">Ad quod inueſtigandum ſiue ſciendum <lb/>ſit f. ꝓportio inter a. maiorem numerum et b. mi-<lb/>norem: tunc aut inter a. et b. eſt numerus qui ſit me­<lb/>dium ꝓportionabile aut non. </s>
            <s xml:id="N146C6" xml:space="preserve">ſi nõ: iam ſequitur / <lb/> non habet ſubquadruplam rationalē nec ſub-<lb/>octuplam etc. / vt patet ex nona concluuſione: ſi ſic <lb/>ſignetur ille et ſit h. / et tunc videndum eſt an nume­<lb/>rus / qui fit ex ductu h. in b. ſit quadratus: et ſi ſic iã <lb/>talis ꝓportio f. que eſt inter a. et b. habet ſubqua-<lb/>druplam: ſi vero talis numerus non ſit quadratꝰ <lb/>dico /  talis proportio non habet ſubquadruplã <lb/>rationalem. </s>
            <s xml:id="N146D9" xml:space="preserve">Primum iſtorum probatur. </s>
            <s xml:id="N146DC" xml:space="preserve">quia ſi <lb/>talis numerus qui fit ex ductu h. in b. ſit quadra-<lb/>tus: iam inter h. et b. eſt numerus medio loco pro-<lb/>portionabilis qui ſit k. / vt patet ex quarto correla­<lb/>rio preallegato ſexte concluſionis ſecundi capitis <lb/>huius: et ex conſequenti iam ꝓportio h. ad b. que <lb/>eſt ſubdupla ad ꝓportionem f. habet ſubduplam <lb/>proportionem rationalem / vt patet ex correlario <lb/>none concluſionis: et ſi habet ſubduplam iam pro­<lb/>portio f. habet ſubquadruplam: quia omne ſub-<lb/>duplum ſubdupli eſt ſubquadruplum dupli / vt pa­<lb/>tet ex ſecundo correlario quarte concluſionis q̈r-<lb/>ti capitis huius / quod erat oſtendendum. </s>
            <s xml:id="N146F7" xml:space="preserve">Iam pro­<lb/>batur ſecundum: quia ſi numerus qui fit ex ductu <lb/>h. in b. non ſit quadratus iam proportio que eſt ī-<lb/>ter h. et b. non habet numerū medio loco ꝓportio­<lb/>nabilem / vt patet ex ſecundo correlario ſexte con-<lb/>cluſionis preallegate: et ſi non habet mediū nume­<lb/>rū ꝓportionabilem iã non habet ſubduplã ratio­<lb/>nalem: et ſic eius medietas non eſt proportio rõa-<lb/>lis et eius medietas eſt ſubquadruplum ꝓportio­<lb/>nis f. que eſt a. ad b. / vt cõſtat: igitur proportio ſub­<lb/>quadrupla ad f. non eſt rationalis / quod fuit oſtē-<lb/>dendum. </s>
            <s xml:id="N14710" xml:space="preserve">Alie particule correlarii ſimilem demon­<lb/>ſtrationem ſortiuntur. </s>
            <s xml:id="N14715" xml:space="preserve">Si eni3 non inueniatur ra­<lb/>tionalis ſubquadrupla: nec ſuboctuplã rõnalem <lb/>inuenies. </s>
            <s xml:id="N1471C" xml:space="preserve">Si vero ſubquadrupla reperta fuerit ra­<lb/>tionalis: conſidera an ex ductu vnius extremita-<lb/>lis ſubquadrupli in alterum reſultat numerꝰ qua­<lb/>dratus: et ſi ſic concludas datam ꝓportionem ha­<lb/>bere ſuboctuplam rationalē: quia ſua quarta ha­<lb/>bet ſubduplam rationalem. </s>
            <s xml:id="N14729" xml:space="preserve">ſin minus concludas <lb/>eam non habere talem ſuboctuplam rationalem. <lb/></s>
            <s xml:id="N1472F" xml:space="preserve">Et ſic in aliis operaberis.             <anchor type="note" xlink:href="note-0045-04" xlink:label="note-0045-04a"/>             </s>
            <s xml:id="N14737" xml:space="preserve">¶ Sequitur tertio /  ſi­<lb/>gnata quauis ꝓportione rationali: inueſtigare et <lb/>ſcire poterimus an habeat ſexquialteram ratio-<lb/>nalem, ſexquiquartaꝫ, ſexquioctauam, ſexquiſex­<lb/>decimã, ſexquitrigeſimã ſecundam, ſexquitrigeſi­<lb/>mã quartã, et ſic in infinituꝫ: ꝓcedendo per ſpecies <lb/>ꝓportionis ſuperparticularis denominatas a ꝑ­<lb/>tibus aliquotis que partes aliquote a nūeris pa-<lb/>riter paribus denominantur. </s>
            <s xml:id="N1474A" xml:space="preserve">vt ꝓpoſita ꝓportio­<lb/>ne quadrupla: volo inueſtigare et ſcire an ip̄a ha­<lb/>beat ſexquialteram rationalem: tūc videbo an ha­<lb/>beat medietatem rationalem per doctrinam deci­<lb/>me concluſionis huius: et tunc ſi habeat medieta-<lb/>tem rationalem: manifeſtum eſt  habet ſexquial&lt;lb/&gt;teram rationalem: quia non oportet ad dandam <lb/>ſexquialteram ipſius quadruple aliud quam ad-<lb/>dere ipſi quadruple ſuã medietatem puta duplã:             <pb chead="Secunde partis." file="0046" n="46"/>             quia aggregatum ex aliquo et medietate eiꝰ ē ſex­<lb/>quialterum ad illud / vt conſtat ex diffinitione ſex-<lb/>quialteri. </s>
            <s xml:id="N14764" xml:space="preserve">Et iſto modo inuenitur octuplam eē ſex­<lb/>quialteram ad quadruplam. </s>
            <s xml:id="N14769" xml:space="preserve">Si vero inueſtigare <lb/>et ſcire velis an q̈drupla habeat ſexquiquartam <lb/>ſcias primo ꝑ doctrinam ſecundi correlarii: an ip­<lb/>ſa proportio quadrupla habeat ſubquadruplaꝫ <lb/>rationalem: et ſi ſic concludas /  habet ſexquiq̈r-<lb/>tam rationalem: quoniam reperta quarta ipſius <lb/>quadruple ad dandam ſexquiquartam ad ipſam <lb/>quadruplam nihil aliud oportet quaꝫ addere ipſi <lb/>quadruple ſuam quartam: et tunc aggregatuꝫ ex <lb/>ipſa quadrupla et ſua quarta rationali ſe habet <lb/>ad ipſaꝫ quadrumplam in proportiõe ſexquiquar­<lb/>ta. </s>
            <s xml:id="N14782" xml:space="preserve">Continet enim illud aggregatum ipſam qua-<lb/>druplam et vnam quartam eius adequate. </s>
            <s xml:id="N14787" xml:space="preserve">Et iſto <lb/>modo inuenitur trigecuplam ſecūdam eſſe ſexqui­<lb/>quartam ad ſexdecuplam. </s>
            <s xml:id="N1478E" xml:space="preserve">Et iſto modo in quali-<lb/>bet proportione rationali īueſtigare poteris: an <lb/>habeat ſexquioctauam, ſexquiſexdecimam, et ſic <lb/>conſequēter rationales. </s>
            <s xml:id="N14797" xml:space="preserve">Et ſic patet correlarium <lb/>             <anchor type="note" xlink:href="note-0046-01" xlink:label="note-0046-01a"/>             </s>
            <s xml:id="N147A1" xml:space="preserve">¶ Ex quo ſequitur quarto /  ſi aliqua ꝓportio ra­<lb/>tionalis non habet ſubduplam rationalem: ipſa <lb/>non habet ſexquialteram rationalem, nec ſexqui­<lb/>q̈rtã: nec ſexquioctauam: nec ſexquiſexdecimam: et <lb/>ſic conſequenter. </s>
            <s xml:id="N147AC" xml:space="preserve">Probatur / quia ſi talis ꝓportio <lb/>non habeat ſubduplam rationaleꝫ: ſequitur /  nõ <lb/>habet numerum qui ſit medium ꝓportionale īter <lb/>ſua extrema: et ſi nõ hꝫ numerū mediū etc. / ſequit̄̄  <lb/> non habet ſubquadruplam, nec ſuboctuplam, <lb/>nec ſubſexdecuplam rationalem / et ſic in infinituꝫ <lb/>aſcendendo per numeros pariter pares / vt patet <lb/>ex nona concluſione huius: et ſi non habet ſubdu-<lb/>plam, nec ſubquadruplam: nec ſuboctuplam ra-<lb/>tionales: et ſic conſequenter: iam manifeſtum eſt / <lb/> non habet ſexquialteram rationalem: nec ſex-<lb/>quiquartam: nec ſexquioctauam: et ſic ſine fine / vt <lb/>patet ex probatione precedentis correlarii. </s>
            <s xml:id="N147C7" xml:space="preserve">Et ſic <lb/>ſi data proportio rationalis nõ habet ſubduplaꝫ <lb/>rationalem: ipſa non habet ſexquialteram ratio­<lb/>nalem: nec ſexquiquartaꝫ: nec ſexquioctauã etc. / qḋ <lb/>fuit probandum. </s>
            <s xml:id="N147D2" xml:space="preserve">Et ſic patet correlarium.             <anchor type="note" xlink:href="note-0046-02" xlink:label="note-0046-02a"/>             </s>
            <s xml:id="N147DA" xml:space="preserve">¶ Se-<lb/>quitur quinto /  ſi aliqua proportio ꝓpoſita non <lb/>habuerit ſubduplam rationalem: ipſa non habe­<lb/>bit duplam ſexquialteram rationalem nec duplã <lb/>ſexquiquartam nec ſuprapartienteꝫ quartas, nec <lb/>aliquam ſuprapartientem denominatam ab vni­<lb/>tate et partibus aliquotis denominatis a nume-<lb/>ro pariter pari: nec aliquam multiplicē ſuperpar­<lb/>ticularem, aut multiplicē ſuprapartientem deno­<lb/>minatã a numero et a parte vel partibus aliquo-<lb/>tis que denominantur a numeris pariter paribꝰ <lb/></s>
            <s xml:id="N147F2" xml:space="preserve">Patet hoc correlarium facile: quia ſi data ꝓpor­<lb/>tio non habuerit ſubduplam rationalem: iam nõ <lb/>habet illas partes aliquotas rationales deno-<lb/>minatas a numeris pariter paribus: vt patet ex <lb/>quarto correlario: et ſi non habet illas partes ali­<lb/>quotas que ſunt ꝓportiones rationales: iam non <lb/>habet illas proportiones rationales denomina-<lb/>tas ab illis partibus / vt conſtat.             <anchor type="note" xlink:href="note-0046-03" xlink:label="note-0046-03a"/>             </s>
            <s xml:id="N14808" xml:space="preserve">¶ Ex quo ſequi-<lb/>tur ſexto /  nec tripla, nec dupla, habent ꝓportio­<lb/>nē ſexquialterã: ſexquiquartam: ſexquioctauam: <lb/>duplã ſupratripartientē quartas rationalem: et <lb/>ſic de multis aliis. </s>
            <s xml:id="N14813" xml:space="preserve">Patet / quia neutra illarum ha­<lb/>bet ſubduplam rationalem: vt patet ex primo cor­<lb/>relario: igitur neutra illarum habet ſexquialterã <lb/>ſexquiquartam etc. / vt patet ex īmediate preceden-<lb/>ti. </s>
            <s xml:id="N1481E" xml:space="preserve">Inferas tu ſimilia correlaria particularia ex <lb/>dictis.</s>
          </p>
          <div xml:id="N14823" level="4" n="7" type="float">
            <note position="left" xlink:href="note-0045-02a" xlink:label="note-0045-02" xml:id="N14827" xml:space="preserve">correĺm.</note>
            <note position="right" xlink:href="note-0045-03a" xlink:label="note-0045-03" xml:id="N1482D" xml:space="preserve">2. correĺ.</note>
            <note position="right" xlink:href="note-0045-04a" xlink:label="note-0045-04" xml:id="N14833" xml:space="preserve">3. correl.</note>
            <note position="left" xlink:href="note-0046-01a" xlink:label="note-0046-01" xml:id="N14839" xml:space="preserve">4. correl.</note>
            <note position="left" xlink:href="note-0046-02a" xlink:label="note-0046-02" xml:id="N1483F" xml:space="preserve">5. correl.</note>
            <note position="left" xlink:href="note-0046-03a" xlink:label="note-0046-03" xml:id="N14845" xml:space="preserve">6. correl.</note>
          </div>
          <cb chead="Capitulum ſextum"/>
          <p xml:id="N1484D">
            <s xml:id="N1484E" xml:space="preserve">Undecima concluſio. </s>
            <s xml:id="N14851" xml:space="preserve">Nulla propor-<lb/>tio rõnalis ſe habet ī aliqua proportiõe multipli­<lb/>ci ad aliquam rationalem niſi inter primos nūe-<lb/>ros eius reperiantur tot numeri cõtinuo ꝓportio­<lb/>nabiles computatis etiam extremis vno plꝰ ade-<lb/>quate: quotus eſt numerus a quo denomīatur da­<lb/>ta ꝓportio multiplex. </s>
            <s xml:id="N14860" xml:space="preserve">Exemplum. </s>
            <s xml:id="N14863" xml:space="preserve">vt ſi velis inue-<lb/>ſtigare et ſcire vtrum ꝓportio quadrupla ſe habe­<lb/>at in ꝓportione dupla ad aliquam ꝓportioneꝫ <lb/>rationalem: conſidera primum a quo numero de­<lb/>nominatur proportio dupla: et īuenies /  a bina­<lb/>rio iuxta doctrinam primi correlarii ſecunde ſup­<lb/>poſitionis quarti capitis huius: tunc capias pri­<lb/>mos numeros eius qui ſunt .4. et .1: et vide ſi inue-<lb/>nias ibi tres numeros continuo ꝓportionabiles <lb/>eadem ꝓportione cõputatis extremis: et ſi ſic dico / <lb/> ꝓportio quadrupla ſe habet in ꝓportione du-<lb/>pla ad aliquaꝫ rationalem. </s>
            <s xml:id="N1487C" xml:space="preserve">Si enim ibi ſunt tres <lb/>numeri continuo ꝓportionabiles computatis ex­<lb/>tremis: iam illa ꝓportio quadrupla que eſt extre-<lb/>mi ad extremum eſt dupla ad vtrã interdiarum: <lb/>vt patet ex octaua concluſione: et ſi velis ſcire an <lb/>quadrupla ſit tripla ad aliquam ꝓportionem ra­<lb/>tionalem: quia tripla denominatur a numero ter­<lb/>nario. </s>
            <s xml:id="N1488D" xml:space="preserve">videas vtrum inter primos numeros ꝓpor­<lb/>tionis quadruple reperiantur tres nūeri vno plꝰ <lb/>puta quatuor continuo ꝓportionabiles aliqua ꝓ­<lb/>portione: et ſi ſic: tunc quadrupla ſe habet in pro-<lb/>portione tripla ad aliquam ꝓportionē rationalē <lb/>puta ad quãlibet illarum conſtitutarum inter ali­<lb/>quos ex illis numeris continuo ꝓportionabilibꝰ <lb/>et īmediatis: et quia tu non inuenies inter primos <lb/>numeros ꝓportionis quadruple quatuor nume-<lb/>ros continuo ꝓportionabiles computatis extre-<lb/>mis: concludas /  quadrupla nõ habet ſubtriplã <lb/>rationalem. </s>
            <s xml:id="N148A6" xml:space="preserve">Probatur hec concluſio. </s>
            <s xml:id="N148A9" xml:space="preserve">q2 ſi data ꝓ­<lb/>portio rationalis que ſit a. ſe habeat in aliqua ꝓ­<lb/>portione multiplici ad aliquam proportioneꝫ ra­<lb/>tionalem que ſit b. / ſequitur /  a. aliquoties conti-<lb/>net b. adequate / et ſic b. erit pars aliquota ipſius <lb/>a denominata a numero a quo denominatur pro­<lb/>portio multiplex in qua a. ſe habet ad b. / vt puta ſi <lb/>a. ſe habet ad b: in proportione quadrupla erit b. <lb/>vna quarta ipſius a. et ſic erit b. pars aliquota de­<lb/>nominata a numero quaternario a quo denomi-<lb/>natur ꝓportio illa multiplex puta quadrupla in <lb/>qua a. ſe habet ad b: et ſi ſic iam neceſſe eſt  b. re-<lb/>periatur inter aliquos numeros ipſius a. toties <lb/>quoties eſt numerus a quo denominatur talis ꝓ-<lb/>portio multiplex in qua a. ſe habet ad b. et ſi ſic iã <lb/>inter terminos ipſius a. computatis extremis re-<lb/>perientur tot nūeri quotus eſt ille numerus a quo <lb/>denominatur data ꝓportio multiplex in qua a. ſe <lb/>habet ad b. vno plus: quoniam ſemper termini ſi­<lb/>ue numeri continuo ꝓportionabiles ſunt vno plu­<lb/>res proportionibus inter ipſos ad inuentis / vt ptꝫ <lb/>ex octaua concluſione huius: et ex conſequēti ſi nõ <lb/>fuerint reperti tot numeri continuo ꝓportionabi-<lb/>les inter aliquos numeros ipſius proportionis a. <lb/>quotus eſt numerus a quo denominatur propor-<lb/>tio multiplex in qua ponitur a. ſe habere ad b. / di-<lb/>co /  tūc b. non eſt ꝓportio rationalis nec a. ſe ha­<lb/>bet in tali ꝓportione multiplici ad aliquam pro-<lb/>portionem rationalem. </s>
            <s xml:id="N148E4" xml:space="preserve">Probatur hec conſequē-<lb/>tia / quia ſi ſe haberet ad b. proportioneꝫ rationa­<lb/>lem in tali ꝓportione multiplici: iam aliquoties <lb/>componeretur ex ipſa b. ꝓportione rationali et ꝑ <lb/>conſequens aliquoties reperiretur b. inter nume-<lb/>ros eius: puta toties quotus ē numerus a quo de-             <pb chead="Secūde partis" file="0047" n="47"/>            nominatnr data ꝓportio multiplex: et ſi ſic iã in-<lb/>ter terminos eius computatis extremis reperiren­<lb/>tur tot numeri continuo ꝓportionabiles quotus <lb/>eſt numerus a quo denominatur dicta proportio <lb/>multiplex: puta quoties a. cõtinet b. vno plus. </s>
            <s xml:id="N148FE" xml:space="preserve">igi­<lb/>tur ex oppoſito: ſi non reperiantur tot numeri cõ-<lb/>putatis extremis iam a. non ſe habet in tali ꝓpor­<lb/>tione multiplici ad b. ꝓportionem rationalem.</s>
          </p>
          <note position="left" xml:id="N14907" xml:space="preserve">nota.</note>
          <p xml:id="N1490B">
            <s xml:id="N1490C" xml:space="preserve">¶ Utrum autē inter aliquos numeros date ꝓpor­<lb/>tionis a. reperiantur tot numeri continuo ꝓpor-<lb/>tionabiles computatis extremis vno plus quotꝰ <lb/>eſt numerus a quo denominatur proportio multi­<lb/>plex in qua ponitur a. ſe habere ad b. videndū eſt <lb/>vtrum inter primos numeros eius inueniant̄̄ tot <lb/>numeri continuo proportionabiles: et ſi ſic conclu­<lb/>das /  inter numeros ipſius a. reperiuntur tot nu­<lb/>meri continuo ꝓportionabiles: et ſi non inuenian­<lb/>tur tot inter primos numeros date ꝓportionis: <lb/>dicas /  inter nullos numeros eius reperiunt̄̄ tot <lb/>numeri continuo ꝓportinoabiles computatis ex­<lb/>tremis. </s>
            <s xml:id="N14927" xml:space="preserve">Patet hec conſequentia / et deductio tota <lb/>ex octaua ꝓpoſitione octaui elementorum eucli-<lb/>dis in qua habetur /  ſi inter duos numeros ceci-<lb/>derint aliqui numeri continuo ꝓportionabiles: <lb/>inter quoſcun duos in eadem ꝓportione ſe ha-<lb/>bentes cadent tot numeri continuo ꝓportionabi­<lb/>les eadem ꝓportione qua ꝓportionautur alii. </s>
            <s xml:id="N14936" xml:space="preserve">ex <lb/>qua immediate infertur /  ſi inter duos numeros <lb/>ſe habentes in ꝓportio a. ceciderint aliqui nume-<lb/>ri continuo ꝓportionabiles ꝓportiõe que eſt vna <lb/>tertia: aut vna quarta: aut vna quinta: ipſius a. in­<lb/>ter primos numeros ipſius a. tot numeri cadēt ꝓ­<lb/>portionabiles eadeꝫ ꝓportione que ſit tertia aut <lb/>quarta: aut quinta ipſius a. / igitur ex oppoſito cõ­<lb/>ſequentis ſi inter primos numeros a. proportio-<lb/>nis non reperiantur aliqui numeri continuo pro­<lb/>portionabiles ꝓportione que eſt vna tertia: vna <lb/>quarta: quinta: ipſius a. et c. nec inter aliquos nūe­<lb/>ros ipſius a. reperientur: quod fuit oſtendendum: <lb/></s>
            <s xml:id="N14952" xml:space="preserve">Et ſic patet concluſio.             <anchor type="note" xlink:href="note-0047-01" xlink:label="note-0047-01a"/>             </s>
            <s xml:id="N1495A" xml:space="preserve">¶ Ex quo ſequitur primo. /  <lb/>ꝓportio dupla ad nullam ꝓportionem rationa-<lb/>lem ſe habet in ꝓportione dupla: aut tripla. aut <lb/>quadrupla: aut in aliqua alia multiplici: nec quin­<lb/>tupla, nec ſextupla etc. </s>
            <s xml:id="N14965" xml:space="preserve">Probatur / quia inter pri-<lb/>mos numeros ꝓportionis duple nullus numerus <lb/>reperitur (computamus enim vnitatem pro nume­<lb/>ro). </s>
            <s xml:id="N1496E" xml:space="preserve">Item inter primos numeros proportionis <lb/>quintuple qui ſunt .5. et .1. non reperiuntur aliqui <lb/>numeri continuo ꝓportionabiles adequate com­<lb/>putatis extremis / vt conſtat. </s>
            <s xml:id="N14977" xml:space="preserve">Et ſic patet etiam de <lb/>ſextupla. </s>
            <s xml:id="N1497C" xml:space="preserve">Patet igitur correlarium.             <anchor type="note" xlink:href="note-0047-02" xlink:label="note-0047-02a"/>             </s>
            <s xml:id="N14984" xml:space="preserve">¶ Sequitur <lb/>ſecundo /  nulla ꝓportio ſuperparticularis ſe ha­<lb/>bet in aliqua ꝓportione multiplici ad aliquam ꝓ­<lb/>portionem rationalem. </s>
            <s xml:id="N1498D" xml:space="preserve">Patet / quia inter cuiuſli­<lb/>bet ſuperparticularis primos terminos nullꝰ re-<lb/>peritur numerus: igitur.             <anchor type="note" xlink:href="note-0047-03" xlink:label="note-0047-03a"/>             </s>
            <s xml:id="N14999" xml:space="preserve">¶ Sequitur tertio /  pro­<lb/>poſita quauis proportione rationali inueſtigare <lb/>poſſumus an habeat aliquam ꝓportionem ratio­<lb/>nalem que ſe habeat ad ipſam in ꝓportione ſexq̇-<lb/>altera: ſexquitertia: ſexquiquarta etc. / vt ꝓpoſita <lb/>ꝓportione dupla: videre an ſit aliqua ꝓportio ra­<lb/>tionalis que ſe habeat ad ipſam duplam in pro-<lb/>portione ſexquialtera, ſexquitertia, aut in aliqua <lb/>alia ſuperparticulari. </s>
            <s xml:id="N149AC" xml:space="preserve">Ad quod inueſtiganduꝫ et <lb/>ſciendum videndum eſt an inter primos numeros <lb/>ꝓportiouis duple aut cuiuſuis alterius rationa-<lb/>lis ſint tres numeri continuo ꝓportionabiles cõ-<lb/>putatis extremis: et ſi ſic: talis ꝓportio habet me­<lb/>dietatem rationalem: et per conſequens ſexquial­             <cb chead="Capitulum ſextum"/>             teram rationalem ad ipſam. </s>
            <s xml:id="N149BC" xml:space="preserve">Addendo enī et me-<lb/>dietatem ſui conſtituetur ſexquialtera rationalis <lb/>ad ipſaꝫ. </s>
            <s xml:id="N149C3" xml:space="preserve">Et ſi inter primos numeros eius compu­<lb/>tatis extremis inueniantur quatuor numeri conti­<lb/>nuo ꝓportionabiles: ipſa habebit tertiam ratio­<lb/>nalem et per conſequens ſexquitertiam rationa-<lb/>lem ad ſeipſam: et ſi reperiuntur .5. numeri conti-<lb/>nuo ꝓportionabiles computatis extremis ip̄a ha­<lb/>bebit quartam rationalem: et per conſequens ſex­<lb/>quiquartam rationalem / et ſic conſequenter. </s>
            <s xml:id="N149D4" xml:space="preserve">Et <lb/>ſic patet correlarium.             <anchor type="note" xlink:href="note-0047-04" xlink:label="note-0047-04a"/>             </s>
            <s xml:id="N149DE" xml:space="preserve">¶ Sequitur quarto /  ꝓpo­<lb/>ſita quauis ꝓportione rationali: inquirere et ſci-<lb/>re poterimus an habeat aliquam ſuprapartien-<lb/>tem, multiplicem ſuperparticulareꝫ, vel multipli­<lb/>cem ſuprapartientem, rationales. </s>
            <s xml:id="N149E9" xml:space="preserve">vt ꝓpoſita pro­<lb/>portione octupla īueſtigare poterimus et ſcire ex <lb/>dictis an habeat ſuprabipartientem tertias ſu-<lb/>prapartientem quartas rationales etc. </s>
            <s xml:id="N149F2" xml:space="preserve">Ad quod <lb/>ſciendum et inueſtigandum: conſiderandum ē an <lb/>data proportio rationalis habeat illam partem <lb/>aliquotam rationalem: hoc eſt an aliqua propor­<lb/>tio rationalis ſit tota pars aliquota eius quota <lb/>eſt illa a qua denominatur dicta proportio ſupra­<lb/>partiens, ant multiplex ſuperparticularis, aut <lb/>multiplex ſuprapartiens: quod inueſtigari et ſciri <lb/>debet ex vndecima concluſione: et ſi repperias /  <lb/>habet proportionem aliquam rationalem que ſit <lb/>talis pars aliquota eius: tunc manifeſtum ē /  ha­<lb/>bet proportionem rationalem que denominatur <lb/>a tali parte aliquota vel talibus partibus aliquo­<lb/>tis (quod dico ꝓpter ſuprapartientes) ſi vero nõ: <lb/>tunc manifeſtum eſt illam proportionem rationa­<lb/>lem propoſitam non habere proportionem ratio­<lb/>nalem denominatam a tali parte aliquota vel ta­<lb/>libus partibus. </s>
            <s xml:id="N14A17" xml:space="preserve">Probatur hoc demonſtratione <lb/>particulari que equiualebit vniuerſali. </s>
            <s xml:id="N14A1C" xml:space="preserve">Data em̄ <lb/>ꝓportione ſexdecupla volo inueſtigare et ſcire an <lb/>habeat proportionem ſupratripartientem quar-<lb/>tas ad quod inueſtigandum conſiderabo ex doc-<lb/>trina vndecime concluſionis an talis ꝓportio ſex­<lb/>decupla habeat ſubquadruplam rationaleꝫ que <lb/>ſit vna quarta eius: et inuento  ſic eo /  inter ter­<lb/>minos eius computatis extremis inueniuntur <lb/>quin numeri continuo ꝓportionabiles ꝓportio­<lb/>ne dupla: aſſeuerabo conſtanter illam proportio­<lb/>nem habere proportionem rationalem ſupertri-<lb/>partientem quartas: et multiplicem ſexquiquar-<lb/>tam et multiplicem ſupratripartientem quartas <lb/>rationales. </s>
            <s xml:id="N14A39" xml:space="preserve">Quod ſic monſtratur </s>
            <s xml:id="N14A3C" xml:space="preserve">Nam ſi ſupra il­<lb/>lam proportionem ſexdecuplam que eſt .16. ad .1. <lb/>addantur tres proportiones duple: tunc aggre-<lb/>gatum ex ſexdecupla et illis tribus duplis ſuꝑ ad­<lb/>ditis qualis eſt proportio .128. ad .1. ſe habebit ad <lb/>proportionem ſexdecuplam in proportiõe ſupra-<lb/>tripartiente quartas. </s>
            <s xml:id="N14A4B" xml:space="preserve">Continet enim ſexdecu-<lb/>plam et tres quartas eius. </s>
            <s xml:id="N14A50" xml:space="preserve">Item triplando illam <lb/>proportionem ſexdecuplam / et addendo vnam ſui <lb/>quartam habebis ꝓportionem triplam ſexquiq̈r­<lb/>tam ad ſexdecuplam: et addendo ei duas quartas <lb/>habebis triplam ſexquialteram: et addendo ſuꝑ <lb/>illam triplatam .3. quartas habebis triplam ſu-<lb/>pratripartientem quartas rationalem ad ſexde-<lb/>cuplam. </s>
            <s xml:id="N14A61" xml:space="preserve">Omnia iſta patet ex diffinitionibus ſu-<lb/>prapartiētis, multiplicis ſuperparticularis. </s>
            <s xml:id="N14A66" xml:space="preserve">aut <lb/>multiplicis ſuprapartientis. </s>
            <s xml:id="N14A6B" xml:space="preserve">hoc addito /  cuili-<lb/>bet proportioni rationali addi poteſt queuis alia <lb/>rationalis: aggregato ex ipſis manente rationa­<lb/>li proportione. </s>
            <s xml:id="N14A74" xml:space="preserve">Ex quibuſcnn enim rationalibꝰ <lb/>et quotcun: rationalis componitur: q2 alias in             <pb chead="Secunde partis" file="0048" n="48"/>             nūeris reperirent̄̄ irratiõales ꝓportiões: vt ſatis <lb/>cõſtat ītelligēti. </s>
            <s xml:id="N14A80" xml:space="preserve">Et ſic ptꝫ correlariū.             <anchor type="note" xlink:href="note-0048-01" xlink:label="note-0048-01a"/>             </s>
            <s xml:id="N14A88" xml:space="preserve">¶ Sequit̄̄ q̇n­<lb/>to:  ꝓpoſita q̈uis ꝓportiõe ratiõali: nõ difficile ē <lb/>īueſtigare et ſcire an habeat ꝓportionē rõnalē ſub <lb/>multiplicē: an aliquã aliã rationalē minoris ineq̈­<lb/>litatꝪ: vt ꝓpoſita ꝓportiõe dupla īueſtigare et ſci­<lb/>re poterimꝰ an habeat ſubduplã: ſubtriplã: ſubq̈-<lb/>druplã rationalē .etc̈. nec ne: cõſiderando primū ex <lb/>doctrina vndecime ↄ̨cluſiõis: an habeat medieta-<lb/>tem: tertiã: quartã: quintã rationales: et cõperien-<lb/>tes  nõ: dicemus ipſam nõ habere ſubtriplam: <lb/>ſubquadruplã .etc̈. rationales. </s>
            <s xml:id="N14A9F" xml:space="preserve">Et eadem ratione <lb/>dicemꝰ ipſam nõ habere ſubſexq̇tertiã rationalē: <lb/>q2 nõ habet ꝓportionē cõpoſitã ex tribus quartis <lb/>eius rationalibus: nec ſubſexquialterã rationalē: <lb/>q2 nõ habet ꝓportionē compoſitã ex duabus ter-<lb/>tiis eius rationalibus. </s>
            <s xml:id="N14AAC" xml:space="preserve">Et ſic in omnibus aliis di­<lb/>ces. </s>
            <s xml:id="N14AB1" xml:space="preserve">Demonſtratio huius correlarii innititur huic <lb/>baſi et fundamento /  nun̄ aliqua ꝓportio ratio­<lb/>nalis cõponitur adequate ex vna rationali et vna <lb/>irrationali. </s>
            <s xml:id="N14ABA" xml:space="preserve">Applica tu demonſtrationē. </s>
            <s xml:id="N14ABD" xml:space="preserve">Iſto mo­<lb/>do inquirere debes an habet ſubſuprapartientē <lb/>rationalē aut ſub multiplicē ſubſuprapartientem <lb/>rationalē: aut ſub multiplicē ſubſuꝑparticularē: <lb/>īueſtigando et inquirendo ex cõcluſione vndecima <lb/>an talis ꝓportio rationalis ꝓpoſita habeat par­<lb/>tem aliquotã rationalē vel partes a qua vel a qui­<lb/>bus denominatur dicta ꝓportio minoris inequa­<lb/>litatis: et ſi ſic aſcribenda eſt ei talis ꝓportio mi-<lb/>noris inequalitatis rationalis: ſin minus: aſſeren­<lb/>dum eſt ipſam nõ habere talē ꝓportionē minoris <lb/>inequalitatis rationalē. </s>
            <s xml:id="N14AD6" xml:space="preserve">Patet igit̄̄ correlarium. <lb/></s>
            <s xml:id="N14ADA" xml:space="preserve">Profundius em̄ velle illud demonſtrare eſt ipſuꝫ <lb/>tenebris īuoluere.             <anchor type="note" xlink:href="note-0048-02" xlink:label="note-0048-02a"/>             </s>
            <s xml:id="N14AE4" xml:space="preserve">¶ Sequitur ſexto per modum <lb/>epilopi oīm eoꝝ / que preſenti capite digeſta ſunt: <lb/> quauis ꝓportione rationali ꝓpoſita: ſcire po-<lb/>terimus an habeat aliquã ꝓportionē rationalem <lb/>maioris inequalitatis ad ſeipſam et minoris ine-<lb/>qualitatis: et quas habeat: et quas nõ. </s>
            <s xml:id="N14AF1" xml:space="preserve">Et hoc ca-<lb/>put diligenter conſidera quoniã ex eo pendet fer-<lb/>me vniuerſalis huiꝰ materie īquiſitio: et ſuprema <lb/>eius difficultas. </s>
            <s xml:id="N14AFA" xml:space="preserve">¶ His adde /  doctrina huius ca-<lb/>pitis habita: ꝓpoſita aliqua certa velocitate ꝓ-<lb/>ueniente ab aliqua ꝓportione rationali nota: iu-<lb/>dicare poterꝪ de quacū alia velocitate a quauis <lb/>alia ꝓportiõe ꝓueniente cõmenſurabiles ſint. </s>
            <s xml:id="N14B05" xml:space="preserve">nec <lb/>ne. </s>
            <s xml:id="N14B0A" xml:space="preserve">Item ꝓpoſita quauis velocitate ꝓueniente ab <lb/>aliqua ꝓportione ratiõali nota: ſcire de quacū <lb/>alia velocitate date velocitati cõmenſurabili a q̈ <lb/>ꝓportiõe ꝓueniat: ratiõali vcꝫ vĺ irrationali / q̊ ex <lb/>his ſcito et ſequētibꝰ: particulariꝰ ſcire poteris ex <lb/>qua rationali vel irrationali ꝓueniat ſpecifice.</s>
          </p>
          <div xml:id="N14B17" level="4" n="8" type="float">
            <note position="left" xlink:href="note-0047-01a" xlink:label="note-0047-01" xml:id="N14B1B" xml:space="preserve">1. correl.</note>
            <note position="left" xlink:href="note-0047-02a" xlink:label="note-0047-02" xml:id="N14B21" xml:space="preserve">2. correĺ.</note>
            <note position="left" xlink:href="note-0047-03a" xlink:label="note-0047-03" xml:id="N14B27" xml:space="preserve">3. correl.</note>
            <note position="right" xlink:href="note-0047-04a" xlink:label="note-0047-04" xml:id="N14B2D" xml:space="preserve">4. correl.</note>
            <note position="left" xlink:href="note-0048-01a" xlink:label="note-0048-01" xml:id="N14B33" xml:space="preserve">5. correĺ.</note>
            <note position="left" xlink:href="note-0048-02a" xlink:label="note-0048-02" xml:id="N14B39" xml:space="preserve">6. correĺ.</note>
          </div>
        </div>
        <div xml:id="N14B3F" level="3" n="7" type="chapter" type-free="capitulum">
          <head xml:id="N14B44" xml:space="preserve">Capitum ſeptimū / in quo agitur de medie <lb/>rei inuentione et proportione proportionuꝫ <lb/>rationalis et irrationalis.</head>
          <p xml:id="N14B4B">
            <s xml:id="N14B4C" xml:space="preserve">AD habendam aliqualē noti-<lb/>ciã de ꝓportiõe ꝓportiõis rationalis et <lb/>irrationalis et duarū irrationaliū ſit.</s>
          </p>
          <p xml:id="N14B53">
            <s xml:id="N14B54" xml:space="preserve">Prima ſuppoſitio. </s>
            <s xml:id="N14B57" xml:space="preserve">Oīs numerus ha­<lb/>bet numerū ad ſe duplū, triplū, quadruplū, et ſic <lb/>in infinitū: aſcēdendo per ſpecies ꝓportionis mul­<lb/>tiplicis. </s>
            <s xml:id="N14B60" xml:space="preserve">Iſta ſuppoſitio patet ex ſe / qm̄ dato vno <lb/>numero ex duabus vnitatibus adequate cõpoſito <lb/>dabitur vnus alter compoſitus ex quatuor: et ille <lb/>erit duplus: et alter ex ſex: et erit triplus: et alter ex <lb/>octo: et erit quadrupus: et ſic ſine termino.</s>
          </p>
          <p xml:id="N14B6B">
            <s xml:id="N14B6C" xml:space="preserve">Secunda ſuppoſitio. </s>
            <s xml:id="N14B6F" xml:space="preserve">Omnis nume­<lb/>rus rerum diuiſibiliū ſiue quantitas habet cuius             <cb chead="Capitulū ſeptimū."/>             cū denominationis aliquam partem aliquotaꝫ <lb/>cum fractione vel ſine fractione. </s>
            <s xml:id="N14B79" xml:space="preserve">Uolo dicere /  ſi-<lb/>gnato quocun numero rerū diuiſibiliū talis nu­<lb/>merus habet medietatē tertiam, quartam, quin-<lb/>tam, ſextam, ſeptimam, et ſic in infinitū. </s>
            <s xml:id="N14B82" xml:space="preserve">Proba-<lb/>tur: quia capto numero duodenario ille habet me­<lb/>dietatem, puta numerum ſenariū: habet numerū <lb/>quaternariū pro tertia, ternariū pro quarta, pro <lb/>quinta vero habet numerū cū fractione, ad quam <lb/>fractionē inueniendã oportet duodecim per quī <lb/>diuidere: et exibit binariꝰ cū duabꝰ q̇ntis iuxta do-<lb/>ctrinã ſuperiꝰ poſitã octauo capite ṗme partꝪ. </s>
            <s xml:id="N14B93" xml:space="preserve">Et <lb/>ſic operãdū eſt in cuiꝰ vis alteriꝰ ꝑtꝪ aliq̊te īuētiõe.</s>
          </p>
          <p xml:id="N14B98">
            <s xml:id="N14B99" xml:space="preserve">Tertia ſuppoſitio. </s>
            <s xml:id="N14B9C" xml:space="preserve">Supra quēcū <lb/>numerū rerum diuiſibiliū contingit dare numeꝝ <lb/>continentē ipſum et medietatē: et alium continentē <lb/>ipſum et vnam tertiam, et duas tertias: aut tres <lb/>quartas: et ſic de qnibuſcun aliis partibus ali-<lb/>quotis. </s>
            <s xml:id="N14BA9" xml:space="preserve">Patet / qm̄ ad dandū numerū continentē <lb/>ipſum et medietatē ſufficit addere illi medietatem <lb/>ſui: et ad dandum numerū continentē ipſum et du-<lb/>as tertias ſufficit ei addere illas duas tertias: vt <lb/>patet ex ſe aſpicienti in numeris. </s>
            <s xml:id="N14BB4" xml:space="preserve">Quomodo autē <lb/>tales partes īueniant̄̄ p̄cedēs ſuppoſitio declarat</s>
          </p>
          <p xml:id="N14BB9">
            <s xml:id="N14BBA" xml:space="preserve">Quarta ſuppoſitio. </s>
            <s xml:id="N14BBD" xml:space="preserve">Quodlibet con-<lb/>tinuū eſt duplū ad ſuã medietatē: triplū ad tertiã: <lb/>quadruplū ad quartã: ſexquialterū ad duas ter-<lb/>tias: et ſic de qualibet alia ſpecie ꝓportionis. </s>
            <s xml:id="N14BC6" xml:space="preserve">Pa­<lb/>tet hec ſuppoſitio ex diffinitionibus terminorum.</s>
          </p>
          <p xml:id="N14BCB">
            <s xml:id="N14BCC" xml:space="preserve">Quinta ſuppoſitio. </s>
            <s xml:id="N14BCF" xml:space="preserve">Omnis ꝓportio <lb/>habet medietatē: tertiam: quartã: et ſic in infinitū. <lb/></s>
            <s xml:id="N14BD5" xml:space="preserve">Probatur hec ſuppoſitio / q2 oīs quantitas cõti-<lb/>nua: et quodlibet cõtinuo ſucceſſiue diminuibile eſt <lb/>huiuſmodi et oīs ꝓportio eſt quantitas continua <lb/>aut cõtinuo partibiliter diminuibilis (et diſtribu-<lb/>at ly omnis pro generibus ſingulorum more ma-<lb/>themathicorum) / igitur propoſitum.</s>
          </p>
          <p xml:id="N14BE2">
            <s xml:id="N14BE3" xml:space="preserve">Sexta ſuppoſitio. </s>
            <s xml:id="N14BE6" xml:space="preserve">Si aliq̄ due quã-<lb/>titates cõtinue ſe habeant in aliqua proportione <lb/>ratiõali vel irratiõali: dabilis eſt vna tertia qua-<lb/>libet illarū maior que ſe habeat in eadē ꝓportiõe <lb/>ad maiorē illaꝝ. </s>
            <s xml:id="N14BF1" xml:space="preserve">vt ſi .4. et .2. ſe habeãt in aliqua ꝓ­<lb/>portione dabilis eſt alter numerus puta .8. qui in <lb/>eadem ꝓportione ſe habeat ad .4. et ſi diameter a. <lb/>ſe habeat in aliqua ꝓportione ad coſtã b. dabilis <lb/>eſt vna alia quãtitas puta c. que ſe habet in eadeꝫ <lb/>ꝓportione ad b. </s>
            <s xml:id="N14BFE" xml:space="preserve">Patet hec ſuppoſitio ex ſe.</s>
          </p>
          <p xml:id="N14C01">
            <s xml:id="N14C02" xml:space="preserve">His poſitis ſit prima cõcluſio. </s>
            <s xml:id="N14C05" xml:space="preserve">Que-<lb/>libet ꝓportio ratiõalis in q̈libet ꝓportiõe multi-<lb/>plici ab aliq̈ ratiõali excedit̄̄. </s>
            <s xml:id="N14C0C" xml:space="preserve">Hoc eſt q̈libet ꝓpor-<lb/>tio ratiõalis hꝫ ꝓportionē duplã: triplã: q̈druplã <lb/>et ſic in īfinitū rõnales. </s>
            <s xml:id="N14C13" xml:space="preserve">Probat̄̄ hec ↄ̨cĺo / qm̄ ſi illa <lb/>ꝓportio fuerit mĺtiplex manifeſtū ē /  ad nūeꝝ eiꝰ <lb/>maiorē dabit̄̄ aliq̇s nūerꝰ ſe hñs in eadē ꝓportiõe / <lb/>ad illū ſicut ille partes hꝫ ad minorē / vt ptꝫ ex ṗma ſup­<lb/>poſitiõe: et tūc illiꝰ ad minimū erit ꝓportio dupla <lb/>ad ꝓportionē medii ad minimū: qm̄ illa cõponit̄̄ <lb/>ex duabꝰ eq̈libꝰ illi: et ſi addat̄̄ q̈rtꝰ nūerꝰ ſe hñs in <lb/>eadē ꝓportione ad tertiū in qua tertius ſe habet <lb/>ad ſecundū: ſicut poteſt fieri ex prima ſuppoſitiõe: <lb/>iã ꝓportio illius ad minimū erit tripla ad ꝓpor-<lb/>tionē ſcḋi ad minimū: et cū poſſint ſic addi infiniti <lb/>ṫmini ↄ̨tinuo ꝓportiõabiles illa ꝓportiõe mĺtipli­<lb/>ci / vt ptꝫ ex ṗma ſuppõe: ſequit̄̄ /  ad illã ꝓportionē <lb/>dabit̄̄ ꝓportio dupla, tripla, q̈drupla, et ſic ī īfini­<lb/>tū. </s>
            <s xml:id="N14C32" xml:space="preserve">Ptꝫ ↄ̨ña ex octaua ↄ̨cĺiõe p̄cedētꝪ capitꝪ </s>
            <s xml:id="N14C35" xml:space="preserve">Si o <lb/>illa ſit ſuꝑparticĺarꝪ ad maximū extremū eiꝰ adde­             <pb chead="Secunde partis" file="0049" n="49"/>             tur aliquis numeris cū fractione vel ſine habens <lb/>ſe in eadem proportione ad illud maius extremū: <lb/>vt patet ex tertia ſuppoſitione: et tūc illius nume-<lb/>ri ad minimū numerū erit ꝓportio dupla ad illaꝫ <lb/>ſuperparticularē: q2 ibi erūt tres termini cõtinuo <lb/>ꝓportionabiles .etc̈. </s>
            <s xml:id="N14C49" xml:space="preserve">Et iſto modo poteris cõſttue-<lb/>re .5. terminos .6.7. continuo ꝓportionabiles: illa <lb/>ꝓportione ſuperparticulari data: et ſic in infinitū / <lb/>igit̄̄ dabitur ad eam quadrupla, quītupla, ſextu-<lb/>pla rationalis: et ſic in infinitū. </s>
            <s xml:id="N14C54" xml:space="preserve">Et eodē modo pro­<lb/>babis de quocū genere ꝓportionū rationaliuꝫ <lb/></s>
            <s xml:id="N14C5A" xml:space="preserve">Et ſic patet concluſio.</s>
          </p>
          <p xml:id="N14C5D">
            <s xml:id="N14C5E" xml:space="preserve">Secūda cõcluſio. </s>
            <s xml:id="N14C61" xml:space="preserve">Quãuis quelibet <lb/>ꝓportio rationalis in qualibet ꝓportione multi-<lb/>plici ab aliqua ꝓportione ratiõali excedatur: ita­<lb/> quelibet ꝓportio rationalis habeat duplã, tri-<lb/>plam, quadruplã, rationales / et ſic in infinitū: ni-<lb/>chilominus nõ quelibet ꝓportio ratiõalis habet <lb/>ſubduplã, ſubtriplã, ſubquadruplã, rationales. <lb/>etc̈. </s>
            <s xml:id="N14C72" xml:space="preserve">Prima pars huiꝰ concluſionis patet ex priori <lb/>concluſione: et ſecunda ꝓbatur: quia ꝓportio du-<lb/>pla non habet ſubduplã rationalē, nec ſubtriplã, <lb/>nec ſubquadruplã .etc̈. / vt patet ex doctrina vnde-<lb/>cime concluſionis precedentis capitis: igitur non <lb/>quelibet ꝓportio rationalis habet ſubduplã ſub­<lb/>triplã, ſubq̈druplã ratiõales .etc̈. </s>
            <s xml:id="N14C81" xml:space="preserve">Ptꝫ igit̄̄ ↄ̨cluſio</s>
          </p>
          <p xml:id="N14C84">
            <s xml:id="N14C85" xml:space="preserve">Tertia cõcluſio. </s>
            <s xml:id="N14C88" xml:space="preserve">Aliqua ꝓportio ra-<lb/>tionalis eſt dupla, tripla, quadrupla, et ſic in infi­<lb/>nitū alicui ꝓportioni irratiõali. </s>
            <s xml:id="N14C8F" xml:space="preserve">Probatur / quia <lb/>ꝓportio dupla eſt huiuſmodi / igitur. </s>
            <s xml:id="N14C94" xml:space="preserve">Antecedens <lb/>ꝓbatur / quia ꝓportio dupla habet medietatē ter­<lb/>tiam, quartã, quintã .etc̈. / vt patet ex quinta ſuppo­<lb/>ſitione: et ad medietatē ſui eſt dupla, et ad tertiaꝫ <lb/>tripla, et ſic in infinitū / vt patet ex quarta ſuppo-<lb/>ſitione: et nec eius medietas, nec eius tertia, et ſic <lb/>in infinitū ſunt ꝓportiones rationales / vt patet ex <lb/>ꝓbatione precedentis cõcluſionis: igit̄̄ ſunt ꝓpor­<lb/>tiões irratiõales: igit̄̄ ipſa ꝓportio dupla eſt du-<lb/>pla, tripla, quadrupla, et ſic in infinitū alicui pro­<lb/>portioni irrationali / quod fuit probandum.</s>
          </p>
          <p xml:id="N14CAB">
            <s xml:id="N14CAC" xml:space="preserve">Quarta cõcluſio. </s>
            <s xml:id="N14CAF" xml:space="preserve">Quelibet ꝓportio <lb/>rationalis eſt cõmenſurabilis alicui proportioni <lb/>irrationali. </s>
            <s xml:id="N14CB6" xml:space="preserve">Probatur hec concluſio / qm̄ nulla ꝓ-<lb/>portio ratiõalis habet quãlibet ſui partē aliquo-<lb/>tam rationalē ꝓportionē: igitur quelibet eſt com­<lb/>menſurabilis alicui rationali. </s>
            <s xml:id="N14CBF" xml:space="preserve">Patet cõſequētia <lb/>ſuppoſita cõſtantia: qm̄ quelibet quãlibet aliquo­<lb/>tam habet) vt ly quãlibet diſtribuat pro generibꝰ <lb/>ſingulorū (et nõ quãlibet habet rationalē ꝓporti-<lb/>onē: igitur aliquam habet que eſt irrationalis ꝓ-<lb/>portio: et illi eſt cõmenſurabilis / vt patet ex quarta <lb/>ſuppoſitione: igitur ꝓpropoſitū. </s>
            <s xml:id="N14CCE" xml:space="preserve">Probat̄̄ antecedēs / <lb/>qm̄ inter nulliꝰ ꝓportionis terminos inueniūtur <lb/>tot numeri cõtinuo ꝓportionabiles quot poſſunt <lb/>ſignari partes aliquote: igitur aliqua pars ali-<lb/>quota erit ꝓportio irratiõalis. </s>
            <s xml:id="N14CD9" xml:space="preserve">Et ſic ptꝫ ↄ̨cluſio:</s>
          </p>
          <p xml:id="N14CDC">
            <s xml:id="N14CDD" xml:space="preserve">Quinta cõcluſio. </s>
            <s xml:id="N14CE0" xml:space="preserve">Non oīs proportio <lb/>irrationalis eſt ſubdupla, aut ſubtripla, et ſic con­<lb/>ſequēter ad aliquã irrationalē: īmo multe irrati-<lb/>onales ſunt ſubduple aut ſubtriple .etc̈. ad ratio-<lb/>nales. </s>
            <s xml:id="N14CEB" xml:space="preserve">Probatur hec ↄ̨cluſio facile: qm̄ medietas <lb/>duple, quintuple, triple, octuple .etc̈. nõ eſt ſubdu-<lb/>pla ad aliquã irrationalē: et tñ eſt irrationalis / vt <lb/>ſatis patet ex decima ↄ̨cluſione cū ſuo primo cor-<lb/>relario precedentis capitis / igitur concluſio vera.</s>
          </p>
          <p xml:id="N14CF6">
            <s xml:id="N14CF7" xml:space="preserve">Sexta concluſio. </s>
            <s xml:id="N14CFA" xml:space="preserve">Quelibet ꝓportio             <cb chead="Capitulum ſeptimū."/>             in qualibet proportione rationali ab aliqua pro­<lb/>portione rationali vel irratiõali exceditur. </s>
            <s xml:id="N14D02" xml:space="preserve">Pro-<lb/>batur hec concluſio: quoniã data quacū propor­<lb/>tione ad illam poteſt dari dupla, tripla, quadru­<lb/>pla, et ſic cõſequenter procedendo per oēs ſpecies <lb/>ꝓportionis multiplicis: quoniã poſſunt dari tres <lb/>termini continuo ꝓportionabiles tali ꝓportione <lb/>data: et quatuor, et quin, et ſex, et ſic conſequēter <lb/>vt docet ſexta ſuppoſitio: et etiam data quacun <lb/>dabitur vna que contineat ipſam et medietatē eiꝰ <lb/>et alia que continet ipſam et vnã tertiã eius, et vnã <lb/>quartam, et ſic in infinituꝫ. </s>
            <s xml:id="N14D19" xml:space="preserve">Item dabitur vna que <lb/>cõtinet ipſam et duas tertias eius, vel tres quar-<lb/>tas: et ſic in infinītum ſecundū omnē ſpeciem pro-<lb/>portionis rationalis tam ſimplicis quam cõpo-<lb/>ſite: et quelibet talis proportio erit rationalis vel <lb/>irrationalis / vt patet ex primo capite prime par-<lb/>tis: igitur quelibet proportio in qualibet propor­<lb/>tione rationali ab aliqua proportione rationali <lb/>vel irrationali exceditur. </s>
            <s xml:id="N14D2C" xml:space="preserve">Patet igitur concluſio.</s>
          </p>
          <p xml:id="N14D2F">
            <s xml:id="N14D30" xml:space="preserve">Septima cõcluſio. </s>
            <s xml:id="N14D33" xml:space="preserve">Quelibet ꝓpor-<lb/>tio in qualibet proportione rationali aliquã ra-<lb/>tionalem vel irratiõalem excedit. </s>
            <s xml:id="N14D3A" xml:space="preserve">Probatur / qm̄ <lb/>quelibet proportio poteſt diuidi in duas equales <lb/>ratiõales vel non rationales: in .3. in .4. in .5. in .6. / <lb/>et ſic in infinitū. </s>
            <s xml:id="N14D43" xml:space="preserve">vt patet ex quinta ſuppoſitione / et <lb/>ſui medietatē in proportione dupla excedit: et ter-<lb/>tiã in tripla: et quartã in q̈drupla: et ſic in infinitū / <lb/>vt patet ex prima ſuppoſitione: et duas tertias in <lb/>ſexquialtera: et tres quartas ī ſexquitertia: et tres <lb/>quintas in ſuprabipartiente tertias: et ſic in infi-<lb/>nitum diſcurrendo per ſingulas ſpecies propor-<lb/>tionuꝫ rationalium: igitur quelibet proportio in <lb/>qualibet proportione rationali aliquam ratio-<lb/>nalem vel irrationalem excedit.</s>
          </p>
          <p xml:id="N14D58">
            <s xml:id="N14D59" xml:space="preserve">Ad generandas autē proportiones <lb/>irrationales inter terminos proportionis ratio­<lb/>nalis mediantes ſit.</s>
          </p>
          <p xml:id="N14D60">
            <s xml:id="N14D61" xml:space="preserve">Octaua cõcluſio que vocat̄̄ cõcluſio <lb/>medie rei inuentionis. </s>
            <s xml:id="N14D66" xml:space="preserve">Si datis duabus rectis li-<lb/>neis proportionabilibus proportione rationali <lb/>vel irrationali in directum protractis coniūctis <lb/>at ligatis: deſcribatur ſemicirculus: et a cõmuni <lb/>medio ſiue puncto in quo vniuntur eleuetur linea <lb/>directe orthogonaliter ad peripheriam vſ ſemi­<lb/>circuli. </s>
            <s xml:id="N14D75" xml:space="preserve">talis linea ſcḋm cõtinuã ꝓportionalitatē <lb/>inter datas lineas mediabit. </s>
            <s xml:id="N14D7A" xml:space="preserve">Huiꝰ cõcluſionis ſen­<lb/>ſus talis eſt. </s>
            <s xml:id="N14D7F" xml:space="preserve">Si velis inter duas lineas ꝓportiõa-<lb/>biles ꝓportione dupla aut quacun alia īuenire <lb/>vnã que ſe habeat in eadē ꝓportione ad minorē in <lb/>qua ſe habet maior ad ipſam: ↄ̨iūge illas duas li­<lb/>neas et ſuꝑ illas deſcribas ſemicirculū: et a pūcto <lb/>in quo iūgunt̄̄ ille due linee oriat̄̄ directe et ortho-<lb/>gonaliter vna alia linea vſ ad circūferentiã cir-<lb/>culi: et illa eſt linea q̄ querit̄̄: et ꝓportio maioris li-<lb/>nee ad illã mediã eſt medietas ꝓportiõis q̄ eſt īter <lb/>illã lineã maiorē et minimã ſic ↄ̨iunctas. </s>
            <s xml:id="N14D94" xml:space="preserve">Exemplū / <lb/>huius concluſionis patet in hac figura.</s>
          </p>
          <figure xml:id="N14D99">
            <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0049-01"/>
          </figure>
          <pb chead="Secunde partis." file="0050" n="50"/>
          <p xml:id="N14DA1">
            <s xml:id="N150E9" xml:space="preserve">             <anchor type="note" xlink:href="note-0052-01" xlink:label="note-0052-01a"/>             Iſta cõncluſio / vt dicit thomos branardinꝰ in ſua <lb/>geometria in capitulo de proportionalitate con-<lb/>cluſione quarta longã et prolixã expetit demõſtra­<lb/>tionem.             <anchor type="note" xlink:href="note-0052-02" xlink:label="note-0052-02a"/>             </s>
            <s xml:id="N15100" xml:space="preserve">Ideo ſufficiat ad eam euclidis auctoritas <lb/>ſexto elementoꝝ propoſitione decima tertia.</s>
          </p>
          <div xml:id="N15105" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0051-02a" xlink:label="note-0051-02" xml:id="N15109" xml:space="preserve">1. correl.</note>
            <note position="left" xlink:href="note-0051-03a" xlink:label="note-0051-03" xml:id="N1510F" xml:space="preserve">2. correl. <lb/>cal. ī capi­<lb/>te de aug</note>
            <note position="right" xlink:href="note-0051-04a" xlink:label="note-0051-04" xml:id="N15119" xml:space="preserve">3. correl.</note>
            <note position="left" xlink:href="note-0052-01a" xlink:label="note-0052-01" xml:id="N1511F" xml:space="preserve">Branar­<lb/>dinus.</note>
            <note position="left" xlink:href="note-0052-02a" xlink:label="note-0052-02" xml:id="N15127" xml:space="preserve">Eu. 6. ele</note>
          </div>
          <p xml:id="N1512D">
            <s xml:id="N1512E" xml:space="preserve">Nona cõcluſio. </s>
            <s xml:id="N15131" xml:space="preserve">Ad inueniendã pro-<lb/>portionē ſubduplã duple, aut alicuiꝰ alterius, cõ-<lb/>ſtituantur due linee ſe habentes in ꝓportione illa <lb/>cuiꝰ medietas queritur: et inueniatur media linea <lb/>inter eas per artem precedentis cõcluſionis: et tūc <lb/>maioris linee ad illam mediã et etiam illius medie <lb/>ad minimã erit proportio que eſt media ſiue me-<lb/>dietas talis proportionis. </s>
            <s xml:id="N15142" xml:space="preserve">Et ſi velis īuenire ſub-<lb/>quadruplã proportionē īuenias lineã mediã inter <lb/>primã, et ſecundã et vnã aliam inter ſecundã et ter-<lb/>tiam, et tunc quelibet illarū intermediarū erit ſub­<lb/>quadrupla: q2 erūt ibi .5. termini continuo ꝓpor-<lb/>tionabiles: igitur proportio extremi ad extremū <lb/>eſt quadrupla ad quãlibet intermediam. </s>
            <s xml:id="N15151" xml:space="preserve">Et ſi vis <lb/>īuenire ſuboctuplã poſtquã īueniſti ſubq̈druplam <lb/>inter quaſlibet duas lineas īmediate ſe habentes <lb/>eleua vnã. </s>
            <s xml:id="N1515A" xml:space="preserve">Et ſi vis īuenire ſubſexdecuplã poſtquã <lb/>īueniſti ſuboctuplã: īter quaſlibet duas eleua vnã <lb/>artificio precedentis cõcluſionis / et ſic in infinitum <lb/>duplicando. </s>
            <s xml:id="N15163" xml:space="preserve">Hec concluſio patet ex priori patro-<lb/>cinio octaue concluſionis precedentis capitis.</s>
          </p>
          <p xml:id="N15168">
            <s xml:id="N15169" xml:space="preserve">Decima cõcluſio. </s>
            <s xml:id="N1516C" xml:space="preserve">Quãuis facile ſit <lb/>cuilibet ꝓportioni īuenirē ſubduplã, ſubquadru-<lb/>plam, ſuboctuplã, ſubſexdecuplã, et ſic in infinitū <lb/>aſcendendo per numeros pariter pares: difficile <lb/>tamen eſt ſubtriplã, ſubquintuplã, ſubſextuplam / <lb/>et ſic in infinitū per numeros impares vel impari­<lb/>ter pares aſcendendo īuenire. </s>
            <s xml:id="N1517B" xml:space="preserve">Prima pars patet <lb/>ex priori concluſione: et ſecūda eſt michi experimē­<lb/>to cõperta: quãuis nicholaꝰ horen in ſuo tractatu <lb/>ꝓportionū capite quarto velit dare modum per <lb/>artem medie rei inuentionis ad īueniendam pro-<lb/>portionem et ſubduplam, et ſubtriplam, et ſubſex-<lb/>quialteram.             <anchor type="note" xlink:href="note-0052-03" xlink:label="note-0052-03a"/>             </s>
            <s xml:id="N1518F" xml:space="preserve">¶ Sed ſaluo meliori indicio et aucto-<lb/>ritate tam circuaſpecti viri ſignanter in mathe-<lb/>mathicis ſciētiis: videtur michi /  per artē medie <lb/>rei īuentionis nõ poſſunt īueniri quatuor linee cõ­<lb/>tinuo proportionabiliter ſe habentes. </s>
            <s xml:id="N1519A" xml:space="preserve">Quod ſic <lb/>oſtendo: quia captis duabus lineis ſe habentibꝰ <lb/>in ꝓportione dupla ad īueniendã quatuor lineas <lb/>cõtinuo ꝓpprtionabiles: oportet inter illas duas <lb/>īuenire alias duas cõtinuo ꝓportionabiles inter <lb/>ſe et cū extremis / vt ipſemet fatetur: ſed hoc nõ põt <lb/>fieri per medii rei īuentionē igitur. </s>
            <s xml:id="N151A9" xml:space="preserve">Minor proba­<lb/>tur / q2 vel prima illarū duarū linearū que īuenit̄̄ <lb/>inter illas duas īuenitur per illã artē vel nõ. </s>
            <s xml:id="N151B0" xml:space="preserve">ſi non <lb/>habeo ꝓpropoſitū /  oportet dare aliã artē: ſi ſic tū <lb/>manifeſtū eſt /  illa erit medio loco ꝓportionabi­<lb/>lis inter lineas ſe habentes in ꝓportione dupla: <lb/>et per cõſequens maioris linee ad ipſam / et etiam <lb/>ipſius ad minimū erit proportio que eſt medietas <lb/>duple: et tūc quero de īuentione ſecūde linee inter­<lb/>medie: q2 vel ille īuenietur per artem medie rei in-<lb/>uentionis vel nõ: ſi nõ habeo ꝓpoſitū: ſi ſic quero <lb/>vel illa debet īueniri per illam artem inter illam <lb/>mediam lineam et vltimam: vel inter primã et illã <lb/>mediam: ſed neutrū iſtorum eſt diceudum igitur. <lb/></s>
            <s xml:id="N151CA" xml:space="preserve">Probatur minor: quoniã ſi inueniatur inter me-<lb/>diam et vltimam: iam ille quatuor linee nõ erunt <lb/>continuo proportionabiles: quoniã prime ad ſe-<lb/>cundam erit medietas duple: et ſecunde ad tertiã <lb/>et etiam tertie ad quartam erit ſubquadrupla du­             <cb chead="Capitulū octauū."/>             ple: quia erit medietas medietatis duple: vt patet <lb/>ex nona concluſione huius: ſi vero īueniatur inter <lb/>primam et mediam idē ſequitur.             <anchor type="note" xlink:href="note-0052-04" xlink:label="note-0052-04a"/>             </s>
            <s xml:id="N151E1" xml:space="preserve">¶ Ex quo ſequi-<lb/>tur horen non tradidiſſe doctrinam ad inuenien-<lb/>dam proportionē compoſitam ex duabus tertiis <lb/>proportiõis duple puta ſubſequialterã ad duplã <lb/></s>
            <s xml:id="N151EB" xml:space="preserve">Probatur / quia vt ſonant verba eius videtur in-<lb/>nuere illas lineas īueniendas eſſe per artē medie <lb/>rei īuentionis / quod ſtare nõ poteſt / vt probatū eſt <lb/></s>
            <s xml:id="N151F3" xml:space="preserve">Et ſi hec nõ fuit intentio et mens venerabilis ma-<lb/>giſtri. </s>
            <s xml:id="N151F8" xml:space="preserve">Nicholai horen detur imbecillitati et par-<lb/>uitati ingenioli mei venia. </s>
            <s xml:id="N151FD" xml:space="preserve">Eligat igitur vnuſq̇ſ-<lb/> / quod vult et me magis ſtudioſum quã maliuo-<lb/>lum probet.</s>
          </p>
          <div xml:id="N15204" level="4" n="5" type="float">
            <note position="left" xlink:href="note-0052-03a" xlink:label="note-0052-03" xml:id="N15208" xml:space="preserve">Contra <lb/>horeu:</note>
            <note position="right" xlink:href="note-0052-04a" xlink:label="note-0052-04" xml:id="N15210" xml:space="preserve">Correĺ.</note>
          </div>
        </div>
        <div xml:id="N15216" level="3" n="8" type="chapter" type-free="capitulum">
          <head xml:id="N1521B" xml:space="preserve">Capitulum octauū / in quo agitur decre-<lb/>mento et decremento ꝓportionū.</head>
          <p xml:id="N15220">
            <s xml:id="N15221" xml:space="preserve">QUoniã inſequētibus plerū <lb/>ſeſe offert diminutio proportionis ex <lb/>augmento reſiſtentie: aut virtutis decre­<lb/>mento / et etiam augmentatio proueniens ex decre­<lb/>mento reſiſtētie aut virtutis augmento. </s>
            <s xml:id="N1522C" xml:space="preserve">Ideo ope­<lb/>re precium eſt in huiꝰ ſecunde partis calce aliquid <lb/>de augmento et decremento ꝓportionū adiicere.</s>
          </p>
          <p xml:id="N15233">
            <s xml:id="N15234" xml:space="preserve">Pro quo ſuppono primo. </s>
            <s xml:id="N15237" xml:space="preserve">Augere ſi-<lb/>ue augmentare aliquã proportionē cõtingit mul-<lb/>tipliciter: aut em̄ maiori numero aliquid additur <lb/>minore īuariato: aut decreſcente: aut minori ali-<lb/>quid demitur maiore nõ variato aut creſcēte. </s>
            <s xml:id="N15242" xml:space="preserve">aut <lb/>vtro creſcente velocius tamen ꝓportiõabiliter <lb/>creſcente maiore quã minore. </s>
            <s xml:id="N15249" xml:space="preserve">Aut vtro diminu-<lb/>to velocius tamē ꝓportionabiliter diminuto mi-<lb/>nore quã maiore. </s>
            <s xml:id="N15250" xml:space="preserve">Probat̄̄ / qm̄ capta proportione <lb/>dupla que eſt .8. ad .4. cõtingit eã augeri ꝑ cremen­<lb/>tū ipſoꝝ .8. ipſis .4. īuariatis vel decreſcētibus. </s>
            <s xml:id="N15257" xml:space="preserve">vt <lb/>ſi .8: acquirãt vnitatē ipſis .4. īuariatis: manebit <lb/>ꝓportio maior dupla: nouē ad .4. q̄ eſt dupla ſex-<lb/>quiquarta: ſi quãdo .8. acquirūt vnitatē .4. deper­<lb/>dūt vnitatē: etiã manebit proportio maior dupla <lb/>puta tripla. </s>
            <s xml:id="N15264" xml:space="preserve">Itē ſi quieſcētibꝰ .8.4. deꝑdant bina­<lb/>riū: augmentabit̄̄ ꝓportio / vt cõſtat: et ſi etiã tūc .8 <lb/>aliquid acquirãt: etiã augmētabitur ꝓportio. </s>
            <s xml:id="N1526B" xml:space="preserve">Si <lb/>vero .8. acquirãt quaternariū numeꝝ puta ꝓpor-<lb/>tionē ſexquialterã: et q̈ternariꝰ numerꝰ acq̇rat vni­<lb/>tatē puta ꝓportionē ſexquiquartã: ꝓportio effi-<lb/>cietur maior: </s>
            <s xml:id="N15276" xml:space="preserve">Efficiet̄̄ em̄ dupla ſuprabipartiens <lb/>quītas. </s>
            <s xml:id="N1527B" xml:space="preserve">Si aūt .8: deꝑdant duo et .4. / ſiĺr duo aug-<lb/>mētabit̄̄ etiã ꝓportio: q2 maiorē ꝓportionē deꝑ-<lb/>dit numerꝰ mīor quã maior. </s>
            <s xml:id="N15282" xml:space="preserve">Et ſic ptꝫ ſuppoſitio.</s>
          </p>
          <p xml:id="N15285">
            <s xml:id="N15286" xml:space="preserve">Secūda ſuppoſitio. </s>
            <s xml:id="N15289" xml:space="preserve">Augmētare pro­<lb/>portionē eſt addere ꝓportioni ꝓportionē ceteris <lb/>paribꝰ: vt augere duplã eſt ei addere aliquã ꝓpor­<lb/>tionē ceteris aliis manentibus paribus.</s>
          </p>
          <p xml:id="N15292">
            <s xml:id="N15293" xml:space="preserve">Ex quo ſequit̄̄ tertia ſuppoſitio ꝓpo-<lb/>ſita vna ꝓportione quauis et duabꝰ aliis minori-<lb/>bus: īueſtigare vtrū illa maior ex illis duabꝰ mi-<lb/>noribꝰ adeq̈te ↄ̨ponit̄̄: vt ꝓpoſita ꝓportiõe dupla <lb/>et ſexq̇altera, et ſeq̇tertia minoribꝰ, videre vtrum <lb/>dupla ex ſexq̇altera et ſexq̇tertia adeq̈te cõponat̄̄. <lb/></s>
            <s xml:id="N152A1" xml:space="preserve">Probat̄̄ / ſit a. ꝓportio maior b: et c: mīores: et volo <lb/>videre vtrū adeq̈te ↄ̨ponat̄̄ a. ex b. et c. </s>
            <s xml:id="N152A6" xml:space="preserve">Ad qḋ vidē-<lb/>dū: addã c. ipſi b. / et ſi tūc ꝓportio ↄ̨poſita ex b. et c. <lb/>adeq̈te eſt eq̈lis ipſi a. / ex illis adeq̈te cõponit̄̄ a. <lb/>ſin minus: nõ ex his adequate componitur: ſed ex <lb/>duabus maioribus, aut duabus minoribus.</s>
          </p>
          <pb chead="Secunde partis" file="0053" n="53"/>
          <p xml:id="N152B5">
            <s xml:id="N152B6" xml:space="preserve">Quarta ſuppoſitio. </s>
            <s xml:id="N152B9" xml:space="preserve">Diminuere ꝓ-<lb/>portionē maioris ineq̈litatꝪ eſt ab ea demere ali-<lb/>quã ꝓportionē maioris inequalitatis ceteris pa-<lb/>ribus. </s>
            <s xml:id="N152C2" xml:space="preserve">Et hec diffinitio eſt. </s>
            <s xml:id="N152C5" xml:space="preserve">Contingit autē tot mo-<lb/>dis proportionē maioris inequalitatis diminui: <lb/>quot modis ipſam contingit augeri: de quibus in <lb/>prima ſuppoſitione.</s>
          </p>
          <p xml:id="N152CE">
            <s xml:id="N152CF" xml:space="preserve">Quinta ſuppoſitio. </s>
            <s xml:id="N152D2" xml:space="preserve">Sēper plus di-<lb/>minuitur ꝓportio maioris īequalitatis per aug-<lb/>mentū minoris termini maiore nõ variato: quam <lb/>per equale decrementū maioris minore nõ varia-<lb/>to ceteris paribus. </s>
            <s xml:id="N152DD" xml:space="preserve">Et ſemper plus creſcit ꝓpor-<lb/>tio per decrementū minoris termini: quã ꝑ equa-<lb/>augmentū maioris ceteris paribꝰ. </s>
            <s xml:id="N152E4" xml:space="preserve">Prima pars <lb/>huius ſuppoſitionis probatur: ſit vna ꝓportio f. <lb/>inter a maiorē terminū et b. minorem. </s>
            <s xml:id="N152EB" xml:space="preserve">et perdat a. <lb/>terminus aliquã partē ſui manente b. inuariato: <lb/>tunc dico /  ſi a: nichil deperderet: et b. acquireret <lb/>tantã partē quantã iam deperdit a. ceteris pari-<lb/>bus: maiorē ꝓportionē deꝑderet f. ꝓportio quam <lb/>iam deperdit. </s>
            <s xml:id="N152F8" xml:space="preserve">Quod ꝓbatur ſic: q2 b. per acquiſi-<lb/>tionē illiꝰ partis maiorē ꝓportionē acquirit quã <lb/>deꝑdat a: ꝑ deperditionē eiuſdē partis vel equa-<lb/>lis: quod patet: q2 ſi tam a. quã b. deperderent illã <lb/>partē: maiorē ꝓportionē deperderet b. quam a. / vt <lb/>patet ex octaua ſuppoſitione quarti capitis huiꝰ <lb/>partis: igitur quando b. acquirit illam partē et a. <lb/>deperdit illam: maiorē ꝓportione acquirit b. quã <lb/>deperdat a. </s>
            <s xml:id="N1530B" xml:space="preserve">(Suppono em̄ /  ſemꝑ a. maneat ma­<lb/>ius) / et ex conſequenti ſequitur /  maiorē ꝓportio-<lb/>nem perdit f. / per augmentū minoris termini pu-<lb/>ta b. / quã per equale decrementū maioris puta a. / <lb/>quod fuit ꝓbandū. </s>
            <s xml:id="N15316" xml:space="preserve">Patet hec cõſequētia / quoniã <lb/>ſemper ꝓportio inter aliqua duo īequalia perdit <lb/>illã ꝓportionē quã acquirit minꝰ extremū: et etiã <lb/>illam quã deperdit maius extremū ceteris paribꝰ / <lb/>vt patet ex ꝓbationibus none et decime ſuppoſi-<lb/>tionū ſecundi capitis huius. </s>
            <s xml:id="N15323" xml:space="preserve">Patet igitur prima <lb/>pars. </s>
            <s xml:id="N15328" xml:space="preserve">Et eodem modo demonſtrabis ſecundam <lb/></s>
            <s xml:id="N1532C" xml:space="preserve">Intelligo /  ſemper maior terminus maior ma-<lb/>neat. </s>
            <s xml:id="N15331" xml:space="preserve">Alias denmõſtratio nõ ꝓcederet.             <anchor type="note" xlink:href="note-0053-01" xlink:label="note-0053-01a"/>             </s>
            <s xml:id="N15339" xml:space="preserve">¶ Ex quo <lb/>ſequitur /  aliquando tantū diminuitur ꝓportio <lb/>maioris inequalitais per crementū minoris nu-<lb/>meri adequate ceteris paribus: quantū diminui-<lb/>tur per equale decrementū maioris numeri. </s>
            <s xml:id="N15344" xml:space="preserve">Pro­<lb/>batur: et volo /  ſit vna ꝓportio inter quadrupe-<lb/>dale et octupedale  manente quadrupedali in-<lb/>uariato octupedale ꝑdat quadrupedale adequa-<lb/>te: et ſequitur /  illa proportio diminuitur vſ ad <lb/>ꝓportionē equalitatis: volo igitur iterū /  manē­<lb/>te octupedali inuariato: quadrupedale acquirat <lb/>ſupra ſe quadrupedale adequate: et ſequit̄̄ /  tunc <lb/>etiã diminuitur proportio dupla vſ ad propor-<lb/>tionē equalitatis: igitur correlariū verū             <anchor type="note" xlink:href="note-0053-02" xlink:label="note-0053-02a"/>             </s>
            <s xml:id="N1535E" xml:space="preserve">¶ Sequi­<lb/>tur ſecūdo /  per equale decrementū maioris ter-<lb/>mini et ſimul equale crementū minoris proportio <lb/>manet equalis. </s>
            <s xml:id="N15367" xml:space="preserve">Patet correlariū poſito /  octu-<lb/>pedale a. deperdat quadrupedale: et quadrupeda­<lb/>le b. acquirat tantū puta quadrupedale. </s>
            <s xml:id="N1536E" xml:space="preserve">quo poſi­<lb/>to ſequitur /  in fine inter illos terminos erit pro­<lb/>portio dupla ſicut erat in principio. </s>
            <s xml:id="N15375" xml:space="preserve">Nã in fine b. <lb/>erit octupedale a. vero quadrupedale: igitur.</s>
          </p>
          <div xml:id="N1537A" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0053-01a" xlink:label="note-0053-01" xml:id="N1537E" xml:space="preserve">1. correĺ.</note>
            <note position="left" xlink:href="note-0053-02a" xlink:label="note-0053-02" xml:id="N15384" xml:space="preserve">2. correĺ.</note>
          </div>
          <p xml:id="N1538A">
            <s xml:id="N1538B" xml:space="preserve">His iactis ſit prima concluſio. </s>
            <s xml:id="N1538E" xml:space="preserve">Si <lb/>vtra duaꝝ latitudinū inequaliū vniformiter cõ-<lb/>tinuo diminuatur ſiue in tēpore equali ſiue ineq̈li <lb/>ꝑdendo equalē latitudinē oīno: maiorē ꝓportionē <lb/>deꝑdet minor latitudo quã maior: hoc eſt īter ipſã             <cb chead="Capitulum octauū."/>             minorē latitudinem in principio diminutionis et <lb/>ſeipſam in fine erit maior ꝓportio quã inter alte-<lb/>ram maiorē latitudinē in principio et ſeipſam in <lb/>fine. </s>
            <s xml:id="N153A2" xml:space="preserve">Exēplū / vt captis duabus latitudinibus puta <lb/>pedali et bipedali ſiue vniꝰ gradꝰ et duoꝝ graduū <lb/>(nõ eſt cura:) ſi latitudo pedalis ꝑdat in hora vni-<lb/>formiṫ ſemipedale: et latitudo bipedalis in tãto <lb/>tēpore vel maiore vel minori </s>
            <s xml:id="N153AD" xml:space="preserve">(Non īpedit ꝓpoſi-<lb/>tum) perdat vniformiter ſemipedale adequate: <lb/>maiorē ꝓportionē deperdit pedale quã ſemipeda­<lb/>le: qm̄ inter pedale in principio et ſeipſum in fine <lb/>eſt ꝓportio dupla: inter bipedale vero in prīcipio <lb/>et ſeipſum in fine eſt ꝓportio ſexquialtera. </s>
            <s xml:id="N153BA" xml:space="preserve">Pro-<lb/>batur hoc cõcluſio facile: qm̄ quandocun latitu-<lb/>do maior et minor equalē partē ſiue exceſſū ſiue la­<lb/>titudinē deperdūt: maiorē ꝓportionē deperdit la­<lb/>titudo minor quã maior: vt ptꝫ manifeſte ex octa-<lb/>ua ſuppoſitione quarti capitis huiꝰ partis: igit̄̄ <lb/>concluſio vera.             <anchor type="note" xlink:href="note-0053-03" xlink:label="note-0053-03a"/>             </s>
            <s xml:id="N153CE" xml:space="preserve"><pb chead="Secunde partis" file="0052" n="52"/>¶ Ex hac concluſione ſequitur /  ſi <lb/>aliq̈ latitudo maior puta a. vniformiṫ cõtinuo in <lb/>aliquo tēpore deperdat aliquam partē ſui: et vna <lb/>alia latitudo minor puta b. deperdat cõtinuo vni-<lb/>formiter in tanto tēpore, maiori, vel minori (non <lb/>curo) tantã partē adequate ſui: maior ꝓportio eſt <lb/>inter latitudinē minorem in medio inſtanti prime <lb/>medietatis tēporis in quo ipſa diminuitur et ſeip­<lb/>ſam in medio inſtanti ſecūde medietatis eiuſdē tē­<lb/>poris: quã īter latitudinē maiorē in inſtãti medio <lb/>prime medietatis tēporis / in quo ipſa diminuitur <lb/>et ſeipſaꝫ in inſtãti medio ſecūde medietatꝪ eiuſdē <lb/>tēporis. </s>
            <s xml:id="N153E9" xml:space="preserve">Exemplū / vt capta latitudine .12. graduū <lb/>et .8. graduū: et diminuatur latitudo: 12. graduuꝫ <lb/>in hora cõtinuo vniformiter, deperdendo adequa­<lb/>te quatuor gradus. </s>
            <s xml:id="N153F2" xml:space="preserve">et in tanto tēpore vel maiori vĺ <lb/>minori (nõ curo) cõtinuo vniformiter deperdat la-<lb/>titudo .8. graduū etiã quatuor gradus adequate: <lb/>tunc ipſius latitudinis minoris in inſtanti medio <lb/>ṗme medietatꝪ tꝑis in quo ipſa diminuit̄̄ ad ipſã <lb/>in inſtãti medio ſecūde medietatis eiuſdē tēporis <lb/>eſt maior ꝓportio: quã inter latitudinē maiorē in <lb/>inſtanti medio prime medietatis temporis in quo <lb/>diminuitur et ſeipſam in inſtanti medio ſecūde me­<lb/>dietatis eiuſdē tēporis. </s>
            <s xml:id="N15407" xml:space="preserve">Nam illa eſt ꝓportio ſu-<lb/>prabipartiens quintas puta .7. ad .5. hec vero eſt <lb/>ſuprabipartiens nonas puta .11. ad .9. </s>
            <s xml:id="N1540E" xml:space="preserve">Modo illa <lb/>maior eſt hac / vt conſtat ex predictis. </s>
            <s xml:id="N15413" xml:space="preserve">Hoc correla-<lb/>riū eandē cū cõcluſione petit demonſtrationē: qm̄ <lb/>ipſa latitudo maior ab inſtanti medio prime me-<lb/>dietatis tēporis in quo diminuitur vſ ad inſtãs <lb/>mediū ſecunde medietatis eiuſdē tēporis tantam <lb/>latitudinē deperdit adequate: quantam latitudo <lb/>minor perdit ab inſtanti medio prime medietatis <lb/>tēporis in quo diminuitur vſ ad inſtans mediū <lb/>ſecūde medietatis eiuſdē tēporis: q2 illa tempora <lb/>ſunt medietates totaliū tēpoꝝ / vt conſtat in quibꝰ <lb/>deperduntur medietates latitudinū deꝑdendarū <lb/>adequate / igit̄̄ maiorē ꝓportionē deꝑdit minor la­<lb/>titudo in tali tēpore: quã maior in tꝑe correſpõdē­<lb/>ti. </s>
            <s xml:id="N15430" xml:space="preserve">Patet hec ↄ̨ña ex ſcḋa parte octaue ſuppoſiti-<lb/>onis p̄allegate: et ꝓportio deꝑdita ab aliqua lati­<lb/>tudine in aliquo tꝑe eſt ꝓportio īter eandē latitu-<lb/>dinē in prīcipio talis tꝑis et ſeipſã in fine / vt patet / <lb/>ergo maior eſt ꝓportio inter minorē latitudinē in <lb/>inſtãti medio prime medietatis temporis in quo <lb/>diminuit̄̄ ad ſeipſam in in inſtanti medio ſcḋe me­<lb/>dietatis tꝑis eiuſdē: quã īter latitudinē maiorē in <lb/>inſtãti medio ṗme medietatꝪ tꝑis in quo diminuit̄̄ <lb/>et ſeipſã in inſtãti medio ſcḋe medietatis eiuſdem <lb/>tꝑis / quod fuit ꝓbandū. </s>
            <s xml:id="N15447" xml:space="preserve">Patet igitur correlariū. <lb/></s>
            <s xml:id="N14DA2" xml:space="preserve">¶ Ex quo ſequitur ſecundo /  ſi latitudo motus a. <lb/>maior et b. minor diminuantur vniformiter cõti-<lb/>nue in tempore equali vel inequali perdendo ade-<lb/>quate equalem latitudinem: maior eſt proportio <lb/>inter motum b. in principio temporis in quo ipſe <lb/>diminuitur et ſeipſum in fine talis temporis: quã <lb/>inter motum a. in principio temporis in quo ipſe <lb/>diminuitur et ſeipſum in fine eiuſdem temporis: et <lb/>ſimiliter maior eſt ꝓportio inter motum b. in inſtã­<lb/>ti medio prime medietatis temporis in quo ipſe <lb/>diminuitur et ſeipſum in inſtanti medio ſecunde. <lb/>medietatis eiuſdem temporis: quam inter motuꝫ <lb/>a. in inſtanti medio prime medietatis temporis ī <lb/>quo ipſe diminuitur et ſeipſum in inſtanti medio <lb/>ſecunde medietatis eiuſdem temporis. </s>
            <s xml:id="N14DC1" xml:space="preserve">Prima <lb/>pars huius auxilio concluſionis precedentis oſtē­<lb/>ditur et ſecunda ex correlario facile ſuam demon­<lb/>ſtrationem aſſumit.             <anchor type="note" xlink:href="note-0050-01" xlink:label="note-0050-01a"/>             </s>
            <s xml:id="N14DCF" xml:space="preserve">Et hoc correlarium eſt quar-<lb/>tum ſuppoſitum calculatoris ī capite de motu lo­<lb/>cali cõcluſione .38. / quod ponit ſub his verbis.</s>
          </p>
          <div xml:id="N14DD6" level="4" n="1" type="float">
            <note position="left" xlink:href="note-0050-01a" xlink:label="note-0050-01" xml:id="N14DDA" xml:space="preserve">calcu. de <lb/>mo. loca.</note>
          </div>
          <p xml:id="N14DE2">
            <s xml:id="N14DE3" xml:space="preserve">Omniū duarū latitudinum equalium extenſiue et <lb/>inique intenſarum maior eſt proportio gradꝰ me­<lb/>dii medietatis intenſioris in latitudine remiſſio-<lb/>ri ad graduꝫ medium medietatis remiſſioris eiuſ­<lb/>dem latitudinis / quam eſt proportio graduum me­<lb/>diorum medietatum latitudinis remiſſioris.</s>
          </p>
          <p xml:id="N14DF0">
            <s xml:id="N14DF1" xml:space="preserve">Quas auteꝫ vocat latitudines extenſiue equales <lb/>vide ibi. </s>
            <s xml:id="N14DF6" xml:space="preserve">Et ex hoc probatur etiam regula / quã po­<lb/>nit calculator in capite eodem ſoluendo argumen­<lb/>tum factum contra .33. concluſionem / quam ibi nõ <lb/>probat: ſed ipſa facile oſtenditur ex hac concluſio­<lb/>ne et ſuo correlario / hoc addito /  in omni latitu-<lb/>dine vniformiter difformi partium equalium ex-<lb/>trema equaliter ſeſe excedunt: quia de talibus la­<lb/>titudinibus intelligitur regula eius.</s>
          </p>
          <p xml:id="N14E07">
            <s xml:id="N14E08" xml:space="preserve">Secunda concluſio. </s>
            <s xml:id="N14E0B" xml:space="preserve">Quando inter <lb/>aliquos terminos eſt ꝓportio maioris inequali-<lb/>tatis, et maior illorum terminorum acquirit ali-<lb/>quam proportionem ſtante minore inuariato: vel <lb/>minor terminus deperdit aliquam ꝓportionem ī­<lb/>uariato maiore: proportio inter illos terminos <lb/>augmentantur. </s>
            <s xml:id="N14E1A" xml:space="preserve">Probatur / et ſint b. terminus ma­<lb/>ior et .cd. minor inter quos ſit ꝓportio f. / et acqui-<lb/>rat terminus b. vnam ꝓportionem que ſit .ab. ad <lb/>b. / tunc dico /  proportio f. auget̄̄ ceteris aliis ma­<lb/>nentibus paribus. </s>
            <s xml:id="N14E25" xml:space="preserve">Item ſi .cd. perdat ꝓportionē / <lb/>que eſt .cd. ad d. proportio f. augmentatur. </s>
            <s xml:id="N14E2A" xml:space="preserve">Pri-<lb/>mum probatur / quia quando b. acquirit propor-<lb/>tionē que eſt .ab. ad b. ceteris manentibus paribꝰ <lb/>ipſi ꝓportioni f. que eſt b. ad .cd. / additur ꝓportio <lb/>.ab. ad b. / ergo ſequitur /  ipſa ꝓportio f. augetur <lb/></s>
            <s xml:id="N14E36" xml:space="preserve">Patet hec conſequentia ex ſecunda ſuppoſitio­<lb/>ne huius. </s>
            <s xml:id="N14E3B" xml:space="preserve">Secunda pars ſimiliter oſtenditur: quo­<lb/>niam quando terminus minor .cd. perdit ꝓportio­<lb/>nem que eſt: cd. ad d. ꝓportioni f. que eſt b. ad .cd. / <lb/>additur ꝓportio que eſt .cd. ad d. / quoniam in fine <lb/>totalis ꝓportio componitur ex proportione b. ad <lb/>.cd. et .cd. ad d. / ergo proportioni f. que eſt b. ad .cd. <lb/>fuit addita ꝓportio que eſt .cd. ad d. / ergo ꝓportio <lb/>f. fuit augmentata. </s>
            <s xml:id="N14E4C" xml:space="preserve">Patet hec conſequentia ex ſe­<lb/>cunda ſuppoſitione preallegata. </s>
            <s xml:id="N14E51" xml:space="preserve">Et ſic patet con-<lb/>cluſio.             <anchor type="note" xlink:href="note-0050-02" xlink:label="note-0050-02a"/>             </s>
            <s xml:id="N14E5B" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  <lb/>cum inter aliquos terminos eſt ꝓportio maioris <lb/>inequalitatis: et vtro creſcente maiorem propor­<lb/>tionem acquirit maior terminus quam minor / tūc <lb/>ꝓportio inter datos terminos augetur. </s>
            <s xml:id="N14E66" xml:space="preserve">Proba-<lb/>tur / ſint duo termini .abc. maior: de. minor: et ſit ꝓ­<lb/>portio c. ad .e.f et ꝓportio .abc. ad c. / excedat pro-<lb/>portionē .de. ad e. per proportionē que eſt .abc. ad             <cb chead="Capitulum ſextum"/>             bc. / et acquirat e. ꝓportionem .de. ad e. et c. ꝓportio­<lb/>nem que eſt .abc. ad c. / et tūc dico /  proportio f. au­<lb/>getur. </s>
            <s xml:id="N14E76" xml:space="preserve">Quod ſic ꝓbatur / quia ſi c. acquireret adeq̈­<lb/>te tantam proportionem quanta eſt .de. ad e. quaꝫ <lb/>acquirit e. adhuc inter illos terminos maneret ꝓ­<lb/>portio f. / vt patet ex correlario decime ſuppoſitio­<lb/>nis ſecundi capitis huius partis: ſed modo c. ter-<lb/>minus maior acquirit vltra proportionem quam <lb/>acquirit terminus minor proportioneꝫ q̄ eſt .abc. <lb/>ad .bc. / ergo ꝓportioni f. que eſt .bc. ad .de. / additur <lb/>proportio .abc. ad .bc. / et per conſequens ꝓportio <lb/>f. augetur / quod fuit probandum. </s>
            <s xml:id="N14E8B" xml:space="preserve">Patet conſeq̄n-<lb/>tia ex ſecunda ſuppoſitione. </s>
            <s xml:id="N14E90" xml:space="preserve">Patet igitur correla­<lb/>rium.             <anchor type="note" xlink:href="note-0050-03" xlink:label="note-0050-03a"/>             </s>
            <s xml:id="N14E9A" xml:space="preserve">¶ Sequitur ſecundo /  datis duobus termi­<lb/>nis inter quos eſt ꝓportio maioris inequalitatis <lb/>et diminuatur vter terminus: minore maiorem <lb/>proportionem deperdente quam maior ꝓportio ī­<lb/>ter datos terminos augetur. </s>
            <s xml:id="N14EA5" xml:space="preserve">Probatur / ſint .ab. <lb/>terminꝰ maior: et .cde. minor. </s>
            <s xml:id="N14EAA" xml:space="preserve">et ſit inter .ab. et .cde. <lb/>ꝓportio f. / et deperdat .ab. ꝓportionem que eſt .ab. <lb/>ad b. et .cde. deperdat ꝓportionem que eſt .cde. ad <lb/>e. / excedat proportio .cde. ad e. ꝓportionem .ab. <lb/>ad b. per proportionem .cde. ad .de. / et tunc dico /  <lb/>tali decremento facto in vtro illorum termino-<lb/>rum ꝓportio f. augetur. </s>
            <s xml:id="N14EB9" xml:space="preserve">Quod ſic probatur. </s>
            <s xml:id="N14EBC" xml:space="preserve">quo-<lb/>niam ſi .ab. terminus maior et .cde. terminus mi-<lb/>nor equalem proportioneꝫ deperderent puta .ab. ꝓ­<lb/>portionem que eſt .ab. ad b. et .cde. ꝓportionē que <lb/>eſt .cde. ad .de. / tunc adhuc maneret ꝓportio f. / vt pa­<lb/>tet ex ſecunda parte decime ſuppoſitionis. </s>
            <s xml:id="N14EC9" xml:space="preserve">ſecun-<lb/>di capitis huius: ſed modo vltra illam proportio­<lb/>nem adhuc minor terminus deperdit ꝓportioneꝫ <lb/>.de. ad e. / ergo ſequitur /  ipſi proportioni f. addi-<lb/>tur ꝓportio .de. ad e. et ſic ꝓportio illa f. auget̄̄ / qḋ <lb/>fuit probandum.             <anchor type="note" xlink:href="note-0050-04" xlink:label="note-0050-04a"/>             </s>
            <s xml:id="N14EDB" xml:space="preserve">¶ Sequitur tertio /  quãdo duo <lb/>termini ſe habent in proportione maioris īequa-<lb/>litatis: et minor perdit aliquam ꝓportionē et ma­<lb/>ior acquirit: ꝓportio inter illos terminos auge-<lb/>tur. </s>
            <s xml:id="N14EE6" xml:space="preserve">Patet correlarium ex concluſione.</s>
          </p>
          <div xml:id="N14EE9" level="4" n="2" type="float">
            <note position="left" xlink:href="note-0050-02a" xlink:label="note-0050-02" xml:id="N14EED" xml:space="preserve">1. correl.</note>
            <note position="right" xlink:href="note-0050-03a" xlink:label="note-0050-03" xml:id="N14EF3" xml:space="preserve">2. correl.</note>
            <note position="right" xlink:href="note-0050-04a" xlink:label="note-0050-04" xml:id="N14EF9" xml:space="preserve">3. correl.</note>
          </div>
          <p xml:id="N14EFF">
            <s xml:id="N14F00" xml:space="preserve">Tertia concluſio. </s>
            <s xml:id="N14F03" xml:space="preserve">Qnando inter ali-<lb/>quos terminos eſt ꝓportio maioris īequalitatis <lb/>et maior illorum diminuitur ſtante minore: vel mi­<lb/>nor augetur ſtante maiore: proportio inter illos <lb/>terminos diminuitur. </s>
            <s xml:id="N14F0E" xml:space="preserve">Probatur prima pars: et <lb/>ſit proportio f. inter .ab. maiorem terminum et c. <lb/>minorem: et ſtante c. deperdat .ab. ꝓportionem q̄ <lb/>eſt .ab. ad b. / quam deperdit deperdendo a. parteꝫ <lb/>ſui: tunc dico /  proportio f. diminuitur. </s>
            <s xml:id="N14F19" xml:space="preserve">Quod ſic <lb/>probatur / quia a ꝓportione f. demitur aliqua ꝓ-<lb/>portio puta proportio que eſt .ab. ad b. / igitur pro­<lb/>portio f. diminuitur. </s>
            <s xml:id="N14F22" xml:space="preserve">Patet cõſequentia ex quar-<lb/>ta ſuppoſitione: et antecedens probatur / quia ꝓ-<lb/>portio f. componitur ex ꝓportione .ab. ad b. et b. <lb/>ad c. in principio diminutionis / vt patet ex ſuperi­<lb/>us dictis capite quarto huius: et ex illa prpportio­<lb/>ne f. non manet niſi ꝓportio b. ad c. / igitur propor­<lb/>tio f. perdit proportionem que eſt .ab. ad b. / qḋ fuit <lb/>probandum. </s>
            <s xml:id="N14F33" xml:space="preserve">Secunda pars probatur: et ſint duo <lb/>termini ſe habentes in proportione maioris ineq̈­<lb/>litatis a. maior et c. minor inter quos eſt f. propor­<lb/>tio: et acquirat c. terminus minor aliquam ꝓpor-<lb/>tionem acquirendo b. ſupra ſe: ip̄o aggregato ex <lb/>.bc. manente minore ipſo a. </s>
            <s xml:id="N14F40" xml:space="preserve">(Hoc enim ſupponit <lb/>concluſio) et maneat a. inuariatum / tunc dico / <lb/> proportio f. diminuitur. </s>
            <s xml:id="N14F47" xml:space="preserve">Quod ſic probatur: <lb/>quia ꝓportio f. in principio componitur ex pro-<lb/>portione a. ad .bc. et ex ꝓportione .bc. ad c. / vt cõſtat <lb/>et in fine talis augmentationionis termini mino-<lb/>ris: ꝓportio illa manet p̄ciſe proportio a. ad .bc. /             <pb chead="Secūde partis" file="0051" n="51"/>            vt conſtat: ergo ſequitur /  perdit proportionem <lb/>que eſt .bc. ad c. / et ex conſequiti ſequitur /  diminui­<lb/>tur / vt patet ex quarte ſuppoſitione. </s>
            <s xml:id="N14F5B" xml:space="preserve">Et ſic patet <lb/>concluſio.             <anchor type="note" xlink:href="note-0051-01" xlink:label="note-0051-01a"/>             </s>
            <s xml:id="N14F65" xml:space="preserve">Ex quo ſequitur primo /  quando inter <lb/>aliquos duos terminos eſt proportio maioris in­<lb/>equalitatis: et vtro decreſcente maiorem ꝓpor-<lb/>tionem deperdit maior quam minor: ꝓportio īter <lb/>illos diminuitur: et vtro creſcente maiorem pro­<lb/>portionem acquirat minor quam maior: propor-<lb/>tio inter illos diminuitur. </s>
            <s xml:id="N14F74" xml:space="preserve">Probatur. </s>
            <s xml:id="N14F77" xml:space="preserve">prima ꝑs. <lb/></s>
            <s xml:id="N14F7B" xml:space="preserve">et ſint .abc. maior terminus: et .de. minor īter quos <lb/>ſit f: proportio: et excedat ꝓportio .abc. ad c. pro-<lb/>portionem .de. ad e. per proportionem que eſt .bc. <lb/>ad c. / et perdat maior terminus proportionē .abc. <lb/>ad c. et minor ꝓportionem .de. ad e. / tunc dico /  ꝓ-<lb/>portio f. inter illos terminos diminuitur. </s>
            <s xml:id="N14F88" xml:space="preserve">Quod <lb/>ſic probatur / quia ſi maior terminus et minor per­<lb/>derent equales ꝓportiones puta minor propor-<lb/>tionē .de. ad e. et maior proportionem .abc. ad .bc. <lb/>proportio inter illos terminos nec augeretur nec <lb/>diminueretur ſed ſemper maneret f. / vt patet ex ſe-<lb/>cūda parte decīe ſuppoſitionis ſecūdi capitꝪ huiꝰ <lb/>partis: ſed modo maior terminus vltra illam pro­<lb/>portionem equalem illi quaꝫ deperdit minor: ſtã­<lb/>te minore ab vlteriori decremento adhuc perdit <lb/>aliquam proportioneꝫ puta proportioneꝫ .bc. ad <lb/>c. / ergo ſequitur /  proportio f. inter illos termīos <lb/>diminuitur. </s>
            <s xml:id="N14FA3" xml:space="preserve">Patet conſequentia ex tertia conclu­<lb/>ſione. </s>
            <s xml:id="N14FA8" xml:space="preserve">Quare patet prima pars. </s>
            <s xml:id="N14FAB" xml:space="preserve">Et ſecunda ꝓba-<lb/>tur eodem modo auxilio correlarii decime ſuppo­<lb/>ſitionis ſecundi capitis huius partis: et iuuami-<lb/>ne ſecunde partis huius concluſionis tertie.</s>
          </p>
          <div xml:id="N14FB4" level="4" n="3" type="float">
            <note position="left" xlink:href="note-0051-01a" xlink:label="note-0051-01" xml:id="N14FB8" xml:space="preserve">1. correl.</note>
          </div>
          <note position="left" xml:id="N14FBE" xml:space="preserve">2. correl.</note>
          <p xml:id="N14FC2">
            <s xml:id="N14FC3" xml:space="preserve">¶ Sequitur ſecundo. /  quando inter aliquos ter­<lb/>minos eſt proportio maioris inequalitatis: et ma­<lb/>ior decreſcit: creſcente minore manente tamen mi­<lb/>nore: proportio inter illos terminos diminuitur. <lb/></s>
            <s xml:id="N14FCD" xml:space="preserve">Patet correlarium ex concluſione tertia iuuante <lb/>loco a maiori.</s>
          </p>
          <p xml:id="N14FD2">
            <s xml:id="N14FD3" xml:space="preserve">Quarta concluſio </s>
            <s xml:id="N14FD6" xml:space="preserve">Quando inter ali­<lb/>quos terminos eſt aliqua proportio maioris ine­<lb/>q̈litatis: et vter terminꝰ eq̈lem proportionē ac-<lb/>quirit vel deperdit: tunc proportio inter illos nec <lb/>augetur nec diminuitur. </s>
            <s xml:id="N14FE1" xml:space="preserve">Patet hec concluſio fa-<lb/>cile quantum ad deperditioneꝫ ex ſecunda parte <lb/>decime ſuppoſitionis: et quantum ad acquiſitio-<lb/>nem ex correlario eiuſdem decime ſuppoſitionis <lb/>ſecundi capitis huins.             <anchor type="note" xlink:href="note-0051-02" xlink:label="note-0051-02a"/>             </s>
            <s xml:id="N14FF1" xml:space="preserve">¶ Ex quo ſequitur primo /  <lb/>ſi vter duorum terminorum equalium eque velo­<lb/>citer proportionabiliter creſcat vel deſcreſcat con­<lb/>tinuo: inter illos terminos continuo manet eadeꝫ <lb/>proportio / et ſi continuo inter duos terminos in-<lb/>ter quos eſt proportio maioris inequalitatis cre­<lb/>ſcentes vel deſcreſcentes maneat eadem propor-<lb/>tio continuo eque velociter ꝓportionabiliter cre­<lb/>ſcunt vel deſcreſcunt. </s>
            <s xml:id="N15004" xml:space="preserve">Patet hec correlarium ex ſe­<lb/>cunda parte decime ſuppoſitionis ſecūdi capitis <lb/>huius cum ſuo correlario et loco a coniuncta pro­<lb/>portione.             <anchor type="note" xlink:href="note-0051-03" xlink:label="note-0051-03a"/>             </s>
            <s xml:id="N15012" xml:space="preserve">¶ Sequitur ſecundo /  ſi ꝓportio maio­<lb/>ris ad minus minoretur: et vter terminus mino­<lb/>ret̄̄: velociꝰ ꝓportionabiliṫ minorat̄̄ maior ṫminꝰ <lb/>quam minor. </s>
            <s xml:id="N1501B" xml:space="preserve">Et ſi illa ꝓportio minoretur ꝑ ma-<lb/>iorationem vtriuſ termini tardius ꝓportiona-<lb/>biliter maioratur maior quam minor. </s>
            <s xml:id="N15022" xml:space="preserve">Probatur <lb/>prima pars: quia ſi eque velociter ꝓportiõabiliṫ <lb/>vter terminꝰ diminueret̄̄ ↄ̨inuo inter illos termi­<lb/>nos maneret eadem proportio / vt patet ex priori <lb/>correlario: et ſi minor terminus velocius propor-<lb/>tionabiliter minoretur quam maior: tunc propor­<lb/>tio inter illos terminos augetur / vt patet ex ſecū-             <cb chead="Capitulum octauum"/>             do correlario ſecunde concluſionis huius: igitur <lb/>ſi vtro termino decreſcente ꝓportio inter eos di­<lb/>minuatur: velocius proportionabiliter minorat̄̄ <lb/>maior quam minor / quod fuit probandum. </s>
            <s xml:id="N1503A" xml:space="preserve">Pa-<lb/>tet conſequentia / quia vtro termino decreſcente <lb/>nõ poſſunt illi termini ſe habere pluribus modis <lb/>quam  eque velociter proportionabiliter decre-<lb/>ſcant, vel  minor velocius ꝓportionabiliter ma­<lb/>iore vel eocontra: ſed primo et tertio modo vtro <lb/>decreſcente non poteſt ꝓportio inter eos dimi­<lb/>nuitur oportet /  velocius ꝓportionabiliter ma-<lb/>ioretur maior quã minor. </s>
            <s xml:id="N1504D" xml:space="preserve">Et ſic patet prima pars <lb/></s>
            <s xml:id="N15051" xml:space="preserve">Secunda pars probatur / quia ſi vter terminus <lb/>maior videlicet et minor eque velociter proportio­<lb/>nabiliter maioretur: proportio inter eos nec au-<lb/>getur nec diminuitur / vt patet ex primo correla-<lb/>rio huius quarte concluſionis: et ſi vtro illoruꝫ <lb/>creſcente velocius ꝓportionabiliter creſcat ma-<lb/>ior quam minor proportio inter eos augetur / vt <lb/>patet ex primo correlario ſecunde concluſiõis hu­<lb/>ius: igitur ſi vtro creſcente ꝓportio īter illos di­<lb/>minuitur: tardius proportionabiliter maioratur <lb/>maior quã minor / quod fuit ꝓbandum. </s>
            <s xml:id="N15068" xml:space="preserve">Patet cõ-<lb/>ſequentia vt prius. </s>
            <s xml:id="N1506D" xml:space="preserve">Et ſic patet correlarium. </s>
            <s xml:id="N15070" xml:space="preserve">Et <lb/>hoc correlarium eſt quedam ſuppoſitio calculato­<lb/>ris in capitulo de augmentatione ↄ̨cluſione ſepti­<lb/>ma prime opinionis.             <anchor type="note" xlink:href="note-0051-04" xlink:label="note-0051-04a"/>             </s>
            <s xml:id="N1507E" xml:space="preserve">¶ Sequitur tertio /  quãdo <lb/>inter aliquos terminos eſt proportio maioris in­<lb/>equalitatis: et vtro termino creſcente, inter ac-<lb/>quiſitum maiori termino et acquiſitū minori ē ma­<lb/>ior ꝓportio quã ſit ꝓportio inter illos terminos: <lb/>tunc data ꝓportio augetur. </s>
            <s xml:id="N1508B" xml:space="preserve">et ſi ſit minor propor-<lb/>tio inter datos terminos diminuitur. </s>
            <s xml:id="N15090" xml:space="preserve">et intelligo <lb/>ſemper maiori termino acquirente maiorem lati­<lb/>tudineꝫ quã acquirat minor: quia alias non opor­<lb/>teret. </s>
            <s xml:id="N15099" xml:space="preserve">Exēplū / vt capto pedali et bipedali īter que <lb/>eſt proportio dupla: et pedali acquirente vnã q̈r-<lb/>tam pedalis: bipedale acquirat pedale: tunc pro-<lb/>portio inter illas duas quantitates augetur: q2 ī <lb/>fine manet inter illas quantitates ꝓportio dupla <lb/>ſuprabipartiens quintas qualis eſt .12. ad .5. ſi <lb/>vero pedali acquirente pedale: bipedale acquirat <lb/>pedale cum dimidio: tunc proportio inter illas du­<lb/>as quantitates diminuitur: quia in fine manet ꝓ-<lb/>portio ſupratripartientes quartas dūtaxat qua­<lb/>lis eſt .7. ad 4. </s>
            <s xml:id="N150B0" xml:space="preserve">Probatur prima pars: et ſint b. ter­<lb/>minus maior: et d. minor inter quos ſit f. ꝓportio / <lb/>et acquirat b.a. latitudinem: et d. acquirat c. et ip-<lb/>ſius a. ad ipſum c. ſit proportio g. maior propor-<lb/>tione f. / et tunc dico /  illa proportio f. augetur ita­<lb/> ī fine ipſius .ab. ad .cd. erit maior ꝓportio quã <lb/>f. </s>
            <s xml:id="N150BF" xml:space="preserve">Quod ſic probatur / et capio vnam aliam latitu­<lb/>dinem / que ſit h. ad quam a. ſe habet in ꝓportione <lb/>f. / et ſequitur /  ſi d. acquireret h. / quando b. acqui-<lb/>rit a. / tunc inter .ab. et .hd. maneret proportio f. / vt <lb/>patet ex quinto correlario quinte concluſionis ſe­<lb/>cundi capitis huius: ſed modo .cd. eſt minus ipſo <lb/>.hd. / ergo ſequitur /  ipſius .ab. ad ipſum .cd. eſt <lb/>maior ꝓportio quam ipſius .ab. ad ipſum .hd. / q2 <lb/>idem comparatum ad duo inequalia maiorem ꝓ­<lb/>portionem habet ad minus illorum quam ad ma­<lb/>ius / et ex conſequenti .ab. ad ipſum .cd. eſt maior ꝓ­<lb/>portio quam f. / quod fuit ꝓbandnm. </s>
            <s xml:id="N150D8" xml:space="preserve">Sed reſtat ꝓ­<lb/>bare /  .hd. eſt maius quam .cd. quia h. eſt maius <lb/>ipſo c. cum a. maiorem ꝓportionem habeat ad c. <lb/>quam ad h. / vt ponitur: ergo ſequitur /  .hd. ē ma-<lb/>ius .cd: </s>
            <s xml:id="N150E3" xml:space="preserve">Patet conſequentia / quia ab vtro illo-<lb/>rum dempto eodem equali d. illud quod remanet <lb/></s>
            <s xml:id="N1544B" xml:space="preserve"><pb chead="Secunde partis." file="0054" n="54"/>             maius fuit pars maioris: ſed remanet h. maiꝰ / er-<lb/>go erat pars maioris et erat pars ipſius .hd. / er-<lb/>go .hd. eſt maius / quod fuit ꝓbandum. </s>
            <s xml:id="N15456" xml:space="preserve">Et ſic patet <lb/>prima pars. </s>
            <s xml:id="N1545B" xml:space="preserve">iam probatur ſecūda pars et volo /  <lb/>inter b. et d. ſit ꝓportio f. et acquirat b.a. ſupra ſe: <lb/>et d. acquirat c. ſupra ſe: ſit ipſius a. acquiſiti b. <lb/>maiori termino ad ipſum c. acquiſituꝫ minori ter­<lb/>mino proportio g. minor ꝓportione f. / tunc dico /  <lb/>ꝓportio f. inter illos terminos diminuitur: ita  <lb/>in fine ipſius .ab. ad ipſum .cd. erit minor ꝓportio <lb/>quam f. </s>
            <s xml:id="N1546C" xml:space="preserve">Quod ſic ꝓbo et capio / h. latitudinem ad <lb/>quam a. habet ꝓportionem f. / et arguo ſic / ſi quãdo <lb/>b. acquireret h. adhuc inter illos terminos ma-<lb/>neret ꝓportio f. puta inter .ab. et .hd. / vt patet <lb/>ex quinto correlario quinte concluſionis ſecundi <lb/>capitis huius: ſed modo .cd. eſt maius ipſo .hd. / er­<lb/>go ipſius .ab. ad ipſum .cd. eſt minor ꝓportio quã <lb/>ad ipſum .hd. / et per conſequens minor quaꝫ f. / qḋ <lb/>fuit ꝓbandum. </s>
            <s xml:id="N1547F" xml:space="preserve">Sed reſtat probare /  ipſum .cd. <lb/>eſt maius ipſo .hd. / quod ſic oſtenditur / quia dem-<lb/>pto eodem communi ab .hd. et a.cd. / videlicet dē-<lb/>pto ipſo d. ex .cd. manet maius quam ex .hd. / igi-<lb/>tur .cd. eſt maius ipſo .hd. </s>
            <s xml:id="N1548A" xml:space="preserve">Patet cõſequentia ex <lb/>dignitate arithmetica: et probatur aſſumptuꝫ / q2 <lb/>ex .hd. manet h. et ex .cd. manet c. adequate / vt con­<lb/>ſtat et a. habet maiorem proportionem ad h. quã <lb/>idem a. habeat ad c. / vt poſitum eſt: igitur c. eſt ma­<lb/>ius h. et c. manet ex .cd. et h. ex .hd. / igitur qḋ ma-<lb/>net ex .cd. eſt maius illo quod manet ex .hd. eodeꝫ <lb/>communi dempto / quod fuit probanduꝫ. </s>
            <s xml:id="N1549B" xml:space="preserve">Et ſic pa­<lb/>tet correlarium.             <anchor type="note" xlink:href="note-0054-01" xlink:label="note-0054-01a"/>             </s>
            <s xml:id="N154A5" xml:space="preserve">¶ Sequitur quarto /  quando in­<lb/>ter aliquos terminos eſt proportio maioris ine-<lb/>qualitatis: et vtro termino creſcente: ꝓportio ī­<lb/>ter eos augetur: tunc inter acquiſitum maiori ter­<lb/>mino et acquiſitum minori eſt ꝓportio quaꝫ ſit ꝓ­<lb/>portio inter illos terminos quibus ſit acquiſitio <lb/></s>
            <s xml:id="N154B3" xml:space="preserve">Si auteꝫ ꝓportio inter datos terminos diminua­<lb/>tur creſcente vtro: inter acquiſitum maiori et ac­<lb/>quiſitum minori erit minor ꝓportio quam inter <lb/>datos terminos. </s>
            <s xml:id="N154BC" xml:space="preserve">Patet hoc correlarium ex prio­<lb/>ri demonſtratione paucis mutatis.             <anchor type="note" xlink:href="note-0054-02" xlink:label="note-0054-02a"/>             </s>
            <s xml:id="N154C6" xml:space="preserve">¶ Sequit̄̄ quī­<lb/>to /  quando inter aliquos terminos eſt propor-<lb/>tio maioris inequalitatis: et vtro decreſcente in­<lb/>ter deperditum a maiori termino et deperditum <lb/>a minori eſt minor ꝓportio quam inter datos ter­<lb/>minos. </s>
            <s xml:id="N154D3" xml:space="preserve">tunc ꝓportio inter datos terminos maio­<lb/>ratur: et ſi ſit maior ꝓportio inter illa deperdita <lb/>proportio inter datos terminos diminuitur. </s>
            <s xml:id="N154DA" xml:space="preserve">Ex-<lb/>emplum / vt capto bipedali et pedali: ſi bipedale ꝑ­<lb/>dat pedale: et pedale quartam pedalis: tunc pro-<lb/>tio inter datos terminos diminuitur: quia in fine <lb/>talis diminutionis illorum terminorum manet ꝓ­<lb/>portio ſexquitertia quatuor quartarum videlicet <lb/>ad tres quartas et ſi bipedale perdat pedale et pe­<lb/>dale tres quartas ꝓportio maioratur: </s>
            <s xml:id="N154EB" xml:space="preserve">Manet eī <lb/>in fine ꝓportio quadrupla vnius pedalis ad q̈r-<lb/>taꝫ. </s>
            <s xml:id="N154F2" xml:space="preserve">Probatur / ſit .ab. maior terminus .cd. minor / <lb/>inter quos ſit proportio f. / et inter a. et c. partes il-<lb/>lorum terminorum ſit ꝓportio g. minor ipſa pro-<lb/>portione f. et deperdat .ab. ipſam a. partem et .cd. <lb/>c. partem: tunc dico /  in fine talis deperditionis <lb/>ꝓportio inter illos terminos augetur: ita  pro-<lb/>tio b. ad d. qui ſunt termini manentes eſt maior ꝓ­<lb/>portione f. </s>
            <s xml:id="N15503" xml:space="preserve">Quod probatur ſic / quia facta tali di-<lb/>minutione in vtro illorum terminorum: manet <lb/>preciſe proportio inter b. et d. et illa eſt maior ꝓ-<lb/>portione f. / igitur propoſituꝫ. </s>
            <s xml:id="N1550C" xml:space="preserve">Maior eſt nota cuꝫ <lb/>conſequentia: et probatur minor: et ſit h. vna lati­<lb/>tudo ad quam a. ſe habet in ꝓportione f. / et arguo             <cb chead="Capitulum octauum"/>             ſic ſi quando .ab. perdit a.cd. perdit h. / tunc inter <lb/>illos terminos maneret ꝓportio f. / vt patet ex ter­<lb/>tio correlario quinte concluſionis ſecundi capitis <lb/>huius partis: ſed modo quando .ab. perdit a.cd. <lb/>perdit c. quod eſt maius ipſo h. / ergo ipſum .cd. qñ <lb/>perdit c. manet minus quam quando deperdit h. <lb/>et ex conſequenti ipſius b: ad id quod manet deꝑ-<lb/>dito c. ab ipſo .cd. puta ad ipſum d. eſt maior pro-<lb/>portio quã ipſius b. ad id quod manet ex ipſo .cd. <lb/>deperdito h. </s>
            <s xml:id="N15528" xml:space="preserve">Patet conſequentia ex ſe: et ex con-<lb/>ſequenti ſequitur /  proportio b. ad d. eſt maior ꝓ­<lb/>portione f. / quod fuit probanduꝫ. </s>
            <s xml:id="N1552F" xml:space="preserve">Sed iam probo <lb/>illam minorem videlicet /  quando .ab. ꝑdit a.cd. <lb/>perdit c. / quod eſt maius ipſo h. </s>
            <s xml:id="N15536" xml:space="preserve">Quod ſic proba-<lb/>tur / quia ipſius a. ad ipſum h. eſt maior proportio <lb/>quam eiuſdem a. ad ipſum c. / vt patet ex caſu / igit̄̄ <lb/>c. eſt maius ipſo h. / quod fuit oſtendendum. </s>
            <s xml:id="N1553F" xml:space="preserve">Patet <lb/>conſequentia / quia eiuſdem ſemper eſt maior pro­<lb/>portio ad minus quam ad maius. </s>
            <s xml:id="N15546" xml:space="preserve">Et ſic patet pri­<lb/>ma pars. </s>
            <s xml:id="N1554B" xml:space="preserve">Secunda pars probatur: ſint .ab. termi­<lb/>nus maior .cd. minor inter quos ſit ꝓportio f. et in­<lb/>ter a. et c. ſit proportio g. maior ꝓportione f. et de­<lb/>perdat .ab.a. et .cd.c. / ita  in fine maneat preciſe <lb/>proportio inter b. et d. / et tunc dico /  in fine illa ꝓ­<lb/>portio ipſius b. ad d. manet minor f. </s>
            <s xml:id="N15558" xml:space="preserve">Quod ſic ꝓ-<lb/>batur: et volo /  quando .ab. perdit a.cd. perdat <lb/>h. ad quam latitudinem h.a. habet ꝓportionem f. / et <lb/>arguo ſic / ſi quando .ab. perdit a.cd. perderet h. / <lb/>tunc illi termini manerent in eadem proportione <lb/>puta f. / vt patet ex tertio correlario quinte conclu­<lb/>ſionis ſecundi capitis huius: ſed modo in caſu cõ­<lb/>cluſionis quando .ab. ꝑdit a.cd. perdit c. / quod eſt <lb/>minus ipſo h. / ergo ipſum .cd. quando ꝑdit c. ma-<lb/>net maius quam quando perdit h. / et ex conſequē-<lb/>ti ipſius b. ad id quod manet deperdito c: a.cd. eſt <lb/>minor proportio quam ſit f. que eſt ipſius b. ad id <lb/>quod manet ex .cd. deperdito h. / quod fuit proban­<lb/>dum. </s>
            <s xml:id="N15575" xml:space="preserve">Sed iam probo /  c. ſit maius ipſo h. / q2 ipſi-<lb/>us a. ad ipſum h. eſt maior proportio quam eiuſ-<lb/>dem a. ad ipſum c. ex hypotheſi: ergo ipſum c. eſt <lb/>maius ipſo h. / quod fuit oſtendendum. </s>
            <s xml:id="N1557E" xml:space="preserve">Patet con­<lb/>ſequentia vt prius et per conſequens correlariuꝫ <lb/>             <anchor type="note" xlink:href="note-0054-03" xlink:label="note-0054-03a"/>             </s>
            <s xml:id="N1558A" xml:space="preserve">¶ Sequitur ſexto /  quando inter aliquos termi-<lb/>nos eſt ꝓportio maioris inequalitatis: et decre-<lb/>ſcente vtro termino ꝓportio inter eos augetur: <lb/>tunc deperditi a maiori termino ad deperdituꝫ a <lb/>minori eſt minor ꝓportio quam ſit proportio īter <lb/>datos terminos in principio talis diminutionis. <lb/></s>
            <s xml:id="N15598" xml:space="preserve">Et ſi vtro illoruꝫ decreſcente: ꝓportio inter eos <lb/>diminuitur: tunc deperditi a maiori termino ad <lb/>deperditum a minori eſt maior ꝓportio / quam ſit <lb/>ꝓportio inter datos terminos in principio talis <lb/>diminutionis. </s>
            <s xml:id="N155A3" xml:space="preserve">Hoc conuerſum precedentis corre-<lb/>larii ex eius probatione facile oſtenditur paucis <lb/>adiunctis. </s>
            <s xml:id="N155AA" xml:space="preserve">¶ Et circa predicta correlaria aduerte / <lb/> ipſa moderanda ſunt cum maior terminus ma­<lb/>nens continuo maior maiorem latitudinem acqui­<lb/>rit vel deperdit quam minor: alias correlaria nõ <lb/>erunt īmunia a falſitate: nec ſequentibus aliquo <lb/>modo ſeruirent.             <anchor type="note" xlink:href="note-0054-04" xlink:label="note-0054-04a"/>             </s>
            <s xml:id="N155BC" xml:space="preserve">¶ Sequitur ſeptimo /  datis duo­<lb/>bus terminis ſe habentibus in aliqua ꝓportione / <lb/>et capta aliqua parte maioris ſe habente ad cer-<lb/>tam parteꝫ minoris in ea ꝓportione in qua ſe ha­<lb/>bent dati termini: reſidua maioris et minoris ſe <lb/>habent etiam in eadem proportione dati termi-<lb/>ni exemplum / vt capto pedali et bipedali ſe habē-<lb/>tibus in ꝓportiõe dupla: et capta vna quarta ma­<lb/>ioris et altera quarta minoris que etiaꝫ ſe habēt <lb/>in proportione dupla: reſidua, puta tres quarte             <pb chead="Secūde partis" file="0055" n="55"/>             maioris, et tres quarte. minoris. </s>
            <s xml:id="N155D6" xml:space="preserve">ſe habent etiam <lb/>in proportione dupla. / vt promptum eſt videre.</s>
          </p>
          <div xml:id="N155DB" level="4" n="2" type="float">
            <note position="right" xlink:href="note-0053-03a" xlink:label="note-0053-03" xml:id="N155DF" xml:space="preserve">1. correĺ.</note>
            <note position="left" xlink:href="note-0054-01a" xlink:label="note-0054-01" xml:id="N155E5" xml:space="preserve">4. correl.</note>
            <note position="left" xlink:href="note-0054-02a" xlink:label="note-0054-02" xml:id="N155EB" xml:space="preserve">5. correl.</note>
            <note position="right" xlink:href="note-0054-03a" xlink:label="note-0054-03" xml:id="N155F1" xml:space="preserve">6. correĺ.</note>
            <note position="right" xlink:href="note-0054-04a" xlink:label="note-0054-04" xml:id="N155F7" xml:space="preserve">7. correl.</note>
          </div>
          <p xml:id="N155FD">
            <s xml:id="N155FE" xml:space="preserve">Probatur / ſit .ab. terminus maior .cd. minor in-<lb/>ter quos ſit ꝓportio f. et ſit etiam eadem ꝓportio <lb/>f. inter a. partem maiores et c. partem minoris: et <lb/>tunc dico /  inter reſiduas partes puta inter b. et <lb/>d: eſt etiam proportio f. </s>
            <s xml:id="N15609" xml:space="preserve">Quod ſic probatur facile <lb/>et volo /  .ab. perdat a. et .cd. perdat c. / et arguitur <lb/>ſic / inter deperditum a termino maiori et deperdi­<lb/>tum a termino minori eſt eadem ꝓportio que ē in-<lb/>ter ipſos terminos puta f. / igitur illis deperditis <lb/>adhuc inter reſidua manet eadem ꝓportio f. / vt pa­<lb/>tet ex tertio correlario quinte ↄ̨cluſionis prealle-<lb/>gato: ſed reſidua ſunt b. et d. / ergo inter b. et d. ē ꝓ­<lb/>portio f. / quod fuit probandum. </s>
            <s xml:id="N1561C" xml:space="preserve">Patet igitur cor-<lb/>relarium.             <anchor type="note" xlink:href="note-0055-01" xlink:label="note-0055-01a"/>             </s>
            <s xml:id="N15626" xml:space="preserve">¶ Sequitur octauo /  quando inter ali­<lb/>quos terminos eſt aliqua proportio et vtro illo­<lb/>rum decreſcente manet inter eos continuo eadem <lb/>proportio et alter illorum remittitur vſ ad non <lb/>gradum: etiam et alter. </s>
            <s xml:id="N15631" xml:space="preserve">Probatur / et ſint a. et b. il­<lb/>li termini inter quos ſit proportio f. et decreſcēte <lb/>vtro illorum continuo inter eos manet f. ꝓpor-<lb/>tio / et remittatur b. ad non gradum / tunc dico /  ēt <lb/>a. remittitur ad non gradum </s>
            <s xml:id="N1563C" xml:space="preserve">Quod ſic ꝓbatur / <lb/>quia inter a. et b. continuo terminos decreſcentes <lb/>continuo manet proportio f. / igitur continuo a. et <lb/>b. eque velociter proportionabiliter decreſcunt / vt <lb/>patet ex primo correlario quarte concluſionis hu­<lb/>ius ſed infinitam proportioneꝫ deperdit b. / igit̄̄ a. <lb/>in eodem tempore adequate infinitam deperdit et <lb/>ſic in eodem tempore deuenit vſ ad non graduꝫ / <lb/>quod fuit probandum.</s>
          </p>
          <div xml:id="N1564F" level="4" n="3" type="float">
            <note position="left" xlink:href="note-0055-01a" xlink:label="note-0055-01" xml:id="N15653" xml:space="preserve">8. correl.</note>
          </div>
          <p xml:id="N15659">
            <s xml:id="N1565A" xml:space="preserve">Quinta concluſio. </s>
            <s xml:id="N1565D" xml:space="preserve">Quando aliqua <lb/>proportio maioris inequalitatis maioratur per <lb/>maioris extremi crementum ſtante minori: tūc da­<lb/>ta ꝓportio efficitur maior per illam proportionē <lb/>per quam maior terminus augmentatur. </s>
            <s xml:id="N15668" xml:space="preserve">Et quã-<lb/>do aliqua proportio maioris inequalitis ma-<lb/>ioratur per minoris termini decrementum ſtante <lb/>maiori: tunc ipſa data proportio efficitur maior <lb/>per illam proportionem quam deperdit terminꝰ <lb/>minor ſiue per quam terminus minor efficitur mi­<lb/>nor / quod idem eſt. </s>
            <s xml:id="N15677" xml:space="preserve">Probatur prima pars huiꝰ cõ­<lb/>cluſionis / et ſit f. proportio inter b. terminum ma-<lb/>iorem et c. minorem et b. acquirit ſupra ſe a. acqui­<lb/>rendo h. proportionem que eſt .ab. ad b. / tunc dico / <lb/> proportio f. per h. proportionem maioratur ꝑ <lb/>quam etiam maioratur ipſum b. maior terminus <lb/></s>
            <s xml:id="N15685" xml:space="preserve">Quod probatur ſic / q2 facto tali cremento: ꝓpor-<lb/>tio .ab. ad c. componitur ex proportiõe .ab. ad b. <lb/>et b. ad c. / ergo proportioni f.b. ad c. fuit addita ꝓ­<lb/>portio h. que eſt .ab. ad b. / vt patet rx hypoteſi: igi-<lb/>tur ex conſequenti proportio f.b. ad c. fuit augmē­<lb/>tata per h. proportionem / per quaꝫ augmentatur <lb/>b. terminus maior / quod fuit probandum. </s>
            <s xml:id="N15694" xml:space="preserve">Patet <lb/>conſequentia ex ſecunda ſuppoſitione: et ex conſe­<lb/>quenti prima pars. </s>
            <s xml:id="N1569B" xml:space="preserve">Eodem modo demonſtrabis <lb/>ſecundam partem concluſionis </s>
            <s xml:id="N156A0" xml:space="preserve">Et ſic manifeſta ē <lb/>concluſio.             <anchor type="note" xlink:href="note-0055-02" xlink:label="note-0055-02a"/>             </s>
            <s xml:id="N156AA" xml:space="preserve">¶ Ex hoc ſequitur primo /  quando ali­<lb/>qua proportio maioris inequalitatis augetur ꝑ <lb/>maiorationem maioris termini. </s>
            <s xml:id="N156B1" xml:space="preserve">et minorationē <lb/>minoris: tunc data ꝓportio augetur et efficit̄̄ ma­<lb/>ior per proportionem compoſitam ex proportio-<lb/>ne per quam maior terminus efficitur maior ſiue <lb/>quam ſupra ſe acquirit terminus maior, et ex pro­<lb/>portione per quam minor terminus efficitur mi-<lb/>nor, ſiue quam minor terminus deperdit / qḋ idem <lb/>eſt. </s>
            <s xml:id="N156C2" xml:space="preserve">Patet hec correlarium ex concluſione: quoni-<lb/>aꝫ ſi ſtante minore termino in prima parte tempo­             <cb chead="Capitulum octauum"/>             ris in quo fit talis maioratio ꝓportionis: maior <lb/>terminus acquireret totam illam ꝓportionē quã <lb/>debet acquirere in toto tēpore: et in ſecunda par-<lb/>te eiuſdem temporis ſtante iam maiore: minor de­<lb/>perderet illam ꝓportionem quam debet deperde­<lb/>re in toto tempore: tunc ꝓportio īter illos termi-<lb/>nos in prima parte temporis efficietur maior per <lb/>proportionem per quam maior terminus effici-<lb/>tur maior / vt patet ex prima parte concluſionis: et <lb/>in ſecunda parte eiuſdem temporis efficiet̄̄ adhuc <lb/>maior ceteris manentibus paribus per proportio­<lb/>nem per quam minor terminus efficitur minor / vt <lb/>patet ex ſecunda parte huius concluſionis: igitur <lb/>in toto illo tempore cathegorematice efficitur il-<lb/>la proportio maior per ꝓportionem compoſitaꝫ <lb/>ex proportione per quam maior terminus effici-<lb/>tur maior et ex proportione per quam minor ter-<lb/>minus efficitur minor: vt patet, et in caſu correla-<lb/>rii data ꝓportio in fine talis crementi manet ade­<lb/>quate tanta quanta modo in caſu dato: igitur in <lb/>caſu correlarii per tantam ꝓportionem efficit̄̄ ma­<lb/>ior per quam iam in caſu dato: et in caſu dato effi­<lb/>citur maior per proportionem compoſitam ex ꝓ-<lb/>portione per quam maior terminus efficitur ma-<lb/>ior et ex proportione per quam minor efficitur mi­<lb/>nor: igitur per illam compoſitam ex illis duabus <lb/>data ꝓportio efficitur maior ī caſu correlarii / qḋ <lb/>fuit probandum.             <anchor type="note" xlink:href="note-0055-03" xlink:label="note-0055-03a"/>             </s>
            <s xml:id="N15705" xml:space="preserve">¶ Sequitur ſecundo /  quando <lb/>aliqua proportio maioris inequalitatis augetur <lb/>vtro eius termino creſcente: tunc ipſa efficietur <lb/>maior per proportionem per quam proportio ac­<lb/>quiſita maiori termino excedit ꝓportionem acq̇ſi­<lb/>tam minori termino. </s>
            <s xml:id="N15712" xml:space="preserve">Probatur / et ſit f. proportio <lb/>inter b. maiorem et d. minorem: et acquirat b. ter-<lb/>minus ꝓportionem g. acquirendo ſupra ſe a. lati­<lb/>tudinem: et d. acquirat h. ꝓportionem acquirēdo <lb/>ſupra ſe c. latitudinem / ita  in fine maneat ꝓpor-<lb/>tio ipſius .ab. ad: cd. excedat tamen proportio g. <lb/>proportionem h. per e. proportionem: et tunc di-<lb/>co /  data proportio f. efficitur maior per e. ꝓpor­<lb/>tionem. </s>
            <s xml:id="N15725" xml:space="preserve">Quod ſic probatur / quoniam ſi quando <lb/>minor terminus acquirit h. proportionem: maior <lb/>terminus acquireret tantaꝫ adequate: inter illos <lb/>termīos adhuc maneret proportio f. / adequate vt <lb/>patet ex correlario decime ſuppoſitionis ſecundi <lb/>capitis huius: ſed modo vltra h. proportionē ma-<lb/>ior terminus acquirit adhuc e. proportionem: mi­<lb/>nore vltra nichil acquirente: igitur illa ꝓportio f. <lb/>per e. proportionem efficitur maior / quod fuit pro­<lb/>bandum. </s>
            <s xml:id="N1573A" xml:space="preserve">Patet conſequentia ex concluſione </s>
            <s xml:id="N1573D" xml:space="preserve">Ma­<lb/>nifeſtum igitur correlarium.             <anchor type="note" xlink:href="note-0055-04" xlink:label="note-0055-04a"/>             </s>
            <s xml:id="N15747" xml:space="preserve">¶ Sequitur tertio /  <lb/>quando aliqua proportio maioris inequalitatis <lb/>augetur vtro eius termino decreſcente: tnnc ip̄a <lb/>proportio efficitur maior per illam proportiõem <lb/>per quam proportio deperdita a termino minori <lb/>excedit proportionem deperditam a termino ma­<lb/>iori. </s>
            <s xml:id="N15756" xml:space="preserve">Probatur: et ſit .ab. terminus maior: et .cde. <lb/>minor inter quos ſit ꝓportio f. et perdat terminꝰ <lb/>maior proportionem que eſt .ab. ad b. et minor ꝓ­<lb/>portionem .cde. ad e. que excedat proportionē de­<lb/>perditam a maiori termino per proportionē .de. <lb/>ad .e. que vocetur g: et tunc dico /  proportio f. effi­<lb/>citur maior per proportionem g. </s>
            <s xml:id="N15765" xml:space="preserve">Quod ſic ꝓba-<lb/>tur / quoniam ſi quando maior terminus .ab. per-<lb/>dit proportionem .ab. ad b. minor perderet adeq̈­<lb/>te ꝓportionem .cde. ad .de. / tunc inter b. et .de. ma­<lb/>neret adhuc proportio f. / vt patet ex ſecunda par-<lb/>te decime ſuppoſitionis ſecundi capitis huiꝰ par­<lb/>tis: et mõ minor terminus, nichil deperdente aut             <pb chead="Secunde partis" file="0056" n="56"/>             acquirente maiore, deperdit vltra proportioneꝫ <lb/>g. que eſt d.e. ad e. / igitur per illam propotionē g. <lb/>proportio f. efficitur maior. </s>
            <s xml:id="N1577D" xml:space="preserve">Patet conſequentia <lb/>ex ſecunda parte cõcluſionis.             <anchor type="note" xlink:href="note-0056-01" xlink:label="note-0056-01a"/>             </s>
            <s xml:id="N15787" xml:space="preserve">¶ Sequitur quarto / <lb/> ſi ſint quatuor quãtitates equales quarū ſecun­<lb/>da ſtantibus aliis creſcat, aliquam quantitatem <lb/>acquirendo ſupra primaꝫ: et deinde tertia creſcat <lb/>ſtante prima, ſecunda, et quarta tantã quantitatē <lb/>adequate acquirendo ſupra ſecundã quantã ſecū-<lb/>da habet ſupra primã: et deinde quarta omnibus <lb/>aliis īuariatis creſcat eandem quantitatem ac-<lb/>quirendo ſupra tertiam: in fine proportio maxi-<lb/>ma, que ſcilicet eſt inter duas quantitates mino-<lb/>res, per maiorem proportionem excedit tertiam <lb/>que eſt illarum trium proportionū minima: vt ca-<lb/>ptis quatuor pedalibus ſi ſecundum illorū peda-<lb/>lium creſcat aliis quieſcentibus acquirendo ſemi­<lb/>pedale: et deinde tertium illorum pedalium aliis <lb/>inuariatis acquirat ſemipedalem quantitatē ſu-<lb/>pra ſecundum, quod iam eſt pedale cum dimidio: <lb/>et poſtremo quartum illorum aliis ſimiliter inua-<lb/>riatis creſcat acquirendo tantam quantitatē ade­<lb/>quate ſupra tertium illorum: ita  fiat bipedale <lb/>cum dimidio in fine proportio maxima que vide-<lb/>licet eſt ipſius pedalis cum dimidio ad pedale per <lb/>maiorem proportionem excedit ſecundam pro-<lb/>portionem vt puta bipedalis ad pedale cum dimi­<lb/>dio quam iſtamet ſecunda excedit tertiam que eſt <lb/>bipedalis cum dimidio ad bipedale quia prima <lb/>et maxima que eſt ſexquialtera excedit ſecundã pu­<lb/>ta ſexquitertiam per proportionē ſexquioctauaꝫ <lb/>ſecunda autem excedit tertiam que eſt ſexquiquar­<lb/>ta per proportionem ſexquiquīdecimam / vt patet <lb/>ex quarta concluſione quarti capitis huiꝰ partis <lb/></s>
            <s xml:id="N157C7" xml:space="preserve">Modo ſexquioctaua ſexquiquindecima maior eſt / <lb/>vt conſtat. </s>
            <s xml:id="N157CC" xml:space="preserve">Probatur correlarium / et ſint quatuor <lb/>quãtitates equales ſiue continue ſiue diſcrete (in <lb/>idem redit) a.b.c.d. quarum ſecunda puta b. acqui­<lb/>rat ceteris quieſcentibus k. latitudinem ſupra ip-<lb/>ſum a. / ita <gap/>ta b. quantitas excedat a. quanti-<lb/>tatem per k. latitudinē: et deinde tertia quantitas <lb/>puta c. ceteris inuariatis eandem k. latitudinem <lb/>acquirat ſupra b. et poſtremo quarta quantitas <lb/>puta d. eandem k. latitudinem acquirat ſupra c. / <lb/>tunc dico /  in fine et poſt iſtorum quatuor diuerſa­<lb/>rum quantitatum equalium diuerſaꝝ latitudinū <lb/>acquiſitionē, proportio maxima puta ipſiꝰ b. ad a. <lb/>per maiorē ꝓportionē excedit ſecundã ꝓportionē <lb/>puta ipſius c. ad b. quã ipſa ꝓportio c. ad b. exce-<lb/>dit ꝓportionē minimã que videlicet eſt ipſiꝰ d. ad <lb/>c. </s>
            <s xml:id="N157EF" xml:space="preserve">Quod ſic ꝓbatur / et ſit ꝓportio ipſiꝰ b. ad ipſum <lb/>a.f. et ꝓportio ipſius c. ad b.m. et ꝓportio ipſius d. <lb/>ad c.n. ſit e. quantitas que habeat ad ipſã b. quã­<lb/>titatē ꝓportionē f. et h. altera quantitas que ha-<lb/>beat ad c. ꝓportionē m. quo poſito q2 ipſa e. quan­<lb/>titas maior eſt ipſa c. quantitate quia e. quantitas <lb/>maiorē ꝓportionē habet ad vnã tertiū vtpote ad <lb/>b. quantitatē quã c. quia ipſius e. ad b. eſt f. ꝓpor-<lb/>tio et ipſius c. ad .b. eſt m. ꝓportio minor f. ꝓporti-<lb/>one / vt patet diligenter intuenti: ſit igitur latitu-<lb/>do ſiue quantitas qua ipſa e. quantitas excedit c. <lb/>quantitatem p. et quia eadem ratione h. eſt maior <lb/>quantitas quam ipſum d. ſit exceſſus ipſius h. ſu-<lb/>pra d.q. </s>
            <s xml:id="N1580C" xml:space="preserve">Quibus poſitis ſic argumentor ꝓportio <lb/>f. excedit ꝓportionem m. per ꝓportionem que eſt <lb/>e. ad c. / vt patet ex primo correlario quarte conclu­             <cb chead="Capitulū octauū."/>             ſionis quarti capitis huius ſecunde partis et pro­<lb/>portio m. excedit proportionem n. per proportio-<lb/>nem h. ad d. eadem ratione et proportio e. ad c. eſt <lb/>maior quam proportio h. ad d. / igitur proportio <lb/>maxima puta ipſius b. ad a. que eſt f. ex hypotheſi <lb/>per maiorem proportionem excedit ſecundam pu­<lb/>ta ipſius c. ad b. que eſt m. quam ipſa proportio c. <lb/>ad b. excedit proportionem minimã / que videlicet <lb/>eſt ipſius d. ad c. puta n. / quod fuit probandum. </s>
            <s xml:id="N15826" xml:space="preserve">Cõ­<lb/>ſequētia eſt nota et ſimiliter maior: ſed minor pro-<lb/>batur / quia exceſſus ipſius e. ſupra ipſum c. eſt ma­<lb/>ior quam exceſſus ipſius h. ſupra ipſum d. et c. eſt <lb/>minus quam d. / vt patet ex caſu / igitur maior eſt ꝓ­<lb/>portio ipſius e. ad c. quaꝫ ipſius h. ad ipſum d. / qḋ <lb/>erat oſtendendum. </s>
            <s xml:id="N15835" xml:space="preserve">Conſequentia patet per hanc <lb/>maximam. </s>
            <s xml:id="N1583A" xml:space="preserve">Maior exceſſus additus minori, maio­<lb/>rem proportionem facit quam minor vel equalis <lb/>additꝰ maiori. </s>
            <s xml:id="N15841" xml:space="preserve">Que maxima clara euadit ex octa­<lb/>ua ſuppoſitione quarti capitis huius. </s>
            <s xml:id="N15846" xml:space="preserve">Et maior <lb/>probatur / et capio latitudinem reſultantem ex k. et <lb/>p. coniunctis qua quidē latitudine e. excedit ipſuꝫ <lb/>b. / vt patet aſpicienti caſum et latitudinē reſultan-<lb/>tē ex k. et q. coniūctis qua latitudine h. excedit ipſū <lb/>c. / et arguo ſic / latitudo .kp. maior eſt quaꝫ latitudo <lb/>kq. / ergo eodē cõmuni vel equali dempto ab vtra <lb/>puta k. id quod manet ex .kp. maiori puta p. maiꝰ <lb/>eſt quam id quod manet ex .kq. minori puta q. et p. <lb/>eſt exceſſus ipſius e. ſupra c. et q. eſt exceſſus ipſius <lb/>h. ſupra d. / vt dicit hypotheſis / igitur exceſſus ipſiꝰ <lb/>e. ſupra c. maior eſt ꝙ̄ exceſſus ipſius h. ſupra d. / qḋ <lb/>fuit probandum. </s>
            <s xml:id="N15861" xml:space="preserve">Conſequētia eſt manifeſta / et an-<lb/>tecedens arguitur videlicet /  latitudo .kp. maior <lb/>eſt quam latitudo .kq. quia latitudo .kp. maiorem <lb/>proportionem habet ad vnū tertium puta k. quaꝫ <lb/>latitudo kq. / igitur latitudo kp. maior eſt quã lati­<lb/>tudo kq. </s>
            <s xml:id="N1586E" xml:space="preserve">Conſequentia claret et antecedēs proba-<lb/>tur / quia latitudo kp. habet f. ꝓportionē ad ipſuꝫ <lb/>k. et latitudo .kq. habet m. proportionem ad idē k. <lb/>et f. proportio maior eſt proportione. m. / igitur la-<lb/>titudo .kp. maiorem proportionem habet ad vnū <lb/>tertium quam latitudo .kq. </s>
            <s xml:id="N1587B" xml:space="preserve">Cõſequentia patet cū <lb/>minore / et maior probatur et prius quo ad priorē <lb/>partem / quia iſte tres quantitates a. et b. et e. ſunt <lb/>continuo proportionabiles f. proportione / vt pa-<lb/>tet ex caſu: ergo inter exceſſum quo maxima illa-<lb/>rum quãtitatum excedit mediam, et exceſſum quo <lb/>media excedit minimam eſt f. proportio. </s>
            <s xml:id="N1588A" xml:space="preserve">Conſe-<lb/>quentia patet ex quinta concluſione ſecundi capi-<lb/>tis huius ſecunde partis: et exceſſus quo maxima <lb/>quantitas puta e. excedit mediam que eſt b. eſt la-<lb/>titudo .kp. et exceſſus quo media quantitas puta <lb/>b. excedit minimam vtpote a. eſt latitudo k. / igitur <lb/>latitudo .kp. habet f. proportionem ad ipſum .k. / <lb/>qḋ fuit ꝓbãdū. </s>
            <s xml:id="N1589B" xml:space="preserve">Et ſic ptꝫ prior pars. </s>
            <s xml:id="N1589E" xml:space="preserve">Et poſterior <lb/>probatur videlicet /  latitudo .kq. habet m. pro-<lb/>portionem ad idem k. / quia iſte tres quantitates <lb/>b.c.h. ſunt continuo proportionabiles m. propor­<lb/>tione: vt patet ex caſu: igitur inter exceſſum quo <lb/>maxima puta h. excedit mediam puta c. et exceſſuꝫ <lb/>quo media quantitas puta c. excedit minimam <lb/>puta b. eſt m. proportio: vt patet ex quinta conclu­<lb/>ſione preallegata: et exceſſus quo h. excedit c. eſt la­<lb/>titudo k.q. et exceſſus quo c. excedit b. eſt ipſum k. / <lb/>igitur latitudo .kq. habet m. proportionem ad ip­<lb/>ſum l2. / quod fuit probandum. </s>
            <s xml:id="N158B7" xml:space="preserve">Patet igitur poſte­<lb/>rior pars maioris et per conſequens totum corre-<lb/>larium.</s>
          </p>
          <div xml:id="N158BE" level="4" n="4" type="float">
            <note position="left" xlink:href="note-0055-02a" xlink:label="note-0055-02" xml:id="N158C2" xml:space="preserve">1. correl.</note>
            <note position="right" xlink:href="note-0055-03a" xlink:label="note-0055-03" xml:id="N158C8" xml:space="preserve">2. correl.</note>
            <note position="right" xlink:href="note-0055-04a" xlink:label="note-0055-04" xml:id="N158CE" xml:space="preserve">3. correl.</note>
            <note position="left" xlink:href="note-0056-01a" xlink:label="note-0056-01" xml:id="N158D4" xml:space="preserve">4. correĺ.</note>
          </div>
          <pb chead="Secunde partis" file="0057" n="57"/>
          <note position="left" xml:id="N158DE" xml:space="preserve">5. correĺ. <lb/>Calcu. de <lb/>lo. elo.</note>
          <p xml:id="N158E6">
            <s xml:id="N158E7" xml:space="preserve">¶ Hinc patet primum notabile calculatoris / quod <lb/>ponit in capitulo de loco elementi circa principiū <lb/>in ſecundo argumento ſub iſta forma. </s>
            <s xml:id="N158EE" xml:space="preserve">Si ſint qua­<lb/>tuor termini continuo proportionales arithme-<lb/>tice: proportio maxima que ſcilicet eſt inter termi­<lb/>nos duos minores eorum quatuor per plus exce-<lb/>dit ſecundam proportionem quam iſta ſecunda ex­<lb/>cedat tertiam que eſt minima illarum trium pro-<lb/>portionum que ſunt inter illos quatuor terminos</s>
          </p>
          <p xml:id="N158FD">
            <s xml:id="N158FE" xml:space="preserve">Sexta cõcluſio. </s>
            <s xml:id="N15901" xml:space="preserve">Quando aliqua pro­<lb/>portio diminuitur per decrementum termini ma-<lb/>ioris ſtante minore: tunc ꝓportio illa efficitur mi-<lb/>nor per eam proportionem per quam maior ter-<lb/>minus efficitur minor, ſiue per eam quam termi-<lb/>nus maior deperdit. </s>
            <s xml:id="N1590E" xml:space="preserve">Et quando aliq̈ proportio <lb/>efficitur minor per crementū minoris termini ſtã-<lb/>te maiore: tunc proportio inter illos terminos ef-<lb/>ficitur minor per proportione quam acquirit mi-<lb/>nor terminus ſiue per quam efficitur maior. </s>
            <s xml:id="N15919" xml:space="preserve">Exē-<lb/>plum / vt capta ꝓportione dupla bipedalis ad pe-<lb/>dale que efficiatur minor per decrementum bipe-<lb/>dalis ſtante pedali: proportio illa dupla efficitur <lb/>minor per proportionem quam deperdit bipeda-<lb/>le. </s>
            <s xml:id="N15926" xml:space="preserve">Sic exēplificabis de alia parte. </s>
            <s xml:id="N15929" xml:space="preserve">Probatur pri­<lb/>ma pars / ſit a.b. maior terminus: et c. minor inter <lb/>quos ſit proportio f. et deperdat a.b. proportionē <lb/>a.b. ad b. ſtante c. / tunc dico /  proportio illa f. effi-<lb/>citur minor per proportionem a.b. ad b. quã per-<lb/>dit terminus maior. </s>
            <s xml:id="N15936" xml:space="preserve">Quod probatur ſic / quia ãte <lb/>tale decrementum termini maioris: proportio a. <lb/>b. ad c. componitur ex proportione a.b. ad b. et b. <lb/>ad c: / et per tale decrementum termini maioris de-<lb/>mitur a b. illa proportione f. proportio a.b. ad b. / <lb/>igitur proportio illa f. efficitur minor per propor­<lb/>tionem a.b. ad b. / quod fuit probandum. </s>
            <s xml:id="N15945" xml:space="preserve">Et ſic ptꝫ <lb/>prima pars. </s>
            <s xml:id="N1594A" xml:space="preserve">Et eodem modo probabis ſecūdã. <lb/>             <anchor type="note" xlink:href="note-0057-01" xlink:label="note-0057-01a"/>             </s>
            <s xml:id="N15954" xml:space="preserve">¶ Ex quo ſequitur primo /  quando aliqua ꝓpor­<lb/>tio diminuitur per decremētum maioris termini <lb/>et crementum minoris: tunc talis proportio effici-<lb/>tur minor per proportionem compoſitam ex pro-<lb/>portiõe / quam deperdit maior terminus et ex pro-<lb/>portione quam acquirit minor. </s>
            <s xml:id="N15961" xml:space="preserve">Patet hoc corre-<lb/>larium facile ex dictis et concluſione.             <anchor type="note" xlink:href="note-0057-02" xlink:label="note-0057-02a"/>             </s>
            <s xml:id="N1596B" xml:space="preserve">¶ Sequitur <lb/>ſecūdo /  quando aliqua proportio maioris ine-<lb/>qualitatis diminuitur per crementū vtriuſ ter-<lb/>mini: ipſa efficitur minor per proportionem per <lb/>quam proportio acquiſita minori excedit propor­<lb/>tionem acquiſitam maiori. </s>
            <s xml:id="N15978" xml:space="preserve">Probatur / et ſit ꝓpor­<lb/>tio f. inter b. terminū maiorē et d. minorē et acqui-<lb/>rat b. terminus proportionē g. acquirando a. la-<lb/>titudinem ſupra ſe: et terminus d. acquirat ꝓpor-<lb/>tionem h. per acquiſitionem c. excedat propor-<lb/>tio acquiſita ipſi d. proportionem acquiſitã ipſi <lb/>b. per proportionem e. / tunc dico /  in fine talis cre­<lb/>menti illorum terminorum proportio inter illos <lb/>terminos a.b. et c.d. eſt minor proportiõe f. que eſt <lb/>inter b. et d. per proportionem e. per quã propor-<lb/>tio acquiſita termino minori excedit proportio-<lb/>nem acquiſitam termino maiori. </s>
            <s xml:id="N15991" xml:space="preserve">Quod ſit proba­<lb/>tur: quoniam ſi quando b. acquirit proportioneꝫ <lb/>g.d. acquireret tantaꝫ adequate: ſemꝑ inter illos <lb/>maneret eadem proportio / vt ſepius argutum eſt / <lb/>ſed modo terminus minor puta d. vltra illã pro-<lb/>portionem g. quam acquirit terminus maior ac-<lb/>quirit proportionem e, quieſcente maiori a.b. vl-<lb/>teriori acquiſitiõe / igitur illa proportio que eſt in <lb/>fine videlicet / a.b. ad c.d. efficitur minor per ꝓpor-<lb/>tionem per quã proportio acquiſita termino mi-             <cb chead="Capitulum octauū."/>             nori excedit proportionem acquiſitam termino <lb/>maiori / quod fuit probandum.             <anchor type="note" xlink:href="note-0057-03" xlink:label="note-0057-03a"/>             </s>
            <s xml:id="N159B0" xml:space="preserve">¶ Sequitur tertio / <lb/> quando aliqua proportio maioris inequalita­<lb/>tis diminuitur per vtriuſ eius termini decremē­<lb/>tum: talis proportio efficitur minor per propor-<lb/>tionem per quam proportio deperdita a maiori <lb/>termino excedit proportionem deperditam a mi-<lb/>nori. </s>
            <s xml:id="N159BF" xml:space="preserve">Probatur / ſit a.b.c. maior terminus d.e. mi-<lb/>nor inter quos ſit f. proportio: et deperdat termi-<lb/>nus maior proportionem que eſt a.b.c. ad c. et ter-<lb/>minus minor proportionē d.e. ad e. excedat pro­<lb/>portio deperdita a termino maiori proportionē <lb/>deperditam a termino minori per proportionem <lb/>h. que ſit b.c. ad c. / et tunc dico /  in fine talis decre-<lb/>menti proportio f. efficitur minor per proportio-<lb/>nem h. </s>
            <s xml:id="N159D2" xml:space="preserve">Quod ſic probatur / quia ſi quando d.e. <lb/>perdit proportionē d.e. ad e., a.b.c. perderet pro-<lb/>portionem a.b.c. ad b.c. / tunc inter tales terminos <lb/>adhuc manent f. proportio / vt ſepius probatū eſt: <lb/>ſed modo ipſe terminus maior a.b.c. vltra talem <lb/>proportionem perdit adhuc proportionem h. que <lb/>eſt b.c. ad c. / ergo per illam proportioneꝫ h. que eſt <lb/>b.c. ad c. illa proportio f. efficitur minor / quod fuit <lb/>probandum. </s>
            <s xml:id="N159E5" xml:space="preserve">Patet igitur correlarium.</s>
          </p>
          <div xml:id="N159E8" level="4" n="5" type="float">
            <note position="left" xlink:href="note-0057-01a" xlink:label="note-0057-01" xml:id="N159EC" xml:space="preserve">1. correĺ.</note>
            <note position="left" xlink:href="note-0057-02a" xlink:label="note-0057-02" xml:id="N159F2" xml:space="preserve">2. correĺ.</note>
            <note position="right" xlink:href="note-0057-03a" xlink:label="note-0057-03" xml:id="N159F8" xml:space="preserve">3. correĺ.</note>
          </div>
          <note position="right" xml:id="N159FE">
            <s xml:id="N15A00" xml:space="preserve">4. correĺ. <lb/></s>
            <s xml:id="N15A04" xml:space="preserve">Calcu. in <lb/>capite de <lb/>aug.</s>
          </note>
          <p xml:id="N15A0B">
            <s xml:id="N15A0C" xml:space="preserve">¶ Sequitur quarto /  ſi ſint duo proportionabi-<lb/>lia aliqua proportione maioris inequalitatis et <lb/>proportio inter illa minoratur per vtriuſ mino-<lb/>rationem: proportio deperdita a maiori erit ma-<lb/>ior proportione deperdita a minori per propor-<lb/>tionem per quam proportio inter maius et minus <lb/>fiet minor: hoc eſt per proportionem que deperdi-<lb/>tur inter maius et minus. </s>
            <s xml:id="N15A1D" xml:space="preserve">Probatur / ſit proportio <lb/>f. inter a. terminum maiorem et b. terminum mino­<lb/>rem et decreſcente tam a. quam b. efficiatur f. pro-<lb/>portio minor per proportionem h. / tunc dico /  h. <lb/>eſt proportio per quam proportio deperdita ab <lb/>a. termino maiore excedit proportionem deperdi­<lb/>tam a.b. termino minore. </s>
            <s xml:id="N15A2C" xml:space="preserve">Quod ſic ꝓbatur / quo-<lb/>niam quando aliqua proportio maioris inequa-<lb/>litatis minoratur. </s>
            <s xml:id="N15A33" xml:space="preserve">per decrementum vtriuſ ex-<lb/>tremi: ipſa efficitur minor per proportionem / per <lb/>quam proportio deperdita a maiore termino ex-<lb/>cedit proportionem deperditam a minori / vt patꝫ <lb/>ex anteriori correlario: ſed proportio f. que eſt a. <lb/>ad b. minoratur decreſcente vtro termino: ergo <lb/>ſequitur /  ipſa proportio f.a. ad b. efficitur mi-<lb/>nor per proportionē per quam proportio deper-<lb/>dita a termino maiori puta a. excedit proportio-<lb/>nem deperditam a minore puta b. ſed illa propor­<lb/>tio eſt h. ex hypotheſi: igitur proportio h. eſt pro-<lb/>portio per quam proportio deperdita a maiori <lb/>termino puta a. excedit proportionem deperditã <lb/>a minori puta b. / quod fuit probandum. </s>
            <s xml:id="N15A50" xml:space="preserve">Et hec eſt <lb/>quedam regula et ſuppoſitio quam calculator po­<lb/>nit in reſponſione ad argumentum / quod facit cõ-<lb/>tra duas vltimas concluſiões in capitulo de aug-<lb/>mentatione in opinione prima.</s>
          </p>
          <p xml:id="N15A5B">
            <s xml:id="N15A5C" xml:space="preserve">Septima concluſio. </s>
            <s xml:id="N15A5F" xml:space="preserve">Si aliqua quã-<lb/>titas maior creſcat reſpectu quantitatis minoris <lb/>non variate acquirendo ſupra ſe aliquã propor-<lb/>tionem: tantam proportionem acquirit ſupra nu­<lb/>merum minorem hoc eſt ſupra proportionem quã <lb/>habet ad numerum minorem quantam acquirit <lb/>ſupra ſe. </s>
            <s xml:id="N15A6E" xml:space="preserve">Et ſi quantitas maior manens maior re­<lb/>ſpectu quantitatis minoris inuariate deſcreſcat ſi­<lb/>ue perdat aliquam proportionem: quantam pro-<lb/>portionem deperdit a ſeipſa tantam deperdit re-<lb/>ſpectu quantitatis minoris: hoc eſt a proportiõe             <pb chead="Secunde partis" file="0058" n="58"/>             quam habet ad quantitatem minorem. </s>
            <s xml:id="N15A7E" xml:space="preserve">Exempluꝫ / <lb/>vt capta proportione que eſt .12. ad .8. volo /  nu-<lb/>merus maior puta .12. creſcat quouſ conſtituant <lb/>16. / tūc manifeſtū eſt /  numerus maior acquiſiuit <lb/>ſupra ſe proportionem ſexquitertiam: et tantam <lb/>acquiſiuit ꝓportio .12. ad .8. / vt conſtat. </s>
            <s xml:id="N15A8B" xml:space="preserve">In fine em̄ <lb/>illa componitur ex ſexquialtera et ſexquitertia. <lb/></s>
            <s xml:id="N15A91" xml:space="preserve">Si vero .12. diminuantur vſ ad .9. ſtantibus. <lb/>8. / tunc proportio .12. ad .8. deperdit proportio-<lb/>nē ſexquitertiam quam deperdit numerus maior. <lb/></s>
            <s xml:id="N15A99" xml:space="preserve">Prima pars huius concluſionis patet ex prima <lb/>parte quinte concluſionis: et ſecunda ex prima ſex­<lb/>te concluſionis huius. </s>
            <s xml:id="N15AA0" xml:space="preserve">¶ Ex quo ſequitur primo /  <lb/>ſi quantitas maior creſcat vel decreſcat manens <lb/>maior reſpectu quantitatis minoris inuariate: <lb/>tantam proportionem acquirit vel deperdit re-<lb/>ſpectu quantitatis minoris quantam reſpectu ſui <lb/></s>
            <s xml:id="N15AAC" xml:space="preserve">Patet ex concluſione.             <anchor type="note" xlink:href="note-0058-01" xlink:label="note-0058-01a"/>             </s>
            <s xml:id="N15AB4" xml:space="preserve">¶ Sequitur ſecundo /  ſi <lb/>quantitas maior creſcat vel decreſcat manēs ma­<lb/>ior reſpectu duarum quantitatum minorum ſiue <lb/>equalium ſiue inequalium: equalem propotionē <lb/>acquirit vel deperdit reſpectu vtriuſ quantita-<lb/>tis ipſis inuariatis manentibus. </s>
            <s xml:id="N15AC1" xml:space="preserve">Patet hoc cor-<lb/>relarium / quoniam aliquam proportionem acqui­<lb/>rit vel deperdit quantitas maior reſpectu ſui: et <lb/>quantãcun acquirit vel deperdit reſpectu ſui tã­<lb/>tam acquirit vel deperdit reſpectu cuiuſcun quã­<lb/>titatis minoris inuariate / vt patet ex priori: igitur <lb/>quantam acquirit vel deperdit reſpectu ſui tantū <lb/>reſpectu duarum quantitatum minorū ſiue equa-<lb/>lium ſiue inequalium / quod fuit probandum.</s>
          </p>
          <div xml:id="N15AD4" level="4" n="6" type="float">
            <note position="left" xlink:href="note-0058-01a" xlink:label="note-0058-01" xml:id="N15AD8" xml:space="preserve">1. correĺ.</note>
          </div>
          <p xml:id="N15ADE">
            <s xml:id="N15ADF" xml:space="preserve">Octaua concluſio. </s>
            <s xml:id="N15AE2" xml:space="preserve">Si quantitas mi­<lb/>nor creſcat reſpectu quantitatis maioris non va-<lb/>riate: quantam proportionem acquirit ſupra ſe <lb/>tantam deperdit quantitas maior reſpectu mino­<lb/>ris. </s>
            <s xml:id="N15AED" xml:space="preserve">Hoc eſt per tantam proportionem proportio <lb/>maioris quantitatis ad minorem efficitur minor. <lb/></s>
            <s xml:id="N15AF3" xml:space="preserve">Si vero quantitas minor decreſcat reſpectu ma-<lb/>ioris quantitatis inuariate: tantam proportionē <lb/>acquirit quãtitas maior ſupra minorem per quã­<lb/>tam ipſa minor fiet minor. </s>
            <s xml:id="N15AFC" xml:space="preserve">Hoc eſt proportio quã­<lb/>titatis maioris ad minorē efficitur maior per pro­<lb/>portionem quam deperdit quãtitas minor. </s>
            <s xml:id="N15B03" xml:space="preserve">Pri-<lb/>ma pars huius concluſionis patet ex ſecūda par-<lb/>te quinte cõcluſionis et ſecunda, ex ſecunda parte <lb/>ſexte concluſionis huius </s>
            <s xml:id="N15B0C" xml:space="preserve">¶ Ex quo ſequitur primo / <lb/> ſi quantitas minor creſcat vel decreſcat reſpe-<lb/>ctu maioris inuariate: tantam proportionem ac-<lb/>quirit vel deperdit proportio quantitatis maio-<lb/>ris ad minorē quãtam acquirit vel deperdit quã-<lb/>titas minor manens minor reſpectu ſui ipſius.</s>
          </p>
          <p xml:id="N15B19">
            <s xml:id="N15B1A" xml:space="preserve">Patet hec correlarium ex concluſione.             <anchor type="note" xlink:href="note-0058-02" xlink:label="note-0058-02a"/>             </s>
            <s xml:id="N15B22" xml:space="preserve">¶ Sequi-<lb/>tur ſecundo /  ſi quantitas minor creſcat vel de-<lb/>creſcat reſpectu duarum quantitatum maiorum <lb/>ſiue equalium ſiue inequalium: tantam proporti-<lb/>onem acquiret vel deperdet vna quantitas maior <lb/>reſpectu quantitatis minoris ſicut altera maior <lb/>reſpectu eiuſdem quãtitatis minoris. </s>
            <s xml:id="N15B31" xml:space="preserve">Patet hoc <lb/>correlarium / quia vtra illarum quantitatū ean­<lb/>dem proportionem acquiret vel deperdet: puta il­<lb/>lam quam acquirit vĺ deperdit quantitas minor / <lb/>vt patet ex concluſione             <anchor type="note" xlink:href="note-0058-03" xlink:label="note-0058-03a"/>             </s>
            <s xml:id="N15B41" xml:space="preserve">¶ Sequitur tertio /  ſi due <lb/>quãtitates maiores inequales eque velociter cre-<lb/>ſcant vĺ decreſcant reſpectu eiuſdem quantitatis <lb/>minoris inuariate: maiorem proportionē acqui-<lb/>rit vel deperdit minor illarum quantitatum ma-<lb/>iorum quam maior reſpectu eiuſdem quantitatis <lb/>minoris inuariate. </s>
            <s xml:id="N15B50" xml:space="preserve">Probatur / quoniam quanti-             <cb chead="Capitulū octauū."/>             tas minor maiorem proportioneꝫ acquirit ſupra <lb/>ſe aut deperdit reſpectu ſui quam maior illarum <lb/>quantitatum maiorum: igitur maiorem propor-<lb/>tionem acquirit vĺ deperdit reſpectu quantitatis <lb/>minoris inuariate minor illarum quantitatum <lb/>quam maior. </s>
            <s xml:id="N15B60" xml:space="preserve">Patet conſequentia ex primo corre­<lb/>lario ſeptime concluſionis / et antecedens patet ex <lb/>octaua ſuppoſitione quarti capitis huius partis <lb/>             <anchor type="note" xlink:href="note-0058-04" xlink:label="note-0058-04a"/>             </s>
            <s xml:id="N15B6E" xml:space="preserve">¶ Sequitur quarto /  ſi due quãtitates minores <lb/>inequales eque velociter creſcant vel decreſcant <lb/>reſpectu quantitatis vtra maioris inuariate: <lb/>maiorem proportionē acquirit vel deperdit quã-<lb/>titas illa maior reſpectu minoris quam reſpectu <lb/>maioris. </s>
            <s xml:id="N15B7B" xml:space="preserve">Hoc correlarium ex ſecundo correlario <lb/>huius concluſionis octaue iuncta octaua ſuppo-<lb/>ſitione quarti capitis preallegati ſuam demon-<lb/>ſtrationem ſortitur. </s>
            <s xml:id="N15B84" xml:space="preserve">¶ Sequitur quinto /  ſi due <lb/>quantitates maiores ſiue equales ſiue inequales <lb/>acquirant vel deperdant equales proportiones <lb/>ipſis tamen manentibus maioribus reſpectu du-<lb/>arum quantitatum minorum ſiue equalium ſiue <lb/>inequalium: vtra illarum equalem proportionē <lb/>acquirit vel deperdit reſpectu vtriuſ mīoris in-<lb/>uariate. </s>
            <s xml:id="N15B95" xml:space="preserve">Patet hoc correlarium / quoniam tantaꝫ <lb/>proportionem vtra illarum acquirit vel deper-<lb/>dit reſpectu vtriuſ minoris quantam reſpectu <lb/>ſui / vt patet ex primo correlario ſeptime concluſi-<lb/>onis / ſed equalem vtra illarum acquirit vel de-<lb/>perdit reſpectu ſui / igitur equalem reſpectu vtriuſ­<lb/> quantitatis minoris inuariate. </s>
            <s xml:id="N15BA4" xml:space="preserve">¶ Sequitur ſex­<lb/>to /  ſi due quantitates minores eque proportio-<lb/>nabiliter creſcant vel decreſcant reſpectu quanti-<lb/>tatum vtra maiorum: equalem proportionem <lb/>vtra illarum maiorum acquirit vel deperdit re-<lb/>ſpectu vtriuſ minoris. </s>
            <s xml:id="N15BB1" xml:space="preserve">Patet hoc correlarium <lb/>ex primo correlario huius octaue concluſionis.</s>
          </p>
          <div xml:id="N15BB6" level="4" n="7" type="float">
            <note position="left" xlink:href="note-0058-02a" xlink:label="note-0058-02" xml:id="N15BBA" xml:space="preserve">2. correĺ.</note>
            <note position="left" xlink:href="note-0058-03a" xlink:label="note-0058-03" xml:id="N15BC0" xml:space="preserve">3. correĺ.</note>
            <note position="right" xlink:href="note-0058-04a" xlink:label="note-0058-04" xml:id="N15BC6" xml:space="preserve">4. correĺ</note>
          </div>
          <p xml:id="N15BCC">
            <s xml:id="N15BCD" xml:space="preserve">¶ Multe alie cõcluſiones et correlaria ex his dua-<lb/>bus vltimis concluſionibus auxiliantibus ceteris <lb/>predictis poſſent facile induci ſed ſufficiãt iſte que <lb/>ordinãtur ad infendas regulas quas ponit calcu­<lb/>lator de motu locali </s>
            <s xml:id="N15BD8" xml:space="preserve">¶ Et hec de ſecunda parte hu­<lb/>ius operis: in qua ſi quid ex paruitate ingenii aut <lb/>defectu mathematice artis inculte aut rudi miner­<lb/>ua depromptū ſit: veniam peto. </s>
            <s xml:id="N15BE1" xml:space="preserve">Uix enim hec poſ-<lb/>ſunt leuigato ſermone exarari.             <anchor type="note" xlink:href="note-0058-05" xlink:label="note-0058-05a"/>             </s>
            <s xml:id="N15BEB" xml:space="preserve">Si vero quid lau-<lb/>ro dignum reperiatur: deo optimo maximo gra-<lb/>tie reddantur a quo omne datum optimum et om-<lb/>ne donum perfectum iacobi primo. </s>
            <s xml:id="N15BF4" xml:space="preserve">¶ Sequentem <lb/>vero partem in quatuor tractatus diſtribuam.</s>
          </p>
          <div xml:id="N15BF9" level="4" n="8" type="float">
            <note position="right" xlink:href="note-0058-05a" xlink:label="note-0058-05" xml:id="N15BFD" xml:space="preserve">Iacobi <lb/>primo.</note>
          </div>
          <p xml:id="N15C05">
            <s xml:id="N15C06" xml:space="preserve">Primus ad ſcribetur motui locali penes cauſam <lb/></s>
            <s xml:id="N15C0A" xml:space="preserve">Secundus motui locali penes effectum. </s>
            <s xml:id="N15C0D" xml:space="preserve">Tertius <lb/>motui rarefactionis at augmentatiõis. </s>
            <s xml:id="N15C12" xml:space="preserve">Quar-<lb/>tus autem motui alterationis.</s>
          </p>
        </div>
      </div>
      <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
        <p xml:id="N15C1C">
          <s xml:id="N15C1D" xml:space="preserve">Sequitur liber de triplici mo­<lb/>tu huius operis tertia pars</s>
        </p>
        <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
          <p xml:id="N15C27">
            <s xml:id="N15C28" xml:space="preserve">Tertie partis tractatus pri-<lb/>mus ī quo agitur de motu quo <lb/>ad cauſam.</s>
          </p>
          <div xml:id="N15C2F" level="4" n="1" type="chapter" type-free="capitulum">
            <pb chead="Primi partis" file="0059" n="59"/>
            <head xml:id="N15C38" xml:space="preserve">Capitulum primum / in quo ponitur <lb/>et improbatur vna opinio: de cauſa <lb/>velocitatis motus.</head>
            <p xml:id="N15C3F">
              <s xml:id="N15C40" xml:space="preserve">QUoniã errores elimi-<lb/>nãdi et extirpandi ſunt antea <lb/>̄ veritas inferatur: ideo pre-<lb/>mittūtur et improbantur falſe <lb/>opiniones more communiter <lb/>hanc tractantium materiam.</s>
            </p>
            <p xml:id="N15C4D">
              <s xml:id="N15C4E" xml:space="preserve">Prima opinio de velo­<lb/>citate motuum penes cauſam fuit aliquorum phi­<lb/>loſophorū dicentium velocitatem in motu atten-<lb/>di debere penes proportionem exceſſus potentia-<lb/>rum ſupra ſuas reſiſtētias: ita  ſi exceſſus vnius <lb/>potentie ſupra ſuam reſiſtentiaꝫ fuerit duplus ad <lb/>exceſſum alterius potentie ſupra ſuam reſiſtentiã <lb/>motus / ille erit duple velocitatis ad alium motuꝫ / <lb/>vt ſi .6. moueant .3 / et .4. moueant .2. / hoc eſt actiui-<lb/>tas vt .4. / quia exceſſus .6. ad .3. eſt ſexquialterus <lb/>ad exceſſum .4. ad .2. in ſexquialtero velocius .6. <lb/>mouebunt .3. ꝙ̄ .4.2. </s>
              <s xml:id="N15C67" xml:space="preserve">Et ſic conſequenter dicas in <lb/>aliis. </s>
              <s xml:id="N15C6C" xml:space="preserve">Hanc opinionem fundant eius factores in <lb/>verbo philoſophi primo celi et mundi capitulo de <lb/>infinito. </s>
              <s xml:id="N15C73" xml:space="preserve">inferentis velocitatem motuum penes ex­<lb/>cellentiã exceſſus: et in verbo commentatoris quar­<lb/>to phiſicorum cõmento .35. et .39. in quibus locis vi-<lb/>detur huic opinioni ſatis applaudere.</s>
            </p>
            <note position="left" xml:id="N15C7C" xml:space="preserve">Contra <lb/>primam <lb/>opinio-<lb/>nē inſtat̄̄</note>
            <p xml:id="N15C86">
              <s xml:id="N15C87" xml:space="preserve">Sed cõtra iſtam opinionē arguitur / <lb/>qui ſi illa eſſet vera / ſequeretur /  motus proueni-<lb/>tes ab equalibus proportionibus eſſent inequa-<lb/>les: ſed conſequens eſt falſum / igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N15C92" xml:space="preserve">Sequela probatur et volo /  potentia vt <lb/>8. moueat reſiſtentiam vt .4. et potentia vt .4. mo-<lb/>reſiſtentiaꝫ vt .2. / quo poſito arguitur ſic. </s>
              <s xml:id="N15C99" xml:space="preserve">Ille due <lb/>proportiones potentiarum ad reſiſtentias ſunt <lb/>equales cum vtra ſit dupla: et tamen vna illarū <lb/>puta .8. ad .4. velocius mouet ꝙ̄ altera igitur pro­<lb/>poſitum. </s>
              <s xml:id="N15CA4" xml:space="preserve">Minor probatur / quia exceſſus eſt maior / <lb/>igitur ſecundum opinionem velocitas eſt maior. <lb/></s>
              <s xml:id="N15CAA" xml:space="preserve">¶ Dices concedendo ſequelam: et negando falſi-<lb/>tatem conſequentis.</s>
            </p>
            <p xml:id="N15CAF">
              <s xml:id="N15CB0" xml:space="preserve">Sed contra / quia tunc ſequeretur  <lb/>aliquam duo mobilia mouerentur ab equalibꝰ pro­<lb/>portionibus: tamen vnum in duplo velocius mo-<lb/>ueretur altero / ſed conſequens eſt falſum / ergo il-<lb/>lud ex quo ſequitur. </s>
              <s xml:id="N15CBB" xml:space="preserve">Sequela probatur retento ſu­<lb/>periori caſu. </s>
              <s xml:id="N15CC0" xml:space="preserve">Nam potentia vt .8. mouebit reſiſtē-<lb/>tiam vt quatuor in duplo velocius ꝙ̄ potentia vt <lb/>quatuor moueat reſiſtentiaꝫ vt .2. quoniã exceſſus <lb/>eſt duplus / et tamen ille proportiões ſunt equales <lb/>igitur propoſitum.               <anchor type="note" xlink:href="note-0059-01" xlink:label="note-0059-01a"/>               </s>
              <s xml:id="N15CD0" xml:space="preserve">¶ Dices concedendo qnod in-<lb/>fertur: nec illud habes pro inconuenienti: īmo pro <lb/>ſequela opinionis.</s>
            </p>
            <div xml:id="N15CD7" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0059-01a" xlink:label="note-0059-01" xml:id="N15CDB" xml:space="preserve">Dicitur</note>
            </div>
            <note position="left" xml:id="N15CE1" xml:space="preserve">Replica</note>
            <p xml:id="N15CE5">
              <s xml:id="N15CE6" xml:space="preserve">Sed contra / quia tunc ſequeretur  <lb/>ſi aliqua potentia moueret aliquam reſiſtentiam <lb/>aliquali velocitate: medietas potentie non moue-<lb/>ret medietatē reſiſtentie tanta velocitate cõſequēs <lb/>eſt falſum: et contra philoſophum ſeptimo phiſi-<lb/>corum expreſſe ponentem oppoſitum / igitur illud <lb/>ex quo / ſequitur ſequela probatur et volo /  poten­<lb/>tia vt .8. moueat reſiſtentiam vt quatuor: deinde <lb/>medietas potentie vt octo puta .4. moueat medie-<lb/>tatē reſiſtentie puta duo quo poſito arguo ſic / po­<lb/>tentia vt octo in duplo plus excedit ſuam reſiſten­               <cb chead="Capitulum primū."/>               tiam ꝙ̄ medietas eius / que eſt vt quatuor excedat <lb/>medietatem ſue reſiſtentie / que eſt vt .2. cum vna ex-<lb/>cedat per quatuor et alia per .2. / igitur non tanta <lb/>velocitate medietas potentie mouet medietatem <lb/>reſiſtentie / quanta tota potentia mouet totam re-<lb/>ſiſtentiam / quod fuit inferendum.</s>
            </p>
            <note position="right" xml:id="N15D0A" xml:space="preserve">Cõfirma­<lb/>tio.</note>
            <p xml:id="N15D10">
              <s xml:id="N15D11" xml:space="preserve">¶ Et confirmatur / quia ſi opinio eſſet vera / ſeque-<lb/>retur /  ſi duo equi traherent duas nauas diuiſim <lb/>per vnã horam:  illi equi coniūcti traherent illas <lb/>duas naues coniūctim in duplo velocius: ſed con­<lb/>ſequens eſt contra experientiã / igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N15D1E" xml:space="preserve">Sequela ꝓbatur / quoniã ipſis coniūctis <lb/>exceſſus eſſet duplus ad exceſſum vtriuſ diuiſim / <lb/>igitur velocitas eſſet dupla: conſequentia patet ex <lb/>opinione. </s>
              <s xml:id="N15D27" xml:space="preserve">Sed antecedēs probatur / quia quando­<lb/>cun ſunt due proportiones equales: ſi minores <lb/>numeri vniantur et maiores ſimiliter / et fiat vna ꝓ­<lb/>portio: exceſſus in tali proportiõe eſſet duplus ad <lb/>exceſſum cuiuſlibet alterius. </s>
              <s xml:id="N15D32" xml:space="preserve">Exemplum / vt capta <lb/>proportiõe .4. ad .2. / et vna alia ſibi equali in eiſdē <lb/>terminis puta .4. ad .2. / deinde vniendo minores <lb/>numeros puta binarium cum binario et maiores <lb/>puta quaternarium cum quaternario: reſultabit <lb/>proportio dupla .8. ad .4. / et ibi numerus maior ex­<lb/>cedet minorem numerum duplo exceſſu ad exceſſū <lb/>aliarum proportionum / vt patet ad ſenſum. </s>
              <s xml:id="N15D43" xml:space="preserve">Aliud <lb/>exemplum: capiantur due proportiones ſexquial­<lb/>tere in eiſdem terminis: puta .6. ad .4. et .6. ad .4. / et <lb/>manifeſtum eſt /  exceſſus in talibus proportioni­<lb/>bus eſt binarius. </s>
              <s xml:id="N15D4E" xml:space="preserve">Et ſi vniantur numeri mino-<lb/>res et maiores reſultabit proportio .12. ad .8. / que <lb/>erit ſexquialtera: in qua maior numerꝰ excedit mi­<lb/>norē quaternario: et per cõſequens duplo exceſſus <lb/>ad aliū exceſſū et ſic infallibiliter īuenies in omni <lb/>ſpecie proportiones cuiuſcun generis fuerit: vt <lb/>patet abunde ex ſecūda parte in tertio correlario <lb/>tertie concluſionis quarti capitis.</s>
            </p>
            <note position="right" xml:id="N15D5F" xml:space="preserve">Cõfirma­<lb/>tio ſcḋa.</note>
            <p xml:id="N15D65">
              <s xml:id="N15D66" xml:space="preserve">¶ Confirmatur ſecundo / quoniam ſi poſitio eſſet <lb/>vera: ſequeretur /  capta vna libra plumbi ele-<lb/>uantis in rota mediam libram ex oppoſito per <lb/>aliquod ſpacium in aliquo tempore:  due libre <lb/>eleuarent vnam libram ex oppoſito in duplo mi-<lb/>nori tempore: et per conſequens in duplo velocius / <lb/>ſed hoc eſt manifeſte falſum: et contra experientiã <lb/>que ſatis facile haberi poteſt: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N15D79" xml:space="preserve">Sequela probatur / quia exceſſus eſſet du­<lb/>plus ad priorem exceſſum: puta exceſſus quo due <lb/>libre excedunt vnam libram / ad exceſſum quo vna <lb/>libra excedit mediam libram: vt in priori ↄ̨firma-<lb/>tione probatum eſt. </s>
              <s xml:id="N15D84" xml:space="preserve">¶ Et propter hoc relinquitur <lb/>hec opinio contraria experimento et rationi et ſen­<lb/>tentie paripatheticorum.</s>
            </p>
            <p xml:id="N15D8B">
              <s xml:id="N15D8C" xml:space="preserve">Ad fulcimentum autem predicte opi­<lb/>nionis que innititur auctoritatibus philoſophi <lb/>et cõmentatoris. </s>
              <s xml:id="N15D93" xml:space="preserve">Dicitur cõcedendo predictas au-<lb/>ctoritates: et negando conſequentiam: et ratio eſt: <lb/>quia cum philoſophus aut cõmentator dicunt ve-<lb/>locitatem motus ſequi exceſſum aut excellentiam <lb/>potentie motoris ſupra ſuam reſiſtentiam: intelli­<lb/>gitur per excellentiam ſiue exceſſum potentie mo-<lb/>toris ſupra ſuam reſiſtentiam exceſſus vnius pro-<lb/>portionis ſupra alteram ita  ſit ſenſus: quanto <lb/>vna ꝓportio excedit alteram tanto velocitas mo-<lb/>tus proueniens ab illa excedit velocitatem motus <lb/>prouenientem ab alia. </s>
              <s xml:id="N15DAA" xml:space="preserve">Et  iſta ſit intentio philo­<lb/>ſophi patet ex regula / quam ponit in ſeptimo phi­<lb/>ſicorū ſuperius allegata que (vt latius poſtea di-<lb/>citur) ſic intelligi debet. </s>
              <s xml:id="N15DB3" xml:space="preserve">Si aliqua virtus moueat               <pb chead="Primi partis" file="0060" n="60"/>               aliquod mobile / hoc eſt aliquam reſiſentiam ali-<lb/>quãta velocitate ſubdupla virtus mouet ſubdu-<lb/>plam reſiſtentiam equali velocitate: hoc eſt. </s>
              <s xml:id="N15DBF" xml:space="preserve">Si a-<lb/>liqua proportio maioris inequalitatis moueat <lb/>aliquam proportionē minoris inequalitatis ali-<lb/>qua velocitate: proportio equalis illi in minori-<lb/>bus terminis mouebit equali velocitate: quod la-<lb/>tius poſtea declarabitur.</s>
            </p>
          </div>
          <div xml:id="N15DCC" level="4" n="2" type="chapter" type-free="capitulum">
            <head xml:id="N15DD1" xml:space="preserve">Capitulum ſecundū / in quo recitantur <lb/>et improbantur ſecunda et tertia opinio-<lb/>nes. de cauſa velocitatis motuum.</head>
            <p xml:id="N15DD8">
              <s xml:id="N15DD9" xml:space="preserve">SEcunda opinio ponit velocita­<lb/>tem motus ſequi proportionem exceſſus <lb/>potentie motoris ad potentiã rei mote. <lb/></s>
              <s xml:id="N15DE1" xml:space="preserve">Et vult dicere hec opinio /  velocitas in motibus <lb/>ſequitur proportionem exceſſus actiuitatis moto­<lb/>ris ad actiuitatem rei mote. </s>
              <s xml:id="N15DE8" xml:space="preserve">Ita  ſi vnus motor <lb/>ita ſe habeat reſpectu ſui mobilis /  actiuitas eiꝰ <lb/>excedaṫ actiuitateꝫ mobilis per quatuor gradus / <lb/>et actiuitas alterius motoris excedat actiuitatem <lb/>ſui modilis per duos gradus:  tunc primus mo-<lb/>tor mouebit in duplo velocius ſecūdo. </s>
              <s xml:id="N15DF5" xml:space="preserve">Et iſta opi-<lb/>nio videtur coincidere cum prima dempto /  vna <lb/>comparat actiuitatem ad reſiſtentiã: et altera acti-<lb/>uitatem ad actiuitatem.</s>
            </p>
            <note position="left" xml:id="N15DFE" xml:space="preserve">Obiicit̄̄ <lb/>ſecunde <lb/>opinioni</note>
            <p xml:id="N15E06">
              <s xml:id="N15E07" xml:space="preserve">Sed contra hanc opinionem arguit̄̄ <lb/>ſic / quia ſi illa eſſet vera / ſequeretur /  aliquod mo-<lb/>uens ſucceſſiue moueret ſine reſiſtētia: īmo ita cito <lb/>cum reſiſtentia ſicut ſine reſiſtentia / ſed conſequēs <lb/>eſt falſum igitur, illud ex quo ſequitur: ſequela ꝓ-<lb/>batur et pono caſum /  ſit virtus: vt .8. agentis: et <lb/>virtus vt quatuor patientis in quo ſit reſiſtentia: <lb/>vt .2. / et ſit aliquod aliud paſſum in quo nulla ſit re­<lb/>ſiſtentia ſed dumtaxat actiuitas vt quatuor: quo <lb/>poſito arguitur ſic. </s>
              <s xml:id="N15E1C" xml:space="preserve">Agens vt .8. eque velociter a-<lb/>git in vtrū iſtorum paſſorum: cum proportiones <lb/>actiuitatum ſint equales: et tamen in vno paſſo a-<lb/>git cum reſiſtentia: et in alio ſine reſiſtentia igitur <lb/>propoſitum.</s>
            </p>
            <p xml:id="N15E27">
              <s xml:id="N15E28" xml:space="preserve">Tertia opinio eſt /  ponit velocitatē <lb/>in motu ſequi proportionem reſiſtentiarum inter <lb/>ſe: ita  ſi ſint duo agentia equalia: et moueãt du-<lb/>as reſiſtentias inequales: in quacun ꝓportione <lb/>vna reſiſtentia eſt minor alia in eadē proportione <lb/>velocius mouetur: vt ſi virtus vt octo moueat re-<lb/>ſiſtentiam: vt .4: et reſiſtentiam: vt .3. quia reſiſten-<lb/>tia: vt .3. eſt in ſexquitertio minor reſiſtentia: vt .4. <lb/>ideo virtus vt .8. in ſexquitertio velocius mouebit <lb/>reſiſtentiam vt .3. ꝙ̄ reſiſtentiam vt .4.</s>
            </p>
            <p xml:id="N15E3D">
              <s xml:id="N15E3E" xml:space="preserve">Sed contra iſtaꝫ opinionē arguitur <lb/>ſic. </s>
              <s xml:id="N15E43" xml:space="preserve">Supponendo /  ſi aliqua virtus puta vt .8. / ſuf­<lb/>ficiat mouere aliquod mobile aliquanta velocita­<lb/>te /  eadē virtus ſufficit mouere aliquod aliud mo­<lb/>bile in duplo tardius, et aliquod in triplo, et aliqḋ <lb/>in quadruplo, et ſic in infinitum. </s>
              <s xml:id="N15E4E" xml:space="preserve">Ita  ſi virtus vt <lb/>8. ſufficit mouere aliquod mobile in hora ꝑ leucã: <lb/>eadem virtus ſufficit mouere aliquod maius mo-<lb/>bile in hora per mediam leucam: et illamet virtus <lb/>ſufficit mouere aliquod maius in hora per tertiã <lb/>partem leuce: et aliquod aliud per quartaꝫ: et ſic in <lb/>infinitū. </s>
              <s xml:id="N15E5D" xml:space="preserve">quo poſito ſic arguitur / ſi opinio eſſet ve-<lb/>ra ſequeretur /  mouens vt .8. poſſet mouere quã-<lb/>tumcun mobile: ſed conſequens eſt falſum: quia <lb/>tunc eſſet infinite actiuitatis: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N15E68" xml:space="preserve">Sequela probatur: et pono /  mouens vt               <cb chead="Capitulū ſcḋm  tertiū."/>               8. moueat reſiſtentiam vt .4. per leucã in hora ade­<lb/>quate: quo poſito tale mouens poteſt mouere ali-<lb/>quod mobile in duplo tardius puta in hora per <lb/>mediam leucam, vt patet ex ſuppoſitione: et nõ ni­<lb/>ſi mobile vt .8. / vt patet ex opinione: quoniã ꝓpor-<lb/>tio velocitatem ſequitur ꝓportionem reſiſtentiaꝝ <lb/>ſed velocitas eſt ſubdupla: ergo reſiſtentia dupla <lb/></s>
              <s xml:id="N15E7B" xml:space="preserve">Itē aliquod mobile poteſt mouere illa virtus ſub-<lb/>tripla velocitate: vt patet ex ſuppoſitione: et non <lb/>niſi triple reſiſtentie / vt patet ex opinione: et ſic in <lb/>infinitum: igitur propoſitū. </s>
              <s xml:id="N15E84" xml:space="preserve">Et hec ſola ratio ſuffi­<lb/>cienter hanc opinionem deſtruit et elidit.</s>
            </p>
          </div>
          <div xml:id="N15E89" level="4" n="3" type="chapter" type-free="capitulum">
            <head xml:id="N15E8E" xml:space="preserve">Capitulum tertium / in quo ponitur <lb/>alia opinio et vera.</head>
            <p xml:id="N15E93">
              <s xml:id="N15E94" xml:space="preserve">QUarta opinio et vera eſt que <lb/>nūc cõmuniter tenetur: et ponit velocita-<lb/>tem motus ſequi ꝓportionē ꝓportionū <lb/>hoc eſt proportionē geometricã: vt ſi aliqua virtꝰ <lb/>moueat aliquã reſiſtentiã a proportione dupla: et <lb/>vna alia moueat eandē reſiſtentiam vel vnã aliaꝫ <lb/>(in idem reddit) a proportione quadrupla: talis <lb/>virtus mouēs a proportione quadrupla in eadeꝫ <lb/>proportione velocius mouet in qua proportione <lb/>quadrupla proportio duplam excedit: et quia ex-<lb/>cedit quadrupla duplam in proportione dupla, <lb/>vt ptꝫ ex ſexto capite ſecunde partis: ideo quadru­<lb/>pla proportio in duplo velocius mouet. </s>
              <s xml:id="N15EAF" xml:space="preserve">Et ſi ali-<lb/>qua virtus moueat aliquam reſiſtentiã a propor-<lb/>tione ſexquialtera: et alia mouet eandem reſiſten-<lb/>tiam in proportione tripla: tunc virtus mouens a <lb/>proportione tripla velocius mouet virtute mouē-<lb/>proportione ſexquialtera in ea proportione qua <lb/>tripla ſexquialteram exuperat: et quia talis ꝓpor­<lb/>tio que eſt inter triplam et ſexquialteram eſt irra-<lb/>tionalis: vt ex ſexto et ſeptimo capitibꝰ ſecūde par­<lb/>tis facile monſtratur: ideo nec ſpaciū pertranſitū <lb/>a ꝓportione tripla excedit ſpaciū pertranſitum a <lb/>proportione ſexquialtera in proportione aliqua <lb/>multiplici, nec ſuperparticulari, nec ſupraparti-<lb/>ente, nec multiplici ſuperparticulari, nec multipli­<lb/>ci ſuprapartiente, quod poſtea magis elucidabit̄̄ <lb/></s>
              <s xml:id="N15ECF" xml:space="preserve">Et pro fundamento et baſi huius opinionis pono <lb/>duas concluſiones.</s>
            </p>
            <p xml:id="N15ED4">
              <s xml:id="N15ED5" xml:space="preserve">Prima concluſio / velocitas motꝰ nec <lb/>penes proportionem exceſſus potentiarū ad inui-<lb/>cem, nec penes proportionem actiuitatū ad inuicē / <lb/>nec reſiſtentiarum inter ſe attenditur. </s>
              <s xml:id="N15EDE" xml:space="preserve">Probatur <lb/>hec concluſio ex hiis / que in ſuperioribus capitibꝰ <lb/>in impugnationibus triū opinionū dicta ſunt.</s>
            </p>
            <p xml:id="N15EE5">
              <s xml:id="N15EE6" xml:space="preserve">Secunda concluſio. </s>
              <s xml:id="N15EE9" xml:space="preserve">Uelocitas mo-<lb/>tuū ſequit̄̄ / et attendi hꝫ penes ꝓportionē propor-<lb/>tionū: ita  in quacū proportione vna ꝓportio <lb/>eſt maior aut mīor alia: ī eadē ꝓportiõe velocitas <lb/>maior aut minor euadet. </s>
              <s xml:id="N15EF4" xml:space="preserve">Et ſi fuerat proportio ꝓ­<lb/>portionū rationalis: rationales velocitates erūt <lb/>et ſi irrationalis: cõmenſurari nõ poterunt veloci-<lb/>tates taliū motuū. </s>
              <s xml:id="N15EFD" xml:space="preserve">Probatur hec concluſio ſic / de­<lb/>clarata per ſillogiſmum diuiſim eo ordine quo <lb/>eam paulus venetus inducit quoniã velocitas et <lb/>tarditas motus attendi habet penes ꝓportioneꝫ <lb/>exceſſiuū inter ſe, aut penes ꝓportionē actiuitatū <lb/>inter ſe, aut reſiſtentiarum, aut penes ꝓportiõe <lb/>ꝓportionū: ſed nõ penes .3. prima / vt ptꝫ ex ãterio-<lb/>ri cõcluſione. </s>
              <s xml:id="N15F0E" xml:space="preserve">igitur penes quartum / quod fuit pro­<lb/>bandum. </s>
              <s xml:id="N15F13" xml:space="preserve">Cõſequentia patet a ſufficienti diuiſiõe <lb/></s>
              <s xml:id="N15F17" xml:space="preserve">Nõ em̄ ymaginari valent aliqui alii modi ſaltem <lb/>um apparentia quibus attendi habet motuū ve-<lb/>ocitas et tarditas / igitur diuiſio ſufficiens.</s>
            </p>
            <pb chead="Primi partis" file="0061" n="61"/>
            <p xml:id="N15F22">
              <s xml:id="N15F23" xml:space="preserve">Sed pro maiori explanatione predi­<lb/>cte opiniones.               <anchor type="note" xlink:href="note-0061-01" xlink:label="note-0061-01a"/>               </s>
              <s xml:id="N15F2D" xml:space="preserve">Cõtra eã arguit̄̄. </s>
              <s xml:id="N15F30" xml:space="preserve">Primo ſic alique <lb/>due ꝓportiones in caſu ſunt equales / et tamen ve-<lb/>locitates ex eis prouenientes nõ ſunt equales / igr̄ <lb/>opinio falſa ꝓbatur antecedens / et volo /  ſit vnū <lb/>pedale terre graue vt .8. / et vnū ſemipedale graue <lb/>vt .4. / et duo aeres quoꝝ vnus ſit duplus ad alterū <lb/>in magnitudine / et maior ſit reſiſtentie vt .4. / et mi-<lb/>nor vt .2. / et moueat̄̄ terra grauitatis vt .4. per <lb/>aerem reſiſtentie vt .2. / quo poſito ſic arguo: iſte ꝓ-<lb/>portiones ſunt equales / vt patet / q2 vtra dupla <lb/>et tamen velocitates ex eis ꝓuniētes ſunt īequa-<lb/>leꝝ / igitur ꝓpoſitū maior eſt nota / et minor ꝓbatur / <lb/>et quero an diuiſio maioris aeris ſit maior diuiſi­<lb/>one minoris aut minor aut equalis: ſed nõ equa-<lb/>les q2 alias ſequeret̄̄ aerē maiorē et minorem eſſe <lb/>equales / vtra em̄ ꝓportio ſuū mediū diuidet to-<lb/>taliter / igitur erit maior aut minor / et per cõſequēs <lb/>tales diuiſiones erunt inequales / qḋ fuit ꝓbandū</s>
            </p>
            <div xml:id="N15F55" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0061-01a" xlink:label="note-0061-01" xml:id="N15F59" xml:space="preserve">Cõtra ve­<lb/>rã opini­<lb/>onē obii-<lb/>citur.</note>
            </div>
            <p xml:id="N15F65">
              <s xml:id="N15F66" xml:space="preserve">Reſpõdeo negãdo añs. </s>
              <s xml:id="N15F69" xml:space="preserve">Et ad ꝓbati­<lb/>onē admiſſo caſu dico ad punctū argumēti /  ille <lb/>diuiſiões totales erūt inequales / q2 forte vna erit <lb/>diuiſio vniꝰ leuce et alia dimidie leuce et cū infert̄̄ / <lb/>ergo velocitates erūt inequales / nego illã conſe-<lb/>quentiã / ſed bene ſequitur /  velocitates erūt ine-<lb/>quales quãtitatiue. </s>
              <s xml:id="N15F78" xml:space="preserve">Dupliciter autē cõtingit et ve-<lb/>locitates et reſiſtentias eſſe inequales puta quãti­<lb/>tatiue et qualitatiue. </s>
              <s xml:id="N15F7F" xml:space="preserve">Tūc em̄ velocitates ſūt equa­<lb/>les qualitatiue quãdo ab equalibus ꝓportionibꝰ <lb/>ꝓueniūt et reſiſtentie / tūc ſunt equales qualitatiue <lb/>quando equalē difficultatē faciūt potētie agenti: <lb/>ſed tūc ſunt equales quãtitatiue quãdo ſunt equa­<lb/>lis quãtitatis. </s>
              <s xml:id="N15F8C" xml:space="preserve">De hoc latius vide thomã brauar-<lb/>dīnū / qui hoc argumentum format in ſuo tractatu <lb/>proportionum penultimo capite.</s>
            </p>
            <p xml:id="N15F93">
              <s xml:id="N15F94" xml:space="preserve">Secūdo contra eandē opinionē ar-<lb/>guitur ſic / magnes eque velociter trahit ad ſe ma­<lb/>gnū ferrū et paruū ferrū et tamen ad magnū et ad <lb/>paruū / nõ habet equales ꝓportiões / igitur ab ine-<lb/>qualibꝰ ꝓportionibus equales effectus ꝓueniunt / <lb/>quod eſt cõtra opinionē antecedēs / ꝓbatur ꝑ expe­<lb/>rientiã nã capto magnete / et poſito prope illū fer-<lb/>ro alicuiꝰ quãtitatis ita  ferrū cõiungatur ei: et <lb/>poſtea moueatur magnes eque cito mouebit̄̄ fer-<lb/>rum ſicut magnes etiã ſi apponatur aliquod fer-<lb/>rum maius illo / quod tunc magnes ſufficiat attra­<lb/>here / et moueatur magnes eque velociter mouebi-<lb/>tur ferrū cum magnete / igitur propoſitū. </s>
              <s xml:id="N15FAF" xml:space="preserve">Omnia <lb/>iſta ex experientia haurire oportet.</s>
            </p>
            <p xml:id="N15FB4">
              <s xml:id="N15FB5" xml:space="preserve">¶ Et confirmatur / quia ſi in horolohio ſolarī .etc̈. <lb/>lari ponatur magnes taliter /  ſi circūgeretur in <lb/>circuitu: horologii eque cito acus ſiue ferrum exi-<lb/>ſtens intus / quo demonſtratur polus articus ſicut <lb/>magnes. </s>
              <s xml:id="N15FC0" xml:space="preserve">Et ſi maioretur ferrū dū tamen ſufficiet <lb/>moueri a magnete eque velociter mouebitur ſicut <lb/>magnes et ſicut mouebitur minus ferrū / igitur ꝓ-<lb/>poſitum videlicet /  eque velociter magnes mouet <lb/>magnū ferrū et paruū.               <anchor type="note" xlink:href="note-0061-02" xlink:label="note-0061-02a"/>               </s>
              <s xml:id="N15FD0" xml:space="preserve">¶ Reſpondet cõmentator <lb/>ſeptimo phiſicorū / cõmento quarto ad punctū ar-<lb/>gumentatiõis /  in argumento falſum ſupponit̄̄ <lb/>videlicet /  magnes moueat et attrahat ad ſe fer-<lb/>rum / ſed dicit ferrū mouere ad magnetem ex natu­<lb/>rali inclinatione ſicut mouetur ad locū naturalē / <lb/>hoc tñ ſit mediãte qualitate quadã ꝓducta ab ip̄o <lb/>gnete in iṗo ferro / et ſic negat̄̄ maior argumēti.</s>
            </p>
            <div xml:id="N15FE1" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0061-02a" xlink:label="note-0061-02" xml:id="N15FE5" xml:space="preserve">Cõmēta-<lb/>tor ſepti-<lb/>mo phi.</note>
            </div>
            <p xml:id="N15FEF">
              <s xml:id="N15FF0" xml:space="preserve">Sed cõtra hanc ſolutionem replicat               <cb chead="Capitulum tertiū."/>               brauardinus / quia ſi illud eſſet verum ſequeretur / <lb/> nõ ita velociter moueretur magnum ferrum ad <lb/>magnetem ſicut paruū, quod tamē eſt falſum: ſal-<lb/>tem vt ipſi opinantur. </s>
              <s xml:id="N15FFC" xml:space="preserve">Sequela tamen probatur / <lb/>quoniam citius valet magnes alterare magnum <lb/>ferrum ꝙ̄ paruum: igitur citius mouebitur fer-<lb/>rum paruum /  magnū ad magnete.               <anchor type="note" xlink:href="note-0061-03" xlink:label="note-0061-03a"/>               </s>
              <s xml:id="N1600A" xml:space="preserve">Huic reſpõ-<lb/>det brauardinus negando conſequentiam ſed ra-<lb/>tionē non aſſignat vel ſi cauſam aſſignat eam nõ <lb/>capio: et ideo reſpõdeo negando ſimiliter ſequelã <lb/></s>
              <s xml:id="N16014" xml:space="preserve">Et ad probationem nego illud quod aſſumis vide­<lb/>licet /  velocius magnes alterat paruum ferrum: <lb/>̄ magnum qm̄ in tali alteratione nulla eſt cõtra­<lb/>rietas nec magis reſiſtit magnum ferrum ꝙ̄ par-<lb/>uum / quare eque cito alterantur.</s>
            </p>
            <div xml:id="N1601F" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0061-03a" xlink:label="note-0061-03" xml:id="N16023" xml:space="preserve">Brauar-<lb/>dinus.</note>
            </div>
            <p xml:id="N1602B">
              <s xml:id="N1602C" xml:space="preserve">Sed contra / quia ſi ea que dicta ſunt <lb/>eſſent vera / ſequeretur /  quantūcun ferrum mo­<lb/>ueretur ad magnetem. </s>
              <s xml:id="N16033" xml:space="preserve">Item  maius ferrum al-<lb/>teratū a magnete velocius moueretur paruo fer-<lb/>ro: ſed vtrum iſtorum eſt falſum vt ratio et expe-<lb/>rientia docet igitur ſolutio nulla. </s>
              <s xml:id="N1603C" xml:space="preserve">Sequela tamē <lb/>quo ad primam partem deducitur quoniã ſi ma-<lb/>gnes non attrahat ferrum: et moueat ferrum: ſed <lb/>ipſum ferrum alteratum ad magnetem mouetur: <lb/>ſequitur /  ita bene mouebitur magnū ferrum ſi-<lb/>cut paruum cum tam paruū ꝙ̄ magnum habeant <lb/>naturales inclinationes: vt moueãtur ad magne-<lb/>tem. </s>
              <s xml:id="N1604D" xml:space="preserve">Sed ſequelū quo ad ſecundaꝫ partem probo <lb/>quoniã maior virtus eſt motiua in maiori ferro ̄ <lb/>in minori: ergo ſequitur /  ceteris paribus velo-<lb/>cius ex natura a propria mouetur vel ſaltem natuꝫ <lb/>eſt moueri ad quēcū locū ad quē naturaliṫ moue­<lb/>t̄̄: ſed ad magnetē mouet̄̄ naturaliṫ / igit̄̄ ꝓpoſitum</s>
            </p>
            <p xml:id="N1605A">
              <s xml:id="N1605B" xml:space="preserve">Reſpondeo negando ſequelaꝫ quo ad <lb/>vtram partem. </s>
              <s xml:id="N16060" xml:space="preserve">Et ad probationem dico /  ideo <lb/>quantūcun magnū ferrum non mouetur ad ma­<lb/>gnetem / quia ſemper in tali motu eſt aliqua reſiſtē­<lb/>tia ex parte grauitatis: et hoc dummodo magnes <lb/>non ſit deorſum et ferrum ſurſum: quoniã tunc mo­<lb/>ueret grauitas. </s>
              <s xml:id="N1606D" xml:space="preserve">Quare in iſto loco tali vtendum <lb/>cenſeo diſtinctione et ſuppoſitione. </s>
              <s xml:id="N16072" xml:space="preserve">Suppono em̄ / <lb/> ferrum non mouetur ad magnetē niſi mediante <lb/>qualitate producta a magnete inferro: et quanto <lb/>illa eſt intenſior tanto velocius ferrum mouet ſe-<lb/>met ipſum ad magnetem. </s>
              <s xml:id="N1607D" xml:space="preserve">Deinde ſit talis diſtin-<lb/>ctio: quia vel qualitas producta a magnete eſt e-<lb/>qualis in intenſione ipſi grauitati ipſius ferri: <lb/>aut eſt maioris intentionis aut minoris. </s>
              <s xml:id="N16086" xml:space="preserve">Si mino­<lb/>ris vel equalis: cum grauitas reſiſtat / vt dictuꝫ eſt <lb/>nulla tenus fiet motus cum equalitatis vel mino-<lb/>ris inequalitatis obſtet proportio: ſi vero eſt ma-<lb/>ioris intenſiõis ipſa qualitas qua a magnete fer­<lb/>rum alteratur ꝙ̄ ipſa grauitas ferri: impune fa-<lb/>tendum eſt ferrum ad magnetem moueri a ſeipſo</s>
            </p>
            <p xml:id="N16095">
              <s xml:id="N16096" xml:space="preserve">Sed contra quoniam iam ex hoc ſe-<lb/>quitur ferrum paruum / quod minoris grauitatis <lb/>eſt velocius ad magnetem moueri maiori ferro ce­<lb/>teris eque libratis / qnoniam proportio actiuita-<lb/>tis ad reſiſtentiam minoris ferri erit maior ꝓpor­<lb/>tione eiuſdem actiuitatis ad maiorem reſiſtentiã <lb/>eiuſdam ferri / ſed hoc eſt falſum igitur.</s>
            </p>
            <note position="right" xml:id="N160A5" xml:space="preserve">Cõtra cõ­<lb/>mēta.</note>
            <p xml:id="N160AB">
              <s xml:id="N160AC" xml:space="preserve">Rñdeo ↄ̨̨cedēdo / qḋ infert̄̄ q̇cq̇d dicat <lb/>mentator et alii </s>
              <s xml:id="N160B1" xml:space="preserve">Non enim occurit mihi aliꝰ ſol-<lb/>uendi modus. </s>
              <s xml:id="N160B6" xml:space="preserve">De hac materia vide brauardinuꝫ <lb/>preallegato loco et auctoreꝫ .6. inconuenientium <lb/>queſtione .3. in illo articulo / in quo dubitat nunq̇d               <pb chead="Primi tractatus" file="0062" n="62"/>               magnes ſufficiat ſibi ſuppoſitum ferrum altera-<lb/>re / vbi multa de virtute motiua magnetis ſubtili-<lb/>ter et calculatorie inquirit. </s>
              <s xml:id="N160C6" xml:space="preserve">Non tamen pretereū­<lb/>da cenſeo duo correlaria que thomas brauardi-<lb/>nus in hac materia perpulchre infert.               <anchor type="note" xlink:href="note-0062-01" xlink:label="note-0062-01a"/>               </s>
              <s xml:id="N160D2" xml:space="preserve">¶ Quorum <lb/>primum eſt /  ſi ſortes habeat in manu magneteꝫ <lb/>que ſufficiat alterare ferrum vnius libre: et eleue-<lb/>tur illud ferrum ad magnetem et coniungatur ei: <lb/>ita  tã magnes ꝙ̄ ferrū pendeat a manu ſortis: <lb/>non plus ponderat magnes ꝙ̄ magnes et ferrum <lb/>ſimul nec econtra. </s>
              <s xml:id="N160E1" xml:space="preserve">Huius ratio eſt quoniam ma-<lb/>gnes non attrahit ferrū ſed ferrū alteratū ſuapte <lb/>natura magnetem expedit.               <anchor type="note" xlink:href="note-0062-02" xlink:label="note-0062-02a"/>               </s>
              <s xml:id="N160ED" xml:space="preserve">¶ Secundum correla­<lb/>riū /  ſi in aliqua equilibra ſiue ſtatera ex vno la-<lb/>tere ponatur ſcutum: et ex alio ponatur pondꝰ ſcu­<lb/>ti factum ex magnete: et ſimul cum pondere pona­<lb/>tur aliquod ferrum quod magnes ille ſufficit alte­<lb/>rare / non plus ponderabit ferrum et pondus ſcu-<lb/>ti ꝙ̄ pondus ſcuti preciſe. </s>
              <s xml:id="N160FC" xml:space="preserve">Cuius ratio eſt quoniaꝫ <lb/>ſtatera non ſuſtinet ferrū ſed magnes. </s>
              <s xml:id="N16101" xml:space="preserve">Iſta tamen <lb/>correlaria vulgo afferunt admirationem.</s>
            </p>
            <div xml:id="N16106" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0062-01a" xlink:label="note-0062-01" xml:id="N1610A" xml:space="preserve">1. correl.</note>
              <note position="left" xlink:href="note-0062-02a" xlink:label="note-0062-02" xml:id="N16110" xml:space="preserve">2. correl.</note>
            </div>
          </div>
          <div xml:id="N16116" level="4" n="4" type="chapter" type-free="capitulum">
            <head xml:id="N1611B" xml:space="preserve">Quartum capitulum / in quo <lb/>ponunt̄̄ ſeptē regule de propor­<lb/>tionalitate motus quas ponit <lb/>philoſophus ſeptimo phiſico-<lb/>rum quas etiam in preſenti ca-<lb/>pite examinandas duxi.</head>
            <p xml:id="N16128">
              <s xml:id="N16129" xml:space="preserve">QUoniam philoſophi regulas <lb/>de comparabilitate motuum facile dã-<lb/>nãt: ideo nõ inconcinue hoc in loco eas <lb/>examinare decreuimus</s>
            </p>
            <p xml:id="N16132">
              <s xml:id="N16133" xml:space="preserve">Prima regula / ſi aliqua virtus ſiue <lb/>aliqua potentia moueat aliquod mobile per ali-<lb/>quod ſpacium in aliquo tempore: eadem potentia <lb/>mouebit medietatem illius mobilis per duplum <lb/>ſpacium in eodem tempore.</s>
            </p>
            <p xml:id="N1613E">
              <s xml:id="N1613F" xml:space="preserve">Secunda regula / ſi aliqua potentia <lb/>moueat aliquod mobile per aliquod ſpaciuꝫ ī ali <lb/>aliquo tempore eadem virtus mouebit medieta-<lb/>tem illius mobilis per idem ſpacium in ſubduplo <lb/>tempore. </s>
              <s xml:id="N1614A" xml:space="preserve">¶ Ex quibus regulis infertur talis regu­<lb/>la. </s>
              <s xml:id="N1614F" xml:space="preserve">Si aliqua potentia moueat aliquod mobile ꝑ <lb/>aliquod ſpacium in aliquo tempore: dupla virtꝰ <lb/>mouebit idem mobile per duplum ſpacium in eo­<lb/>dem tempore.</s>
            </p>
            <p xml:id="N16158">
              <s xml:id="N16159" xml:space="preserve">Tertia regula / ſi aliqua potentia mo­<lb/>ueat aliquod mobile per aliquod ſpacium in ali-<lb/>quo tempore: eadem potentia mouebit idem mo-<lb/>bile per medietatem illius ſpacii in ſubduplo tem­<lb/>pore.</s>
            </p>
            <p xml:id="N16164">
              <s xml:id="N16165" xml:space="preserve">Quarta regula / ſi aliqua potētia mo­<lb/>ueat aliquod mobile per aliquod ſpacium in ali-<lb/>quo tempore: medietas talis potētie mouebit me­<lb/>dtetatem mobilis per idem ſpacium in eodem tē-<lb/>pore.</s>
            </p>
            <p xml:id="N16170">
              <s xml:id="N16171" xml:space="preserve">Quinta regula / ſi aliqua potētia mo­<lb/>ueat aliquod mobile per aliquod ſpacium in ali-<lb/>quo tempore: non eſt neceſſe eandem potentiã mo­<lb/>uere duplum mobile per idem ſpacium in duplo <lb/>tempore.</s>
            </p>
            <p xml:id="N1617C">
              <s xml:id="N1617D" xml:space="preserve">Sexta regula / ſi aliqua potētia mo-<lb/>ueat aliquod mobile per aliquod ſpacium in ali-<lb/>quo tempore: non eſt neceſſe medietatem talis vir­<lb/>tutis mouere idem mobile in duplo tempore.</s>
            </p>
            <cb chead="Capitulum quartum"/>
            <p xml:id="N16188">
              <s xml:id="N16189" xml:space="preserve">Septima regule / ſi aliqua potentie <lb/>moueant aliqua mobilia per aliquod ſpacium in <lb/>aliquo tempore diuiſim: et eedem potentie coniun­<lb/>ctim mouebunt illa mobilia coniuncta per idem <lb/>ſpacium in aliquo eodem tempore. </s>
              <s xml:id="N16194" xml:space="preserve">¶ Sed ꝓ cla-<lb/>riori intelligentia harum regularum.</s>
            </p>
            <p xml:id="N16199">
              <s xml:id="N1619A" xml:space="preserve">Contra primã arguitur / ſi b. moueat <lb/>reſiſtentiam / vt quatuor medietas talis reſiſten-<lb/>tie non mouebitur a tali virtute per duplū ſpaciū <lb/>in eodem tempore: igitur. </s>
              <s xml:id="N161A3" xml:space="preserve">Añs probatur / quoniaꝫ <lb/>virtus vt ſex mouebit reſiſtentiam vt duo magis ̄ <lb/>ī duplo velocius / igitur nõ mouebit in eodē tēpore <lb/>per duplū ſpaciū adequate. </s>
              <s xml:id="N161AC" xml:space="preserve">Probatur ãtecedēs / <lb/>qm̄ ꝓportio .6. ad duo que eſt tripla excedit ꝓpor­<lb/>tionē ſexquialterã que eſt .6. ad .4. pluſ̄ in duplo / <lb/>igitur velocitas ab ea ꝓueniens eſt maior ꝙ̄ du-<lb/>pla reſpectu velocitatis ꝓuenientis a ꝓportione <lb/>ſexquialtera. </s>
              <s xml:id="N161B9" xml:space="preserve">Patet cõſequētia ex opinione quar­<lb/>ta quã ſuſtentamus. </s>
              <s xml:id="N161BE" xml:space="preserve">Sed antecedens ꝓbatur / quia <lb/>ꝓportio tripla adequate ex proportione dupla / et <lb/>ꝓportione ſexquialtera cõponitur / vt ptꝫ ex quar-<lb/>to capite ſecūde partis / et ille due ſunt inequales / <lb/>vt ptꝫ ex eodē quarto capite / ergo ad minorē illaꝝ <lb/>que eſt ſexquialtera ipſa proportio tripla eſt ma-<lb/>ior ꝙ̄ dupla / patet hec conſequentia ex ſexta ſup-<lb/>poſitione quarti capitis ſecunde partis.               <anchor type="note" xlink:href="note-0062-03" xlink:label="note-0062-03a"/>               </s>
              <s xml:id="N161D4" xml:space="preserve">¶ Dices <lb/>forte /  argumentū nõ concludit contra regulam. <lb/></s>
              <s xml:id="N161DA" xml:space="preserve">quoniã in regula non ponitur /  preciſe illa potē-<lb/>tia mouebit medietatem in duplo velocius: ſed di­<lb/>cit /  mouebit in duplo velociꝰ. </s>
              <s xml:id="N161E1" xml:space="preserve">Sed hoc nichil eſt <lb/>dicere quoniam eodē modo dixiſſet in ſexquialte-<lb/>ro velocius vel in ſexquitertio. </s>
              <s xml:id="N161E8" xml:space="preserve">Et ideo non ſatiſ-<lb/>cit. </s>
              <s xml:id="N161ED" xml:space="preserve">Item nec ſic intellecta regula eſt vera quoniaꝫ <lb/>ſi virtus / vt .12. moueat reſiſtentiaꝫ / vt quatuor ali­<lb/>qua velocitate eadeꝫ potentia non poterit medie­<lb/>tatem reſiſtentie / que eſt vt duo dupla velocitate <lb/>immo mouebit minus ꝙ̄ dupla velocitate / igit̄̄ re-<lb/>gula ſic intellecta falſa. </s>
              <s xml:id="N161FA" xml:space="preserve">Probatur antecedens / <lb/>quoniã virtus / vt .12. mouet reſiſtentiam / vt quatu-<lb/>or a proportione tripla et reſiſtentiam / vt duo a ꝓ­<lb/>pprtione ſextupla modo proportio ſextupla ē mi­<lb/>nor ꝙ̄ dupla reſpectu triple / igitur non mouet ī du­<lb/>plo velocius. </s>
              <s xml:id="N16207" xml:space="preserve">Patet conſequentia ex opinione / et <lb/>arguitur antecedens quoniã ſextupla cõponitur <lb/>ex tripla et dupla adequate / vt patet ex quarto ca­<lb/>pite preallegato / et tripla eſt maior dupla: vt pa-<lb/>tet ex eodem capite / igitur ipſa ſextupla eſt minor <lb/>̄ dupla reſpectu triple. </s>
              <s xml:id="N16214" xml:space="preserve">patet conſequentia ex ſex­<lb/>ta ſuppoſitione eiuſdem capitis</s>
            </p>
            <div xml:id="N16219" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0062-03a" xlink:label="note-0062-03" xml:id="N1621D" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N16223">
              <s xml:id="N16224" xml:space="preserve">Sed contra illam regulam quam in­<lb/>tuli ex duabus primis arguitur ſic. </s>
              <s xml:id="N16229" xml:space="preserve">Aliqua poten­<lb/>tia mouet aliquam reſiſtentiam aliquanta velo-<lb/>citate: et tamen ipſa duplicata non mouet in du-<lb/>plo velocius eandem reſiſtentiam: igit̄̄ regula fal­<lb/>ſa. </s>
              <s xml:id="N16234" xml:space="preserve">Probatur antedens et volo /  aliqua poten-<lb/>tia moueat reſiſtentiam a proportione ſexquial-<lb/>tera qualis eſt .6. ad .4. aliquanta velocitate. </s>
              <s xml:id="N1623B" xml:space="preserve">quo <lb/>poſito ipſa potentia duplata / que erit vt .12. mo-<lb/>uebit reſiſtentiam vt .4. pluſ̄ in duplo velocius. <lb/></s>
              <s xml:id="N16243" xml:space="preserve">igitur aſſumptum verum. </s>
              <s xml:id="N16246" xml:space="preserve">Probatur antecendens / <lb/>quoniã .12. ad .4. eſt proportio tripla modo tripla <lb/>maior ꝙ̄ dupla eſt ad ſexquialteram / vt probatuꝫ <lb/>eſt in primo argumento / igitur velocitas ab ea ꝓ-<lb/>ueniens maior ꝙ̄ dupla eſt ad proportionem ſex-<lb/>quialteram.</s>
            </p>
            <p xml:id="N16253">
              <s xml:id="N16254" xml:space="preserve">Tertio arguitur contra quintam re­<lb/>gulam / quoniã ſi potentia vt octo moueat reſiſten­               <pb chead="Primi tractatus" file="0063" n="63"/>               tiam vt .2. aliquanta velocitate neceſſe eſt eandem <lb/>potentiam vt octo natam eſſe mouere duplam re-<lb/>ſiſtentiaꝫ in ſubdupla velocitate. </s>
              <s xml:id="N16262" xml:space="preserve">et potentia vt .8 <lb/>eſt aliqua potentia: et reſiſtentia vt duo aliqua re­<lb/>ſiſtentia: igitur. </s>
              <s xml:id="N16269" xml:space="preserve">Si aliqua potētia moueat aliquã <lb/>reſiſtentiã in aliquo tempore ali̄ta velocitate: ea­<lb/>dem mouebit duplam reſiſtentiã in ſubdupla ve-<lb/>locitate / quod eſt oppoſitum regule. </s>
              <s xml:id="N16272" xml:space="preserve">Patet hec cõ­<lb/>ſequentia ab inferiori ad ſuuꝫ ſuperius.</s>
            </p>
            <p xml:id="N16277">
              <s xml:id="N16278" xml:space="preserve">Quarto contra ſeptimam arguitur <lb/>ſic / quoniã ſi potētia vt ſex moueat reſiſtentiaꝫ vt <lb/>quatuor et potentia vt .8. moueat reſiſtentiã etiaꝫ <lb/>vt .4. diuiſim ille potentie coniuncte non mouebūt <lb/>eaſdem potentias coniunctas in duplo velocius. <lb/></s>
              <s xml:id="N16284" xml:space="preserve">igitur regula falſa. </s>
              <s xml:id="N16287" xml:space="preserve">Probatur antecendens / quoni­<lb/>am proportio reſultans ex illis duabus potētiis <lb/>ſimul ſumptis et duabus reſiſtentiis etiam ſimul <lb/>ſumptis eſt proportio .14. ad .8. que eſt minor du-<lb/>pla. eſt enim proportio ſupertripartiēs quartas. <lb/></s>
              <s xml:id="N16293" xml:space="preserve">Modo illa eſt minor dupla / vt ptꝫ ex tertia ſuppo­<lb/>ſitiõe ſuperiꝰ allegati q̈rti capitis / g̊ ſequit̄̄ /  nõ <lb/>eque velociter manebit talis proportio ſicut ãtea <lb/>mouebat dupla que eſt .8. ad .4.</s>
            </p>
            <p xml:id="N1629C">
              <s xml:id="N1629D" xml:space="preserve">Ad iſta reſpondetur ꝑ ordinē ad pri-<lb/>ma duo argumenta reſpondet paulus venetus et <lb/>brauardinus  ille regule philoſophi intelligun­<lb/>tur preciſe de proportione dupla: modo inſtantie <lb/>fuerunt adducte in alia ſpecie proportionis </s>
              <s xml:id="N162A8" xml:space="preserve">¶ Ad <lb/>tertium reſpondeo /  non eſt ad propoſitum ma-<lb/>terie non valet eni3 conſequentia ab inferiori ad <lb/>ſuum ſuperius cum dictione illatiua. </s>
              <s xml:id="N162B1" xml:space="preserve">Adduxi ta-<lb/>men illud argumentum / qm̄ ſemper tenet in pro-<lb/>portione quadrupla. </s>
              <s xml:id="N162B8" xml:space="preserve">¶ Ad quartuꝫ reſpondeo /  <lb/>regula philoſophi ſeptima intelligitur dūmodo <lb/>ille proportiões ſint equales. </s>
              <s xml:id="N162BF" xml:space="preserve">Que aūt ſunt equa­<lb/>les patet ex tertia ſuppoſitione quarti capitis ſe­<lb/>cunde partis. </s>
              <s xml:id="N162C6" xml:space="preserve">Sed quia ex ſolutione quã dat bra-<lb/>uardinus ad primū argumentū / ſequitur philoſo­<lb/>phum poſuiſſe regulas ſatis inſufficientes: que p̄­<lb/>ciſe in vna ſpecie proportionis tenerent.               <anchor type="note" xlink:href="note-0063-01" xlink:label="note-0063-01a"/>               </s>
              <s xml:id="N162D4" xml:space="preserve">Ideo di­<lb/>co aliter /  philoſophus capit potentiaꝫ pro pro­<lb/>portione maioris inequalitatis. </s>
              <s xml:id="N162DB" xml:space="preserve">Et iſto modo ca-<lb/>piendo regule habēt veritatem in omni genere ꝓ­<lb/>protionum. </s>
              <s xml:id="N162E2" xml:space="preserve">Et argumentum nichil concludit / qm̄ <lb/>oportet quando duplatur potentia duplare pro-<lb/>portionem: et non curare de potentia: ita  ſit ſen­<lb/>ſus prime regule ſi aliqua potētia moueat aliquã <lb/>reſiſtentiã per aliquod ſpacium in aliquo tempo-<lb/>re etc. eadem mouebit ſubduplam reſiſtentiam etc. <lb/>id eſt ſi aliqua virtus moueat aliquã reſiſtentiam <lb/>ab aliqua proportione eadem virtus mouebit re-<lb/>ſiſtentiam ad quam habet proportionem duplaꝫ <lb/>ad aliam proportionem .i. ad quam habet ꝓpor-<lb/>tionē duplicatã in duplo velocius. </s>
              <s xml:id="N162F9" xml:space="preserve">Et ſenſus huiꝰ <lb/>regule eſt ſi aliqua potentia moueat aliquam reſi­<lb/>ſtentiam in aliquo tempore etc. dupla virtus mo-<lb/>uebit eandem reſiſtentiam in duplo velocius hoc ē <lb/>ſi aliqua virtus moueat aliquam reſiſtentiam ab <lb/>aliqua proportione: dupla proportio mouebit in <lb/>duplo velocius. </s>
              <s xml:id="N16308" xml:space="preserve">Et ſic intelliguntur alie regule.</s>
            </p>
            <div xml:id="N1630B" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0063-01a" xlink:label="note-0063-01" xml:id="N1630F" xml:space="preserve">Qūo in-<lb/>telligunt̄̄ <lb/>regule <lb/>phī.</note>
            </div>
            <note position="left" xml:id="N1631B" xml:space="preserve">1. correl.</note>
            <p xml:id="N1631F">
              <s xml:id="N16320" xml:space="preserve">¶ Ex quo ſequitur /  ſi virtus ſe habens ad aliquã <lb/>reſiſtentiam in proportione irrationali diametri <lb/>ad coſtam moueat ali̄tum velociter: proportio <lb/>dupla ad eandē reſiſtentiã mouebit in duplo velo­<lb/>cius.               <anchor type="note" xlink:href="note-0063-02" xlink:label="note-0063-02a"/>               </s>
              <s xml:id="N16330" xml:space="preserve">¶ Secundo igitur /  non oportet q̄rere in q̈-<lb/>libet proportione proportionem rationalem ī du­<lb/>plo tardius mouentem eam reſiſtentiam: ſed ſa-<lb/>tis eſt /  detur ꝓportio rationalis vel irrationa-               <cb chead="Capitulum quintum"/>               lis. </s>
              <s xml:id="N1633C" xml:space="preserve">et hec de regulis philoſophi.</s>
            </p>
            <div xml:id="N1633F" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0063-02a" xlink:label="note-0063-02" xml:id="N16343" xml:space="preserve">2. correl.</note>
            </div>
          </div>
          <div xml:id="N16349" level="4" n="5" type="chapter" type-free="capitulum">
            <head xml:id="N1634E" xml:space="preserve">Capitulum quintum / in quo ponuntur <lb/>regule ſiue concluſiones velocitatis et tar­<lb/>ditatis motus penes proportionem pro­<lb/>portionum conformiter ad intentionem <lb/>calculatoris.</head>
            <p xml:id="N16359">
              <s xml:id="N1635A" xml:space="preserve">AD inducendas ſeriatim ma­<lb/>thematico more concluſiones docētes <lb/>velocitatem et tarditatē motus penes <lb/>cauſam iuxta opinionem quartam ſit.</s>
            </p>
            <p xml:id="N16363">
              <s xml:id="N16364" xml:space="preserve">Prima ſuppoſitio / ab equalibus pro­<lb/>portionibus equales velocitates proueniunt: et ab <lb/>inequalibus inequales. </s>
              <s xml:id="N1636B" xml:space="preserve">et a rationalibus rationa­<lb/>les: et ab incõmēſurabilibus īcõmēſurabiles </s>
              <s xml:id="N16370" xml:space="preserve">Pa­<lb/>tet hec ſuppoſitio ex opinione que ponit velocita­<lb/>tem ſequi proportionem ꝓproportionum.</s>
            </p>
            <p xml:id="N16377">
              <s xml:id="N16378" xml:space="preserve">Secundua ſuppoſitio ab equalibꝰ pro­<lb/>portionibus que ſunt partes aliarum proportio­<lb/>num ſiue equalium ſiue inequalium equales velo­<lb/>citates proueniunt. </s>
              <s xml:id="N16381" xml:space="preserve">Declaro hanc ſuppoſitionem <lb/>et capio proportionem triplam et duplam: et ma­<lb/>nifeſtum eſt:  vtriuſ proportio ſexquialtera eſt <lb/>pars. </s>
              <s xml:id="N1638A" xml:space="preserve">dico tunc /  quãtam velocitatē producit ſex­<lb/>quialtera que eſt pars duple tantam velocitatem <lb/>ꝓducit ſexquialtera que eſt pars triple. </s>
              <s xml:id="N16391" xml:space="preserve">Proba-<lb/>tur ex priori ſuppoſitione / quia ſexquialtera que <lb/>eſt pars duple et ſexquialtera que eſt pars triple <lb/>ſunt equales proportiones.</s>
            </p>
            <p xml:id="N1639A">
              <s xml:id="N1639B" xml:space="preserve">Tertia ſuppoſitio / ꝑ additionē equa­<lb/>lium proportionum ſuper proportiones equales <lb/>vel inequales: velocitates equaliter intenduntur <lb/></s>
              <s xml:id="N163A3" xml:space="preserve">Declaro hoc in terminis et capio proportionem <lb/>duplam et quadruplam / et volo /  vtri addatur <lb/>proportio ſexquialtera: qua addita dico /  equa­<lb/>liter intendunt proportiones ille ſiue ille potentie <lb/>motū ſuum intendunt / et tantam velocitatem acq̇-<lb/>rit proportio maior ſicut et minor ſupra velocita­<lb/>tem habitam ante additionem proportionis ſexq̇­<lb/>altere. </s>
              <s xml:id="N163B4" xml:space="preserve">Probatur hec ſuppoſitio ex ſecūda / quia il­<lb/>la proportio ſexquialtera efficitur pars duaꝝ ꝓ-<lb/>portionum inequalium / igitur cum vtra equalē <lb/>velocitatem producet.</s>
            </p>
            <p xml:id="N163BD">
              <s xml:id="N163BE" xml:space="preserve">Quarta ſuppoſitio / ꝑ decremētū dua­<lb/>rum proportionū equalium que ſunt partes dua­<lb/>rum proportionū ſiue equalium ſiue inequalium: <lb/>equales velocitates perdētur. </s>
              <s xml:id="N163C7" xml:space="preserve">¶ Declarat̄̄ hec ſup­<lb/>poſitio et capio proportionem duplam et triplaꝫ / <lb/>et volo /  vtra deperdat proportionem ſexqui-<lb/>alterã / tunc dico /  ſi proportio dupla ꝑdat duos <lb/>gradus velocitatis etiam duos adequate perdit <lb/>proportio tripla. </s>
              <s xml:id="N163D4" xml:space="preserve">Patet hec ſuppoſitio ex priori / <lb/>quoniam ille due proportiones deperdite cū eēnt <lb/>equales: equalē velocitatem producebant: igitur <lb/>per decrementum illarum equales velocitates ꝑ-<lb/>duntur / quia perduntur ipſemet quas ipſe produ­<lb/>cebant.</s>
            </p>
            <p xml:id="N163E1">
              <s xml:id="N163E2" xml:space="preserve">Quinta ſpupoſitio / ꝑ additionē equa­<lb/>lis ̄titatis maiori et minori ̄titati maior ꝓpor­<lb/>tio acquiritur minori ̄titati ꝙ̄ maiori. </s>
              <s xml:id="N163E9" xml:space="preserve">¶ Hec eſt <lb/>octaua ſuppoſitio quarti capitis ſecunde partis.</s>
            </p>
            <p xml:id="N163EE">
              <s xml:id="N163EF" xml:space="preserve">Sexta ſuppoſitio eq̄ velociṫ intēde­<lb/>re motum: eſt in equali tempore equales ꝑtes ade­<lb/>quate acquirere: et eque proportionabiliter intē-<lb/>dere eſt in equali tempore equales proportiones <lb/>acquirere: </s>
              <s xml:id="N163FA" xml:space="preserve">Et ſimiliter dicendum eſt de eque velo-<lb/>citer remittere et eque proportionabiliter / vt ſi nu­               <pb chead="Primi tractatus" file="0064" n="64"/>               merus ſenarius aequirit binarium et numerꝰ qui­<lb/>narius in eodem tempore etiam binariuꝫ: dico /  <lb/>eque velociter intenduntur ſed non eque ꝓportio-<lb/>nabiliter ſed ſi numerus ternarius acquirat vni-<lb/>tatem et numerus ſenarius acquirat in eodem tē-<lb/>pore dualitatem: dico /  tunc eque proportionabi­<lb/>liter acquirunt et non eque velociter. </s>
              <s xml:id="N16410" xml:space="preserve">quoniam tã­<lb/>ternarius numerus quam ſenarius ꝓportionem <lb/>ſexquitertiaꝫ acquirit / vt facile eſt intueri. </s>
              <s xml:id="N16417" xml:space="preserve">Hec dif­<lb/>finitio eſt.</s>
            </p>
            <p xml:id="N1641C">
              <s xml:id="N1641D" xml:space="preserve">His ſuppoſitis p̄miſſis ſit prima con­<lb/>cluſio. </s>
              <s xml:id="N16422" xml:space="preserve">Si aliqua potentia creſcit reſpectu reſiſtē-<lb/>tie non variate: tantam proportioneꝫ acquirit ſu­<lb/>pra ſe quantam ſupra ſuam reſiſtentiam et eocon­<lb/>tra: </s>
              <s xml:id="N1642B" xml:space="preserve">Probatur hec concluſio auxiliante ſeptima <lb/>concluſione octaui capitis precedentis partis.</s>
            </p>
            <p xml:id="N16430">
              <s xml:id="N16431" xml:space="preserve">Nam potentia ſe habet vt quantitas maior et re-<lb/>ſiſtentia vt minor ſi actiuitas ꝓdeat.</s>
            </p>
            <p xml:id="N16436">
              <s xml:id="N16437" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N1643A" xml:space="preserve">Si aliqua vir-<lb/>tus decreſcat reſpectu reſiſtentie non variate. </s>
              <s xml:id="N1643F" xml:space="preserve">tan­<lb/>tam proportionem deperdit reſpectu ſue reſiſten­<lb/>tie quantam reſpectu ſui ipſius. </s>
              <s xml:id="N16446" xml:space="preserve">vt capta potentia <lb/>vt .4. et reſiſtentia vt .2. ſi potentia / vt quatuor effi­<lb/>ciatur in ſexquitertio minor perdendo vnitatem <lb/>ſiue proportionem ſexquitertiam: eandem ꝓpor-<lb/>tionem ſexquitertiam perdit reſpectu ſue reſiſten­<lb/>tie vt duo. </s>
              <s xml:id="N16453" xml:space="preserve">Probatur hec concluſio ex ſeptima cõ­<lb/>cluſione i capitis preallegata eo modo quo <lb/>prior.</s>
            </p>
            <p xml:id="N1645A">
              <s xml:id="N1645B" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N1645E" xml:space="preserve">Si aliqua reſiſtē-<lb/>tia creſcat vel decreſcat reſpectu potentie non va­<lb/>riate: tantam proportionem acquiret vel deper-<lb/>det reſpectu ſui ipſius quantam acquiret vel deꝑ-<lb/>det reſpectu talis potentie. </s>
              <s xml:id="N16469" xml:space="preserve">Hoc eſt: tantam acqui­<lb/>rit vel deperdit talis potentia reſpectu eiuſdeꝫ re­<lb/>ſiſtentie. </s>
              <s xml:id="N16470" xml:space="preserve">Patet hec concluſio ex octaua concluſio­<lb/>ne octaui capitis p̄allegati et ſuo prīo correlario</s>
            </p>
            <p xml:id="N16475">
              <s xml:id="N16476" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N16479" xml:space="preserve">Si potētia creſ-<lb/>cat vel decreſcat reſpectu potentie non variate: tã­<lb/>tam proportionem acquirit vel deperdit reſpectu <lb/>ſue reſiſtentie qnantam acquirit vel deperdit reſ­<lb/>pectu ſui ipſius. </s>
              <s xml:id="N16484" xml:space="preserve">Probatur hec concluſio ex primo <lb/>correlario ſeptime concluſionis capitis prealle-<lb/>gati / et facile ex prima et ſecunda huius deducitur</s>
            </p>
            <p xml:id="N1648B">
              <s xml:id="N1648C" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N1648F" xml:space="preserve">Si aliqua potē-<lb/>tia eque velociter creſcit vĺ decreſcit reſpectu dua­<lb/>rum reſiſtentiarum ſiue equalium ſiue inequaliuꝫ <lb/>eque velociter cum vtra illarum intendet vel re­<lb/>mittet motum ſuum </s>
              <s xml:id="N1649A" xml:space="preserve">Probatur hec concluſio / quo­<lb/>niam illa potentia equalem ꝓportionem acquirit <lb/>vel deperdit reſpectu vtriuſ reſiſtentie / vt patet <lb/>ex prima concluſione huius / et ſecunda parte ſepti­<lb/>me concluſionis octaui capitis preallegati et ſuo <lb/>ſecundo correlario / igitur equalem velocitatē ac-<lb/>quirit vel deperdit reſpectu vtriuſ reſiſtentie.</s>
            </p>
            <p xml:id="N164A9">
              <s xml:id="N164AA" xml:space="preserve">Patet conſequentia ex tertia ſuppoſitione.</s>
            </p>
            <p xml:id="N164AD">
              <s xml:id="N164AE" xml:space="preserve">Sexta concluſio </s>
              <s xml:id="N164B1" xml:space="preserve">Si aliqua reſiſtē-<lb/>tia creſcat vel decreſcat reſpectu duarum poten-<lb/>tiarum ſiue equalium ſiue inequaliū non variata­<lb/>rum: vtra potentia eque velociter cum illa reſi-<lb/>ſtentia intendet vel remittet motum ſuum. </s>
              <s xml:id="N164BC" xml:space="preserve">Pro-<lb/>batur hec concluſio / quoniam reſpectu vtriuſ po­<lb/>tentie equalem ꝓportionem acquirit vel deperdit / <lb/>vt patet ex ſecundo correlario octaue concluſiõis <lb/>octaui capitis preallegati: igitur vtra potentia <lb/>equalem velocitatem acquirit vel deperdit.</s>
            </p>
            <cb chead="Capitulum quintum"/>
            <p xml:id="N164CB">
              <s xml:id="N164CC" xml:space="preserve">Septima concluſio </s>
              <s xml:id="N164CF" xml:space="preserve">Si due potētie <lb/>inequales eque velociter creſcant vel decreſcãt reſ­<lb/>pectu eiuſdem reſiſtentie non variate: potentia mi­<lb/>nor velocius intendet vel remittet motū ſuū </s>
              <s xml:id="N164D8" xml:space="preserve">Pro­<lb/>batur hec concluſio / quoniam ſemper potentia mi­<lb/>nor per equale crementum vel decrementū additū <lb/>ſibi vel deperditum et maiori: maiorem ꝓportio-<lb/>nem acquiret vel deperdet quam maior. </s>
              <s xml:id="N164E3" xml:space="preserve">vt ptꝫ ex <lb/>quinta ſuppoſitiõe huius capitis: igitur talis po­<lb/>tentia velocius intendet vel remittet motum ſuuꝫ <lb/></s>
              <s xml:id="N164EB" xml:space="preserve">Conſequentia patet ex prima ſuppoſitione. </s>
              <s xml:id="N164EE" xml:space="preserve">Ab <lb/>equalibus enim ꝓportionibus acquiſitis ſiue de-<lb/>perditis inequales velocitates acquiruntur ſiue <lb/>deperduntur / et per idem ſequitur /  ad acquiſitio­<lb/>nem vel deperditionem maioris maior velocitas <lb/>acquiritur vel deperditur</s>
            </p>
            <p xml:id="N164FB">
              <s xml:id="N164FC" xml:space="preserve">Octaua concluſio </s>
              <s xml:id="N164FF" xml:space="preserve">Si due reſiſtētie <lb/>inequales eque velociter creſcant vel decreſcãt reſ­<lb/>pectu eiuſdem potentie non variate: illa potentia <lb/>velocius intendet vel remittet motum ſuum cū mi­<lb/>nori reſiſtentia quam cum maiori. </s>
              <s xml:id="N1650A" xml:space="preserve">Probatur hec <lb/>concluſio / quoniam ſemper minor reſiſtentia ma-<lb/>iorem proportionem acquirit vel deperdit ꝑ equa­<lb/>lem deperditionē vel additionē ipſi et maiori / igi­<lb/>tur potentia cum ea velocius intendet vel remittet <lb/>motū ſuum. </s>
              <s xml:id="N16517" xml:space="preserve">Patet conſequentia auxilio duarum <lb/>primarum ſuppoſitionum.</s>
            </p>
            <p xml:id="N1651C">
              <s xml:id="N1651D" xml:space="preserve">Nona concluſio </s>
              <s xml:id="N16520" xml:space="preserve">Si due potentie in-<lb/>equales eque velociter creſcant vel decreſcant reſ­<lb/>pectu duarum reſiſtentiarum ſiue equalium ſiue ī­<lb/>equalium: potentia minor ſemper velocius inten­<lb/>det vel remittet motum ſuum ſiue agat cum reſiſtē­<lb/>tia maiore ſiue minore. </s>
              <s xml:id="N1652D" xml:space="preserve">Patet hec concluſio ex ſe-<lb/>ptima huius.</s>
            </p>
            <p xml:id="N16532">
              <s xml:id="N16533" xml:space="preserve">Decima concluſio </s>
              <s xml:id="N16536" xml:space="preserve">Si due reſiſten-<lb/>tie inequales creſcant vel decreſcant reſpectu dua­<lb/>rum potentiarum ſiue equalium ſiue inequalium: <lb/>potentia agens cum minore velocius intendet vel <lb/>remittet motum ſuum. </s>
              <s xml:id="N16541" xml:space="preserve">Hec patet ex octaua.</s>
            </p>
            <p xml:id="N16544">
              <s xml:id="N16545" xml:space="preserve">Undecima concluſio </s>
              <s xml:id="N16548" xml:space="preserve">Si due potētie <lb/>equales vel inequales eque ꝓporrionabiliter creſ­<lb/>cant vel decreſcant reſpectu eiuſdem reſiſtentie nõ <lb/>variate: tales potentie eque velociter intendēt vel <lb/>remittēt motus ſuos. </s>
              <s xml:id="N16553" xml:space="preserve">Patet hec concluſio ex ſexta <lb/>ſuppoſitione / que diffinit iſtum terminum eque ꝓ­<lb/>portionabiliter auxilio prime ſuppoſitionis.</s>
            </p>
            <p xml:id="N1655A">
              <s xml:id="N1655B" xml:space="preserve">Duodecima concluſio </s>
              <s xml:id="N1655E" xml:space="preserve">Si due reſi-<lb/>ſtentie equales ſiue inequales eque ꝓportionabi-<lb/>liter creſcant vel decreſcant reſpectu eiuſdem po-<lb/>tentie non variate. </s>
              <s xml:id="N16567" xml:space="preserve">talis potentia cum vtra illa­<lb/>rum reſiſtentiarum eque velociter intendet vel re-<lb/>mittet motum ſuum. </s>
              <s xml:id="N1656E" xml:space="preserve">Hec cum precedente eandem <lb/>ſortitur demonſtrationem.</s>
            </p>
            <p xml:id="N16573">
              <s xml:id="N16574" xml:space="preserve">Tridecima concluſio </s>
              <s xml:id="N16577" xml:space="preserve">Si due poten-<lb/>tie inequales eque ꝓportionabiliter creſcant vel <lb/>decreſcant reſpectu duarum reſiſtentiaruꝫ ſiue eq̄­<lb/>lium ſiue inequalium non variatarum: ipſe eque­<lb/>velociter intendent vel remittent motus ſuos. </s>
              <s xml:id="N16582" xml:space="preserve">Pa­<lb/>tet hec concluſio ex prima ſuppoſitione auxiliãte <lb/>vltima diffiniente eque velociter et eque propor-<lb/>tionabiliter.</s>
            </p>
            <p xml:id="N1658B">
              <s xml:id="N1658C" xml:space="preserve">Quartadecima concluſio </s>
              <s xml:id="N1658F" xml:space="preserve">Si due re­<lb/>ſiſtentie inequales creſcant vel decreſcant eque ꝓ­<lb/>portionabiliter reſpectu duarum potentiarum ſi­<lb/>ue equalium ſiue inqualium: tales potentie eque               <pb chead="Primi tractatus" file="0065" n="65"/>               velociter intendent vel remittent motus ſuos. </s>
              <s xml:id="N1659D" xml:space="preserve">Ex <lb/>probatione prioris hec probata euadit.</s>
            </p>
            <p xml:id="N165A2">
              <s xml:id="N165A3" xml:space="preserve">Quindemica concluſio </s>
              <s xml:id="N165A6" xml:space="preserve">Si due po-<lb/>tentie per earum intenſionem eque velociter inten­<lb/>dunt motus ſuos cum eadem vel diuerſis reſiſten­<lb/>tiis non variatis: ipſe eque proportionabiliṫ creſ­<lb/>cunt: et ſi per earum remiſſionem etc. eque velociter <lb/>remittunt motus ſuos. </s>
              <s xml:id="N165B3" xml:space="preserve">ipſe eque proportionabili­<lb/>ter decreſcunt. </s>
              <s xml:id="N165B8" xml:space="preserve">Hec patet ex vndecima. </s>
              <s xml:id="N165BB" xml:space="preserve">Et dicit cal­<lb/>culator /  eſt eius ↄ̨uerſa. </s>
              <s xml:id="N165C0" xml:space="preserve">Intellige ad ſenſuꝫ ma­<lb/>thematicum.</s>
            </p>
            <p xml:id="N165C5">
              <s xml:id="N165C6" xml:space="preserve">Decimaſexta concluſio </s>
              <s xml:id="N165C9" xml:space="preserve">Si ꝑ cremē­<lb/>ta aliquarum reſiſtentiarum vel decrementa, po-<lb/>tentia vel potentie cum illis reſiſtentiis mouentes <lb/>vniformiter moueantur: tales potentie eque pro-<lb/>portionabiliter creſcunt vel decreſcunt cuꝫ ſuis re­<lb/>ſiſtentiis. </s>
              <s xml:id="N165D6" xml:space="preserve">Patet concluſio quia ad hoc /  propor­<lb/>tio maneat ſemper equalis et numeri eius creſcūt <lb/>vel decreſcunt. </s>
              <s xml:id="N165DD" xml:space="preserve">neceſſe ē /  quãtãcu ꝓportionē nu­<lb/>merus maior acquirat vel deperdat tantam pro-<lb/>portioneꝫ acquirat vel deperdat numerus minor / <lb/>vt patet ex primo correlario quarte concluſionis <lb/>octaui capitis ſecunde partis igitur.</s>
            </p>
            <p xml:id="N165E8">
              <s xml:id="N165E9" xml:space="preserve">Decimaſeptima concluſio </s>
              <s xml:id="N165EC" xml:space="preserve">Si potē-<lb/>tia creſcens vel decreſcens vniformiter mouetur et <lb/>eque velociter: neceſſe eſt reſiſtentiam eque ꝓpor-<lb/>tionabiliter creſcere vel decreſcere et eocõtra </s>
              <s xml:id="N165F5" xml:space="preserve">Hec <lb/>ex primo correlario quarte concluſionis prealle-<lb/>gato patrocinio prime ſuppoſitionis huius ma-<lb/>nifeſta euadit.</s>
            </p>
            <p xml:id="N165FE">
              <s xml:id="N165FF" xml:space="preserve">Decimaoctaua cõcluſio </s>
              <s xml:id="N16602" xml:space="preserve">Si reſiſten­<lb/>tia creſcat vel decreſcat et potentia eque velociter <lb/>mouetur ipſa potentia eque proportionabiliter <lb/>creſcit vel deſcreſcit cum ſua reſiſtentia et eocontra <lb/></s>
              <s xml:id="N1660C" xml:space="preserve">Hec precedentis probationem aſſumit.</s>
            </p>
            <p xml:id="N1660F">
              <s xml:id="N16610" xml:space="preserve">Decimanona concluſio </s>
              <s xml:id="N16613" xml:space="preserve">Si potētia <lb/>eque velociter moueatur et ipſa difformiter creſ-<lb/>cit vel decreſcit: neceſſe eſt ſuam reſiſtentiam dif-<lb/>formiter creſcere vel decreſcere. </s>
              <s xml:id="N1661C" xml:space="preserve">Patet hoc ex pro­<lb/>batione aliarum.</s>
            </p>
            <p xml:id="N16621">
              <s xml:id="N16622" xml:space="preserve">Uigeſima concluſio </s>
              <s xml:id="N16625" xml:space="preserve">Si aliqua reſi-<lb/>ſtentia vniformiter creſcat vel decreſcat potētia <lb/>eque velociter mouente: neceſſe eandem potentiaꝫ <lb/>creſcere vel decreſcere vniformiter. </s>
              <s xml:id="N1662E" xml:space="preserve">Patet conclu­<lb/>ſio / quia alias non maneret eadeꝫ proportio / vt pa­<lb/>tet ex correlario preallegato et per conſequēs nec <lb/>eandem velocitas.</s>
            </p>
            <p xml:id="N16637">
              <s xml:id="N16638" xml:space="preserve">Uigeſimaprima cõcluſio </s>
              <s xml:id="N1663B" xml:space="preserve">Si aliqua <lb/>potentia vniformiter creſcat reſpectu reſiſtentie <lb/>non variate: talis potentia tardius et tardius in­<lb/>tendit motum ſuum </s>
              <s xml:id="N16644" xml:space="preserve">Probatur hec concluſio ex <lb/>ſexta ſuppoſitione. </s>
              <s xml:id="N16649" xml:space="preserve">Continuo enim eadem latitu-<lb/>do addetur maiori et maiori numero: igitur con-<lb/>tinuo acquiretur minor ꝓportio et ſic cõtinuo mo­<lb/>tus tardius et tardius intendetur.</s>
            </p>
            <p xml:id="N16652">
              <s xml:id="N16653" xml:space="preserve">Uigeſimaſecūda concluſio </s>
              <s xml:id="N16656" xml:space="preserve">Si ali-<lb/>qua potentia vniformiter decreſcat reſiſtentia nõ <lb/>variata: ipſa continuo velocius et velocius remit­<lb/>tet motum ſuum. </s>
              <s xml:id="N1665F" xml:space="preserve">Hec itidem patet ex ſexta ſuppo­<lb/>ſitione.</s>
            </p>
            <p xml:id="N16664">
              <s xml:id="N16665" xml:space="preserve">Uigeſimatertia cõcluſio </s>
              <s xml:id="N16668" xml:space="preserve">Si aliqua <lb/>reſiſtentia vniformiter creſcat reſpectu potētie nõ <lb/>variate: talis potentia tardius et tardius remit-<lb/>tet motum ſuum. </s>
              <s xml:id="N16671" xml:space="preserve">Hec modo quo precedens ꝓbat̄̄.</s>
            </p>
            <cb chead="Capitulum quintum"/>
            <p xml:id="N16676">
              <s xml:id="N16677" xml:space="preserve">Uigeſimaquarta ↄ̨̨cluſio </s>
              <s xml:id="N1667A" xml:space="preserve">Si aliqua <lb/>reſiſtentia vniformiter decreſcat potentia nõ va-<lb/>riata: talis potentia velocius et velocius intendet <lb/>motum ſuum. </s>
              <s xml:id="N16683" xml:space="preserve">Patet / quoniam continuo maioreꝫ <lb/>proportionem acquirit. </s>
              <s xml:id="N16688" xml:space="preserve">vt patet ex ſexta ſuppo-<lb/>ſitione.</s>
            </p>
            <p xml:id="N1668D">
              <s xml:id="N1668E" xml:space="preserve">Uigeſimaquinta concluſio </s>
              <s xml:id="N16691" xml:space="preserve">Si ali-<lb/>qua potentia tardius et tardius creſcat reſpectu <lb/>reſiſtentie non variate. </s>
              <s xml:id="N16698" xml:space="preserve">ipſa tardius cõtinuo et tar­<lb/>dius intendet motum ſuum. </s>
              <s xml:id="N1669D" xml:space="preserve">Patet hec concluſio <lb/>ex vigeſimaprima per locum a maiori: quoniaꝫ ſi <lb/>ſemper vniformiter creſceret: tardius continuo et <lb/>tardius intenderet motum ſuum. </s>
              <s xml:id="N166A6" xml:space="preserve">igitur ſi cõtinuo <lb/>tardius creſcat: a fortiori tardius et tardius iutē­<lb/>det motum ſuum.</s>
            </p>
            <p xml:id="N166AD">
              <s xml:id="N166AE" xml:space="preserve">Uigeſimaſexta concluſio </s>
              <s xml:id="N166B1" xml:space="preserve">Si aliqua <lb/>potentia velocius continuo decreſcat reſpectu re­<lb/>ſiſtentie non variate: ipſa contiuuo velocius remit­<lb/>tet motum ſuum. </s>
              <s xml:id="N166BA" xml:space="preserve">Patet ex vigeſimaſecunda ſuf-<lb/>fragante loco a maiori.</s>
            </p>
            <p xml:id="N166BF">
              <s xml:id="N166C0" xml:space="preserve">Uigeſimaſeptima concluſio </s>
              <s xml:id="N166C3" xml:space="preserve">Si ali-<lb/>qua reſiſtentia tardius continuo creſcat reſpectu <lb/>potentie non variate: ipſa potentia continuo tar­<lb/>dius remittet motum ſuum. </s>
              <s xml:id="N166CC" xml:space="preserve">Patet ex vigeſimater­<lb/>tia auxilio loci a fortiori.</s>
            </p>
            <p xml:id="N166D1">
              <s xml:id="N166D2" xml:space="preserve">Uigeſimaoctaua concluſio </s>
              <s xml:id="N166D5" xml:space="preserve">Si ali-<lb/>qua reſiſtentia continuo velocius decreſcat reſpe­<lb/>ctu potentie non variate: talis potentia continuo <lb/>velocius intendet motum ſuum </s>
              <s xml:id="N166DE" xml:space="preserve">Patet ex vigeſi-<lb/>ma quarta.</s>
            </p>
            <p xml:id="N166E3">
              <s xml:id="N166E4" xml:space="preserve">Uigeſimanona cõcluſio </s>
              <s xml:id="N166E7" xml:space="preserve">Si due vel <lb/>tres, vel quatuor, aut quotlibet potentie inequa-<lb/>les, eque velociter creſcant vel decreſcant reſpectu <lb/>eiuſdem reſiſtentie non variate: minima illarum <lb/>velocius intendet vel remittet motum ſuum. </s>
              <s xml:id="N166F2" xml:space="preserve">Pa-<lb/>tet hec concluſio ex ſexta ſuppoſitione. </s>
              <s xml:id="N166F7" xml:space="preserve">quoniaꝫ il­<lb/>li minori potentie per additionem vel remotionē <lb/>equalis latitudinis, ſemper accreſcit vel decreſcit <lb/>maior proportio.</s>
            </p>
            <p xml:id="N16700">
              <s xml:id="N16701" xml:space="preserve">Triceſima cõcluſio </s>
              <s xml:id="N16704" xml:space="preserve">Si due aut tres <lb/>aut quatuor: aut quotlibet reſiſtentie: eque veloci-<lb/>ter creſcant vel decreſcant reſpectu eiuſdem potē-<lb/>tie non variate: ſemper talis potentia cum mini-<lb/>ma illarum velocius intendet vel remittet motum <lb/>ſuum. </s>
              <s xml:id="N16711" xml:space="preserve">Hec et precedens equaleꝫ ſubeunt demõſtra­<lb/>tionem. </s>
              <s xml:id="N16716" xml:space="preserve">¶ Nunc modicum a ſerie diſcedentes ope­<lb/>re precium eſt aliquas concluſiones his aducere.</s>
            </p>
            <p xml:id="N1671B">
              <s xml:id="N1671C" xml:space="preserve">Triceſimaprima concluſio. </s>
              <s xml:id="N1671F" xml:space="preserve">Si du-<lb/>plum et ſubduplum eque velociter ad non graduꝫ <lb/>remittantur: in maiori tempore remittitur duplū <lb/>quam ſubduplum. </s>
              <s xml:id="N16728" xml:space="preserve">Probatur hec concluſio. </s>
              <s xml:id="N1672B" xml:space="preserve">quo-<lb/>niam capto quaternario et binario ſi eque veloci­<lb/>ter et vniformiter remittantur quando due vnita­<lb/>tes quaternarii remiſſe ſunt: reſtant due: et bina-<lb/>rius eſt complete remiſſus. </s>
              <s xml:id="N16736" xml:space="preserve">igitur oportet /  in tē-<lb/>pore ſequenti remittantur alie due vnitates qua-<lb/>teruarii: poſt̄ binarius eſt ad non gradum dedu­<lb/>ctus et per conſequens concluſio vera.</s>
            </p>
            <p xml:id="N1673F">
              <s xml:id="N16740" xml:space="preserve">Triceſimaſecunda concluſio </s>
              <s xml:id="N16743" xml:space="preserve">Si du­<lb/>plum et ſubduplum vniformiter remittant̄̄ et con­<lb/>tinuo eque velociter: tempus remiſſionis dupli eſt <lb/>duplum ad tempus remiſſionis ſubdupli. </s>
              <s xml:id="N1674C" xml:space="preserve">Et conſi­<lb/>militer dicatur de triplo, quadruplo, ſexqualte-<lb/>ro, et ſic in infinitum. </s>
              <s xml:id="N16753" xml:space="preserve">quoniam tempus tripli erit               <pb chead="Primi tractatus" file="0066" n="66"/>               triplum: et quadrupli quadruplum: et ſexquialte­<lb/>ri ſexquialterum, et ſic deīceps. </s>
              <s xml:id="N1675D" xml:space="preserve">Probatur hec cõ­<lb/>cluſio / quoniam duplum continet bis ſubduplum <lb/>et triplum ter ſubtriplum et ſic in infinitum / ergo <lb/>ſi remittantur vniformiter et eque velociter conti­<lb/>nuo neceſſe eſt cum ſubduplum fuerit remiſſum: re­<lb/>ſtat tantum de duplo remittendum quantuꝫ erat <lb/>ſubduplum: et cum ſubtriplum fuerit remiſſum re­<lb/>ſtet bis tantum remittendum etc.</s>
            </p>
            <p xml:id="N1676E">
              <s xml:id="N1676F" xml:space="preserve">Triceſimatertia cõcluſio </s>
              <s xml:id="N16772" xml:space="preserve">Si dupluꝫ <lb/>et ſubduplum vniformiter et eque velociter remit­<lb/>tantur ad non gradum: et quodlibet illorum cõti-<lb/>nuo tardius et tardius ſubduplum in minori tem­<lb/>pore quam ſubduplum remittetur. </s>
              <s xml:id="N1677D" xml:space="preserve">ita  ſi duo re­<lb/>mittantur in vna hora .4. remittentur in maiori tē­<lb/>pore quam ſit tempus duarum horaruꝫ. </s>
              <s xml:id="N16784" xml:space="preserve">Probat̄̄ <lb/>hec concluſio et capio .4. et .8. et volo /  vniformi-<lb/>ter et eque velociter remittantur: ſed continuo ta-<lb/>men quodlibet illorum tardius et tardius. </s>
              <s xml:id="N1678D" xml:space="preserve">Uolo <lb/>dicere /  ſemper quando remittitur vnitas vnius <lb/>puta ſubdupli remittatur vnitas alterius ſed con­<lb/>tinuo tardius et tardius / hoc eſt  ſi vtriuſ vni­<lb/>tas prima fuerit remiſſa in media hora alia vni-<lb/>tas ī maiori tempore adequate remittatur. </s>
              <s xml:id="N1679A" xml:space="preserve">Quo <lb/>poſito manifeſtum eſt:  ſi in vna hora fuerit re-<lb/>miſſus quaternarius etiam in eadem hora remiſ-<lb/>ſus eſt quaternarius ab octonario et ab ip̄o octo­<lb/>nario reſtat remittendus quaternarius et conti-<lb/>nuo tardius remittetur. </s>
              <s xml:id="N167A7" xml:space="preserve">igitur in maiori tempore <lb/>quam alter quaternarius / igitur totum tempus in <lb/>quo duplum remittitur adequate eſt maius quaꝫ <lb/>duplum ad tempus in quo remittitur ſubduplum</s>
            </p>
            <p xml:id="N167B0">
              <s xml:id="N167B1" xml:space="preserve">Triceſimaquarta concluſio. </s>
              <s xml:id="N167B4" xml:space="preserve">Si du-<lb/>plum et ſubduplum remittantur eque velociter et <lb/>continuo velocius et velocius: totale tempus re-<lb/>miſſionis dupli eſt minus quam duplum ad tem-<lb/>pus totalis remiſſiõis ſubdupli. </s>
              <s xml:id="N167BF" xml:space="preserve">Et volo dicere /  <lb/>ſi duo et quatuor remittant̄̄: ita  quando remit-<lb/>titur vnitas binarii / tunc adequate remittatur vni­<lb/>as quaternarii ſed tamen velocius: ſic  ſi prima <lb/>vnitas binarii et quaternarii remittatur in hora: <lb/>ſecunda vnitas in minori tempore remittatur. </s>
              <s xml:id="N167CC" xml:space="preserve">di­<lb/>co /  tempus totale in quo remittūtur ipſa .4. eſt <lb/>minus quam duplum ad tempus totalis remiſſio­<lb/>nis ipſorum .2. </s>
              <s xml:id="N167D5" xml:space="preserve">Probatur hec concluſio / q2 ſi eque­<lb/>velociter et vniformiter remittentur quo ad tem-<lb/>pus: tunc tempus remiſſionis dupli eſſet adequa-<lb/>te duplum ad tempus remiſſionis ſubdupli / vt di-<lb/>cit triceſimaſecunda concluſio / ſed modo cõtinuo <lb/>velocius remittuntur duplum et ſubduplum: igi-<lb/>tur duplum in minori tempore quam duplum ad <lb/>tempus remiſſionis ipſius ſubdupli totaliter re-<lb/>mittetur. </s>
              <s xml:id="N167E8" xml:space="preserve">¶ Et confirmatur / quia quãdo .2. et .4. re­<lb/>mittuntur eque velociter. </s>
              <s xml:id="N167ED" xml:space="preserve">et continuo velocius et ve­<lb/>locius: tempus in quo remittetur prima medietas <lb/>ipſorum .4. erit equale tempore in quo remittun-<lb/>tur .2. et tempus remiſſionis alterius medietatis <lb/>ipſorum .4. eſt minus tempori remiſſionis prime <lb/>medietatis: ergo totum tempus remiſſionis ipſo-<lb/>rum .4. eſt minus quam ſubduplū ad tēpus remiſ-<lb/>ſionis ipſius dualitatis.</s>
            </p>
            <p xml:id="N167FE">
              <s xml:id="N167FF" xml:space="preserve">Triceſimaquinta concluſio </s>
              <s xml:id="N16802" xml:space="preserve">Aliquid <lb/>alio pluſ̄ in duplo citius remittitur: et tamē quã­<lb/>diu manent ambo eque velociter continuo remit-<lb/>tuntur. </s>
              <s xml:id="N1680B" xml:space="preserve">Probatur hec concluſio. </s>
              <s xml:id="N1680E" xml:space="preserve">et capio pedale et <lb/>bipedale: ſiue albedinem vnius gradus et albedi­<lb/>nem duorum graduum: et volo /  incipiant remit­<lb/>ti / et ↄ̨tinuo taliter remittant̄̄:  in eq̈libus tꝑibus               <cb chead="Capitulum quintum"/>               equales partes deperdant: continuo tamen tardi­<lb/>us et tardius quo poſito ſic arguo. </s>
              <s xml:id="N1681C" xml:space="preserve">vnus gradus <lb/>pluſquã in duplo citius remittetur quam duo gra­<lb/>dus. </s>
              <s xml:id="N16823" xml:space="preserve">vt patet ex triceſimatertia concluſione. </s>
              <s xml:id="N16826" xml:space="preserve">et ta-<lb/>men continuo eque velociter quamdiu ſimul ma-<lb/>ment remittuntur. </s>
              <s xml:id="N1682D" xml:space="preserve">vt patet ex caſu / igitur conclu-<lb/>ſio vera.</s>
            </p>
            <p xml:id="N16832">
              <s xml:id="N16833" xml:space="preserve">Triceſimaſexta concluſio /  iſta con­<lb/>ſequentia nihil valet a. eſt duplum et b. ſubduplū <lb/>et pluſquã in duplo citius deperditur b. / ſubduplū <lb/>quam a. / duplum igitur velocius deperditur b. ſub­<lb/>duplum quã. duplū </s>
              <s xml:id="N1683E" xml:space="preserve">Stat em̄ cū añte /  a. duplum <lb/>in aliquo tēpore ita velociter mouetur ſicut b. ſub­<lb/>duplū ex anteriori concluſione / quod eſt oppoſitū <lb/>tertie exponentis ipſius conſequentis. </s>
              <s xml:id="N16847" xml:space="preserve">Sed hec cõ­<lb/>ſequentia eſt bona b. eſt ſubduplū et a. duplū eius <lb/>et pluſquã in duplo velociꝰ deperditur ſiue remit­<lb/>titur quã b. / et vtrum illorum ſemper remittitur <lb/>vniformiter: ergo a. velocius remittetur quã b. / ſꝫ <lb/>antecedens talis conſequentie eſt impoſſibile: vt <lb/>patet ex triceſimaſecunda concluſione. </s>
              <s xml:id="N16856" xml:space="preserve">Partes eī <lb/>antecedentis repugnant.</s>
            </p>
            <p xml:id="N1685B">
              <s xml:id="N1685C" xml:space="preserve">Triceſimaſeptima concluſio </s>
              <s xml:id="N1685F" xml:space="preserve">Si ali­<lb/>qua potentia inuariata mouetur per mediū vni-<lb/>formiter difforme inuariatum a remiſſiori extre-<lb/>mo incipiendo: talis potentia continuo tardius et <lb/>tardius acquirit ſibi reſiſtentiam. </s>
              <s xml:id="N1686A" xml:space="preserve">Probatur hec <lb/>concluſio ſupponendo /  oīm duarū partiū equa­<lb/>lium corporis vniformiter difformis extremum ī­<lb/>tenſius per equalem latitudinem excedit extremū <lb/>remiſſius. </s>
              <s xml:id="N16875" xml:space="preserve">vt capta latitudīe vniformiter difformi <lb/>a quarto vſ ad octauum: prime quarte extremū <lb/>intenſius puta vt .5. excedit remiſſius per vnū gra­<lb/>dum: et ſecunde quarte extremum intenſius / puta <lb/>vt ſex excedit extremum remiſſius eiuſdem quarte / <lb/>vt .5. etiam per vnum gradum: et ſic conſequenter <lb/></s>
              <s xml:id="N16883" xml:space="preserve">Et hoc non ſolum habet verum de partibus equa­<lb/>libus immediatis verumetiam de mediatis / vt <lb/>facile eſt intueri et etiam hoc in capite decimo hu­<lb/>ius tractatus probabitur. </s>
              <s xml:id="N1688C" xml:space="preserve">Iſto ſuppoſito proba-<lb/>tur concluſio quoniam continuo pertranſitioneꝫ <lb/>duarum partium equalium equaliter acquiret de <lb/>reſiſtentia </s>
              <s xml:id="N16895" xml:space="preserve">Quando enim pertranſibit ſecundam <lb/>quartã: tantã reſiſtentiã acquiret ſuper reſiſtentiã <lb/>habitã quantã tranſeundo primã quartam ade-<lb/>quate: et tantã reſiſtentiã acquiret adequate tran­<lb/>ſeundo primã octauã ſicut ſecundã: et ſicut tertiaꝫ <lb/>et ſicut quartam. </s>
              <s xml:id="N168A2" xml:space="preserve">et ſic de quibuſcun partibꝰ eq̈-<lb/>libus: et continuo tardius et tardius talis poten­<lb/>tia mouetur: quia ſemper ſibi accreſcet reſiſtentia <lb/>ipſa inuariata: igitur tardius continue acquiret <lb/>ſibi reſiſtentiam.</s>
            </p>
            <p xml:id="N168AD">
              <s xml:id="N168AE" xml:space="preserve">Triceſimaoctaua concluſio </s>
              <s xml:id="N168B1" xml:space="preserve">Si ali-<lb/>qua potentia non variata continuo moueatur ꝑ <lb/>medium vniformiter difforme implendo ab extre­<lb/>mo intenſiori continuo velocius et velocius decreſ­<lb/>cet ſibi de reſiſtentia. </s>
              <s xml:id="N168BC" xml:space="preserve">Patet / quia continuo veloci­<lb/>us et velocius mouetur et continuo equalem par-<lb/>tem tranſeundo equalem reſiſtentiaꝫ deperdit / igi­<lb/>tur continuo velocius et velocius decreſcit ſibi de <lb/>reſiſtentia.</s>
            </p>
            <p xml:id="N168C7">
              <s xml:id="N168C8" xml:space="preserve">Triceſimanona cõcluſio </s>
              <s xml:id="N168CB" xml:space="preserve">Si aliqua <lb/>potentia non variata mouetur per mediū vnifor­<lb/>miter difforme ab extremo remiſſiori incipiendo: <lb/>talis potentia continuo tardius et tardius remit­<lb/>tit motum ſuum. </s>
              <s xml:id="N168D6" xml:space="preserve">Patet / quia tardius et tardiꝰ ac-<lb/>creſcet ſibi de reſiſtentia: igitur continuo tardius <lb/>et tardius remittit motum ſuum. </s>
              <s xml:id="N168DD" xml:space="preserve">Patet conſequē­               <pb chead="Primi tractatus" file="0067" n="67"/>               tis ex vigeſimaſeptima concluſione.</s>
            </p>
            <p xml:id="N168E5">
              <s xml:id="N168E6" xml:space="preserve">Quadrageſima concluſio </s>
              <s xml:id="N168E9" xml:space="preserve">Si aliqua <lb/>potentia non variata mouetur per mediuꝫ vnifor­<lb/>miter difforme incipiendo ab extremo intenſiori: <lb/>talis potentia continuo velocius et velocius intē-<lb/>dit motū ſuum. </s>
              <s xml:id="N168F4" xml:space="preserve">Patet / quia continuo velocius et <lb/>velocius decreſcit ſibi de reſiſtentia: igitur conti-<lb/>nuo velocius et velocius intendit motuꝫ ſuum </s>
              <s xml:id="N168FB" xml:space="preserve">Pa­<lb/>tet conſequentia ex vigeſimaoctaua concluſione.</s>
            </p>
            <p xml:id="N16900">
              <s xml:id="N16901" xml:space="preserve">Quadrageſimaprima ↄ̨̨cluſio </s>
              <s xml:id="N16904" xml:space="preserve">Stat <lb/>duas potētias equales moueri per mediū vnifor­<lb/>miter difforme incipiendo ab extremo remiſſiori <lb/>eiuſdē medii ipſis et medio ſimplicter inuariatis <lb/>et tamē vnam moueri velocius altera </s>
              <s xml:id="N1690F" xml:space="preserve">Probatur <lb/>hec concluſio et capio vnum mediū quadratū vni­<lb/>formiter difforme a non gradu vſ ad octauū vel <lb/>a certo gradu (in idē redit) / et volo /  a. et b. ſint due <lb/>potentie equales: et incipiat vna moueri ab extre­<lb/>mo remiſſiori per diametrū et alia per lineam re-<lb/>ctã ab eodem extremo: quo poſito ſic arguo a. et b. <lb/>mouebuntur: et a. non mouebitur tardius ipſo b. <lb/>nec eque velociter adequate: ergo velocius. </s>
              <s xml:id="N16922" xml:space="preserve">Ma-<lb/>ior ptꝫ cum conſequentia. </s>
              <s xml:id="N16927" xml:space="preserve">et minor probatur. </s>
              <s xml:id="N1692A" xml:space="preserve">q2 ſi <lb/>mouerentur equaliter ſequeretur /  equales potē­<lb/>tie cum inequalibus reſiſtentiis equaliter mouerē­<lb/>tur / et per conſequens ab inequalibus proportio-<lb/>nibus equales motus proueniunt: quod eſt contra <lb/>primã ſuppoſitionē huius capitis et directe cõtra <lb/>opinionem. </s>
              <s xml:id="N16939" xml:space="preserve">Sequela tamen probatur / quoniam <lb/>capto quocū pūcto diametri equaliter diſtante <lb/>ab angulo quadrati: hoc eſt a linea quadrati fa-<lb/>ciente angulum ſicut certus pūctus: eſt minoris re­<lb/>ſiſtentie quã pūctus exiſtens in linea recta equali-<lb/>ter diſtante cum ipſo. </s>
              <s xml:id="N16946" xml:space="preserve">ergo ſequitur /  ſemꝑ a. ha-<lb/>bebit minorē reſiſtentiam / et per conſequens maio­<lb/>rem proportionem ad talem pūctū quã b. in pun-<lb/>cto ſibi correſpondente: et tamen per te a. et b. mo­<lb/>uentur equaliter: igitur ꝓpoſituꝫ. </s>
              <s xml:id="N16951" xml:space="preserve">Q, aūt in tali <lb/>puncto diametri ſit ſemper reſiſtentia minor quã <lb/>in puncto ſibi correſpõdente ī linea directe / et per-<lb/>pendiculariter ꝓcedente ꝓbatur / quoniaꝫ ſemper <lb/>talis punctus plus diſtat a gradu ſūmo illius cor­<lb/>poris / quam punctus ſibi correſpondens in linea <lb/>directe et perpēdiculariter procedente. </s>
              <s xml:id="N16960" xml:space="preserve">igitur ſem­<lb/>per in eo eſt minor reſiſtentia et per conſequens ꝓ­<lb/>portio maior </s>
              <s xml:id="N16967" xml:space="preserve">Patet hec demonſtratio aſpicienti <lb/>figuram quadrataꝫ vniformiter difformē quo ad <lb/>reſiſtentiam / que ſit .a.b. et .c.d. et extremū remiſſiſ­<lb/>ſimū ſit .ac. et linea diametralis ꝑ quã a. mouetur <lb/>ſit .ad. et linea per quam mouetur b. ſit .cd.</s>
            </p>
            <figure xml:id="N16972">
              <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0067-01"/>
            </figure>
            <p xml:id="N16976">
              <s xml:id="N16977" xml:space="preserve">qua figura inſpecta patet facile ꝓpoſitum. </s>
              <s xml:id="N1697A" xml:space="preserve">Et hec <lb/>de his concluſionibus in quibus ferme ſequutus <lb/>ſum calculatorem in capitulo de motu locali dem­<lb/>pta vltima quam adiunxi.</s>
            </p>
          </div>
          <div xml:id="N16983" level="4" n="6" type="chapter" type-free="capitulum">
            <head xml:id="N16988" xml:space="preserve">Sextum capitulum / in quo ponūtur <lb/>alique obiectiones contra aliquas <lb/>concluſiones ſuperioris capitis.</head>
            <p xml:id="N1698F">
              <s xml:id="N16990" xml:space="preserve">COntra quintam concluſio-<lb/>nem arguitur ſic. </s>
              <s xml:id="N16995" xml:space="preserve">per intenſionem et cre­<lb/>mētum alicuius reſiſtētie reſpectu dua­<lb/>rum potentiarum inequalium minor potentia ve­               <cb chead="Capitulum ſextum"/>               locius remittit motū ſuum quã maior: igitur ſex-<lb/>ta ↄ̨cluſio falſa. </s>
              <s xml:id="N169A1" xml:space="preserve">Arguit̄̄ antecedēs et pono /  ſit a. <lb/>potētia vt .8. et b. potētia vt .4. et c. reſiſtētia vt 2. <lb/>et d. reſiſtētia vt vnū: et agat vtra illaꝝ potētiaꝝ <lb/>cū vtra illarum reſiſtentiarū: et creſcat c. reſiſten­<lb/>tia vt .2. vniformiter / quo ad vſ ſit vt .4. et d. reſiſtē­<lb/>tia itidem vniformiter creſcat / quo ad vſ ſit vt .4. <lb/>creſcat tamen reſiſtētia vt .2. in duplo velociꝰ quã <lb/>reſiſtentia vt vnū. </s>
              <s xml:id="N169B2" xml:space="preserve">ita  quando reſiſtentia vt vnuꝫ <lb/>acquiſiuerit vnum gradum reſiſtentie: reſiſtentia <lb/>vt duo acquirat duos. </s>
              <s xml:id="N169B9" xml:space="preserve">quo poſito ſic argumentor <lb/>b. potentia vt .4. velocius remittit motum ſuum <lb/>cū c. reſiſtentia vt .2. quã a. potentia vt .8. cum ea-<lb/>dem reſiſtentia vt duo. </s>
              <s xml:id="N169C2" xml:space="preserve">igitur aſſumptum verum.</s>
            </p>
            <p xml:id="N169C5">
              <s xml:id="N169C6" xml:space="preserve">Probatur antecedens / quoniaꝫ eque velociter po­<lb/>tentia a. vt .8. remittet motū ſuum cum reſiſtentia <lb/>c. vt .2. ſicut potentia b. vt .4. cū reſiſtentia d. / vt vnū <lb/>quoniam proportiones erunt equales: et eque ve-<lb/>lociter ꝓportionabiliter deperduntur. </s>
              <s xml:id="N169D1" xml:space="preserve">igitur ſem­<lb/>per manebunt equales ad inuicem ſed b. potentia <lb/>vt .4. velocius remittet motū ſuum cū c. reſiſtentia <lb/>vt .2. quam cū d. reſiſtentia vt vnum / ergo b. poten­<lb/>tia vt .4. velocius remittet cum c. motū ſuum. </s>
              <s xml:id="N169DC" xml:space="preserve">quaꝫ <lb/>a. potentia vt .8. cū eodē c. / quod fuit probandum. <lb/></s>
              <s xml:id="N169E2" xml:space="preserve">Conſequentia patet cū maiore: et minor probatur / <lb/>quoniam velocius deperditur proportio b. ad c. <lb/>quam proportio b. ad d. / ergo velocius remittitur <lb/>motus proueniens a proportione b. ad c. / quã mo­<lb/>tus proueniens a proportione b. ad d. </s>
              <s xml:id="N169ED" xml:space="preserve">Conſequen­<lb/>tia eſt nota et arguitur antecedens. </s>
              <s xml:id="N169F2" xml:space="preserve">quoniam pro­<lb/>portio b. potētie vt 4. ad c. reſiſtētiã vt .2. ē ī duplo <lb/>minor ꝓportione b. potētie vt .4. ad d. reſiſtentiã vt <lb/>vnum: quoniam vna dupla et alia quadrupla. </s>
              <s xml:id="N169FB" xml:space="preserve">et <lb/>plꝰquã ī duplo citiꝰ remittet̄̄ ꝓportio b. ad c. quã <lb/>ꝓportio b. ad d. / igr̄ velociꝰ remittet̄̄ ꝓportio b. ad <lb/>c. quã b. ad .d. / quod fuit probandū. </s>
              <s xml:id="N16A04" xml:space="preserve">Conſequentia <lb/>eſt nota / vt apparet cum maiore: et minor ꝓbatur / <lb/>quoniam quando reſiſtentia c. acquiſiuerit duos <lb/>gradus reſiſtentie / tunc proportio b. ad c. erit omī­<lb/>no deperdita. </s>
              <s xml:id="N16A0F" xml:space="preserve">et in eodem tempore adequate ꝑde­<lb/>tur proportio dupla ipſi quadruple, et acquiretur <lb/>vnus gradus dūtaxat ipſi reſiſtentie d. / et reſtabūt <lb/>acquirendi duo qui debēt acquiri vniformiter: er­<lb/>go illi acquirentur adequate ī duplo tempore ad <lb/>acquiſitionem primi: et ſic ſequitur /  tempus de-<lb/>perditionis proportionis b. ad c. eſt ſubtriplū, ad <lb/>tempus deperditionis proportionis b. ad d. / et per <lb/>conſequens pluſquã in duplo citius deperditur ꝓ­<lb/>portio b. ad c. quã b. ad d. / quod fuit probanduꝫ.</s>
            </p>
            <p xml:id="N16A24">
              <s xml:id="N16A25" xml:space="preserve">Reſpondeo negando antecedens: et <lb/>ad probationē admiſſo caſu negat̄̄ añs: et ad pro-<lb/>bationē negatur hec minor b. velociꝰ remittet mo­<lb/>tū ſuū cū c. quã cum d. / et ad ꝓbationē negatur an-<lb/>tecedens et ad probationē antecedētis negat̄̄ hec <lb/>ↄ̨ña in qua eſt virtus argumenti: proportio b. ad <lb/>c. ē in duplo minor ꝓportione b. ad d. / et pluſquaꝫ <lb/>in duplo citius deperdetur proportio b. ad c. quã <lb/>ꝓportio b. ad .d. / ergo velocius deperdetur propor­<lb/>portio b. ad .c. / quã deperdetur proportio b. ad d. / ſi­<lb/>cut eam eſſe negandam docet triceſimaſexta con-<lb/>cluſio               <anchor type="note" xlink:href="note-0067-01" xlink:label="note-0067-01a"/>               </s>
              <s xml:id="N16A43" xml:space="preserve">In probatione tamē ↄ̨ñe negate adducit <lb/>calculator duas conditionales: quarū neutra eſt <lb/>bona ↄ̨ña. </s>
              <s xml:id="N16A4A" xml:space="preserve">Ipſe tamē nihil ad eas reſpondet </s>
              <s xml:id="N16A4D" xml:space="preserve">Pro <lb/>quarū impugnatione pono aliqua correlaria.</s>
            </p>
            <div xml:id="N16A52" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0067-01a" xlink:label="note-0067-01" xml:id="N16A56" xml:space="preserve">inq̇rit̄̄ bo­<lb/>uitaſ ↄ̨ña­<lb/>rū calcu.</note>
            </div>
            <note position="right" xml:id="N16A60" xml:space="preserve">1. correl.</note>
            <p xml:id="N16A64">
              <s xml:id="N16A65" xml:space="preserve">¶ Primū correlariū in caſu argumenti d. reſiſtē-<lb/>tia vt vnum et .c. reſiſtentia vt .2. / non vniformiter <lb/>creſcūt / et tamē vtra illarum vniformiter creſcit. <lb/></s>
              <s xml:id="N16A6D" xml:space="preserve">Probatur / quia quando reſiſtentia vt vnum acq̇-<lb/>rit vnitatem: reſiſtentia vt .2. acquirit dualitē gra­               <pb chead="Primi tractatus" file="0068" n="68"/>               duū. </s>
              <s xml:id="N16A77" xml:space="preserve">igitur nõ vniformiter creſcūt. </s>
              <s xml:id="N16A7A" xml:space="preserve">Antecedēs ptꝫ <lb/>ex caſu. </s>
              <s xml:id="N16A7F" xml:space="preserve">Sed ſecūda pars ꝓbatur: qm̄ vtra illaꝝ <lb/>inequalibus tēporibus equales latitudines reſiſ­<lb/>ſtentie acquirūt: vt ptꝫ ex caſu. </s>
              <s xml:id="N16A86" xml:space="preserve">Ex hac correlariuꝫ <lb/>eſt ſimile dialectico ſortes / et brunellꝰ nõ ſunt fra-<lb/>tres: et tamen vter illoꝝ eſt fratrer.               <anchor type="note" xlink:href="note-0068-01" xlink:label="note-0068-01a"/>               </s>
              <s xml:id="N16A92" xml:space="preserve">¶ Secunduꝫ <lb/>correlariū ſtat /  ſubduplū in ſubduplo tempore <lb/>adequate ad tēpus deꝑditionis dupli deꝑdatur: <lb/>et quãdo deperdat̄̄ ſubduplū etiã duplū deperdat̄̄ <lb/>quãius nõ totaliter: et nichilominꝰ nõ eque velociṫ <lb/>deperdat̄̄ ſubduplū cum duplo. </s>
              <s xml:id="N16A9F" xml:space="preserve">Probat̄̄ et pono <lb/>caſum /  ſint pedale a. et bipedale b. / et incipiat de-<lb/>perdi taliter:  īmedietate hore future deperdat̄̄ <lb/>pedale a. adequate: et tūc ſit deperditū a. bipedali <lb/>b. p̄ciſe ſemipedale: et totū reſiduū deperdat ī me-<lb/>dietate ſeq̄nti adequate: quo poſito iam ptꝫ corre­<lb/>larium.               <anchor type="note" xlink:href="note-0068-02" xlink:label="note-0068-02a"/>               </s>
              <s xml:id="N16AB3" xml:space="preserve">¶ Ex quo ſequitur tertiū correlariū:  hec <lb/>cõſequentia nichil valet. </s>
              <s xml:id="N16AB8" xml:space="preserve">Si a. ſubduplū in ſubdu­<lb/>plo tēpore adequate deperdit̄̄ ad b. duplū: a. et b. <lb/>eque velociter deperdūtur. </s>
              <s xml:id="N16ABF" xml:space="preserve">In caſu em̄ poſito an-<lb/>tecedens eſt verū et cõſequēs falſum. </s>
              <s xml:id="N16AC4" xml:space="preserve">Nec puto cal­<lb/>culatorē voluiſſe illã cõcedere. </s>
              <s xml:id="N16AC9" xml:space="preserve">Iſta tamen cõſequē­<lb/>tia eſt bona: ſi ſubduplū in ſubduplo tēpore ade-<lb/>quate deperdit̄̄ et vniformiter cū ſuo duplo: iam <lb/>eque velociter deperdit̄̄.               <anchor type="note" xlink:href="note-0068-03" xlink:label="note-0068-03a"/>               </s>
              <s xml:id="N16AD7" xml:space="preserve">¶ Quartū correlarium. <lb/></s>
              <s xml:id="N16ADB" xml:space="preserve">Iſta cõſequentia nichil valet: pluſquã in duplo ci-<lb/>tius deperdit̄̄ ſubduplū quã duplū: igitur velociꝰ <lb/>perditur ſubduplū quã duplū. </s>
              <s xml:id="N16AE2" xml:space="preserve">Patet hoc correla­<lb/>riū ex dictis in ſolutione argumentati.               <anchor type="note" xlink:href="note-0068-04" xlink:label="note-0068-04a"/>               </s>
              <s xml:id="N16AEC" xml:space="preserve">¶ Quintum <lb/>correlariū. </s>
              <s xml:id="N16AF1" xml:space="preserve">Stat duas ꝓportiones eque velociter <lb/>deperdi per crementū ſuaꝝ reſiſtentiarū: et tamen <lb/>reſiſtentias nõ eque velociter creſcere: īmo hoc ne­<lb/>ceſſariū eſt vbi reſiſtētie ſūt īeq̈les .etc̈. </s>
              <s xml:id="N16AFA" xml:space="preserve">Probat̄̄ cor­<lb/>relariuū ſupponēdo  ad hoc /  aliquã ꝓportio eq̄ <lb/>velociṫ ↄ̨tinuo et vniformiṫ cū deꝑdat̄̄: req̇rit̄̄ /  in­<lb/>eq̈libꝰ tēporibꝰ equales ꝓportiones partiales ille <lb/>due deperdant: vt ſi ꝓportio quadrupla eque ve-<lb/>lociter debeat deperdi cū ꝓportione dupla: requi-<lb/>ritur /  quando adequate quadrupla perdit ſex-<lb/>quitertiã. </s>
              <s xml:id="N16B0B" xml:space="preserve">etiã dupla ſexquitertiã perdat adequa-<lb/>te: et ſic cõſequenter. </s>
              <s xml:id="N16B10" xml:space="preserve">Sed ad hoc /  due reſiſtentie <lb/>eque velociter et vniformiter deperdãtur requirit̄̄ / <lb/> inequalibꝰ tēporibꝰ equales latitudines reſiſtē-<lb/>tiarū deperdant. </s>
              <s xml:id="N16B19" xml:space="preserve">Hoc patet ex ſexta ſuppoſitione <lb/>p̄cedētis capitis. </s>
              <s xml:id="N16B1E" xml:space="preserve">Ad hoc em̄  vniformiter remit-<lb/>tatur ꝓportio: requiritur /  inequalibꝰ tēporibꝰ <lb/>equales latitudines ꝓportionū deperdãtur: et ad <lb/>hoc /  vniformiter remittatur reſiſtentia: requirit̄̄ / <lb/> inequalibꝰ tēporibꝰ equales latitudines reſiſtē­<lb/>tiarū deperdãtur vt ptꝫ. </s>
              <s xml:id="N16B2B" xml:space="preserve">Quo ſuppoſito ꝓbatur <lb/>correlariū in caſu argumentati. </s>
              <s xml:id="N16B30" xml:space="preserve">ibi em̄ reſiſtentia c. / <lb/>vt .2. in duplo velocius creſcit quã reſiſtentia d. / vt <lb/>vnū et tamen quãdo ꝓportio a. potentie / vt .8. ad c. <lb/>reſiſtentiã / vt 2. perdit ꝓportionē duplã: etiã pro-<lb/>portio ipſiꝰ b. potētie / vt 4. ad d. reſiſtentiã / vt vnū <lb/>ꝑdit ꝓportionē duplã: et ſic ibi ſtat proportiões per <lb/>crementū reſiſtētiaꝝ eque vĺociter deꝑdi: et tamen <lb/>reſiſtētias nõ eque velociter creſcere. </s>
              <s xml:id="N16B41" xml:space="preserve">Et  hoc ſit <lb/>neceſſariū vbi reſiſtētie ſiue mīores termini ꝓpor-<lb/>tionū fuerit inequales: ptꝫ / q2 īplicat duo inequa-<lb/>lia eque velociter creſcere et eque ꝓportiõabiliter / <lb/>vt ptꝫ ex octaua ſuppoſitione quarti capitis et ex <lb/>octauo capite ſecūde partis per totū. </s>
              <s xml:id="N16B4E" xml:space="preserve">¶ In his q̄ <lb/>quaſi demõſtratiue ꝓcedūt: deducas locoꝝ diuer-<lb/>ſitatē: cū ceterꝪ litigioſis captiūculis ſophiſtarū <lb/>               <anchor type="note" xlink:href="note-0068-05" xlink:label="note-0068-05a"/>               </s>
              <s xml:id="N16B5C" xml:space="preserve">¶ Aduerte tamen /  nõ in toto tꝑe ille ꝓportiões <lb/>puta dupla et quadrupla eque velociter deperdū­<lb/>tur: et loquor de ꝓportione b. potentie vt .4. ad re­<lb/>ſiſtentiã c. vt duo et ꝓportione b. potentie vt .4. ad               <cb chead="Capitulū ſextū."/>               d. reſiſtentiã vt vnū. </s>
              <s xml:id="N16B68" xml:space="preserve">Sed quãdiu ſimul remittunt̄̄ <lb/>eque velociter decreſcunt ſiue remittuntur.               <anchor type="note" xlink:href="note-0068-06" xlink:label="note-0068-06a"/>               </s>
              <s xml:id="N16B72" xml:space="preserve">¶ Sed <lb/>q2 ex ſentētia philoſophi primo celi veritates in-<lb/>quiſitores arbitros eſſe decet et nõ inimicos: ideo <lb/>ſecūdo loco aduerte:               <anchor type="note" xlink:href="note-0068-07" xlink:label="note-0068-07a"/>                in cõſequētia calculatoris <lb/>ly eque velociter poteſt capi dupliciter: videlicet <lb/>reſolutorie / vt eq̇ualeat huic aliqua equali veloci-<lb/>tate. </s>
              <s xml:id="N16B86" xml:space="preserve">vt ſit ſenſus huiꝰ ꝓpropoſitionis ſubduplū eque­<lb/>velociter remittitur cū duplo: id eſt aliqua equali <lb/>velocitate ſubduplū equaliter remittitur cum du­<lb/>plo. </s>
              <s xml:id="N16B8F" xml:space="preserve">Et iſto modo cõſequentia calculatoris eſt bo­<lb/>na cū his que ſupponit ex parte antecedētis. </s>
              <s xml:id="N16B94" xml:space="preserve">Alio <lb/>modo ly eque velociter poteſt capi exponibiliter / <lb/>vt ſit ſenſus huiꝰ ꝓpoſitionis ſubduplū eque velo­<lb/>citer remittit̄̄ cū duplo: hoc eſt ita velociṫ remittit̄̄ <lb/>ſubduplū ſicut duplū et ē cõtra. </s>
              <s xml:id="N16B9F" xml:space="preserve">Et in iſto ſenſu hec <lb/>conſequentia nõ valet b. ſubduplū puta pedale in <lb/>ſubduplo tēpore adequate deꝑditur ad a. dupluꝫ <lb/>puta bipedale: ergo eque velociter ꝑditur b. ſub-<lb/>duplū ſicut a. duplū. </s>
              <s xml:id="N16BAA" xml:space="preserve">Probatur: nam poſito  pe­<lb/>dale remittatur vniformiter in hora: et bipedale <lb/>in duabus horis adequate remittatur vſ ad nõ <lb/>quantū: ita tamen  in tēpore in quo remittit̄̄ pe-<lb/>dale remittatur aliquid de bipedali: in triplo tar­<lb/>dius tamen gratia exēpli: et in aliqua parte ſecū-<lb/>de hore remittatur etiã aliquid de bipedali ita ve­<lb/>lociter ſicut antea remittebat̄̄ pedale: et in aliqua <lb/>alia parte remittatur ipſum bipedale velociꝰ quã <lb/>vti̄ remittebatur pedale ſubduplum: quo poſito <lb/>antecedens eſt verum et conſequens falſum. </s>
              <s xml:id="N16BC1" xml:space="preserve">Nam <lb/>tertia exponens conſequentis eſt falſa / videlicet <lb/>iſta in nullo tempore a. duplum velocius remitti-<lb/>tur quam b. ſubduplū / vt patet.               <anchor type="note" xlink:href="note-0068-08" xlink:label="note-0068-08a"/>               </s>
              <s xml:id="N16BCF" xml:space="preserve">Et ita debet dari <lb/>tertia exponens in talibus addendo ly tēpore / qm̄ <lb/>alias oporteret vti circulatione in exponendo: ꝑ-<lb/>inde at alti concedunt quod michi non placet. <lb/></s>
              <s xml:id="N16BD9" xml:space="preserve">Hac diſtinctione vtendo pariter et expoſitione: fa­<lb/>cile hec dicta in predictis correlariis dictis calcu-<lb/>latoris conciliabis: eſto  calculator de facto nõ <lb/>aduerſetur dictis. </s>
              <s xml:id="N16BE2" xml:space="preserve">¶ Hec ex ſcriniis dialectice non <lb/>abs re nec inconſulte huic argumento interſeren-<lb/>da decreui: quoniam defeſſam mathemathicis et <lb/>ſcientia demonſtratiua mentem dialectice at ſo­<lb/>phiſtice argumētiones plurimū oblectant. </s>
              <s xml:id="N16BED" xml:space="preserve">               <anchor type="note" xlink:href="note-0068-09" xlink:label="note-0068-09a"/>               Nam <lb/>teſte philoſopho decima octaua particula pro-<lb/>blematum ſecundo problemate. </s>
              <s xml:id="N16BF9" xml:space="preserve">Agoniſtice, ligi-<lb/>tioſe, at ſophiſtice argumentatioues, et pluri-<lb/>mum ſunt exercitatiue: et vltra alias diſputatio-<lb/>nes: lõge plus iuuant at delectant.               <anchor type="note" xlink:href="note-0068-10" xlink:label="note-0068-10a"/>               </s>
              <s xml:id="N16C07" xml:space="preserve">His adde / <lb/> iſte terminus citius dupliciter poteſt capi: pri-<lb/>mo modo / vt dicit temporis propinquitatem: ſe-<lb/>cundo vero modo / vt dicit tēporis breuitatem: et <lb/>hoc poſteriori modo accommodatius propoſito <lb/>deſeruit.</s>
            </p>
            <div xml:id="N16C14" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0068-01a" xlink:label="note-0068-01" xml:id="N16C18" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0068-02a" xlink:label="note-0068-02" xml:id="N16C1E" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0068-03a" xlink:label="note-0068-03" xml:id="N16C24" xml:space="preserve">4. correĺ.</note>
              <note position="left" xlink:href="note-0068-04a" xlink:label="note-0068-04" xml:id="N16C2A" xml:space="preserve">5. correĺ.</note>
              <note position="left" xlink:href="note-0068-05a" xlink:label="note-0068-05" xml:id="N16C30" xml:space="preserve">Aduerte</note>
              <note position="right" xlink:href="note-0068-06a" xlink:label="note-0068-06" xml:id="N16C36" xml:space="preserve">Aduerte <lb/>pḣs pri-<lb/>mo celi.</note>
              <note position="right" xlink:href="note-0068-07a" xlink:label="note-0068-07" xml:id="N16C40" xml:space="preserve">Eque ve-<lb/>lociter ca­<lb/>pitur du­<lb/>pliciter.</note>
              <note position="right" xlink:href="note-0068-08a" xlink:label="note-0068-08" xml:id="N16C4C" xml:space="preserve">Expoſi-<lb/>tio ipſiꝰ <lb/>ita et ſi-<lb/>cut.</note>
              <note position="right" xlink:href="note-0068-09a" xlink:label="note-0068-09" xml:id="N16C58" xml:space="preserve">pḣs deci­<lb/>ma octa­<lb/>ua partꝪ <lb/>ꝓble.</note>
              <note position="right" xlink:href="note-0068-10a" xlink:label="note-0068-10" xml:id="N16C64" xml:space="preserve">Citiꝰ ca-<lb/>pit̄̄ du-<lb/>pliciter</note>
            </div>
            <p xml:id="N16C6E">
              <s xml:id="N16C6F" xml:space="preserve">Secundo contra primam ſuppoſi-<lb/>tionem: et vniuerſaliter contra fundamentum to-<lb/>tius opinionis arguitur ſic: quia ſi illa ſuppoſi-<lb/>tio eſſet vera: ſequeretur /  aliqua potētia poſſet <lb/>pertranſire aliquam reſiſtentiam: et tamen non <lb/>poſſet illam pertranſire: hoc manifeſte implicat: <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N16C7E" xml:space="preserve">Sequela probatur / et <lb/>pono caſum /  ſit vna reſiſtentia vniformiter dif-<lb/>formis a gradu / vt duo vſ̄ ad quartum et ſit vna <lb/>potentia vt .4. / que inuariata incipiat pertranſi-<lb/>re talem reſiſtentiam ſiue incipiat moueri in tali <lb/>reſiſtentia: ab extremo remiſſiori: quo poſito ar-<lb/>guitur ſic / illa potentia nun̄ perueniet ad finem <lb/>illius reſiſtentie: igitur non pertranſibit illam.</s>
            </p>
            <pb chead="Primi tractatus" file="0069" n="69"/>
            <p xml:id="N16C93">
              <s xml:id="N16C94" xml:space="preserve">Sed  illã ꝑtranſibit arguitur: q2 quãlibet par-<lb/>tem eius proportionalē ꝓportione dupla mino-<lb/>ribus terminatis verſus extremū intenſius per-<lb/>tranſibit: igitur totã reſiſtentiã pertranſibit. </s>
              <s xml:id="N16C9D" xml:space="preserve">Cõ-<lb/>ſequentia patet: q2 oēs partes ꝓportionales pro­<lb/>portione dupla illius reſiſtentie totã illam reſi-<lb/>ſtentiã conſtituūt. </s>
              <s xml:id="N16CA6" xml:space="preserve">Sed iam reſtat ꝓbare pro ꝓba­<lb/>tione alterius partis /  nun̄ ad finē deueniet: q2 <lb/>nõ ſufficit in tēpore finito tranſire illã reſiſtentiã: <lb/>igitur nun̄ deueniet ad finē illius reſiſtentie. </s>
              <s xml:id="N16CAF" xml:space="preserve">Ar-<lb/>guitur antecedens et capio vnã aliam reſiſtentiam <lb/>difformiter difformē diuiſam per partes ꝓpor-<lb/>tionales ꝓportione dupla: cuius prima pars pro­<lb/>portionales ſit vniformis vt duo et ſecūda vt tria <lb/>et tertia vt .3. cū dimidio et quarta vt tria cū dimi-<lb/>dio et dimidio dimidii / et ſic ↄ̨ſequenter aſcenden-<lb/>do: ita  quelibet pars ꝓportionalis tali ꝓpor-<lb/>tionis duple diuiſione / ſit vniformiter intenſa in <lb/>iſta reſiſtentia difformiter difformi ſicut punctus <lb/>initiatiuus conſimilis partis in reſiſtētia vnifor-<lb/>miter difformi: et ſint tales reſiſtentie equales ex-<lb/>tenſiue / quo poſito ſic argumentor iſta potētia vt <lb/>4. non ſufficit ꝑtranſire iſtã reſiſtentiã difformem <lb/>in tēpore finito / et iſta reſiſtentia minꝰ reſiſtit quã <lb/>alia vniformiter difformis / vt conſtat reſpiciēdo <lb/>ad reſiſtentiã partiū ꝓportionaliū vniꝰ et alteriꝰ: <lb/>igitur talis potentia vt .4. nõ ſufficit pertranſire <lb/>talē reſiſtentiã vniformiter difformē a ſecūdo gra­<lb/>du vſ ad quartū / quod fuit ꝓbandū. </s>
              <s xml:id="N16CD8" xml:space="preserve">Cõſequētia <lb/>eſt nota cū minore et maior arguitur / q2 aliquantū <lb/>tēpus requirit illa potentia ad pertranſeundum <lb/>primã partē ꝓportionalē: et tantū vel maiꝰ requi­<lb/>rit ad ꝑtrãſeundū ſcḋam: et iterū tantū vel maius <lb/>ad ꝑtranſeundū tertiã: et ſic cõſequenter: et ſunt in­<lb/>finite partes ꝓportionales: igitur in nullo tēpo-<lb/>re finito ſufficit talis potentia illã reſiſtentiã dif-<lb/>formiter difformē ꝑtranſire. </s>
              <s xml:id="N16CEB" xml:space="preserve">Conſequentia patet / <lb/>et ꝓbatur antecedēs / qm̄ tranſeundo primã partē <lb/>ꝓportionalē / que eſt vt duo mouetur a ꝓportione <lb/>dupla: et tranſeundo ſcḋam / que eſt vt .3. mouetur a <lb/>ꝓportione ſexquitertia: et tranſeundo tertiã / que <lb/>eſt vt .3. cū dimidio mouetur a ꝓportione ſexqui-<lb/>ſeptima / et ſic conſequenter ſemꝑ a minori ꝓpor-<lb/>tione quã ſubdupla ad precedentē: igitur cõtinuo <lb/>tranſeundo partē ꝓportionalē ſequentē, requirit <lb/>maiꝰ tēpus quã trãſeūdo partē precedentē. </s>
              <s xml:id="N16D00" xml:space="preserve">Patet <lb/>cõſequentia / qm̄ ſi cotinuo moueretur a ſubdupla <lb/>ꝓportione in parte ꝓportionali ſequenti ad pro-<lb/>portionē qua mouebatur in parte īmediate pre-<lb/>cedenti: ſemꝑ adequate tantū tēpus requireret ad <lb/>tranſeundū partē ſequentē ſicut īmediate prece-<lb/>dentē: q2 partes continuo ſe habent in ꝓportione <lb/>dupla et ſimiliter ꝓportiones ſe tunc haberent in <lb/>ꝓportione dupla: ſed modo cõtinuo in parte ſe-<lb/>quenti mouetur a minori ꝓportione quã ſubdu-<lb/>pla ad ꝓportionē / qua mouetur in parte īmediate <lb/>precedenti: igitur continuo maius tēpus requirit <lb/>ad pertranſeundū partē ſequentē quã precedentē <lb/></s>
              <s xml:id="N16D1C" xml:space="preserve">Sed  cõtinuo moueatur a minori ꝓportiõe quã <lb/>ſubdupla in parte ſequenti quã in parte īmediate <lb/>precedenti patet / q2 in prima mouetur a ꝓportiõe <lb/>dupla / et in ſecūda a ꝓportiõe ſexquitertia modo <lb/>ſexquitertia minor eſt quã ſubdupla duple / vt ptꝫ <lb/>ex ꝓbatione tertie cõcluſiõis quarti capitis ſcḋe <lb/>partis et ſexta ſuppoſitione capitis eiuſdē. </s>
              <s xml:id="N16D2B" xml:space="preserve">Itē in <lb/>tertia mouet̄̄ a ꝓportiõe ſexquiſeptīa: modo ſexq̇­<lb/>ſeptīa minor eſt quã ſubdupla ſexq̇tertie / et ſic cõ-<lb/>ſequenter / vt patet ex ſexta ſuppoſitione quarti ca­<lb/>pitis preallegati: igitur.</s>
            </p>
            <cb chead="Capitulum ſextū."/>
            <p xml:id="N16D38">
              <s xml:id="N16D39" xml:space="preserve">Reſpõdeo ad argumentum breuiter / <lb/>negando ſequelã: et ad ꝓbationē dico /  illa ↄ̨ña <lb/>nichil valet: quãlibet partē ꝓportionalē ſecundū <lb/>hanc diuiſionē hoc mobile ꝑtranſibit: ergo totuꝫ <lb/>ſpaciū ſiue reſiſtentiã ꝑtranſibit: īmo ſicut ꝓbat <lb/>argumentū ſi mobile et illa reſiſtentia ſimul ma-<lb/>nerent ꝑ infinitū tēpus: ꝑ īfinitū tēpus mobile mo­<lb/>ueret̄̄ ſupra reſiſtentiã / et nū̄ veniret ad terminū.</s>
            </p>
            <p xml:id="N16D4A">
              <s xml:id="N16D4B" xml:space="preserve">Sed ↄ̨̨tra q2 poſſibile eſt /  potētia vt <lb/>4. ꝑtranſeat reſiſtentiã difformē in tꝑe finito, cuiꝰ <lb/>ṗma pars ꝓportiõalis eſt vniformiter difformis <lb/>a duobꝰ vſ ad tertiū, et ſecūda etiã vniformiter <lb/>difformis a tertio vſ ad tertiū cū dimidio, et ſic <lb/>cõſequenter vſ ad quartū excluſiue: igit̄̄ poſſibi-<lb/>le eſt potentiã vt .4. ꝑtranſire reſiſtentiã vniformi-<lb/>ter difformē a duobꝰ vſ ad quartū: et per conſe-<lb/>quens male negatū eſt hoc. </s>
              <s xml:id="N16D5E" xml:space="preserve">Arguit̄̄ antecedens: et <lb/>pono /  ſit vna reſiſtentia pedalis diuiſa per par­<lb/>tes ꝓportionales ꝓportione quadrupla: cuiꝰ pri-<lb/>ma pars ꝓportionalis ſit vniformiter difformis <lb/>a ſecūdo vſ ad tertiū, et ſecunda a tertio vſ ad <lb/>tertiū cū dimidio, et ſic cõſequēter vſ ad quarū <lb/>excluſiue: deinde capio vnã aliã reſiſtentiã ſimili-<lb/>ter pedalē: diuiſam per partes ꝓportionales ꝓ-<lb/>portione quadrupla: cuiꝰ prima pars ꝓportiona­<lb/>lis ſit vniformis vt .3. et ſecūda vt .3. cū dimidio, et <lb/>tertia vt .3. cū dimidio et dimidio dimidii, et ſic cõ-<lb/>ſequēter: ita  quelibet pars ꝓportiõalis in tali <lb/>reſiſtentia ſit vniformiter intēſa ſicut gradus in-<lb/>ſiſſimꝰ in parte cõſimili ſiue correſpondēte in alia <lb/>reſiſtentia pedali cuiꝰ partes ꝓportionales ſunt <lb/>vniformiter difformes: quo poſito ſic argumētor <lb/>iſta ſecūda reſiſtentia cuiꝰ partes ꝓportiõales ſūt <lb/>vniformes eſt maioris reſiſtentie quã altera: vt ſa­<lb/>tis facile ptꝫ intelligenti reſiſtentiã partiū ꝓpor-<lb/>tionabiliū in vna et in altera: et tamen potentia vt <lb/>4. ſufficit in tēpore finito ꝑtranſire iſtã ſecundam <lb/>reſiſtentiã: igit̄̄ et alterã cuiꝰ partes ꝓportionales <lb/>ſunt vniformiter difformes. </s>
              <s xml:id="N16D8D" xml:space="preserve">Cõſequētia ptꝫ ꝑ locū <lb/>a maiori et maior ſimiliter: et minor ꝓbat̄̄: ſuppo-<lb/>nendo /  oīs ꝓportio ſuꝑparticularis diuidit̄̄ in <lb/>duas ꝓportiones / quaꝝ vna eſt medii numeri ad <lb/>minimū et alia maximi ad mediū: et illa que eſt ma­<lb/>ximi ad mediuꝫ, eſt maior quã tertia pars totius <lb/>ꝓportionis ſuꝑparticularis: vt ptꝫ ex decimo cor­<lb/>relario tertie cõcluſionis quarti capitis ſecunde <lb/>partis. </s>
              <s xml:id="N16DA0" xml:space="preserve">Hoc ſuppoſito ſic arguo potentia / vt .4. in <lb/>aliquo tēpore ꝑtranſit prima partē ꝓportionalē <lb/>talis reſiſtentie: et in ſubſexquitertio tēpore ꝑtran­<lb/>ſit ſcḋam: et ſic cõſequēter ita  quãlibet ſequentē <lb/>ꝑtranſit in ſubſexq̇tertio tēpore ad tēpus in quo <lb/>ꝑtrãſit īmediate p̄cedentē: igit̄̄ totū tēpus in quo <lb/>pertranſit oēs partes alias a prima eſt triplū ad <lb/>tempus in quo pertranſit primã: vt patet intelli-<lb/>genti quintum caput prime partis: et tempus in <lb/>quo pertrãſit primam eſt finitū: igitur totū tēpus <lb/>aggregatū eſt finituꝫ. </s>
              <s xml:id="N16DB7" xml:space="preserve">Sed iam probo antecedens / <lb/>quoniam in aliquo tempore pertranſit primam: <lb/>ſignetur igitur illud tempus et ſit vna hora gra-<lb/>tia exempli: et in illa hora per illam partem con-<lb/>tinuo mouetur a proportione ſexquitertia: quia <lb/>reſiſtentia eſt vt .3. et potentia vt .4. et tranſeundo <lb/>ſecundam partem proportionalem / que eſt vt .3. cū <lb/>dimidio mouetur a proportione ſexquiſeptima: <lb/>que vt patet ex ſuppoſitione non eſt ſubtripla ad <lb/>ſexquitertiam ſed maior quam ſubtripla: ſed ſi <lb/>illa eſſet ſubtripla tranſiret ſecundam partem <lb/>ꝓportiõalē in ſubſexquitertio tēpore / ergo modo               <pb chead="Primi tractatus" file="0070" n="70"/>               ꝑtranſit illã in ſubſexquitertio tēpore vel minori. <lb/></s>
              <s xml:id="N16DD6" xml:space="preserve">Cõſequentia eſt nota et minor ꝓbatur: q2 ſi tran-<lb/>ſeundo ſecundã moueretur a ſubtripla ꝓportiõe <lb/>et ſecūda eſſet equalis prime extēſiue / tūc in triplo <lb/>tēpore ꝑtranſiret illã ad tēpus in quo pertranſit <lb/>primã puta in tribus horis qm̄ ꝑtranſit primã in <lb/>hora / vt poſitū eſt: ſed modo illa ſecunda pars eſt <lb/>ſubquadrupla ad primaꝫ / ergo in ſubquadruplo <lb/>tēpore ꝑtranſibit eam: ſed ſubquadruplū ad tres <lb/>horas ſunt .3. quarte: et tres quarte ſūt ſubſexqui­<lb/>tertiū ad vnã horã in qua ꝑtranſit primã partem / <lb/>igitur ſecundã trãſit in ſubſexquitertio tēpore ad <lb/>primã. </s>
              <s xml:id="N16DEF" xml:space="preserve">Et ſic ꝓbabis /  tertiã in ſubſexquitertio <lb/>tēpore ꝑtranſit ad ſecundã: et de oībus aliis con-<lb/>ſequenter. </s>
              <s xml:id="N16DF6" xml:space="preserve">adiutorio ſecūdi correlarii quarte con­<lb/>cluſionis quarti capitis ſecunde partis.</s>
            </p>
            <p xml:id="N16DFB">
              <s xml:id="N16DFC" xml:space="preserve">Reſpondeo ad replicã cõcedendo an­<lb/>tecedens: dūmodo ille partes ꝓportiõales illius <lb/>reſiſtentie nõ ſe habeant in ꝓportione dupla nec <lb/>in aliqua minori: et nego cõſequentiã. </s>
              <s xml:id="N16E05" xml:space="preserve">Et ratio eſt / <lb/>q2 talis reſiſtentia de qua cõceditur nõ eſt vnifor-<lb/>miter difformis: nec talis potētia requirit tantū <lb/>tēpus ad ꝑtranſeundū ſecundã partē ꝓportiõa-<lb/>lem quantū ad ꝑtrãſeundū primã: vt iam ꝓbatuꝫ <lb/>eſt.               <anchor type="note" xlink:href="note-0070-01" xlink:label="note-0070-01a"/>               </s>
              <s xml:id="N16E17" xml:space="preserve">¶ Ex deductione et ſolutione huiꝰ argumenti <lb/>ſequitur primo:  ſi potentia vt quatuor cõtinuo <lb/>moueretur per mediū vniformiter difforme a non <lb/>gradu reſiſtentie vſ ad quartū: et perpetuo du-<lb/>raret potentia et mediū taliter diſpoſitū: ꝑpetuo <lb/>ipſa moueretur: et nun̄ ipſuꝫ ꝑtranſiret. </s>
              <s xml:id="N16E24" xml:space="preserve">Patet <lb/>hoc correlariū ex deductiõe et ſolutiõe argumenti <lb/>               <anchor type="note" xlink:href="note-0070-02" xlink:label="note-0070-02a"/>               </s>
              <s xml:id="N16E30" xml:space="preserve">¶ Sequitur ſecūdo:  reſiſtentia vniformiter dif-<lb/>formis nõ correſpõdet gradui medio reſiſtentie: <lb/>ita  tantū reſiſtat ſicut gradus medius. </s>
              <s xml:id="N16E37" xml:space="preserve">Proba­<lb/>tur hoc ex p̄cedenti correlario / q2 alias ſequeretur <lb/> potentia vt .4. poſſet in tēpore finito ꝑtranſire <lb/>reſiſtentiã vniformiter difformē a nõ gradu vel a <lb/>gradu certo minori vſ ad quartū / q2 moueretur <lb/>in ea a ꝓportiõe dupla vel aliqua alia certa eq̇ua­<lb/>lenter per totã illã reſiſtentiam. </s>
              <s xml:id="N16E46" xml:space="preserve">¶ Sed q2 aliquis <lb/>poſſet dicere /  correſpõdet gradui medio: dūmo­<lb/>do g̈dus ſūmꝰ talis teſiſtētie nõ ſit eq̈lis potentie <lb/>mouēti in ea vel minor.               <anchor type="note" xlink:href="note-0070-03" xlink:label="note-0070-03a"/>               </s>
              <s xml:id="N16E54" xml:space="preserve">Ideo aliter ꝓbo p̄dictum <lb/>correlariū ratiõe Gaythani de thebis ſi memini: <lb/>q2 ſi correſpõderet gradui medio ſeq̄ret̄̄ /  poten­<lb/>tia vt .9. in equali tēpore adequate ꝑtranſiret re-<lb/>ſiſtentiã vniformiter difformē a nõ gradu vſ ad <lb/>octauū: in quo adequate ꝑtranſiret ſcḋaꝫ medie-<lb/>tatē eiꝰ: ita  ita cito ꝑtranſiret totū ſicut eiꝰ me-<lb/>dietatē adequate: ſed ↄ̨ñs eſt manifeſte falſū: igit̄̄ <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N16E67" xml:space="preserve">Sequela ꝓbatur / q2 talis po-<lb/>tentia vt .9. haberet ad totã illã reſiſtentiã ꝓpor-<lb/>tionē duplã ſexquiquartã: cū tota illa reſiſtentia <lb/>ſit per te vt .4. qui eſt gradus mediꝰ. </s>
              <s xml:id="N16E70" xml:space="preserve">Modo .9. ad <lb/>4. eſt ꝓportio dupla ſexquiquarta: et ad ſecundaꝫ <lb/>medietatē haberet ꝓportionē ſexquialterã: cum <lb/>gradus eiꝰ medius ſit vt .6. </s>
              <s xml:id="N16E79" xml:space="preserve">Modo .9. ad .6. eſt ꝓ-<lb/>portio ſexquialtera: ſed ꝓportio ſexquialtera eſt <lb/>ſubdupla ad duplã ſexquiquartã / vt patꝫ ex ſexto <lb/>capite ſcḋe partis et ſpaciū trãſeundū ab illa pro­<lb/>portiõe puta ſcḋa medietas eſt ſubduplū ad totã <lb/>illã reſiſtentiã: ergo ſequit̄̄ /  ī equali tēpore ꝑtrã­<lb/>ſit illã ſcḋam medietatē et totã illã reſiſtentiã: qḋ <lb/>fuit ꝓbandū.               <anchor type="note" xlink:href="note-0070-04" xlink:label="note-0070-04a"/>               </s>
              <s xml:id="N16E8F" xml:space="preserve">¶ Sequit̄̄ tertio /  quãuis potentia <lb/>vt .4. nõ ſufficit ꝑtrãſire reſiſtentiam vniformiter <lb/>difformē a ſcḋo g̈du vſ ad quartū: cuiꝰ videlicet <lb/>prima pars ꝓportiõalis ꝓportiõe dupla incipit <lb/>a ſcḋo vſ ad tertiū et ſcḋa īcipit a tertio vſ ad <lb/>tertiū cū dimidio / et ſic cõſequēter: nichilominꝰ tñ               <cb chead="Capitulū ſextū."/>               talis potētia vt .4. ſufficit ꝑtrãſire tantã reſiſten-<lb/>tiã extenſiue: cuiꝰ videlicet prima pars ꝓportiõa-<lb/>lis ꝓportione quadrupla eſt oīno cõſimilis reſi-<lb/>ſtētie cū prima parte ꝓportiõali ꝓportiõe dupla <lb/>alterius reſiſtentie vniformiter difformis, et ſcḋa <lb/>cū ſecūda, et tertia cū tertia, et ſic cõſequēter. </s>
              <s xml:id="N16EA9" xml:space="preserve">Pri­<lb/>ma pars ptꝫ ex deductione et ſolutione argumēti <lb/>et ſecūda ex deductione et ſolutione replice.               <anchor type="note" xlink:href="note-0070-05" xlink:label="note-0070-05a"/>               </s>
              <s xml:id="N16EB5" xml:space="preserve">¶ Se-<lb/>quitur quarto /  quãuis potētia vt .4. nõ ſufficit <lb/>ꝑtranſire in aliquo tēpore finito reſiſtentiã peda­<lb/>lem vniformiter difformē terminatã ad quartū: <lb/>cuiꝰ videlicet prima pars ꝓportiõalis ꝓportione <lb/>dupla incipiat a ſcḋo et terminet̄̄ ad tertiū .etc̈. vt <lb/>poſitū eſt in priori ꝑte p̄cedētꝪ correlarii: nichilo­<lb/>minus vbi talis reſiſtētia pedalis efficeretur qua­<lb/>drupedalis per rarefactionē aut augmentationē <lb/>(nõ eſt cura) ita tamen  ille partes reſiſtētie que <lb/>cõtinuo ſe habebant in ꝓportione dupla cõtinuo <lb/>ſe habeant in ꝓportione quadrupla quo ad extē-<lb/>ſionē: ipſis tamē manētibꝰ ſemꝑ in eodē ſtatu quo <lb/>ad ītēſionē: potētia vt .4. ſufficit tūc illã reſiſtentiã <lb/>in tꝑe finito ꝑtrãſire. </s>
              <s xml:id="N16ED4" xml:space="preserve">Patet ṗma pars correlarii <lb/>ex ṗori correlaro et ſcḋa ex deductiõe replice.               <anchor type="note" xlink:href="note-0070-06" xlink:label="note-0070-06a"/>               </s>
              <s xml:id="N16EDE" xml:space="preserve">¶ Ex <lb/>q̊ correlario ſequitur facile quītū /  quãuis talis <lb/>reſiſtentia ſic ad quadruplū augeat̄̄ extenſiue: ni­<lb/>chilominus tamē infinite partes eiꝰ ꝓportiõales <lb/>diminuūtur, et efficiūtur minores extenſiue. </s>
              <s xml:id="N16EE9" xml:space="preserve">Pri-<lb/>ma pars ponit̄̄ / et ſcḋa ꝓbatur / q2 ſi infinite mane­<lb/>rent tante quãte erant antea: cū maneãt eque in-<lb/>tenſe et eque reſiſtētes: eo modo reſiſterēt quo reſi­<lb/>ſtebant antea quãdo cõtinuo ſe habebãt in ꝓpor­<lb/>tione dupla: ſed antea requirebat̄̄ tēpus infinitū <lb/>ad ꝑtranſeundū illas a tali potentia: cū tantū tē­<lb/>pus requirebat̄̄ ad ꝑtranſeundū aliquã partē vel <lb/>maiꝰ quantū ad quãlibet p̄cedentē: vt ptꝫ ex dedu­<lb/>ctione argumēti: igitur modo etiã requireret̄̄ tē-<lb/>pus infinitū: ſed hoc eſt falſum / vt patꝫ ex p̄cedenti <lb/>correlario / igitur illud ex quo ſequitur: et ꝑ conſe­<lb/>quēs dicendū eſt /  īfinite efficiūtur minores extē-<lb/>ſiue: cū nec etiã dicendū ſit /  efficiant̄̄ maiores vt <lb/>facile eſſet ꝓbare ꝑ locū a maiori. </s>
              <s xml:id="N16F08" xml:space="preserve">Et hoc etiã faci­<lb/>le ptꝫ experimēto: nã capto tali pedali ſic diuiſo <lb/>ꝑ partes ꝓportiõales ꝓportiõe dupla vt poſituꝫ <lb/>eſt: et augeatur prima pars ꝓportiõalis eius ad <lb/>quadruplū: ita  efficiat̄̄ bipedalis: tūc ad hoc /  <lb/>ſecūda efficiatur ſubquadrupla ad ipſaꝫ oportet <lb/>ipſam ſimiliter augeri ad duplū: ita  efficiatur <lb/>ſemipedalis: et oportet tertiam manere nec auctã <lb/>nec diminutã: q2 eſt vna octaua: ſed oportet iam <lb/>quartam minui ad ſubduplū: q2 erat vna decima <lb/>ſexta et oportet  efficiatur vna triceſimaſecūda: <lb/>vt ſit ſubquadrupla ad octauã que eſt tertia pars / <lb/>et tunc manebit equalis cū quīta parte et ſic opor-<lb/>tebit quintã ad ſubquadruplum minui: et ſextam <lb/>ad ſuboctuplum: et ſic in infinitū / vt patet intuenti <lb/>igitur.               <anchor type="note" xlink:href="note-0070-07" xlink:label="note-0070-07a"/>               </s>
              <s xml:id="N16F2E" xml:space="preserve">Et ferme hoc modo intendit calculator ꝓ-<lb/>bare in capitulo de augmentatione concluſione <lb/>quindecima probatione ſecunda:  quantūcun <lb/>modicum ſit aliquod ſubiectum diuiſum per par­<lb/>tes proportionales certa proportione: et ſit aliud <lb/>quantūcun magnum diuiſum in partes propor­<lb/>tionales proportione maiori: aliqua erit pars <lb/>proportionalis minoris, maior parte proporti-<lb/>onali correſpondente maioris.               <anchor type="note" xlink:href="note-0070-08" xlink:label="note-0070-08a"/>               </s>
              <s xml:id="N16F46" xml:space="preserve">¶ Sequitur ſexto / <lb/> quãuis talis reſiſtentia aucta in quantitate ad <lb/>quadruplum vel octuplum quocun modo pla-<lb/>cuerit: dummodo partes reſiſtentie que antea ſe <lb/>habebant in proportione dupla quo ad extenſio­<lb/>nem ſe habeãt quo ad extenſionē in proportione               <pb chead="Primi tractatus" file="0071" n="71"/>               quadrupla, valeat in tēpore finito pertranſiri a <lb/>potentia vt .4. vt dictū eſt: nichilominus ſi dimi-<lb/>nuatur talis reſiſtentia quo ad extenſionē ad ſub-<lb/>duplū vel ad ſubtriplū .etc̈. ita  efficiatur ſemipe­<lb/>dalis, vel vna tertia, vel quarta, vel quinta: et ſic <lb/>in infinitū: dūmodo partes reſiſtentie cõtinuo ma­<lb/>nent in eadē ꝓportione in qua ſe habebant antea <lb/>puta dupla: potentia vt .4. (intelligo ſemꝑ nõ va-<lb/>riata) in nullo tēpore finito valet talē reſiſtentiam <lb/>pertranſire. </s>
              <s xml:id="N16F6A" xml:space="preserve">Patet facile ex primo correlario.</s>
            </p>
            <div xml:id="N16F6D" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0070-01a" xlink:label="note-0070-01" xml:id="N16F71" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0070-02a" xlink:label="note-0070-02" xml:id="N16F77" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0070-03a" xlink:label="note-0070-03" xml:id="N16F7D" xml:space="preserve">Gaytha-<lb/>uus de <lb/>thebis.</note>
              <note position="left" xlink:href="note-0070-04a" xlink:label="note-0070-04" xml:id="N16F87" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0070-05a" xlink:label="note-0070-05" xml:id="N16F8D" xml:space="preserve">4. correĺ.</note>
              <note position="right" xlink:href="note-0070-06a" xlink:label="note-0070-06" xml:id="N16F93" xml:space="preserve">5. correĺ.</note>
              <note position="right" xlink:href="note-0070-07a" xlink:label="note-0070-07" xml:id="N16F99" xml:space="preserve">Calcu. in <lb/>capite de <lb/>augmen.</note>
              <note position="right" xlink:href="note-0070-08a" xlink:label="note-0070-08" xml:id="N16FA3" xml:space="preserve">6. correĺ</note>
            </div>
            <note position="left" xml:id="N16FA9" xml:space="preserve">7. correĺ.</note>
            <p xml:id="N16FAD">
              <s xml:id="N16FAE" xml:space="preserve">¶ Sequitur ſeptimo /  quãuis potentia vt .4. non <lb/>ſufficit in tēpore finito pertranſire pedalē reſiſten­<lb/>tiam diuiſam in partes ꝓportionales ꝓportione <lb/>dupla: ad cuiꝰ primã habet ꝓportionē duplam et <lb/>ad ſecundã ſexquitertiã et ad tertiã ſexquiſeptimã <lb/>et ad quartã ſexquiquīdecimã et ſic in infinitum: vt <lb/>ponebatur in caſu argumenti: nichilominꝰ tamen <lb/>talis potentia ſufficit pertranſire in tēpore finito <lb/>reſiſtentiã pedalē diuiſam in partes ꝓportiõales <lb/>ꝓportione dupla ſimiliter: ad cuius primã habet <lb/>ꝓportionē duplã et ad tertiã ſexquialterã et ad ter­<lb/>tiã ſexquitertiã et ad quartã ſexquiquartã et ſic in <lb/>infinitū aſcendendo per ſpecies ꝓportiõis ſuper-<lb/>particularis nulla pretermiſſa. </s>
              <s xml:id="N16FCB" xml:space="preserve">Prima pars hu-<lb/>ius correlarii probata eſt in argumento: et ſecūda <lb/>ꝓbatur: q2 talis potentia in aliquo tēpore finito <lb/>ſufficit pertãſire primã partē parē que eſt ſecūda <lb/>in ordine: et in minori quã ſit equalis ſufficit ꝑtrã-<lb/>ſire oēs ſequentes pares: et ſimiliter. </s>
              <s xml:id="N16FD8" xml:space="preserve">in aliquo tē-<lb/>pore finito ſufficit pertranſire primã imparē: et in <lb/>minori tēpore quã in triplo ad illḋ ſufficit pertrã-<lb/>ſire oēs ſequentes impares: igitur oēs ſimul tam <lb/>pares quã impares ſufficit ꝑtranſire in tēpore fi-<lb/>nito. </s>
              <s xml:id="N16FE5" xml:space="preserve">Cõſequētia patet ex ſe / et arguitur maior / qm̄ <lb/>ſi illa potentia cõtinuo haberet ꝓportionē ſubdu­<lb/>plam ad partē parem ſequentē ad illã ꝓportionē <lb/>quã habet ad partē parem īmediate precedētem: <lb/>ↄ̨tinuo ꝑtranſiret partē ſequentē parem in duplo <lb/>minori tēpore quã īmediate precedentē cū ipſa ſit <lb/>ſubquadrupla ad parē īmediate precedentem / et ꝑ <lb/>cõſequens ſi tranſiret primã parē in hora adequa­<lb/>te: ſecundã parē tranſiret in media hora: et ſequē-<lb/>tem parē in ſubduplo tēpore: et ſic oēs pares ꝓtrã­<lb/>ſiret in duabus horis / vt patet ex quīto capite pri­<lb/>me partis. </s>
              <s xml:id="N16FFE" xml:space="preserve">modo ad quãlibet ſequentē parē habet <lb/>maiorē ꝓportionē quã ſubduplã ad ꝓportionem <lb/>quã habet ad partē parē īmediate precedentē: igi­<lb/>tur cõtinuo modo velocius mouebitur: et per con-<lb/>ſequens minus quã in equali tēpore ꝑtrãſibit oēs <lb/>pares ſequentes primã / quod fuit probandū. </s>
              <s xml:id="N1700B" xml:space="preserve">Sed <lb/>iam ꝓbo iſtã minorē videlicet /  modo habet ad <lb/>quãlibet partē parē ſeq̄ntē maiorē ꝓportionē quã <lb/>ſubduplã ad ꝓportionē quã hꝫ ad partē parē īme­<lb/>diate p̄cedentē. </s>
              <s xml:id="N17016" xml:space="preserve">Quod ſic ꝓbo / q2 ad primã parteꝫ <lb/>ꝓportionalē parē que eſt ſecunda hꝫ ꝓportionem <lb/>ſexquialterã: ad ſcḋam / q̄ eſt q̈rta hꝫ ꝓportioneꝫ <lb/>ſexquiquartã. </s>
              <s xml:id="N1701F" xml:space="preserve">Modo ſexq̇quarta eſt maior quam <lb/>medietas ſexq̇altere. </s>
              <s xml:id="N17024" xml:space="preserve">Itē ad tertiã partē parē que <lb/>eſt ſexta hꝫ ꝓportionē ſexq̇ſextã / vt ptꝫ ex caſu: mo­<lb/>do ſexq̇ſexta maior eſt quã medietas ſexquiq̈rte / et <lb/>ſic ↄ̨ñter / vt ptꝫ ex octauo correlario tertie ↄ̨cluſio­<lb/>nis q̈rti capitis ſcḋe partis. </s>
              <s xml:id="N1702F" xml:space="preserve">Sed iã ꝓbo maiorem <lb/>prīcipalis argumēti videlicet /  in aliquo tꝑe fini­<lb/>to ſufficit ꝑtrãſire primã partē īparē: et in minori <lb/>quã triplo oēs īpares ſequētes. </s>
              <s xml:id="N17038" xml:space="preserve">Qḋ ſic demõſtro / <lb/>q2 ſi ad quãlibet ſequētē īparē haberet ↄ̨tinuo ꝓ-<lb/>portionē ſubtriplã ad ꝓportionē quã haberet ad <lb/>īparē īmediate p̄cedentē / tūc ꝑtrãſiret oēs īpares <lb/>ſequētes primã in triplo tardius quã primã ade-               <cb chead="Capitulum ſextū."/>               quate: ita  ſi trãſiret primã īparem in vna hora <lb/>oēs īpares ſequētes primã in tribus horis adeq̈-<lb/>te ꝑtrãſiret: ſed modo cõtinuo mouetur a maiori <lb/>ꝓportione tranſeūdo aliquã partē imparē ſequē­<lb/>tem primã quã tūc ꝑtranſeūdo eandē q2 continuo <lb/>a maiori quã ſubtripla / igitur modo in minori tē­<lb/>pore quã triplo ꝑtranſibit oēs īpares ſequentes <lb/>primã quam primã. </s>
              <s xml:id="N17054" xml:space="preserve">Cõſequentia ptꝫ et maior ꝓ-<lb/>batur: q2 ſi tranſiret primã imparē in hora: et trã­<lb/>ſecūdo ſcḋam moueretur a ꝓportione ſubtripla <lb/>et ipſa eſſet equalis prime: tūc in triplo tēpore ꝑ-<lb/>tranſiret ipſam puta in tribꝰ horis: ſed modo il-<lb/>la ſecūda pars ꝓportionalis impar eſt ſubqua-<lb/>drupla / ergo in ſubquadruplo tēpore modo ꝑtrã­<lb/>ſit eam: et per ↄ̨ñs in ſubſexquitertio tēpore ad tē­<lb/>pus in quo ꝑtrãſit primã. </s>
              <s xml:id="N17067" xml:space="preserve">Patet hec ↄ̨ña ex ſcḋo <lb/>correlario quarte cõcluſiõis quarti capitis pre-<lb/>allegati. </s>
              <s xml:id="N1706E" xml:space="preserve">Et ſic ꝓbabitur de quibuſcū aliis dua­<lb/>bus partibꝰ īparibꝰ: videlicet  cõtinuo ꝑtranſi­<lb/>bit quãlibet partē īparem ſequentē in ſexquiter-<lb/>tio tēpore minori quã īmediate precedentē: et ſic ſi <lb/>tranſit primã in hora oēs alias ꝑtranſit in tribꝰ <lb/>horis / vt ptꝫ intelligenti quintū caput prime par­<lb/>tis. </s>
              <s xml:id="N1707D" xml:space="preserve">Sed reſtat ꝓbare minorem videlicet /  modo <lb/>cõtinuo pertranſit a maiori ꝓportione quãlibet <lb/>partē īparem ſequentem / quã tūc faceret eandem. <lb/></s>
              <s xml:id="N17085" xml:space="preserve">Quod ſic probo / qm̄ primã tranſit a ꝓportione <lb/>dupla / vt ptꝫ ex caſu: et ſecundã imparē que eſt ter-<lb/>tia a ꝓportiõe ſexquitertia. </s>
              <s xml:id="N1708C" xml:space="preserve">Modo ſexquitertia <lb/>maior eſt quam ſubtripla duple: vt ptꝫ ex decimo <lb/>correlario tertie ↄ̨cluſiõis q̈rti capitis p̄allegati. <lb/></s>
              <s xml:id="N17094" xml:space="preserve">Itē tranſit tertiã imparē que eſt quinta in ordine <lb/>a ꝓportione ſexquiquinta. </s>
              <s xml:id="N17099" xml:space="preserve">Modo ſexquiquinta <lb/>maior eſt quam ſubtripla īmo maior ꝙ̄ ſubdupla <lb/>ad ſexquitertiã / vt ptꝫ ex octauo correlario eiuſdē <lb/>cõcluſiõis / et ſic cõſequēter / vt facile ꝓbat dictum <lb/>correlariū / igitur cõtinuo ꝑtranſit a maiori ꝓpor­<lb/>tiõe quãlibet partē imparē quã tūc faceret eandē <lb/></s>
              <s xml:id="N170A7" xml:space="preserve">Et ſic ptꝫ correlariū.               <anchor type="note" xlink:href="note-0071-01" xlink:label="note-0071-01a"/>               </s>
              <s xml:id="N170AF" xml:space="preserve">¶ Sequitur octauo /  hec cõ­<lb/>ſequētia nichil valet hoc mobile ſufficit ꝑtranſi-<lb/>re cū hac reſiſtentia quãlibet partē ꝓportionalē <lb/>huiꝰ pedalis: et quãlibet ſequentē in minori tēpo-<lb/>re quã īmediate precedentē: igitur ſufficit trãſire <lb/>pedale cū hac reſiſtentia. </s>
              <s xml:id="N170BC" xml:space="preserve">Et loquor in antecedēte <lb/>de partibus ꝓportionalibꝰ ꝓportione dupla ſe-<lb/>cundū hanc diuiſionē. </s>
              <s xml:id="N170C3" xml:space="preserve">Probatur correlariū / et vo­<lb/>lo /  aliquod pedale diuidatur ꝓportione dupla <lb/>et  aliqua potētia puta et .8. gr̄a exēpli ſufficiat <lb/>ꝑtranſire primã partē ꝓportionalē in hora: et ſe-<lb/>cundã in media hora cū quarta. / et tertiã in media <lb/>hora cū octaua: et quartã in media hora cū decīa <lb/>ſexta: et ſic in īfinitū taliter /  quãlibet preter pri-<lb/>mã ꝑtranſiret in media hora cū aliquo tꝑe vltra: <lb/>qḋ tēpus vltra eſſet cõtinuo ſubduplū: quo poſito <lb/>iã ptꝫ totū correlariū. </s>
              <s xml:id="N170D8" xml:space="preserve">Qm̄ manifeſtū eſt /  requi­<lb/>rerent̄̄ īfinite medie hore ad ꝑtrãſeundū illud pe-<lb/>dale: et tñ q̄libet pars ꝓportiõalis ſequēs in mi-<lb/>nori tꝑe ꝑtrãſit̄̄ quã īmediate p̄cedēs et quamlibet <lb/>ſufficit pertranſire / vt notum eſt: igitur.</s>
            </p>
            <div xml:id="N170E3" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0071-01a" xlink:label="note-0071-01" xml:id="N170E7" xml:space="preserve">8. correĺ.</note>
            </div>
            <p xml:id="N170ED">
              <s xml:id="N170EE" xml:space="preserve">Tertio contra omnes concluſiones <lb/>ſimul arguitur ſic: ille vel maior pars illarum <lb/>ſupponit vnū falſū / ergo ſūt falſe. </s>
              <s xml:id="N170F5" xml:space="preserve">Arguit̄̄ añs / q2 <lb/>ſupponūt aliquã reſiſtentiã poſſe vniformiter ſuc­<lb/>ceſſiue diminui ab aliq̈ ponã: ſed hoc nõ eſt poſſi-<lb/>bile igit̄̄. </s>
              <s xml:id="N170FE" xml:space="preserve">Minor ꝓbat̄̄ / q2 det̄̄ potētia vt .8. q̄ vni-<lb/>formiter corrūpat et remittat reſiſtentiã vt .4. per <lb/>vnã horã / et arguitur ſic: iſta potentia vt .8. remit-<lb/>tit vniformiter in hora reſiſtentiam vt .4. / ergo in <lb/>medietate hore remittit medietatē reſiſtentie: et               <pb chead="Primi tractatus" file="0072" n="72"/>               per conſequens talis potentia agit a proportiõe <lb/>dupla alterius proportionis </s>
              <s xml:id="N17110" xml:space="preserve">Nã antea agebat a <lb/>dupla et mõ a quadrupla. </s>
              <s xml:id="N17115" xml:space="preserve">ſed quadrupla eſt du-<lb/>pla duple. </s>
              <s xml:id="N1711A" xml:space="preserve">vt patet intelligenti ſextū capitulum ſe­<lb/>cunde partis: igitur agit a duplo maiori velocita­<lb/>te. </s>
              <s xml:id="N17121" xml:space="preserve">quoniam velocitas ſequitur proportionem pro­<lb/>portionū / vt patet ex prima ſuppoſitione precedē­<lb/>tis capitis. </s>
              <s xml:id="N17128" xml:space="preserve">et per conſequens corrumpit tantū re­<lb/>ſiſtentie in ſecunda parte proportionali propor-<lb/>tione dupla: et per conſequens non vniformiter / <lb/>quod fuit probandum.               <anchor type="note" xlink:href="note-0072-01" xlink:label="note-0072-01a"/>               </s>
              <s xml:id="N17136" xml:space="preserve">¶ Dices forte concedendo <lb/>quod infertur. </s>
              <s xml:id="N1713B" xml:space="preserve">videlicet  nulla reſiſtentia poteſt <lb/>vniformiter deperdi in aliquo tempore: ſꝫ hoc nõ <lb/>eſt contra concluſiones.</s>
            </p>
            <div xml:id="N17142" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0072-01a" xlink:label="note-0072-01" xml:id="N17146" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1714C">
              <s xml:id="N1714D" xml:space="preserve">Sed contra / quia manifeſtum ē hoc <lb/>eſſe contra viceſimã concluſionem igitur </s>
              <s xml:id="N17152" xml:space="preserve">Item re-<lb/>ſiſtentia poteſt vniformiter remitti a potentia / igi­<lb/>tur ſolutio nulla. </s>
              <s xml:id="N17159" xml:space="preserve">Arguitur antecedens / et pono ca­<lb/>ſum /  eque velociter proportionabiliter ſicut re-<lb/>mittitur reſiſtentia ab aliqua potentia ita ꝓpor-<lb/>tionabiliter potentia decreſcat: ita  potentie ad <lb/>reſiſtentiam maneat cõtinuo eadē proportio: quo <lb/>poſito motus continuo erit vniformis / igitur vni-<lb/>formiter deperdetur tunc reſiſtentia. </s>
              <s xml:id="N17168" xml:space="preserve">Quod vero <lb/>tunc motus erit vniformis / patet ex decima octa-<lb/>ua concluſione precedentis capitis.</s>
            </p>
            <p xml:id="N1716F">
              <s xml:id="N17170" xml:space="preserve">Reſpondeo / igitur ad argumentum <lb/>negando antecedens et ad probationem pono du­<lb/>as concluſiones.</s>
            </p>
            <note position="left" xml:id="N17177" xml:space="preserve">inq̇rit̄̄ an <lb/>poſſit re­<lb/>ſiſtentia <lb/>vniformi­<lb/>ter deꝑdi</note>
            <p xml:id="N17183">
              <s xml:id="N17184" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N17187" xml:space="preserve">Nulla reſiſtentia <lb/>poteſt vniformiter deperdi per actionem alicuius <lb/>potentie non variate, nec ab extrinſeco impedite. <lb/></s>
              <s xml:id="N1718F" xml:space="preserve">Patet hec concluſio ex deductione argumenti.</s>
            </p>
            <p xml:id="N17192">
              <s xml:id="N17193" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N17196" xml:space="preserve">Aliqua reſiſten­<lb/>tia poteſt vniformiter remitti ab aliqua potentia <lb/>continuo eque proportionabiliter variata et mi-<lb/>norata cum ſua reſiſtentia: vel eque proportiona­<lb/>biliter impedita ſicut reſiſtentia remittitur. </s>
              <s xml:id="N171A1" xml:space="preserve">Pa-<lb/>tet hec concluſio ex deductione replice </s>
              <s xml:id="N171A6" xml:space="preserve">Et dico no-<lb/>tanter aut eque proportionabiliter impedita etc. <lb/>quoniaꝫ ſi ſit aliqua reſiſtentia vt .4. que remitta­<lb/>tur a potentia vt .8. non variata ſed ab aliquo ex­<lb/>trinſeco impedita: taliter  quando reſiſtētia fue­<lb/>rit vt .3. impediantur duo gradus actiuitatis ipſi­<lb/>us potentie: et quando reſiſtentia fuerit vt duo im­<lb/>pediantur alii duo gradus actiuitatis ipſius po­<lb/>tentie: continuo fiet actio a proportione dupla.</s>
            </p>
            <note position="left" xml:id="N171B9" xml:space="preserve">correla.</note>
            <p xml:id="N171BD">
              <s xml:id="N171BE" xml:space="preserve">¶ Sequitur ex iſtis correlarium /  vbicū aliqua <lb/>potentia agit in ſuam reſiſtentiam eam corrumpē­<lb/>do ſine reactione: neceſſe eſt reſiſtentiam difformi­<lb/>ter remitti ceteris aliis paribus. </s>
              <s xml:id="N171C7" xml:space="preserve">et vbicun potē-<lb/>tia introducit in aliquod paſſuꝫ ſuam qualitatē: <lb/>difformiter eam introducit ceteris aliis paribus.</s>
            </p>
            <note position="left" xml:id="N171CE" xml:space="preserve">argumē-<lb/>tū calcu.</note>
            <p xml:id="N171D4">
              <s xml:id="N171D5" xml:space="preserve">Quarto contra eaſdes concluſio-<lb/>nes arguitur ſic / quia ſi ille eſſent vere: ſequeretur <lb/>hec concluſio /  omnes potentie inuariate ſiue eq̈­<lb/>les ſiue inequales idem mediū non variatum trã-<lb/>ſeuntes in quo acquiritur aut deperditur motus: <lb/>eandem latitudinem motus acquirerent vel deꝑ­<lb/>derent. </s>
              <s xml:id="N171E4" xml:space="preserve">ſed conſequens eſt falſum: igitur illud ex <lb/>quo ſequitur </s>
              <s xml:id="N171E9" xml:space="preserve">Sequela eſt nota / quia equales pro-<lb/>portiones acquirerent vel deperderent / igitur eq̈-<lb/>les latitudines motus. </s>
              <s xml:id="N171F0" xml:space="preserve">Sed falſitas conſequētis <lb/>oſtenditur / et pono caſum /  ſit vnum medium vni­<lb/>formiter difforme a gradu vſ ad certum graduꝫ <lb/>intenſiorem: et volo /  ſint due potentie equa-               <cb chead="Capitulum ſextum"/>               les a. et b. quarū vna puta a. incipiat moueri a me­<lb/>dio gradu verſus extremum intenſius: et alia pu-<lb/>ta b. īcipiat moueri ab extremo remiſſiori verſus <lb/>medium. </s>
              <s xml:id="N17202" xml:space="preserve">quo poſito ſic argumentor maiorem ꝓ-<lb/>portioneꝫ habet b. potentia ad quodlibet punctū <lb/>medietatis remiſſioris quam habeat a. ad ſimile <lb/>punctum ſiue correſpondens medietatis intenſio­<lb/>ris: creſcat igitur ipſum a. quo ad vſ ad quodli-<lb/>bet punctum medietatis intenſioris habeat maio­<lb/>rem proportionem quam b. ad ſimile punctuꝫ me­<lb/>dietatis remiſſioris: et capio inſtans in quo a. ha­<lb/>bet equalem proportionem ad quodlibet punctuꝫ <lb/>medietatis intenſioris ſicut b. ad ſimile punctum <lb/>medietatis remiſſioris: et volo /  continuo mouea­<lb/>tur a tali proportione. </s>
              <s xml:id="N1721B" xml:space="preserve">quo poſito ſequitur /  a. eq̈­<lb/>liter mouebitur per medietatem intenſiorem ſicut <lb/>b. per medietatem remiſſiorem. </s>
              <s xml:id="N17222" xml:space="preserve">et equalem latitu­<lb/>dinem motus deperdet a. per intenſiorem mouen­<lb/>do ſicut b. ꝑ medietatē remiſſiorē: ſꝫ b. minorē la-<lb/>titudinem deperdet per intenſiorem medietatem <lb/>mouendo quam per remiſſiorem / ergo per intēſio­<lb/>rem medietatem minorem latitudinem motus de­<lb/>perdit b. quam a. / et per conſequens non equalem / <lb/>quod fuit probandum.</s>
            </p>
            <p xml:id="N17233">
              <s xml:id="N17234" xml:space="preserve">Reſpondeo ad argumentum admit-<lb/>tendo caſum et negando illud quod aſſumitur vel <lb/>ſupponitur. </s>
              <s xml:id="N1723B" xml:space="preserve">videlicet /  dabile ſit inſtãs in quo a. <lb/>habeat talem proportionem ad quodlibet pūctū <lb/>medietatis intenſioris qualem habet b. ad pūctū <lb/>ſimile ſiue correſpondens ī medietate remiſſiori.</s>
            </p>
            <p xml:id="N17244">
              <s xml:id="N17245" xml:space="preserve">Quãuis enim poſſibile ſit  habeat maiorem. </s>
              <s xml:id="N17248" xml:space="preserve">et <lb/> habeat minorem: non tamen  habeat equaleꝫ <lb/>               <anchor type="note" xlink:href="note-0072-02" xlink:label="note-0072-02a"/>               </s>
              <s xml:id="N17254" xml:space="preserve">¶ Ex quo ſequitur primo /  hec conſequentia ni-<lb/>chil valet a. tranſit de minori ad maiꝰ: ergo a. trã­<lb/>ſit per eq̈le </s>
              <s xml:id="N1725B" xml:space="preserve">Inſtantia enim eſt in propoſito </s>
              <s xml:id="N1725E" xml:space="preserve">Trã-<lb/>ſit enī a. de minori proportione reſpectu cuiuſlib3 <lb/>puncti ad maiorem: et non equalem cuilibet pun-<lb/>cto: </s>
              <s xml:id="N17267" xml:space="preserve">Analogia poteſt faciliter capi quoniaꝫ dato <lb/> ſint hic tres homines quorum nullus eſt ſortes: <lb/>et mīmus illorum ſit pedalis, alter bipedalis, et <lb/>maximus tripedalis, et ſit ſortes ſemipedalis: et <lb/>creſcat ſucceſſiue ſortes quo ad vſ ſit quadrupe-<lb/>dalis. </s>
              <s xml:id="N17274" xml:space="preserve">tunc manifeſtum eſt /  ſortes tranſibit a mi­<lb/>nori quantitate / quam ſit quantitas alicuius iſto­<lb/>rum ad maiorem quantitatem quam ſit quãtitas <lb/>alicuius iſtorum: et tamen nunquaꝫ tranſibit per <lb/>quantitatem equalem cuilibet quantitati illorum <lb/></s>
              <s xml:id="N17280" xml:space="preserve">Quare iſta conſequentia nichil valet a. tranſibit <lb/>a minori quãtitate quantitate iſtorū. </s>
              <s xml:id="N17285" xml:space="preserve">ad maioreꝫ <lb/>quantitatem quãtitate iſtorum / ergo per equalem <lb/>quantitatem cuilibet quantitati iſtorum. </s>
              <s xml:id="N1728C" xml:space="preserve">Et totū <lb/>hoc prouenit a termino diſtributo.               <anchor type="note" xlink:href="note-0072-03" xlink:label="note-0072-03a"/>               </s>
              <s xml:id="N17296" xml:space="preserve">¶ Sequitur ſe­<lb/>cundo /  iſta conſequentia nihil valet iſte angulꝰ <lb/>tranſit a minori augulo quam ſit angulus ſemi-<lb/>circuli ad maiorem angulum quam ſit angulꝰ ſe-<lb/>micirculi / ergo tranſit per equalem. </s>
              <s xml:id="N172A1" xml:space="preserve">Patet hoc <lb/>correlarium in hac figura.</s>
            </p>
            <div xml:id="N172A6" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0072-02a" xlink:label="note-0072-02" xml:id="N172AA" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0072-03a" xlink:label="note-0072-03" xml:id="N172B0" xml:space="preserve">2. correĺ.</note>
            </div>
            <figure xml:id="N172B6">
              <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0072-01"/>
            </figure>
            <note position="right" xml:id="N172BA" xml:space="preserve">Cãpanꝰ ī <lb/>ↄ̨mē. 16. <lb/>ↄ̨clu. ter-<lb/>tii. ele. eu</note>
            <p xml:id="N172C4">
              <s xml:id="N172C5" xml:space="preserve">Et eſt campani in cõmento decime ſexte concluſio­<lb/>nis tertii elementorum euclidis / vbi oſtendit ſimi-<lb/>les argumentationes non valere.               <anchor type="note" xlink:href="note-0072-04" xlink:label="note-0072-04a"/>               </s>
              <s xml:id="N172D1" xml:space="preserve">Et idem ponit <lb/>brauardinꝰ in capitulo de circulis ↄ̨cluſiõe ſeptīa</s>
            </p>
            <div xml:id="N172D6" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0072-04a" xlink:label="note-0072-04" xml:id="N172DA" xml:space="preserve">Brauar-<lb/>dinꝰ capi­<lb/>te .4. con­<lb/>cluſio .7.</note>
            </div>
            <pb chead="Primi tractatus" file="0073" n="73"/>
            <note position="left" xml:id="N172EA" xml:space="preserve">argumē-<lb/>tū calcu.</note>
            <p xml:id="N172F0">
              <s xml:id="N172F1" xml:space="preserve">Quinto arguitur ſic </s>
              <s xml:id="N172F4" xml:space="preserve">Si ille regule <lb/>eſſent vere: ſequeretur /  ſi aliqua reſiſtentia vni-<lb/>formiter ꝓportionabiliter creſceret reſpectu dua­<lb/>rum potentiarum equaliuꝫ potentium moueri cū <lb/>tali reſiſtentia: tales potentie vniformiter remit-<lb/>terent motus ſuos. </s>
              <s xml:id="N17301" xml:space="preserve">ſed conſequens eſt falſum / igi-<lb/>tur illud ex quo ſequitur. </s>
              <s xml:id="N17306" xml:space="preserve">Sequela eſt nota. </s>
              <s xml:id="N17309" xml:space="preserve">et falſi­<lb/>tas conſequentis oſtenditur. </s>
              <s xml:id="N1730E" xml:space="preserve">q2 ex illo ſequitur /  <lb/>alique due potentie equales ab eodem gradu ve-<lb/>locitatis incipiunt remittere motus ſuos ad non <lb/>gradum ſemper eque velociter remittendo. </s>
              <s xml:id="N17317" xml:space="preserve">et nihi­<lb/>lominus non equaliter mouentur ſed conſequens <lb/>manifeſte implicat / igitur illud ex quo ſequitur.</s>
            </p>
            <p xml:id="N1731E">
              <s xml:id="N1731F" xml:space="preserve">Sequela probatur et pono duas poteutias equa­<lb/>les / vt .8.a. videlicet et b. / et capio duo media equa-<lb/>lis reſiſtētie c. videlicet et d. reſiſtentie vt .4. et c. ſit <lb/>pedalis quãtitatis et d. ſemipedalis. </s>
              <s xml:id="N17328" xml:space="preserve">et moueatur <lb/>a. potentia ſupra c. pedale: et b. ſupra d. ſemipeda­<lb/>le per horam. </s>
              <s xml:id="N1732F" xml:space="preserve">et creſcat reſiſtentia vtriuſ eque ꝓ­<lb/>portionabiliter vniformiter per horam in qua d. <lb/>ſemipedale rarefiat vniformiter ſecundum partē <lb/>non pertranſitam: taliter  in fine hore ſit etiam <lb/>pedale ſicut c. / quo poſito arguitur ſic / a. et b. incipi­<lb/>unt remittere motus ſuos ab equali gradu veloci­<lb/>tatis propter eque proportionale crementum re-<lb/>ſiſtentie: et mouebuntur ſemper vniformiter: et ta-<lb/>men non mouebuntur eque velociter in illa hora. <lb/></s>
              <s xml:id="N17343" xml:space="preserve">igitur propoſitum. </s>
              <s xml:id="N17346" xml:space="preserve">Maior patet ex caſu et minor <lb/>probatur / quoniam a. pertranſibit c. pedale in ho­<lb/>ra et b. nõ pertranſibit d. / quod in fine preciſe erit <lb/>pedale nec aliquod tantum: igitur non equaliter <lb/>mouebuntur. </s>
              <s xml:id="N17351" xml:space="preserve">Maior patet ex caſu et minor ꝓba-<lb/>tur / quoniam b. remittit motum ſuum ad non gra­<lb/>dum in illa hora / et d. ſpacium vniformiter rarefit <lb/>ſecundum partem non pertranſitam / ergo aliquã­<lb/>do in hora / aliqua pars non tranſita velocius mo­<lb/>uebitur quam ipſum b. / et per conſequens nūquã <lb/>ipſum b. perueniet ad illam partem. </s>
              <s xml:id="N17360" xml:space="preserve">Patet hec cõ­<lb/>ſequentia </s>
              <s xml:id="N17365" xml:space="preserve">Nam ſi aliquod mobile mouetur in ali­<lb/>quo medio: et pars aliqua ipſius medii antecedēs <lb/>mouetur velocius ipſo mobili: nun̄ illud mobile <lb/>perueniet ad illam partem / vt ſatis conſtat ſed ſic <lb/>fit in propoſito igitur.               <anchor type="note" xlink:href="note-0073-01" xlink:label="note-0073-01a"/>               </s>
              <s xml:id="N17375" xml:space="preserve">¶ Et confirmatur quoniaꝫ / <lb/>ſi illud conſequens eſſet verum ſequeretur in caſu <lb/>poſito /  b. pertrauſiret d. ante finem hore et tamē <lb/>non pertranſiret in hora ipſum d. / hoc manifeſte ī­<lb/>plicat igitur. </s>
              <s xml:id="N17380" xml:space="preserve">Secunda pars huius conſequentis <lb/>deducta eſt. </s>
              <s xml:id="N17385" xml:space="preserve">et prima probatur ſupponendo /  qñ <lb/>aliquid mouetur vniformiter difformiter vſ ad <lb/>non gradum in aliquo tempore: ſpaciū pertran-<lb/>ſitum in prima medietate illius temporis eſt tri-<lb/>plum ad ſpacium pertranſitum in ſecunda medie­<lb/>tate / vt poſtea in capite tertio ſecundi tractatꝰ oſtē­<lb/>detur. </s>
              <s xml:id="N17394" xml:space="preserve">Suppono ſecundo /  d. ſemipedale in inſtã­<lb/>ti medio temporis motus erit tres quarte / vt patet <lb/></s>
              <s xml:id="N1739A" xml:space="preserve">Quoniam ipſum d. acquirit ſemipedalem quan-<lb/>titatem vniformiter in illa hora / igitur ī ṗma me-<lb/>dietate hore acq̇rit medietateꝫ ſemipedalis puta <lb/>vnam quartã adequate </s>
              <s xml:id="N173A3" xml:space="preserve">Quo poſito ſic argumē-<lb/>tor motus ipſius b. eſt vniformiter difformis ad <lb/>uon gradum in illa hora / vt patet ex caſu et moue­<lb/>tur equaliter cum a. / ſed a. in prima medietate ho-<lb/>re pertranſit tres quartas pedalis / vt patet ex pri­<lb/>ma ſuppoſitione: igitur tunc b. pertranſit tres q̈r­<lb/>tas pedalis adeq̈te ipſius d. ſꝫ d. tūc adeq̈te ē quã­<lb/>titatis trium quartarum / vt patet ex ſecunda ſup-<lb/>poſitione: igitur tunc d. in medio hore eſt adequa­<lb/>te pertranſitum / quod fuit probandum.               <anchor type="note" xlink:href="note-0073-02" xlink:label="note-0073-02a"/>               </s>
              <s xml:id="N173BD" xml:space="preserve">Confirma­<lb/>tur ſecundo / quia ſi illud conſequens eſſet verū ſe-               <cb chead="Capitulum ſextum"/>               queretur /  per motum vniformiter difformē ad <lb/>non gradum non pertranſiretur in triplo maius <lb/>ſpacium in prima medietate temporis quam in ſe­<lb/>cunda / ſed iſtud conſequens eſt falſum / vt inferiꝰ lo­<lb/>co preallegato oſtendetur / igitur illud ex quo ſe-<lb/>quitur. </s>
              <s xml:id="N173CF" xml:space="preserve">Sequela probatur / quoniam in caſu <lb/>poſito in inſtanti medio temporis .b. non pertran­<lb/>ſit tres quartas: et illud eſt triplum ſpacium ad re­<lb/>ſiduum pedalis puta ad vnã quartam / igitur pro­<lb/>poſitum </s>
              <s xml:id="N173DA" xml:space="preserve">Minor eſt nota et maior probatur / quo-<lb/>niam ex caſu b. ſpacium ſiue medium debet conti-<lb/>nue per horam vniformiter rarefieri ſecundum ꝑ-<lb/>tem non pertranſitam: ergo in ipſa hora in quoli­<lb/>bet inſtanti intrinſeco debet eſſe aliqua pars non <lb/>pertranſita: ſed ſi in medio inſtanti temporis b. ꝑ­<lb/>tranſiret tres quartas in illo inſtanti ipſum b. eſ­<lb/>ſet in termino illius ſpacii / et nulla pars tunc eſſet <lb/>non pertrãſita </s>
              <s xml:id="N173ED" xml:space="preserve">(Erit enim d. ſpacium in inſtanti <lb/>medio adequate quantitatis trium quartarū pe­<lb/>dalis adequate / vt probatum eſt in anteriori con-<lb/>firmatione) / igitur in tali inſtanti ille tres quarte <lb/>non ſunt adequate pertranſite / quod fuit proban­<lb/>dum. </s>
              <s xml:id="N173FA" xml:space="preserve">Alias enim iam non rarefieret / tunc ſecū­<lb/>dum partem non pertranſitam.               <anchor type="note" xlink:href="note-0073-03" xlink:label="note-0073-03a"/>               </s>
              <s xml:id="N17404" xml:space="preserve">¶ Confirmat̄̄ ter­<lb/>tio / quia ſi illud conſequens eſſet veruꝫ ſequeretur <lb/>in caſu poſito /  cū motus vniformiter difformis <lb/>deueniret ad velocitatem equalem velocitati rare­<lb/>factionis (rarefactio enim motus localis eſt) nul-<lb/>lum penitus punctum talis ſpacii poſſet pertran-<lb/>ſire. </s>
              <s xml:id="N17413" xml:space="preserve">quoniam poſt illud inſtans / quodlibet pūctuꝫ <lb/>precedens mobile mouebitur velocius ipſo mobi­<lb/>li quoniam tale punctum mouebitur vniformiter / <lb/>et b. continuo remittet motum ſuum. </s>
              <s xml:id="N1741C" xml:space="preserve">ſed hoc ē fal-<lb/>ſum igitur illud ex quo ſequitur </s>
              <s xml:id="N17421" xml:space="preserve">Falſitas conſeq̄n­<lb/>tis oſtenditur / quoniam tunc ſequeretur /  b. ãtea <lb/>quam deueniret ad non gradum motus: ceſſaret <lb/>moueri ſuper dato ſpacio vel in dato ſpacio d.</s>
            </p>
            <div xml:id="N1742A" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0073-01a" xlink:label="note-0073-01" xml:id="N1742E" xml:space="preserve">1. ↄ̨firma­<lb/>tio.</note>
              <note position="left" xlink:href="note-0073-02a" xlink:label="note-0073-02" xml:id="N17436" xml:space="preserve">2. confir.</note>
              <note position="right" xlink:href="note-0073-03a" xlink:label="note-0073-03" xml:id="N1743C" xml:space="preserve">3. confir.</note>
            </div>
            <p xml:id="N17442">
              <s xml:id="N17443" xml:space="preserve">Item ſequeretur /  ipſum b. equalis potētie cū a. <lb/>non poſſet pertranſire equalem reſiſtentiam cū a. / <lb/>et hoc eſt impoſſibile igitur. </s>
              <s xml:id="N1744A" xml:space="preserve">Sequela probat̄̄ / quo­<lb/>niam b. non poteſt pertranſire mediuꝫ d. poſtquã <lb/>deueniret ad equalitatem motus cum medio: et ta­<lb/>men medium d. eſt equalis reſiſtentie cuꝫ medio c / <lb/>quod pertranſit a. igitur propoſitum.</s>
            </p>
            <p xml:id="N17455">
              <s xml:id="N17456" xml:space="preserve">Reſpondeo breuiter ad argumentuꝫ <lb/>cum duabus confirmationibus non admittendo <lb/>caſum. </s>
              <s xml:id="N1745D" xml:space="preserve">Argumenta enim probant caſum implica­<lb/>re </s>
              <s xml:id="N17462" xml:space="preserve">Probant enim /  b. nunquam deueniet ad ter-<lb/>minum ipſius d. / et confirmatio prima ꝓbat /  de­<lb/>ueniet ad terminum eius in medio īſtanti tempo-<lb/>ris: et ſic implicat /  rarefiat dūtaxat ſecundum ꝑ­<lb/>tem non pertranſitam cum ceteris particulis ca-<lb/>ſus. </s>
              <s xml:id="N1746F" xml:space="preserve">¶ Pro ſolutione tertie confirmationis ſup-<lb/>ponendem eſt /  rarefactio eſt motus localis.               <anchor type="note" xlink:href="note-0073-04" xlink:label="note-0073-04a"/>               </s>
              <s xml:id="N17479" xml:space="preserve">Se­<lb/>cundo ſupponendum eſt /  duplex eſt medium per <lb/>quod aliquid mouetur quando ipſum mediū ra-<lb/>refit </s>
              <s xml:id="N17482" xml:space="preserve">Quoddam enim eſt medium quod per motuꝫ <lb/>ſuum etiam mouet mobile in eo exiſtens. </s>
              <s xml:id="N17487" xml:space="preserve">cuiuſmo­<lb/>di eſt nauis que mouet nautã ad motū ſui: ita  ſi <lb/>nauta moueatur verſus illam partem verſus quã <lb/>mouetur nauis duplici motu mouetur: et motu na­<lb/>uis et motu proprio. </s>
              <s xml:id="N17492" xml:space="preserve">Ita etiam ſit de homine natã­<lb/>te in flumine qui ſi natet verſus fluctum illius flu­<lb/>minis duplici motu mouetur et motu proprio et <lb/>motu fluminis trahentis ipſum. </s>
              <s xml:id="N1749B" xml:space="preserve">Aliud eſt mediuꝫ <lb/>ad cuius motum localem nõ mouetur mobile ī eo <lb/>exiſtens cuiuſmodi eſt aer. </s>
              <s xml:id="N174A2" xml:space="preserve">Diuidit enim mobile <lb/>potius aerem quam trahetur ab aere. </s>
              <s xml:id="N174A7" xml:space="preserve">¶ His poſi­<lb/>tis reſpondeo ad confirmationem diſtinguendo               <pb chead="Primi tractatus" file="0074" n="74"/>               illatum / quia aut illud medium d. eſt medium pri-<lb/>mo modo puta trahens mobile cuiuſmodi eſt na-<lb/>uis aut aqua trahens natantem / et ſic ego nego ſe­<lb/>quelam. </s>
              <s xml:id="N174B7" xml:space="preserve">Dico enim /  tale mobile quod ꝑ tale me­<lb/>dium mouetur: mouetur tota velocitate qua mo-<lb/>uetur ipſum mediū et inſuper velocitate propria: <lb/>et ſic aggregatum ex illis duabus velocitatibus <lb/>conſtituit velocitatem maiorē velocitate qua mo-<lb/>uetur ipſum mobile per rarefactionem. </s>
              <s xml:id="N174C4" xml:space="preserve">Et ſic põt <lb/>ſemper pertingere quamdiu mouetur: aliqḋ pun­<lb/>ctum precedens ipſuꝫ. </s>
              <s xml:id="N174CB" xml:space="preserve">quoniam quãdiu mouetur <lb/>intenſiori velocitate (computatis vtriuſ velocita­<lb/>tibus) mouetur quã aliquod punctum precedens <lb/>ipſum. </s>
              <s xml:id="N174D4" xml:space="preserve">Sed cū motu proprio deuenerit ad nõ gra­<lb/>dum mouebitur a medio dūtaxat / et ſemper mane­<lb/>bit in eodem puncto medii. </s>
              <s xml:id="N174DB" xml:space="preserve">Si vero medium d. ſit <lb/>medium ſecundo modo non trahens ipſum mobi­<lb/>le concedo illatum / et ad probationem dico /  non <lb/>habeo pro inconuenienti quando vna illarum re­<lb/>ſiſtentiarum mouetur et alia quieſcit </s>
              <s xml:id="N174E6" xml:space="preserve">Ibi enim ce­<lb/>tera non ſunt paria. </s>
              <s xml:id="N174EB" xml:space="preserve">¶ Hec argumenta partim <lb/>ſunt ex calculatore traducta: que ideo huic operi ī­<lb/>terſerui quoniam aliquid ſubtilitatis et difficul-<lb/>tatis pre ſe ferunt. </s>
              <s xml:id="N174F4" xml:space="preserve">Tum etiam vt redderetur ipſe <lb/>calculator peruius et vadis plenus.</s>
            </p>
            <div xml:id="N174F9" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0073-04a" xlink:label="note-0073-04" xml:id="N174FD" xml:space="preserve">duplex ē <lb/>mediuꝫ ꝑ <lb/>qḋ aliq̇d <lb/>mouetur</note>
            </div>
          </div>
          <div xml:id="N17509" level="4" n="7" type="chapter" type-free="capitulum">
            <head xml:id="N1750E" xml:space="preserve">Septimum capitulum / in quo inquiri­<lb/>tur: vtrum aliqua potentia non varia-<lb/>riata per medium vniforme aut diffor-<lb/>me, vniformiter ad non gradum vel ad <lb/>gradum ſuum motum remittere aut in­<lb/>tendere valeat.</head>
            <p xml:id="N1751B">
              <s xml:id="N1751C" xml:space="preserve">ÃTea materia que ī titulo hu­<lb/>ius capitis tangitur valeat clare expe­<lb/>diri: ponam aliquas concluſiones qui­<lb/>bus probandis vnicam duobus correlariis adiū­<lb/>ctam ſuppoſitionem premittam. </s>
              <s xml:id="N17527" xml:space="preserve">Que talis eſt.</s>
            </p>
            <p xml:id="N1752A">
              <s xml:id="N1752B" xml:space="preserve">Si b. latitudo motus minor  a. ma­<lb/>ior diminuantur vniformiter in tempore equali <lb/>vel inequali perdendo adequate equalem latitu-<lb/>dinem motus: maior eſt proportio motus b. in pri­<lb/>ma medietate temporis in quo ipſum b. diminui-<lb/>tur ad ſeipſum in ſecunda medietate eiuſdem tem­<lb/>poris, quam ſit motus a. in prima medietate tem­<lb/>poris in quo ipſum a. diminuitur ad ſeipſum ī ſe-<lb/>cunda medietate eiuſdem tēporis. </s>
              <s xml:id="N1753E" xml:space="preserve">Patet hec ſup­<lb/>poſitio ex ſecunda parte ſecundi correlarii prime <lb/>concluſionis vltimi capitis ſecunde partis / hoc ad­<lb/>dito /  motus vniformiter difformis et vniformi-<lb/>ter remiſſus correſpondet motui exiſtēti in medio <lb/>inſtanti temporis / in quo remittitur vniformiter: <lb/>quia talis motus eſt ſuus gradus medius.               <anchor type="note" xlink:href="note-0074-01" xlink:label="note-0074-01a"/>               </s>
              <s xml:id="N17552" xml:space="preserve">¶ Ex <lb/>quo ſequitur primo /  ſi b. potentia minor in ali-<lb/>quo tempore c. medium tranſeundo vniformiter <lb/>remittet motū ſuum. </s>
              <s xml:id="N1755B" xml:space="preserve">et a. potentia maior in tempo­<lb/>re minori (vt opꝫ) idē c. mediū trãſeūdo vniformiṫ <lb/>remittit motum ſuum: maior eſt ꝓportio velocita­<lb/>tis ipſius b. in prima medietate tēporis in quo b. <lb/>vniformiter remittit motum ſuum ad velocitateꝫ <lb/>ſecunde medietatis eiuſdem temporis quam velo­<lb/>citatis ipſius a. ī prima medietate temporis ī quo <lb/>idem a. vniformiter remittit motum ſuum ad velo­<lb/>citatem ſecunde medietatis eiuſdē temporis. </s>
              <s xml:id="N1756E" xml:space="preserve">Pa­<lb/>tet hoc correlarium ex ſuppoſitione / quia quando <lb/>b. potentia minor vniformiter remittit motū ſuū <lb/>in aliquo tempore c. medium tranſeundo: et a po-<lb/>tentia maior in tempore minori etiam vniformi-<lb/>ter remittit motum ſuum: iam latitudo motꝰ qua <lb/>mouetur b. potentia minor et latitudo motus ma­               <cb chead="Capitulum ſeptimum"/>               ior qua mouetur a. potentia maior in tempore eq̈­<lb/>li vel inequali diminuuntur vniformiter equalem <lb/>latitudinem adequate deperdendo / ergo maior ē <lb/>proportio motus ſiue velocitatis ipſius b. / in pri-<lb/>ma medietate temporis in quo ipſum b. vniformi­<lb/>ter remittit motum ſuum ad motum / quo idem b. <lb/>mouetur in ſecunda medietate eiuſdem temporis / <lb/>quam ſit proportio motus ipſius a. / in prima me-<lb/>dietate temporis in quo vniformiter remittit mo­<lb/>tum ſuum ad motum in ſecunda medietate eiuſdē <lb/>temporis. </s>
              <s xml:id="N17594" xml:space="preserve">Conſequentia patet ex ſuppoſitione et <lb/>antecedens ex iſta concluſione. </s>
              <s xml:id="N17599" xml:space="preserve">Diuerſe potentie <lb/>inuariate idem medium inuariatum tranſeuntes <lb/></s>
              <s xml:id="N1759F" xml:space="preserve">(Nam de inuariatis potentiis et medio inuaria-<lb/>to eſt ſermo) / in quo medio acquiritur aut deperdi­<lb/>tur motus equalem latitudinem motus acquirūt <lb/>vel deperdunt.               <anchor type="note" xlink:href="note-0074-02" xlink:label="note-0074-02a"/>               </s>
              <s xml:id="N175AD" xml:space="preserve">¶ Ex quo ſequitur ſecundo /  ſi b. <lb/>potētia minor in d. tempore c. medium tranſeūdo <lb/>vniformiter remittit motū ſuū: et a. potētia maior <lb/>in e. tempore mouendo equalem latitudinem mo-<lb/>tus vniformiter deperdit adequate ſicut b. / tunc ſi <lb/>velocitatis b. in prima medietate d. temporis ad <lb/>velocitatem eiuſdē b. in ſecunda medietate eiuſdē <lb/>temporis ſit f. proportio: minor proportio erit ve­<lb/>locitatis a. in prima medietate e. temporis ad ve-<lb/>locitatem a. in ſecunda medietate eiuſdē temporis <lb/>quam f. ꝓportio. </s>
              <s xml:id="N175C4" xml:space="preserve">Patet hoc correlarium ex ſup-<lb/>poſitione.</s>
            </p>
            <div xml:id="N175C9" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0074-01a" xlink:label="note-0074-01" xml:id="N175CD" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0074-02a" xlink:label="note-0074-02" xml:id="N175D3" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N175D9">
              <s xml:id="N175DA" xml:space="preserve">His premiſſis ſit prima cõcluſio. </s>
              <s xml:id="N175DD" xml:space="preserve">Ali­<lb/>qua potentia non variata ſemper tranſeundo re-<lb/>ſiſtentiam vniformē: vniformiter continuo remit-<lb/>tit motum ſuum ad non gradum et ad gradum.</s>
            </p>
            <p xml:id="N175E6">
              <s xml:id="N175E7" xml:space="preserve">Probatur hec concluſio / et volo /  ſit aliquod me­<lb/>dium vniforme reſiſtens vt .4. et potentia vt .8. q̄ <lb/>non variata moueatur per illud: ſic tamen  illḋ <lb/>medium creſcat in reſiſtentia vniformiter ꝓportio­<lb/>nabiliter per totum. </s>
              <s xml:id="N175F2" xml:space="preserve">ita  inequalibus tempori-<lb/>bus equales proportiones reſiſtentiarum acqui-<lb/>rat per totum / quo ad ſit reſiſtentia vt .8. / quo poſi-<lb/>to illud mobile tranſeundo illud medium remit-<lb/>tit motum ſuum vniformiter primo ad certū gra-<lb/>dum deinde ad non gradum / igitur concluſio ve-<lb/>ra. </s>
              <s xml:id="N17601" xml:space="preserve">Antecedens probatur / quoniam reſiſtentia creſ­<lb/>ſcit ſemper eque proportionabiliter / igitur poten­<lb/>tia non variata mouens per eam vniformiter mo­<lb/>tum ſuū / remittit ſiue ad gradum ſiue ad non gra-<lb/>dum. </s>
              <s xml:id="N1760C" xml:space="preserve">Patet conſequētia ex ſexta et quarta ſuppo­<lb/>ſitionibus quīti capitis huius tractatus coniunc­<lb/>tis. </s>
              <s xml:id="N17613" xml:space="preserve">¶ Hic tamen tu aduerte /  quãuis illa potētia <lb/>non variata ſemꝑ mouetur per medium vniforme / <lb/>hoc eſt per medium / quod in quolibet īſtanti tem-<lb/>poris in quo mouetur eſt vniforme: per nullum ta­<lb/>men mediū aliqua vniformitate vniforme ſemper <lb/>mouetur / quia illḋ medium continuo habet aliam <lb/>et aliaꝫ vniformitatē.               <anchor type="note" xlink:href="note-0074-03" xlink:label="note-0074-03a"/>               </s>
              <s xml:id="N17627" xml:space="preserve">¶ Ex quo ſequitur /  aliqua <lb/>potentia non variata ſemper tranſeūdo medium / <lb/>quod in quolibet inſtanti temporis in quo moue-<lb/>tur eſt vniforme: vniformiter intendit motum ſuuꝫ <lb/></s>
              <s xml:id="N17631" xml:space="preserve">Patet / ſi illa potentia vt .8. incipiat moueri per <lb/>reſiſtentiam vt .8. vniformiter proportionabili-<lb/>ter in reſiſtentia decreſcentem per totum.</s>
            </p>
            <div xml:id="N17638" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0074-03a" xlink:label="note-0074-03" xml:id="N1763C" xml:space="preserve">corelar.</note>
            </div>
            <p xml:id="N17642">
              <s xml:id="N17643" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N17646" xml:space="preserve">Aliqua potentia <lb/>non variata pertranſeundo mediuꝫ difforme: vni­<lb/>formiter remittit motum ſuum et ad gradum et ad <lb/>non gradum. </s>
              <s xml:id="N1764F" xml:space="preserve">Probatur hec concluſio et capio <lb/>duo media equalia quorum vtrū ſit reſiſtētie vt <lb/>4. per totum: et volo /  fiat de vno illorum omni-<lb/>no eodem modo ſicut ponitur in precedenti cõclu­               <pb chead="Primi tractatus" file="0075" n="75"/>               ſione: et moueatur per illud potentia vt .8. nõ va-<lb/>riata. </s>
              <s xml:id="N1765F" xml:space="preserve">ſecundum vero per quod mouetur alia po-<lb/>tentia vt .8. non variata taliter diſponatur /  qñ <lb/>in priori medio fuerit aliqua reſiſtentia per totū: <lb/>in ſolo puncto vbi eſt mobile in ſecundo medio ſit <lb/>adequate tanta reſiſtentia ceteris inuariatis ita­<lb/> poſtquã alicui puncto aliqua latitudo reſiſten-<lb/>tie addita eſt nulla ei vlteriꝰ addatur aut remouea­<lb/>tur ita  manet per totum difforme in fine quo po­<lb/>ſito mobile motum in ſecundo medio remittet mo­<lb/>tum ſuum vniformiter primo ad gradum et dein-<lb/>de ad non gradum / igitur concluſio vera. </s>
              <s xml:id="N17676" xml:space="preserve">Antece-<lb/>dens probatur / quia mobile motum in primo me-<lb/>dio vniformiter remittit motum ſuū / vt ptꝫ ex prio­<lb/>ri concluſione: et ſecundum mobile motū in ſecun-<lb/>do medio in quolibet inſtãti temporis / quo ſic mo-<lb/>uetur eſt motum equali velocitate adequate cū pri­<lb/>mo: igitur ſecundum mobile etiam vniformiter re­<lb/>mittet motū ſuum. </s>
              <s xml:id="N17687" xml:space="preserve">Patet conſequentia / quia ſi il-<lb/>la duo continuo equaliter mouentur et vnum illo­<lb/>rum in medietate temporis perdit aliquam velo-<lb/>citatem et in quarta. et in quinta. / et ſic conſequēter / <lb/>igitur et alterū in medietate temporis tantã velo-<lb/>citateꝫ deperdit adequate ſicut ṗmū et in q̈rta tan­<lb/>tã: et in quinta tantã: et ſic conſequenter: igitur ſi <lb/>vnum vniformiter remittit motū ſuū etiam alterū <lb/>motū ſuū vniformiter remittet / quod fuit proban-<lb/>dum.               <anchor type="note" xlink:href="note-0075-01" xlink:label="note-0075-01a"/>               </s>
              <s xml:id="N176A1" xml:space="preserve">¶ Ex quo ſequitur /  aliqua potentia nõ va-<lb/>riata tranſeundo medium difforme inuariatū: va­<lb/>let vniformiter remittere motum ſuum. </s>
              <s xml:id="N176A8" xml:space="preserve">Proba-<lb/>tur hoc correlarium et volo /  illud ſecundum mo-<lb/>bile quod mouetur per medium difforme poſtquã <lb/>ſemel tale ſecundum medium difforme pertranſie­<lb/>rit / quando idem medium variabatur: ipſo medio <lb/>quieſcente mobile inuariatum pertranſeat idem <lb/>medium eo modo quo antea pertranſibat: hoc eſt <lb/>incipiendo ab eodem puncto verſus idem pūctuꝫ: <lb/>quo poſito illud mobile tranſeundo illud mediuꝫ <lb/>inuariatum remittit motū ſuū vniformiter / igitur <lb/>correlarium verum. </s>
              <s xml:id="N176BF" xml:space="preserve">Probatur antecedens / q2 ta-<lb/>le mobile continuo eque velociter pertranſit illud <lb/>medium inuariatum ſicut pertranſibat illud quã­<lb/>do medium variabatur: ſed quando variabatur <lb/>vniformiter remittit motū ſuū: ergo et quando nõ <lb/>variatur etiam vniformiter remittit motū ſuum.</s>
            </p>
            <div xml:id="N176CC" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0075-01a" xlink:label="note-0075-01" xml:id="N176D0" xml:space="preserve">1. correl. <lb/>triceſīa <lb/>ſeptīa cõ­<lb/>cluſio cal­<lb/>cu.</note>
            </div>
            <p xml:id="N176DE">
              <s xml:id="N176DF" xml:space="preserve">Patet maior / quoniam continuo partes medii il­<lb/>lius inuariati et intenſiue et extenſiue tantum reſi-<lb/>ſtunt ipſi mobili quantum conſimiles partes me-<lb/>dii variati cum illa media ſint oīno equalia exten­<lb/>ſiue: et continuo partes conſimiles que pertranſe-<lb/>untur equaliter reſiſtunt omnino. </s>
              <s xml:id="N176EC" xml:space="preserve">In punctis em̄ <lb/>correſpondentibus equalem omnino reſiſtentiaꝫ <lb/>habent.               <anchor type="note" xlink:href="note-0075-02" xlink:label="note-0075-02a"/>               </s>
              <s xml:id="N176F8" xml:space="preserve">¶ Sequitur ſecundo /  aliqua potentia ī­<lb/>uariata mediū inuariatum tranſeundo: vniformi­<lb/>ter continuo intendit motum ſuum. </s>
              <s xml:id="N176FF" xml:space="preserve">Probat̄̄ hoc <lb/>correlarium poſito /  potentia que pertranſit ali­<lb/>quod medium inuariatum a pūcto remiſſiori mo-<lb/>uendo verſus punctum intenſius remittendo vni-<lb/>formiter continuo motum ſuum: iterum motu re-<lb/>trogrado moneatur a puncto intenſiori verſus re­<lb/>miſſius. </s>
              <s xml:id="N1770E" xml:space="preserve">quo poſito talis potentia vniformiter in­<lb/>tendit motum ſuum quē antea vniformiter remit­<lb/>tebatur igitur.</s>
            </p>
            <div xml:id="N17715" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0075-02a" xlink:label="note-0075-02" xml:id="N17719" xml:space="preserve">2. confir.</note>
            </div>
            <p xml:id="N1771F">
              <s xml:id="N17720" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N17723" xml:space="preserve">Nulla potentia nõ <lb/>variata tranſeundo mediuꝫ vniformiter difforme <lb/>non variatum: poteſt vniformiter remittere aut ī­<lb/>tendere motū ſuum. </s>
              <s xml:id="N1772C" xml:space="preserve">Patet hec concluſio ex trige-<lb/>ſima nona et quadrageſima concluſionibus quin­<lb/>ti capitis huius tractatꝰ. </s>
              <s xml:id="N17733" xml:space="preserve">¶ Ex quo ſequitur /  ali­               <cb chead="Capitulum ſeptimum"/>               <anchor type="note" xlink:href="note-0075-03" xlink:label="note-0075-03a"/>               qua potentia non variata tranſeundo mediū vni­<lb/>formiter difforme non variatum taliter poteſt ip­<lb/>ſum pertranſire:  vniformiter continuo mouea-<lb/>tur. </s>
              <s xml:id="N17744" xml:space="preserve">Probatur / quoniam ſi moueatur ab vno ex-<lb/>tremo laterali ad aliud extremum ſibi correſpon­<lb/>dens ſemper vniformiter mouebitur / igitur corre-<lb/>larium verum. </s>
              <s xml:id="N1774D" xml:space="preserve">Probatur antecedens / quoniã ſem­<lb/>per mouebitur cum equali reſiſtentia. </s>
              <s xml:id="N17752" xml:space="preserve">cum omnia <lb/>puncta in linea recta laterali exiſtentia in tali me­<lb/>dio equalis ſunt reſiſtentie. </s>
              <s xml:id="N17759" xml:space="preserve">Et hoc ſiue mobile ſit <lb/>diuiſibile ſiue indiuiſibile.               <anchor type="note" xlink:href="note-0075-04" xlink:label="note-0075-04a"/>               </s>
              <s xml:id="N17763" xml:space="preserve">¶ Iam ex hoc ſequitur / <lb/> tribus modis poteſt ſpacium vniformiter dif-<lb/>forme pertranſiri a potentia non variata: </s>
              <s xml:id="N1776A" xml:space="preserve">Uno <lb/>modo ipſa continuo remittente motum. </s>
              <s xml:id="N1776F" xml:space="preserve">Alio mo-<lb/>do ipſa continuo intendente motã. </s>
              <s xml:id="N17774" xml:space="preserve">Tertio modo <lb/>ipſa continuo vniformiter mota. </s>
              <s xml:id="N17779" xml:space="preserve">Non excludo ta­<lb/>men alios modos. </s>
              <s xml:id="N1777E" xml:space="preserve">Si enim moueretur in circulo ī <lb/>tali ſpacio aliquando intenderet motuꝫ et aliquã­<lb/>do remitteret.</s>
            </p>
            <div xml:id="N17785" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0075-03a" xlink:label="note-0075-03" xml:id="N17789" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0075-04a" xlink:label="note-0075-04" xml:id="N1778F" xml:space="preserve">2: correl.</note>
            </div>
            <note position="right" xml:id="N17795" xml:space="preserve">Triceſīa­<lb/>octaua ↄ̨­<lb/>cluſio cal­<lb/>cu.</note>
            <p xml:id="N1779F">
              <s xml:id="N177A0" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N177A3" xml:space="preserve">Si aliqua poten-<lb/>tia non variata tranſeundo aliquod medium non <lb/>variatum vniformiter remittit motū ſuum ad gra­<lb/>dum vel ad non gradū: nulla maior vel minor idē <lb/>medium tranſeundo medio et ipſa inuariatis vni­<lb/>formiter motū ſuū remittit. </s>
              <s xml:id="N177B0" xml:space="preserve">Probatur / ſit b. potē­<lb/>tia minor que inuariata in d. tempore pertranſit <lb/>c. medium inuariatū: continuo vniformiter remit­<lb/>tendo motum ſuum. </s>
              <s xml:id="N177B9" xml:space="preserve">et ſit a. poña maior que iuua-<lb/>riata in e. tempore c. medium inuariatū tranſit. </s>
              <s xml:id="N177BE" xml:space="preserve">et <lb/>dico /  a. potentia maior c. mediuꝫ tranſeundo nõ <lb/>continuo vniformiter remittit motū ſuū </s>
              <s xml:id="N177C5" xml:space="preserve">Quod ſic <lb/>probatur / ſit g. ſpacium quod pertranſitur in me-<lb/>dietate d. temporis a b. potentia minore perden-<lb/>do medietatē velocitatis deperdende: et ſit h. ſpa-<lb/>cium pertranſitum ab eadē potentia in ſcḋa me-<lb/>dietate eiuſdē temporis adequate ad quod h. ſpa­<lb/>cium habeat g. proportionē f. que proportio f. eſt <lb/>ꝓportio velocitatis qua mouetur b. potētia ī pri­<lb/>ma medietate d. tēporis ad velocitatē qua moue-<lb/>tur eadē potentia in ſecunda medietate eiuſdē tē-<lb/>poris. </s>
              <s xml:id="N177DC" xml:space="preserve">quo poſito ꝓbo /  a. potentia maior c. medi­<lb/>um tranſeundo non continuo vniformiter remit-<lb/>tit motū ſuū. </s>
              <s xml:id="N177E3" xml:space="preserve">quia ſi non: detur oppoſitum videli­<lb/>cet /  in caſu a. potentia maior inuariata c. mediū <lb/>inuariatū in e. tempore adequate tranſeundo. </s>
              <s xml:id="N177EA" xml:space="preserve">vni­<lb/>formiter remittit motū ſuū / et arguo ſic / a. potētia <lb/>maior et c. vniformiter remittit motū ſuū in e. tem­<lb/>pore / igitur in prima medietate eiuſdē e. temporis <lb/>pertranſit g. ſpaciū et in ſecunda h. ſpacium inter <lb/>que ſpacia eſt proportio f. ex hypotheſi: et vltra in <lb/>prima medietate e. temporis a. pertranſit g. ſpa-<lb/>cium et in ſecunda h. inter que eſt proportio f. / ergo <lb/>velocitatis qua a. mouetur in prima medietate <lb/>e. temporis ad velocitatem qua mouetur in ſecun­<lb/>da eſt f. proportio: conſequens eſt contra ſecundū <lb/>correlarium ſuppoſitionis huius capitis / igitur et <lb/>antecedens: et per conſequens contradictorum an­<lb/>tecedentis eſt verum / quod fuit probandum </s>
              <s xml:id="N17807" xml:space="preserve">Secū­<lb/>da conſequentia patet per hanc maximam </s>
              <s xml:id="N1780C" xml:space="preserve">Eadē <lb/>eſt proportio velocitatū equalibus temporibꝰ co­<lb/>extenſarum: et ſpaciorum ab eiſdē pertranſitoruꝫ <lb/></s>
              <s xml:id="N17814" xml:space="preserve">Et prima conſequentia probatur in qua eſt vis ꝓ­<lb/>bationis / q2 ſi a. potentia maior et c. in e. tempore <lb/>vniformiter remittit motum ſuum. </s>
              <s xml:id="N1781B" xml:space="preserve">ipſa a. potētia <lb/>in prima medietate e. temporis medietatē veloci-<lb/>tatis deperdende adequate deperdit: et ipſa a. po­<lb/>tentia illam medietatem velocitatis deperdende <lb/>deperdendo adequate, g. ſpacium adequate per­<lb/>tranſit / igitur a. potentia in prima medietate: tē­               <pb chead="Primi partis" file="0076" n="76"/>               poris g. ſpacium pertranſit adequate et eadem ra-<lb/>tione h. ſpacium in ſecunda medietate eiuſdem <lb/>temporis pertranſit / quod fuit probandum. </s>
              <s xml:id="N17831" xml:space="preserve">Ma-<lb/>ior eſt nota / et minor probatur / quia b. potentia il-<lb/>lam medietatem velocitatis deperdende deper-<lb/>dendo adequate g. ſpacium adequate pertranſit / <lb/>vt patet ex hypotheſi: igitur a. potentia eandem <lb/>medietatem deperdendo idem g. ſpacium adequa­<lb/>te pertranſit: quia diuerſe potentie ſiue equales <lb/>ſiue inequales idem medium et eaſdem partes me-<lb/>dii difformis in quibus acquiritur vel deperditur <lb/>motus tranſeundo equalem latitudinem motus <lb/>acquirunt vel deperdunt / vt patet ex quarto argu-<lb/>mento ſexti capitis huius tractatus: igitur minor <lb/>vera. </s>
              <s xml:id="N1784C" xml:space="preserve">Et eodem modo probabis ſecundam par-<lb/>tem concluſionis videlicet /  vbi aliqua potentia <lb/>etc̈. nulla minor inuariata idem medium inuaria-<lb/>tum tranſeundo: vniformiter continuo remittit <lb/>motum ſuum: quia ſi ſic: ſit illa potentia minor b. <lb/>et potentia que inuariata ſufficit illud c. medium <lb/>pertranſire continuo vniformiter remittendo mo-<lb/>tum ſuum ſit a. / et arguo ſic / a. pertranſeundo c. me-<lb/>dium vniformiter continuo remittit motum ſuum <lb/>et b. potentia minor idem c. medium tranſeundo <lb/>vniformiter continuo remittit motum ſuum: igitur <lb/>vbi b. potentia minor tranſeundo c. medium, vni-<lb/>formiter continuo remittit motum ſuum a. poten-<lb/>tia maior idem c. medium tranſeundo vniformi-<lb/>ter continuo remittit motum ſuum / quod eſt contra <lb/>priorem partem concluſionis. </s>
              <s xml:id="N1786D" xml:space="preserve">Patet igitur con-<lb/>cluſio.               <anchor type="note" xlink:href="note-0076-01" xlink:label="note-0076-01a"/>               </s>
              <s xml:id="N17877" xml:space="preserve">¶ Ex hac cõcluſione facile ſequitur /  nulle <lb/>due potentie inequales nõ variate tranſeuntes idē <lb/>mediū adequate poſſunt ad nõ gradū ſuos motus <lb/>remittere. </s>
              <s xml:id="N17880" xml:space="preserve">Probatur correlariū / quia ſi nõ ſit verū <lb/>detur oppoſitū videlicet /  aliquarū duarū poten­<lb/>tiarum inequaliū vtra idē mediū adequate tran-<lb/>ſeundo remittat motū ſuū ad nõ gradū / et arguitur <lb/>ſic / vtra potentiarū inequaliū idem mediū ade-<lb/>quate tranſeundo remittit motū ſuū ad nõ gradū / <lb/>igitur maiorē latitudinē motus deperdit potentia <lb/>maior quã minor idem mediū adequatū tranſeund-<lb/>do / ſed conſequens eſt falſum / et contra concluſionē <lb/>quarti argumenti ſexti capitis preallegatã: igitur <lb/>et antecedens. </s>
              <s xml:id="N17897" xml:space="preserve">Sequela tamen probatur / qm̄ ſi ille <lb/>potentie ſunt inequales nõ variate: maior illarum <lb/>intenſiori latitudine motus mouetur ſupra eãdem <lb/>reſiſtentiã quã minor: et tamē vtra per te remittit <lb/>motum ſuū ad nõ gradū: igitur maiorē latitudineꝫ <lb/>motus perdit maior quã minor;: etc̈. igitur.               <anchor type="note" xlink:href="note-0076-02" xlink:label="note-0076-02a"/>               </s>
              <s xml:id="N178A9" xml:space="preserve">¶ Sequi­<lb/>tur ſecūdo /  ſi aliqua potētia nõ variata tranſeū-<lb/>do aliquod mediū nõ variatū remittit motum ſuū <lb/>ad nõ gradum: oīs potentia maior nõ variata re-<lb/>mittens in eodem medio motum ſuū remittit illum <lb/>ad gradū. </s>
              <s xml:id="N178B6" xml:space="preserve">et oīs minor remittit ad nõ gradū in ali-<lb/>quo puncto medii intrinſeco. </s>
              <s xml:id="N178BB" xml:space="preserve">Probat̄̄ prima pars / <lb/>qm̄ illa potentia maior remittit ibi motum ſuū et <lb/>nõ remittit ad non gradum / vt patet ex antecedenti <lb/>correlario: igitur remittit illū ad gradum. </s>
              <s xml:id="N178C4" xml:space="preserve">Secun-<lb/>da pars probatur / qm̄ oīs minor potētia in aliquo <lb/>puncto intrinſeco deueniet ad proportionem equa­<lb/>litatis: igitur in aliquo puncto intrinſeco remittet <lb/>motū ſuum ad nõ gradū. </s>
              <s xml:id="N178CF" xml:space="preserve">Patet hoc etiã facile exē-<lb/>plo / quoniã ſi ſit aliqua potentia vt .4. et incipiat re­<lb/>mittere motum ſuum et remittat ad non gradū ali-<lb/>quod medium pertranſeundo: neceſſe eſt cum ipſa <lb/>ſit inuariata medium illud in ſuo extremo intenſio­               <cb chead="Capitulū ſeptimū."/>               ri reſiſtere vt .4. et in nullo puncto alio ãteriori tan­<lb/>tum reſiſtere quoniã alias iam in tali puncto motꝰ <lb/>ad non gradum deueniret et ſic non pertranſiret to­<lb/>tum: capiatur tunc alia potentia minor vt tria vel <lb/>vt duo (in idem redit) remittens in eodē medio mo-<lb/>tum ſuum / tunc manifeſtum eſt /  illa potētia ad nõ <lb/>gradum remittet motum ſuum cum deueneret ad <lb/>punctum reſiſtentie vt duo vel ad punctum reſiſten­<lb/>tie vt tria ſi ipſa fuerit vt tria: et tale punctū eſt pun­<lb/>ctum intrinſecum / vt ſatis patet quoniam extrinſe­<lb/>cum reſiſtit et .4. / igitur talis potentia minor ad nõ <lb/>gradum remittet motum ſuum in aliquo puncto in­<lb/>trinſeco / quod fuit probandum.</s>
            </p>
            <div xml:id="N178F5" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0076-01a" xlink:label="note-0076-01" xml:id="N178F9" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0076-02a" xlink:label="note-0076-02" xml:id="N178FF" xml:space="preserve">2. correĺ.</note>
            </div>
            <note position="right" xml:id="N17905" xml:space="preserve">Trigeſi-<lb/>ma .9. cõ­<lb/>cluſio cal­<lb/>culatorꝪ</note>
            <p xml:id="N1790F">
              <s xml:id="N17910" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N17913" xml:space="preserve">Si aliqua poten-<lb/>tia non variata in aliquo medio difformi non va-<lb/>riato vniformiter ad non gradum motum ſuum re­<lb/>mittit: omnis potentia maior inuariata idem me-<lb/>dium tranſeundo inuariatum in infinitum veloci-<lb/>ter remittit motum ſuum verſus extremum inten-<lb/>ſius eiuſdem medii deueniēdo. </s>
              <s xml:id="N17922" xml:space="preserve">Probatur / ſit b. po-<lb/>tentia minor que inuariata c. medium inuariatum <lb/>tranſeundo: vniformiter remittit motum ſuum ad <lb/>non gradum continuo d. gradu velocitatis. </s>
              <s xml:id="N1792B" xml:space="preserve">ſit a. <lb/>potentia maior que inuariata ipſum c. medium in­<lb/>uariatum totaliter pertranſeat remittendo motuꝫ <lb/>ſuuꝫ procedendo continuo per eandem lineam per <lb/>quam ꝓcedit b. </s>
              <s xml:id="N17936" xml:space="preserve">(Semper enim hoc modo intelligo <lb/>et ſi propter breuiloquium id non explicem) / tunc di­<lb/>co /  a. potentia maior verſus extremum intenſius <lb/>c. medii deueniendo in infinitum velociter remittit <lb/>motum ſuum. </s>
              <s xml:id="N17941" xml:space="preserve">Quod ſic probatur / quia a. verſus ex­<lb/>tremum intenſius c. medii deueniendo in infinitum <lb/>velocius remittit motum ſuum quam b. et b. conti-<lb/>nuo certe velociter remittit motum ſuum puta <lb/>d. gradu / ergo a. in infinitum velociori gradu re-<lb/>mittit motum ſuum quam ſit d. gradus / et per con-<lb/>ſequens in infinitum velociter remittit motum ſuū / <lb/>quod eſt probandū. </s>
              <s xml:id="N17952" xml:space="preserve">Conſequentie ſunt manifeſte et <lb/>minor ex hypotheſi patet / et maior arguitur / quia <lb/>a. et b. cum ſint potentie inuariate idem medium in­<lb/>uariatum traſeuntes eaſdem partes eiuſdem me-<lb/>dii tranſeundo equales latitudines motus deper-<lb/>dunt adequate / vt iam ſepius argutum eſt / ſed a. <lb/>verſus extremū ītēſiꝰ c. medii deueniendo in infini­<lb/>tum velocius pertranſibit aliquam partem ipſius <lb/>c: medii quam b. pertranſibit eandem / ergo a. in in-<lb/>finitum velocius remittet motum ſuum verſus ex-<lb/>tremum intenſius c. medii deueniendo quã b. / quod <lb/>fuit probandum. </s>
              <s xml:id="N1796B" xml:space="preserve">Patet hec conſequentia / quoniã <lb/>ita velociter ſicut a. pertranſit aliquam partem c. <lb/>medii ita velociter remittit motum ſuū deperden-<lb/>dum in illa parte medii et b. ſimiliter: ſed in infini-<lb/>tum velocius pertranſibit a. aliquam partem ipſi-<lb/>us c. medii quam b. pertranſibit eandem: igitur in <lb/>infinitum velocius a. remittet motum ſuum verſus <lb/>extremum intenſius c. medii deueniendo quam b. <lb/></s>
              <s xml:id="N1797D" xml:space="preserve">Sed iam probatur minor / et capio proportionem / <lb/>quam habet a. ad extremum intenſius c. medii que <lb/>ſit f. / et arguo ſic: continuo a. mouebitur a propor-<lb/>tione f. vĺ a. maiori: et b. ab īfinite modica propor-<lb/>tione mouebitur tranſeundo illud medium: ergo <lb/>ab in infinitū maiori proportione tranſeundo ali-<lb/>quam partem c. medii mouebitur a. quam b. ean-<lb/>dem partem tranſeundo: igitur a. verſus extremū <lb/>intenſiꝰ c. medii deueniēdo in īfinitū velociꝰ ꝑtrã-<lb/>ſibit aliquã partē eiuſdē c. medii quã b. ꝑtranſibit               <pb chead="Primi tractatus" file="0077" n="77"/>               eadē / quod erat probandum. </s>
              <s xml:id="N17997" xml:space="preserve">Et ſic patet concluſio <lb/>               <anchor type="note" xlink:href="note-0077-01" xlink:label="note-0077-01a"/>               </s>
              <s xml:id="N179A1" xml:space="preserve">¶ Ex quo ſequitur:  ſi aliqua potentia inauriata <lb/>aliquod mediū inuariatū tranſeundo continuo re­<lb/>mittat motū ſuū vſ ad nõ gradum ſiue vniformi-<lb/>ter ſiue difformiter: oīs potentia maior inuariata <lb/>idem mediū inuariatū tranſeūdo continuo remit-<lb/>tendo motum ſuū ad extremū intenſius eiuſdē me-<lb/>dii deueniendo: in infinitū velocius remittit motuꝫ <lb/>ſuū quã data potentia minor. </s>
              <s xml:id="N179B2" xml:space="preserve">Probatur / quia illa <lb/>potentia quecū detur in infinitū velocius moue-<lb/>bitur aliquam partē illius medii tranſeūndo ſus <lb/>extremū intenſius deueniendo quaꝫ data potentia <lb/>minor: igitur in infinitū velocius remittit motū ſuū <lb/>quã illa data potētia minor. </s>
              <s xml:id="N179BF" xml:space="preserve">Patet hec cõſequētia / <lb/>qm̄ ita velociter ſicut potentia maior pertranſit a-<lb/>liquã partē c. medii ita velociter remittit motū de-<lb/>perdendum in illa: et ſimiliṫ. </s>
              <s xml:id="N179C8" xml:space="preserve">potentia minor: igitur <lb/>ſi in infinitū velocius potentia maior mouetur trã-<lb/>ſeūdo aliquam partē c. medii quã potentia minor <lb/>tranſeundo eandē: ipſa potētia maior in infinitum <lb/>velocius remittit motū ſuū quã potētia minor. </s>
              <s xml:id="N179D3" xml:space="preserve">An­<lb/>tecedens ꝓbatur / vt ſupra qm̄ potentia maior a ꝓ-<lb/>portiõe quã habet ad extremū intēſius ipſiꝰ medii <lb/>cõtinuo mouebit̄̄ vel a maiori: et potētia minor ab <lb/>in infinitū minori verſus extremū intēſius deueniē-<lb/>do: igitur in infinitū maiori velocitate mouebitur <lb/>ꝑtrãſeūdo aliquã partē ipſiꝰ medii potētia maior <lb/>quã potētia minor ꝑtrãſeūdo eanſdē ſus extremū <lb/>intenſius deueniendo. </s>
              <s xml:id="N179E6" xml:space="preserve">Et ſic patet correlarium.</s>
            </p>
            <div xml:id="N179E9" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0077-01a" xlink:label="note-0077-01" xml:id="N179ED" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N179F3" xml:space="preserve">q̄drage-<lb/>ſima con­<lb/>cĺio cal-<lb/>cĺatoris</note>
            <p xml:id="N179FD">
              <s xml:id="N179FE" xml:space="preserve">Sexta concluſio. </s>
              <s xml:id="N17A01" xml:space="preserve">Si aliqua potentia <lb/>īuariata tranſeūdo aliqḋ mediū difforme īuaria-<lb/>tum vniformiter remittit motū ſuū ad nõ gradū in <lb/>extremo intēſiori: oīs potentia minor in infinitum <lb/>tarde remittit motū ſuū mouēdo per idē mediū ver­<lb/>ſus punctū intrinſecū eiuſdem medii ad quē habet <lb/>ꝓportionē equalitatis deueniendo. </s>
              <s xml:id="N17A10" xml:space="preserve">Probatur / ſit <lb/>b. potētia maior que īuariata c. mediū īuariatum <lb/>tranſeūdo vniformiter cõtinuo d. gradu velocita-<lb/>tis remittit motū ſuū ad nõ gradū in extremo intē­<lb/>ſiori c. medii: et ſit a. potentia minor que inuariata <lb/>ꝑtē c. medii (vt oportet) trãſeundo remittat ↄ̨tinuo <lb/>motū ſuū verſus e. pūctū intrinſecū ad quē hꝫ ꝓpor­<lb/>tionem equalitatis: q2 neceſſe eſt / ipſam habere ad <lb/>aliquē punctū intrinſecū illꝰ c. medii ꝓportionem <lb/>equalitatis / vt ptꝫ ex ſecūdo correlario quarte con-<lb/>cluſionis huiꝰ. </s>
              <s xml:id="N17A27" xml:space="preserve">Tūc dico /  a. potentia verſus e. pū­<lb/>ctum veniendo in infinitū tarde remittit motū ſuū. <lb/></s>
              <s xml:id="N17A2D" xml:space="preserve">Quod ſic ꝓbatur / q2 a. potentia verſus e. punctū ve­<lb/>niendo in infinitū tardius remittit motū ſuū quam <lb/>b. potentia: et b. potentia certe velociter cõtinuo pu­<lb/>ta d. gradu velocitatis remittit motū ſuū ex hypo-<lb/>theſi: igitur a. potentia in infinitum tarde remittit <lb/>motū ſuū. </s>
              <s xml:id="N17A3A" xml:space="preserve">Patet ↄ̨ſequentia cū minore: et arguitur <lb/>maior: q2 a. potentia verſus e. punctū veniendo in <lb/>infinitū tardius pertranſit aliquam partē ipſius c. <lb/>medii quam b. pertrãſeat eandē: et tam a. quam b. <lb/>eaſdem partes c. medii tranſeundo equalē latitu-<lb/>dinē motus deperdunt adequate: vt ſepe argutum <lb/>eſt: igitur a. potentia verſus e. punctuꝫ veniendo in <lb/>infinitū tardius remittit motum ſuū quam b. potē-<lb/>tia: quod fuit probandum. </s>
              <s xml:id="N17A4D" xml:space="preserve">Cõſequentia probatur: <lb/>quoniã a. tranſeundo aliquam partem c. medii ver-<lb/>ſus e. punctum veniendo tantam latitudinem mo-<lb/>tus deperdit ſicut b. pertranſeundo eandē adequa­<lb/>te. </s>
              <s xml:id="N17A58" xml:space="preserve">ergo ſi a. in infinitum tardius pertranſit aliquã <lb/>partem ipſius c. medii verſus e. pūctum deuenien-<lb/>do quam b pertranſeat eandem in infinitum tardi­<lb/>us remittit motum ſuum tranſeundo talem parteꝫ /               <cb chead="Capitulum ſeptimū."/>               quam b. tranſeundo eandem. </s>
              <s xml:id="N17A64" xml:space="preserve">Sed probatur maior <lb/>et capio proportionem / quam habet b. ad punctum <lb/>e. ipſius c. medii que ſit f. / et arguo ſic / a verſus e. pū-<lb/>ctum deueniendo ab in infinitum minori proporti-<lb/>one mouetur tranſeundo aliquã partem quam ſit <lb/>f. proportio a qua vel maiori continuo mouetur b. <lb/>tranſeundo talem partem: quia ab infinite modi-<lb/>ca proportione mouebitur a. verſus c. punctum ve-<lb/>niendo: cum ſucceſſiue remittat motum ſuum conti­<lb/>nuo verſus idem e. punctum veniendo ad non gra-<lb/>dū: et b. verſus e. punctū veniendo ↄ̨tinuo mouet̄̄ ab <lb/>f. proportione vel a maiori: ergo ſequitur /  in in-<lb/>finitū tardius mouetur a. tranſeūdo aliquam par-<lb/>tem c. medii verſus e. punctum veniendo quam mo-<lb/>ueatur b. eandem partem tranſeundo: et ex conſe-<lb/>quenti in infinitum tardius a. potentia verſus e. <lb/>punctū veniendo aliquam partem c. medii pertran­<lb/>ſit quam b. pertranſeat eandem / quod fuit proban­<lb/>dum.               <anchor type="note" xlink:href="note-0077-02" xlink:label="note-0077-02a"/>               </s>
              <s xml:id="N17A90" xml:space="preserve">¶ Ex quo ſequitur primo /  vbicun aliqua <lb/>potentia inuariata aliquod medium tranſeundo <lb/>ſucceſſiue remittit motum ſuum vſ ad non gradū <lb/>ſiue vniformiter continuo, ſiue difformiter, ſiue de­<lb/>uendo ad extremum illius medii, ſiue ad punctum <lb/>intrinſecum: omnis potentia minor inuariata re-<lb/>mittens motum ſuū ad non gradum in aliquo pun­<lb/>cto, in infinitum tardius ad idem punctum venien-<lb/>do remittit motum ſuum quam data potentia ma­<lb/>ior cum ad idem punctū deuenit in quo illa minor <lb/>habet non gradum motus. </s>
              <s xml:id="N17AA7" xml:space="preserve">Probatur hoc correla­<lb/>rium: et ſit a. potentia maior que remittat inuaria-<lb/>ta c. medium inuariatum tranſeundo vel partē eiꝰ <lb/>vniformiter, vel difformiter ſucceſſiue cõtinuo, mo­<lb/>tum ſuum ad non gradum: et b potentia minor que <lb/>in puncto citeriori eiuſdem medii qui punctus ſit d. <lb/>remittat ad non gradum motum ſuum: ipſa b. po-<lb/>tentia inuariata cum ad d. punctum ipſius c. medii <lb/>inuariati deuenit vniformiter vel difformiter re-<lb/>mittente motum ſuum continuo ſucceſſiue: tunc di-<lb/>co /  b. potentia in infinitum tardius remittet mo-<lb/>tum ſuum verſus d. punctum deueniendo quam a. <lb/>potentia maior verſus idem d. punctum veniendo. <lb/></s>
              <s xml:id="N17AC3" xml:space="preserve">Et ſic dicendum eſt de quibuſcun duabus inequa­<lb/>libus potentiis: et de infinitis potentiis ſimiliter <lb/>quarum nulla eſt equalis alteri. </s>
              <s xml:id="N17ACA" xml:space="preserve">Quod probatur <lb/>ſic: quia in infinitum tardius pertranſibit b. poten­<lb/>tia minor aliquam partem c. medii verſus d. pun-<lb/>ctum veniendo quam a. potentia maior pertranſi-<lb/>bit eandem: et a. et b. eaſdem partes c. medii tranſe-<lb/>undo equales latitudines motus deperdunt: vt ſe-<lb/>pe argutum eſt: igitur b. potentia minor verſus <lb/>d. punctum veniendo in infinitum tardius remittet <lb/>motum ſuum quam a. potentia verſus idem d. pun­<lb/>ctum veniendo. </s>
              <s xml:id="N17ADF" xml:space="preserve">Conſequentia et maior ſuperius ar­<lb/>gute ſunt. </s>
              <s xml:id="N17AE4" xml:space="preserve">Patet igitur correlarium.               <anchor type="note" xlink:href="note-0077-03" xlink:label="note-0077-03a"/>               </s>
              <s xml:id="N17AEC" xml:space="preserve">¶ Sequitur <lb/>ſecundo /  vbicū aliqua potentia nõ variata me-<lb/>dium inuariatum tranſeundo vniformiter conti-<lb/>nuo remittit motum ſuum ad extremum intenſius <lb/>deueniendo ad gradum vel ad non gradum: ipſa <lb/>ſiue ei equalis idem medium tranſeundo continuo <lb/>ſucceſſiue procedendo ab extremo intenſiori verſus <lb/>extremum remiſſius continuo per eandem lineam <lb/>per quam antea mouebatur remittendo motum ſu­<lb/>um, vniformiter continuo intendit motum ſuum: et <lb/>omnis maior inuariata ab eodem puncto intenſio­<lb/>ri ꝓcedēdo per eandē lineã, per quã ꝓcedit potētia <lb/>intendens motū ſuū vniformiter inuariata diffor-<lb/>miter cõtinuo ītendit motū ſuū: et ſimiliter oīs mi-<lb/>nor habēs ad extremū intenſius eiuſdē medii pro-<lb/>portionē maioris īequalitatis. </s>
              <s xml:id="N17B0D" xml:space="preserve">Prima pars huiꝰ               <pb chead="Primi tractatus" file="0078" n="78"/>               correlarii patet ex ſecūdo correlario ſecūde cõclu-<lb/>ſionis huius capitis: et ſecūda breuiter ꝓbatur ſic / <lb/>q2 vbicū aliqua potentia īuariata mediū īuaria­<lb/>tum tranſeūdo ↄ̨tinuo vniformiter remittit motū <lb/>ſuū ad extremū intenſius deueniendo: oīs maior <lb/>vel minor verſus idem extremū veniendo per ean-<lb/>dem lineã cõtinuo difformiter remittit motū ſuum <lb/>ipſa et medio continuo inuariatis / vt ptꝫ ex quarta <lb/>concluſione huiꝰ: et oīs potentia inuariata mediū <lb/>inuariatū tanſeundo ab extremo intenſiori rece-<lb/>dendo per eandem lineam oīno eodē modo inten-<lb/>dit motum ſuū ſicut remittit ab extremo remiſſiori <lb/>ꝓcedendo per eandē lineam verſus extremū inten­<lb/>ſius: ergo oīs maior ab eodē puncto intenſiori ꝓ-<lb/>cedendo per eandē lineã per quam ꝓcedit potētia <lb/>intendens motum ſuū vniformiter: ipſo medio in-<lb/>uariato: difformiter cõtinuo intendit motum ſuuꝫ <lb/>et ſimiliter oīs minor habens ad extremū intēſius <lb/>eiuſdem medii ꝓportionē maioris inequalitatis. <lb/></s>
              <s xml:id="N17B3A" xml:space="preserve">Et ſic patet correlariū. </s>
              <s xml:id="N17B3D" xml:space="preserve">Et ſi fortiorē demonſtrati-<lb/>onē exoptas: vtaris demonſtratione adducta ad <lb/>quartã concluſionē paucis mutatis: que ſeſe ṗma <lb/>fronte intelligenti probationē illius concluſionis <lb/>offerūt.               <anchor type="note" xlink:href="note-0078-01" xlink:label="note-0078-01a"/>               </s>
              <s xml:id="N17B4D" xml:space="preserve">¶ Sequitur tertio /  vbicū aliqua potē-<lb/>tia īuariata vniformiter cõtinuo ſucceſſiue intēdit <lb/>motū ſuū vſ ad nõ gradum: mediū īuariatū trã-<lb/>ſeundo ab extremo intenſiori verſus remiſſius: oīs <lb/>potentia maior ab eodem extremo intenſiori ꝓce-<lb/>dens continuo per eandē lineã in infinitū velociter <lb/>intendit motum ſuū. </s>
              <s xml:id="N17B5C" xml:space="preserve">Probatur facile: qm̄ quãdo <lb/>ipſa potentia maior mouetur verſus extremū in-<lb/>tenſius cõtinuo remittendo motum ſuū .etc̈. in infi-<lb/>nitum velociter remittit motū ſuū / vt patet ex quin­<lb/>ta cõcluſione huius capitis: et oīno eadem veloci-<lb/>tate intendit motū ſuū retrogrado motu per ean-<lb/>dem lineã mouēdo ſicut antea remittebat in eiſdeꝫ <lb/>partibus eiuſdem linee: ergo oīs talis potentia <lb/>maior que ſic mouetur motu retrogrado ab extre­<lb/>mo intenſiori verſus remiſſius per eandē lineam <lb/>etc̈. in infinitū velociter intendit motum ſuū / quod <lb/>fuit probandū. </s>
              <s xml:id="N17B75" xml:space="preserve">Et ſic patꝫ correlariū.               <anchor type="note" xlink:href="note-0078-02" xlink:label="note-0078-02a"/>               </s>
              <s xml:id="N17B7D" xml:space="preserve">¶ Sequitur <lb/>quarto /  vbicun aliqua potentia īuariata me-<lb/>dium īuariatum tranſeundo cõtinuo ſucceſſiue in­<lb/>tēdit motum ſuū ad nõ gradum ſiue vniformiter <lb/>ſiue difformiter: oīs potentia minor habens pro-<lb/>portionē maioris inequalitatis ad aliquã parteꝫ <lb/>eiuſdē medii in infinitū tardius intendit motum <lb/>ſuū a puncto ad quē habet proportionē equalita­<lb/>tis recedendo verſus remiſſius extremū: quã data <lb/>potētia maior ab eodē puncto recedendo verſus <lb/>extremū remiſſiꝰ. </s>
              <s xml:id="N17B94" xml:space="preserve">Ptꝫ hoc correlariū ex predictis</s>
            </p>
            <div xml:id="N17B97" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0077-02a" xlink:label="note-0077-02" xml:id="N17B9B" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0077-03a" xlink:label="note-0077-03" xml:id="N17BA1" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0078-01a" xlink:label="note-0078-01" xml:id="N17BA7" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0078-02a" xlink:label="note-0078-02" xml:id="N17BAD" xml:space="preserve">4. correĺ.</note>
            </div>
          </div>
          <div xml:id="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
            <head xml:id="N17BB8" xml:space="preserve">Capitulū octauū / in quo inquiritur an due <lb/>potentie īequales idē mediū īuariatū tran-<lb/>ſeūtes valeãt vniformiter remittere aut intē­<lb/>dere motum ſuum per ambarū vel alterius <lb/>earum variationem.</head>
            <p xml:id="N17BC3">
              <s xml:id="N17BC4" xml:space="preserve">POſt̄ ſuperiori capite oſtēſū <lb/>eſt nullas duas potētias īequales īua-<lb/>riatas: id eſt quarum nulla variat̄̄ idem <lb/>mediū īuariatū trãſeūtes poſſe vniformiter intē-<lb/>dere aut remittere motū ſuū: iã īquirendū eſt an ꝑ <lb/>alteriꝰ eaꝝ vel ambaꝝ variationē id fieri valeat.</s>
            </p>
            <p xml:id="N17BD1">
              <s xml:id="N17BD2" xml:space="preserve">Cuiꝰ inq̇ſitiõi p̄mittat̄̄ ꝓ baſi  fūda­<lb/>mēto talis ſuppoſitio. </s>
              <s xml:id="N17BD7" xml:space="preserve">Si aliq̈ potētia vniformiṫ <lb/>ↄ̨tinuo ſuū motū remittēs aut ītēdēs aliq̈ potētia <lb/>in certa ꝓportione cõtinuo velocius mouetur: ne-<lb/>ceſſe eſt potentiã ipſam tardius motã cõtinuo vni­<lb/>formiter motū ſuū remittere aut intendere. </s>
              <s xml:id="N17BE2" xml:space="preserve">Et ſi               <cb chead="Capitulū octauū."/>               aliqua potentia vniformiter cõtinuo ſuū motum <lb/>remittens aut intendens aliqua alia potentia in <lb/>certa ꝓportione cõtinuo tardius mouetur: neceſſe <lb/>eſt potentiã velocius motã vniformiter itidē con-<lb/>tinuo motū ſuū remittere aut intendere. </s>
              <s xml:id="N17BF0" xml:space="preserve">Exemplū / <lb/>vt data potētia que incipit a gradu octauo exclu-<lb/>ſiue moueri cõtinuo vniformiter remittēdo motū <lb/>ſuū: et in dupla ꝓportione cõtinuo velocius moue­<lb/>do quã vna alia potētia que incipit moueri a gra­<lb/>du quarto excluſiue: tūc dico /  neceſſe eſt /  illa po­<lb/>tentia que incipit moueri a quarto gradu excluſi-<lb/>ue cõtinuo vniformiter remittat motum ſuū: </s>
              <s xml:id="N17C01" xml:space="preserve">Pro­<lb/>batur / et ſit a. potentia remittens continuo vnifor-<lb/>miter motū ſuū: et ſit b. potentia que cõtinuo in f. <lb/>ꝓportiõe tardius mouetur quã a. potentia: et ma-<lb/>nifeſtū eſt /  etiã b. potentia remittit motū ſuū: q2 <lb/>alias motus illarū potentiarū nõ cõtinuo mane-<lb/>rent in eadē ꝓportione. </s>
              <s xml:id="N17C10" xml:space="preserve">Uolo igitur /  potētia a. <lb/>perdat in toto tēpore adequate in quo mouetur c. <lb/>latitudinē motus: et b.d. latitudinē motus: et tunc <lb/>dico /  d. latitudo motus deperdenda a b. poten-<lb/>tia tardius mota vniformiter cõtinuo remittetur <lb/></s>
              <s xml:id="N17C1C" xml:space="preserve">Probatur / q2 d. latitudo motus in qualibet me-<lb/>dietate tēporis in quo deperdetur perdet vnã me-<lb/>dietatē ſui, et in qualibet tertia vnã tertiam, et in <lb/>qualibet quarta, vnã quartã, et ſic conſequenter: <lb/>igitur d. latitudo deperdenda a b. potentia tar-<lb/>dius mota vniformiter continuo remittetur. </s>
              <s xml:id="N17C29" xml:space="preserve">Pa-<lb/>tet conſequentia ex diffitione remiſſionis vnifor-<lb/>mis alicuius latitudinis. </s>
              <s xml:id="N17C30" xml:space="preserve">Probatur antecedens: <lb/>quoniã quandocun aliqua pars aliquota c. la-<lb/>titudinis ab a. potentia deperdende deperdetur <lb/>adequate conſimilis pars aliquota et eiuſdem de­<lb/>nominationis deperdet d. latitudo: ſed in quali-<lb/>bet medietate temporis in quo ille latitudines re­<lb/>mittuntur c. latitudo perdit vnam medietateꝫ ſui: <lb/>et in qualibet tertia vnam tertiam ſui, et in quali-<lb/>bet quarta quartam, et ſic conſequenter: quia c. la­<lb/>titudo vniformiter remittitur continuo / vt patet <lb/>ex hypotheſi / igitur d. latitudo in qualibet medie-<lb/>ta temporis in quo remittitur perdit vnã medie-<lb/>tatem ſui, et in qualibet tertia tertiam, et in quali-<lb/>bet quarta quartam, et ſic cõſequenter. </s>
              <s xml:id="N17C4D" xml:space="preserve">Patet cõ-<lb/>ſequentia cum minore: et probatur maior: quoniã <lb/>continuo latitudo motus quo mouetur a. ad lati-<lb/>tudinem motus quo mouetur b. eſt proportio f. ex <lb/>hypotheſi: et continuo motus quo mouetur a. et <lb/>etiam latitudo motus quo mouetur b. remittūtur / <lb/>ergo inter latitudinem deperditam a. motu quo <lb/>mouetur a. maiore, et latitudinem deperditam a <lb/>motu minori quo mouetur b. eſt continuo propor­<lb/>tio f. / vt patet ex primo correlario quinte concluſi-<lb/>onis ſecūdi capitis ſecunde partis: et latitudo de-<lb/>perdenda a motu quo mouet̄̄ a. eſt c. et latitudo de­<lb/>ꝑdēda a motu quo mouet̄̄ b. eſt d. / igit̄̄ inter c. et d. <lb/>eſt ꝓportio f. / et ex cõſequēti ſequit̄̄ /  inter partes <lb/>aliquotas eiuſdē denoīatiõis ipſiꝰ c. et ipſiꝰ d. pu-<lb/>ta īter medietatatē c. et medietatē d, et īter tertias <lb/>et īter quartas, et ſic cõſequēter eſt etiã ꝓportio f. <lb/></s>
              <s xml:id="N17C71" xml:space="preserve">Ptꝫ hec ↄ̨ña ex vndecima ſuppoſitiõe ſcḋi capitis <lb/>p̄allegati: et vltra īter ꝑtes aliq̊tas eiuſdē denoīa­<lb/>tionis c. latitudīs eſt ꝓportio f. et ↄ̨tinuo īter ꝑteꝫ <lb/>deꝑditã ab ipſo c. et deꝑditã a d. eſt f. ꝓportio / vt ꝓ­<lb/>batū eſt / g̊ quãdocū aliq̈ pars aliq̊ta c. latitudīs <lb/>ab a. potētia deꝑdēde deꝑdet̄̄: adeq̈te ↄ̨ſimilis ꝑs <lb/>aliq̊ta et eiuſdē denoīatiõis deꝑdet d. latitudo / qḋ <lb/>fuit probandum. </s>
              <s xml:id="N17C82" xml:space="preserve">Et eodem modo probabis cum <lb/>vtra potentia iutendit motum ſuum altera illa-<lb/>rum que cotinuo in certa ꝓportione velocius mo-               <pb chead="Primi tractatus" file="0079" n="79"/>               uetur vniformiter cõtinuo intendēte motū ſuū. </s>
              <s xml:id="N17C8E" xml:space="preserve">Et <lb/>conſimiliter et ex eiſdem principiis ſecundam par­<lb/>tem deduces.</s>
            </p>
            <p xml:id="N17C95">
              <s xml:id="N17C96" xml:space="preserve">Secūda ſuppoſitio. </s>
              <s xml:id="N17C99" xml:space="preserve">Si aliqua potē-<lb/>tia nõ variata tranſeūdo mediū nõ variatu vnifor­<lb/>miter cõtinuo remittit motū ſuū: maiorē latitudi-<lb/>nem motus deperdit tranſeundo partē magis re-<lb/>ſiſtentē quã ſibi equalē minus reſiſtentē. </s>
              <s xml:id="N17CA4" xml:space="preserve">Patet / q2 <lb/>diutius inmoratur tranſeundo partē magis reſi-<lb/>ſtentē quã ei equalē minus reſiſtentē: ergo ſi vnifor­<lb/>miter remittat motū ſuū maiorē latitudinē motꝰ <lb/>deperdit tranſeundo partē magis reſiſtentē quaꝫ <lb/>ſibi equalē minꝰ reſiſtentē: igitur ſuppoſitio vera.</s>
            </p>
            <p xml:id="N17CB1">
              <s xml:id="N17CB2" xml:space="preserve">Tertia ſuppoſitio. </s>
              <s xml:id="N17CB5" xml:space="preserve">Alicuiꝰ medii ſuꝑ <lb/>quo īuariato aliqua potentia īuariata mouēs cõ­<lb/>tinuo vniformiter remittit motū ſuū duabus par­<lb/>tibus īequalibus, ſignatis quarū vtrã in aliquo <lb/>tēpore adequato adequate pertranſit: et quãlibet <lb/>partē exceſſus per quē maior pars excedit minorē <lb/>illa potentia tranſeundo, cū maiori reſiſtentia cõ-<lb/>tinuo mouetur quã quãlibet partē equalē minoris <lb/>tranſeundo: maior eſt ꝓportio velocitatis deper-<lb/>dite a tali potentia ſuper maiori parte mouendo <lb/>ad velocitatē deperditã mouendo ſuper parte mi­<lb/>nori quã ſit taliū partiū ꝓportio: </s>
              <s xml:id="N17CCE" xml:space="preserve">Exemplū / vt ſi a. <lb/>potentia ſuꝑ c. mediū mouēs vniformiter remittit <lb/>motū ſuū: ſignatis prima quarta c. medii et ſecun-<lb/>da medietate eiuſdē c. medii quaꝝ vtrã in aliquo <lb/>tēpore adequate peranſit: maior eſt ꝓportio quaꝫ <lb/>dupla (que eſt inter partes ſignatas) velocitatis <lb/>deperdite ab a. potentia mouēdo ſuꝑ ſecūda me-<lb/>dietate ad velocitatē deperditã in prima quarta <lb/>eiuſdē medii mouendo. </s>
              <s xml:id="N17CE1" xml:space="preserve">Probatur / et ſit medium c. <lb/>ſuper quo īuariato vniformiter continuo a. poten­<lb/>tia remittit motū ſuū cuius vna pars minor ſit d. <lb/>et ſecūda maior ſit .ef. excedat .ef. ipſum d. per f. <lb/>partē: et quamlibet partē ipſius f. minorē d. tran-<lb/>ſeundo moueatur a. cū maiori reſiſtentia quã mo-<lb/>uetur quãlibet ſibi equalē tranſeundo cū ſuper d. <lb/>parte mouetur: et vtram illarū partiū puta d. et <lb/>ef. in aliquo tēpore adequato adequate pertrãſit: <lb/>ita  in tēpore adequato in quo pertrãſit d. nichil <lb/>pertrãſeat ſuꝑficiale quin ſit d. aut pars illius: et <lb/>in tēpore in quo adequate pertrãſit .ef. nichil ſuꝑ-<lb/>ficiale pertranſeat quin ſit .ef. aut pars eius (ſeclu­<lb/>do multas alias cauillationes que nichil ꝓpoſito <lb/>conducūt) et ſit inter .ef. et d. ꝓportio g. moueatur <lb/>potentia a. pertranſeundo e. partē cū equali reſi-<lb/>ſtentia adequate ſicut tranſeundo d. partē vel cum <lb/>maiori / vt oportet / tūc dico /  velocitas deperdita <lb/>ab a. tranſeundo partē .ef. ſe habet in maiori pro-<lb/>portione ad velocitatē deperditã ab eadē potētia <lb/>a. tranſeundo d. partē quã ſit ꝓportio g. </s>
              <s xml:id="N17D0C" xml:space="preserve">Quod ſic <lb/>ꝓbatur: q2 tēporis in quo adequate ꝑtranſitur .ef. <lb/>pars ab ipſa potētia a. ad tēpus in quo adequate <lb/>pertranſitur d. pars eſt maior ꝓportio quã g. / ergo <lb/>velocitatis deperdite in pertranſitione .ef. partis <lb/>adequate ad velocitatē deperditã in pertranſitiõe <lb/>d partis adequate eſt maior ꝓportio quã g. / quod <lb/>fuit ꝓbandū. </s>
              <s xml:id="N17D1D" xml:space="preserve">Patet cõſequētia: q2 quãdo aliqua <lb/>latitudo in aliquo tēpore cõtinuo vniformiter re-<lb/>mittitur ſiue deperditur in qua ꝓportiõe ſe habēt <lb/>tēpora in eadē ſe habent latitudines deperdite: vt <lb/>facile ex diffinitione vniformis remiſſionis alicu-<lb/>ius latitudinis ptꝫ. </s>
              <s xml:id="N17D2A" xml:space="preserve">Sed ꝓbatur antecedens: quia <lb/>velocitas qua pertranſitur adequate .ef. pars ve-<lb/>locitate qua pertranſitur d. pars eſt minor: ergo               <cb chead="Capitulum octauū."/>               tēporis in quo adequate pertrãſitur .ef. pars ade­<lb/>quate ad tēpus in quo pertrãſitur d. pars adequa­<lb/>te eſt maior ꝓportio quã g. </s>
              <s xml:id="N17D38" xml:space="preserve">Conſequentia ptꝫ / q2 ſi <lb/>velocitas qua pertranſitur .ef. pars eſſet equalis <lb/>velocitati qua pertranſitur d. pars iam temporis <lb/>in quo pertrãſitur .ef. ad tēpus in quo pertrãſitur <lb/>ipſū d. eſſet g. ꝓportio que videlicet eſt inter illas <lb/>partes .ef. et d. / igitur ſi velocitas qua pertrãſitur <lb/>ef. pars adequate velocitate qua pertranſitur d. <lb/>eſt minor: iam ꝓportio tēporis in quo pertrãſitur <lb/>ef. pars adequate, ad tēpus in quo pertrãſitur d. <lb/>pars adequate eſt maior ꝓportio quã g. </s>
              <s xml:id="N17D4D" xml:space="preserve">Ptꝫ hec <lb/>cõſequeatia / q2 maius tēpus requiritur ad pertrã-<lb/>ſeundū ſpaciū .ef. adequate minori velocitate quã <lb/>ad pertranſeundū ipſum adequate aliqua maiori <lb/></s>
              <s xml:id="N17D57" xml:space="preserve">Sed iam probatur antecedens: videlicet  veloci-<lb/>tas qua pertranſitur adequate .ef. pars velocita-<lb/>te qua pertranſitur d. pars minor, eſt minor: quia <lb/>velocitas qua pertranſitur e. pars ab ipſa poten-<lb/>tia a. eſt equalis vel minor velocitate qua adequa­<lb/>te pertraſitur ab eadem potentia d. pars cū ex hy-<lb/>potheſi in pertranſitione e. partis adequate mo-<lb/>ueatur a. potentia cum equali vel maiori reſiſten-<lb/>tia quã in pertrãſitione d. partis adequate: et ipſi <lb/>velocitati qua pertranſitur e. pars adequate addi­<lb/>tur extenſiue adhuc minor velocitas in pertranſi-<lb/>tione f. partis magis reſiſtentis / vt conſtat: igitur <lb/>tota velocitas qua pertranſitur .ef. pars adequa-<lb/>te eſt minor tota velocitate qua ꝑtranſitur d. pars <lb/>adequate: quod fuit inferendum. </s>
              <s xml:id="N17D76" xml:space="preserve">Ptꝫ hec cõſequē-<lb/>tia: q2 ſi alicui latitudini intenſionis addatur ex-<lb/>tenſiue aliqua latitudo minoris intenſionis (cete-<lb/>ris paribꝰ) totalis illa latitudo aggregata ex ad­<lb/>dita et preexiſtenti efficitur minoris intenſionis: vt <lb/>ſi latitudini vniformiter difformi ab octauo vſ <lb/>ad quartū addatur vna latitudo minoris intēſio-<lb/>nis puta a. quatuor vſ ad ſecundū: aggregatum <lb/>ex eis efficitur minoris intenſionis: q2 preexiſtens <lb/>erat vt .6. aggregata vero ex preexiſienti et addita <lb/>eſt vt .5. </s>
              <s xml:id="N17D8D" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
            </p>
            <p xml:id="N17D90">
              <s xml:id="N17D91" xml:space="preserve">Quarta ſuppoſitio. </s>
              <s xml:id="N17D94" xml:space="preserve">Alicuius medii <lb/>ſuꝑ quo īuariato aliqua potentia īuariata mouēs <lb/>cõtinuo vniformiter remittit motū ſuū duabꝰ par­<lb/>tibus inequalibus ſignatis: quarū vtram in ali­<lb/>quo tēpore adequato adequate pertranſit: et quã-<lb/>libet partē exceſſus per quē maior pars excedit mi­<lb/>norē illa potentia tranſeundo cū minori reſiſtētia <lb/>cõtinuo mouetur, quã quãlibet partē equalē mino­<lb/>ris tranſeundo: velocitatis deperdite a. tali potē-<lb/>tia ſuꝑ maiore parte mouēdo ad velocitatē deper­<lb/>ditam mouendo ſuper parte minori: nec eſt talium <lb/>partiū ꝓportio nec maior. </s>
              <s xml:id="N17DAD" xml:space="preserve">Probatur: et ſit mediū <lb/>c. ſuꝑ quo īuariato vniformiter cõtinuo a. potētia <lb/>inuariata remittit motum ſuū: cuius vna pars mi­<lb/>nor ſit d. et ſecunda maior ſit .ef. excedat .ef. ipſū <lb/>d. per f. partem: et quamlibet partem ipſius f. mi-<lb/>norem d. tranſeundo moueatur a. cum minori re-<lb/>ſiſtentia quam mouetur quamlibet ſibi equalem <lb/>tranſeūdo cum ſuper d. parte mouetur: et vtram <lb/>illarum partium puta d. et .ef. in aliquo tempore <lb/>adequato adequate pertranſit .etc̈. </s>
              <s xml:id="N17DC2" xml:space="preserve">Et ſit inter .ef. <lb/>et d. proportio g. moueatur potentia a. tranſeū-<lb/>do c. partem cum equali reſiſtentia adequate ſicut <lb/>tranſeundo d. partem vel cum minori / vt oportet: <lb/>tunc dico /  velocitas deperdita ab a. tranſeundo <lb/>partem .ef. nun̄ ſe habet ad velocitatem deper-<lb/>ditam ab eadem potentia a. tranſeūdo d. partem <lb/>in g. proportione: nec in maiori.</s>
            </p>
            <pb chead="Primi tractatus" file="0080" n="80"/>
            <p xml:id="N17DD7">
              <s xml:id="N17DD8" xml:space="preserve">Quod ſic ꝓbatur: q2 tēporis in quo adequate per­<lb/>tranſitur .ef. ab ipſa potentia a. ad tēpus in quo <lb/>adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec <lb/>maior: ergo velocitatis deꝑdite in pertranſitiõe <lb/>ef. partis adequate ad velocitatē deꝑditã in ꝑtrã­<lb/>ſitiõe d. partis adequate nõ eſt ꝓportio g. nec ma-<lb/>ior: quod fuit ꝓbandū. </s>
              <s xml:id="N17DE7" xml:space="preserve">Patet cõſequētia vt ſupra / <lb/>et antecedens ꝓbatur: q2 velocitas qua adequate <lb/>ꝑtranſitur .ef. pars eſt maior velocitate qua ꝑtrã-<lb/>ſitur d. pars adequate: et .ef. ad d. eſt proportio g. / <lb/>ergo tēporis in quo adequate ꝑtranſitur .ef. pars <lb/>ad tēpus in quo adequate ꝑtranſitur d. pars non <lb/>eſt ꝓportio g. nec maior. </s>
              <s xml:id="N17DF6" xml:space="preserve">Cõſequentia patꝫ: quia ſi <lb/>velocitas qua adequate ꝑtranſitur .ef. pars eſſet <lb/>equalis velocitati qua ꝑtranſitur d. pars: iam tē-<lb/>poris in quo ꝑtranſitur .ef. ad tēpus in quo ꝑtrã-<lb/>ſitur d. pars eſſet ꝓportio g. (que videlicet eſt inter <lb/>illas partes .ef. et d. / vt conſtat) / igitur ſi velocitas <lb/>qua ꝑtranſitur .ef. pars eſt maior velocitate qua <lb/>pertranſitur d. pars adequate iam tēporis in quo <lb/>adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec <lb/>maior. </s>
              <s xml:id="N17E0B" xml:space="preserve">Patet hec cõſequentia / q2 minus tēpus re-<lb/>quiritur ad ꝑtranſeundū ſpaciū .ef. adequate ma­<lb/>iori velocitate quã ad ꝑtranſeundū ipſum adequa-<lb/>te aliqua velocitate minori. </s>
              <s xml:id="N17E14" xml:space="preserve">Sed iam ꝓbatur an-<lb/>tecedens videlicet /  velocitas qua adequate per-<lb/>tranſitur adequate .ef. pars eſt maior velocitate <lb/>qua adequate ꝑtrãſitur d. pars: q2 velocitas qua <lb/>ꝑtranſitur adequate .e. pars ab ipſa potētia a. eſt <lb/>equalis vel maior velocitate qua adequate ꝑtran-<lb/>ſitur d. pars (cū ex hypotheſi in pertranſitione .e. <lb/>partis adequate moueatur a. potētia cū equali vĺ <lb/>minori reſiſtentia quã in pertranſitione d. partis <lb/>adequate) et ipſi velocitati qua ꝑtranſitur .e. pars <lb/>adequate additur extēſiue adhuc maior velocitas <lb/>in pertranſitione f. partis minus reſiſtentis / vt cõ­<lb/>ſtat: igitur tota velocitas qua ꝑtranſitur .ef. pars <lb/>adequate eſt maior tota velocitate qua pertranſi-<lb/>tur d. pars adequate: quod fuit oſtēdendū. </s>
              <s xml:id="N17E33" xml:space="preserve">Patet <lb/>hec cõſequentia: q2 ſi alicui latitudini intenſionis <lb/>addatur extēſiue aliqua latitudo maioris intēſio­<lb/>nis .etc̈. totalis illa latitudo aggregata ex addita <lb/>et preexiſtenti efficitur maioris intēſionis: vt ſi la-<lb/>titudini vniformiter difformi q̈rto vſ ad octa-<lb/>uum addatur vna alia maioris intēſiõis puta ab <lb/>octauo vſ ad duodecimū: aggregatū ex eis effi-<lb/>cit̄̄ maioris intēſiõis / vt cõſtat. </s>
              <s xml:id="N17E46" xml:space="preserve">Et ſic ptꝫ ſuppoſitio</s>
            </p>
            <note position="left" xml:id="N17E49" xml:space="preserve">q̈drageſi­<lb/>ma ṗma <lb/>ↄ̨cĺo. cal.</note>
            <p xml:id="N17E51">
              <s xml:id="N17E52" xml:space="preserve">His ſuppoſitis. </s>
              <s xml:id="N17E55" xml:space="preserve">Sit prima concluſio <lb/></s>
              <s xml:id="N17E59" xml:space="preserve">Ubi aliqua potentia non variata vniformiter re-<lb/>mittit motū ſuū ad nõ gradū mediū īuariatū trã-<lb/>ſeūdo: aliqua maior ꝑ ſui cõtinuã intenſionē idem <lb/>mediū īuariatū trãſeūdo valet motū ſuū vniformi­<lb/>ter ad gradū remittere. </s>
              <s xml:id="N17E64" xml:space="preserve">Probat̄̄: ſit b. potētia que <lb/>īuariata c. mediū īuariatū trãſeūdo vniformiter <lb/>ad nõ gradū motū ſuū remittat: ſit a. potentia <lb/>maior q̄ ab eodē puncto c. medii incipiēdo moueri <lb/>cū ipſo b. ab in duplo maiori ꝓportiõe īcipiat mo­<lb/>ueri quã b. et cõtinuo in duplo velociꝰ moueat̄̄ quã <lb/>b. ꝑ variationē ipſiꝰ a. potētie (q2 alias medio īua­<lb/>riato hoc nequit fieri / vt ptꝫ ex quarta ↄ̨cluſiõe pre­<lb/>cedētis capitis): tūc dico /  a. potētia ↄ̨tinuo vni-<lb/>formiter remittit motū ſuū ad gradū ↄ̨tinuo intē-<lb/>tendo potentiã ſuã. </s>
              <s xml:id="N17E7B" xml:space="preserve">Quod ꝓbatur ſic: q2 a. poten-<lb/>tia cõtinuo vniformiter remittit motū ſuū trãſeū-<lb/>do illud mediū: et per nullū tēpus ſtabit inuariata <lb/>aut remittet potentiã ſuã idē mediū trãſeūdo: igit̄̄ <lb/>cõtinuo vniformiter remittit motū ſuū, cõtinuo in­<lb/>tendendo potentiã ſuã. </s>
              <s xml:id="N17E88" xml:space="preserve">Cõſequētia ptꝫ ex ſe: et ꝓba­<lb/>tur maior / q2 a. potentia cõtinuo in duplo velocius               <cb chead="Capitulū octauū."/>               mouetur quam b. potentia / vt ptꝫ ex hypotheſi: et b. <lb/>potētia cõtinuo vniformiter remittit motū ſuum: <lb/>igitur a potētia idem mediū tranſeūdo vniformi-<lb/>ter remittit motū ſuū cõtinuo. </s>
              <s xml:id="N17E96" xml:space="preserve">Patet hec cõſequē-<lb/>tia ex ſecūda parte prime ſuppoſitionis. </s>
              <s xml:id="N17E9B" xml:space="preserve">Iam pro­<lb/>batur minor / q2 ſi a. per aliquod tēpus ſtat īuaria-<lb/>ta vel remittit potentiã ſuam: detur illud et ſit g. et <lb/>pars pertranſita ab ipſa .a. potentia in g. tēpore <lb/>adequate ſit .ef. et pars ꝑtranſita ab ipſa b. poten­<lb/>tia in eodē g. tēpore ſit d. / et manifeſtū eſt /  ipſius <lb/>ef. ad ipſam d. partē eſt ꝓportio dupla, cū ſemper <lb/>a. moueatur in duplo velocius ipſa potentia b. / vt <lb/>ptꝫ ex hypotheſi: quo poſito arguitur ſic: latitudi­<lb/>nis motus deperdite ab ipſa b. potētia tranſeūdo <lb/>ef. partē adequate, ad latitudinē motus deꝑditã <lb/>ab ipſa b. potētia tranſeūdo d. partē adequate in <lb/>g. tēpore eſt maior ꝓportio quã dupla que eſt īter <lb/>illas partes .ef. et d. / ergo latitudinis deperdite ab <lb/>a. potētia ſtante vel remittente potentiã ſuam trã-<lb/>ſeundo .ef. partē in g. tēpore adequate ad velocita­<lb/>tem deperditã ab ipſa b. potentia tranſeundo d. <lb/>partē adequate in g. tēpore eſt maior ꝓportio quã <lb/>dupla: ſed cõſequens eſt falſum: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N17EC4" xml:space="preserve">Probatur cõſequentia: q2 oēs potentie <lb/>īuariate idem mediū īuariatū trãſeūtes .etc̈. equa-<lb/>lem latitudinē motus deꝑdunt: et ſi aliqua potētia <lb/>trãſeundo mediū īuariatū remittendo motū ſuum <lb/>etc̈. et remittat potentiã: ipſa maiorē latitudinem <lb/>motus deperdit quã ſi ſtaret idem mediū tranſeū-<lb/>do / vt conſtat: et ptꝫ ex quarto argumento ſexti ca-<lb/>pitis huius. </s>
              <s xml:id="N17ED5" xml:space="preserve">Sed falſitas cõſequentis ꝓbatur: q2 <lb/>ſi latitudinis motus deperdite ab ipſa a. potētia <lb/>in g. tēpore ad latitudinē motꝰ deperditã ab ipſa <lb/>b. potentia in eodē g. tēpore eſt maior ꝓportio quã <lb/>dupla: et a principio latitudinis motus ipſius a. <lb/>ad latitudinem motus ipſius b. erat proportio <lb/>duplo: ſequitur /  facta tali deperditione: latitu-<lb/>dinis motus ipſius a. ad latitudinem motus ipſi-<lb/>us b. eſt minor ꝓportio quam dupla: quod eſt con-<lb/>tra hypotheſim. </s>
              <s xml:id="N17EEA" xml:space="preserve">Conſequentia tamen ptꝫ / ex ſecū-<lb/>da parte quinti correlarii quarte ↄ̨cluſionis octa­<lb/>ui capitis ſecunde partis. </s>
              <s xml:id="N17EF1" xml:space="preserve">Iam ꝓbatur antecedēs <lb/>videlicet /  latitudinis deperdite ab b. potētia trã­<lb/>ſeundo .ef. partē adequate ad velocitatē deperdi-<lb/>tam etc̈. q2 ipſius .ef. partis ad d. partē eſt propor­<lb/>tio dupla ex caſu: et ipſa potētia b. tranſeūdo quã­<lb/>libet partem exceſſus ipſius .ef. partis minoreꝫ d. <lb/>parte mouetur cū maiori reſiſtentia quã tranſeun­<lb/>do quãlibet partē equalē ipſius d. partis (cū que-<lb/>libet pars exceſſus quo .ef. pars excedit d. partem <lb/>magis diſtat a puncto initiatiuo c. medii a quo in­<lb/>cipit motus quam aliqua pars ipſius d. partis q2 <lb/>per totum illum exceſſum ad minus a potentia b. <lb/>potentiam precedit) / ergo latitudinis deperdite a <lb/>b. potentia tranſeundo .ef. partem adequate ad ve­<lb/>locitatem deperditam ab ipſa b. potentia tranſe-<lb/>undo d. partem adequate in g. tempore eſt maior <lb/>proportio quam dupla: quod fuit inferendū. </s>
              <s xml:id="N17F14" xml:space="preserve">Pa­<lb/>tet conſequentia ex tertia ſuppoſitione huius. </s>
              <s xml:id="N17F19" xml:space="preserve">Q, <lb/>vero a. potentia remittat motum ſuuꝫ ad gradum <lb/>in extremo intenſiori / patet ex ſecundo correlario <lb/>quarte concluſionis ſeptimi capitis huius tracta­<lb/>tus, auxiliante loco a maiori: quia illa potētia cõ­<lb/>tinuo intenditur. </s>
              <s xml:id="N17F26" xml:space="preserve">Et ſic patet concluſio.               <anchor type="note" xlink:href="note-0080-01" xlink:label="note-0080-01a"/>               </s>
              <s xml:id="N17F2E" xml:space="preserve">¶ Ex quo <lb/>ſequitur. </s>
              <s xml:id="N17F33" xml:space="preserve">Q, vbi aliqua potentia non variata vni­<lb/>formiter continuo remittit motum ſuum ad non <lb/>gradū mediū īuariatū trãſeūdo: oīs potentia ma­<lb/>ior ꝑ ſui ↄ̨tinuã ītenſionē idē mediū īuariatū tran-<lb/>ſeūdo valet motū ſuū vniformiṫ ad g̈dū remittere.</s>
            </p>
            <div xml:id="N17F3E" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0080-01a" xlink:label="note-0080-01" xml:id="N17F42" xml:space="preserve">1. correĺ.</note>
            </div>
            <pb chead="Primi tractatus" file="0081" n="81"/>
            <p xml:id="N17F4C">
              <s xml:id="N17F4D" xml:space="preserve">Probat̄̄: ſit b. potētia que c. mediū inuariatū trã­<lb/>ſeūdo vniformiter cõtinuo īuariata ad nõ gradū <lb/>remittit motū ſuū: et ſit a. potētia maior (q̄cū ſit <lb/>illa) que ab eodē puncto c. medii īcipiat moueri cū <lb/>b. potētia a ꝓportione in h. ꝓportiõe maiori quã <lb/>ſit ꝓportio a qua excluſiue incipit moueri b. et cõ-<lb/>tinuo moueat̄̄ a. potētia per ſui variationē in h. ꝓ-<lb/>portione velociꝰ ipſa b. potetia / et tūc dico /  a po-<lb/>tētia vniformiṫ cõtinuo remittit motū ſuū ad g̈dū <lb/>tranſeūdo c. mediū per ſui cõtinuã intenſionē. </s>
              <s xml:id="N17F62" xml:space="preserve">Qḋ <lb/>ſic ꝓbatur: q2 a. potētia ↄ̨tinuo vniformiṫ remittit <lb/>motū ſuū tranſeūdo c. mediū: et per nullū tempus <lb/>ſtat īuariata aut remittit potētiã ſuã: igit̄̄ cõtinuo <lb/>vniformiter remittit motū ſuū trãſeūdo c. mediū <lb/>per ſui cõtinuã intenſionē. </s>
              <s xml:id="N17F6F" xml:space="preserve">Cõſequentia ptꝫ: et pro­<lb/>batur maior: q2 a. potentia cõtinuo in h. ꝓportiõe <lb/>velocius mouetur quã b. potentia: vt ptꝫ ex hypo-<lb/>theſi: et b. potētia cõtinuo vniformiter remittit mo­<lb/>tum ſuū: ergo a. potentia cõtinuo vniformiter re-<lb/>mittit motū ſuū. </s>
              <s xml:id="N17F7C" xml:space="preserve">Patet cõſequentia / vt in ꝓbatiõe <lb/>cõcluſiõis. </s>
              <s xml:id="N17F81" xml:space="preserve">Iam ꝓbatur minor / q2 ſi a. per aliquod <lb/>tēpus ſtat īuariata, aut remittit potentiã ſuã, det̄̄ <lb/>illud tēpus: et ſit g. in quo a. potentia adequate ꝑ-<lb/>tranſit .ef. partē: et in eodē g. tēpore b. potētia per­<lb/>trãſeat d. partē: et manifeſtū eſt /  ipſius .ef. partis <lb/>ad partē d. eſt proportio h. cū ſemꝑ a. moueatur in <lb/>h. ꝓportiõe velocius / vt ptꝫ ex hypotheſi. </s>
              <s xml:id="N17F90" xml:space="preserve">Quo po­<lb/>ſito arguitur ſic / latitudinis deperdite ab ipſa b. <lb/>potentia tranſeūdo .ef. partē adequate ad latitu-<lb/>dinē motus deperditã ab eadē b. potētia tranſeū-<lb/>do d. partē adequate in g. tēpore eſt maior ꝓpor-<lb/>tio quã h. / igitur latitudinis deperdite ab a. potē-<lb/>tia īuariata vel remittente potentiã ſuã tranſeun-<lb/>do .ef. partē adequate ad latitudinē deperditã ab <lb/>ipſa b. potētia tranſeūdo d. partē adequate in g. <lb/>tēpore eſt maior ꝓportio quã h. / ſed conſequens eſt <lb/>falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N17FA7" xml:space="preserve">Cõſequentia <lb/>ptꝫ vt ſupra: et antecedens ſimiliter cum falſitate <lb/>conſequentis. </s>
              <s xml:id="N17FAE" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <note position="left" xml:id="N17FB1" xml:space="preserve">q̈drageſi­<lb/>ma ſecū-<lb/>da cõclu-<lb/>ſio calcu.</note>
            <p xml:id="N17FBB">
              <s xml:id="N17FBC" xml:space="preserve">Secūda ↄ̨̨cluſio. </s>
              <s xml:id="N17FBF" xml:space="preserve">Ubi aliqua potētia <lb/>nõ variata tranſeūdo aliquod mediū īuariatum <lb/>vniformiter cõtinuo ad nõ gradū remittit motum <lb/>ſuū: aliqua potentia maior per cõtinuã eiꝰ remiſ-<lb/>ſionē tranſeūdo idē mediū remittit motū ſuū vni-<lb/>formiter cõtinuo ad nõ gradū. </s>
              <s xml:id="N17FCC" xml:space="preserve">Probatur: ſit b. po­<lb/>tentia que nõ variata c. mediū īuariatū tranſeūdo <lb/>vniformiter cõtinuo motū ſuū remittat ad nõ gra­<lb/>dum: et ſit a. potentia que habet in duplo maiorē <lb/>ꝓportionē ad punctū initiatiuū c. medii in extre-<lb/>mo remiſſiori quã habeat b. potentia ad punctuꝫ <lb/>mediū eiuſdem c. medii: et ponatur b. potentia ad <lb/>punctū mediū ipſius c. medii: et a. potētia in pūcto <lb/>initiatiuo eiuſdē c. medii remiſſiori: et incipiant in <lb/>eodē inſtanti moueri ab illis punctis verſus extre­<lb/>mū intēſius: et taliter varietur a.  cõtinuo mouea­<lb/>tur in duplo velocius quã ipſa b. potentia: et tunc <lb/>dico /  ipſa potentia a. cõtinuo vniformiter motū <lb/>ſuū et hoc vſ ad nõ gradū remittit per continuã <lb/>eius remiſſionē. </s>
              <s xml:id="N17FEB" xml:space="preserve">Quod ſic ꝓbatur: q2 a. potētia cõ­<lb/>tinuo remittit motū ſuū vniformiter c. mediū trã-<lb/>ſeundo: et per nullū tēpus ſtabit īuariata in poten­<lb/>tia aut intendet potentiã ſuã: igitur a. potētia trã­<lb/>ſeūdo c. mediū īuariatū cõtinuo vniformiter remit­<lb/>tit motū ſuū per continuã eius remiſſionē. </s>
              <s xml:id="N17FF8" xml:space="preserve">Cõſequē­<lb/>tia ptꝫ ex ſe: et maior iam arguta eſt in precedenti <lb/>concluſione: et minor ꝓbatur / q2 ſi per aliquod tē-<lb/>pus potentia a. ſtat inuariata, aut intendit potē-<lb/>tiam ſuã, detur illud tēpus, et ſit g. in quo a. poten­<lb/>tia pertranſeat adequate .ef. partē: et b. potentia               <cb chead="Capitulum octauū."/>               d. partem adequate: et manifeſtum eſt /  ipſius .ef. <lb/>partis ad ipſam d. partē eſt proportio dupla cum <lb/>a. potētia continuo moueatur in duplo velociꝰ b. / <lb/>ex hypotheſi </s>
              <s xml:id="N1800E" xml:space="preserve">Quo poſito arguitur ſic / latitudinis <lb/>motus deperdite ab ipſa potentia b. tranſeundo <lb/>ef. partem ad latitudinē deperditam ab eadē po-<lb/>tētia b. tranſeūdo d. partem adequate in g. tēpo-<lb/>re nõ eſt proportio dupla nec maior: igitur latitu-<lb/>dinis deperdite ab a. potentia inuariata vel inten­<lb/>dente potentiã ſuam tranſeundo .ef. partem ad la­<lb/>titudinē deperditam a b. potentia tranſeundo d. <lb/>partem in g. tempore adequate non eſt proportio <lb/>dupla nec maior: ſed conſequēs eſt falſum: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N18025" xml:space="preserve">Cõſequentia probatur / quia <lb/>oēs potentie inuariate idem mediū īuariatū tran­<lb/>ſeuntes .etc̈. equalē latitudinem motus deperdunt <lb/>et ſi aliqua potentia mediū inuariatum tranſeun-<lb/>do remittat motum ſuū intendens potentiã ſuam: <lb/>minorem latitudinem motus deperdit quam ſi ſta­<lb/>ret idem mediū tranſeundo .etc̈. / vt conſtat: et argu-<lb/>tum eſt ſupra. </s>
              <s xml:id="N18036" xml:space="preserve">Sed falſitas conſequētis probatur / <lb/>quia ſi latitudinis motus deperdite ab ipſa a. po­<lb/>tentia tranſeundo .ef. partem in g. tempore ade-<lb/>quate ad latitudinem deperditam ab ipſa b. potē­<lb/>tia tranſeundo d. partem adequate in eodē g. tem­<lb/>pore nõ eſt proportio dupla nec maior dupla: et a <lb/>principio latitudinis motus ipſius a. potentie ad <lb/>latitudinē motus ipſius b. potentie quarū vtra <lb/>remittitur erat ꝓportio dupla: ergo facta tali re-<lb/>miſſione latitudinis motus ipſius a. ad latitudinē <lb/>motus ipſius b. nõ eſt proportio dupla: quod eſt <lb/>contra hypotheſim. </s>
              <s xml:id="N1804F" xml:space="preserve">Cõſequentia patet ex primo <lb/>correlario quinte concluſionis ſecundi capitis ſe-<lb/>cunde partis. </s>
              <s xml:id="N18056" xml:space="preserve">Iam probatur antecedens videlicet / <lb/> latitudinis deperdite ab ipſa potentia b. tran-<lb/>ſeundo .ef. partem ad latitudineꝫ deperditam ab <lb/>eadem potentia b. in g. tempore adequate non eſt <lb/>proportio dupla, aut maior dupla: quia ipſiꝰ .ef. <lb/>partis ad ipſam d. parteꝫ eſt proportio dupla ex <lb/>caſu: et ipſa potentia b. tranſeundo quãlibet par-<lb/>tem exceſſus quo .ef. excedit d. minorē ipſa d. par-<lb/>te mouetur cum minori reſiſtentia quam quãlibet <lb/>partem equalem ipſius d. partis tranſeundo: cum <lb/>q̄libet pars exceſſus quo .ef. pars excedit d. partē <lb/>minꝰ diſtet a. puncto remiſſiori initiatiuo c. medii <lb/>quã aliqua pars ipſiꝰ d. partꝪ. </s>
              <s xml:id="N18071" xml:space="preserve">(Signo em̄ exceſſū <lb/>ſus punctū īitiatiuū c. medii minꝰ reſiſtentē quē <lb/>exceſſū ſemꝑ voco f) / igit̄̄ latitudīs deꝑdite ab ipſa <lb/>b. potētia trãſeūdo .ef. partē adeq̈te ad latitudinē <lb/>deꝑditã ab eadē potētia trãſeūdo d. partē adeq̈te <lb/>in g. tꝑe nõ eſt ꝓportio dupla aut maior dupla / qḋ <lb/>fuit īferendū. </s>
              <s xml:id="N18080" xml:space="preserve">Ptꝫ ↄ̨ña ex quarta ſuppoſitiõe huiꝰ <lb/></s>
              <s xml:id="N18084" xml:space="preserve">Sed q2 cõcluſio ſupponit potētiã a. eſſe maiorē b. / <lb/>ideo reſtat illud ꝓbare. </s>
              <s xml:id="N18089" xml:space="preserve">Qḋ ſic ꝓbo / q2 a. ꝑ ↄ̨tinuã <lb/>ſui remiſſionē ꝑtrãſit totū c. mediū in tēpore ī quo <lb/>adequate b. ꝑtrãſit eiuſdē c. medii īuariati medie-<lb/>tatē: igitur ipſa a. potentia eſt maior b. potentia. <lb/></s>
              <s xml:id="N18093" xml:space="preserve">Patet conſequentia ex ſe / et antecedens probatur / <lb/>quia a. in duplo velocius cõtinuo mouetur quam <lb/>b. / vt patet ex hypotheſi: et a. incipit moueri a. pun-<lb/>cto iniciatiuo c. medii: et b. a puncto medio eiuſdeꝫ <lb/>c. medii in eodē inſtanti cum ceteris poſitꝪ in caſu: <lb/>igitur eque cito erunt in termino ipſius c. medii: et <lb/>per conſequens in tēpore in quo adequate b. per-<lb/>tranſit vnam medietatem c. medii inuariati a. ꝑ-<lb/>trãſit totū c. mediū / quod fuit ꝓbandū. </s>
              <s xml:id="N180A6" xml:space="preserve">Q, autē a. <lb/>potētia remittat motū ſuū ad nõ gradū / ꝓbat̄̄ / qm̄ <lb/>cõtinuo ex hypotheſi inter motū ipſius a. et motū <lb/>ipſius b. eſt proportio dupla vtro illorū motuū               <pb chead="Primi tractatus" file="0082" n="82"/>               decreſcente: et motus ipſius b. potentie remittitur <lb/>ad non gradum: igitur etiam motus ipſius a. ī eo­<lb/>dem tempore remittitur ad non gradum. </s>
              <s xml:id="N180B8" xml:space="preserve">Patet <lb/>conſequentia clare ex octauo correlario quarte cõ­<lb/>cluſionis octaui capitis ſecunde partis. </s>
              <s xml:id="N180BF" xml:space="preserve">Et ſic pa­<lb/>tet concluſio.               <anchor type="note" xlink:href="note-0082-01" xlink:label="note-0082-01a"/>               </s>
              <s xml:id="N180C9" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua po-<lb/>tentia non variata aliquod medium inuariatum <lb/>tranſeundo continuo vniformiter remittit motuꝫ <lb/>ſuum: omnis potentia maior per ſui continuã re-<lb/>miſſionem idem medium inuariatum tranſeundo <lb/>continuo vniformiter remittit motum ſuum </s>
              <s xml:id="N180D6" xml:space="preserve">Pro­<lb/>batur: et ſit b. potentia que inuariata c. mediū trã­<lb/>ſeundo inuariatum vniformiter continuo remit-<lb/>tit motū ſuum: ſit a. potentia maior que ad pun­<lb/>ctum initiatiuū c. medii habeat proportionem ī h. <lb/>proportione maiorem quam ſit proportio quam <lb/>habet b. potentia ad punctum medium eiuſdem c. <lb/>medii: et a. poña continuo quãdiu mouetur prece­<lb/>dente b. potentia moueatur in h. proportione ve-<lb/>locius per ſui variationem (medio ſemper inua-<lb/>riato) et incipiant in eodem īſtanti moueri b. a pū­<lb/>cto medio a. vero a puncto initiatiuo c. medii ī ex-<lb/>tremo remiſſiori. </s>
              <s xml:id="N180F1" xml:space="preserve">tunc dico /  a. potentia tranſeū-<lb/>do aliquam partem ipſius c. medii vniformiter cõ­<lb/>tinuo remittit motū ſuum: et hoc per ſui cõtinuam <lb/>remiſſionem. </s>
              <s xml:id="N180FA" xml:space="preserve">Quod ſic probatur / quia per quam­<lb/>libet partem prime medietatis quaꝫ pertranſibit <lb/>mouendo vniformiter continuo remittit motum: <lb/>et hoc continuo remittendo potentiam ſuam: igi-<lb/>tur a. potentia aliquam partem c. medii tranſeū-<lb/>do continuo vniformiter remittit motum ſuum ꝑ <lb/>ſui continuam remiſſionem. </s>
              <s xml:id="N18109" xml:space="preserve">Conſequentia patet: <lb/>et probatur maior vt ſupra in hac cõcluſione: et mi­<lb/>nor oſtenditur ſic / quia per nullum tempus talem <lb/>partem tranſeundo manet inuariata, aut intēdit <lb/>potentiam ſuam cum caſu: igitur continuo talem <lb/>partem tranſeundo remittit potentiam ſuã. </s>
              <s xml:id="N18116" xml:space="preserve">An-<lb/>tecedens probatur / quia ſi per aliquod tempus ta­<lb/>lē partē trãſeundo ſtat aut remittit potentiã ſuaꝫ <lb/>cum caſu: detur illud tempus: et ſit g. in quo a. po-<lb/>tentia pertranſeat adequate partem c. medii .ef. et <lb/>b. pertranſeat partem d. in eodē g. tempore: et ma­<lb/>nifeſtum eſt /  ipſius .ef. partis ad ipſam d. parteꝫ <lb/>eſt proportio h. cum a. in h. proportione continuo <lb/>velocius moueatur quaꝫ b. / ex hypotheſi. </s>
              <s xml:id="N18129" xml:space="preserve">Quo po­<lb/>ſito arguitur ſic / latitudinis motꝰ deperdite ab ip­<lb/>ſa b. potentia tranſeūdo .ef. partem adequate ad <lb/>latitudinem deperditam ab eadeꝫ potentia b. trã­<lb/>ſeundo d. partem in g. tempore adequate non ē ꝓ­<lb/>portio h. nec maior: igitur latitudinis deꝑdite ab <lb/>a. potentia inuariata vel intendente potentiã ſuã <lb/>tranſeundo .ef. partem adequate in g. tempore ad <lb/>latitudinem deperditam ab ipſa b. potentia tran­<lb/>ſeundo d. partem in eodem g. tempore adequate <lb/>non eſt proportio h. nec maior: ſed conſequens <lb/>eſt falſum: igitur illud ex quo ſequitur: videlicet /  <lb/>potentia a. tranſeundo .ef. partem continuo ma-<lb/>net inuariata aut intendit potentiam ſuam. </s>
              <s xml:id="N18146" xml:space="preserve">Con­<lb/>ſequentia patet vt ſupra in hac concluſione: et ſimi­<lb/>liter conſequens cum falſitate conſequentis</s>
            </p>
            <div xml:id="N1814D" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0082-01a" xlink:label="note-0082-01" xml:id="N18151" xml:space="preserve">correla.</note>
            </div>
            <p xml:id="N18157">
              <s xml:id="N18158" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N1815B" xml:space="preserve">Ubi aliqua poten-<lb/>tia non variata vniformiter continuo remittit mo­<lb/>tum ſuum aliquod medium inuariatum tranſeun­<lb/>do: omnis maior valet idem medium inuariatum <lb/>tranſeundo motum ſuum continuo vniformiter re­<lb/>mittere: et hoc aliquando ꝑ ſui cõtinuam remiſſio-<lb/>nem: et aliquando per ſui continuam intenſionem <lb/></s>
              <s xml:id="N1816B" xml:space="preserve">Probatur / ſit b. potentia que inuariata vniformi­<lb/>ter continuo remittat motum ſuum c. medium īua­               <cb chead="Capitulum octauum"/>               riatum tranſeundo: ſit a. potentia maior cuiꝰ ꝓ­<lb/>portio ad punctum initiatiuum in extremo remiſ­<lb/>ſiori ipſius c. medii ſe habet ad proportionem b. <lb/>potentie ad idem punctum in proportione f. / et po­<lb/>natur b. potentia in principio ſecunde partis pro­<lb/>portionalis ipſius c. medii diuiſi proportione f. <lb/>(ſiue f. proportio rationalis ſit ſiue non. </s>
              <s xml:id="N1817F" xml:space="preserve">nõ eſt cu-<lb/>ra) et a. potentia ponatur in puncto initiatiuo ip-<lb/>ſius c. medii in extremo remiſſiori: et manifeſtum ē / <lb/> proportionis ipſius a. ad punctum initiatiuuꝫ <lb/>ipſius c. medii in extremo remiſſiori ad proportio­<lb/>nem ipſius b. potentie ad punctum initiatiuum ſe­<lb/>cunde partis proportionalis ipſius c medii diuiſi <lb/>proportione f. eſt maior proportio quam f. que ſit <lb/>h. </s>
              <s xml:id="N18192" xml:space="preserve">Nam proportio a. ad punctum initiatiuū ſe ha­<lb/>bet in proportione f. ad proportionem ipſiꝰ b. ad <lb/>idem punctum: et proportio ipſius b. ad punctum <lb/>initiatiuum ſecunde partis proportionalis ꝓpor­<lb/>tione f. eſt minor quaꝫ ſit proportio ipſius b. ad pū­<lb/>ctum initiatiuum: ergo idem tertium puta ꝓpor-<lb/>tio ipſius a. ad punctum initiatiuum habet maio­<lb/>rem proportionem ad proportionem b. potentie <lb/>ad punctum initiatiuum ſecunde partis propor-<lb/>tionalis c. medii quam ad proportioneꝫ ipſius b. <lb/>potentie ad punctum initiatiuum ipſius c. medii.</s>
            </p>
            <p xml:id="N181A9">
              <s xml:id="N181AA" xml:space="preserve">Incipiat / igitur a. potentia moueri in eodem inſtã­<lb/>ti a puncto initiatiuo c. medii in h. proportione ve-<lb/>locius quam b. potentia incipiat moueri a pūcto <lb/>initiatiuo ſecunde partis proportionalis etc. et a. <lb/>per ſui continuam variationem continuo mouea­<lb/>tur in h. ꝓportione velocius ad terminum vſ c. <lb/>medii deueniēdo ꝙ̄ b. potētia. </s>
              <s xml:id="N181B9" xml:space="preserve">Et tūc dico /  a. po­<lb/>tentia continuo vniformiter remittit motū ſuum <lb/>c. medium inuariatum tranſeundo quod inuaria­<lb/>tum b. potentia inuariata tranſit vniformiter cõ-<lb/>tinuo remittēdo motū ſuum: et hoc aliquando per <lb/>ſui continuam remiſſionem, aliquando vero per <lb/>ſui continuam intenſioneꝫ: </s>
              <s xml:id="N181C8" xml:space="preserve">Quod ſic probatur / q2 <lb/>a. potentia continuo vniformiter remittit motum <lb/>ſuum c. medium tranſeundo: et per aliquam par-<lb/>tem talis temporis in quo remittit motum ſuum <lb/>continuo remittetur in potentia ſua: et per totam <lb/>reſiduam parteꝫ continuo intendet̄̄ ī potentia: er-<lb/>go a. poña continuo vniformiter remittit motum <lb/>ſuum c. medium inuariatum tranſeundo, aliquan­<lb/>do per ſui continuam remiſſionem, aliquando ve­<lb/>ro per ſui continuam intenſionem. </s>
              <s xml:id="N181DD" xml:space="preserve">Conſequentia <lb/>patet: et minor probatur: quia a. poña continuo in <lb/>h. proportione velocius mouetur quam b. poten-<lb/>tia vniformiter continuo remittens motum ſuum / <lb/>igitur a. potentia continuo vniformiter remittit <lb/>motum ſuum. </s>
              <s xml:id="N181EA" xml:space="preserve">Patet conſequentia ex prima ſup-<lb/>poſitione huius. </s>
              <s xml:id="N181EF" xml:space="preserve">Prima pars minoris probatur / <lb/>quia a. potentia per aliquam partem temporis ī <lb/>quo vniformiter remittit motum ſuuꝫ ſequetur b. <lb/>potentiam cum reſiſtentia minori mouendo conti­<lb/>nuo: igitur potentia a. per illud tempus conti-<lb/>nuo remittet potentiam ſuam. </s>
              <s xml:id="N181FC" xml:space="preserve">Patet conſequen-<lb/>tia / quia ſi per aliquod tempus ſtaret vel intende-<lb/>ret̄̄ in potentia b. potentiã ſeq̄ndo: et mouendo ↄ̨ti­<lb/>nuo cum reſiſtentia minori medio inuariato et per <lb/>illud tempus non continuo remittit potentiam ſu­<lb/>am: ſignetur illud tempus: et ſit g. in quo a. pertan­<lb/>ſeat adequate .ef. partem: et b. potentia d. partem <lb/>adequate: et manifeſtum eſt /  ipſius .ef. partis ad <lb/>ipſam d. partem eſt proportio h. cum a. potentia <lb/>continuo moueatur in h. proportione velocius ip­<lb/>ſa b. potentia ex hypotheſi. </s>
              <s xml:id="N18213" xml:space="preserve">quo poſito arguitur / <lb/>ſic latitudinis motus deperdite ab ipſa potentia               <pb chead="Primi tractatus" file="0083" n="83"/>               b. tranſeundo .ef. partem ad latitudinem deperdi­<lb/>tam ab eadem potentia tranſeundo d. parteꝫ ade­<lb/>quate in g. tempore nõ eſt proportio h. nec maior: <lb/>igitur ſi a. potentia ſtat vel intenditur in potentia <lb/>per g. tempus tranſeundo .ef. partem etc. / ſequēdo <lb/>b. potentiam latitudinis deperdite ab a. potentia <lb/>inuariata vel intendente potentiam ſuam tranſe­<lb/>undo .ef. partem ad latitudinem deperditam a b. <lb/>potentia tranſeundo d. partem in g. tempore ade­<lb/>quate non eſt proportio h. nec maior: ſed cõſeq̄ns <lb/>eſt falſum / igitur et antecedens videlicet /  a. potē-<lb/>tia ſtat vel intenditur in potentia per g. tempꝰ trã­<lb/>ſeundo .ef. partem etc. / et per conſequens oppoſitū <lb/>conſequentis non ſtat cum antecedente / et per con-<lb/>ſequens conſequentia bona / quod fuit probãdum <lb/></s>
              <s xml:id="N1823A" xml:space="preserve">Conſequentia patet / quia omnes potentie inequa­<lb/>les idem medium tranſeuntes etc. equalem latitu-<lb/>dinem motus deperdunt: et ſi aliqua poña mediuꝫ <lb/>inuariatum tranſeundo remittat continuo motū <lb/>ſuum intendens potentiam ſuam: minorem latitu­<lb/>dinem motus deperdit quam ſi ſtaret etc. / vt ſepiꝰ <lb/>dictum eſt. </s>
              <s xml:id="N18249" xml:space="preserve">Sed falſitas conſequentis probata ē <lb/>in ſecunda concluſione: et etiam antecedens. </s>
              <s xml:id="N1824E" xml:space="preserve">Sed <lb/>iam probo ſecūdam partem minoris / quia illa po­<lb/>tentia a. per aliquod tempus adequate continuo / <lb/>ſequitur potentiam b. mouendo / tunc cum reſiſten-<lb/>tia minori: et per totum reſiduum precedet potētiã <lb/>b. mouendo continuo cum reſiſtentia maiori: et per <lb/>totum illud tempus in quo ſic precedit potentiam <lb/>b. continuo intenditur in potētia: igitur illa pars <lb/>vera. </s>
              <s xml:id="N18261" xml:space="preserve">Probatur maior / quia a. potentia attinget <lb/>potentiã b. antea quã b. potentia deueniat ad ter­<lb/>minum c. medii: et cum attigerit eam: continuo pre­<lb/>det eam cum continuo in h. proportione velocius <lb/>moueatur: igitur a. potentia per aliquod tempus <lb/>adequate ſequetur b. potentiam: et per totum reſi-<lb/>duum temporis precedet eam. </s>
              <s xml:id="N18270" xml:space="preserve">Probatur maior <lb/>videlicet /  a. potentia attinget b. potentiam ante <lb/>terminum c. medii q2 a. in h. proportione cõtinuo <lb/>velocius mouetur: et a. deuenit vſ ad terminum <lb/>c. medii ex hypotheſi: igitur cum a. deuenit ad ter-<lb/>minum c. medii b. / adhuc eſt in aliquo pūcto intrin­<lb/>ſeco ipſius c. medii: et per conſequens aliquando <lb/>attingit eam: et continuo poſtea p̄cedit eam. </s>
              <s xml:id="N18281" xml:space="preserve">Pa-<lb/>tet conſequentia / quia ſi eque primo eſſent in termi­<lb/>no c. medii vel b. ante a. iam ſpacium pertranſituꝫ <lb/>in totali illo tempore ab ipſa a. potentia ad ſpa-<lb/>cium pertranſitum ab ipſa b. potentia in eodeꝫ tē­<lb/>pore non eſſet proportio h. / vt patet ex hypotheſi: <lb/>hoc addito /  diuiſo aliquo corpore per partes ꝓ­<lb/>portionales proportione f. illud corpus ſe habet <lb/>ad totum a prima parte proportionali in propor­<lb/>tio .f. / vt patet ex prima concluſione quinti capitis <lb/>prime partis: et ex conſequenti ſequitur /  veloci-<lb/>tatis ipſius a. ad velocitatem ipſius b. non eſt con­<lb/>tinuo ꝓportio h: et per conſequens a. non cõtinuo <lb/>in h. proportione velocius mouetur quam b. / quod <lb/>eſt oppoſitum antecedentis et ſic oppoſitum cõſe-<lb/>quentis infert oppoſitum antecedentis / et per con­<lb/>ſequens conſequentia bona. </s>
              <s xml:id="N182A4" xml:space="preserve">Sed iam probo /  a. <lb/>potentia continuo per totum illud tempus in quo <lb/>precedet potentiam b. continuo intendit potētiaꝫ <lb/>ſuam: quia per nullam partē illius temporis ſtat <lb/>inuariata aut remittit potentiam ſuam: et conti-<lb/>nuo variatur / vt patet ex quarta concluſione pre-<lb/>cedentis capitis. </s>
              <s xml:id="N182B3" xml:space="preserve">igitur continuo per totum illud <lb/>tempus in quo ſic precedit intendit potentiam ſuã <lb/></s>
              <s xml:id="N182B9" xml:space="preserve">Iam probatur /  a. per nullam partem illius tem­<lb/>poris ſtat inuariata aut remittit potentiam ſuã:               <cb chead="Capitulum octauum"/>               quia ſi non: detur illḋ tꝑs: et ſit g: et in illo a. poten­<lb/>tia adequate pertranſeat .ef. partem: et in eodem <lb/>g. tempore b. poña pertranſeat d. partem: et mani­<lb/>feſtum eſt /  ipſius .ef. partis ad partem d. eſt pro­<lb/>portio h. cum ſemper a. moueatur in h. proportio­<lb/>ne velocius / vt patet ex hypotheſi. </s>
              <s xml:id="N182CB" xml:space="preserve">Quo poſito ar­<lb/>guitur ſic / latitudinis motus deperdite ab ipſa b. <lb/>poña tranſeundo .ef. partem adequate ad latitu-<lb/>dinem motus deperditam ab eadem b. potentia <lb/>tranſeundo d. partem adequate in g. tempore eſt <lb/>maior proportio quam h. / igitur latitudinis deꝑ-<lb/>dite ab a. poña inuariata vel remittente potētiaꝫ <lb/>ſuam tranſeundo .ef. partem adequate in g. tēpo-<lb/>re ad latitudinem deperditaꝫ ab ipſa b. poña trã­<lb/>ſeundo d. partem adequate in g. tempore eſt ma-<lb/>ior proportio quam h. </s>
              <s xml:id="N182E2" xml:space="preserve">Conſequentia patet / vt <lb/>ſupra in prima concluſione: et antecedens itidem <lb/>cum falſitate conſequentis. </s>
              <s xml:id="N182E9" xml:space="preserve">Et ſic patet concluſio.</s>
            </p>
            <note position="right" xml:id="N182EC" xml:space="preserve">q̈drageſi­<lb/>ma cõclu­<lb/>ſio calcu.</note>
            <p xml:id="N182F4">
              <s xml:id="N182F5" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N182F8" xml:space="preserve">Ubi aliqua poten­<lb/>tia non variata vniformiter cõtinuo remittit mo­<lb/>tum ſuum ad non gradum mediū inuariatum trã­<lb/>ſeundo: aliqua minor per continuã eius intenſio-<lb/>nem continuo vniformiter remittit motum ſuum: <lb/>et hoc ad non gradum idem medium inuariatum <lb/>trãſeundo. </s>
              <s xml:id="N18307" xml:space="preserve">Probatur / ſit b. poña que īuariata cõ­<lb/>tinuo vniformiter remittit motuꝫ ſuum ad nõ gra­<lb/>dum totum c. medium tranſeundo īuariatum: ſit <lb/>a. potentia que ad punctuꝫ initiatiuum vltime q̈r­<lb/>te puta magis reſiſtentis habeat proportionem <lb/>in quadruplo minorem proportione quam habet <lb/>b. poña ad pūctum initiatiuum c. medii: et īcipiãt ī <lb/>eodem inſtanti b. potentia inuariata moueri a pū­<lb/>cto īitiatiuo c. medii in extremo remiſſiori: et a. po­<lb/>tentia a puncto initiatiuo vltime quarte ipſius c. <lb/>medii et moueat̄̄ a. poña cõtinuo in quadruplo tar­<lb/>dius ipſa b. poña. </s>
              <s xml:id="N18320" xml:space="preserve">tunc dico /  tam a. quam b. vni-<lb/>formiter continuo remittit motum ſuum vltimaꝫ <lb/>quartam c. medii tranſeundo vſ ad non graduꝫ <lb/>et a. eſt minor b. et tranſeundo illam vltimam quar­<lb/>tam continuo ītendit potentiam ſuam. </s>
              <s xml:id="N1832B" xml:space="preserve">Quod ſic <lb/>oſtenditur / quia a. continuo vniformiter remittit <lb/>motum ſuum: et a. eſt minor quam b. et continuo in­<lb/>tendit potentiam: et remittit motum ſuum ad non <lb/>gradum: igitur ꝓpoſitum. </s>
              <s xml:id="N18336" xml:space="preserve">Conſequentia patet: et <lb/>probatur maior / quia a. in certa ꝓportione conti-<lb/>nuo tardius mouetur quaꝫ b. et b. continuo vnifor­<lb/>miter remittit motum ſuum / ergo et a. </s>
              <s xml:id="N1833F" xml:space="preserve">Conſequen-<lb/>tia patet ex prima parte prime ſuppoſitionis hu-<lb/>ius: et antecedēs ex hypotheſi. </s>
              <s xml:id="N18346" xml:space="preserve">Sed iam probatur <lb/>prima pars minoris / quia b. potentia ad pūctum <lb/>initiatiuum vltime quarte habet ꝓportionē ſub-<lb/>duplam ad ꝓportionem quam habet eadem potē­<lb/>tia b. ad pūctum initiatuum c. medii: cum remittat <lb/>motum ſuum ad non gradum vniformiter c: medi­<lb/>um tranſeundo. </s>
              <s xml:id="N18355" xml:space="preserve">et ſic ī inſtanti medio totius tem-<lb/>poris eſt in principio vltime quarte: et tunc habet <lb/>ꝓportionem ſubduplam adequate ad proportio­<lb/>nem quam habet in principio motus / vt patet ex ṗ­<lb/>mo notato tertii capitis ſecundi tractatus huius <lb/>partis: et ad idem punctum a. potentia habet mi-<lb/>norem ꝓportionem / vt patet ex hypotheſi / igit̄̄ ip-<lb/>ſa eſt minor b. poña / quod erat ꝓbandum. </s>
              <s xml:id="N18366" xml:space="preserve">Secun-<lb/>da pars minoris ꝓbatur / quia ſi a. per aliquod tē­<lb/>pus ſtat inuariata vel remittit poñam ſuam, de-<lb/>tur illud, et ſit g. et pars pertranſita ab a. in g. tem­<lb/>pore ſit d: et pars pertranſita adequate in eodē g. <lb/>tempore ab ipſa poña b. ſit .ef. / et manifeſtum eſt /  <lb/>ipſius .ef. ad ipſam d. partem eſt ꝓportio quadru­<lb/>pla: cum ſemper b. poña moueatur in quadruplo               <pb chead="Primi tractatus" file="0084" n="84"/>               velociꝰ ipſa poña a. / vt patet ex hypotheſi / quo po­<lb/>ſito arguitur ſic / latitudinis motus deperdite ab <lb/>ipſa b. potentia tranſeundo .ef. partem in g. tem­<lb/>pore adequate ad latitudinem motus deperditaꝫ <lb/>ab eadem poña b. tranſeundo d. partem non eſt ꝓ­<lb/>portio quadrupla nec maior: ergo latitudinis de­<lb/>perdite ab b. poña tranſeundo .ef. partem in tēpo­<lb/>re g. ad latitudinem motus deperditam ab a. po-<lb/>tentia ſtante inuariata vel remittente poñam ſuã <lb/>tranſeundo d. partem in g. tempore adequate nõ <lb/>eſt proportio quadrupla nec maior quadrupla: ſꝫ <lb/>conſequens eſt falſum: igitur illud ex quo ſequit̄̄. <lb/></s>
              <s xml:id="N18393" xml:space="preserve">Patet conſequentia / quia omnes poñe inuariate <lb/>idem medium tranſeuntes etc. equalem latitudinē <lb/>motus deperdunt. </s>
              <s xml:id="N1839A" xml:space="preserve">et ſi aliqua poña tranſeūdo idē <lb/>medium īuariatum remittendo motum ſuum etc. <lb/>remittat poñam ſuam: ipſa maiorem latitudineꝫ <lb/>motus deperdit quam ſi ſtaret idem medium inua­<lb/>riatum tranſeundo: vt conſtat ex quarto argumē­<lb/>to ſexti capitis. </s>
              <s xml:id="N183A7" xml:space="preserve">Sed falſitas conſequentis proba­<lb/>tur / quia ſi latitudinis deperdite ab ipſa b. poten­<lb/>tia tranſeundo .ef. partem in g. tempore ad veloci­<lb/>tatem deperditam ab a. poña tranſeundo d. par-<lb/>tem in eodem g. tempore non eſt ꝓportio quadru-<lb/>pla nec maior: et a principio latitudinis motus ip­<lb/>ſius b. ad latitudinem motus ipſius a. eſt ꝓportio <lb/>quadrupla: ſequitur /  facta tali variatione lati-<lb/>tudinis motus ipſius b. ad latitudinem motus ip­<lb/>ſius a. non eſt ꝓportio quadrupla: quod eſt cõtra <lb/>hypotheſim. </s>
              <s xml:id="N183BE" xml:space="preserve">Conſequentia tamen patet ex primo <lb/>correlario et ſecundo quinte concluſionis ſecundi <lb/>capitis ſecunde partis. </s>
              <s xml:id="N183C5" xml:space="preserve">Iam ꝓbatur antecedens <lb/>videlicet /  latitudinis motus deperdite a b. poña <lb/>tranſeundo in g. tempore .ef. partem ad latitudi-<lb/>nem deꝑditam ab eadem b. poña tranſeundo d. ꝑ­<lb/>tem nõ eſt ꝓportio quadrupla nec maior: quia ip̄i­<lb/>us .ef. ꝑtis ad d. partem eſt ꝓportio quadrupla ex <lb/>caſu: et ipſa poña b. tranſeundo quãlibet ꝑtem ex­<lb/>ceſſus ip̄ius .ef. ꝑtis minorem d. ꝑte: mouetur cum <lb/>minori reſiſtentia quam tranſeundo quamlibet ꝑ­<lb/>tem equalem ipſius d. ꝑtis: cum quelibet pars ex-<lb/>ceſſus quo .ef. pars excedit d. ꝑtem minus diſtet a <lb/>puncto iniciatiuo c. medii a quo incipit motus (ſi­<lb/>gno enim exceſſum illum verſus punctum remiſſiꝰ <lb/>c. medii a quo incipit motus) / ergo latitudinis de­<lb/>perdite ab ipſa b. poña tranſeundo .ef. ꝑtem in g. <lb/>tempore adequate ad latitudinem deꝑditaꝫ ab ea­<lb/>dem b. poña tranſeundo d. ꝑtem non eſt ꝓportio <lb/>quadrupla nec maior: quod fuit ꝓbandum. </s>
              <s xml:id="N183EA" xml:space="preserve">Pa-<lb/>tet conſequentia ex quarta ſuppoſitione huius</s>
            </p>
            <p xml:id="N183EF">
              <s xml:id="N183F0" xml:space="preserve">Q, autem a. poña remittit motum ſuum ad non <lb/>gradum: ꝓbatur / quoniam cõtinuo ex hypotheſi ī­<lb/>ter motum ipſius b. et motum ipſius a. eſt ꝓportio <lb/>quadrupla: vtro illorum motuum decreſcente: <lb/>et motus ipſius b. poñe tranſeuntis quatuor quar­<lb/>tas ipſius c. medii in extremo intenſiori eiuſdeꝫ c. <lb/>medii remittitur ad non gradum: igitur etiã mo-<lb/>tus ipſius a. poñe mouentis in quadruplo tardiꝰ <lb/>in eodem tempore tranſeundo vltimam quartam <lb/>c. medii in extremo intenſiori remittitur ad nõ gra­<lb/>dum. </s>
              <s xml:id="N18407" xml:space="preserve">Patet conſequētia ex octauo correlario q̈r­<lb/>te concluſionis octaui capitis ſecunde ꝑtis: </s>
              <s xml:id="N1840C" xml:space="preserve">Et ſic <lb/>patet concluſio. </s>
              <s xml:id="N18411" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua <lb/>poña non variata aliquod medium tranſeūdo vni­<lb/>formiter remittit motum ſuum: omnis minor hñs <lb/>ꝓportionem maioris inequalitatis ad punctū in­<lb/>itiatiuum eiuſdem medii in extremo remiſſiori vni­<lb/>formiter continuo remittit motum ſuum idē medi­<lb/>um tranſeundo īuariatum per continuam ſui intē­               <cb chead="Capitulum octauum"/>               ſſonem. </s>
              <s xml:id="N18423" xml:space="preserve">Probatur / ſit b. poña que variata totuꝫ c. <lb/>medium inuariatum tranſeundo vniformiter re-<lb/>mittit motum: et a poña minor habens ad initiati­<lb/>uum punctum c. medii in extremo remiſſiori ꝓpor­<lb/>tionem maioris inequalitatis: et cum ipſa a. poña <lb/>habeat ad aliquem punctum intrinſecum eiuſdeꝫ <lb/>c. medii etiam ꝓportionem maioris inequalitatis <lb/>ponatur ip̄a poña a. in tali puncto et b. poña in ṗn­<lb/>cipio c. medii in extremo remiſſiori: et ꝓportionis <lb/>ipſius b. ad punctum initiatiuum c. medii ad pro-<lb/>portionem ipſius a. quam habet ad punctum in-<lb/>trinſecum ad quod ponitur ſit h. ꝓportio: et incipi­<lb/>at ī eodē īſtãti ab illis pūctis moueri a. et b. ſꝫ b. cõ­<lb/>tinuo in h. ꝓportione velocius ip̄a poña a. / et mani­<lb/>feſtum eſt /  non ſubito b. poña deueniet ad pūctū <lb/>a quo incipit moueri a. poña: capio igitur ſpaciuꝫ / <lb/>quod abſoluet a. poña in tempore in quo b. poña <lb/>deueniet ad pūctum a quo incipit moueri a. poña <lb/>et ſit illud ſpacium d. / et tunc dico /  tam a. quam b. <lb/>tranſeundo d. mediū vniformiter remittet motuꝫ <lb/>ſuum: et a. poña continuo d. medium tranſeundo ī­<lb/>tendit poñam ſuam. </s>
              <s xml:id="N18450" xml:space="preserve">Quod ſic oſtenditur / quia a. <lb/>poña tranſeundo d. medium continuo vniformi-<lb/>ter remittit motum ſuum / vt ſupra in concluſione <lb/>quarta probatum eſt: et ipſa a. poña continuo trã­<lb/>ſeundo d. ꝑtem intendit poñam ſuam: igitur ꝓpo­<lb/>poſitum. </s>
              <s xml:id="N1845D" xml:space="preserve">Probatur minor / quia ſi a. per aliquod <lb/>tempus d. medium inuariatum tranſeundo ſtat ī-<lb/>uariata vel remittit potentiam ſuam. </s>
              <s xml:id="N18464" xml:space="preserve">detur illud <lb/>tempus et ſit g. et pars pertranſita ab a. in g. tēpo­<lb/>re adequate ſit e. et pars pertranſita adequate in <lb/>eodem g. tempore ab ip̄a poña b. ſit .ef. / et manife-<lb/>ſtum eſt /  ip̄ius .ef. partis ad e. partem eſt ꝓportio <lb/>h. quia continuo potentia b. in h. ꝓportione velo-<lb/>cius mouetur quaꝫ ipſa potentia a. / vt patet ex hy­<lb/>potheſi. </s>
              <s xml:id="N18475" xml:space="preserve">Quo poſito arguitur ſic / latitudinis mo-<lb/>tus deperdite ab ipſa b. potentia tranſeundo .ef. <lb/>partem in g. tempore adequate ad latitudinē mo­<lb/>tus deperditam ab eadeꝫ potentia b. tranſeundo <lb/>e. partem non eſt proportio h. nec maior: ergo la-<lb/>titudinis deperdite ab ip̄a b. poña tranſeundo .ef: <lb/>ꝑtem in g. tempore adequate ad latitudinem mo-<lb/>tus deperditam ab a. potentia ſtãte inuariata vel <lb/>remittente potentiam ſuam tranſeundo e. parteꝫ <lb/>in g. tempore adequate non eſt ꝓportio h. nec ma­<lb/>ior: ſed conſequens eſt falſum: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N1848E" xml:space="preserve">Conſequentia patet cum antecedente ex <lb/>ꝓbatione concluſionis: et ſimiliter falſitas conſe­<lb/>quentis </s>
              <s xml:id="N18495" xml:space="preserve">Patet igitur correlarinm.</s>
            </p>
            <note position="right" xml:id="N18498" xml:space="preserve">q̈drageſi­<lb/>ma q̈rta <lb/>ↄ̨clu. cal.</note>
            <p xml:id="N184A0">
              <s xml:id="N184A1" xml:space="preserve">Quinta concluſio </s>
              <s xml:id="N184A4" xml:space="preserve">Ubi aliqua poten­<lb/>tia inuariata inuariarum medium tranſeundo <lb/>vniformiter continuo remittit motum ſuum ad nõ <lb/>gradum: aliqua minor per cõtinuam ſui remiſſio­<lb/>nem continuo vniformiter remittit motum ſuum <lb/>ad non gradum in aliquo puncto intrinſeco dati <lb/>medii idem medium inuariatum trãſeundo </s>
              <s xml:id="N184B3" xml:space="preserve">Pro­<lb/>batur / ſit b. poña que vniformiter continuo remit­<lb/>tit motum ſuum totum c. medium tranſeundo vſ <lb/>ad nõ gradum: ſit a. poña minor que habeat ad <lb/>punctum initiatiuum c. medii in extremo remiſſio­<lb/>ri ꝓportionem in ſexquialtero maiorem quam b. <lb/>poña habeat ad punctum initiatiuum vltime q̈r-<lb/>te magis reſiſtentis: ponatur a. poña in puncto <lb/>initiatiuo c. medii in extremo remiſſiori: et b. poña <lb/>in puncto initiatiuo vltime quarte magis reſiſten­<lb/>tis: et in eodem inſtanti incipiant ab illis punctis <lb/>moueri a. cõtinuo in ſexquialtero velocius ip̄o b. <lb/>quo ad b. deueniat ad extremum intenſius c. medii <lb/>in quo habet non gradum motus: et manifeſtū eſt /               <pb chead="Primi tractatus" file="0085" n="85"/>               cum ſemper a. moueatur in ſexquialtero velocius <lb/>ipſa b. poña:  cum b. deſcripſerit vltimam quar­<lb/>tam pertranſibit a. adequate tres octauas: tunc <lb/>dico /  a tranſeundo illas tres octauas continuo <lb/>remittit vniformiter motum ſuum: et hoc ad non <lb/>gradum continuo remittendo potentiam ſuam.</s>
            </p>
            <p xml:id="N184DF">
              <s xml:id="N184E0" xml:space="preserve">Quod ſic oſteditur / quia a. tranſeundo illas tres <lb/>octauas continuo vniformiter remittit motū ſuū / <lb/>vt patet ex prima ſuppoſitione iuncta hypotheſi: <lb/>et tranſeundo illas tres octauas continuo remit-<lb/>tit potentiam ſuaꝫ / igitur etc. </s>
              <s xml:id="N184EB" xml:space="preserve">Minor probatur / q2 <lb/>ſi per aliquod tempus ipſa potentia a. tranſeūdo <lb/>illas tres octauas ſtat, aut intenditur ſignetur il­<lb/>lud et ſit g. in quo a. tranſeat .ef. adequate, et b. in <lb/>eodem tempore g.d. partem adequate pertranſe­<lb/>at ad quam d. partem pars .ef. habet ꝓportiõem <lb/>ſexquialteram / vt patet intuēti hypotheſim: </s>
              <s xml:id="N184FA" xml:space="preserve">Quo <lb/>poſito arguo ſic / latitudinis motus deperdite ab <lb/>ipſa b. potentia tranſeundo .ef. partem adequate <lb/>ad latitudinem motus deperditã ab eadem potē-<lb/>tia tranſeundo d. partem in g. tempore adequate <lb/>non eſt ꝓportio ſexquialtera nec maior: igitur la­<lb/>titudīs deperdite ab ipſa potētia a. inuariata vel <lb/>intendente potentiam ſuam tranſeundo .ef. ꝑtem <lb/>in g. tempore adequate ad latitudinem deperdi-<lb/>tam ab ipſa potentia b. tranſeundo adequate d. <lb/>partem in eodem tempore g. non ē ꝓportio ſexqui­<lb/>altera nec maior: ſed conſequens eſt falſuꝫ: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N18515" xml:space="preserve">Conſequentia patet / vt ſu-<lb/>pra in concluſione ſecunda et ſimiliter antecedēs <lb/>cum falſitate conſequentis: </s>
              <s xml:id="N1851C" xml:space="preserve">Et ſic patet concluſio. <lb/>               <anchor type="note" xlink:href="note-0085-01" xlink:label="note-0085-01a"/>               </s>
              <s xml:id="N18526" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia inuaria­<lb/>ta aliquod medium inuariatum tranſeundo vni-<lb/>formiter continuo remittit motum ſuum ad non <lb/>gradum: omnis potentia minor habens ad pun-<lb/>ctum initiatiuum eiuſdem medii ī extremo remiſ­<lb/>ſiori ꝓportionem maioris inequalitatis ideꝫ me­<lb/>dium inuariatum tranſeundo continuo vniformi­<lb/>ter remittit motum ſuum vſ ad non gradum in <lb/>aliquo puncto intrinſeco per continuam ſue po-<lb/>tentie remiſſionem. </s>
              <s xml:id="N1853B" xml:space="preserve">Probatur / ſit b. potentia que <lb/>inuariata c. medium inuariatum vniformiter re-<lb/>mittit motum ſuum ad non gradum: ſit a. poña <lb/>minor que habeat ad punctum initiatiuum eiuſ-<lb/>dem c. medii in exiremo remiſſiori ꝓportionem in <lb/>h. ꝓportione minorem quam ſit ꝓportio ipſiꝰ po­<lb/>tentie b. ad idem punctum initiatiuum ponatur <lb/>b. potentia in īitio ſecunde partis ꝓportionabi-<lb/>lis ipſius c. medii diuiſi ꝓportione h. minoribus <lb/>verſus extremu <lb/>m intenſius terminatis: et incipiãt <lb/>in eodem inſtanti a punctis in quibus ponuntur <lb/>moueri verſus extremum intenſius: ſit continuo <lb/>inter motus illarum potentiaruꝫ ea ꝓportio ade­<lb/>quate que eſt inter ꝓportionem quam habet a. ad <lb/>punctum initiatiuum c. medii et ꝓportionem quaꝫ <lb/>habet b. ad punctum initiatiuum ſecunde partis <lb/>ꝓportionalis ipſius c. medii diuiſi h. ꝓportione: <lb/>tunc dico /  a. et b. continuo vniformiter remittūt <lb/>motum ſuum vſ ad non gradum idem medium <lb/>inuariatum tranſeundo: a. continuo remittēte po­<lb/>tentiam ſuam. </s>
              <s xml:id="N18568" xml:space="preserve">Quod ſic oſtenditur / quia vel pro-<lb/>portio ipſius a. ad punctum initiatiuum ipſius c. <lb/>medii eſt equalis ꝓportioni ipſius b. ad punctum <lb/>initiatiuum ſecunde partis ꝓportionalis c. medii <lb/>diuiſi etc. vel maior vel minor </s>
              <s xml:id="N18573" xml:space="preserve">(Eſt enim altera al-<lb/>teri comparabilis: cum vtra ſit maioris inequa­<lb/>litatis ex hypotheſi) </s>
              <s xml:id="N1857A" xml:space="preserve">Si ſit equalis ſequitur /  cõ-<lb/>tinuo equaliter mouebuntur ex hypotheſi: et ex cõ­<lb/>ſequenti cum b. fuerit in termino c. medii ī quo mo­               <cb chead="Capitulum octauum"/>               tus eius eſt remiſſus ad non gradum ex hypothe-<lb/>ſi a. erit in aliquo puncto intrinſeco tantum vide-<lb/>licet diſtante ab extremo remiſſiori c. medii quan­<lb/>tum diſtat extremū intenſius a puncto a quo ince­<lb/>pit moueri b. / vt ↄ̨ſtat (eq̄ velociṫ eī a. cū b. ↄ̨tinuo <lb/>mouetur) et in tali puncto a. poña remittit motum <lb/>ſuum ad non gradum cum nunquam moueat̄̄ ve-<lb/>locius aut tardius quam b. / igitur a. poña tranſe-<lb/>undo illam partem c. medii continuo vniformiter <lb/>remittit motum ſuum ad non gradum: et continuo <lb/>tranſeundo illam partem remittit potentiam ſuã / <lb/>igitur propoſitum. </s>
              <s xml:id="N1859A" xml:space="preserve">Probatur minor videlicet /  <lb/>a. potentia continuo tranſeundo illam partem re­<lb/>mittit potentiam ſuam: quia ſi non detur tempus <lb/>per quod poña a. tranſeundo illam partem c. me­<lb/>dii ſtet inuariata, aut intendat poñam ſuam, et ſit <lb/>g. ſit pars pertranſita ab a. potentia in g. tem-<lb/>pore adequate f. et pertranſita .ab. potentia in eo­<lb/>dem tempore e. / quo poſito arguitur ſic. </s>
              <s xml:id="N185AB" xml:space="preserve">maior eſt <lb/>latitudo motus deperdita a b. poña tranſeundo <lb/>e. partem quam latitudo deperdita ab eadem <lb/>poña b. tranſeundo f. parteꝫ adequate / vt patet ex <lb/>ſecunda ſuppoſitione huius capitis </s>
              <s xml:id="N185B6" xml:space="preserve">(Magis eni3 <lb/>reſiſtit e. quam f. / vt patet intuenti) / ergo maior eſt <lb/>latitudo motus deperdita ab ipſa poña b. tranſe­<lb/>undo e. partem in g. tempore adequate quã ſit la-<lb/>titudo deperdita ab a. poña ſtante inuariata vel ī­<lb/>tendente continuo poñam ſuam f. partem tranſe-<lb/>undo in eodem g. tempore adequate: ſed cõſequēs <lb/>eſt falſum / igitur illud ex quo ſequitur: </s>
              <s xml:id="N185C7" xml:space="preserve">Patet hec <lb/>conſequentia / quia potentie inequales inuariate <lb/>idem medium etc. tranſeundo equalem latitudinē <lb/>motus deperdunt. </s>
              <s xml:id="N185D0" xml:space="preserve">et ſi aliqua potentia tranſeūdo <lb/>idem medium inuariatum remittendo motum ſuuꝫ <lb/>etc. intendo motum ſuum etc. intendat potentiam <lb/>ſuam: minorem latitudinem motus deperdit quã <lb/>ſi ſtaret idem medium inuariatum tranſeundo / vt <lb/>patet ex quarto argumento ſexti capitis ſepius <lb/>allegato. </s>
              <s xml:id="N185DF" xml:space="preserve">Sed falſitas conſequentis probatur: q2 <lb/>ſi latitudo motus deperdita ab ipſa b. potētia e. <lb/>ꝑtē trãſeūdo ī g. tꝑe adeq̈te ē maior quã latitudo <lb/>deperdita ab eadē b. poña trãſeūdo f. ꝑtē in g. tꝑe <lb/>adeq̈te: et a prīcipio motus ipſiꝰ b. eſt eq̈lis motui <lb/>ipſius a. / ergo ſequitur /  facta tali variatione la­<lb/>titudo motus ipſius b. non eſt equalis latitudini <lb/>motus ipſius a. / quod eſt contra hypotheſim. </s>
              <s xml:id="N185F0" xml:space="preserve">Cõ-<lb/>ſequentia patet ex primo correlario quinte cõclu­<lb/>ſionis ſecundi capitis ſecunde partis. </s>
              <s xml:id="N185F7" xml:space="preserve">Si autē ꝓ-<lb/>portio a. ad punctum initiatiuum c. medii eſt ma-<lb/>ior ꝓportione b. ad punctum initiatiuum ſecunde <lb/>partis ꝓportionalis c. medii diuiſi per partes ꝓ­<lb/>portionales ꝓportione h. ſit maior in l. ꝓportio-<lb/>ne / et ſequitur /  cõtinuo in l. ꝓportione ipſa potē-<lb/>tia a. velocius mouebitur quaꝫ potentia b. / et ex cõ­<lb/>ſequenti cū b. fuerit in termino c. medii in quo mo­<lb/>tus eius eſt remiſſus ad non gradum / ex hypothe-<lb/>ſi a. erit in aliquo puncto in l. ꝓportione magꝪ di­<lb/>ſtante ab extremo remiſſiori c. medii quam diſtat <lb/>extremum intenſius a puncto a quo a. poña ince-<lb/>pit moueri: et in tali puncto remittit motū ſuū ad <lb/>non gradum / vt facile ex octauo correlario quar-<lb/>te concluſionis octaui capitis ſecunde partis ar-<lb/>gui poteſt eo modo quo ſepius argutum eſt: et con­<lb/>tinuo deueniendo vſ ad illud punctum vniformi­<lb/>ter remittit motum ſuum: quemadmodum ſepius <lb/>argutum eſt: et continuo remittit potentiam ſuam <lb/>et punctus ille in quo motus eius remiſſns ē ad nõ <lb/>gradum eſt intrinſecus: igitur propoſitum. </s>
              <s xml:id="N18622" xml:space="preserve">Sed <lb/>probatur /  a. poña continuo remittit potentiam               <pb chead="Primi tractatus" file="0086" n="86"/>               ſuam quia a. potentia nunquam attinget b. poten­<lb/>tiam precedentem: igitur continuo mouebitur cum <lb/>minori reſiſtentia. </s>
              <s xml:id="N18630" xml:space="preserve">et per conſequens cõtinuo remit-<lb/>tit potentiam ſuam. </s>
              <s xml:id="N18635" xml:space="preserve">Patet hec conſequentia ex ſe-<lb/>pius ſuperius dictis. </s>
              <s xml:id="N1863A" xml:space="preserve">Et probatur antecedens vide­<lb/>delicet /  a. nūquam attinget b. quia ſi attingit de-<lb/>tur in quo inſtanti attingit / et ſequitur /  ſemper an­<lb/>tea a principio mouebatur cum minori reſiſtentia: <lb/>et per conſequens remittebat poñam ſuam cõtinuo <lb/>vt iam ſepe argutum eſt: igitur continuo manſit mi­<lb/>nor: et in illo tempore adequate pertranſit maius <lb/>ſpacium per te: q2 b. precedebat: et continuo moue-<lb/>batur: igitur in eodem tempore adequate mai ſpa­<lb/>cium pertranſit poña minor continuo manens mi-<lb/>nor cum eadem reſiſtentia non variata quam potē­<lb/>tia maior manēs maior / quod eſt impoſſibile: et per <lb/>conſequens illud ex quo ſequitur videlicet /  aliquã­<lb/>do a. attingat b. </s>
              <s xml:id="N18657" xml:space="preserve">Et ex hoc ſatis cõſtat /  punctus il­<lb/>le in quo motus eius eſt remiſſus ad non graduꝫ eſt <lb/>punctus intrinſecus: quia motus eius eſt remiſſus <lb/>ad non gradum in eodem inſtanti in quo motus b. <lb/>et non in eodem puncto medii: quia iam attingeret <lb/>b. et b. ī extrinſeco. </s>
              <s xml:id="N18664" xml:space="preserve">Si autem proportio ipſius a. ad <lb/>punctum initiatiuum c. medii eſt minor ꝓportione <lb/>ipſius b. ad punctum initiatiuum ſecunde partis ꝓ­<lb/>portionalis ipſius c. medii diuiſi ꝓportiõe h. etc. ſit <lb/>minor in l. ꝓportione: et ſequitur /  continuo ip̄a po­<lb/>tentia a. in l. ꝓportione tardius mouebitur quam <lb/>poña b. / et ex conſequenti cum b. fuerit in termino c. <lb/>medii in quo motus eius eſt remiſſus ad non gradū / <lb/>ex hypotheſi a. erit in puncto aliquo intrinſeco in l. <lb/>ꝓportione minus diſtante ab extremo remiſſiori c. <lb/>medii / quam diſtet extremuꝫ a puncto a quo incepit <lb/>moueri b. / vt conſtat: et in tali puncto a. poña remit-<lb/>tit motum ſuum ad non gradum / vt patet ex ſuperi-<lb/>oribus et continuo vniformiter remittendo motum <lb/>ſuum: et hoc per continuam eius remiſſionem / igitur <lb/>ꝓpoſitum. </s>
              <s xml:id="N18685" xml:space="preserve">Prima pars minoris patet ex prīa ſup­<lb/>poſitione huius. </s>
              <s xml:id="N1868A" xml:space="preserve">Sed  continue remittat potētiaꝫ <lb/>ſuam probatur: quia ſemper mouebitur cum mino­<lb/>ri reſiſtentia quam b. in l. ꝓportione tardius conti-<lb/>nuo remittendo motum vniformiter: igitur cõtinue <lb/>remittit poñam ſuam: </s>
              <s xml:id="N18695" xml:space="preserve">Conſequentia patet intelli-<lb/>genti modum probandi alias concluſiones: et an­<lb/>tecedens ſimiliter. </s>
              <s xml:id="N1869C" xml:space="preserve">Et ſic ptꝫ correlarium.</s>
            </p>
            <div xml:id="N1869F" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0085-01a" xlink:label="note-0085-01" xml:id="N186A3" xml:space="preserve">correla.</note>
            </div>
            <p xml:id="N186A9">
              <s xml:id="N186AA" xml:space="preserve">Sexta concluſio </s>
              <s xml:id="N186AD" xml:space="preserve">Ubi aliqua potentia <lb/>inuariata aliquod medium inuariatum tranſeun-<lb/>do vniformiter continuo remittit motum ſuum ad <lb/>non gradum: omnis poña minor habens ꝓportio-<lb/>nem maioris inequalitatis ad punctum initiatiuū <lb/>c. medii in extremo remiſſiori valet motum ſuum cõ­<lb/>tinuo vniformiter ad non gradum remittere idem <lb/>medium inuariatum tranſeundo. </s>
              <s xml:id="N186BE" xml:space="preserve">aliquando inten­<lb/>dendo potentiam, quando vero continuo remit-<lb/>tendo. </s>
              <s xml:id="N186C5" xml:space="preserve">Probatur hec concluſio / et ſit b. poña que in­<lb/>uariata c. medium inuariatum tranſeundo conti-<lb/>nuo vniformiter remittit motū ſuū ad nõ gradū ī ex­<lb/>tremo intenſiori c. medii: ſit a. poña minor habēs <lb/>ad punctum initiatiuum c. medii in extremo remiſ-<lb/>ſiori ꝓportionem maioris inequalitatis in h. ꝓpor­<lb/>tione minorem quam ad idem punctum habeat b. <lb/>potentia: et manifeſtum eſt /  ad aliquod punctum <lb/>intrinſecum habet a. potentia proportionem <lb/>equalitatis: capio igitur totam illam partem <lb/>c. medii a puncto videlicet initiatiuo in extremo re-<lb/>miſſiori vſ ad illum punctum ad quem habet pro­<lb/>portionem equalitatis ipſa a. poña: et diuido illaꝫ <lb/>partem per partes ꝓportionales ꝓportione h. et po­               <cb chead="Capitulum octauum"/>               natur a. poña in initio ſecūde partis ꝓportionalis <lb/>illius partis c. medii ſic diuiſi ꝓportione h. / et cõſtat <lb/>ꝓportionem quam habet b. ad punctum initiatiuū <lb/>c. medii in extremo remiſſiori ſe habere in maiori ꝓ­<lb/>portione quam h. ad ꝓportionem quaꝫ habet a. po­<lb/>tentia minor ad illum punctum intrinſecum in quo <lb/>pouitur: ſit igitur illa ꝓportio l. et incipiat ab eo-<lb/>dem inſtanti moueri illa poñe: b. a puncto initiati-<lb/>uo c. medii in extremo remiſſiori: a. vero a puncto il­<lb/>lo in quo ponitur: et ita varietur a. /  continuo mo-<lb/>ueatur in l. ꝓportione tardius ipſa b. poña. </s>
              <s xml:id="N186F9" xml:space="preserve">tunc di­<lb/>co /  a. continuo vniformiter remittit motum ſuum <lb/>ad non gradū, aliquando intendendo continuo po­<lb/>tentiam ſuam, aliquando vero continuo remitten-<lb/>do. </s>
              <s xml:id="N18704" xml:space="preserve">Quod ſic probatur: quia a. continuo vniformi-<lb/>ter remittit motum ſuum vſ ad non gradum cum <lb/>continuo in l. ꝓportione tardius moueatur ꝙ̄ ipſa <lb/>potentia b. continuo vniformiter remittens motuꝫ <lb/>ſuum vſ ad non gradum in eodem tempore adeq̈-<lb/>te: et per totum tempus quo precedet a. poña, ipſam <lb/>potentiam b. (quia precedit ex hypotheſi) ipſa con-<lb/>tinuo intendet poñam ſuaꝫ: et per totum tempꝰ quo <lb/>ſequetur b. potentiam, ipſa continuo remittit po-<lb/>tentiam ſuam: igitur a. potentia continuo vniformi­<lb/>ter remittit motum ſuum ad non gradum aliquãdo <lb/>continuo intendendo poñam et aliquando cõtinuo <lb/>remittendo. </s>
              <s xml:id="N1871F" xml:space="preserve">Conſequentia patet: et probatur ante-<lb/>cedens: ꝓbando primum /  a. poña aliquando p̄ce­<lb/>det: et aliquando ſequitur b. poñam: quia b. poten-<lb/>tia deueniet ad punctum ad quem habet a. potētia <lb/>ꝓportioneꝫ equalitatis in principio motus: et tunc <lb/>a. poña ſequetur eam: igitur a. poña aliquando ſe-<lb/>quetur b. poñam: et aliquando precedet / vt patet ex <lb/>hypotheſi: igitur per aliquod tempus precedet / et ꝑ <lb/>aliquod ſequetur: </s>
              <s xml:id="N18732" xml:space="preserve">Sed ꝓbatur /  cum b. erit ad pū­<lb/>ctum ad quem a principio motus a. habet propor-<lb/>tionem equalitatis. </s>
              <s xml:id="N18739" xml:space="preserve">ipſa b. potentia precedet a. / q2 <lb/>ſi continuo b. potentia moueretur velocius in h. ꝓ-<lb/>portione quam a. cum reſiduo hypotheſis: eque pri­<lb/>mo a. et b. deuenirent ad illum punctum ad quem a. <lb/>potentia habet proportionem equalitatis a prin-<lb/>cipio motus: quoniam tunc pertranſirent in eodem <lb/>tempore adequate ſpacia ſe habentia in h. ꝓportio­<lb/>ne / vt patet ex hypotheſi: iuuamine prime concluſio­<lb/>nis quinti capitis prime partis: ſed b. modo conti-<lb/>nuo in maiori ꝓportione velocius mouetur ip̄a po­<lb/>tentia a. / quam tunc ceteris omnibus paribus: igi-<lb/>tur citius modo et prius b. potentia attinget illū pū­<lb/>ctum quam a. potentia: et per conſequens cuꝫ b. erit <lb/>ad punctum ad quem a principio motus a. habet ꝓ­<lb/>portionem equalitatis: ipſa b. potentia precedet a. / <lb/>quod fuit probandum. </s>
              <s xml:id="N1875A" xml:space="preserve">Et iſto probato iam probo <lb/>primam partem minoris videlicet /  per illud tem-<lb/>pus quo precedet a. potentia ipſaꝫ poñam b. ip̄a a. <lb/>poña continuo intendit poñam ſuam: quia per nul­<lb/>lam partem talis temporis ipſa poña a. ſtat inua-<lb/>riata, aut remittit poñam ſuam: igitur continuo in­<lb/>tendit poñam ſuam. </s>
              <s xml:id="N18769" xml:space="preserve">Probatur antecedens: quia ſi <lb/>per aliquam partem illius temporis poña a. ſtat in­<lb/>uariata, aut remittit poñam ſuam: ſignetur illud. </s>
              <s xml:id="N18770" xml:space="preserve">et <lb/>ſit g. et pars pertranſita adequate in eodem g. tem­<lb/>pore ab ipſa potentia b. ſit .ef. et pars ꝑtranſita ab <lb/>a. poña in eodem d. tꝑe ſit d. / et manifeſtum eſt /  ip-<lb/>ſius .ef. partis ad d. partem eſt ꝓportio l. cum ſem-<lb/>per b. poña in l. proportione velocius moueatur ip­<lb/>ſa a. poña / vt patet ex hypotheſi. </s>
              <s xml:id="N1877F" xml:space="preserve">Quo poſito argui­<lb/>tur ſic / latitudinis motus deperdite ab ipſa poña <lb/>b. tranſeundo .ef. parteꝫ in g. tempore adequate ad <lb/>latitudinem motus deperditam ab eadem potētia               <pb chead="Primi tractatus" file="0087" n="87"/>               b. tranſeundo d. partem non eſt proportio l. nec ma­<lb/>ior: ergo latitudinis motus deperdite ab ipſa b. po­<lb/>tentia tranſeundo .ef. partem in tempore g. adequa­<lb/>te ad latitudinem motus deperditam ab a. potētia <lb/>ſtante inuariata vel remittente potentiam ſuã tran­<lb/>ſeundo d. partem in g. tempore adequate non eſt ꝓ­<lb/>portio l. nec maior: ſed conſequens eſt falſuꝫ: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N1879B" xml:space="preserve">Patet conſequentia: q2 om-<lb/>nes poñe inuariate ſiue equales ſiue inequales ideꝫ <lb/>medium etc. tranſeundo equalem latitudinem mo-<lb/>tus deperdunt: et ſi aliqua potentia tranſeundo ali­<lb/>quod medium inuariatum remittendo motum ſuuꝫ <lb/>etc. remittat potentiam ſuam: ipſa maiorem latitu­<lb/>dinem motus deperdit quam ſi ſtaret idem mediuꝫ <lb/>inuariatum tranſeundo etc. / vt conſtat ex quarto ar­<lb/>gumento ſexti capitis ſepius allegato. </s>
              <s xml:id="N187AE" xml:space="preserve">Sed falſi­<lb/>tas conſequentis ꝓbatur / quia ſi latitudinis deper­<lb/>dite ab ipſa potentia b. tranſeundo .ef. partem ī g. <lb/>tempore ad velocitatem deperditam ab a. poña trã­<lb/>ſeundo d. partem in eodem g. tempore non eſt pro-<lb/>portio l. nec maior: et a prīcipio motus ipſius b. ad <lb/>motum ipſius a. eſt proportio l. / ſequitur /  facta ta­<lb/>li variatione latitudinis motus ipſius b. ad latitu­<lb/>dinem motus ipſius a. non eſt ꝓportio l. nec maior / <lb/>quod eſt contra hypotheſim. </s>
              <s xml:id="N187C3" xml:space="preserve">Conſequentia tamen <lb/>patet ex primo et ſecundo correlariis quinte conclu­<lb/>ſionis ſecundi capitis ſecunde partis: </s>
              <s xml:id="N187CA" xml:space="preserve">Sed antece-<lb/>dens eodem modo ꝓbabis omnino quo probatum <lb/>eſt in quarta concluſione huius. </s>
              <s xml:id="N187D1" xml:space="preserve">Iam probat̄̄ ſecun­<lb/>da pars minoris videlicet /  per totum tēpus quo <lb/>a. poña b. poñam ſequetur: continuo a. poña remit­<lb/>tet potentiam ſuam. </s>
              <s xml:id="N187DA" xml:space="preserve">quia ſi per aliquam partem il­<lb/>lius temporis ſtat inuariata, aut intendit potentiã <lb/>ſignetur illa pars temporis, et ſit g. in quo a. tranſe­<lb/>at d. partem adequate, et b. in eodem g. tempore .ef. <lb/>partem adequate pertranſeat: et manifeſtum ē /  ip­<lb/>ſius .ef. partis ad ipſam d. partem eſt ꝓportio l. / vt <lb/>patet intuenti hypotheſim. </s>
              <s xml:id="N187E9" xml:space="preserve">Quo poſito arguo ſic / <lb/>latitudinis motus deperdite ab ipſa b. poña tran­<lb/>ſeūdo .ef. partem adequate ad latitudinē motus de­<lb/>perditam ab eadem b. poña tranſeundo d. partem <lb/>adequate eſt maior ꝓportio ꝙ̄ l. / igitur latitudinis <lb/>motus deperdite ab ipſa poña b. tranſeundo .ef. ꝑ-<lb/>tem in g. tempore adequate ad latitudinem motus <lb/>deperditam ab ipſa poña a. ſtante inuariata vel in­<lb/>tendente poñam ſuam tranſeundo adequate d. par­<lb/>tem in eodem g. tempore eſt maior ꝓportio ꝙ̄ l. / ſed <lb/>conſequens eſt falſum / igitur illud ex quo ſequitur. <lb/></s>
              <s xml:id="N18801" xml:space="preserve">Conſequentia cum falſitate conſequentis patet: et <lb/>antecedens ꝓbatur videlicet /  latitudinis motus <lb/>deperdite ab ipſa poña b. tranſeundo .ef. parteꝫ in <lb/>g. tempore adequate ad latitudinem motus deper-<lb/>ditam ab eadem poña b. tranſeundo d. partem ade­<lb/>quate: eſt maior ꝓportio quam l. quia ipſius .ef. ꝑ-<lb/>tis ad d. partem eſt ꝓportio l. et quamlibet partem <lb/>exceſſus minorem d. parte ipſius .ef. partis b. poña <lb/>tranſeundo continuo mouetur cum maiori reſiſten­<lb/>tia quam tranſeundo quãlibet partem equalem ip­<lb/>ſius d. partis: quoniaꝫ quelibet pars illius exceſſus <lb/>plus diſtat a puncto initiatiuo c. medii quam que-<lb/>libet pars ipſius d. partis diſtat ab eodem puncto <lb/>(ſigno enim exceſſum verſus extremum intenſius) / <lb/>igitur ex tertia ſuppoſitione huius. </s>
              <s xml:id="N18820" xml:space="preserve">latitudinis de­<lb/>perdite ab ipſa b. poña tranſeundo .ef. partem ī g. <lb/>tempore adequate ad latitudinem motus deperdi­<lb/>tam ab eadem b. poña tranſeundo d. partem ade­<lb/>quate eſt maior ꝓportio quam l. / quod erat oſtendē­<lb/>dum. </s>
              <s xml:id="N1882D" xml:space="preserve">Patet igitur concluſio.</s>
            </p>
            <p xml:id="N18830">
              <s xml:id="N18831" xml:space="preserve">Septima concluſio / vbi aliqua poten­               <cb chead="Capitulum octauum"/>               tia vniformiter continuo remittit motum ſuum ad <lb/>non gradum aliquod medium inuariatum tranſe-<lb/>undo: poña ei equalis valet continuo vniformiter <lb/>remittere motum ſuum ad non gradum idem medi­<lb/>um tranſeundo per ſui continuam remiſſionem.</s>
            </p>
            <p xml:id="N1883F">
              <s xml:id="N18840" xml:space="preserve">Probatur / ſit b. poña que īuariata vniformiter cõ­<lb/>tinuo remittit motum ſuum ad non gradum c. me-<lb/>dium tranſeundo inuariatum: ſit a. poña ei equa­<lb/>lis: et ponatur b. poña in puncto initiatiuo vltime <lb/>quarte magis reſiſtentis ad quem habet proportio­<lb/>nem ſubduplam ad illam quam habet ad punctum <lb/>initiatiuum c. medii in extremo remiſſiori / et pona-<lb/>tur poña a. ad punctum initiatiuū c. medii in extre-<lb/>mo remiſſiori ad quam habet ꝓportioneꝫ in duplo <lb/>maiorem ad ꝓportionem quam habet b. ad punctū <lb/>in quo ponitur / vt conſtat: cum ſint equales: incipi-<lb/>ant / igitur moueri ille due poñe in eodē īſtanti a pū­<lb/>ctis in quibus ponuntur et moueatur a. continuo in <lb/>duplo velocius b. / tunc dico /  a. continuo vniformi­<lb/>formiter remittit motum ſuum ad non gradum: et <lb/>hoc per ſue poñe continuam remiſſioneꝫ. </s>
              <s xml:id="N18861" xml:space="preserve">Quod ſic <lb/>ꝓbatur / quia a. continuo vniformiter remittit mo-<lb/>tum ſuum / vt ſepius ꝓbatuꝫ eſt: et remittit ad nõ gra­<lb/>dum: et continuo remittit potentiam ſuam: igitur ꝓ­<lb/>poſitum. </s>
              <s xml:id="N1886C" xml:space="preserve">Probatur prima pars minoris / quoniaꝫ <lb/>ſemper a. mouetur in duplo velocius quam b. ex hy­<lb/>potheſi: igitur / quando b. potentia erit in termino <lb/>c. medii a. potentia erit in termino duarum ṗmarū <lb/>quartarum. </s>
              <s xml:id="N18877" xml:space="preserve">Patet hec conſequentia adiecta hypo­<lb/>theſi antecedenti: ſed cum b. remittit motum ſuum <lb/>ad non gradum etiam a remittit motum ſuum ad <lb/>non gradum: quia continuo motus illarum poten-<lb/>tiarum ſe habent in proportione dupla: igitur cum <lb/>vnus totaliter deperditur: etiam et alter: et ex conſe­<lb/>quenti cuꝫ b. poña remittit motum ſuum ad nõ gra­<lb/>dum in extremo intenſiori c. medii a. potentia remit­<lb/>tit motum ſuum ad non gradum in fine duarū pri-<lb/>marum quartarum. </s>
              <s xml:id="N1888C" xml:space="preserve">Sed iam probo ſecundam par­<lb/>tem minoris videlicet /  a. continuo remittit poten­<lb/>tiam ſuam: quia ſi per aliquod tempus ſtaret aut ī­<lb/>tenderet potentiam ſuam, ſignetur illud tempus et <lb/>ſit g. in quo a. potentia tranſeat adequate .ef. par-<lb/>tem, et in eodem g. tempore b. potentia pertran-<lb/>ſeat d. partem adequate: et manifeſtum eſt /  .ef. ꝑ-<lb/>tis ad d. partem eſt proportio dupla. / quo poſito ar­<lb/>guitur ſic latitudinis motus deperdite ab ipſa po­<lb/>tentia b. tranſeundo .ef. partem ad latitudinem de­<lb/>perditam ab eadem poña b. tranſeundo d. partem <lb/>in g. tempore adequate non eſt ꝓportio dupla: igi-<lb/>tur latitudinis deperdite ab a. poña ſtante inuaria­<lb/>ta vel intendente poñam ſuam tranſeundo .ef. par­<lb/>tem adequate ī g. tempore ad latitudinem deper­<lb/>ditam a b. poña tranſeundo d. partem in eodem g. <lb/>tempore adequate non eſt ꝓportio dupla: ſed con-<lb/>ſequens eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N188B1" xml:space="preserve">Cõ­<lb/>ſequentia patet cum falſitate conſequentis ex ſupe­<lb/>rius dictis. </s>
              <s xml:id="N188B8" xml:space="preserve">Iam probatur antecedens / quia .ef. par­<lb/>tis ad d. partem eſt ꝓportio dupla et b. poña tran-<lb/>ſeundo quamlibet parteꝫ exceſſus minorem d. quo <lb/>exceſſu .ef. pars excedit d. partem mouetur cõtinuo <lb/>cum maiori reſiſtentia quam tranſeundo quamli-<lb/>bet partem equalem ipſius d. partis quia quelibet <lb/>pars talis exceſſus īmo tota .ef. pars minus reſiſtit <lb/>cum ſit ꝓpinquior extremo remiſſiori ipſius c. me-<lb/>dii / vt patet ex ꝓbatione prioris partis: igitur lati­<lb/>tudinis motus deperdite ab ipſa potentia b. tran­<lb/>ſeundo .ef. partem adequate ad latitudinem deꝑ-<lb/>ditam ab eadem poña tranſeundo d. partem ade-<lb/>quate non eſt ꝓportio dupla. </s>
              <s xml:id="N188D3" xml:space="preserve">Patet hec cõſeq̄ntia               <pb chead="Primi partis" file="0088" n="88"/>               ex quarta ſuppoſitiõe huius. </s>
              <s xml:id="N188DB" xml:space="preserve">Et ſic patet concluſio. <lb/>               <anchor type="note" xlink:href="note-0088-01" xlink:label="note-0088-01a"/>               </s>
              <s xml:id="N188E5" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia inuaria-<lb/>ta vniformiter continuo remittit motum ſuum .etc̈. <lb/>potentia ei equalis idem medium inuariatū tran-<lb/>ſeundo valet vniformiter continuo motum ſuum re­<lb/>mittere per ſui continuam intēſionem. </s>
              <s xml:id="N188F0" xml:space="preserve">Probatur / <lb/>ſit b. potena que inuariata totnm c. medii tran-<lb/>ſeundo vniformiter continuo valet motum ſuū re-<lb/>mittere: ſit a. potentia equalis que ponatur ad <lb/>punctum initiatiuū vltime quarte magis reſiſten-<lb/>tis b. potētia poſita in extremo remiſſiori c. medii / <lb/>et manifeſtum eſt /  proportio b. ad punctuꝫ in quo <lb/>ponitur eſt dupla ad proportionem a. ad punctum <lb/>in quo ponitur: incipiant igtur in eodem inſtãti ab <lb/>illis punctis continuo moueri a: et b. b potentia cõ-<lb/>tinuo in duplo velociꝰ ipſa a. ponã. </s>
              <s xml:id="N18907" xml:space="preserve">Tūc dico /  a. <lb/>poña illã vltimã quartã trãſeundo (quã īuariatã b. <lb/>potentia inuariata tranſeundo vniformiter contic­<lb/>nuo remittit motum ſuum) vniformiter cõtinuo re-<lb/>mittit motum ſuum per ſue potentie coutinuã intē-<lb/>ſionem. </s>
              <s xml:id="N18914" xml:space="preserve">Quod ſic probatur / quia a. potentia conti­<lb/>nuo vniformiter remittit motum ſuum / vt conſtat: et <lb/>hoc continuo inteudendo potentiam ſuam: igitur <lb/>propoſitum. </s>
              <s xml:id="N1891D" xml:space="preserve">Probatur minor: quia ſi ipſa poten-<lb/>tia a. per aliquod tempus ſtat inuariata aut remit­<lb/>tit potentiam ſuam, ſignetur illud tempus, et ſit g. <lb/>in quo b. potentia tranſeat .ef. partem adequate: <lb/>et in eodem g. tempore a potentia pertrãſeat d. par­<lb/>tem adequate: et cõſtat / ipſius .ef. partis ad d. par-<lb/>tem eſſe duplam proportionem / et ptꝫ ex hypotheſi: <lb/>quo poſito arguitur ſic / latitudinis motus deperdi­<lb/>te ab ipſa potentia b. tranſeundo .ef. partem ad la­<lb/>titudinem motus deperditam ab eadem potentia <lb/>b. tranſeundo d. partem adequate non eſt propor-<lb/>tio dupla: igitur latitudinis motus deperdite ab <lb/>ipſa b. potentia tranſeundo .ef. partem in g. tempo­<lb/>re adequate ad latitudinem deperditam ab a. po-<lb/>tentia tranſeundo d. partem in g. tempore adequa­<lb/>te non eſt proportio dupla: ſed conſequens eſt fal-<lb/>ſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N18940" xml:space="preserve">Conſequentia ptꝫ <lb/>cum falſitate conſequentis ex ſuperius dictis: et ar­<lb/>guitur antecedens quia ipſius .ef. partis ad ipſam <lb/>d. partem eſt proportio dupla: et quamlibet parteꝫ <lb/>exceſſus minorē ipſa d. parte quo exceſſu .ef. pars <lb/>excedit d. partem tranſeundo b. potentia mouetur <lb/>cum minori reſiſtentia quam equalem partem ipſi­<lb/>us d. partis tranſeundo: quoniam quelibet pars <lb/>illius exceſſus: īmo tota .ef. pars minus reſiſtit quã <lb/>ipſa d. pars: igitur latitudinis motus deꝑerdite a <lb/>b. potentia tranſeundo .ef. partem in g. tēpore ade­<lb/>quate ad latitudinem motus deperditã ab eadem <lb/>potentia b. tranſeundo d. partem non eſt propor-<lb/>tio dupla. </s>
              <s xml:id="N1895D" xml:space="preserve">Et ſic ptꝫ correlariū. </s>
              <s xml:id="N18960" xml:space="preserve">¶ Patet etiã quibꝰ <lb/>modis poña equalis potētie remittēti motū ſuū cõ­<lb/>tinuo vniformiter īuariatū mediū trãſeundo valet <lb/>motū ſuū remittere.               <anchor type="note" xlink:href="note-0088-02" xlink:label="note-0088-02a"/>               </s>
              <s xml:id="N1896E" xml:space="preserve">Utrū autē poña aliqua vnifor­<lb/>miter medio īuariato remittēte cõtinuo motū ſuū, <lb/>valeat equalis poña cõtinuo vniformiter remitte-<lb/>re motū ſuū, aliqñ ītendendo poñam, aliqñ vero re­<lb/>mittendo: tu ipſe inq̇ras. </s>
              <s xml:id="N18979" xml:space="preserve">Et ſi em̄ michi id īpoſſibi­<lb/>le eſſe appareat nichilominus demõſtratio efficax <lb/>non occurrit.</s>
            </p>
            <div xml:id="N18980" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0088-01a" xlink:label="note-0088-01" xml:id="N18984" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0088-02a" xlink:label="note-0088-02" xml:id="N1898A" xml:space="preserve">Dubiū</note>
            </div>
            <p xml:id="N18990">
              <s xml:id="N18991" xml:space="preserve">Octaua cõcluſio. </s>
              <s xml:id="N18994" xml:space="preserve">Ubi aliqua potētia <lb/>īuariata mediū īuariatū tranſeundo cõtinuo vni-<lb/>formiter remittit motū ſuū: aliqua maior valet cõ-<lb/>tinuo vniformiter: et eque velociter cū eadē motum <lb/>ſuū remittere per ſui continuã intenſionē. </s>
              <s xml:id="N1899F" xml:space="preserve">Proba-<lb/>tur / ſit b. potentia que īuariata c. mediū inuariatū               <cb chead="Capitulū octauū."/>               trãſeundo cõtinuo vniformiter remittit motū ſuuꝫ <lb/>ſit a. potentia maior que ad aliquē punctū intrī-<lb/>ſecū ipſius c. medii habeat equalē proportionē illi <lb/>ꝓportioni quã habet b. potentia ad punctū initia-<lb/>tiuū c. medii in extremo remiſſiori: et moueãtur ille <lb/>potentie cõtinuo ab eadē ꝓportione: et tunc dico /  <lb/>ipſa a. potentia cõtinuo vniformiter et eque veloci-<lb/>ter cū b. potentia remittit motū ſuū illam partē c. <lb/>medii tranſeundo que intercipitur inter punctū ter­<lb/>minatiuū c. medii in extremo intenſiori et punctum <lb/>a quo incipit ipſa a. potentia moueri. </s>
              <s xml:id="N189BB" xml:space="preserve">Quod ſic ꝓ-<lb/>batur / q2 a. potentia continuo vniformiter motum <lb/>ſuū: et continuo eque velociter remittit ſicut b. potē­<lb/>tia tranſeundo illam partē c. medii que ſignatur in <lb/>hypotheſi. </s>
              <s xml:id="N189C6" xml:space="preserve">Et cõtinuo intendit potentiã ſuã: igitur <lb/>ꝓpoſitū. </s>
              <s xml:id="N189CB" xml:space="preserve">Maior ꝓbatur / q2 motus ipſius a. ↄ̨tinuo <lb/>eſt equalis motui ipſiꝰ b. ex hypotheſi: et b. cõtinuo <lb/>vniformiter remittit motū ſuū datã partē c. medii <lb/>quã etiã pertranſit a. trãſeuudo: igitur a. continuo <lb/>vniformiter et eque velociter remittit motū ſuū cuꝫ <lb/>ipſa b. potentia tranſeundo datam partē c. medii. <lb/></s>
              <s xml:id="N189D9" xml:space="preserve">Patet cõſequentia: quoniã ſi ab equalibus equa-<lb/>lia demas remanētia ſunt equalia. </s>
              <s xml:id="N189DE" xml:space="preserve">Et demo rema­<lb/>nentes motus a. motibus deperditis. </s>
              <s xml:id="N189E3" xml:space="preserve">Iam ꝓbatur <lb/>minor: quoniã ſi per aliquod tēpus a. potentia ſtat <lb/>inuariata, aut remittit potentiã ſuã: ſignetur illud <lb/>et ſit g. in quo b. potentia pertranſeat adequate d. <lb/>partē c. medii et a. potentia in eodē g. tēporē pertrã­<lb/>ſeat e. partē adequate. </s>
              <s xml:id="N189F0" xml:space="preserve">Et manifeſtū eſt /  ipſius e. <lb/>ad d. eſt ꝓportio equalitatis / vt patet ex hypotheſi <lb/></s>
              <s xml:id="N189F6" xml:space="preserve">Quo poſito arguitur ſic / latitudinis motus deper­<lb/>dite ab ipſa b. potentia tranſeundo e. partē ad la-<lb/>titudinē motus deperditam ab eadem b. potentia <lb/>tranſeundo d. partem in g. tēpore adequate non eſt <lb/>ꝓportio equalitatis: igitur latitudinis motus de-<lb/>perdite ab a. poteutia ſtante aut remittente poten­<lb/>tiam ſuã tranſeundo e. partē in g. tēpore adequate <lb/>ad latitudinē motus deperditã a b. potentia tran-<lb/>ſeundo d. partē in eodem g. tēpore adequate nõ eſt <lb/>proportio equalitatis. </s>
              <s xml:id="N18A0B" xml:space="preserve">Conſequens eſt falſum: vt <lb/>patet ex probatione maioris: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N18A12" xml:space="preserve">Conſequentia patet per locum a maiori <lb/>auxiliante quarto argumento ſexti capitis huius <lb/>tractatus: vbi habetur /  omnes potentie inuari-<lb/>ate idem medium inuariatum tranſeuntes .etc̈. </s>
              <s xml:id="N18A1B" xml:space="preserve">An-<lb/>tecedens autem patet manifeſte ex ſecunda ſuppo-<lb/>ſitione huius capitis: hoc addito /  e. pars magis <lb/>reſiſtit ꝙ̄ d. quia a. continuo mouetur in parte ma-<lb/>gis reſiſtente ex hypotheſi. </s>
              <s xml:id="N18A26" xml:space="preserve">Et ſic patet concluſio.</s>
            </p>
            <p xml:id="N18A29">
              <s xml:id="N18A2A" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia non va-<lb/>riata continuo vniformiter remittit motum ſuum <lb/>ad non gradum medium inuariatum tranſeundo: <lb/>omnis potentia maior per ſui continuam intenſi-<lb/>onem idem medium inuariatum tranſeundo valet <lb/>motum ſuum continuo vniformiter remittere. </s>
              <s xml:id="N18A37" xml:space="preserve">Et <lb/>hoc continuo ꝙ̄ data potentia inuariata velocius <lb/>remittendo. </s>
              <s xml:id="N18A3E" xml:space="preserve">Prima pars huius correlarii eſt pri-<lb/>mum correlarium prime concluſionis huius capi-<lb/>tis. </s>
              <s xml:id="N18A45" xml:space="preserve">Et ſecunda probatur: ſuppoſſto hypotheſi pre­<lb/>dicti correlarii videlicet /  a. potentia maior ipſa <lb/>b. potentia continuo moueatur velocius in h. pro-<lb/>portione ꝙ̄ eadem b. potentia. </s>
              <s xml:id="N18A4E" xml:space="preserve">Et tunc dico /  a. po­<lb/>tentia continuo velocius remittit motum ſuum ̄ <lb/>ipſa b. potentia. </s>
              <s xml:id="N18A55" xml:space="preserve">Quod ſic probatur: quia a. potē-<lb/>tia continuo velocius in h. ꝓportione remittit mo­<lb/>tum ſuū ꝙ̄ b. / igitur continuo velocius remittit mo-<lb/>tum ſuū ꝙ̄ b. ↄ̨ña patet. </s>
              <s xml:id="N18A5E" xml:space="preserve">Et probatur añs / q2 motus <lb/>b. et a. continuo remittuntur cõtinuo ſe habentes               <pb chead="Primi tractatus" file="0089" n="89"/>               in eadē ꝓportione puta h. et motꝰ a. cõtinuo eſt ma-<lb/>ior: igr̄ cõtinuo motus deꝑditꝰ ab a. eſt in h: ꝓpor-<lb/>tione maior motu deꝑdito a b. et ꝑ ↄ̨ñs a. potentia <lb/>cõtinuo velociꝰ in h. ꝓportiõe remittit motū ſuū ̄ <lb/>b. / qḋ fuit ꝓbandū: ptꝫ ↄ̨ña ex ṗmo correlario quīte <lb/>cõcluſiõis ſecūdi capitis ſcḋe partꝪ.               <anchor type="note" xlink:href="note-0089-01" xlink:label="note-0089-01a"/>               </s>
              <s xml:id="N18A77" xml:space="preserve">¶ Seq̇tur ſcḋo / <lb/> vbi aliq̈ poña nõ variata .etc̈. oīs maior ꝑ ſui cõti-<lb/>nuã remiſſionē idē mediū īuariatū trãſeundo cõti-<lb/>nuo vniformiter remittit motū ſuū. </s>
              <s xml:id="N18A80" xml:space="preserve">Et hoc cõtinuo <lb/>velociꝰ data potētia minori. </s>
              <s xml:id="N18A85" xml:space="preserve">Prima pars huiꝰ cor­<lb/>relarii eſt correlariū ſecūde cõcluſiõis huiꝰ capitis <lb/></s>
              <s xml:id="N18A8B" xml:space="preserve">Et ſcḋa pars (ſuppoſita hypotheſi eiuſdē correla-<lb/>rii) eandē cū precedenti demonſtrationem affectat <lb/>               <anchor type="note" xlink:href="note-0089-02" xlink:label="note-0089-02a"/>               </s>
              <s xml:id="N18A97" xml:space="preserve">¶ Sequit̄̄ tertio. </s>
              <s xml:id="N18A9A" xml:space="preserve">Ubi aliqua potētia nõ variata cõ­<lb/>tinuo mediū nõ variatū trãſeūdo motū ſuū vnifor­<lb/>miṫ ad nõ gradū remittit: oīs minor hñs ad pūctū <lb/>eiuſdē medii initiatiuū in extremo remiſſiori ꝓpor­<lb/>tionē maioris īequalitatis valet motū ſuū cõtinuo <lb/>vniformiter remittere ꝑ ſui cõtinuã remiſſionē. </s>
              <s xml:id="N18AA7" xml:space="preserve">Et <lb/>hoc cõtinuo ita velociter remittēdo ſicut ipſa potē­<lb/>tia maior īuariata. </s>
              <s xml:id="N18AAE" xml:space="preserve">Prima pars huiꝰ eſt correla-<lb/>riū quīte cõcluſionis. </s>
              <s xml:id="N18AB3" xml:space="preserve">Et ſcḋa demõſtrationē huius <lb/>exq̇rit.               <anchor type="note" xlink:href="note-0089-03" xlink:label="note-0089-03a"/>               </s>
              <s xml:id="N18ABD" xml:space="preserve">¶ Seq̇tur q̈rto:  vbi aliqua potētia īuaria­<lb/>ta mediū īuariatū trãſeundo .etc̈. </s>
              <s xml:id="N18AC2" xml:space="preserve">Oīs minor hñs. <lb/>etc̈. (ſub tenore p̄cedētis). </s>
              <s xml:id="N18AC7" xml:space="preserve">Et hoc cõtinuo velociꝰ re-<lb/>mittēdo motū ſuū ꝙ̄ potētia maior īuariata.               <anchor type="note" xlink:href="note-0089-04" xlink:label="note-0089-04a"/>               </s>
              <s xml:id="N18AD1" xml:space="preserve">¶ Se­<lb/>quit̄̄ quīto:  vbi aliqua poña īuariata .etc̈. (ſub te­<lb/>nore ſexte cõcluſionis). </s>
              <s xml:id="N18AD8" xml:space="preserve">Et hoc cõtinuo tardiꝰ poña <lb/>minore remittente quaꝫ poña maior īuariata. </s>
              <s xml:id="N18ADD" xml:space="preserve">Hec <lb/>duo correlaria facile ex dictis oſtenſionē accipiūt <lb/>manifeſtã </s>
              <s xml:id="N18AE4" xml:space="preserve">¶ His adde /  tot correlaria et cõcluſiões <lb/>poſſunt īferri et demõſtrari de intēſione motꝰ cõti-<lb/>nuo vniformi in medio īuariato, ſicut de remiſſiõe <lb/></s>
              <s xml:id="N18AEC" xml:space="preserve">Quēadmodū em̄ dictū eſt /  vbi aliqua potētia in­<lb/>uariata mediū īuariatū trãſeundo vniformiter cõ­<lb/>tinuo remittit motū ſuū a certo gradu vſ ad non <lb/>gradū: aliqua maior ꝑ ſui cõtinuam intēſionē vni-<lb/>formiter cõtinuo valet motū ſuū remittere idē me-<lb/>diū trãſeundo. </s>
              <s xml:id="N18AF9" xml:space="preserve">ita etiã poteſt poni talis cõcluſio  <lb/>vbi potētia aliqua īuariata aliqḋ mediū trãſeūdo <lb/>īuariatū, vniformiter ↄ̨tinuo motū ſuū a nõ gradu <lb/>vſ ad certū gradū intendit: aliqua poña maior ꝑ <lb/>ſui cõtinuã remiſſionē valet motū ſuū cõtinuo vni-<lb/>formiter intēdere idē mediū īuariatū tranſeundo. <lb/></s>
              <s xml:id="N18B07" xml:space="preserve">Et iſto modo multa ſimilia poteris inferre. </s>
              <s xml:id="N18B0A" xml:space="preserve">Que <lb/>oīa predictorum auxilio ſuam ſortiuntur oſtenſio-<lb/>nem ſiue demonſtrationem.</s>
            </p>
            <div xml:id="N18B11" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0089-01a" xlink:label="note-0089-01" xml:id="N18B15" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0089-02a" xlink:label="note-0089-02" xml:id="N18B1B" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0089-03a" xlink:label="note-0089-03" xml:id="N18B21" xml:space="preserve">4. correĺ.</note>
              <note position="left" xlink:href="note-0089-04a" xlink:label="note-0089-04" xml:id="N18B27" xml:space="preserve">5. correĺ.</note>
            </div>
          </div>
          <div xml:id="N18B2D" level="4" n="9" type="chapter" type-free="capitulum">
            <head xml:id="N18B32" xml:space="preserve">Capitulum nonum / quod obiicit cõcluſioni­<lb/>bus duoꝝ p̄cedentium capitum.</head>
            <p xml:id="N18B37">
              <s xml:id="N18B38" xml:space="preserve">COntra ſcḋaꝫ ↄ̨̨cluſionē ſepti-<lb/>mi capitis argr̄ ſic: q2 illa cõcluſio eſt ī-<lb/>poſſibilis: igr̄ nõ eſt bene poſita. </s>
              <s xml:id="N18B3F" xml:space="preserve">Pro-<lb/>batur añs: q2 ſi illa poſſet verificari maxīe eſſet in <lb/>caſu poſito ad eã oſtendendã capite ſeptimo: ſed in <lb/>illo caſu m mobile / qḋ cõtinuo mouet̄̄ ꝑ mediū dif­<lb/>forme cõtinuo mouet̄̄ cū minori reſiſtētia quã mo-<lb/>bile primū / qḋ mouet̄̄ ꝑ mediū 6vniforme: igit̄̄ illud <lb/>mobile m, qḋ mouet̄̄ in illo ſcḋo medio difformi <lb/>cõtinuo velociꝰ mouet̄̄ quã primū mobile in illo ca­<lb/>ſu illiꝰ cõcluſionis: et ꝑ ↄ̨ñs in tali caſu m mobile <lb/>nõ vniformiter remittit motū ſuū. </s>
              <s xml:id="N18B54" xml:space="preserve">Probat̄̄ minor / <lb/>q2 cõtinuo vna medietas ſcḋi mobilis qḋ in medio <lb/>difformi mouet̄̄ cū minori reſiſtētia mouet̄̄ quã cor­<lb/>reſpõdēs medietas alteriꝰ mobilis in ṗmo medio: <lb/>et ſcḋa medietas ſcḋi mobilis cõtinuo mouet̄̄ cū re-<lb/>ſiſtētia eq̈li aut minori quã correſpõdēs medietas <lb/>alteriꝰ mobilis qḋ mouet̄̄ in ṗmo medio: igr̄ cõti-<lb/>nuo m mobile mouet̄̄ cū minori reſiſtētia in ſuo ſe­               <cb chead="Capitulum nonū."/>               cūdo medio difformi quã motū ī ṗmo medio. </s>
              <s xml:id="N18B68" xml:space="preserve">Pro­<lb/>batur añs / q2 ex caſu ibi poſito cõtinuo vnꝰ punctꝰ <lb/>ad quē eſt mobile in illo medio difformi tantū reſi­<lb/>ſtit adequate ſicut q̇libet punctꝰ ṗmi medii: et nullꝰ <lb/>aliꝰ tm̄: igr̄ tota vna medietas ſcḋi mobilis ꝓpin-<lb/>quior videlicet pūcto remiſſiori mouet̄̄ cõtinuo cū <lb/>minori reſiſtētia quã correſpõdēs medietas mobi­<lb/>lis / qḋ mouet̄̄ in ṗmo medio: et ſcḋa medietas ſcḋi <lb/>mobilis nõ hꝫ tantã reſiſtentiã quantã hꝫ correſpõ­<lb/>dens medietas mobilis in ṗmo medio niſi in vno <lb/>pūcto puta in quo eſt extremitas ipſiꝰ ſecūdi mobi­<lb/>lis / vt ponit caſus: igr̄ continuo vna medietas ſcḋi <lb/>mobilis / qḋ in medio difformi mouet̄̄ cū minori re-<lb/>ſiſtentia mouet̄̄ quã correſpõdēs medietas alteriꝰ <lb/>mobilis in ṗmo medio: et ſcḋa medietas ſecūdi mo­<lb/>bilis cõtinuo mouet̄̄ cū reſiſtētia equali aut mino-<lb/>ri quã correſpõdēs medietas alteriꝰ mobilis / quod <lb/>mouet̄̄ in ṗmo medio: qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0089-05" xlink:label="note-0089-05a"/>               </s>
              <s xml:id="N18B92" xml:space="preserve">¶ Dices for­<lb/>te negãdo minorē: et ad ꝓbationē: dices breuiṫ ar-<lb/>guentē ſupponere falſū. </s>
              <s xml:id="N18B99" xml:space="preserve">Supponit em̄ /  mobilia <lb/>de quibꝰ ſit mētio in caſu illiꝰ cõcluſiõis ſint quãta <lb/>ſiue diuiſibilia quo ad trinã dimēſionē: et hoc (vt in <lb/>quis) eſt falſū: q2 loq̄ris de mobili īdiuiſibili vĺ ſal­<lb/>tē lineali. </s>
              <s xml:id="N18BA4" xml:space="preserve">Et de talibus non procedit argumentū.</s>
            </p>
            <div xml:id="N18BA7" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0089-05a" xlink:label="note-0089-05" xml:id="N18BAB" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N18BB1">
              <s xml:id="N18BB2" xml:space="preserve">Sed ↄ̨̨tra qm̄ hoc nõ ſoluit argumē-<lb/>tū.               <anchor type="note" xlink:href="note-0089-06" xlink:label="note-0089-06a"/>               </s>
              <s xml:id="N18BBC" xml:space="preserve">Tū ṗmo / q2 īdiuiſibile nõ eſt ꝓprie mobile ſcḋm <lb/>pḣm ſexto phiſicoꝝ: et ṗmo de gñatiõe. </s>
              <s xml:id="N18BC1" xml:space="preserve">Tū ſcḋo / q2 <lb/>m mediū cõtinuo minꝰ reſiſtit illi mobili quã pri-<lb/>mū reſiſtat ṗmo mobili / eſto /  ſint illa mobilia īdi­<lb/>uiſibilia: igr̄ ponere illa mobilia īdiuiſibilia non <lb/>ſoluit argumentū: et ꝑ ↄ̨ñs ſolutio nulla. </s>
              <s xml:id="N18BCC" xml:space="preserve">Probat̄̄ <lb/>añs / qm̄ cõtinuo tota pars ꝑtrãſeunda ipſiꝰ ſecūdi <lb/>medii minꝰ reſiſtit ſuo mobili quã cõſimilis pars <lb/>in primo medio reſiſtat mobili / qḋ in eo mouet̄̄: et <lb/>ſole ille partes diuidende ſiue ꝑtrãſeunde reſiſtunt <lb/>illis mobilibꝰ: igr̄ m mediū cõtinuo minꝰ reſiſtit <lb/>illi mobili quã primū reſiſtat ṗmo mobili. </s>
              <s xml:id="N18BDB" xml:space="preserve">Maior <lb/>ꝓbatur / q2 p̄ciſe vnū punctū illiꝰ partis ad qḋ vide­<lb/>licet eſt illud mobile reſiſtit tm̄ ſicut qḋlibet punctū <lb/>partis correſpõdētꝪ in ṗmo medio: et qḋlibet alioꝝ <lb/>pūctoꝝ in eadē parte ſcḋi medii minꝰ reſiſtit quam <lb/>qḋlibet pūctū correſpõdēs in ṗmo medio: vt ptꝫ ex <lb/>caſu. </s>
              <s xml:id="N18BEA" xml:space="preserve">Nã in illo caſu ponit̄̄ /  cū in priori medio fue­<lb/>rit aliq̈ reſiſtētia ꝑ totū: in ſolo pūcto vbi eſt mobi­<lb/>le in ſcḋo medio ſit adeq̈te tanta reſiſtentia ceteris <lb/>īuariatis: igr̄ pars ꝑtrãſeūda in ſcḋo medio minꝰ <lb/>reſiſtit quã correſpõdens pars in primo medio. </s>
              <s xml:id="N18BF5" xml:space="preserve">Et <lb/>minor ꝓbat̄̄ / q2 ꝑ te ideo ponit̄̄ mobile indiuiſibile <lb/>ne partes ſequētes ei reſiſtēt. </s>
              <s xml:id="N18BFC" xml:space="preserve">Et ſi dicas /  ei reſi-<lb/>ſtãt: cū ſint minoris reſiſtētie in ſcḋo medio quã in <lb/>ṗmo: ſemꝑ habebo /  m mediū minꝰ reſiſtit quam <lb/>primū / qḋ īferre intēdebã.               <anchor type="note" xlink:href="note-0089-07" xlink:label="note-0089-07a"/>               </s>
              <s xml:id="N18C0A" xml:space="preserve">¶ Dices forte ṗmo ad au­<lb/>ctoritatē pḣi /  ipſe loq̇tur de mobili ꝓprie. </s>
              <s xml:id="N18C0F" xml:space="preserve">Tum <lb/>etiã / q2 poſſūt illa mobilia ſignari linealia. </s>
              <s xml:id="N18C14" xml:space="preserve">Ad ali­<lb/>ud dices negãdo añs vcꝫ /  m mediū minꝰ reſiſtat <lb/>ſuo mobili: et ad punctū ꝓbatiõis dices /  arguēs <lb/>ſupponit falſū. </s>
              <s xml:id="N18C1D" xml:space="preserve">Supponit em̄ /  ille ꝑtes oēs ꝑtrã­<lb/>ſeūde reſiſtãt reſiſtētia accidētali: qḋ tu nõ cõcedis. <lb/>               <anchor type="note" xlink:href="note-0089-08" xlink:label="note-0089-08a"/>               Nõ em̄ in motu locali aut diuiſiõis oēs ꝑtes illius / <lb/>qḋ diuidit̄̄ reſiſtūt / vt dicit calculator in capitulo de <lb/>reactiõe ſoluēdo quartū experimentū </s>
              <s xml:id="N18C2D" xml:space="preserve">Et ideo (vt in­<lb/>quis) ſolꝰ pūctꝰ ꝑtrãſeūdꝰ reſiſtit mobili, ſiue linea <lb/>diuidēda q̄ linea in vtro medio eſt eq̈lis reſiſtētie</s>
            </p>
            <div xml:id="N18C34" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0089-06a" xlink:label="note-0089-06" xml:id="N18C38" xml:space="preserve">pḣs ſex-<lb/>to phiſi. <lb/>ṗmo de <lb/>gñatiõe.</note>
              <note position="right" xlink:href="note-0089-07a" xlink:label="note-0089-07" xml:id="N18C44" xml:space="preserve">Dicitur.</note>
              <note position="right" xlink:href="note-0089-08a" xlink:label="note-0089-08" xml:id="N18C4A" xml:space="preserve">Calcu. in <lb/>capite de <lb/>reactiõe.</note>
            </div>
            <p xml:id="N18C54">
              <s xml:id="N18C55" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N18C58" xml:space="preserve">Tū primo / q2 nullū mediū <lb/>reſiſtit alicui indiuiſibili quo ad localē mutationē <lb/></s>
              <s xml:id="N18C5E" xml:space="preserve">Non em̄ mediū reſiſtit mutationi locali niſi q2 reſi­<lb/>ſtit ſue diuiſioni. </s>
              <s xml:id="N18C63" xml:space="preserve">Modo īdiuiſibile nõ diuidit me-<lb/>diū vt illud ꝑtrãſeat: cū ſimĺ poſſet eſſe cū quolibet               <pb chead="Primi partis" file="0090" n="90"/>               pūcto medii. </s>
              <s xml:id="N18C6D" xml:space="preserve">Tū ſecūdo / q2 tunc ſequeret̄̄ /  nullum <lb/>mobile extenſū et vndiqua diuiſibile poſſet vnifor­<lb/>miter cõtinuo motū ſuū remittere mediū difforme <lb/>tranſeūdo / ſed hoc eſt falſū: igit̄̄ illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N18C77" xml:space="preserve">Falſitas cõſequētꝪ ptꝫ: q2 tūc ſequeret̄̄ /  nullū mo-<lb/>bile corporeū poſſet motū ſuū cõtinuo vniformiter <lb/>remittere mediū īuariatū trãſeūdo: qm̄ oporteret <lb/>tale eſſe difforme. </s>
              <s xml:id="N18C80" xml:space="preserve">Sequela ꝓbat̄̄ / qm̄ ſi aliqḋ mobi­<lb/>le vndiqua diuiſibile poſſet vniformiter cõtinuo <lb/>remittere motū ſuū mediū difforme tranſeūdo: ma­<lb/>xime eſſet in caſu cõcluſiõis quã īpugnamꝰ: ſed hoc <lb/>eſt falſum: igitur nullū mobile corporeū poteſt mo­<lb/>tum ſuū cõtinuo vniformiter remittere mediū īua-<lb/>riatū trãſeūdo. </s>
              <s xml:id="N18C8F" xml:space="preserve">Maior ptꝫ: et ſi neges illã: des aliū <lb/>caſum. </s>
              <s xml:id="N18C94" xml:space="preserve">Et minor probatur / q2 in illo caſu mobile qḋ <lb/>mouetur in ſecūdo medio velociꝰ mouetur cotinuo <lb/>quã mobile motū in primo medio: igitur in illo ca-<lb/>ſu illud mobile nõ vniformiter cõtinuo remittit mo­<lb/>tum ſuū, vel ſaltē ſequitur /  ꝓbatio illiꝰ cõcluſiõis <lb/>eſt īefficax: q2 principaliter inititur huic fundamē-<lb/>to qḋ illa duo mobilia cõtinuo eque velociter mo-<lb/>uentur / vt ptꝫ ibi. </s>
              <s xml:id="N18CA5" xml:space="preserve">Probatur ãtecedes / q2 vt diceba-<lb/>tur in argumento prma medietas ſecundi mobilis <lb/>mouetur cõtinuo cū mīori reſiſtētia quã ſibi corre-<lb/>ſpõdens in mobili qḋ mouetur in primo medio: et <lb/>alia medietas ſecūdi mobilis mouetur cõtinuo cuꝫ <lb/>equali aut minori reſiſtētia quã medietas ſibi cor-<lb/>reſpõdens alteriꝰ mobilis qḋ mouetur in ſcḋo me-<lb/>dio / vt probatū eſt: ergo mobile qḋ mouetur in ſcḋo <lb/>medio velociꝰ mouetur cõtinuo quã mobile motum <lb/>in primo medio. </s>
              <s xml:id="N18CBA" xml:space="preserve">Patet cõſequentia / q2 ex caſu illa <lb/>mobilia ſūt oīno equalis virtutis: igit̄̄ ſi m moue­<lb/>tur continuo cum minori reſiſtētia: ip̄m ↄ̨tinuo ve-<lb/>lociꝰ mouetur. </s>
              <s xml:id="N18CC3" xml:space="preserve">¶ Dices forte ad punctū argumenti / <lb/> illud mediū non reſiſtit niſi ſue diuiſioni. </s>
              <s xml:id="N18CC8" xml:space="preserve">Et ideo <lb/>m partes iã diuiſas inter quas eſt mobile tale me­<lb/>diū nõ reſiſtit mobili: ſed p̄ciſe m partes diuiden-<lb/>das. </s>
              <s xml:id="N18CD1" xml:space="preserve">Et nõ adhuc m quãlibet diuidendã: ſed p̄ciſe <lb/>m lineã vel ſuꝑficiē diuidendã cui ex termitas mo-<lb/>bilis eſt ꝓxima: ita  vult hec reſpõſio ymaginari <lb/> cū gladiꝰ aliquid diuidit: partes iã diuiſe inter <lb/>quas eſt gladius nõ reſiſtūt gladio ne diuidat ſiue <lb/>moueatur diuidendo, nec etiã tota pars q̄ reſtat di­<lb/>uidenda reſiſtit illi gladio m ſe et qḋlibet ſui: ſed <lb/>p̄ciſe m ſuꝑficiē vel lineã cui ↄ̨tinuo acuties gladii <lb/>eſt ꝓxima.               <anchor type="note" xlink:href="note-0090-01" xlink:label="note-0090-01a"/>               </s>
              <s xml:id="N18CE9" xml:space="preserve">Et huic reſpõſioni videt̄̄ ſuffragari au­<lb/>ctoritas calculatoris in capitulo de reactione lo-<lb/>co paulo ante allegato.</s>
            </p>
            <div xml:id="N18CF0" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0090-01a" xlink:label="note-0090-01" xml:id="N18CF4" xml:space="preserve">Calcula. <lb/>de reacṫ.</note>
            </div>
            <p xml:id="N18CFC">
              <s xml:id="N18CFD" xml:space="preserve">Sed contra. </s>
              <s xml:id="N18D00" xml:space="preserve">Tū primo / q2 hec ſolutio <lb/>nullo pacto eſt apparens noīali qui huiuſcemodi <lb/>ſuperficies et lineas negat. </s>
              <s xml:id="N18D07" xml:space="preserve">Tum ſecundo / quia quã­<lb/>do aliquid diuiditur per motū localē in duas me-<lb/>dietates oportet vtrã illaꝝ medietatū lo­<lb/>caliter cedēdo: et tūc vtra illaꝝ medietatū reſiſtit <lb/>mobili ne a ſuo loco moueat̄̄. </s>
              <s xml:id="N18D12" xml:space="preserve">Tū tertio / q2 tunc ſe-<lb/>queretur /  eque facile eſſet diuidere vnã groſſam <lb/>trabē ꝑ mediū ſicut vnã paruã partē illius / qḋ tñ eſt <lb/>manifeſte falſū et ↄ̨tra expēriētiã. </s>
              <s xml:id="N18D1B" xml:space="preserve">Sequelã tñ ptꝫ / q2 <lb/>īſtrumēto diuiſio nõ maior pars reſiſtit cū diui-<lb/>dit totã trabē quã cū diuidit paruã partē eiꝰ q2 nõ <lb/>niſi ſuꝑficies aut linea ex ſolutiõe.               <anchor type="note" xlink:href="note-0090-02" xlink:label="note-0090-02a"/>               </s>
              <s xml:id="N18D29" xml:space="preserve">Tū quarto / quia <lb/>motus naturalis factꝰ ꝑ mediū vniforme velocior <lb/>eſt in fine quam in principio vt inquit pḣus octauo <lb/>phiſicoꝝ textu cõmenti ſeptuageſimi ſexti: cuiꝰ cau­<lb/>ſa talis a naturalibꝰ aſſignatur:  illud mediū mi­<lb/>nus reſiſtit in fine quã in principio: quia tūc minor <lb/>pars eiꝰ reſtat diuidenda: et per ↄ̨ñs magis reſiſtit <lb/>magnū mediū quã paruū. </s>
              <s xml:id="N18D3A" xml:space="preserve">Quod tñ nõ eſſet verum               <cb chead="Capitulū nonū."/>               ſi nõ quelib3 pars medii diuidēdi reſiſteret mobili <lb/>diuidenti. </s>
              <s xml:id="N18D42" xml:space="preserve">Itē experiūtur natantes in flumine cum <lb/>īmergūtur vſ ad fundum: et poſtea iteꝝ ad ſuper­<lb/>ficiē aque redeūtes tanto aquã eis minus reſiſtere <lb/>quãto ꝓximiores ſunt ſuꝑficiei: qḋ nõ eſſet ſi dūta-<lb/>xat ſuperficies illa diuidenda reſiſteret.</s>
            </p>
            <div xml:id="N18D4D" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0090-02a" xlink:label="note-0090-02" xml:id="N18D51" xml:space="preserve">pḣus .8. <lb/>phi. tex. <lb/>cõ. 76.</note>
            </div>
            <p xml:id="N18D5B">
              <s xml:id="N18D5C" xml:space="preserve">Et ideo reſpõdeo ad argumentū ne-<lb/>gando añs: et ad ꝓbationē cõceſia maiore negãdo <lb/>minorē: et ad ꝓbationē dico breuiter /  oportet di­<lb/>cere partes / iam diuiſas nõ reſiſtere illi mobili ſed <lb/>dūtaxat ſuꝑficies vel linea diuidenda / vt dictū eſt: <lb/>et cū ꝓbatur /  quelibet pars diuidenda reſiſtit: di­<lb/>co /  illud apparet michi verū naturaliter loquē-<lb/>do. </s>
              <s xml:id="N18D6D" xml:space="preserve">Ad ſingula em̄ entia naturalia aſpiciēs nullibi <lb/>inſtantiã cõperto. </s>
              <s xml:id="N18D72" xml:space="preserve">Quapropter et ſi illa cõcluſio et <lb/>ſuus modus ꝓbandi nõ cohereat naturalibus ni-<lb/>chilominꝰ tamē illa eſt poſſibilis. </s>
              <s xml:id="N18D79" xml:space="preserve">Nõ tamē audeo <lb/>aſſeuerare nullã potentiã poſſe naturaliter motuꝫ <lb/>ſuū cõtinuo vniformiter remittere mediū īuariatū <lb/>difforme cõtinuo trãſeūdo: ne numero indoctoruꝫ <lb/>aſcribar qui ad pauca reſpiciētes enūciat facile: <lb/>               <anchor type="note" xlink:href="note-0090-03" xlink:label="note-0090-03a"/>               teſte pḣo primo de gñatione textu cõmenti ſeptimi</s>
            </p>
            <div xml:id="N18D8B" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0090-03a" xlink:label="note-0090-03" xml:id="N18D8F" xml:space="preserve">primo ḋ <lb/>gñatiõe <lb/>tex. cõ. ſe­<lb/>ptimi.</note>
            </div>
            <p xml:id="N18D9B">
              <s xml:id="N18D9C" xml:space="preserve">Scḋo / ↄ̨̨tra primã ↄ̨̨cluſionē octaui ca­<lb/>pitis arguitur ſic / q2 vbi aliqua potētia nõ varia-<lb/>ta idem mediū īuariatū tranſeūdo vniformiter cõ­<lb/>tinuo remittit motū ſuū ad non g̈dū: oīs maior ad <lb/>extremū intēſiꝰ deueniendo in īfinitū velociter re-<lb/>mittit motū ſuū idem mediū tranſeundo: igitur in <lb/>tali medio nulla maior vniformiter remittit motū <lb/>ſuū. </s>
              <s xml:id="N18DAD" xml:space="preserve">Cõſequētia eſt nota: qm̄ nulla que vniformiter <lb/>remittit motū ſuū in īfinitū velociter remittit mo-<lb/>tum ſuū: qm̄ iam non vniformiter remitteret. </s>
              <s xml:id="N18DB4" xml:space="preserve">Sed <lb/>añs eſt quinta cõcluſio ſeptimi capitis huiꝰ tracta­<lb/>tus.               <anchor type="note" xlink:href="note-0090-04" xlink:label="note-0090-04a"/>               </s>
              <s xml:id="N18DC0" xml:space="preserve">¶ Dices / et bene diſtinguēdo añs / aut vbi illa po­<lb/>tentia maior manet cõtinuo nõ variata, et ſic cõce-<lb/>do, aut ſi potētia varietur, et ſic ego nego: et ad ꝓ-<lb/>bationē nego /  ſit quīta cõcluſio ſeptī capitis .etc̈. <lb/></s>
              <s xml:id="N18DCA" xml:space="preserve">Dicit em̄ / illa cõcluſio oīs poña maior nõ variata.</s>
            </p>
            <div xml:id="N18DCD" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0090-04a" xlink:label="note-0090-04" xml:id="N18DD1" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N18DD7">
              <s xml:id="N18DD8" xml:space="preserve">Sed cõtra hãc ſolutionē arguitur ſic / <lb/>qm̄ vbi illa poña maior variatur iuxta tenorē hu-<lb/>ius ṗme ↄ̨cluſiõis: adhuc ipſa in īfinitū velociṫ re-<lb/>mittit motū ſuū ſus extremū <lb/>ītēſiꝰ deueniēdo: igr̄ <lb/>ſolutio nulla. </s>
              <s xml:id="N18DE5" xml:space="preserve">Cõſequētia eſt nota / et argr̄ añs: et ca­<lb/>pio vnã potētiã / vt .8. q̄ vniformiṫ cõtinuo nõ varia­<lb/>ta c. mediū īcipiēs a duobꝰ et termīatū ad .8. trãſeū­<lb/>do remittit motum ſuum ad nõ grdum / et capio vnã <lb/>aliã maiorē vt .16. q̄ variata ſufficit vniformiter cõ­<lb/>tinuo remittē motū ſuū ad g̈dū totale c. mediū trã­<lb/>ſeūdo: ꝑ ſui ↄ̨tinuã ītēſionē / et capio vnã ṫciã poñam <lb/>q̄ ſit vt .10. / q̄ nõ variata trãſit idē mediū: et volo /  po­<lb/>tētia vt .16. et poña vt .10. ponãtur in prīcipio vltime <lb/>q̈rte magis reſiſtētꝪ ipſiꝰ c. medii vtpote in puncto <lb/>reſiſtētie vt .4. a quo ſiĺ īcipiãt moueri ſus extre-<lb/>mū ītēſiꝰ: q̊ poſito argr̄ ſic / poña vt .16. velociꝰ cõti-<lb/>nuo remittit motū ſuū quã poña vt .10. illã q̈rtã trã­<lb/>ſeūdo: et potētia vt .10. in īfinitū velociṫ remittit mo­<lb/>tū ſuū / vt ptꝫ ex quīta cõcluſiõe ſeptimi capiꝪ p̄alle-<lb/>gata: igr̄ poña / vt .16. in īfinitū velociṫ remittit mo­<lb/>tū ſuū / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N18E08" xml:space="preserve">Ptꝫ ↄ̨ña cū mīore: et argr̄ ma­<lb/>ior / q2 cõtinuo maiorē ꝓportionē ꝑdit poña vt .16. <lb/>quam potentia vt .10. / igitur potentia vt .16. cõtinue <lb/>velocius remittit motū ſuū quã potentia vt .10. </s>
              <s xml:id="N18E11" xml:space="preserve">Ar-<lb/>guitur antecedens / q2 potentia vt .16. continuo mo­<lb/>uetur velociꝰ quã potentia vt .10. qm̄ continuo mo-<lb/>uebitur a ꝓportione dupla: et potentia vt .10. nū̄ <lb/>poſt illū punctū qui eſt vt .5. mouebitur ab illa pro-<lb/>portione: igitur cõtinuo potentia vt .16. trãſit par-               <pb chead="Primi tractatus" file="0091" n="91"/>               tem equalē vel maiorē magis reſiſtentiã quã potē-<lb/>tia vt .10. / et per cõſequēs ↄ̨tinuo potentia illa vt .16. <lb/>maiorē proportionē deperdit per acquiſitionē re-<lb/>ſiſtentie quã potentia vt .10. </s>
              <s xml:id="N18E29" xml:space="preserve">Patet hec conſequētia <lb/>ex ſecūda ſuppoſitione octaui capitis huiꝰ. </s>
              <s xml:id="N18E2E" xml:space="preserve">Quã-<lb/>uis em̄ hec potentia varietur: nichilominus ex par­<lb/>te acquiſitionis reſiſtentie tantã ꝓportionē vel ma­<lb/>iorem deperdit ac ſi maneret cõtinuo īuariata: igi­<lb/>tur cõtinuo maiorē ꝓportionē deperdit / quod fuit <lb/>probandum.</s>
            </p>
            <p xml:id="N18E3B">
              <s xml:id="N18E3C" xml:space="preserve">Reſpondeo negãdo antecedens:  ad <lb/>ꝓbationē admiſſo caſu nego maiorē: et ad ꝓbatio-<lb/>nem nego antecedens videlicet /  continue maiorē <lb/>ꝓpõrtionē deperdit: et cum ꝓbatur concedo antece­<lb/>cedens / et nego cõſequentiã: ſed bene ſequitur /  ma­<lb/>iorē reſiſtentiã ꝓportiõabiliter acquirit. </s>
              <s xml:id="N18E49" xml:space="preserve">Quãuis <lb/>em̄ deperdat cõtinue ꝓportionē maiorē per acqui-<lb/>ſitionē reſiſtentie tamen ſemper aliquã ꝓportionē <lb/>acquirit per intenſionē potentie. </s>
              <s xml:id="N18E52" xml:space="preserve">Et ſic argumentū <lb/>bene ꝓbaret ꝓpropoſitū ſi potentia non intenderetur</s>
            </p>
            <p xml:id="N18E57">
              <s xml:id="N18E58" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>ſi potentia illa remitteretur cõtinuo ipſa nõ poſſet <lb/>vniformiter remittere motū ſuū illud mediū tran-<lb/>ſeundo: ſed cõſequens eſt contra correlariū ſecūde <lb/>ↄ̨cluſionis octaui capitis huiꝰ / igitur ſolutio nulla <lb/></s>
              <s xml:id="N18E64" xml:space="preserve">Probatur ſequela / q2 tūc talis potentia continuo <lb/>moueretur velocius alia potentia maiore nõ varia­<lb/>ta difformiter remittente motū ſuū idem medium <lb/>tranſeundo verſus extremū intenſius: igitur con-<lb/>tinuo maiorē ꝓportionē deperderet: et per conſe-<lb/>quens velocius continuo remitteret motū ſuū quã <lb/>potentia maior vt .10. nõ variata: et ſic nõ vniformi­<lb/>ter. </s>
              <s xml:id="N18E75" xml:space="preserve">Cõſequentia tamen ptꝫ ex ſecūda ſuppoſitione <lb/>octaui capitis preallegata. </s>
              <s xml:id="N18E7A" xml:space="preserve">Sed ãtecedens arguit̄̄ <lb/>videlicet /  potentia illa vt .16. cõtinuo velociꝰ mo-<lb/>ueretur: et pono potentiã vt .16. ſimul cum potentia <lb/>vt .10. ad principiū vltime quarte puta ad punctum <lb/>vt .4. / et pono potentiã vt .8. q̄ nõ variata ꝑtrãſeūdo <lb/>c. mediū īuariatū cõtinuo vniformiter remittit mo-<lb/>tū ſuū ad punctū ītrīſecū eiuſdē vltime q̈te / ad qḋ ha­<lb/>bet ꝓportionē irrationalē ſubduplã duple: et mo-<lb/>ueantur ſic oēs ille potentie ſimul ab eodē inſtanti / <lb/>quo poſito ptꝫ /  maior potentia variata puta vt <lb/>16. cõtinuo velocius mouebitur quã potentia vt .10. <lb/>qm̄ potentia vt .16. incipit moueri a multo maiori <lb/>proportione: igitur propoſitum. </s>
              <s xml:id="N18E95" xml:space="preserve">Hec em̄ a dupla <lb/>ſexquialtera: illa autem a quadrupla ſuum motum <lb/>inchoat / vt patet ex caſu.</s>
            </p>
            <p xml:id="N18E9C">
              <s xml:id="N18E9D" xml:space="preserve">Reſpõdeo negando ſequelã /  ad pro-<lb/>bationē nego /  potentia vt .16. continuo velocius <lb/>mouebitur quã potentia vt .10. maior nõ variata / et <lb/>cū ꝓbatur admiſſo caſu nego antecedens. </s>
              <s xml:id="N18EA6" xml:space="preserve">Dico em̄ / <lb/> illa potentia maior vt .16. variata antea quã de-<lb/>euniat ad finē ab in infinitū parua ꝓportione mo-<lb/>uebitur qm̄ ipſa ſic cõtinue remittente cū altera re­<lb/>mittente motū ſuū ad nõ gradū: neceſſe eſt ipſã ad <lb/>nõ gradū remittere ſimiliter motū ſuū: et ſic ab in <lb/>īfinitū parua ꝓportiõe moueri / vt ſepiꝰ ſupra argu­<lb/>gutū eſt.               <anchor type="note" xlink:href="note-0091-01" xlink:label="note-0091-01a"/>               </s>
              <s xml:id="N18EBC" xml:space="preserve">¶ Ex quo ſequit̄̄ /  ſi aliqua potētia varia­<lb/>ta moueretur vniformiter cõtinuo remittēs motuꝫ <lb/>ſuū ad nõ gradū cū alia nõ variata: et moueret̄̄ cõ-<lb/>tinuo a ꝓportiõe in cētuplo vel millecuplo vel quã-<lb/>tūcun volueris maiori: ipſã ab in infinitū parua <lb/>ꝓportiõe mouebit̄̄ antea quã deueniat ad finē quã­<lb/>quecū potētia quãtacū parua nõ remittēte mo­<lb/>tum ſuū ad nõ gradū idē mediū trãſeūdo. </s>
              <s xml:id="N18ECD" xml:space="preserve">Hoc ptꝫ <lb/>ex ꝓbatione concluſionum precedentis capitis.</s>
            </p>
            <div xml:id="N18ED2" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0091-01a" xlink:label="note-0091-01" xml:id="N18ED6" xml:space="preserve">1. correĺ.</note>
            </div>
            <cb chead="Capitulum nonū."/>
            <p xml:id="N18EDE">
              <s xml:id="N18EDF" xml:space="preserve">Tertio principaliter cõtra eandē cõ-<lb/>cluſione arguit̄̄ ſic / q2 ſi illa eſſet vera / ſeq̄ret̄̄ a. potē­<lb/>tiã maiorē variatã in īfinitū intēdi: ſed ↄ̨ſequēs eſt <lb/>falſū: igit̄̄ illud ex quo ſequit̄̄: falſitas cõſequentis <lb/>apparet manifeſte: qm̄ tūc nõ cõtinuo remittet mo­<lb/>tum ſuū. </s>
              <s xml:id="N18EEC" xml:space="preserve">Plus em̄ aliquãdo accreſceret ſibi de pro­<lb/>portiõe ꝑ intēſionē ſue potentie quã deꝑderet̄̄ ꝑ re-<lb/>ſiſtentie acquiſitionē. </s>
              <s xml:id="N18EF3" xml:space="preserve">Seq̄la tamē ꝓbat̄̄ / qm̄ in īfi-<lb/>nitū vetociter intendit̄̄ ipſa a. potētia: igit̄̄ ipſa in <lb/>īfinitū ītendit̄̄. </s>
              <s xml:id="N18EFA" xml:space="preserve">Aneecedēs ꝓbat̄̄: qm̄ in īfinitū velo-<lb/>citer ꝓportiõabiliter accreſcet ſibi reſiſtētia / vt ptꝫ <lb/>ex ꝓbatiõe quīte cõcluſiõis ſeptimi capitis huiꝰ: et <lb/>ipſa cõtinuo vniformiter remittit motū ſuū: igit̄̄ in <lb/>īfinitū velociter accreſcit ſibi potentia. </s>
              <s xml:id="N18F05" xml:space="preserve">Minor eſt <lb/>nota ex cõcluſiõe: et ꝓbat̄̄ ↄ̨ña / qm̄ ſi ſolū finite velo-<lb/>citer accreſceret ſibi potētia: et reſiſtētia in īfinitum <lb/>velociter ei accreſceret ſequeret̄̄ /  nõ ſemꝑ eque ve­<lb/>lociter deꝑderet ꝓportionē: et ꝑ ↄ̨ñs nõ vniformiter <lb/>remitteret motū ſuū: igit̄̄ ſi cõtinuo vniformiter re­<lb/>mittit motū ſuū: et in īfinitū velociter ꝓportiõabi-<lb/>liter acquirit̄̄ ſibi reſiſtētia: ſequit̄̄ /  potētia eiꝰ in <lb/>īfinitū velociter intēdit̄̄. </s>
              <s xml:id="N18F18" xml:space="preserve">Patet hec ↄ̨ña / qm̄ oppo-<lb/>ſitū cõſcqrētis cū altera parte ãtecedētis īfert op-<lb/>poſitū alteriꝰ partis eiuſdē ãtecedētis. </s>
              <s xml:id="N18F1F" xml:space="preserve">Sed iã ꝓbo <lb/>ãtecedēs / q̄ eſt vna cõditiõalis videlicet /  ſi ſolū fini­<lb/>te velociter creſceret ſibi potētia et reſiſtētia in īfini­<lb/>tū velociter ei accreſceret / tã ſeq̄ret̄̄ /  nõ ſemꝑ eque­<lb/>velociter deꝑderet ꝓportionē: et ſic nõ vniformiter <lb/>cõtinuo remitteret motū ſuū: q2 ſi ſolū finite veloci-<lb/>ter accreſceret ſibi potētia: et reſiſtētia in īfinitū ve-<lb/>lociter ei accreſceret: tã ſeq̄ret̄̄ /  in īfinitū velocius <lb/>ꝓportiõabiliter accreſceret ei reſiſtētia quã poten-<lb/>tia: et ꝑ ↄ̨ñs in īfinitū maiorē ꝓportionē deꝑderet ꝑ <lb/>acquiſitionē reſiſtētie quã acquireret ꝑ acquiſitio-<lb/>nē potētie: et ex cõſequēti in īfinitū velociter deper-<lb/>deret ꝓportionē: et ſic nõ ſemꝑ eque velociter deper­<lb/>deret ꝓportionē nec continuo vniformiter remitte­<lb/>ret motū ſuū: et ſic de primo ad vltimū ptꝫ illa ↄ̨ña <lb/>ꝓbanda. </s>
              <s xml:id="N18F40" xml:space="preserve">Cõſequētia ptꝫ videlicet /  ſi ſolū finite ve­<lb/>lociter accreſceret ſibi potētia: reſiſtētia in īfinitū <lb/>velociter ei accreſceret ſequeret̄̄ /  in īfinitū velociꝰ <lb/>ꝓportionabiliter accreſceret ei reſiſtentia quã po-<lb/>tentia: qm̄ ſi cõtinuo eque velociter accreſceret ſibi <lb/>reſiſtētia ſicut potētia: velocius ꝓportiõabiliter ac­<lb/>creſceret quã potētia / vt ptꝫ ex octaua ſuppõe q̈rta <lb/>capitꝪ ſcḋe partꝪ: hoc addito /  ↄ̨tinuo potētia ma­<lb/>net maior: ſꝫ modo ī īfinitū velociꝰ accreſcit ſibi re­<lb/>ſiſtētia quã potētia: g̊ in īfinitū velociꝰ ꝓportiõabi­<lb/>liṫ accreſcit ſibi reſtētia quã potētia / qḋ fuit ꝓbãdū</s>
            </p>
            <p xml:id="N18F57">
              <s xml:id="N18F58" xml:space="preserve">Reſpõdeo negãdo ſeq̄lã:  ad ꝓbatio-<lb/>nē nego ↄ̨ñam / q̄ nulliꝰ eſt apparētie. </s>
              <s xml:id="N18F5D" xml:space="preserve">Stat em̄ /  ali­<lb/>quid in īfinitū velociṫ intēdi in hora: et tñ ſolū finite <lb/>intēdi: vt ſatis cõſtat ſi diuiſa hora ꝑ partes ꝓpor­<lb/>tiõales ꝓportiõe q̈drupla: in ṗma illaꝝ acq̇rit̄̄ ali-<lb/>cui corpori vnꝰ gradꝰ calditatis, et in ſcḋa dimidiꝰ <lb/>et ī ṫcia, vna q̈rta, et ſic ↄ̨ñter: ꝑ partes ꝓportioãles <lb/>ꝓportione dupla: tunc manifeſtuꝫ eſt /  tota illa ca­<lb/>liditas erit duorum graduum in fine adequate / vt <lb/>patet ex ſecundo correlario tertie concluſionis quī-<lb/>ti capitis prime partis: </s>
              <s xml:id="N18F72" xml:space="preserve">Ibi enim acquiritur illa q̈-<lb/>litas per partes ꝓportionales ꝓportione dupla: <lb/>igitur reſiduuꝫ a prima eſt equale prime: et prima <lb/>erit vnus gradus: ergo totum eſt duorum graduuꝫ <lb/>adequate / vt patet ex ſucūdo correlario preallega-<lb/>to: et tamen in infinitum velociter acquiritur illa ca­<lb/>liditas: quoniam qualitas illa acquiritur in ſecun­<lb/>da parte ꝓportionali in duplo velocius quã in pri­<lb/>ma et in tertia in duplo velocius quam in ſecunda. /               <pb chead="Primi tractatus" file="0092" n="92"/>               et ſic conſequenter: igitur ꝓpoſitum. </s>
              <s xml:id="N18F8A" xml:space="preserve">Arguitur an-<lb/>tecedens / quoniam qualitas acquiſita in ſecunda ꝑ­<lb/>te propoſtiouali eſt equalis qualitati acquiſite in <lb/>medietate prime partis proportionalis </s>
              <s xml:id="N18F93" xml:space="preserve">(Uolo em̄ <lb/> acquirat vniformiter) et aquiritur in duplo mino­<lb/>ri tempore quam ſit illa medietas prime partis ꝓ-<lb/>portionalis / vt conſtat intelligenti quintum caput <lb/>prime partis: igitur ī duplo velocius acquiritur il­<lb/>la qualitas in ſecunda parte ꝓportionali quam in <lb/>prima. </s>
              <s xml:id="N18FA2" xml:space="preserve">Et iſto modo arguatur de qualitate acquiſi­<lb/>ta in tertia parte ꝓportionali reſpectu qualitatis <lb/>acquiſite in ſecunda. </s>
              <s xml:id="N18FA9" xml:space="preserve">Bene tamen concedo pro reſo­<lb/>lutione argumenti /  illa poña verſus extremum in­<lb/>tenſius deueniendo in infinitum velociter intendi-<lb/>tur / vt probat argumentum.               <anchor type="note" xlink:href="note-0092-01" xlink:label="note-0092-01a"/>               </s>
              <s xml:id="N18FB7" xml:space="preserve">¶ Ex quo ſequitur pri-<lb/>mo /  ſtat aliquid in infinitum velociter augeri ac-<lb/>quirendo preciſe quantitatem pedalem in hora.</s>
            </p>
            <div xml:id="N18FBE" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0092-01a" xlink:label="note-0092-01" xml:id="N18FC2" xml:space="preserve">1. correl.</note>
            </div>
            <p xml:id="N18FC8">
              <s xml:id="N18FC9" xml:space="preserve">Patet hoc ſupponendo /  hora diuidatur per par­<lb/>tes proportionales proportione quadrupla, aut <lb/>quintupla (in idem redit) et vnum corpus in prima <lb/>parte ꝓportionali acquirat ſemipedale, et in ſecun­<lb/>da quartam partem pedalis, et in tertia octauaꝫ, et <lb/>ſic conſequenter in ſubdupla ꝓportione. </s>
              <s xml:id="N18FD6" xml:space="preserve">quo poſi-<lb/>to manifeſtū ē (vt patet ex ſolutione argumenti) /  <lb/>illud corpus in infinitum velociter augetur: et tamē <lb/>ſolum finite augetur acquirendo adequate quan-<lb/>titatem pedalem in hora: </s>
              <s xml:id="N18FE1" xml:space="preserve">Nam acquirit infinita cõ­<lb/>tinue ſe habentia in ꝓportione dupla: igit̄̄ reſiduū <lb/>a primo eſt equale primo / vt patet ex ſecundo corre-<lb/>lario tertie concluſionis quinti capitis preallega-<lb/>to: et primo acquiſitum eſt ſemipedale: ergo totum <lb/>eſt pedale.               <anchor type="note" xlink:href="note-0092-02" xlink:label="note-0092-02a"/>               </s>
              <s xml:id="N18FF3" xml:space="preserve">¶ Sequitur ſecundo /  aliquid in infini-<lb/>tum tarde intenditur: et tamen finite intenditur.</s>
            </p>
            <div xml:id="N18FF8" level="5" n="9" type="float">
              <note position="left" xlink:href="note-0092-02a" xlink:label="note-0092-02" xml:id="N18FFC" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N19002">
              <s xml:id="N19003" xml:space="preserve">Probatur ponendo /  hora diuidatur per partes <lb/>ꝓportionales ꝓportione dupla: et in prima parte <lb/>ꝓportiõali aliquod corpus acquirat quatuor gra­<lb/>dus, et in ſecunda vnum, et in tertia vnam quartam <lb/>vnius gradus: et ſic conſequenter procedendo per ꝑ­<lb/>tes ꝓportionales proportione quadrupla. </s>
              <s xml:id="N19010" xml:space="preserve">quo po­<lb/>ſito manifeſtum eſt /  illud corpus in infinitum tar­<lb/>de intenditur: quoniaꝫ in ſecunda parte proportio­<lb/>nali in duplo tardius quaꝫ in prima, et ī tertia ī du­<lb/>plo tardius quam in ſecunda, et ſic conſequēter: igi­<lb/>tur in infinitum tarde intenditur. </s>
              <s xml:id="N1901D" xml:space="preserve">Probatur ante-<lb/>cedens / quoniam in ſecunda parte tale corpꝰ acqui­<lb/>rit ſubduplam intenſionem ad intenſionem acqui-<lb/>ſitam in medietate prime partis: et medietas prime <lb/>et ſecunda ſunt equales: igitur ī equali tempore ſub­<lb/>duplam intenſionem acquirit / et per conſequens in <lb/>duplo tardius intenditur. </s>
              <s xml:id="N1902C" xml:space="preserve">Et ſic ꝓbabitur de qua-<lb/>litate acquiſita in tertia, et de quacun alia reſpe-<lb/>ctu qualitatis acquiſite in parte precedenti eaꝫ im­<lb/>mediate. </s>
              <s xml:id="N19035" xml:space="preserve">igitur propoſitum. </s>
              <s xml:id="N19038" xml:space="preserve">Sed  finite intenda-<lb/>tur patet: quia preciſe in toto tempore illo acquirit <lb/>quin gradus cum tertia. </s>
              <s xml:id="N1903F" xml:space="preserve">Nam in prima parte ꝓ-<lb/>portionali acquirit quatuor gradus: et in ſecunda <lb/>vnum: et ſic conſequenter ꝓcedendo per partes pro­<lb/>portionales proportione quadrupla: ergo reſiduū <lb/>ab acquiſito in prima eſt ſubtriplum ad illud / vt pa­<lb/>tet ex ſecundo correlario preallegato: ſed acquiſi-<lb/>tum in prima eſt quatuor graduum: igitur acquiſi-<lb/>tum in omnibus ſequentibus a prima eſt gradꝰ cū <lb/>tertia: et ſic totum eſt quin graduum cuꝫ tertia / qḋ <lb/>fuit probandum.               <anchor type="note" xlink:href="note-0092-03" xlink:label="note-0092-03a"/>               </s>
              <s xml:id="N19059" xml:space="preserve">¶ Sequitur tertio /  infinite intē­<lb/>di eſt infinitam qualitatem acquirere vel infinitam <lb/>intenſionem: ſed in infinitum velociter intendi eſt in <lb/>aliquo tempore aliquam qualitatē acquirere ali-<lb/>quanta velocitate: et aliam in duplo maiori veloci-<lb/>tate (ſiue ſit tanta ſiue minor non eſt cura) et aliam               <cb chead="Capitulum nonum"/>               in triplo maiori: et ſic conſequenter vt poteſt exem-<lb/>plo primi correlarii oſtendi. </s>
              <s xml:id="N1906B" xml:space="preserve">Conſimiliter diffini-<lb/>as in infinnitum tarde intendi.</s>
            </p>
            <div xml:id="N19070" level="5" n="10" type="float">
              <note position="left" xlink:href="note-0092-03a" xlink:label="note-0092-03" xml:id="N19074" xml:space="preserve">3. correl.</note>
            </div>
            <note position="right" xml:id="N1907A" xml:space="preserve">4. correl.</note>
            <p xml:id="N1907E">
              <s xml:id="N1907F" xml:space="preserve">¶ Sequitur quarto /  quamuis poña non variata <lb/>intendens motum ſuum per medium vniformiter <lb/>difforme velocius intendat motum ſuum continuo <lb/>tranſeundo partem minus reſiſtentem quam ma-<lb/>gis reſiſtentem: nichilominus tamen poña non va-<lb/>riata difformiter intendens motum ſuum per me-<lb/>dium difforme per quod poña minor continuo vni­<lb/>formiter intendit motum ſuum: velocius ītendit ip­<lb/>ſa potentia maior non variata motum ſuum tran-<lb/>ſeundo partem magis reſiſtentem quam minus re-<lb/>ſiſtentem. </s>
              <s xml:id="N19096" xml:space="preserve">Prima pars correlarii patet ex quadra­<lb/>geſima concluſione quinti capitis huius tractatus <lb/></s>
              <s xml:id="N1909C" xml:space="preserve">Et ſecunda probatur / quia quacun parte data ꝓ-<lb/>portionabili illius medii procedendo a minoribus <lb/>verſus maiores in qua aliqualiter ītendit talis po­<lb/>tentia maior motum ſuum: in aliqua minore prece­<lb/>dente magis reſiſtente velocius intendebat motum <lb/>ſuum cum in infinitum velociter antea intendebat <lb/>motum ſuum / vt patet ex tertio correlario quinte cõ­<lb/>cluſionis ſeptimi capitis huius tractatus: igitur ve­<lb/>locius intendebat talis potentia motum ſuum cum <lb/>parte magis reſiſtente / quod fuit probandum.</s>
            </p>
            <p xml:id="N190B1">
              <s xml:id="N190B2" xml:space="preserve">Quarto contra ſecundam concluſio-<lb/>nem octaui capitis arguitur ſic / quia ſi illa eſſet ve-<lb/>ra ſequeretur /  vbi aliqua potentia inuariata ali­<lb/>quod medium inuariatum tranſeundo cõtinuo vni­<lb/>formiter remittit motum ſuum ad non gradum in <lb/>puncto terminatiuo eiuſdem medii in extremo intē­<lb/>ſiori: omnem potentiam maiorem idem mediã trã­<lb/>ſeundo adequate vniformiter continuo poſſe remit­<lb/>tere motum ſuum ad non gradum in eodem puncto <lb/>terminatiuo per continuam ſue potentie remiſſio-<lb/>nem / ſed hoc eſt falſum: igitur et concluſio. </s>
              <s xml:id="N190C9" xml:space="preserve">Falſitas <lb/>conſequentis probatur / et capio a. poñam que habe­<lb/>at ad punctum initiatiuum c. medii quod inuaria-<lb/>tum b. poña inuariata pertranſit continuo vnifor-<lb/>miter remittēdo motum ſuum ad non gradum etc. <lb/>ꝓportionem in ſexquialtero maiorem quam b. ad <lb/>idem punctum: et arguo ſic / a. potentia tranſeūdo c. <lb/>medium non valet vniformiter continuo remittere <lb/>motum ſuum vſ ad non gradum in puncto termi­<lb/>natiuo c. medii in extremo intenſiori per continuaꝫ <lb/>ſue potentie remiſſionem: igitur non vbi potentia ī­<lb/>uariata aliquod medium tranſeundo inuariatum <lb/>etc. ad non gradum in puncto terminatiuo etc. om-<lb/>nis potentia maior idem medium tranſeundo ade­<lb/>quate, vniformiter continuo poteſt remittere motū <lb/>ſnum vſ ad non gradum in eodem puncto termi-<lb/>natiuo per continuam ſue potentie remiſſionem. </s>
              <s xml:id="N190EC" xml:space="preserve">qḋ <lb/>eſt oppoſitum conſequentis. </s>
              <s xml:id="N190F1" xml:space="preserve">Antecedens probatur / <lb/>quia ſi a. potentia tranſeundo c. medium valet re-<lb/>mittere motum ſuum vſ ad non gradum in pūcto <lb/>terminatiuo etc. per continuam ſue poñe remiſſio-<lb/>nem: maxime remitteret vniformiter continuo mo-<lb/>tum ſuum vſ ad non gradum in puncto termina-<lb/>tiuo etc. caſu quo b. poña inuariata inciperet moue­<lb/>ri a puncto initiatiuo ſecunde partis ꝓportionalis <lb/>c. medii diuiſi in partes ꝓportionales ꝓportione <lb/>ſexquialtera verſus extremum intenſius eiuſdem c. <lb/>medii: et a. potentia a puncto initiatiuo c. medii ver­<lb/>ſus extremum intenſius eiuſdem: taliter  cõtinuo <lb/>per ſui variationem in ſexquialtero velocius moue­<lb/>retur a. quam b. ſed hoc non: igitur </s>
              <s xml:id="N1910E" xml:space="preserve">Maior ptꝫ / q2 <lb/>tunc tam a. quam b. eque primum deuenirent ad pū­<lb/>ctum terminatiuum c. medii in quo vtra remitte-<lb/>ret motū ſuum ad non gradum: cū a. per caſum in               <pb chead="Primi tractatus" file="0093" n="93"/>               ſexquialtero velocius continuo moueretur quam <lb/>b. / vt conſtat igitur: </s>
              <s xml:id="N1911E" xml:space="preserve">Sed minor probatur / quia a. po­<lb/>tentia in illo caſu c. medium tranſeundo non remit­<lb/>tit motum ſuum ad non gradum in puncto termi-<lb/>natiuo eiuſdem c. medii: igitur minor vera: </s>
              <s xml:id="N19127" xml:space="preserve">Antece­<lb/>dens probatur / q2 a. potentia citius deueniet ad pū­<lb/>ctum terminatiuum c. medii quam b. poña: ergo cū <lb/>caſu ſequitur /  a. poña c. medium tranſeundo non <lb/>remittit motum ſuum ad non gradum in pūcto ter­<lb/>minatiuo c. medii etc. </s>
              <s xml:id="N19134" xml:space="preserve">Probatur antecedens / quia ſi <lb/>a. poña continuo in ſexquialtero velocius mouere-<lb/>tur quam b. poña: eque primo a. et b. deuenirent ad <lb/>pnnctum terminatiuum c. medii. </s>
              <s xml:id="N1913D" xml:space="preserve">ſed modo a. poten­<lb/>tia mouetur velocius quam tunc: ergo modo citius <lb/>deuenit ad punctum terminatiuum c. medii quaꝫ b. <lb/>potentia: </s>
              <s xml:id="N19146" xml:space="preserve">Maior patet: et minor ꝓbatur / quia a. po­<lb/>tentia ad punctum initiatiuum c. medii habet maio­<lb/>rem ꝓportionem quam ſexquialteram ad ꝓportio­<lb/>nem b. potentie ad punctum initiatiuum ſecunde ꝑ­<lb/>tis ꝓportionalis c. medii diuiſi in partes ꝓportio-<lb/>nales ꝓportione ſexquialtera: et a. poña nõ deper-<lb/>dit ſubito aliquam latitudinem potentie (vt volo) / <lb/>igitur īmediate poſt inſtans initiatiuum motus a. <lb/>potentia plus quam in ſexquialtero velocius mo-<lb/>uebitur b. poña / quod erat ꝓbandum: </s>
              <s xml:id="N1915B" xml:space="preserve">Conſequētia <lb/>patet / quia ſi a. potentia ad punctum initiatiuū etc. <lb/>habet maiorem ꝓportionem quam ſexquialteram <lb/>ad ꝓportionem b. potentie ad punctum initiatiuū <lb/>ſecunde partis etc. et a. poña non perdit ſubito ali-<lb/>quam latitudinem potentie: proportio ipſius a. ad <lb/>punctum initiatiuum etc. continet ꝓportionem ſex-<lb/>quialteram ad ꝓportionem ipſius b. ad punctuꝫ in­<lb/>itiatiuum ſecunde partis proportionalis etc. et ali-<lb/>quam proportionem vltra illam. </s>
              <s xml:id="N19170" xml:space="preserve">quam ꝓportionē <lb/>vltra non ſubito deperdit: et per conſequens īmedi­<lb/>ate poſt inſtans initiatiuum motus a. potentia plꝰ <lb/>quã in ſexquialtero velocius mouebitur b. poña.</s>
            </p>
            <p xml:id="N19179">
              <s xml:id="N1917A" xml:space="preserve">Et ſic de primo ad vltimum patet conſequentia.</s>
            </p>
            <p xml:id="N1917D">
              <s xml:id="N1917E" xml:space="preserve">Sed maior probatur videlicet /  a. poña ad pūctuꝫ <lb/>initiatiuum c. medii habet maioreꝫ ꝓportionē quã <lb/>ſexquialteram ad proportionem b. poñe ad pūctuꝫ <lb/>initiatiuum ſecunde partis ꝓportionalis c. medii <lb/>diuiſi etc. quia a. ponã ad punctum initiatiuuꝫ c. me­<lb/>dii habet proportionem ſexquialteram ad ꝓportio­<lb/>nem quam habet b. poña ad ideꝫ punctum / vt patet <lb/>ex caſu: et ꝓportio ipſius b. ad punctum initiatiuuꝫ <lb/>c. medii eſt maior quam ꝓportio eiuſdem b. poten-<lb/>tie ad punctum initiatiuum ſecunde partis ꝓportio­<lb/>nalis: quia b. potentie inuariate minus reſiſtit pun­<lb/>ctum initiatiuum c. medii quam punctum initiuati­<lb/>uum ſecunde partis ꝓportionalis eiuſdem c. medii <lb/>diuiſi etc. / vt conſtat: igitur a. poña ad pūctum īitia-<lb/>tiuum c. medii maiorem habet ꝓportionem quam <lb/>ſexquialteram ad ꝓportionem b. poñe ad punctum <lb/>initiatiuum ſecunde partis ꝓportionalis c. medii <lb/>diuiſi etc. </s>
              <s xml:id="N191A3" xml:space="preserve">Conſequentia patet / quia maior eſt ꝓpor­<lb/>tio alicuiꝰ tertii adminꝰ quam eiuſdem terti ad ma­<lb/>ius / vt patet ex ſecunda parte.</s>
            </p>
            <note position="left" xml:id="N191AA" xml:space="preserve">Dicitur.</note>
            <p xml:id="N191AE">
              <s xml:id="N191AF" xml:space="preserve">¶ Dices forte negando ſequelam īmo / vt bene ꝓbat <lb/>argumentuꝫ illud eſt falſum: niſi poña a. ſubito ali­<lb/>quam latitudinem poñe deperderet. </s>
              <s xml:id="N191B6" xml:space="preserve">Si enim ali-<lb/>qua potentia poneretur ad punctum initiatiuuꝫ c. <lb/>medii cuius ꝓportio ad idem punctum eſſet mille-<lb/>cupla ad ꝓportionē b. poñe ad punctum initiatiuū <lb/>ſecunde partis ꝓportionalis c. medii diuiſi per ꝑ-<lb/>tes ꝓportionales ꝓportione ſexquialtera etc. et illa <lb/>potentia ſic variaretur /  īmediate ab illo puncto ī­<lb/>itiatiuo recedēdo moueretur adequate in ſexquial­<lb/>tero velocius b. poña recedente ad puncto initiatiuo               <cb chead="Capitulum nonum"/>               ſecunde partis ꝓportionalis verſus extremum ītē-<lb/>ſius et continuo ſic moueretur. </s>
              <s xml:id="N191CE" xml:space="preserve">tunc vt conſtat tam il­<lb/>la poña quam b. poña eque primū deuenirent ad ex­<lb/>tremuꝫ intenſius c. medii in quo vtra remittit mo­<lb/>tum ſuum ad non gradum: cõtinuo remittendo mo­<lb/>tum ſuum vniformiter: et hoc per illus poñe conti-<lb/>nuam remiſſionem. </s>
              <s xml:id="N191DB" xml:space="preserve">Sed tunc poña illa ſubito per-<lb/>deret aliquam latitudinem poñe: et etiã ſubito deꝑ­<lb/>deret ꝓportionem quam continet vltra ꝓportiõem <lb/>que eſt ſexquialtera ad ꝓportionem ipſius b. poñe <lb/>ad punctum initiatiuum ſecunde partis ꝓportiona­<lb/>lis c. medii diuiſi etc. </s>
              <s xml:id="N191E8" xml:space="preserve">Attamē alias non eſt veruꝫ (vt <lb/>dicis) quēadmodum bene probat argumentum.</s>
            </p>
            <p xml:id="N191ED">
              <s xml:id="N191EE" xml:space="preserve">Sed contra / quia vbi aliqua potentia <lb/>inuariata aliquod medium inuariatum tranſeun-<lb/>do continuo vniformiter remittit motum ſuum vſ <lb/>ad non gradum in puncto terminatiuo eiuſdē me-<lb/>dii in extremo intenſiori: omnis ponã maior idem <lb/>medium tranſeundo adequate: vniformiter conti-<lb/>nuo remittit motum ſuum vſ ad nõ gradum in eo­<lb/>dem puncto terminatiuo per continuam ſue potētie <lb/>ſucceſſiuam remiſſionem: igitur ſolutio nulla. </s>
              <s xml:id="N19201" xml:space="preserve">Ante­<lb/>cedens probatur ſupponendo /  īter quodlibet pū­<lb/>ctum intrinſecum cuiuſuis medii per quod inuaria­<lb/>tum aliqua poña inuariata continuo vniformiter <lb/>remittit motum ſuum ad non gradum in extremo ī­<lb/>tenſiori, et pūctum initiatiuum eiuſdem medii, me­<lb/>diat prima pars ꝓportionalis illius medii diuiſi <lb/>ꝓportione dupla ad ꝓportionem in qua ſe habet <lb/>ꝓportio illius poñe ad punctum initiatiuum ad ꝓ­<lb/>portionem eiuſdem poñe addatum pūctum intrin­<lb/>ſecum. </s>
              <s xml:id="N19218" xml:space="preserve">Exemplū / vt poſito /  b. poña īuariata c. me-<lb/>dium īuariatum tranſeundo vniformiter continuo <lb/>remittat motum ſum vſ ad non gradum in extre-<lb/>mo intenſiori et dato vno puncto intrinſeco ad quē <lb/>talis poña b. habeat ꝓportionem in duplo mino-<lb/>rem quam ſit ꝓportio quam habeat ad punctuꝫ ini­<lb/>tiatiuum / tunc inter punctum īitiatiuum et illud pū-<lb/>ctum intrinſecum mediat prima pars ꝓportiona-<lb/>lis illius medii diuiſi ꝓportione quadrupla dupla <lb/>duple. </s>
              <s xml:id="N1922D" xml:space="preserve">Quod ſic probatur / quia inter punctum ini-<lb/>tiatiuum illius c. medii et punctum intrinſecum eiuſ­<lb/>dem ad quod b. poña habet in duplo minorem pro­<lb/>portionem quam ad punctum initiatiuum: mediat <lb/>prima pars ꝓportionalis c. medii adequate diuiſi <lb/>per partes ꝓportionales proportione quadrupla <lb/>quia inter illa puncta mediant tres quarte que ſūt <lb/>prima ꝓportionalis ꝓportione quadrupla: quoni­<lb/>am in inſtanti medio totius temporis. </s>
              <s xml:id="N19240" xml:space="preserve">in quo ade-<lb/>quate b. poña c. medium pertranſit continuo remit­<lb/>tendo motum ſuum vſ ad non gradum erit b. po­<lb/>tentia ad punctum terminatiuum trium quartarū <lb/>ab eadē b. ponã pertranſitarum: et in inſtanti me-<lb/>dio totius illius temporis habebit ad punctum in <lb/>quo / tunc eſt ꝓportionem ſubduplam ad ꝓportio-<lb/>nem quam habet ad punctum initiatiatiuum eiuſ-<lb/>dem c. medii quia perdit ſuam ꝓportionem vnifor­<lb/>miter continuo: igitur inter punctum initiatiuuꝫ c. <lb/>medii et punctum ad quod b. poña habet ꝓportio-<lb/>nem in duplo minorem ꝙ̄ habeat eadem b. potētia <lb/>ad punctum īitiatiuum mediant tres quarte: et per <lb/>conſequens prima pars ꝓportionalis c. medii pro­<lb/>portione quadrupla: quod fuit probandum </s>
              <s xml:id="N1925F" xml:space="preserve">Item <lb/>īter punctum īitiatiuum c. medii et pūctum ad quod <lb/>b. poña habet in ſexquitertio minorem ꝓportioneꝫ <lb/>̄ ad punctum īitiatiuum mediat prima pars pro­<lb/>portionalis c. medii proportione ſupraſeptipartiē­<lb/>te nonas que eſt dupla ad ſexquitertiam. </s>
              <s xml:id="N1926C" xml:space="preserve">quia īter               <pb chead="Primi tractatus" file="0094" n="94"/>               illa puncta mediãt ſeptem ſexdecime que ſunt prīa <lb/>pars ꝓportionalis ꝓportione ſupraſeptipartiēte <lb/>nonas / vt patet intelligenti quintum caput prime <lb/>partis: igitur. </s>
              <s xml:id="N1927A" xml:space="preserve">Antecedens probatur / quia b. poña <lb/>in inſtanti terminatiuo prime quarte temporis in <lb/>quo adequate c. medium pertranſit habet ad pun-<lb/>ctum in quo / tunc eſt ꝓportionem in ſexquitertio mi­<lb/>norem ad ꝓportionem quam habet ad punctum in­<lb/>itiatiuum: et in eodem inſtanti terminatiuo prime <lb/>quarte illius temporis eſt in fine ſeptem ſexdecima­<lb/>rum c. medii pertranſitaruꝫ ab ipſa b. poña: igitur <lb/>inter punctum initiatiuum c. medii et punctum ad <lb/>quod b. poña habet in ſexquitertio minorem ꝓpor­<lb/>tionem quam ad punctum initiatiuum mediant ſe-<lb/>ptem ſexdecime c. medii / quod fuit probandum. </s>
              <s xml:id="N19293" xml:space="preserve">Cõ­<lb/>ſequentia patet: et maior ꝓbat̄̄ / q2 in prīa quarta tē­<lb/>poris in quo adequate b. poña c. medium pertran-<lb/>ſit perdit eadem b. poña vnam quartam ꝓportiõis <lb/>quam habet ad punctum initiatiuum c. medii: quia <lb/>illa ꝓportio debet vniformiter continuo deperdi: <lb/>igitur in inſtanti terminatiuo illius quarte habet <lb/>tres quartas preciſe illius proportionis quam ha­<lb/>bet ad punctum initiatiuum: et per conſequens pro­<lb/>portionem in ſexquitertio minorem / quod fuit pro-<lb/>bandum. </s>
              <s xml:id="N192AA" xml:space="preserve">Nunc probo minorem videlicet /  in inſtã­<lb/>ti terminatiuo prime quarte illius temporis eſt in <lb/>fine ſeptem ſexdecimarum ab ea pertranſitaruꝫ etc. <lb/>quia ſi b. poña in prima quarta illius temporis mo­<lb/>ueret̄̄ adequate ita velociter ſicut in tota hora ca-<lb/>thegorematice puta gradu medio totius motus, <lb/>b. poña in illa quarta pertranſiret adequate vnam <lb/>quartam c. medii que eſt quatuor decime ſexte / vt pa­<lb/>tet ex ſecundo notato tertii capitis ſecundi tracta-<lb/>tus: ſed modo mouetur b. poña in illa quarta in ꝓ-­<lb/>portione ſupratripartiente q̈rtas velocius. </s>
              <s xml:id="N192C1" xml:space="preserve">igitur <lb/>modo pertranſit ī illa quarta ſeptem ſexdecimas. <lb/></s>
              <s xml:id="N192C7" xml:space="preserve">(quandoquidem ſeptem ſexdecimaruꝫ ad quatuor <lb/>ſexdecimas eſt ꝓportio ſupratripartiens quartas) / <lb/>et per conſequēs in fine illius prime quarte tempo­<lb/>ris in quo c. medium pertranſit b. poña eſt in fine ſe­<lb/>ptem ſexdecimarum ab ea pertranſitarum / qḋ fuit <lb/>probandum. </s>
              <s xml:id="N192D4" xml:space="preserve">Conſequentia patet cum maiore: et mi­<lb/>nor probatur / quia gradus medius motꝰ quo b. po­<lb/>tentia mouetur in illa quarta eſt in ꝓportione ſu-<lb/>pratripartiente quartas maior quam gradus me-<lb/>dius motus quo eadem b. potentia mouetur adeq̈-<lb/>te in tempore in quo c. ſpacium ſiue medium pertrã­<lb/>ſit: igitur b. poña in illa prima quarta mouetur ī ꝓ­<lb/>portione ſupratripartiente quartas velocius quã <lb/>in toto tempore quo c. mediuꝫ pertranſit / quod fuit <lb/>probandum. </s>
              <s xml:id="N192E9" xml:space="preserve">Antecedens probatur / quia motꝰ qui <lb/>ꝓuenit a ꝓportione quam habet b. poña ad pūctuꝫ <lb/>initiatiuum c. medii cum tribus quartis eiuſdem ꝓ­<lb/>portionis ad motum prouenientem a proportione <lb/>quam habet b. poña ad punctum initiatiuum c. me­<lb/>dii tantummodo eſt proportio ſupratripartiens <lb/>quartas / vt patet: quia inter illas ꝓportiones ē ꝓ-<lb/>portio ſupratripartiens quartas: igitur medietas <lb/>motus ꝓueniens a proportione quã habet b. poña <lb/>ad punctum initiatiuum c. medii cum tribus quar-<lb/>tis eiuſdem ꝓportionis adiunctis: eſt maior in pro­<lb/>portione ſupratripartiente quartas quam medie-<lb/>tas motus prouenientis a ꝓportione quam habet <lb/>b. poña ad punctū initiatiuum c. medii tantūmodo / <lb/>vt patet vndecima ſuppoſitione ſecundi capitis <lb/>ſecunde partis. </s>
              <s xml:id="N1930A" xml:space="preserve">ſed medietas motus prouenientis <lb/>a ꝓportione quam habet b. poña ad punctum īitia­<lb/>tiuum c. medii cum tribus eius quartis adiunctis ē <lb/>gradus medius motus / quod b. poña mouetur in il­               <cb chead="Capitulum nonum"/>               la prima quarta: et medietas motus ꝓuenientis a <lb/>ꝓportione quam habet b. potentia ad punctum in­<lb/>itiatiuum c. medii tantummodo eſt gradus medius <lb/>motus quo b. poña mouetur in tota hora adequa-<lb/>te: igitur gradus medius motus quo mouetur b. po­<lb/>tentia in illa prima quarta eſt maior in proportio­<lb/>ne ſupratriꝑtiente quartas quam gradus medius <lb/>motus quo mouetur eadem b. poña ī tempore ī quo <lb/>c. medium pertranſit / quod fuit probandum. </s>
              <s xml:id="N19326" xml:space="preserve">Conſe­<lb/>quentia patet cum maiore: et probatur maior quo <lb/>ad primam partem videlicet /  medietas motus ꝓ­<lb/>uenientis a proportione quaꝫ habet b. poña ad pū­<lb/>ctum initiatiuum c. medii cum tribus quartis eius <lb/>coniunctis eſt gradus medius motus quo mouetur <lb/>eadem poña b. in prima quarta: quia motus quo <lb/>mouetur b. poña in prima quarta incipit a motu ꝓ­<lb/>ueniente a proportione quam habet b. ad punctum <lb/>initiatiuum c. medii. </s>
              <s xml:id="N1933B" xml:space="preserve">et terminatur ad motum ꝓue-<lb/>nientem a tribus quartis eiuſdem proportionis / vt <lb/>patet intuenti: igitur medietas motus aggregati <lb/>ex motu proueniente a proportione quam habet b. <lb/>poña ad punctum initiatiuum c. medii et ex motu ꝓ­<lb/>ueniente ex tribus quartis eius eſt gradus medius <lb/>inter illos. </s>
              <s xml:id="N1934A" xml:space="preserve">Patet conſequentia ex primo correla-<lb/>rio prime concluſionis ſecundi capitis ſecunde ꝑ-<lb/>tis: et ꝑ conſequens medietas motus prouenientis <lb/>a proportione quam habet b. poña ad punctum in­<lb/>itiatiuum c. medii et tribus quartis eius adiunctis <lb/>eſt gradus medius motus quo mouetur b. poña ī il­<lb/>la prima quarta / quod fuit probandum. </s>
              <s xml:id="N19359" xml:space="preserve">Iam pro-<lb/>bo ſecundã ꝑtem minoris videlicet /  medietas mo­<lb/>tus ꝓuenientis a proportione quam habet b. poña <lb/>ad punctum initiatiuum c. medii eſt gradus mediꝰ <lb/>motus quo mouetur eadem b. poña in tempore in <lb/>quo c. medium pertranſit adequate: quia cuiuſlib3 <lb/>motus vniformiter difformis ad non gradum ter-<lb/>minati gradus medius eſt medietas motus remiſ-<lb/>ſiſſimi qui non eſt in illo motu totali vnifomiṫ dif­<lb/>formi / vt patet facile intelligenti tertium caput ſe-<lb/>cundi tractatus: ſed motus proueniens a propor-<lb/>tione quam habet b. poña ad punctum initiatiuum <lb/>c. medii eſt remiſſiimus qui non eſt in illo motu to-<lb/>tali quo mouetur adequate in tempore in quo c. me­<lb/>dium pertranſit: igitur gradus medius motus quo <lb/>mouetur in tempore. </s>
              <s xml:id="N1937A" xml:space="preserve">in quo b. poña c. medium ꝑtrã-<lb/>ſit eſt medietas motus prouenientis a proportio-<lb/>ne quam habet b. poña ad punctum initiatiuum c. <lb/>medii / quod fuit probandum. </s>
              <s xml:id="N19383" xml:space="preserve">Conſimiliter omnino <lb/>ꝓbabis in omnibus ſpeciebus ꝓportionum: videli­<lb/>cet /  inter punctum initiatiuum c. medii et punctum <lb/>intrinſecuꝫ ad quod b. poña habet in qua volueris <lb/>ſpecie ꝓportionis proportionem minorem, mediat <lb/>prima pars ꝓportionalis adequate c. medii diuiſi <lb/>in partes proportionales ꝓportione dupla ad il-<lb/>lam ſpeciem proportionis.</s>
            </p>
            <p xml:id="N19394">
              <s xml:id="N19395" xml:space="preserve">¶ Hoc ſuppoſito probatur antecedens / quod aſſum­<lb/>ptum eſt in replica. </s>
              <s xml:id="N1939A" xml:space="preserve">et ſit b. poña que c. medium inua­<lb/>riatum tranſeundo continuo vniformiter remittit <lb/>motum ſuum ad non gradum in extremo intenſiori <lb/>eiuſdem c. medii. </s>
              <s xml:id="N193A3" xml:space="preserve">et ſit a. poña maior quecū volue-<lb/>ris: cuius ꝓportio ad punctum initiatiuum c. medii <lb/>in extremo remiſſiori ſit in f. proportione maior ꝓ-<lb/>portione b. poñe ad idem punctum initiatiuuꝫ c. me­<lb/>dii et ponatur b. potentia ad punctum intrinſecum <lb/>c. medii ad quod habet proportionem in f. ꝓportio­<lb/>ne minorem ꝓportione eiuſdem b. poñe ad punctuꝫ <lb/>initiatiuum c. medii. </s>
              <s xml:id="N193B4" xml:space="preserve">et manifeſtū ē /  proportio ip-<lb/>ſius a. ad punctum initiatiuum c. medii eſt in dupli-<lb/>ci f. ꝓportione maior proportione ipſius b. ad illḋ               <pb chead="Primi tractatus" file="0095" n="95"/>               punctum intrinſecum c. medii. </s>
              <s xml:id="N193C0" xml:space="preserve">quia proportionis <lb/>a. ad punctum initiatiuum c. medii ad proportiõeꝫ <lb/>ipſius b. ad idem punctum initiatiuum eſt propor-<lb/>tio f. et proportionis ipſius b. ad punctum initiati-<lb/>uum c. medii ad proportionem eiuſdem b. ad pūctū <lb/>illud intrinſecum eſt etiam proportio f. / igitur pro-<lb/>portionis a. ad punctum initiatiuum c. medii ad ꝓ-<lb/>portionem ipſius b. ad punctum illud intrinſecum <lb/>eſt duplex proportio f. incipiant / igitur in eodem in­<lb/>ſtanti moueri b. ab illo puncto intrinſeco c. medii: et <lb/>a. a puncto initiatiuo continuo per ſui variationeꝫ <lb/>in duplici f. proportione velocius quam b. poña: et <lb/>arguo ſic / a. poña c. medium inuariatnm tranſeun-<lb/>do continuo vniformiter remittit motum ſuum: q2 <lb/>continuo in certa proportione velocius mouetur b. <lb/>poña continuo ſuum motum vniformiter remitten­<lb/>te: et a. et b. eque primo deueniet ad extremum inten­<lb/>ſius c. medii in quo b. remittit motum ſuum ad non <lb/>gradum: et a. potentia continuo ſucceſſiue remittit <lb/>potentiam ſuam: igitur tam a. quam .bc. medium ī­<lb/>uariatum tranſeundo continuo vniformiter remit­<lb/>tit motum ſuum ad non gradum in extremo intenſio­<lb/>ri a. continuo ſucceſſiue remittente poñam ſuam.</s>
            </p>
            <p xml:id="N193EF">
              <s xml:id="N193F0" xml:space="preserve">Conſequentia patet cum maiore / et minor probatur / <lb/>quia totius c. medii ad reſiduum a puncto intrinſe­<lb/>co ad quod ponitur b. poña eſt proportio dupla ad <lb/>ad proportionem f. et a. poña c. medium tranſeūdo <lb/>continuo in dupla ꝓportione ad f. velocius moue-<lb/>tur quam b. poña: igitur in eodem tempore a. poña <lb/>pertranſit totum c. medium in quo b. poña ꝑtranſit <lb/>reſiduum a puncto intrinſeco ad quod ponitur: et ꝑ <lb/>conſequēs a. et b. eque primo deuenerit ad extremū <lb/>intenſius c. medii / quod fuit probandum. </s>
              <s xml:id="N19405" xml:space="preserve">Conſequē­<lb/>tia patet cum minore: et maior ꝓbatur ex prima cõ­<lb/>cluſione quinti capitis prime partis, hoc addito /  <lb/>inter punctum initiatiuum c. medii et punctum intrī­<lb/>ſecum c. medii ad quod ponitur ipſa potentia b. me­<lb/>diat prima pars proportionalis c. medii diuiſi du­<lb/>plici proportione f. / quod patet ex hypotheſi iūcta <lb/>ſuppoſitione. </s>
              <s xml:id="N19416" xml:space="preserve">Sed  a. poña tranſeundo c. mediuꝫ <lb/>continuo ſucceſſiue remittit poñam ſuam eo modo <lb/>probatur / quo ſepius probatum eſt precedēti capi-<lb/>te: </s>
              <s xml:id="N1941F" xml:space="preserve">Et ſic patet aſſumptum.</s>
            </p>
            <p xml:id="N19422">
              <s xml:id="N19423" xml:space="preserve">Reſpondeo igitur ad argumentuꝫ cõ­<lb/>cedendo ſequelam et negando falſitatem conſequē­<lb/>tis: et ad probationem nego antecedens: et ad ꝓba-<lb/>tionem antecedentis nego /  hoc maxime fieret ca-<lb/>ſu quo b. potentia inciperet moueri a puncto initia ­<lb/>tiuo ſecunde partis ꝓportionalis c. medii diuiſi in <lb/>partes proportionales ꝓportione ſexquialtera: ſꝫ <lb/>illud fieret caſu quo b. potentia inciperet moueri a <lb/>puncto illo intrinſeco c. medii ad quod habet in du­<lb/>plo minorem proportionem ad proportionem quã <lb/>habet eadem potentia b. ad punctum initiatiuum <lb/>eiuſdem c. medii: vt ex deductione replice facile pro­<lb/>bari poteſt.</s>
            </p>
            <p xml:id="N1943E">
              <s xml:id="N1943F" xml:space="preserve">Quinto contra eandem concluſioneꝫ <lb/>arguitur ſic / quoniam vbi aliqua poña non varia-<lb/>ta tranſeundo medium inuariatum continuo vni-<lb/>formiter remittit motum ſuum ad non gradum. </s>
              <s xml:id="N19448" xml:space="preserve">om­<lb/>nis maior non variata in infinitum velociter remit­<lb/>tit motum ſuum in eodem medio verſus extremum <lb/>intenſius deueniendo: ſed ſi continuo talis potētia <lb/>maior verſus extremum intenſius deueniēdo remit­<lb/>teretur magis remitteret de motu ſuo quam ſi ſta-<lb/>ret: igitur omnis potentia maior que per tale medi­<lb/>um continuo remittitur in infinituꝫ velociter remit­<lb/>tit motum ſuum: et per conſequens non vniformiter               <cb chead="Capitulum nonum"/>               quod eſt contra concluſionem. </s>
              <s xml:id="N1945E" xml:space="preserve">Conſequentia patet <lb/>per locum a maiori: et maior eſt quinta concluſio ſe­<lb/>ptimi capitis huius tractatus: et minor ꝓbatur / q2 <lb/>potentia maior que continuo remittitur verſns ex-<lb/>tremum intenſius deueniendo maiorem latitudinē <lb/>motus deperdit tranſeundo aliquam partem ꝙ̄ de­<lb/>perderet eandem tranſeundo quando continuo ma­<lb/>neret iuuariata: igitur plus de latitudine motus de­<lb/>perdit quando remittitur ꝙ̄ quando non variatur <lb/></s>
              <s xml:id="N19472" xml:space="preserve">Antecedens probatur / quia quãlibet partem tran-<lb/>ſeundo quando remittitur maiorem proportioneꝫ <lb/>deperdit: quoniam deperdit ratione acquiſitionis <lb/>reſiſtentie tantam quantam deperderet ſi ſtaret īua­<lb/>riata: et inſuper perdit aliquam aliam proportio-<lb/>nem ratione remiſſionis ſue potentie. </s>
              <s xml:id="N1947F" xml:space="preserve">igitur maio-<lb/>rem proportionem deperdit tranſeundo aliquam ꝑ­<lb/>tem quando remittitur ꝙ̄ quando non remittitur. <lb/></s>
              <s xml:id="N19487" xml:space="preserve">et per conſequens maiorem latitudinem motus de­<lb/>perdit tranſeundo aliquam partem quando remit­<lb/>titur ꝙ̄ quando non variatur / quod fuit probandū</s>
            </p>
            <p xml:id="N1948E">
              <s xml:id="N1948F" xml:space="preserve">Reſpondeo breuiter concedendo ma-<lb/>iorem, et minorem, et negando conſequentiam. </s>
              <s xml:id="N19494" xml:space="preserve">Et <lb/>ratio eſt quia quamuis tranſeundo aliquam par-<lb/>tem verſus extremum intenſius deueniendo maio-<lb/>rem latitudinem motus deperdat quando remitti-<lb/>tur ꝙ̄ quando ſtat inuariata: nichilominus illam ꝑ­<lb/>dit tardius. </s>
              <s xml:id="N194A1" xml:space="preserve">Modo ad hoc /  conſequentia valeret <lb/>oportet aſſumere /  quando remittitur tranſeundo <lb/>aliquam partem velocius deperdit ſuam velocita-<lb/>tem ꝙ̄ quando ſtat vel eque velociter: et tunc conſe-<lb/>quentia valeret per locum a maiori: ſed tunc negã-<lb/>dum eſſet aſſumptum.</s>
            </p>
            <note position="right" xml:id="N194AE" xml:space="preserve">argumē-<lb/>tum cal-<lb/>culatorꝪ.</note>
            <p xml:id="N194B6">
              <s xml:id="N194B7" xml:space="preserve">Sexto contra quintam concluſioneꝫ <lb/>octaui capitis arguitur ſic / in caſu concluſionis a. <lb/>potentia minor variata que continuo intenditur in <lb/>infinitum tarde remittit motum ſuum verſus extre­<lb/>mum intenſius deueniendo: igitur non vniformiter <lb/>et per conſequens concluſio falſa. </s>
              <s xml:id="N194C4" xml:space="preserve">Conſequentia eſt <lb/>nota, et antecedens probatur, et pono /  ſimul cum <lb/>ipſa poña a. minore que intenditur īfinite maiores <lb/>ea: minores tamē ipſa poña b. (que inuariata c. me­<lb/>dium inuariatum tranſeundo vniformiter cõtinuo <lb/>remittit motum ſuum ad non graduꝫ) moueantur <lb/>non variate: taliter  continuo cuꝫ a. deuenerit ad <lb/>aliquod punctum c. medii ſit cum eadem potentia <lb/>a. aliqua illarum potentiarum non variatarū que <lb/>que pro eodem puncto et in eodem inſtanti ſit equa­<lb/>lis ipſi a. et in eodem inſtanti incipiant moueri ab <lb/>illo puncto verſus extremum intenſius ita  conti­<lb/>nuo a. ſit cum alia et alia illarum potentiarum que <lb/>pro tunc ſit equalis illi. </s>
              <s xml:id="N194E1" xml:space="preserve">Quo poſito ſic argumētor / <lb/>quelibet illarum potentiarum non variatarū qua­<lb/>rum quelibet eſt minor ipſa poña non variata ī ali­<lb/>quo puncto intrinſeco c. medii mouendo verſus ex-<lb/>tremum intenſius in infinitum tarde remittit mo-<lb/>tum ſuum: et poña a. que continuo intenditur, con-<lb/>tiuuo tardius remittit motum ſuum quam aliqua <lb/>illarum (et volo /  ly aliqua illarum ſtet preciſe con­<lb/>fuſe tantum non diſtributiue) / igitur ipſa potētia <lb/>a. in infinitum tarde remittit motum ſuum / quod fu­<lb/>it probandum: </s>
              <s xml:id="N194F8" xml:space="preserve">Conſequentia patet, et maior pro-<lb/>batur per ſextam concluſionem ſeptimi capitis pre­<lb/>allegati: et minorem ſic arguo / quoniam quocun ī­<lb/>ſtanti dato illius temporis in quo ſic mouentur il-<lb/>le potentie, potentia a. eſt ſimul cum aliqua illaruꝫ <lb/>potentiarum non variatarum in aliquo puncto in­<lb/>trinſeco c. medii / vt patet ex caſu: et incipiunt a. et il-<lb/>la alia pontentia non variata ab eodē pūcto tran­               <pb chead="Finis de motu penes cauſã in medio difformit̄̄ difformi." file="0096" n="96"/>               ſire idem ſpacium: et a. continuo intenditur: et alia <lb/>potentia nõ: ſed manet inuariata: igitur a. tardius <lb/>remittit motum ſuū quam illa potentia: et ſic potē-<lb/>tia a. continuo tardius remittit motum ſuū quam <lb/>aliqua illarum (eſto /  ly aliqua illarum ſtet confu­<lb/>ſe / vt dictum eſt). </s>
              <s xml:id="N19518" xml:space="preserve">Conſequentia tamen patet / q2 in-<lb/>tenſio potentie impedit remiſſionē motus: ſed ipſa <lb/>a. potentia continuo intenditur, alia vero potētia <lb/>nõ: igitur ſua intenſio impedit remiſſionem motus</s>
            </p>
            <p xml:id="N19521">
              <s xml:id="N19522" xml:space="preserve">Reſpondeo negando antecedens vi-<lb/>delicet /  a. in infinitū tarde remittit motum ſuū: et <lb/>ad probationē admiſſo caſu concedo maiorem: et <lb/>nego minorem. </s>
              <s xml:id="N1952B" xml:space="preserve">In nullo enim tēpore a. cõtinuo tar­<lb/>dius remittit motum ſuū quam aliqua illarum po­<lb/>tentiarum (etiam ſi ly aliqua illarum ſupponat cõ­<lb/>fuſe tantū) et ad probationem minoris nego conſe­<lb/>quentiã, et ad probationē nego /  vniuerſaliter in-<lb/>tenſio potentie impediat remiſſionem motus in eo­<lb/>dem tēpore. </s>
              <s xml:id="N1953A" xml:space="preserve">Uolo dicere /  ſtat /  due potentie ſint <lb/>equales, et incipiant ab eodē puncto remittere mo­<lb/>tum ſuū, et vna intenditur, et alia nõ: tamen illa que <lb/>intenditur velocius remittat motum ſuū ꝙ̄ illa que <lb/>nõ intenditur in eodem tempore. </s>
              <s xml:id="N19545" xml:space="preserve">Et etiã poteſt ſta-<lb/>re oppoſitum vt apparebit inferius: ſed bene con-<lb/>cedo /  intenſio potentie impedit remiſſionem ideꝫ <lb/>ſpacium adequate tranſeundo. </s>
              <s xml:id="N1954E" xml:space="preserve">Uolo dicere /  ſi a-<lb/>liqua potētia tranſeundo vnam certam partē illiꝰ <lb/>c. medii remitteret motum ſuū ſi maneret nõ varia-<lb/>ta: dico /  eandem partem tranſeundo quando in-<lb/>tenditur nõ tantū remitteret motum ſuū / vt ſepius <lb/>dictum eſt.               <anchor type="note" xlink:href="note-0096-01" xlink:label="note-0096-01a"/>               </s>
              <s xml:id="N19560" xml:space="preserve">Sed iſto modo intelligēdo probatio nõ <lb/>procedit / q2 velocitas et tarditas remiſſionis latitu­<lb/>dinis motus debet attendi penes tēpus in quo fit et <lb/>nõ penes ſpaciū in quo fit / vt ptꝫ in diffinitione ve-<lb/>locis et tardi ſexto phiſicorū.               <anchor type="note" xlink:href="note-0096-02" xlink:label="note-0096-02a"/>               </s>
              <s xml:id="N19570" xml:space="preserve">¶ Ex his ſequitur pri­<lb/>mo /  ſtat duas potētias equales incipere moueri <lb/>ab eodē puncto alicuiꝰ medii in eodē inſtanti ſus <lb/>idē punctū quarū vna intenditur, et alia nõ varia-<lb/>tur, et ſe habere tripliciter. </s>
              <s xml:id="N1957B" xml:space="preserve">Uno modo /  potentia <lb/>nõ variata remittat motum ſuū, et alia que intēdi-<lb/>tur in potētia continuo moueatur vniformiter, vt ſi <lb/>tantã ꝓportionē acquirat per intenſionē potentie <lb/>quantã deperdit per acquiſitionē reſiſtentie. </s>
              <s xml:id="N19586" xml:space="preserve">Scḋo <lb/>modo poſſunt ſe ita habere /  nõ variata continuo <lb/>remittat motum ſuū, et illa que intenditur continuo <lb/>intendat motū ſuū idē mediū tranſeundo: vt eſto  <lb/>maiorē proportionē acquirat per ſui intenſionem <lb/>quam deperdat per acquiſitionē reſiſtētie. </s>
              <s xml:id="N19593" xml:space="preserve">Tertio <lb/>modo poſſunt ſe habere taliter /  nõ variata conti­<lb/>nuo remittat motū ſuū, et altera que intenditur ſi-<lb/>militer continuo remittat motum ſuū: vt poſito  <lb/>illa que intēditur maiorē proportionem deperdat <lb/>per acquiſitionē reſiſtentie ꝙ̄ acquirat per intēſio­<lb/>nem potentie.               <anchor type="note" xlink:href="note-0096-03" xlink:label="note-0096-03a"/>               </s>
              <s xml:id="N195A7" xml:space="preserve">¶ Sequitur ſecundo /  ſtat duas po-<lb/>tētias equales incipere moueri ab eodē puncto ver­<lb/>ſus idem punctū medii per quod vtra cõtinuo re-<lb/>mittit motum ſuū: et vnam intendi et aliam manere <lb/>īuariatam: et tamen illam que intenditur tardius <lb/>remittere motum ſuū. </s>
              <s xml:id="N195B4" xml:space="preserve">Probatur / et ſit b. potentia <lb/>que nõ variata c. mediū īuariatū pertranſit vnifor­<lb/>miter cõtinuo remittando motum ſuū: et a. potētia <lb/>equalis ei ponatur in puncto intrinſeco c. medii ad <lb/>quod a. potentia habet in h. ꝓportione ꝓportionē <lb/>minorē quã b. potētia habeat ad punctū initiatiuū <lb/>c. medii: et moueatur b. potētia puncto initiatiuo <lb/>c. medii: et a. potentia ſimul a puncto intrinſeco ad <lb/>quod habet in h. ꝓportione ꝓportionē minorē: cõ-<lb/>tinuo in h. ꝓportione tardius mouendo quã b. po-<lb/>tentia: et manifeſtum eſt /  a. potentia cõtinuo vni-               <cb chead="Finis de motu penes cauſã in medio difformit̄̄ difformi."/>               formiter remittit motum ſuū in h. proportione tar­<lb/>dius ꝙ̄ b. potentia: et ante̄ b. attingat a. continuo <lb/>a. intēdit potentiã ſuam. </s>
              <s xml:id="N195D2" xml:space="preserve">Incipiat / igitur vna alia <lb/>potentia equalis ipſi a. ſimul in eodem inſtanti ab <lb/>eodem puncto verſus idem punctum inuariata mo­<lb/>ueri cum a. potentia intendente continuo poñaꝫ ſu­<lb/>am: et clarum eſt /  vtra illarum vniformiter re-<lb/>mittit motuꝫ ſuum: et a. potētia continuo intendēs <lb/>potentiam ſuam continuo in h. proportione tardi­<lb/>us / vt ex dictis in octauo capite facile ꝓbari poteſt: <lb/>igitur correlarium verum               <anchor type="note" xlink:href="note-0096-04" xlink:label="note-0096-04a"/>               </s>
              <s xml:id="N195EA" xml:space="preserve">¶ Sequitur tertio /  ſtat <lb/>duas potentias equales incipere moueri in eodem <lb/>inſtanti, ab eodem puncto, verſus idem punctum, <lb/>alicuius medii per quod vtra continuo remittit <lb/>motum ſuum: et vnam illarum manere inuariatam <lb/>et aliam continuo remitti: et tamen illam que con-<lb/>tinue remittitur velocius continuo remittere motū <lb/>ſuum. </s>
              <s xml:id="N195FB" xml:space="preserve">Probatur correlarium caſu prioris correla­<lb/>rii retento: hoc addito /  b. potētia ponatur in pū­<lb/>cto intrinſeco c. medii: et a. potētia equalis ei in pū-<lb/>cto initiatiuo: et ſimul in eodem inſtanti ab illis pū­<lb/>ctis incipiant moueri a. continuo in ea proportiõe <lb/>velocius in qua proportio ipſius a. ad punctū ini-<lb/>tiatiuū eſt maior proportione ipſius b. ad punctuꝫ <lb/>intrinſecum c. medii / ad quod ponitur cum alia po-<lb/>tentia ei equali inuariata. </s>
              <s xml:id="N1960E" xml:space="preserve">Quo poſito ex dictis in <lb/>octauo capite facile probatur correlarium. </s>
              <s xml:id="N19613" xml:space="preserve">Et hec <lb/>de motu penes cauſam in medio difformiter diffor­<lb/>mi variato, et inuariato, potentia variata, et quie-<lb/>ſcente, dicta ſufficiant.</s>
            </p>
            <div xml:id="N1961C" level="5" n="11" type="float">
              <note position="left" xlink:href="note-0096-01a" xlink:label="note-0096-01" xml:id="N19620" xml:space="preserve">pḣus .6. <lb/>phi.</note>
              <note position="left" xlink:href="note-0096-02a" xlink:label="note-0096-02" xml:id="N19628" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0096-03a" xlink:label="note-0096-03" xml:id="N1962E" xml:space="preserve">2. correĺ</note>
              <note position="right" xlink:href="note-0096-04a" xlink:label="note-0096-04" xml:id="N19634" xml:space="preserve">3. correl.</note>
            </div>
            <p xml:id="N1963A">
              <s xml:id="N1963B" xml:space="preserve">¶ Sequitur de motu locali penes <lb/>cauſam in medio vniformiter diffor-<lb/>mi q̇eſcente: potētia cõtinuo variata.</s>
            </p>
          </div>
          <div xml:id="N19642" level="4" n="10" type="chapter" type-free="capitulum">
            <head xml:id="N19647" xml:space="preserve">Capitulum decimum / in quo oſten-<lb/>ditur, et traditur noticia velocitatis <lb/>motus penes cauſam in medio vni-<lb/>formiter difformi quieſcente: poten-<lb/>tia continuo variata.</head>
            <p xml:id="N19652">
              <s xml:id="N19653" xml:space="preserve">COnſequenter dicēdum eſt de <lb/>velocitate motus / qui fit in medio vni-<lb/>formiter difformi quieſcente variata ta­<lb/>men continuo potentia: inſequendo calculatorē in <lb/>ſecūdo capitulo de medio nõ reſiſtēte: quãuis illud <lb/>caput nõ debet dici ſiue inſcribi de medio non reſi-<lb/>ſtente: q2 in eo non agitur niſi de medio vniformi-<lb/>ter difformiter reſiſtente. </s>
              <s xml:id="N19664" xml:space="preserve">¶ Ad inducendas igit̄̄ cõ-<lb/>cluſiones: vnicam premitto ſuppoſitionem.</s>
            </p>
            <p xml:id="N19669">
              <s xml:id="N1966A" xml:space="preserve">In omni latitudine vniformiter dif-<lb/>formi, oīm duaꝝ partiū equaliū extremū intēſiꝰ ꝑ <lb/>equalē latitudinē excedit extremū remiſſiꝰ. </s>
              <s xml:id="N19671" xml:space="preserve">Proba­<lb/>tur / q2 cuiuſlibet latitudinis vniformiter difformis <lb/>vtriuſ medietatis extremū intēſiꝰ per equalē la-<lb/>titudinem excedit extremum ſuū remiſſius: et cuiuſli­<lb/>bet tertie extremum intenſius per equalem latitudi­<lb/>nem excedit extremū remiſſius, et cuiuſlibet quarte <lb/>et cuiuſlibet quinte .etc̈. et ſic de quibuſcū aliis par­<lb/>tibus equalibus, ſiue partes aliquote ſint ſiue non <lb/>igitur in latitudine vniformiter difformi oīm dua-<lb/>rum partium equaliū extremū intenſius per equa-<lb/>lem latitudinem excedit extremū remiſſius. </s>
              <s xml:id="N19688" xml:space="preserve">Conſe-<lb/>quentia ptꝫ, et probatur antecedens, q2 captis dua­<lb/>bus medietatibus extremū intenſius intenſioris ꝑ <lb/>equalē latitudinē excedit extremū remiſſius eiuſdē: <lb/>ſicut extremū intēſius remiſſioris medietatis extre­<lb/>mū remiſſius eiuſdē remiſſioris medietatis vel nõ <lb/>gradū. </s>
              <s xml:id="N19697" xml:space="preserve">Quod probatur ſic / quia extremū intenſius <lb/>medietatꝪ remiſſioris eſt g̈dus mediꝰ inter extremū <lb/>intēſius intēſioris medietatis et extremū remiſſius               <pb chead="Primi tractatus" file="0097" n="97"/>               remiſſioris medietatis vt cõſtat: igitur per equaleꝫ <lb/>latitudinem diſtat ab vtra: et per conſequens per <lb/>quantum excedit extremū remiſſius medietatis re­<lb/>miſſioris cuius eſt extremuꝫ intenſiua, per tantum <lb/>exceditur ab extremo intenſiori intenſioris medie-<lb/>tatis cuiꝰ medietatis eſt extremū remiſſius. </s>
              <s xml:id="N196AD" xml:space="preserve">Patet <lb/>hec cõſequentia ex vltima ſuppoſitione ſecūdi capi­<lb/>tis ſecūde partis. </s>
              <s xml:id="N196B4" xml:space="preserve">Itē captis tribus tertiis per tan­<lb/>tum extremū intenſius remiſſioris tertie excedit ex­<lb/>tremū remiſſius eiuſdē tertie, per quantuꝫ extremū <lb/>intenſius tertie īmediate ſequētis excedit extremū <lb/>remiſſius eiuſdem tertie: et per quantum extremum <lb/>intenſius vltime tertie excedit extremum remiſſius <lb/>eiuſdem. </s>
              <s xml:id="N196C3" xml:space="preserve">Quod probatur ſic / quia extremū intenſiꝰ <lb/>tertie remiſſioris eſt gradus medius inter extremū <lb/>intenſius tertie īmediate ſequentis et extremum re-<lb/>miſſius remiſſioris tertie: igitur equali latitudine <lb/>diſtat ab extremo intenſiori tertie īmediate ſequē-<lb/>tis et ab extremo remiſſiori tertie remiſſioris: et per <lb/>cõſequens ille gradus medius per equalem latitu-<lb/>dinem excedit extremū remiſſius tertie remiſſioris <lb/>cuiꝰ eſt extremū intenſius ſicut exceditur ab extre-<lb/>mo intenſiori tertie īmediate ſequentis cuiꝰ eſt ex-<lb/>tremū remiſſius. </s>
              <s xml:id="N196DA" xml:space="preserve">Et iſto modo ꝓbabis /  extremuꝫ <lb/>intenſius ſecunde tertie per equalem latitudinem <lb/>excedit extremū remiſſius eiuſdem tertie: ſicut extre­<lb/>mū intenſius vltime tertie īmediate ſequentis exce­<lb/>dit ſuū extremum remiſſius. </s>
              <s xml:id="N196E5" xml:space="preserve">Et ſic habebis /  per <lb/>equalem latitudinem cuiuſlibet illarum tertiarum <lb/>extremum intenſius excedit extremum remiſſius <lb/>eiuſdem. </s>
              <s xml:id="N196EE" xml:space="preserve">Item captis duabus partibus equalibus <lb/>ſiue tribus, ſiue quattuor que nõ ſunt pars aut par­<lb/>tes aliquote: cuiuſlibet illarū extremū intēſius per <lb/>equalem latitudinē excedit ſuū extremū remiſſius. <lb/></s>
              <s xml:id="N196F8" xml:space="preserve">Quod ſic probatur / q2 captis duabus illarū īme-<lb/>diatis extremū intēſius remiſſioris partis eſt gra-<lb/>dus medius inter extremū intenſius intēſioris par­<lb/>tis et extremū remiſſius remiſſioris illarum: igitur <lb/>per equalem latitudinem diſtat ab extremo inten-<lb/>ſiori intēſioris partis et ab extremo remiſſiori par­<lb/>tis remiſſioris: et per conſequēs ille gradus mediꝰ <lb/>per equalem latitudinē excedit extremū remiſſius <lb/>remiſſioris partis illarum cuiꝰ eſt extremū intenſi­<lb/>us: et exceditur ab extremo intenſiori partis inten-<lb/>ſioris cuiꝰ eſt extremū remiſſius. </s>
              <s xml:id="N1970F" xml:space="preserve">Et iſto modo pro-<lb/>babis ſignatis tribus /  per equalē latitudinē ex-<lb/>tremū intenſius tertie excedit ſuū extremū remiſſiꝰ <lb/>et extremū intenſius ſecunde excedit ſuū extremum <lb/>remiſſius. </s>
              <s xml:id="N1971A" xml:space="preserve">Et ſic habebis /  cuiuſlibet illarū trium <lb/>partiū extremū intenſius per equalem latitudineꝫ <lb/>excedit extremū remiſſius. </s>
              <s xml:id="N19721" xml:space="preserve">Et ſic in omnibus aliis <lb/>partibus equalibꝰ operaberis. </s>
              <s xml:id="N19726" xml:space="preserve">Patet igitur ſup-<lb/>poſitio.               <anchor type="note" xlink:href="note-0097-01" xlink:label="note-0097-01a"/>               </s>
              <s xml:id="N19730" xml:space="preserve">¶ Ex quo ſequitur /  oīs potentia latitudi­<lb/>nem vniformiter difformē īuariatam pertranſiēs: <lb/>equales partes tranſeundo incipiēdo ab extremo <lb/>remiſſiori equalem latitudinē reſiſtentie adequate <lb/>acquirit. </s>
              <s xml:id="N1973B" xml:space="preserve">Probatur / q2 talis potentia tranſeundo <lb/>aliquam partē adequate, acquirendo reſiſtentiam <lb/>illã reſiſtentiã adequate acquirit per quã extremū <lb/>intenſius illius partis excedit extremum remiſſius <lb/>eiuſdem partis / vt ſatis conſtat: et cuiuſlibet partis <lb/>equalis (ex precedenti ſuppoſitione) extremū inten­<lb/>ſius per equalem latitudinem excedit extremum re­<lb/>miſſius: igitur talis potentia latitudinem reſiſten­<lb/>tie vniformiter difformem inuariatam pertranſi-<lb/>ens: equalem latitudinem reſiſtentie adequate ac-<lb/>quirit. </s>
              <s xml:id="N19752" xml:space="preserve">Et ſic ptꝫ correlarium.               <anchor type="note" xlink:href="note-0097-02" xlink:label="note-0097-02a"/>               </s>
              <s xml:id="N1975A" xml:space="preserve">¶ Sequitur ſecundo / <lb/> omnis potentia latitudinem reſiſteutie vniformi­<lb/>ter difformē īuariatã pertranſiens incipiendo ab               <cb chead="Capitulū decimū."/>               extremo intēſiori, equales partes tranſeūdo, equa­<lb/>lem latitudinē reſiſtentie adequate deperdit. </s>
              <s xml:id="N19766" xml:space="preserve">Ptꝫ / <lb/>quia incipiēdo ab extremo remiſſiori, equales par­<lb/>tes tranſeundo equalem latitudinē reſiſtentie ade-<lb/>quate acquirit / vt ptꝫ ex precedenti correlario: igit̄̄ <lb/>incipiendo ab extremo intenſiori, equales partes <lb/>tranſeundo equalem latitudinē reſiſteutie adequa­<lb/>te deperdit: quia in eiſdem partibus eandem lati-<lb/>tudinem reſiſtentie adequate deperdit quaꝫ antea <lb/>in eiſdem acquirebat. </s>
              <s xml:id="N19779" xml:space="preserve">Et ſic patet correlarium.</s>
            </p>
            <div xml:id="N1977C" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0097-01a" xlink:label="note-0097-01" xml:id="N19780" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0097-02a" xlink:label="note-0097-02" xml:id="N19786" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N1978C">
              <s xml:id="N1978D" xml:space="preserve">Hoc iacto fundamento ſit prima con-<lb/>cluſio. </s>
              <s xml:id="N19792" xml:space="preserve">Omnis potentia mouens continuo vnifor-<lb/>miter mediū vniformiter difforme īuariatum tran­<lb/>ſeundo incipiendo ab extremo remiſſiori: continuo <lb/>vniformiter intendit potentiam ſuam, ceteris iuua­<lb/>mentis ac impedimētis deductis. </s>
              <s xml:id="N1979D" xml:space="preserve">Probatur: ſit c. <lb/>mediū vniformiter difforme quod inuariatū a. po-<lb/>tentia vniformiter continuo mouendo ab f. propor­<lb/>tione pertranſeat ab extremo remiſſiori incipiēdo <lb/>moueatur continuo a. potentia ſecundū propor-<lb/>tionem quam habet ad īmediatem reſiſtentiam, ce­<lb/>teris aliis iuuaminibus et obſtaculis deductis: tūc <lb/>dico /  a. potentia cõtinuo vniformiter intendit po­<lb/>tentiam ſuam. </s>
              <s xml:id="N197B0" xml:space="preserve">Quod ſic oſtenditur / quia a. poten-<lb/>tia continuo ſe habet in f. proportione ad ſuam re-<lb/>ſiſtentiam. </s>
              <s xml:id="N197B7" xml:space="preserve">Nam a. potentia continuo ab f. propor­<lb/>tione mouetur ex hypotheſi: et ſua reſiſtentia conti-<lb/>nuo vniformiter creſcit: igitur a. potentia cõtinuo <lb/>vniformiter creſcit: et per conſequens a. potentia cõ­<lb/>tinuo vniformiter intendit potentiam ſuam / quod <lb/>fuit probandum. </s>
              <s xml:id="N197C4" xml:space="preserve">Patet hec cõſequentia ex proba-<lb/>tione prime ſuppoſitionis octaui capitis huiꝰ tra-<lb/>ctatus / hoc addito /  reſiſtentia eſt terminus minor <lb/>continuo proportionis f. et potentia a. terminꝰ ma-<lb/>ior. </s>
              <s xml:id="N197CF" xml:space="preserve">Probatur minor / quia a. potentia continuo in <lb/>equalibus partibus temporis equales partes illiꝰ <lb/>reſiſtentie vniformiter difformis pertranſit conti-<lb/>nuo acquirendo reſiſtentiam, quia mouetur conti-<lb/>nuo vniformiter verſus extremū intenſius: et conti-<lb/>nuo equales partes tranſeundo equalem latitudi-<lb/>nem reſiſtentie acquirit / vt ptꝫ ex primo correlario <lb/>ſuppoſitionis: igitur continuo in equalibus parti­<lb/>bus temporis equalem latitudinem reſiſtentie ac-<lb/>quirit: et per conſequens reſiſtentia ipſius a. poten­<lb/>tie vniformiter continuo creſcit / quod fuit proban-<lb/>dum. </s>
              <s xml:id="N197E8" xml:space="preserve">Et ſic patꝫ concluſio.               <anchor type="note" xlink:href="note-0097-03" xlink:label="note-0097-03a"/>               </s>
              <s xml:id="N197F0" xml:space="preserve">¶ Ex quo ſequitur /  oīs <lb/>potentia continuo mouens vniformiter, mediū vni­<lb/>formiter difforme inuariatum tranſeundo, incipi-<lb/>endo ab extremo intenſiori: continuo vniformiter <lb/>remittit potentiã ſuã: ceteris aliis deductis. </s>
              <s xml:id="N197FB" xml:space="preserve">Pro-<lb/>batur: ſit c. medium vt ſupra quod inuariatū a. po-<lb/>tentia vniformiter continuo mouendo ab f. propor­<lb/>tione pertranſeat ab extremo intenſiori incipiēdo / <lb/>tunc dico /  a. potentia continuo vniformiter remit­<lb/>tit potentiam ſuam. </s>
              <s xml:id="N19808" xml:space="preserve">Quod ſic oſtēditur / quia a. po­<lb/>tentia continuo ſe habet in f. proportione ad ſuam <lb/>reſiſtentiam (cum continuo moueatur ab f. propor-<lb/>tione ex hypotheſi) et ſua reſiſtentia vniformiter cõ­<lb/>tinuo decreſcit ſiue diminuitur: igitur a. potentia <lb/>continuo vniformiter remittit potentiam ſuã. </s>
              <s xml:id="N19815" xml:space="preserve">Pa­<lb/>tet cõſequentia ex probatione prime ſuppoſitionis <lb/>octaui capitis preallegati. </s>
              <s xml:id="N1981C" xml:space="preserve">Minor probatur / quia <lb/>a. potentia continuo in equalibus partibus tēpo-<lb/>ris equales partes illius reſiſtētie vniformiter dif-<lb/>formis pertranſit continuo deperdendo reſiſten-<lb/>tiam (cum continuo vniformiter moueatur verſus <lb/>extremū remiſſius ex hypotheſi) et continuo verſus <lb/>extremū remiſſius mouēdo, equales partes tran-<lb/>ſeūdo, equalē latitudinē oīno reſiſtētie deperdit / vt               <pb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato." file="0098" n="98"/>               patet ex ſecundo correlario ſuppoſitionis: igitur <lb/>a. potentia continuo in equalibus partibus tēpo-<lb/>ris equalem latitudinem reſiſtentie deperdit: et per <lb/>conſequens reſiſtentia ipſius a. potentie continuo <lb/>vniformiter decreſcit ſiue diminuitur / qḋ fuit pro-<lb/>bandum. </s>
              <s xml:id="N1983C" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <div xml:id="N1983F" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0097-03a" xlink:label="note-0097-03" xml:id="N19843" xml:space="preserve">3. correĺ.</note>
            </div>
            <note position="left" xml:id="N19849" xml:space="preserve">Prima <lb/>cõcluſio <lb/>calcula.</note>
            <p xml:id="N19851">
              <s xml:id="N19852" xml:space="preserve">Secunda concluſio. </s>
              <s xml:id="N19855" xml:space="preserve">Oīs potentia a <lb/>non gradu potentie creſcens continuo vniformiter <lb/>tranſeundo medium vniformiter difforme īuaria-<lb/>tum ad non gradū terminatum, incipiendo ab ex-<lb/>tremo remiſſiori: continuo vniformiter mouetur. <lb/></s>
              <s xml:id="N19861" xml:space="preserve">Probatur / ſit c. medium vniformiter difforme ad <lb/>non gradum terminatum vt in caſu concluſionis: <lb/>ſit a. potentia que a nõ gradu potentie continuo <lb/>vniformiter creſcens c. medium in d. tempore ade-<lb/>quate pertranſit, ab extremo remiſſiori incipiēdo <lb/>moueatur continuo ſecundum proportionem po­<lb/>tentie ad reſiſtentiam ſibi īmediatam ceteris dedu­<lb/>ctis: ſit etiam b. potentia que in eodem d. tēpore <lb/>adequate continuo vniformiter mouendo per ſui <lb/>variationem pertranſeat idem c. medium ab extre­<lb/>mo remiſſiori incipiendo: et manifeſtum eſt ex con-<lb/>cluſione precedenti b. potentiam a non gradu po-<lb/>tentie continuo vniformiter intendere potentiã ſuã <lb/></s>
              <s xml:id="N1987D" xml:space="preserve">Dico igitur tunc /  a. potentia continuo vniformi-<lb/>ter mouetur c. medium tranſeundo. </s>
              <s xml:id="N19882" xml:space="preserve">Quod ſic oſten­<lb/>ditur / quia a. et b. continuo eque velociter mouētur <lb/>oīno: et b. cõtinuo vniformiter mouetur tranſeundo <lb/>c. mediū / quod etiam pertranſit a. / vt patet ex hypo-<lb/>theſi: igitur a. potentia continuo vniformiter mo-<lb/>uetur c. medium tranſeundo / quod fuit probandum <lb/></s>
              <s xml:id="N19890" xml:space="preserve">Cõſequentia ptꝫ cum minore: et arguitur maior / q2 <lb/>a. et b. potentie cõtinuo ſunt in eodem puncto c. me­<lb/>dii: igitur cõtinuo eque velociter mouētur omnino <lb/></s>
              <s xml:id="N19898" xml:space="preserve">Cõſequentia ptꝫ: et probatur antecedens / quia ſi nõ <lb/>detur inſtans in quo a. ſit in pūcto citeriori, aut vl-<lb/>teriori: et ſit e. / et arguitur ſic / in e. inſtanti d. tēporis <lb/>a. eſt in puncto citeriori vel vlteriori ipſius c. medii <lb/>quam b. et a. et b. cõtinuo ſunt equalis potentie: igit̄̄ <lb/>nõ eque cito pertranſibūt c. medium / quod eſt cõtra <lb/>hypotheſim. </s>
              <s xml:id="N198A7" xml:space="preserve">Patet cõſequentia / q2 ſi a. eſt in pūcto <lb/>vlteriori: et cõtinuo eſt equalis b. / ſequitur /  citius <lb/>deueniet ad terminum c. medii quam b. et ſi in cite-<lb/>riori et cõtinuo eſt equalis ipſi b. / ſequitur /  tardiꝰ <lb/>deueniet ad terminū c. medii. </s>
              <s xml:id="N198B2" xml:space="preserve">Alias eadem potētia <lb/>vel equalis eque cito abſolueret totam reſiſtētiam <lb/>et partem eius adequate / quod eſt impoſſibile dedu­<lb/>ctis litigioſis captiūculis. </s>
              <s xml:id="N198BB" xml:space="preserve">Sed tã probo illas po-<lb/>tentias continuo eſſe equales / q2 detur oppoſitum <lb/>videlicet /  aliquãdo altera illarum ſit altera ma-<lb/>ior: et ſequitur cum cõtinuo vniformiter creſcant in <lb/>eodem tempore a nõ gradu potētie /  ipſa cõtinuo <lb/>erit maior: et per cõſequēs citius abſoluet c. mediū <lb/>quam altera / quod eſt contra hypotheſim. </s>
              <s xml:id="N198CA" xml:space="preserve">Patet <lb/>cõſequentia / quia potentia continuo maior maius <lb/>ſpacium pertranſit in eodem tēpore quam poten-<lb/>tia in eodē tēpore continuo minor ea.               <anchor type="note" xlink:href="note-0098-01" xlink:label="note-0098-01a"/>               </s>
              <s xml:id="N198D8" xml:space="preserve">¶ Et ſic patet <lb/>concluſio / que eſt prima calculatoris in ſecūdo eius <lb/>capite de medio non reſiſtente quam aliter nititur <lb/>demonſtrare: ſed ſaluo meliori iudicio demonſtra­<lb/>tio eſt inefficax. </s>
              <s xml:id="N198E3" xml:space="preserve">Innititur em̄ huic cõſequentie per <lb/>nullū tēpus terminatū ad principiū a. intendit mo­<lb/>tum ſuū nec remittit: ergo a. nun̄ intendit motum <lb/>ſuū aut remittit. </s>
              <s xml:id="N198EC" xml:space="preserve">Modo illa cõſequētia nõ eſt bona <lb/></s>
              <s xml:id="N198F0" xml:space="preserve">Stat em̄ /  a. potentia per nullū tēpus terminatuꝫ <lb/>ad inſtans initiatiuū intendat aut remittat motuꝫ <lb/>ſuū: et tamen per aliquod tēpus nõ terminatum ad <lb/>principium tēporis intēdat aut remittat motū ſuū               <cb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato."/>               </s>
              <s xml:id="N198FC" xml:space="preserve">Diuiſa em̄ hora per partes proportionales mino­<lb/>ribus verſus inſtans initiatiuū motus terminatis <lb/>a. potentia in qualibet impari intendente motum: <lb/>et in qualibet pari remittente: tunc per nullū tēpus <lb/>terminatum ad principium intendit motum ſuum: <lb/>nec per aliquod tale remittit: et tamen intendit mo­<lb/>tuꝫ ſuū: et remittit per aliquod tēpus nõ terminatū <lb/>ad principium temporis. </s>
              <s xml:id="N1990D" xml:space="preserve">Et hoc forte nare ſagaci­<lb/>ol faciens calculator adiecit ſecundam probationē <lb/>aſſumens /  a. potentia per nullum tempus inten-<lb/>dit motum ſuū nec remittit: ita arguens: quia ſi ſic <lb/>ſit illud inſtans c. in quo incipit iutendere motum <lb/>ſuū aut remittere: et ſit f. proportio ex qua cõtinuo <lb/>vniformiter mouebitur ante c. / et ſequitur /  conti-<lb/>nuo ante in f. proportione tardius creſcit reſiſtētia <lb/>̄ eius potentia .etc̈. </s>
              <s xml:id="N19920" xml:space="preserve">In qua probatione calculator <lb/>duo aſſumit dubia et probãda que aduerſarius de­<lb/>monſtrationem vndiqua certam et inuiolabilem <lb/>efflagitans negaret. </s>
              <s xml:id="N19929" xml:space="preserve">Aſſumit em̄ primo pro certo et <lb/>manifeſto /  aliquod eſt inſtans intrinſecum tēpo-<lb/>ris in quo primo incipit intendere motum ſuū aut <lb/>in quo primo incipit remittere motum ſuum ita  <lb/>nun̄ antea remittit nec intendit motum ſuum. </s>
              <s xml:id="N19934" xml:space="preserve">Ad <lb/>amuſſim vero omnia dubitabilia ſibi demonſtrari <lb/>expetens diceret nullum tale eſſe inſtans: ſicut con-<lb/>tingeret cum in qualibet parte pari intenderet in <lb/>qualibet vero impari remitteret / vt dictum eſt. </s>
              <s xml:id="N1993F" xml:space="preserve">Se-<lb/>cundo aſſumit /  ante illud c. inſtans intrinſecū a. <lb/>potentia mouetur vniformiter / quod eſt probandū <lb/></s>
              <s xml:id="N19947" xml:space="preserve">Et ſic ptꝫ modum illum probandi predictam con-<lb/>cluſionem inefficacem eſſe qui et ſi ſcientiam nõ ge-<lb/>neret magnam tamen fidem facit.</s>
            </p>
            <div xml:id="N1994E" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0098-01a" xlink:label="note-0098-01" xml:id="N19952" xml:space="preserve">Contra <lb/>calcula-<lb/>torē.</note>
            </div>
            <p xml:id="N1995C">
              <s xml:id="N1995D" xml:space="preserve">Tertia cõcluſio. </s>
              <s xml:id="N19960" xml:space="preserve">Si potentia que mo­<lb/>uetur vniformiter cõtinuo medium vniformiter <lb/>difforme īuariatum et ad nõ gradum terminatum <lb/>incipiendo ab extremo remiſſiori: et cõtinuo creſcē-<lb/>do vniformiter quouſ deueniat ad extremū intē-<lb/>ſius: et deīde retrograde moueatur verſus extremū <lb/>remiſſius cõtinuo vniformiter et eque velociter de-<lb/>creſcendo ſicut antea creuit: ipſa continuo vnifor-<lb/>miter mouebitur. </s>
              <s xml:id="N19973" xml:space="preserve">Probatur / ſit a. potentia que ab <lb/>extremo remiſſiori c. medii vniformiter difformis <lb/>nõ variati et ad nõ gradum terminati incipiendo, <lb/>continuo vniformiter mouetur per continuum ſue <lb/>potentie vniforme crementum, quo ad vſ ad extre­<lb/>mū intenſius ipſius c. medii deueniat / ad quod ha-<lb/>beat proportionē f. a qua antea continuo moueba­<lb/>tur: ſit b. potētia ei equalis que (vt oportet) ad idē <lb/>extremum intenſius habet f. proportionem. </s>
              <s xml:id="N19986" xml:space="preserve">Uarie-<lb/>tur igitur / ipſa b. potentia taliter continuo ab eodē <lb/>extremo intenſiori verſus remiſſius,  cõtinuo mo­<lb/>ueatur ab f. proportione: et a. ſimul in eodem inſtãti <lb/>incipiat moueri cum b. potentia verſus extremū re­<lb/>miſſius cõtinuo vniformiter et eque velociter remit-<lb/>tendo potentiam ſuam ſicut antea intendebat: ſit <lb/>g. tempus in quo a. antea vniformiter potentiã ſuã <lb/>intendebat totum c. medium adequate tranſeundo <lb/>et h. ſit tempus in quo adequate b. potentia pertrã­<lb/>ſit c. medium. </s>
              <s xml:id="N1999D" xml:space="preserve">Tunc dico /  a. ſic mouendo continuo <lb/>vniformiter mouetur. </s>
              <s xml:id="N199A2" xml:space="preserve">Quod ſic oſtēditur / q2 a. et b. <lb/>continuo eque velociter mouētur: et b continuo vni-<lb/>formiter mouet̄̄ ex hypotheſi: ergo a. vniformiṫ mo­<lb/>uetur cõtinuo / qḋ fuit ꝓbandū. </s>
              <s xml:id="N199AB" xml:space="preserve">Conſequentia ptꝫ cū <lb/>minore: et arguit̄̄ maior / q2 a. et b. poñe cõtinuo ſunt <lb/>in eodē pūcto c. medii: igr̄ a. et b. ↄ̨tinuo eque velociṫ <lb/>mouentur. </s>
              <s xml:id="N199B4" xml:space="preserve">Conſequentia patet: et probatur antece­<lb/>dens / quia ſi non: detur inſtans in quo a. ſit in pun-<lb/>cto vlteriori vel citeriori quam b. et ſit illud inſtans <lb/>e. / et argr̄ ſic in e. inſtãti a. potētia eſt in puncto vlte-               <pb chead="Primi tractatus" file="0099" n="99"/>               riori vel citeriori quam b. et a. continuo eſt equalis <lb/>ipſi b. et incipit ab eodē pūcto cū b. ſus idē pūctū <lb/>moueri per eandem reſiſtentiam .etc̈. / ergo eadē po-<lb/>tentia vel equalis eque cito tranſit aliquod totum <lb/>medium ſicut partem eius adequate / quod eſt īpoſſi­<lb/>bile. </s>
              <s xml:id="N199CC" xml:space="preserve">Conſequentia patet / quia ſi a. eſt in puncto ci-<lb/>teriori quam b. et eſt equalis continuo ipſi b. etc̈. / ſe-<lb/>quitur /  in eodem tēpore in quo a. pertranſit ſpa-<lb/>cium interceptum inter punctum initiatiuum c. me­<lb/>dii a quo incipit motus et punctum in quo a. eſt in <lb/>inſtãti e, b. pertranſit totum illud ſpaciū pertran-<lb/>ſitum ab a. et inſuper partem illam per quam b. pre­<lb/>cedit a. / ergo ſi a. eſt in pūcto citeriori quam b. et eſt <lb/>equalis continuo ipſi b. etc̈. / ſequitur /  eadem po-<lb/>tentia vel equalis eque cito tranſit aliquod totum <lb/>medium ſicut eius partem adequate. </s>
              <s xml:id="N199E3" xml:space="preserve">Et ſi a. ſit in vl­<lb/>teriori, et continuo eſt equalis ipſi b. etc̈. / ſequitur /  <lb/>in eodem tēpore adequate in quo b. pertranſit ade­<lb/>quate ſpacium interceptum inter punctum initia-<lb/>tiuum c. medii a quo incipit motus et punctū in quo <lb/>b. eſt in inſtanti e. ipſa a. potentia pertranſit totum <lb/>illud ſpacium pertranſitum ab ipſa potentia b. et <lb/>inſuper partem illam per quã ipſa potentia a. pre­<lb/>cedit potentiam b. / ergo ſi a. eſt in puncto vlteriori <lb/>quam b. et eſt continuo equalis ipſi b. etc̈. / ſequitur / <lb/> eadem potentia vel equalis eque cito tranſit ali-<lb/>quod totum medium, ſicut eius partem adequate. <lb/></s>
              <s xml:id="N199FD" xml:space="preserve">Iam probatur minor videlicet /  a. continuo eſt e-<lb/>qualis ipſi b. quia a. et b. in principio h. tēporis ſūt <lb/>equales, et tam a. quã b. in h. tempore continuo vni­<lb/>formiter remittitur vſ ad non gradum ſue poten­<lb/>tie: ergo continuo in h. tempore a. eſt equalis ipſi b. <lb/></s>
              <s xml:id="N19A09" xml:space="preserve">Conſequētia patet cum maiore: et probatur minor / <lb/>quia b. vniformiter remittit potentiam ſuam in h. <lb/>tempore ex correlario prime concluſionis, et ad nõ <lb/>gradum / vt patet ex correlario ſecunde cõcluſionis <lb/>et a. etiam in h. tempore cõtinuo vniformiter remit-<lb/>tit potentiam ſuam vſ ad non gradum: igitur tã <lb/>a. quam b. in h. tempore cõtinuo vniformiter remit-<lb/>titur vſ ad non gradum. </s>
              <s xml:id="N19A1A" xml:space="preserve">Conſequētia patet cum <lb/>maiore, et probatur minor, quia g. tēpus eſt equale <lb/>ipſi h. (cum tam in g. quam in h. adequate pertran-<lb/>ſeatur c. ſpacium continuo ab f. proportione / vt fa-<lb/>cile deducitur ex hypotheſi) et a. potentia continuo <lb/>vniformiter et eque velociter remittit potentiam ſu­<lb/>am in tēpore in quo mouetur retrograde ab extre-<lb/>mo intenſiori ſicut antea in g. tempore intendebat <lb/>omnino: et h. eſt tempus a cuius principio incipit a. <lb/>potentia retrograde moueri: et remittere potentiã <lb/>ſuam / vt patet ex hypotheſi: igitur a. potentia vni-<lb/>formiter continuo remittit potentiam ſuam in h. <lb/>tempore vſ ad non gradum / quod fuit probandū. <lb/></s>
              <s xml:id="N19A36" xml:space="preserve">Et ſic patet concluſio.</s>
            </p>
            <note position="left" xml:id="N19A39" xml:space="preserve">1. correĺ.</note>
            <p xml:id="N19A3D">
              <s xml:id="N19A3E" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  ſi talis po-<lb/>tentia que ſic vniformiter cõtinuo mouens, pertrã-<lb/>ſit illam reſiſtentiam vniformiter difformē incipi-<lb/>endo ab extremo remiſſiori ↄ̨tinuo vniformiter in-<lb/>tendendo potentiam ſuam, cum fuerit in termino <lb/>incipiat retrograde moueri ab extremo intenſiori <lb/>verſus remiſſius, vniformiter remittendo potentiã <lb/>ſuam, cõtinuo tamen tardius quam antea intende­<lb/>bat: ipſa potentia citius pertranſibit eandem reſi­<lb/>ſtentiam quam antea. </s>
              <s xml:id="N19A53" xml:space="preserve">Probatur facile et ponatur / <lb/> per idem medium vniformiter difforme inuaria-<lb/>tum ad non gradum terminatum, moueantur due <lb/>potentie puta a. et b. creſcentes a non gradu conti-<lb/>nuo vniformiter et eque velociter, incipiendo in eo-<lb/>dem inſtanti ab extremo remiſſiori: et manifeſtum <lb/>eſt /  eque velociter continuo mouebuntur eque cito               <cb chead="Capitulū decimū."/>               idem medium abſoluentes: cum igitur fuerint in ex­<lb/>tremo ītēſiori īcipiãt ſimĺ in eodē īſtãti retrograde <lb/>moueri ab extremo ītēſiori ſus remiſſiꝰ: et vna pu­<lb/>ta a. vniformiter et eque velociter adeq̈te remittēte <lb/>continuo potentiam ſuam ſicut antea intendebat, <lb/>alia puta b. continuo tardius ſuam potentiam re-<lb/>mittat quam antea. </s>
              <s xml:id="N19A71" xml:space="preserve">Quo poſito ſic arguit̄̄ ille due <lb/>potentie incipiunt in eodem inſtanti ab eodem pū-<lb/>cto moueri: et illa que tardius remittitur puta b. cõ­<lb/>tinuo erit maior altera (vt patet / quia modo ſunt e-<lb/>quales) et mouebuntur per eandem reſiſtentiã om-<lb/>nibus aliis impedimentis ſecluſis: igitur continuo <lb/>b. potentia que tardius remittit potentiam ſuam <lb/>precedit alteram et velocius ea mouetur, quia con-<lb/>tinuo erit maior, et in minori reſiſtentia, et per con-<lb/>ſequens citius deuenit ad terminum illius reſiſtē-<lb/>tie quam altera: et altera eque cito pertrãſit illam <lb/>ſicut antea / vt patet ex probatione precedentis con­<lb/>cluſionis: ergo illa que tardius continuo remittit <lb/>potentiam ſuam ꝙ̄ ãtea, citius pertranſit eandem <lb/>reſiſtentiam quam antea / quod fuit probanduꝫ. </s>
              <s xml:id="N19A90" xml:space="preserve">Et <lb/>ſic patet correlarium               <anchor type="note" xlink:href="note-0099-01" xlink:label="note-0099-01a"/>               </s>
              <s xml:id="N19A9A" xml:space="preserve">¶ Sequitur ſecundo /  b. po-<lb/>tentia que tardius remittitur altera / vt ponitur in <lb/>caſu precedentis correlarii: citius deuenit ad termi­<lb/>num illius medii quod retrograde pertranſit quã <lb/>ad non gradum remittatur. </s>
              <s xml:id="N19AA5" xml:space="preserve">Patet correlarium / q2 <lb/>b. citius deueniet ad terminuꝫ illius medii quã alia <lb/>potentia que velocius continuo remittitur: igitur <lb/>quando b. deuenerit ad terminum dicti medii, alia <lb/>potentia adhuc erit in puncto intrinſeco illius me-<lb/>dii: erit etiã aliqualis intenſionis, b. vero poten-<lb/>tia que continuo tardius remittitur pro tali inſtã-<lb/>ti maioris erit intenſionis: igitur b. potentia que <lb/>tardius remittitur citius deuenit ad terminū illius <lb/>medii / quod retrograde pertranſit ꝙ̄ ad non gra-<lb/>dum remittatur. </s>
              <s xml:id="N19ABC" xml:space="preserve">Et ſic patet correlarium.</s>
            </p>
            <div xml:id="N19ABF" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0099-01a" xlink:label="note-0099-01" xml:id="N19AC3" xml:space="preserve">2. correĺ.</note>
            </div>
            <note position="right" xml:id="N19AC9" xml:space="preserve">3. correĺ.</note>
            <p xml:id="N19ACD">
              <s xml:id="N19ACE" xml:space="preserve">¶ Sequitur tertio /  in caſu primi correlarii b. po-<lb/>tentia que continuo tardius remittitur: continuo <lb/>intendit motum ſuū. </s>
              <s xml:id="N19AD5" xml:space="preserve">Probatur / quia continuo re-<lb/>ſiſtentia cum qua mouetur b. maiorem proportio-<lb/>nem deperdit quam ipſa potentia b. per ſui dimi-<lb/>nutionem: igitur continuo proportio inter b. potē-<lb/>tiam et reſiſtentiã cum qua mouetur augetur: et per <lb/>conſequens continuo b. potentia intendit motum <lb/>ſuum / quod fuit probandum. </s>
              <s xml:id="N19AE4" xml:space="preserve">Conſequentia patet <lb/>ex ſecundo correlario ſecunde concluſionis octaui <lb/>capitis ſecunde partis / hoc addito /  reſiſtentia eſt <lb/>terminus minor, et potentia terminus maior. </s>
              <s xml:id="N19AED" xml:space="preserve">Pro­<lb/>batur antecedens / quia reſiſtentia cum qua moue-<lb/>tur b. continuo maiorem proportionem deperdit <lb/>quam reſiſtentia cum qua mouetur a. et reſiſtentia <lb/>cum qua mouetur a. continuo equalem proportio-<lb/>nem deperdit ſicut ipſa potentia a. / vt patet ex ſecū­<lb/>da parte primi correlarii quarte concluſionis octa­<lb/>ui capitis preallegati </s>
              <s xml:id="N19AFE" xml:space="preserve">(Continuo enim inter a. po-<lb/>tentiam et ſuam reſiſtentiã eſt eadem proportio, a. <lb/>et ſua reſiſtentia continuo deſcreſcentibus) et a. po-<lb/>tentia continuo maiorem proportionem deperdit <lb/>quam b. / vt patet ex ſecunda parte octaue ſuppoſi-<lb/>tionis quarti capitis ſecunde partis iuncto loco a <lb/>maiori (continuo enim a. potētia minor eſt ipſa b. <lb/>potentia: et continuo maiorem latitudinem deper-<lb/>dit / vt patet probatione primi correlarii huius) / <lb/>igitur continuo reſiſtentia cum qua mouetur b. ma­<lb/>iorem proportioneꝫ deperdit quam ipſa potentia <lb/>b. / quod erat probandum. </s>
              <s xml:id="N19B17" xml:space="preserve">Patet hec conſequentia <lb/>per hoc /  quicquid eſt aliquo maius eſt quolibet <lb/>minori illo maius: hoc addito /  continuo propor­<lb/>tio deperdita a reſiſtentia ipſius b. eſt maior pro-               <pb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato." file="0100" n="100"/>               portione deperdita ab ipſa potentia a. et continuo <lb/>proportio deperdita ab ipſa potentia a. eſt adhuc <lb/>maior proportione deperdita ab ipſa potentia b. <lb/></s>
              <s xml:id="N19B2A" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <note position="left" xml:id="N19B2D" xml:space="preserve">4. correĺ.</note>
            <p xml:id="N19B31">
              <s xml:id="N19B32" xml:space="preserve">¶ Sequitur quarto:  illa potentia b. que tardius <lb/>remittitur deueniens verſus non gradum talis me­<lb/>dii ſiue reſiſtentie: in infinitum velociter mouebi-<lb/>tur: in infinitum velociter intendit motum ſuum. <lb/></s>
              <s xml:id="N19B3C" xml:space="preserve">Patet hoc correlariū / et capio gradū quē habebit <lb/>talis potentia b. in fine: et ſit vt .2. (gratia exempli) / <lb/>et arguo ſic / quãdo potentia b. erit in gradu reſiſten­<lb/>tie vt vnū in illa reſiſtentia terminata ad nõ gradū <lb/>mouebitur a ꝓportione dupla, et in ſubduplo gra­<lb/>du reſiſtentie mouebitur a dupla ꝓportione ad du-<lb/>plam puta a quadrupla, et in ſubduplo ad illum a <lb/>proportione octupla, et ſic in īfinitū ꝓcedendo per <lb/>ꝓportiões denoīatas a numeris pariter paribus / <lb/>igitur ab infinita ꝓportione mouetur b. veniendo <lb/>verſus nõ gradū talis reſiſtentie: et ꝑ cõſequens in <lb/>infinitū velociter mouetur. </s>
              <s xml:id="N19B55" xml:space="preserve">Et ſic ptꝫ ſecunda pars <lb/>correlarii videlicet /  in infinitū velociter intendit <lb/>motum ſuū. </s>
              <s xml:id="N19B5C" xml:space="preserve">Ptꝫ igr̄ correlariū.               <anchor type="note" xlink:href="note-0100-01" xlink:label="note-0100-01a"/>               </s>
              <s xml:id="N19B64" xml:space="preserve">¶ Sequitur quinto /  <lb/>ſi aliq̈ potētia / q̄ mouet̄̄ vniformiṫ mediū vniformi-<lb/>ter difforme terminatū ad nõ gradū pertranſeun-<lb/>do per continuū ſue potentie vniforme crementum <lb/>incipiēdo ab extremo remiſſiori, incipiat retrogra­<lb/>de moueri ab extremo intenſiori verſus remiſſius <lb/>vniformiter continuo remittendo potentiaꝫ ſuam <lb/>velocius tamen quam antea intendebat: talis po-<lb/>tentia tardius cõtinuo mouebitur quã antea moue­<lb/>batur tranſeūdo illã reſiſtentiam. </s>
              <s xml:id="N19B79" xml:space="preserve">Et ſic mouendo, <lb/>velociꝰ quã antea vniformiter potētiã ſuã remittēs <lb/>nõ ſufficit venire ad terminū illius reſiſtētie. </s>
              <s xml:id="N19B80" xml:space="preserve">Pro-<lb/>batur ſint a. et b. due potētie equales / q̄ ab extremo <lb/>remiſſiori verſus intenſius extremū c. medii vnifor-<lb/>miter difformis terminati ad nõ gradū moueãtur <lb/>continuo vniformiter per ſue potentie continuū et <lb/>vniforme crementū quo ad vſ deueniant ad termi­<lb/>nū c. medii: cum igitur fuerint in extremo intenſiori <lb/>incipiant retrograde moueri in eodē inſtanti ab ex­<lb/>tremo intenſiori verſus remiſſiꝰ: et vna puta a. vni-<lb/>formiter et eque velociter mouente ſicut antea et vni­<lb/>formiter et eque velociter adequate remittente po-<lb/>tentiã ſuã ſicut antea intendebat: alia puta b. con-<lb/>tinuo velocius vniformiter remittat potentiã ſuaꝫ <lb/>quã antea. </s>
              <s xml:id="N19B9D" xml:space="preserve">Quo poſito argr̄ ſic / prima pars corre-<lb/>larii q2 a. et b. in principio motus retrogradi ſunt <lb/>equales: et b. continuo erit minor: igitur continuo <lb/>tardius mouetur ꝙ̄ a. (cū moueantur per eandē re-<lb/>ſiſtentiã) / et per cõſequens tardius mouetur quã an-<lb/>tea mouebatur q2 a. ita velociter mouetur modo ſi­<lb/>cut antea adequate mouebatur b. / vt ptꝫ. </s>
              <s xml:id="N19BAC" xml:space="preserve">Et ſic ptꝫ <lb/>prima pars. </s>
              <s xml:id="N19BB1" xml:space="preserve">Secūda pars ꝓbatur / q2 cū b. cõtinuo <lb/>tardius moueatur ꝙ̄ a. / vt ptꝫ ex prima parte huius <lb/>correlarii: et incipiant in eodē inſtanti ab eodē pun­<lb/>cto verſus eandē differentiã moueri, cū ceteris po-<lb/>ſitis in caſu, ſequitur /  cum a. fuerit in termino, b. <lb/>nondū erit in termino: ſed in aliquo puncto intrin­<lb/>ſeco illius reſiſtentie: et tunc iam a. potentia erit re­<lb/>miſſa ad nõ gradū: igitur tunc b. potentia iam erit <lb/>remiſſa ad nõ gradum / vt ptꝫ ex caſu per locū a ma­<lb/>iori: et ſi tunc a. potentia erit remiſſa ad non gradū <lb/>iam non poterit ſic ad non gradum remiſſa vlteriꝰ <lb/>moueri vt deueniat ad terminū illius reſiſtentie / qḋ <lb/>fuit probandum. </s>
              <s xml:id="N19BCC" xml:space="preserve">Et ſic ptꝫ correlarium.</s>
            </p>
            <div xml:id="N19BCF" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0100-01a" xlink:label="note-0100-01" xml:id="N19BD3" xml:space="preserve">5. correĺ.</note>
            </div>
            <note position="left" xml:id="N19BD9" xml:space="preserve">Decima <lb/>cõcluſio <lb/>calcu.</note>
            <p xml:id="N19BE1">
              <s xml:id="N19BE2" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N19BE5" xml:space="preserve">Si ab extremo re-<lb/>miſſiori medii vniformiter difformis ad nõ gradū               <cb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato."/>               terminati incipiat aliqua potentia moueri a non <lb/>gradu intendendo potentiam ſuam, continuo ve-<lb/>locius et velocius: ipſa continuo intendit motum <lb/>ſuum. </s>
              <s xml:id="N19BF3" xml:space="preserve">Et ſi tardius et tardius continuo intendatur <lb/>ipſa continuo remittet motum ſuum. </s>
              <s xml:id="N19BF8" xml:space="preserve">Probatur <lb/>prima pars. </s>
              <s xml:id="N19BFD" xml:space="preserve">Sit a. potentia que c. medium tranſe-<lb/>undo / vt ponitur in concluſione: continuo velocius <lb/>et velocius intendat potentiam ſuam a non gradu <lb/>etc̈. </s>
              <s xml:id="N19C06" xml:space="preserve">Tunc dico /  a. potentia continuo intendit mo-<lb/>tum ſuum c. medium tranſeundo. </s>
              <s xml:id="N19C0B" xml:space="preserve">Quod ſic oſtendi­<lb/>tur / quia a. nun̄ vniformiter mouetur: quia alias <lb/>tunc vniformiter intenderet potentiam ſuam (vt pa­<lb/>tet ex prima concluſione) quod tamen eſt contra hy­<lb/>potheſim. </s>
              <s xml:id="N19C16" xml:space="preserve">Nec continuo remittit motum ſuum: nec <lb/>aliquando intendit: et aliquando remittit aut econ­<lb/>tra: igitur continuo a. potentia intendit motum ſu­<lb/>um c. medium tranſeundo / quod fuit probandum: <lb/>Cõſequentia cum maiore patet. </s>
              <s xml:id="N19C21" xml:space="preserve">Et probatur pri-<lb/>ma pars minoris videlicet /  a. nõ continuo remit-<lb/>tit motum ſuum: quia ſi ſic: capio vnam partem il-<lb/>lius temporis per quod continuo remittit termina­<lb/>tam ad principium totius temporis: et ſit propor-<lb/>tio f. quam habet a. ad ſuam reſiſtentiam in inſtan­<lb/>ti medio illius partis. </s>
              <s xml:id="N19C30" xml:space="preserve">Et arguo ſic / in fine ſecunde <lb/>medietatis illius partis a. habet maiorem propor­<lb/>tionem quam f. ad ſuã reſiſtentiam: igitur propor-<lb/>tio a qua mouetur a. non continuo diminuitur: et <lb/>ꝑ conſequens a. non continuo remittit motum ſuū <lb/></s>
              <s xml:id="N19C3C" xml:space="preserve">Patet conſequentia: et probatur antecedens / quia <lb/>inter acquiſitum potentie et acquiſitum reſiſtentie <lb/>in ſecunda medietate illius partis temporis eſt ma­<lb/>ior proportio quam f. et in principio illius medie-<lb/>tatis ſecunde inter potentiã et reſiſtentiam eſt pro-<lb/>portio f. adequate ex caſu: igitur in fine ſecunde me­<lb/>dietatis illius partis ipſa potentia a. habet maio­<lb/>rem proportionem quã f. ad ſuam reſiſtentiã: quod <lb/>erat inferendum: ↄ̨ſequētia ptꝫ ex tertio correlario <lb/>quarte concluſionis octaui capitis ſecunde partis <lb/></s>
              <s xml:id="N19C52" xml:space="preserve">Et probatur antecedens / quia in illa ſecunda me-<lb/>dietate maiorem latitudinē potentie acquirit ꝙ̄ eſt <lb/>tota illa quam acquiſiuit in prima (cum continuo <lb/>velocius creſcat ex hypotheſi) et reſiſtentia minorē <lb/>latitudinem acquirit in illa ſecunda medietate ̄ <lb/>eſt tota illa quã acquiſiuit in prima: quia per te tar­<lb/>dius a. mouetur in ſecunda ꝙ̄ in prima: et equales <lb/>partes c. medii tranſeūdo equales latitudines ade­<lb/>quate acquirit ſua reſiſtentia: igitur inter acquiſi-<lb/>tum potentie et acquiſitū reſiſtentie in ſecunda me-<lb/>dietate illius partis temporis eſt maior proportio <lb/>̄ f. / patet ↄ̨ſequētia / q2 ſi in illa ſcḋa medietate ac-<lb/>quireret tantam potentiam ſicut in prima, et tantã <lb/>reſiſtentiam etiam ſicut in prima: tunc inter illa ac­<lb/>quiſita eſſet proportio f. / igitur ſi maiorem poten-<lb/>tiam acquirit ꝙ̄ tunc et minorem reſiſtentiã ꝙ̄ tunc <lb/>inter acquiſitum potentie et acquiſitum reſiſtentie <lb/>in ſecunda medietate illius temporis eſt maior pro­<lb/>portio ꝙ̄ f. </s>
              <s xml:id="N19C79" xml:space="preserve">Iam probo ſecundam partem minoris <lb/>videlicet /  non aliquando intendit: et aliquando <lb/>remittit. </s>
              <s xml:id="N19C80" xml:space="preserve">Quia ſi poſt̄ intendit remittit motum <lb/>ſuum detur tempus per quod remittit poſt̄ im-<lb/>mediate antea intendebat: et capio vnum inſtans <lb/>in illo tempore remiſſionis in quo habet a. talem <lb/>proportionem qualem habebat antea quando in-<lb/>tendebat motum que ſit f. </s>
              <s xml:id="N19C8D" xml:space="preserve">Et arguo ſic / in aliquo tē­<lb/>pore immediate ſequente illud inſtans in quo a. ha­<lb/>bet proportionem f. ad ſuam reſiſtentiam inter ac-<lb/>quiſitum potentie et inter acquiſitum reſiſtētie erit <lb/>maior proportio quã f. / ergo ſequit̄̄ /  proportio f.               <pb chead="Primi tractatus" file="0101" n="101"/>               intēditur / et per conſequens motus non remittitur: <lb/>patet cõſequētia ex tertio correlario quarte cõclu-<lb/>ſionis octaui capitis ſecūde partis: antecedēs pro­<lb/>batur / q2 in aliquo tēpore īmediate ſequēte illud in­<lb/>ſtans in quo a. habet ꝓportionē f. ad ſuã reſiſten-<lb/>tiã, potētia velociꝰ creſcit ꝙ̄ antea quãdo intende-<lb/>bat motū in aliquo tēpore equali īmediate ſequē-<lb/>te inſtans in quo habuit f. ꝓportionē: et reſiſtentia <lb/>tardiꝰ ſibi creſcit ꝙ̄ antea in tanto tēpore poſcã ha­<lb/>buit f. ꝓportionē. </s>
              <s xml:id="N19CAF" xml:space="preserve">Sed antea quãdo intēdebat mo-<lb/>tū in equali tēpore īmediate ſequēte inſtãs in quo <lb/>a. habuit f. proportionē inter acquiſitū potentie et ac-<lb/>quiſitū reſiſtentie erat maior ꝓportio ꝙ̄ f. / ergo in <lb/>tanto tēpore īmediate ſequēte illud inſtans in tem­<lb/>pore remiſſionis in quo inſtanti a. habet ꝓportio-<lb/>nē f. ad ſuã reſiſtentiã inter acquiſitū potentie et ac-<lb/>quiſitū reſiſtentie erit maior ꝓportio ꝙ̄ f. / ptꝫ con-<lb/>ſequētia per locū a maiori. </s>
              <s xml:id="N19CC2" xml:space="preserve">Probatur tertia pars <lb/>minoris videlicet /  nõ aliquãdo remittit et aliquã­<lb/>do poſtea intēdit: q2 ſi ſic detur inſtãs in quo poſcã <lb/>remiſit incipit intēdere. </s>
              <s xml:id="N19CCB" xml:space="preserve">Et arguo ſic / vel ſemꝑ ante <lb/>illud inſtans remitebãt vel aliquãdo intendebat et <lb/>poſtea remittebat. </s>
              <s xml:id="N19CD2" xml:space="preserve">Sed nõ primum vt dicit prima <lb/>pars minoris: nec ſcḋm vt dicit ſecūda pars mino­<lb/>ris: ergo nõ aliquando remittit, et poſtea intendit / <lb/>quod fuit inferendū: ptꝫ cõſequētia: et maior ꝓba-<lb/>tur / q2 nõ vniformiter mouebitur / vt ptꝫ ex prima cõ­<lb/>cluſione huiꝰ. </s>
              <s xml:id="N19CDF" xml:space="preserve">Et ſic ꝓbabis aliã partē cõcluſionis <lb/>paucis mutatis: ptꝫ igitur concluſio.</s>
            </p>
            <p xml:id="N19CE4">
              <s xml:id="N19CE5" xml:space="preserve">Quinta cõcluſio. </s>
              <s xml:id="N19CE8" xml:space="preserve">Si ab aliquo pūcto <lb/>medii vniformiter difformis incipiat aliqua poña <lb/>per ſue potētie cõtinuū vniforme crementū cõtinuo <lb/>vniformiter moueri, et potētia equalis ei cõſimili-<lb/>ter oīno creſcēs incipiat a pūcto remiſſiori moueri <lb/>in eodē medio: talis potētia cõtinuo remittit motū <lb/>ſuū. </s>
              <s xml:id="N19CF7" xml:space="preserve">Et ſi eadē potentia inciperet moueri a puncto <lb/>inteſiori illiꝰ medii: ipſa cõtinuo intenderet motum <lb/>ſuū. </s>
              <s xml:id="N19CFE" xml:space="preserve">Probatur prima pars cõcluſionis / ſit a. potē-<lb/>tia que vniformiter cõtinuo mouetur c. mediū vni-<lb/>formiter difforme ad nõ gradū terminatū trãſeū-<lb/>do per ſue potentie vniforme cõtinuū crementū, in <lb/>puncto intrinſeco eiuſdē c. medii exiſtens: ſit b. po­<lb/>tentia ei equalis in pūcto remiſſiori eiuſdē c. medii <lb/>exiſtens oīno cõſimiliter creſcens cū a. et moueãtur <lb/>a. et b. ab illis pūctis verſus extremum intenſius c. <lb/>medii: tūc dico /  b. cõtinuo remittit motum ſuum. <lb/></s>
              <s xml:id="N19D12" xml:space="preserve">Quod ſic ꝓbatur / q2 ꝓportio ipſiꝰ b. ad ſuã reſiſtē-<lb/>tiã cõtinuo diminuit̄̄: ergo b. ↄ̨tinuo remittit motū <lb/>ſuū. </s>
              <s xml:id="N19D19" xml:space="preserve">Cõſequentia ptꝫ: et ãtecedēs ꝓbatur / q2 cõtinuo <lb/>reſiſtentia ipſiꝰ b. maiorē ꝓportionē acquirit quã <lb/>ipſa b. potētia: igitur cõtinuo ꝓportio ipſius b. ad <lb/>ſuã reſiſtentiã diminuitur. </s>
              <s xml:id="N19D22" xml:space="preserve">Patet conſequentia ex <lb/>ſecūda parte primi correlarii tertie ↄ̨cluſiõis octa­<lb/>ui capitis ſecūde partis: hoc addito /  b. potentia <lb/>eſt terminus maior et ſua reſiſtentia terminꝰ minor <lb/></s>
              <s xml:id="N19D2C" xml:space="preserve">Antecedens ꝓbatur / q2 cõtinuo reſiſtentia ipſiꝰ b. <lb/>maiorē ꝓportionē acquirit quã reſiſtentia ipſiꝰ a. <lb/>et cõtinuo reſiſtentia ipſius a. et ipſa b. potētia ac-<lb/>quirunt equalē ꝓportionē: igitur cõtinuo reſiſten-<lb/>tia ipſius b. maiorē proportionē acquirit ꝙ̄ ipſa b. <lb/>potentia / quod fuit ꝓbandū. </s>
              <s xml:id="N19D39" xml:space="preserve">Patet cõſequētia per <lb/>hoc /  illud quod aliquo eſt maius: eſt quolibet illi <lb/>equali maius. </s>
              <s xml:id="N19D40" xml:space="preserve">Et maior ꝓbatur / q2 cõtinuo b. potē-<lb/>tia velocius et per minorē reſiſtentiã mouetur ꝙ̄ a. <lb/>potētia: igitur cõtinuo reſiſtētia ipſius b. potentie <lb/>maiorē ꝓportionē acquirit ꝙ̄ reſiſtentia ipſius a. <lb/></s>
              <s xml:id="N19D4A" xml:space="preserve">Cõſequentia patet ex octaua ſuppoſitione quarti <lb/>capitis ſecūde partis iuuamine loci a fortiori. </s>
              <s xml:id="N19D4F" xml:space="preserve">Et               <cb chead="Capitulū decimū."/>               antecedens ptꝫ / q2 b. potentia cõtinuo equalis ipſi <lb/>a. mouetur continuo per reſiſtentiã nõ gradui c. me­<lb/>dii pinquiorē ꝙ̄ a. potentia / vt ptꝫ ex caſu: igitur <lb/>cõtinuo b. potentia velocius et per minorē reſiſten-<lb/>tiã mouetur ꝙ̄ a. potentia / quod fuit ꝓbandū. </s>
              <s xml:id="N19D5D" xml:space="preserve">Sed <lb/>iam ꝓbo minorē videlicet /  cõtinuo reſiſtentia ip-<lb/>ſius a. et ipſa b. potentia acquirūt equalē ꝓportio-<lb/>nem: q2 cõtinuo reſiſtentia ipſius a. et ipſa a. poten­<lb/>tia eqnalē ꝓpottionē acquirūt / vt ptꝫ ex ſecūda par­<lb/>te primi correlarii quarte concluſionis octaui ca-<lb/>pitis preallegati (cū a. potētia cõtinuo moueatur <lb/>ab eadem ꝓportione ipſa a. poteutia et ſua reſiſtē­<lb/>tia continuo creſcentibus) et ipſa a. potētia et ipſa <lb/>b. potentia continuo ſimiliter equalē ꝓportionem <lb/>acquirunt / vt ptꝫ ex caſu: igitur continuo reſiſtentia <lb/>ipſius a. et ipſa b. potentia acquirunt equalē ꝓpor­<lb/>tionē / quod fnit ꝓbandū. </s>
              <s xml:id="N19D78" xml:space="preserve">Patet conſequentia per <lb/>hoc /  illud quod eſt vni equale: eſt cuilibet illi eq̈li <lb/>equale. </s>
              <s xml:id="N19D7F" xml:space="preserve">Et ſic ptꝫ prima pars. </s>
              <s xml:id="N19D82" xml:space="preserve">Iam ꝓbatur ſecun-<lb/>da pars cõcluſionis. </s>
              <s xml:id="N19D87" xml:space="preserve">Sit a. potentia que mouetur <lb/>continuo vniformiter .etc̈. vt ſupra ſit b. potentia <lb/>ei equalis cõſimiliter oīno creſcens ſicut a. poſita <lb/>in puncto intenſiori c. medii: et moueãtur ſimul ab <lb/>illis punctis verſus extremū intenſius c. medii: tūc <lb/>dico /  b. potentia continuo intendit motum ſuum <lb/></s>
              <s xml:id="N19D95" xml:space="preserve">Quod ſic ꝓbatur / q2 cõtinuo ꝓportio ipſius b. ad <lb/>ſuã reſiſtentiã augetur: igitur continuo b. potentia <lb/>intēdit mutū ſuū. </s>
              <s xml:id="N19D9C" xml:space="preserve">Antecedēs ꝓbatur / q2 cõtinuo b. <lb/>poña maiorē ꝓportionē acq̇rit ꝙ̄ ſua reſiſtētia: igr̄ <lb/>cõtinuo ꝓportio ipſius b. ad ſuã reſiſtentiã auget̄̄. <lb/></s>
              <s xml:id="N19DA4" xml:space="preserve">Patet cõſequentia ex primo correlario ſecūde cõ-<lb/>cluſionis octaui capitis: hoc addito /  b. potentia <lb/>ſe habet vt terminus maior et ſua reſiſtentia vt ter­<lb/>minus minor. </s>
              <s xml:id="N19DAD" xml:space="preserve">Sed antecedens ꝓbatur / q2 continuo <lb/>reſiſtētia ipſius a. maiorē ꝓportionē acquirit quã <lb/>reſiſtentia ipſius b. et continuo reſiſtentia ipſius a. <lb/>et ipſa b. potentia equalē ꝓportionē acquirūt: igit̄̄ <lb/>continuo b. potentia maiorē ꝓportionē acquirit ̄ <lb/>reſiſtentia eiuſdē b. / quod fuit probandū. </s>
              <s xml:id="N19DBA" xml:space="preserve">Conſequen­<lb/>tia patet per hoc /  ſi aliquid eſt alio maius quod-<lb/>libet equale illi eſt maius eodem. </s>
              <s xml:id="N19DC1" xml:space="preserve">Et maior ꝓbatur / <lb/>q2 continuo a. potentia velocius et per minorē reſi­<lb/>ſtentiã mouetur ꝙ̄ ipſa b. potentia / vt patet ex caſu / <lb/>igitur continuo reſiſtentia ipſius a. maiorē ꝓpor-<lb/>tionē acquirit ꝙ̄ reſiſtentia ipſius b. </s>
              <s xml:id="N19DCC" xml:space="preserve">Cõſequentia <lb/>patet ex octaua ſuppoſitione quarti capitis ſecū-<lb/>de partis iuncto loco a fortiori: hoc addito /  tam <lb/>a. quã b. equales partes illius medii tranſeūdo .etc̈ <lb/>equalē reſiſtentiã acquirūt / vt ptꝫ ex primo correla­<lb/>rio ſuppoſitionis. </s>
              <s xml:id="N19DD9" xml:space="preserve">Sed iam ꝓbo minorē videlicet / <lb/> continuo reſiſteutia ipſius a. et ipſa b. potentia <lb/>equalē ꝓportionē acquirunt: quia continuo reſiſtē­<lb/>tia ipſius a. et ipſa a. potentia equalē ꝓportioneꝫ <lb/>acquirunt / vt ſupra argumentū eſt: et ipſa a. poten-<lb/>tia et b. potentia continuo itidē equalē ꝓpornalem <lb/>acquirūt / vt ptꝫ: igttur continuo reſiſtentia ipſius <lb/>a. et ipſa b. potentia equalē ꝓportionē acqtirūt / qḋ <lb/>fuit ꝓbandum. </s>
              <s xml:id="N19DEC" xml:space="preserve">Et ſic ptꝫ ſecūda pars et ex hoc tota <lb/>cõcluſio.               <anchor type="note" xlink:href="note-0101-01" xlink:label="note-0101-01a"/>               </s>
              <s xml:id="N19DF6" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. potentia <lb/>cõtinuo mouetur vniformiter per ſui continuum et <lb/>vniforme crementum tranſeundo c. mediū infinitū <lb/>vniformiter difforme vel ſaltē cuius quilibet pars <lb/>finita ſit vniformiter difformis b. potentia ei equa­<lb/>lis poneretur in puncto remiſſiori eiuſdem medii <lb/>̄ ſit punctus in quo pro tunc eſt a. potentia: ipſa b <lb/>potentia eſto /  continuo per infinitū tempus velo­<lb/>cius moueatur uun̄ a. potentiã attinget: ceteris <lb/>iuuamentis et impedimentis deductis. </s>
              <s xml:id="N19E0B" xml:space="preserve">Patet cor-<lb/>relarium / quia alias eadem potentia vel equalis               <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0102" n="102"/>               eque cito / aliquod totum pertranſiret ſicut partem <lb/>eiuſdem ceteris paribus / quod eſt impoſſibile. </s>
              <s xml:id="N19E17" xml:space="preserve">Con­<lb/>ſimiliter dicas /  a. nunquam attingeret b. / eſto /  ꝑ <lb/>infinitum tempus velocius moueretur, ſi b. in pun-<lb/>cto intenſiori c. medii infiniti etc. poneretur.</s>
            </p>
            <div xml:id="N19E20" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0101-01a" xlink:label="note-0101-01" xml:id="N19E24" xml:space="preserve">1. correĺ. <lb/>5. conclu­<lb/>ſio calcu­<lb/>latoris.</note>
            </div>
            <note position="left" xml:id="N19E30" xml:space="preserve">2. correl.</note>
            <p xml:id="N19E34">
              <s xml:id="N19E35" xml:space="preserve">¶ Sequitur ſecūdo /  ſi aliqua poña ab aliquo pū­<lb/>cto intrinſeco medii vniformiter difformis incipi-<lb/>at vniformiter continuo moueri per ſue poñe con-<lb/>tinuum et vniforme crementum: omnis poña maior <lb/>vniformiter et eque velociter omnino creſcens cum <lb/>ea ab eodem puncto incipiens moueri verſus extre­<lb/>mum intenſius, continuo remittit motum ſuum.</s>
            </p>
            <p xml:id="N19E44">
              <s xml:id="N19E45" xml:space="preserve">Probatur / ſit a. poña que vniformiter cõtinue mo­<lb/>netur per ſui continuum et vniforme crementum ꝑ <lb/>c. medium infinitum vniformiter difforme vel ſaltē <lb/>cuius quelibet pars finita ſecundum certam diuiſio­<lb/>nem eſt vniformiter difformis mouendo: ſit po-<lb/>tentia b. maior ꝙ̄ a. omīno eodē mõ creſcens cuꝫ a. et <lb/>moueantur a. et b. potentie ab aliquo puncto ipſiꝰ <lb/>c. medii verſus puncta intenſiora. </s>
              <s xml:id="N19E56" xml:space="preserve">tunc dico /  b. po­<lb/>tentia continuo remittit motum ſuum. </s>
              <s xml:id="N19E5B" xml:space="preserve">Quod ſic ꝓ­<lb/>batur / quia cum a. potentia per c. medium infinituꝫ <lb/>mouendo vniformiter continuo creſcet in potētia <lb/>manifeſtum eſt /  ipſa a. poña ſuper c. medium infi-<lb/>nitum mouendo aliquando erit tante potētie ade-<lb/>quate: quante modo eſt ipſa potētia b. ponatur / igi­<lb/>tur b. quieſcere quo ad vſ a. potentia ad illḋ pun-<lb/>ctum c. medii deuenerit ad quod a. poña erit tante <lb/>poñe adequate quante nunc eſt b. potentia: et tunc <lb/>moueantur in eodem inſtanti verſus puncta inten-<lb/>ſiora .a. a puncto / ad quod tunc eſt .b. vero a puncto <lb/>ad quod ponitur quieſcere continuo omnino eodē <lb/>modo creſcens ſicut a. poña. </s>
              <s xml:id="N19E76" xml:space="preserve">Quod poſito arguitur / <lb/>ſic modo b. poña continuo remittit motum ſuum. </s>
              <s xml:id="N19E7B" xml:space="preserve">et <lb/>modo b. poña eque velociter et eadem velocitate oī­<lb/>no mouetur qua moueretur ſi a. poña in eodem in-<lb/>ſtanti ab eodem puncto a quomodo b. incipit mo-<lb/>ueri, inciperet moueri cum b. verſus eandem diffe-<lb/>rentiam: igitur ſi a. poña in eodem inſtanti ab eo-<lb/>dem puncto a. quomodo b. incipit moueri, incipe-<lb/>ret moueri cum b. verſus puncta intenſiora b. potē-<lb/>tia continuo remittit motum ſuum / quod fuit pro-<lb/>bandum. </s>
              <s xml:id="N19E90" xml:space="preserve">Maior patet / quia a. potentia conti-<lb/>nuo vniformiter mouente per ſue potentie vnifor-<lb/>me crementum: b. poña ei equalis modo: incipit mo­<lb/>ueri per idem mediuꝫ a puncto remiſſiori continuo <lb/>vniformiter et eque velociter creſcens cum a. poten­<lb/>tia: igitur b. potentia continuo remittit motum ſuū <lb/></s>
              <s xml:id="N19E9E" xml:space="preserve">Patet conſequentia ex prima parte concluſionis. <lb/></s>
              <s xml:id="N19EA2" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <note position="left" xml:id="N19EA5" xml:space="preserve">3. correla.</note>
            <p xml:id="N19EA9">
              <s xml:id="N19EAA" xml:space="preserve">¶ Sequitur tertio /  ſi aliqua poña ab aliquo pun­<lb/>cto intrinſeco medii vniformiter difformis īcipiat <lb/>vniformiter continuo moueri per continuuꝫ ſue po­<lb/>tentie vniforme crementum omnis poña minor ha­<lb/>bens proportionem maioris inequalitatis ad ideꝫ <lb/>punctum intrinſecum vniformiter et eque velociter <lb/>omnino creſcens cum ea ab eodem puncto incipiēs <lb/>moueri verſus puncta intenſiora: continuo ītendit <lb/>motum ſuum. </s>
              <s xml:id="N19EBD" xml:space="preserve">Probatur / ſit a. poña que vniformi-<lb/>ter etc. ꝑ c. medium mouendo vt ſupra ſit b. poten-<lb/>tia minor a. habens ad punctum in quo eſt a. ꝓpor­<lb/>tionem maioris inequalitatis, et vniformiter: et eq̄ <lb/>velociter omnino creſcens cum a. moueantur a: et <lb/>b. potentie ſimul ab eodē puncto ipſius c. medii ver­<lb/>ſus puncta intenſiora. </s>
              <s xml:id="N19ECC" xml:space="preserve">tunc dico /  b. poña cõtinuo <lb/>intendit motum ſuum. </s>
              <s xml:id="N19ED1" xml:space="preserve">Quod ſic oſtenditur / q2 cum <lb/>a. poña c. medium vniformiter difforme ad nõ gra­<lb/>dum terminatum vniformiter continuo mouendo <lb/>pertranſit a non gradu poñe vniformiter creſcens:               <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>               manifeſtum eſt /  antea ꝙ̄ a. ad punctum in quomo­<lb/>do eſt deuenerit: fuit tante potentie adequate quan­<lb/>te eſt modo a. poña minor: ponatur igitur a. ad illḋ <lb/>punctum ad quod fuit tante potentie quante ē mo­<lb/>do b. et moueantur ſimul a. et b. verſus extremum in­<lb/>tenſius c. medii .a. a puncto ad quod fuit tante poñe <lb/>quante eſt modo b. poña minor .b. vero a puncto ad <lb/>quod ſimul ponitur cum a. et creſcat b. eque veloci-<lb/>ter omnino et vniformiter ſicut a. </s>
              <s xml:id="N19EED" xml:space="preserve">Quo poſito ar-<lb/>guitur ſic. </s>
              <s xml:id="N19EF2" xml:space="preserve">modo b. poña continuo intendit motum <lb/>ſuum: et modo b. poña eque velociter omnino moue­<lb/>tur ſicut moueretur ſi a. poña in eodem inſtanti ab <lb/>eodem puncto a quomodo b. incipit moueri: incipe­<lb/>ret moueri verſus extremum intenſius: igitur ſi a. <lb/>poña in eodem inſtanti ab eodem puncto a quomo­<lb/>do b. incipit moueri, inciperet moueri cuꝫ b. verſus <lb/>extremū intenſius b. poña cõtinuo intendit motum <lb/>ſuum / quod fuit probandum. </s>
              <s xml:id="N19F05" xml:space="preserve">Antecedens patet ex <lb/>ſecunda parte quinte concluſionis huius / et per con­<lb/>ſequens correlarium</s>
            </p>
            <note position="right" xml:id="N19F0C" xml:space="preserve">4. correl.</note>
            <p xml:id="N19F10">
              <s xml:id="N19F11" xml:space="preserve">¶ Sequitur quarto /  ſi aliqua poña ab aliquo pū­<lb/>cto medii vniformiter difformis infiniti: ſaltem cu­<lb/>ius ſecundum certam diuiſionem quelibet pars eſt <lb/>vniformiter difformis incipiat vniformiter conti-<lb/>nuo moueri per ſue potentie vniforme et continuuꝫ <lb/>crementum. </s>
              <s xml:id="N19F1E" xml:space="preserve">omnis potentia maior vniformiter et <lb/>eque velociter omnino creſcens cuꝫ ea poſſet ad ali­<lb/>quem punctum incipere moueri a quo verſus pūcta <lb/>intenſiora eiuſdem medii mouendo vniformiter cõ­<lb/>tinuo et eque velociter omnino cum ea moueretur. <lb/></s>
              <s xml:id="N19F2A" xml:space="preserve">Probatur et ſit a. poña / que vniformiter continue <lb/>mouetur etc. per c. medium infinitum cuius quelibet <lb/>pars ſecundum certam diuiſionem eſt vniformiter <lb/>difformis: ſit b. poña maior a. in quacun volue-<lb/>ris ꝓportione (non eſt cura) omnino eodem mõ cre­<lb/>ſcens cum a. / tunc dico /  b. poña omnino eodem mõ <lb/>creſcens cum a. ad aliquem punctum c. medii poteſt <lb/>incipere moueri verſus puncta intenſiora vniformi­<lb/>ter continuo et eque velociter ſicut a. mouendo.</s>
            </p>
            <p xml:id="N19F3D">
              <s xml:id="N19F3E" xml:space="preserve">Quod ſic ꝓbatur / quia cum a. poña per c. medium <lb/>infinitum mouendo vniformiter continuo creſcit in <lb/>poña, manifeſtum eſt /  ipſa a. poña ſuper c. mediū <lb/>infinitum mouendo aliquando erit tante potentie <lb/>adequate in aliquo puncto c. medii quante eſt mo-<lb/>do ipſa b. poña: ponatur igitur b. quieſcere in illo <lb/>puncto c. medii quod ad vſ a. poña ad illud punctū <lb/>c. medii deuenerit ad quod ipſa a. poña erit tãte po­<lb/>tentie adequate quante nunc eſt b. poña: et tunc mo­<lb/>ueantur et a. et b. in eodem inſtanti ab illo pūcto ad <lb/>quod a. erit tante potentie quante eſt ꝓ nunc b. qui­<lb/>eſcens verſus puncta intenſiora et b. omnino vnifor­<lb/>miter et eque velociter creſcat cum a. </s>
              <s xml:id="N19F59" xml:space="preserve">Quo poſito <lb/>manifeſtū eſt /  b. poña ab illo puncto recedēdo ver­<lb/>ſus puncta intenſiora vniformiter et eque velociter <lb/>cõtinuo mouebitur ſicut a. cum mõ a. et b. ſint equa-<lb/>les et per equale crementum altera continuo alteri <lb/>manebit equalis: igitur b. poña. </s>
              <s xml:id="N19F66" xml:space="preserve">omnino eodeꝫ mõ <lb/>creſcens cum a. ad aliquem punctum c. medii põt in­<lb/>cipere moueri verſus puncta intenſiora vniformi-<lb/>ter cõtinuo et eque velociter ſicut a. mouendo / quod <lb/>fuit ꝓbandum / et ſic patet correlarium.</s>
            </p>
            <note position="right" xml:id="N19F71" xml:space="preserve">5. correl. <lb/>14. ↄ̨clu-<lb/>ſio cal.</note>
            <p xml:id="N19F79">
              <s xml:id="N19F7A" xml:space="preserve">¶ Sequitur quinto /  ſi aliqua poña ab aliquo pū­<lb/>cto ītrīſeco medii vniformiter difformis ad nõ gra­<lb/>dum terminati incipiat vniformiter continuo mo-<lb/>ueri per ſue poñe a nõ gradu vniforme et cõtinuum <lb/>crementum: omnis poña minor vniformiter et eque­<lb/>velociter omnino creſcens cum ea poſſet ad aliqueꝫ <lb/>punctum eiuſdem medi incipere moueri a quo ver-<lb/>ſus puncta intenſiora eiuſdem medii mouendo vni­               <pb chead="Primi tractatus" file="0103" n="103"/>               formiter continuo et eque velociter omnino cum ea <lb/>moueretur. </s>
              <s xml:id="N19F92" xml:space="preserve">Probatur et ſit a. poña / que vniformi-<lb/>ter cõtinuo mouetur etc. per ſui a non gradu poten­<lb/>tie vniforme et continuum crementum. </s>
              <s xml:id="N19F99" xml:space="preserve">ſit b. poña <lb/>minor a. vtcū volueris (non eſt cura) omnino eo-<lb/>dem mõ creſcens cum a. / tunc dico /  b. poña omni-<lb/>no eodem mõ creſcens cum a. ad aliquem punctum <lb/>c. medii poſſe incipere moueri verſus puncta inten­<lb/>ſiora vniformiter continuo et eque velociter cum ea <lb/>mouendo. </s>
              <s xml:id="N19FA8" xml:space="preserve">Quod ſic ꝓbatur / quia cum a. poña c. me­<lb/>dium tranſeundo a non gradu potentie vniformi-<lb/>ter continuo creſcat: manifeſtum eſt /  a. poña ãtea <lb/>̄ ad punctum in quomodo eſt deuenerit fuit ad ali­<lb/>quod punctum tante potentie adequate quante mõ <lb/>eſt ipſa b. poña minor. </s>
              <s xml:id="N19FB5" xml:space="preserve">ponãtur / igitur a. et b. ſimul <lb/>ad illud punctuꝫ ad quod a. erat tãte poñe adequa­<lb/>te quante mõ eſt ipſa b. poña minor et in eodem in-<lb/>ſtanti incipiant moueri verſus extremum intenſius <lb/>ipſius c. medii </s>
              <s xml:id="N19FC0" xml:space="preserve">Quo poſito manifeſtum eſt /  b. po-<lb/>tentia vniformiter continuo et eque velociter moue­<lb/>tur cum a. cum continuo a. et b. per eandem reſiſten-<lb/>tiam mouentes ſint equales / igitur b. poña omnino <lb/>eodem modo creſcens cum a. ad aliquem punctum <lb/>c. medii poteſt incipere moueri verſus puncta inten­<lb/>ſiora vniformiter continuo et eque velociter ſicut a. <lb/>mouendo / quod fuit probandum. </s>
              <s xml:id="N19FD1" xml:space="preserve">Patet igitur cor­<lb/>relarium.</s>
            </p>
          </div>
          <div xml:id="N19FD6" level="4" n="11" type="chapter" type-free="capitulum">
            <head xml:id="N19FDB" xml:space="preserve">Capitulum vndecimum / in quo pulchre <lb/>admodum comparantur motus diuerſa-<lb/>rum potentiarum in eodem medio vnifor­<lb/>miter difformi inuariato mouentium per <lb/>earum potentiarum vniforme crementum</head>
            <p xml:id="N19FE6">
              <s xml:id="N19FE7" xml:space="preserve">TRadita (vt potuimus) noti-<lb/>cia velocitatis et tarditatꝪ motus penes <lb/>cauſam potentie per ſui crementū in me­<lb/>dio vniformiter difformi inuariato mouentis: con­<lb/>ſequens eſt / vt comparando motus diuerſarum po­<lb/>tentiarum in medio vniformiter difformi inuaria-<lb/>to mouentium per earuꝫ poñarum vniforme cremē­<lb/>tum concluſiones inducamus. </s>
              <s xml:id="N19FF8" xml:space="preserve">Pro quo ſit iſta ſup­<lb/>poſitio.</s>
            </p>
            <p xml:id="N19FFD">
              <s xml:id="N19FFE" xml:space="preserve">Quelibet potentia medium vniformi­<lb/>ter difforme inuariatum ad non gradum termina-<lb/>tum ſuo continuo motu abſoluens ab extremo re-<lb/>miſſiori inchoando: in ea ꝓportione cum maiori re­<lb/>ſiſtentia mouetur continuo in qua plus a remiſſio-<lb/>ri termino eiuſdem medii ipſa potentia diſtat.</s>
            </p>
            <p xml:id="N1A00B">
              <s xml:id="N1A00C" xml:space="preserve">Probatur hec ſuppoſitio. </s>
              <s xml:id="N1A00F" xml:space="preserve">quia in reſiſtentia vni-<lb/>formiter difformi omnis reſiſtentia in ea ꝓportiõe <lb/>eſt maior adequate in qua plus diſtat ab extremo ī <lb/>quo eſt non gradus / vt patet ex diffinitione qualita­<lb/>tis vniformiter difformis quarto tractatu: igitur <lb/>omnis poña medium vniformiter difforme ad non <lb/>gradum terminatum ſuo motu abſoluens ab extre­<lb/>mo remiſſiori inchoando: in ea ꝓportione ma­<lb/>iori reſiſtentia mouetur continuo in qua ſua reſiſtē­<lb/>tia plus diſtat ab extremo remiſſiori eiuſdeꝫ medii / <lb/>et per conſequens in ea ꝓportione cum maiori reſi-<lb/>ſtētia mouetur in qua ipſamet poña plus diſtat ab <lb/>eodem extremo remiſſiori eiuſdem medii: quod fuit <lb/>probandum. </s>
              <s xml:id="N1A02C" xml:space="preserve">Patet conſequentia / quia tantum di­<lb/>ſtat potētia in tali medio vniformiter difformi ab <lb/>extremo remiſſiori eiuſdem medii adequate quãtuꝫ <lb/>reſiſtētia eiuſdem medii ad quam eſt extremitas ta­<lb/>lis potentie. </s>
              <s xml:id="N1A037" xml:space="preserve">Et ſic patet ſuppoſitio.               <anchor type="note" xlink:href="note-0103-01" xlink:label="note-0103-01a"/>               </s>
              <s xml:id="N1A03F" xml:space="preserve">¶ Naſcitur hīc <lb/>omnem poñam altera continuo velocius medium <lb/>vniformiter difforme inuariatum et ad non gradū <lb/>terminatum abſoluentē, in ea ꝓportione continuo               <cb chead="Capitulum vndecimum"/>               moueri cum maiori reſiſtentia ꝙ̄ altera: in qua ip̄a <lb/>velocius quam altera continuo mouetur. </s>
              <s xml:id="N1A04D" xml:space="preserve">Patet <lb/>correlarium / quia talis poña continuo in ea ꝓpor-<lb/>tione mouetur cum maiori reſiſtentia. </s>
              <s xml:id="N1A054" xml:space="preserve">in qua plꝰ di­<lb/>ſtat ab extremo remiſſiori eiuſdem medii termina-<lb/>ti ad non gradum / vt patet ex ſuppoſitione. </s>
              <s xml:id="N1A05B" xml:space="preserve">et talis <lb/>poña continuo in ea ꝓportione pluſ̄ altera diſtat <lb/>ab extremo remiſſiori eiuſdem medii terminati ad <lb/>non gradum in qua velocius mouetur adequate / vt <lb/>conſtat. </s>
              <s xml:id="N1A066" xml:space="preserve">igitur talis poña continuo in ea ꝓportiõe <lb/>mouetur cum maiori reſiſtentia in qua ipſa velociꝰ <lb/>̄ altera continuo mouetur / quod fuit probandum <lb/></s>
              <s xml:id="N1A06E" xml:space="preserve">Et ſic patet correlarium.</s>
            </p>
            <div xml:id="N1A071" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0103-01a" xlink:label="note-0103-01" xml:id="N1A075" xml:space="preserve">correla.</note>
            </div>
            <p xml:id="N1A07B">
              <s xml:id="N1A07C" xml:space="preserve">Hoc premiſſo ſit prima cõcluſio </s>
              <s xml:id="N1A07F" xml:space="preserve">Dua­<lb/>bus potentiis aliquod medium vniformiter diffor­<lb/>me ad non gradum terminatum tranſeundo vnifor­<lb/>miter continuo mouentibus per earum a non gra-<lb/>du poñe vniforme et continuuꝫ crementum vna al­<lb/>tera in certa ꝓportione velocius continuo creſcen-<lb/>te: poña que velocius continuo creſcit velocius con­<lb/>tinuo mouetur: in minori tamen ꝓportione velociꝰ <lb/>continuo quam ſit ꝓportio in qua continuo velociꝰ <lb/>creſcit. </s>
              <s xml:id="N1A094" xml:space="preserve">Probatur / ſit a. poña que c. medium vnifor­<lb/>miter difforme terminatum ad nõ gradum tranſe-<lb/>undo vniformiter continuo mouetur per ſue poten­<lb/>tie a non gradu vniforme crementum: et b. poña c. <lb/>medium tranſeundo in f. ꝓportiõe velocius creſcat <lb/>continuo ꝙ̄ a. poña idem c. medium tranſeundo cõ-<lb/>tinuo vniformiter mouendo. </s>
              <s xml:id="N1A0A3" xml:space="preserve">tunc dico /  b. potētia <lb/>mouetur velocius ipſa poña a. in minori tamen ꝓ-<lb/>portione velocius quam ſit f. ꝓportio in qua b. po-<lb/>tentia velocius continuo creſcit ꝙ̄ poña a. </s>
              <s xml:id="N1A0AC" xml:space="preserve">Quod <lb/>ſic ꝓbatur / q2 b. poña mouetur velocius continuo ̄ <lb/>a. / vt conſtat (citius enim vniformiter continuo mo­<lb/>uendo c. medium pertranſit) et b. poña non mouetur <lb/>in f. ꝓportione velocius nec in maiori: igitur b. po-<lb/>tentia mouetur velocius quam ip̄a poña a. in mino­<lb/>ri tamen ꝓportione velocius quam ſit f. / quod fuit <lb/>ꝓbandum. </s>
              <s xml:id="N1A0BD" xml:space="preserve">Conſequentia patet cum maiore. </s>
              <s xml:id="N1A0C0" xml:space="preserve">et ar-<lb/>guitur prima pars minoris videlicet /  b. poña nõ <lb/>mouetur velocius a. poña in f. ꝓportione quia ſi b. <lb/>potētia mouetur velocius in f. ꝓportione. </s>
              <s xml:id="N1A0C9" xml:space="preserve">ſequitur / <lb/> continuo reſiſtentie ipſius b. ad reſiſtentiam ipſi­<lb/>us a. eſt f. ꝓportio / vt patet ex correlario ſuppoſitio­<lb/>nis: et ex hypotheſi b. poñe ad a. potentiam eſt f. ꝓ-<lb/>portio (cum b. a nõ gradu in f. ꝓportione continuo <lb/>velocius creſcat quam a. etiaꝫ a nõ gradu creſcēs) / <lb/>igitur qualis eſt ꝓportio ipſius b. potentie ad ipſã <lb/>a. poñam talis eſt ꝓportio reſiſtentie ipſius b. ad re­<lb/>ſiſtentiam ipſius a. quia vtra f. / et per conſequens <lb/>permutatim qualis eſt ꝓportio ipſius b. poñe ad re­<lb/>ſiſtentiam eiuſdem b. potentie talis eſt ꝓportio ip-<lb/>ſius a: poñe ad reſiſtentiam eiuſdem a. poñe: et ꝑ cõ-<lb/>ſequēs mouentur ab eadem ꝓportione / qḋ eſt fal-<lb/>ſum. </s>
              <s xml:id="N1A0E6" xml:space="preserve">Et ſic patet /  b. nõ mouetur in f. ꝓportione ve­<lb/>locius ipſa poña a. </s>
              <s xml:id="N1A0EB" xml:space="preserve">Iam probatur ſecūda pars mi­<lb/>noris videlicet /  b. nõ mouetur in maiori ꝓportio-<lb/>ne quam ſit f. velocius a. potentia: quia tunc ſeque­<lb/>retur /  continuo tardius moueretur quam a. potē­<lb/>tia (vt facile deducitur) / quod eſt falſum. </s>
              <s xml:id="N1A0F6" xml:space="preserve">Et ſic patet <lb/>concluſio.               <anchor type="note" xlink:href="note-0103-02" xlink:label="note-0103-02a"/>               </s>
              <s xml:id="N1A100" xml:space="preserve">¶ Ex quo ſequitur primo /  duabus po-<lb/>tētiis aliquod medium vniformiter difforme ad nõ <lb/>gradum terminatum tranſeundo vniformiter con-<lb/>tinuo mouentibus per earum a non gradu poten­<lb/>tie vniforme et continuum crementum. </s>
              <s xml:id="N1A10B" xml:space="preserve">vna in tri-<lb/>plo velociꝰ continuo creſcente ꝙ̄ altera que vnifor-<lb/>miter idem medium tranſeundo mouetur a ꝓpor-<lb/>tione dupla. potentia que in triplo velocius conti-<lb/>nuo creſcit mouetur velocius continuo. </s>
              <s xml:id="N1A116" xml:space="preserve">velocius in­               <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0104" n="104"/>               quam in maiori proportione ꝙ̄ ſexquialtera in mi­<lb/>nori tamen velocius quam dupla. </s>
              <s xml:id="N1A120" xml:space="preserve">Probatur et ſit <lb/>a. potentia / que continuo c. medium tranſeundo mo­<lb/>uetur a ꝓportione dupla per ſue potentie a nõ gra­<lb/>du vniforme et continuū crementum: ſit b. potētia <lb/>que idem c. medium tranſeundo creſcit a non gra-<lb/>du continuo in triplo velocius quam a. poña. </s>
              <s xml:id="N1A12D" xml:space="preserve">tunc <lb/>dico /  b. poña mouetur continuo velocius ꝙ̄ a. po-<lb/>tentia in maiori ꝓportione ꝙ̄ ſexquialtera: et in mi­<lb/>nori quam dupla. </s>
              <s xml:id="N1A136" xml:space="preserve">Quod ſic ꝓbatur / quia b. potētia <lb/>nõ mouetur in ſexquialtera ꝓportione velociꝰ ade-<lb/>quate: nec in minori. </s>
              <s xml:id="N1A13D" xml:space="preserve">Similiter b. poña nõ mouetur <lb/>in dupla ꝓportione velocius: nec in maiori: igitur <lb/>b. potentia mouetur in maiori ꝓportione velocius <lb/>quam ſexquialtera: et in minori ꝙ̄ dupla: quod fuit <lb/>ꝓbandum. </s>
              <s xml:id="N1A148" xml:space="preserve">Maior ꝓbatur / quia ſi b. mouetur in ſex­<lb/>quialtera ꝓportione velocius ꝙ̄ ipſa poña a. ade-<lb/>quate: ſequitur /  cõtinuo reſiſtentia ipſius b. eſt in <lb/>ſexquialtero maior reſiſtentia ipſius a. (quia c. me­<lb/>dium eſt vniformiter difforme ad non graduꝫ ter-<lb/>minatum) et vltra reſiſtentia ipſius b. eſt in ſexqui-<lb/>altero maior reſiſtentia ipſius a. et ipſius b. ad reſi­<lb/>ſtentiam ipſius a. eſt ꝓportio ſextupla (cum compo­<lb/>natur ex tripla que eſt ipſius b. ad potentiam a. et <lb/>ex dupla que eſt ipſius a. ad ſuam reſiſtentiam) / igi-<lb/>tur ipſius b. ad reſiſtentiam eiuſdem b. eſt propor-<lb/>tio quadrupla quia ſexquialterum ad ſubſextuplū <lb/>ad aliquod eſt ſubquadruplum ad illud et per cõſe-<lb/>quens b. mouetur a ꝓportione quadrupla: et ex hoc <lb/>in duplo velocius ꝙ̄ a. continuo mouens a ꝓportio­<lb/>ne dupla: et non in ſexquialtero velocius adequate / <lb/>quod fuit ꝓbandum. </s>
              <s xml:id="N1A16B" xml:space="preserve">Sed  b. non moueatur in <lb/>minori ꝓportione velocius quam ſexquialtera pro­<lb/>batur: quia tunc reſiſtentia ipſius b. ad reſiſtentiaꝫ <lb/>ipſius a. eſſet minor proportio quam ſexquialtera: <lb/>vt patet ex correlario ſuppoſitionis huius et ipſiꝰ <lb/>b. ad reſiſtentiam ipſius a. eſt ꝓportio ſextupla (vt <lb/>ſupra argutum eſt) / ergo ipſius b. ad reſiſtentiaꝫ ip­<lb/>ſius b. eſſet maior ꝓporio quam quadrupla. </s>
              <s xml:id="N1A17C" xml:space="preserve">Pa-<lb/>tet conſequentia per hoc /  quando aliquis nume-<lb/>rus eſt ſextuplus ad alterum talis numerus eſt ma­<lb/>ior quam quadruplus ad omnem numerum qui eſt <lb/>minor ſexquialtero ad ſuum ſubſextuplum (vt pa-<lb/>tet intelligenti quartum caput ſecunde partis) </s>
              <s xml:id="N1A189" xml:space="preserve">Iaꝫ <lb/>ꝓbatur minor / quia ſi b. mouetur in duplo velocius <lb/>̄ a. / ſequitur cum caſu /  reſiſtentia ipſius b. conti-<lb/>nuo eſt dupla ad reſiſtentiam ipſius a. / vt patet ex <lb/>correlario ſuppoſitionis (cum c. mediuꝫ terminetur <lb/>ad non gradum) et vltra reſiſtentia ipſius b. conti-<lb/>nuo eſt dupla ad reſiſtentiaꝫ ipſius a. et ipſius b. ad <lb/>reſiſtentiam ipſius a. eſt ꝓportio ſextupla (vt ꝓba-<lb/>tum eſt) / ergo ipſius b. ad reſiſtentiam eiuſdem b. eſt <lb/>ꝓportio tripla. </s>
              <s xml:id="N1A19E" xml:space="preserve">Patet hec conſequentia per hoc /  <lb/>omne duplum ad ſubſextuplum alicuius numeri ē <lb/>ſubtriplum ad talem numerum (vt patet intelligen­<lb/>ti quartam concluſionem quarti capitis ſecunde ꝑ­<lb/>tis cum ſuis correlariis) / et per conſequens ſequitur / <lb/> b. mouetur a ꝓportione tripla que non eſt dupla <lb/>duple (vt patet intelligenti ſextum caput ſecunde ꝑ­<lb/>tis) / et ex hoc b. non mouetur in duplo velocius a. po­<lb/>tentia mota a ꝓportione dupla: quod fuit ꝓbandū <lb/></s>
              <s xml:id="N1A1B2" xml:space="preserve">Sed  non moueatur a maiori dupla: patet / q2 tūc <lb/>reſiſtentia ipſius b. eſſet maior quam dupla ad reſi­<lb/>ſtentiam ipſius a. et ſic ipſius b. ad reſiſtentiam ipſi­<lb/>us b. eſſet minor ꝓportio quam tripla (vt facile de­<lb/>ducitur ex dictis) / et per conſeqnens non mouetur a <lb/>maiori ꝓportione quam dupla cuꝫ nulla minor tri­<lb/>pla: nec ipſa tripla ſit dupla ad duplam. </s>
              <s xml:id="N1A1C1" xml:space="preserve">Et ſic pa-<lb/>tet correlarium.               <anchor type="note" xlink:href="note-0104-01" xlink:label="note-0104-01a"/>               </s>
              <s xml:id="N1A1CB" xml:space="preserve">¶ Sequitur tertio /  duabus potē­               <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>               tiis aliquod medium vniformiter difforme ad non <lb/>gradum terminatum tranſeundo. </s>
              <s xml:id="N1A1D3" xml:space="preserve">vniformiter cõ-<lb/>tinuo mouentibus per earuꝫ a non gradu poñe vni­<lb/>forme et continuum crementum: vna altera in du­<lb/>plo velocius continuo creſcente: et poña que tardiꝰ <lb/>creſcit continuo mouente a ꝓportione ſexquialte-<lb/>ra: poña que velocius continuo creſcit velocius cõ­<lb/>tinuo mouetur: in minori tamen ꝓportione quã du­<lb/>pla: et maiori quam ſexquialtera. </s>
              <s xml:id="N1A1E4" xml:space="preserve">Probatur / et ſit <lb/>b. poña que in duplo velocius continuo creſcat po­<lb/>tentia a. continuo mouēte a ꝓportione ſexquialte­<lb/>ra c. medium terminatum ad non gradum pertran­<lb/>ſeundo </s>
              <s xml:id="N1A1EF" xml:space="preserve">Quo poſito arguitur ſic / b. poña nõ moue-<lb/>tur in dupla ꝓportione velocius nec in maiori (vt <lb/>patet ex concluſione) / nec b. poña mouetur in ſexqui­<lb/>altera ꝓportione velocius adequate, nec in minori / <lb/>igitur b. potentia mouetur continuo in minori pro­<lb/>portione quam dupla velocius, et in maiori quam <lb/>ſexquialtera: quod fuit ꝓbandum. </s>
              <s xml:id="N1A1FE" xml:space="preserve">Conſequentia <lb/>patet cum maiore et arguitur minor / quia ſi b. po-<lb/>tentia mouetur in ſexquialtera ꝓportione velociꝰ <lb/>quam a. / ſequitur /  reſiſtentia ipſius b. eſt ſexquial­<lb/>tera ad reſiſtentiam ipſius a. / vt patet ex correlario <lb/>ſuppoſitiõis (quia medium eſt terminatum ad non <lb/>gradum) / et vltra reſiſtentia ipſius b. eſt ſexquialte-<lb/>ra ad reſiſtentiam ipſius a. et ipſius b. ad reſiſten-<lb/>tiaꝫ ipſius a. eſt proportio tripla: ergo ipſius b. ad <lb/>reſiſtentiam ipſius b. eſt ꝓportio dupla / et per con-<lb/>ſequens b. mouetur a proportione dupla.</s>
            </p>
            <div xml:id="N1A215" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0103-02a" xlink:label="note-0103-02" xml:id="N1A219" xml:space="preserve">1. correl.</note>
              <note position="left" xlink:href="note-0104-01a" xlink:label="note-0104-01" xml:id="N1A21F" xml:space="preserve">3. correl.</note>
            </div>
            <p xml:id="N1A225">
              <s xml:id="N1A226" xml:space="preserve">Patet tamen cõſequentia per hoc /  omne tripluꝫ <lb/>ad aliquem numerum eſt duplum ad numerum ſex­<lb/>quialterum ad illum numerum ſubtriplum (vt con­<lb/>ſtat intelligenti quartum caput ſepius allegatum <lb/>et vltra b. mouetur a ꝓportione dupla, et dupla nõ <lb/>eſt ſexquialtera ad duplam: </s>
              <s xml:id="N1A233" xml:space="preserve">Sed maior quaꝫ ſexqui­<lb/>altera: vt patet ex ſexto capite ſecunde partis: igi-<lb/>tur b. mouetur in maiori ꝓportione velocius quaꝫ <lb/>ſexquialtera / quod fuit ꝓbandum. </s>
              <s xml:id="N1A23C" xml:space="preserve">Sed  b. nõ mo­<lb/>ueatur in minori ꝓportione quam ſexquialtera ve­<lb/>locius: ꝓbatur / quia tunc reſiſtentia ipſius b. eſt mi­<lb/>nor quam ſexquialtera ad reſiſtentiam ipſius a. / et <lb/>per conſequens ipſius b. ad reſiſtentiam ipſius b. <lb/>eſt maior ꝓportio quam dupla: vt patet per hanc <lb/>maximam. </s>
              <s xml:id="N1A24B" xml:space="preserve">Omnis numerus triplus ad alterum eſt <lb/>maior quam duplus ad omnem numerum minorē <lb/>numero ſexquialtero ad illum ſubtriplum (vt pa-<lb/>tet intuenti) / et ſi b. mouetur a maiori ꝓportiõe quã <lb/>dupla: conſequens eſt /  b. mouetur in maiori pro-<lb/>portione quam ſexquialtera velocius ipſa a. poña <lb/>mouente continuo a ꝓportione ſexquialtera (ſiqui­<lb/>dem dupla, et omnis maior ea, maior eſt quam ſex-<lb/>quialtera ad ſexquialteram) </s>
              <s xml:id="N1A25E" xml:space="preserve">Componitur em̄ du-<lb/>pla ex ſexquialtera, et ſexquitertia: et ſexquitertia <lb/>maior eſt quam medietas ſexquialtere: vt patet ex <lb/>nono correlario tertie concluſionis quarti capitis <lb/>ſecunde partis. </s>
              <s xml:id="N1A269" xml:space="preserve">¶ Infinita ſimilia correlaria intel­<lb/>ligens primam et ſecundam partem huius operis <lb/>ex his / que dicta ſunt / et ſtatim dicent̄̄ propria indu­<lb/>ſtria poterit inferre.               <anchor type="note" xlink:href="note-0104-02" xlink:label="note-0104-02a"/>               </s>
              <s xml:id="N1A277" xml:space="preserve">¶ Et ſi queras / ex quo b. moue-<lb/>tur in minori ꝓportione quam dupla velocius a. et <lb/>in maiori quaꝫ ſexquialtera in qua ꝓportione ade­<lb/>quate b. mouetur velocius quam a.</s>
            </p>
            <div xml:id="N1A280" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0104-02a" xlink:label="note-0104-02" xml:id="N1A284" xml:space="preserve">Nota q̄-<lb/>ſtionem.</note>
            </div>
            <p xml:id="N1A28C">
              <s xml:id="N1A28D" xml:space="preserve">Reſpõdeo  dico primo /  in nulla ſu-<lb/>perparticulari (vt patet) / q2 nulla ſuperparticula-<lb/>ris eſt maior proportione ſexquialtera, nec in ali-<lb/>qua multiplici ſuperparticulari, nec multiplici ſu­<lb/>prapartiente: quia nulla talis eſt minor dupla (vt <lb/>conſtat intelligenti ſextum caput ſecunde partis) <lb/></s>
              <s xml:id="N1A29B" xml:space="preserve">Reſtat igitur / vt moueatur in aliqua ꝓportione ſu-               <pb chead="Primi tractatus" file="0105" n="105"/>               prapartiente velocius: vel in aliqua proportione <lb/>irrationali. </s>
              <s xml:id="N1A2A5" xml:space="preserve">Et ſi queras in qua proportione ſupra­<lb/>partiente vel irrationali.</s>
            </p>
            <note position="left" xml:id="N1A2AA" xml:space="preserve">calcu. ī 2. <lb/>capite de <lb/>medio nõ <lb/>reſiſtēte.</note>
            <p xml:id="N1A2B4">
              <s xml:id="N1A2B5" xml:space="preserve">Reſpondeo et dico ſecundo / cum calcu­<lb/>latore in calce ſexte concluſionis ſecundi capitis de <lb/>medio non reſiſtente  id īquirere maiori egeret ſtu­<lb/>dio quaꝫ vtilitatem afferret.               <anchor type="note" xlink:href="note-0105-01" xlink:label="note-0105-01a"/>               </s>
              <s xml:id="N1A2C3" xml:space="preserve">Et vt beato hieronimo <lb/>placet noctibus diebuſ ad id excogitandum tor-<lb/>queri at incomprehenſibili chaos immergi eſt in <lb/>obſcuritate mentis ambulare.</s>
            </p>
            <div xml:id="N1A2CC" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0105-01a" xlink:label="note-0105-01" xml:id="N1A2D0" xml:space="preserve">hiero. 37. <lb/>d. c. nõne.</note>
            </div>
            <p xml:id="N1A2D8">
              <s xml:id="N1A2D9" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N1A2DC" xml:space="preserve">Duabus poten-<lb/>tiis aliquod medium vniformiter difforme ad non <lb/>gradum terminatum tranſeundo vniformiter con­<lb/>tinuo mouentibus per earum a non gradu poten-<lb/>tie vniforme et continuum crementum: vna velociꝰ <lb/>continuo ꝙ̄ altera creſcente in proportione maio-<lb/>ri in ea proportione a qua altera continuo moue-<lb/>tur: potentia que velocius continuo creſcit: velociꝰ <lb/>continuo mouetur in ea proportione a qua moue-<lb/>tur altera. </s>
              <s xml:id="N1A2F1" xml:space="preserve">Probatur / ſit a. poña que c. medium vni­<lb/>formiter difforme terminatum ad non graduꝫ trã­<lb/>ſeundo vniformiter continuo mouetur ab f. ꝓpor-<lb/>tione per ſue potentie a non gradu vniforme et con­<lb/>tinuum crementum ſit .h. proportio maior f. ꝓpor­<lb/>tione in ipſamet f. ꝓportiõe: et ſit b. poña que idem <lb/>medium pertranſeundo vniformiter continuo mo-<lb/>uetur creſcens continuo in h. ꝓportione velociꝰ: tūc <lb/>dico /  b. poña continuo velocius mouetur ꝙ̄ a. po-<lb/>tentia (velocius inquam in ꝓportione f.) </s>
              <s xml:id="N1A306" xml:space="preserve">Quod ſic <lb/>probatur / quia b. continuo mouetur velocius ipſa <lb/>a. potentia in certa proportiõe (vt patet ex dictis) / <lb/>et non continuo mouetur velocius in maiori ꝓpor-<lb/>tione quaꝫ ſit f. nec in minori: igitur b. continuo mo­<lb/>uetur in f. proportione velocius. </s>
              <s xml:id="N1A313" xml:space="preserve">Conſequentia ē no­<lb/>ta cum maiore: et probatur prima pars minoris vi­<lb/>delicet /  b. non mouetur in maiori ꝓportione quã <lb/>ſit f. velocius: quia ſi b. mouetur velocius ꝙ̄ a. ī ma­<lb/>iori ꝓportione quam ſit f. / ſequitur /  reſiſtentie ip-<lb/>ſius b. ad reſiſtentiam ipſius a. eſt maior proportio <lb/>quam ſit f. </s>
              <s xml:id="N1A322" xml:space="preserve">Patet conſequentia / quia c. medium eſt <lb/>vniformiter difforme ad non gradum terminatum <lb/>et vltra reſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a. <lb/>eſt maior proportio ꝙ̄ ſit f. / ergo ipſius b. ad reſiſtē­<lb/>tiam ipſius b. eſt minor ꝓportio ꝙ̄ ſit h.</s>
            </p>
            <p xml:id="N1A32D">
              <s xml:id="N1A32E" xml:space="preserve">Patet hec conſequentia / quia ipſius a. ad reſiſten-<lb/>tiam eiuſdem a. eſt proportio f. (ex hypotheſi) et re­<lb/>ſiſtentie ipſius b. ad reſiſtentiam ipſius a. eſt ma-<lb/>ior proportio quam ſit f. / ergo maior eſt reſiſten-<lb/>tia ipſius b. quam ipſa potentia a. </s>
              <s xml:id="N1A339" xml:space="preserve">Patet conſeq̄n­<lb/>tia / quia reſiſtentia ipſius b. habet maiorem ꝓpor-<lb/>tionem ad vnum tertium puta ad reſiſtentiam ipſi-<lb/>us a. quam a. potentia habeat ad idem tertium. </s>
              <s xml:id="N1A342" xml:space="preserve">Et <lb/>vltra maior eſt reſiſtentia ipſius b. quam ipſa a. po­<lb/>tentia. </s>
              <s xml:id="N1A349" xml:space="preserve">et b. habet h. proportionem ad a. potentiam / <lb/>ergo b. habet minorem ꝓportionem quam h. ad re­<lb/>ſiſtentiam eiuſdem b. / et per conſequens b. mouetur <lb/>continuo a minori proportione quam h. et h. ꝓpor­<lb/>tio eſt in f. proportione maior quaꝫ ſit f. proportio <lb/>(vt patet ex hypotheſi) / ergo b. continuo mouetur in <lb/>minori proportione velocius quam ſit f. proportio <lb/>et ſic non mouetur in maiori proportione velocius <lb/>a. quam ſit f. ꝓportio / quod fuit ꝓbandum. </s>
              <s xml:id="N1A35C" xml:space="preserve">Sed iaꝫ <lb/>probo ſecundam partem minoris videlicet /  b. nõ <lb/>mouetur velocius ꝙ̄ a. in minori ꝓportione quam <lb/>ſit f. quia ſi mouetur in minori ꝓportione quam ſit <lb/>f. velocius / ſequitur /  continuo reſiſtentie ipſius b. <lb/>ad reſiſtētiã ipſiꝰ a. ē minor ꝓportio quã ſit f. ex cor­<lb/>relario ſuppoſitionis et vltra continuo reſiſtentie               <cb chead="Capitulum vndecimum"/>               ipſius b. ad reſiſtentiam ipſius a. eſt minor propor­<lb/>tio quam ſit f. et b. ad a. habet proportionem h. / igi-<lb/>tur b. habet ad reſiſtentiam ipſius b. maiorem pro­<lb/>portionem quam ſit h. </s>
              <s xml:id="N1A374" xml:space="preserve">Patet conſequentia / q2 reſi­<lb/>ſtentia ipſius b. eſt minor quam a. potentia. </s>
              <s xml:id="N1A379" xml:space="preserve">Sed  <lb/>a. poña ſit maior ꝙ̄ reſiſtentia ipſius b. / patet / quia <lb/>a. habet maiorem proportionem ad ſuam reſiſten-<lb/>tiam quam reſiſtentia ipſius b. habeat ad eandē re­<lb/>ſiſtentiam ipſius a. (cum a. ad ſuam reſiſtentiaꝫ ha­<lb/>beat f. proportionem: reſiſtentia autem ipſius b. ad <lb/>eandem reſiſtentiam per te minorem) / igitur ipſa a. <lb/>potentia maior eſt quam reſiſtentia ipſius b. </s>
              <s xml:id="N1A38A" xml:space="preserve">Pa-<lb/>tet conſequentia per hanc maximam quod habet <lb/>maiorem proportionem ad vnum tertium eſt maiꝰ <lb/></s>
              <s xml:id="N1A392" xml:space="preserve">Et vltra ex illo conſequenti b. habet maiorem pro-<lb/>portionem ad reſiſtentiaꝫ ipſius b. quam ſit h. et b. <lb/>mouetur continuo ab illa proportione quam ſemel <lb/>habet ad ſuam reſiſtentiam (quia continuo vnifor-<lb/>miter) et h. proportio eſt in f. proportione maior ip­<lb/>ſa f. proportione ex hypotheſi: igitur ꝓportio a q̈ <lb/>mouetur b. eſt maior ipſa proportione f. in maiori <lb/>proportione ꝙ̄ ſit f. / et per conſequens b. non moue-<lb/>tur in minori proportione velocius a. quam ſit f. / qḋ <lb/>fuit probandum: et ſic patet minor: et per conſequēs <lb/>tota concluſio.               <anchor type="note" xlink:href="note-0105-02" xlink:label="note-0105-02a"/>               </s>
              <s xml:id="N1A3AE" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. po-<lb/>tentia continuo moueatur a proportione tripla etc. <lb/>et b. a non gradu potentie idem medium tranſeun-<lb/>do continuo creſcat velocius in proportione vicecu­<lb/>pla ſeptupla qualis eſt .27. ad .1. / tunc ipſa b. poten-<lb/>tia maior mouetur continuo in triplo velocius ip-<lb/>ſa a. potentia minore. </s>
              <s xml:id="N1A3BD" xml:space="preserve">Probatur / quia ꝓportio in <lb/>qua b. potentia maior velociꝰ creſcit a. potentia mi­<lb/>nore eſt tripla ad proportionem a qua mouetur a. <lb/>potentia minor: et a. potentia minor mouetur a tri­<lb/>pla proportione: igitur b. potentia maior mouetur <lb/>continuo in triplo velocius a. potentia minore / qḋ <lb/>eſt probandum </s>
              <s xml:id="N1A3CC" xml:space="preserve">Patet conſequentia ex concluſio-<lb/>ne.               <anchor type="note" xlink:href="note-0105-03" xlink:label="note-0105-03a"/>               </s>
              <s xml:id="N1A3D6" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor mo-<lb/>ueatur a proportione quadrupla in caſu concluſio­<lb/>nis: et b. poña maior creſcat continuo velocius in ꝓ­<lb/>portione ducentecupla quingecupla ſextupla qua­<lb/>lis eſt proportio .256. ad .1. / tunc b. potentia maior <lb/>mouebitur in quadruplo velocius adequate. </s>
              <s xml:id="N1A3E3" xml:space="preserve">Pro-<lb/>batur / quia ꝓportio in qua b. poña maior creſcit ve­<lb/>locius a. potentia minore eſt quadrupla ad propor­<lb/>tionem a qua mouetur a. poña minor: et ꝓportio a <lb/>qua mouetur a. poña minor eſt quadrupla: ergo b. <lb/>poña maior mouetur in quadruplo velocius b. po-<lb/>tentia minore / quod eſt probandum. </s>
              <s xml:id="N1A3F2" xml:space="preserve">Patet conſe-<lb/>quentia ex hac concluſione. </s>
              <s xml:id="N1A3F7" xml:space="preserve">Et ſic patet correlariuꝫ <lb/>               <anchor type="note" xlink:href="note-0105-04" xlink:label="note-0105-04a"/>               </s>
              <s xml:id="N1A401" xml:space="preserve">¶ Sequitur tertio /  ſi a. potentia minor in caſu cõ­<lb/>cluſionis moueatur continuo ab illa ꝓportione ir­<lb/>rationali que eſt ſexquialtera ad duplam que voce­<lb/>tur h. et b. poña maior creſcat velocius continuo a. <lb/>potentia minore in proportione k. irrationali que <lb/>ſe habeat ad proportionem h. in ipſa h. proportio­<lb/>ne que eſt ſexquialtera ad duplam / tunc b. potentia <lb/>maior mouebitur velocius ipſa a. poña minore in ꝓ­<lb/>portione h. que eſt ſexquialtera ad duplam. </s>
              <s xml:id="N1A414" xml:space="preserve">Patet <lb/>hoc correlarium facile ex concluſione et probatione <lb/>eius que vniuerſalis eſt. </s>
              <s xml:id="N1A41B" xml:space="preserve">¶ Et ſic poteris inferre pro­<lb/>prio labore quotcun velis ſimilia correlaria ſecū­<lb/>da parte huius operis intellecta.</s>
            </p>
            <div xml:id="N1A422" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0105-02a" xlink:label="note-0105-02" xml:id="N1A426" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0105-03a" xlink:label="note-0105-03" xml:id="N1A42C" xml:space="preserve">2. correl.</note>
              <note position="right" xlink:href="note-0105-04a" xlink:label="note-0105-04" xml:id="N1A432" xml:space="preserve">3. correl.</note>
            </div>
            <p xml:id="N1A438">
              <s xml:id="N1A439" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N1A43C" xml:space="preserve">Duabus potentiis <lb/>aliquod medium vniformiter difforme ad nõ gra-<lb/>dum terminatum tranſeundo vniformiter cõtinuo <lb/>mouentibus per earum a non gradu poñe vnifor-<lb/>me et continuum crementum, vna altera in maio-               <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0106" n="106"/>               iori proportione velocius continuo creſcente quaꝫ <lb/>ſit proportio a qua altera continuo mouetur: potē­<lb/>tia que velocius continuo creſcit velocius continuo <lb/>mouetur in maiori proportiõe ꝙ̄ ſit ꝓportio a qua <lb/>mouetur minor. </s>
              <s xml:id="N1A454" xml:space="preserve">Probatur / ſit a. potentia que c. me­<lb/>dium vniformiter difforme ad non gradum termi-<lb/>natum pertranſeat: vniformiter continuo mouēdo <lb/>ab f. proportione per ſue potentie a non gradu vni­<lb/>forme crementum: ſit b. potentia que idem c. medi­<lb/>um pertranſeundo a non gradu potentie in h. pro-<lb/>portione maiori f. in maiori proportione quam f. <lb/>continuo velocius creſcat vniformiter continuo mo­<lb/>uens. </s>
              <s xml:id="N1A467" xml:space="preserve">tūc dico /  b. potentia mouetur velocius ꝙ̄ ip­<lb/>ſa potentia a. in maiori proportione velocius quã <lb/>ſit f. </s>
              <s xml:id="N1A46E" xml:space="preserve">Quod ſic probatur / quia b. mouetur velociꝰ ̄ <lb/>a. et non mouetur velocius in f. ꝓportione adequa-<lb/>te: nec in minori ꝙ̄ f. / igitur b. mouetur velocius in <lb/>in maiori ꝓportione ꝙ̄ ſit f. </s>
              <s xml:id="N1A477" xml:space="preserve">Conſequentia patet cū <lb/>maiore. </s>
              <s xml:id="N1A47C" xml:space="preserve">Et probatur minor / quo ad primam parteꝫ <lb/>quia ſi b. mouetur velocius a. in f. ꝓportione: ſequit̄̄ <lb/>ex correlario ſuppõis /  ↄ̨tinuo reſiſtētie ipſiꝰ b. ad <lb/>reſiſtentiam ipſius a. eſt f. proportio adequate: et vl­<lb/>tra reſiſtentie ipſius b. ad reſiſtentiã ipſiꝰ a. ↄ̨tinuo <lb/>eſt proportio f. / igitur ipſius b. ad reſiſtentiam ipſi-<lb/>us b. eſt h. proportio: </s>
              <s xml:id="N1A48B" xml:space="preserve">Patet conſequentia / quia re-<lb/>ſiſtentia ipſius b. et ipſa poña a. ſunt equalia: quia <lb/>vtrum habet f. proportionem ad vnum tertiū pu­<lb/>ta ad reſiſtentiam ipſius a. per te: et ipſius b. ad a. ē <lb/>h. proportio / g̊. ipſius b. ad reſiſtentiam ipſius b. ē <lb/>h. proportio: igitur de primo ad vltimum patet cõ-<lb/>ſequentia. </s>
              <s xml:id="N1A49A" xml:space="preserve">Et vltra ipſius b. ad reſiſtentiam ipſius <lb/>b. eſt h. proportio a qua mouetur ipſa b. potentia <lb/>continuo: et h. proportio eſt maior f. proportione in <lb/>maiori proportione quam ſit f. proportio ex hypo­<lb/>theſi: igitur b. mouetur velocius a. in maiori ꝓpor-<lb/>tione velocius quam ſit f. / quod eſt probandum. </s>
              <s xml:id="N1A4A7" xml:space="preserve">Iã <lb/>probatur ſecunda pars minoris videlicet /  b. non <lb/>mouetur in minori proportione velocius quam ſit <lb/>f. </s>
              <s xml:id="N1A4B0" xml:space="preserve">Quod ſic probatur / quia ſi b. mouetur in minori <lb/>proportione velocius ipſa a. potentia quam ſit f. / ſe­<lb/>quitur ex correlario ſuppoſitionis /  continuo re-<lb/>ſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a. eſt minor <lb/>proportio quam f. et vltra reſiſtentie ipſius b. ad re­<lb/>ſiſtentiam ipſius a. eſt minor ꝓportio quam ſit f. et <lb/>b. habet ad a. ꝓportionem h. ex hipotheſi. </s>
              <s xml:id="N1A4BF" xml:space="preserve">igitur b. <lb/>ad reſiſtentiam eiuſdem b. eſt maior ꝓportio quam <lb/>ſit h. </s>
              <s xml:id="N1A4C6" xml:space="preserve">Patet conſequentia / quia a. eſt maior ꝙ̄ reſi-<lb/>ſtentia ipſius b. (cum a. ad vnum puta ad reſiſten-<lb/>tiam eiuſdem a. habet maiorem ꝓportionem ꝙ̄ re-<lb/>ſiſtentia ipſius b. ad idem tertium) / igitur ipſius b. <lb/>ad reſiſtētiã eiuſdē b. ē maior ꝓportio quã ipſius b. <lb/>ad ipſū a. et ipſiꝰ b. ad ip̄3 a. ē ꝓportio h. / igr̄ ipſiꝰ b. <lb/>ad reſiſtentiam eiuſdeꝫ b. eſt maior proportio quã <lb/>h. </s>
              <s xml:id="N1A4D7" xml:space="preserve">Et vltra ipſius b. ad reſiſtentiam ipſius b. eſt ma-<lb/>ior proportio quam h. et ab illa proportione b. con­<lb/>tinuo mouetur (cum moueatur a proportione quaꝫ <lb/>habet ad ſuam reſiſtentiaꝫ) / igitur b. mouetur a ma­<lb/>ori proportione ꝙ̄ ſit h. et h. proportio eſt maior f. <lb/>proportione in maiori proportione quam f. ex hy-<lb/>potheſi: igitur b. mouetur velocius a. in maiori pro­<lb/>portione quam ſit f. ꝓportio. </s>
              <s xml:id="N1A4E8" xml:space="preserve">Patet conſequentia / <lb/>quia ſi aliquid excedit vnum tertium in aliqua pro­<lb/>portione: omne maius illo excedit idem tertiū ī ma­<lb/>iori ꝓportione (vt conſtat) / ſed ſic eſt in ꝓpoſito  h. <lb/>ꝓportio eſt maior f. ꝓportione in maiori ꝓportio-<lb/>ne ꝙ̄ ſit ipſa f. ꝓportio: et ꝓportio a qua mouet̄̄ b. ē <lb/>maior h. / ergo ꝓportio a qua mouetur b. eſt maior <lb/>f. ꝓportione in maiori proportione quam ſit f. et ſic <lb/>habetur  b. mouetur velocius in maiori ꝓportio-               <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>               ne quam ſit f. / quod fuit ꝓbandum. </s>
              <s xml:id="N1A4FE" xml:space="preserve">Et ſic patet con­<lb/>cluſio.               <anchor type="note" xlink:href="note-0106-01" xlink:label="note-0106-01a"/>               </s>
              <s xml:id="N1A508" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. poña minor <lb/>in caſu concluſionis moueatur continuo a ꝓportio­<lb/>ne ſexquitertia et b. poña maior creſcat in duplo ve­<lb/>locius a. poña minore: tunc b. poña maior mouetur <lb/>velocius a. poña minore in maiori ꝓportione ꝙ̄ ſex­<lb/>quitertia: in minori tamen ꝓportione velocius quã <lb/>dupla. </s>
              <s xml:id="N1A517" xml:space="preserve">Secunda pars huius correlarii patet ex pri­<lb/>ma concluſione huius: et prima ex hac concluſione: <lb/>quoniam proportio dupla in qua b. potentia ma-<lb/>ior velocius creſcit quam a. potentia minor: eſt <lb/>maior quam ſexquitertia ad ſexquitertiam immo <lb/>maior quam dupla / vt patet ex quīto correlario ter­<lb/>tie concluſionis quarti capitis ſecunde partis.</s>
            </p>
            <div xml:id="N1A526" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0106-01a" xlink:label="note-0106-01" xml:id="N1A52A" xml:space="preserve">1. correl.</note>
            </div>
            <note position="right" xml:id="N1A530" xml:space="preserve">2. correl.</note>
            <p xml:id="N1A534">
              <s xml:id="N1A535" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor in caſu <lb/>concluſionis moueatur ab aliqua ꝓportione ſuper­<lb/>particulari: et b. poña maior continuo creſcat ī tri­<lb/>pla ꝓportione vel in aliqua alia maiore tripla ve-<lb/>lociꝰ ꝙ̄ a. poña minor: tunc b. poña maior continuo <lb/>velocius mouebitur a. poña minore in maiori pro-<lb/>portione quam ſit aliqua ꝓportio ſuperparticula­<lb/>ris: et in minore ꝓportione ꝙ̄ ſit tripla. </s>
              <s xml:id="N1A546" xml:space="preserve">Patet ſecū­<lb/>da pars correlarii ex prima concluſione huius: et <lb/>prima pars ex hac tertia quia omnis tripla vel ma­<lb/>ior tripla eſt maior quaꝫ ſuperparticularis ad quã­<lb/>libet ſuperparticularem (cum tripla ſit maior ꝙ̄ du­<lb/>pla ad maximam ſuperparticulareꝫ que eſt ſexqui­<lb/>altera) / vt conſtat intelligenti ſecundam partem hu­<lb/>ius operis: qui innumera ſimilia correlaria facile <lb/>poterit inferre.</s>
            </p>
            <p xml:id="N1A559">
              <s xml:id="N1A55A" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N1A55D" xml:space="preserve">Duabus potētiis <lb/>aliquod medium vniformiter difforme ad non gra­<lb/>dum terminatum tranſeuntibus: vniformiter con-<lb/>tinuo mouentibus per earum a non gradu potētie <lb/>continuum et vniforme crementum: vna altera in <lb/>maiori ꝓportione velocius continuo creſcente quã <lb/>ſit ꝓportio a qua altera continuo mouet̄̄ in minori <lb/>tñ ꝓportõe maiori ꝙ̄ ſit illa a q̈ mouet̄̄ alṫa poña q̄ <lb/>velocius continuo creſcit: velocius continuo moue­<lb/>tur altera, in minori tamen ꝓportione ꝙ̄ ſit ꝓpor-<lb/>tio a qua altera mouetur continuo. </s>
              <s xml:id="N1A574" xml:space="preserve">Probatur / ſit <lb/>a. poña que c. medium tranſeundo etc. vt ſupra con­<lb/>tinuo moueatur ab f. ꝓportione ſit b. poña q̄ idē <lb/>c. medium tranſeundo a non gradu potentie in h. ꝓ­<lb/>portione que ſit maior ꝙ̄ f. (maior inquam in mino­<lb/>re tamen ꝓportione ꝙ̄ ſit f.) continuo velocius creſ­<lb/>cat ipſa a. poña: tunc dico /  b. poña mouetur velo-<lb/>cius ꝙ̄ a. in minori tamen ꝓportione velocius quã <lb/>ſit f. </s>
              <s xml:id="N1A587" xml:space="preserve">Quod ſic probatur / quia b. non mouetur velo­<lb/>cius a. in f. ꝓportione: nec in maiori: ergo b. moue-<lb/>tur velocius a. in minori ꝓportione quam ſit f. / qḋ <lb/>fuit ꝓbandum. </s>
              <s xml:id="N1A590" xml:space="preserve">Conſequentia patet ex hypotheſi: et <lb/>ꝓbatur maior: quia ſi b. moueretur velocius a in f. <lb/>ꝓportione: reſiſtentie ipſius b. ad reſiſtentiam ipſiꝰ <lb/>a. continuo eēt f. ꝓportio. </s>
              <s xml:id="N1A599" xml:space="preserve">(Hec conſequentia plerū­<lb/> arguta eſt) et vltra reſiſtentie ipſius b. ad reſiſten­<lb/>tiam ipſius a. continuo eſt f. ꝓportio: et ipſius a. ad <lb/>reſiſtentiam ipſius a. eſt f. ꝓportio: igitur reſiſtētia <lb/>ipſius b. et ipſum a. ſunt equalia. </s>
              <s xml:id="N1A5A4" xml:space="preserve">Conſequentia pa­<lb/>tet / quia habent eandem ꝓportionem ad vnum ter-<lb/>tium: et vltra reſiſtentia ipſius b. et ipſum a. ſunt eq̈­<lb/>lia, et ipſius b. ad ipſum a. eſt h. ꝓportio ex hypothe­<lb/>ſi: igitur ipſius b. ad reſiſtentiam eiuſdem b. eſt h. ꝓ­<lb/>portio. </s>
              <s xml:id="N1A5B1" xml:space="preserve">Patet conſequentia / quia eiuſdem ad duo <lb/>equalia eſt eadem ꝓportio: et vltra ipſius b. ad reſi­<lb/>ſtentiam ipſius b. eſt h. ꝓportio et a tali mouetur ip­<lb/>ſum b. cum continuo moueatur vniformiter a ꝓpor­<lb/>tione quam habet ad ſuam reſiſtentiam: et h. ꝓpor-               <pb chead="Primi tractatus" file="0107" n="107"/>               tio eſt maior f. proportione in minori proportione <lb/>quam ſit f. ex hypotheſi: igitur b. mouetur in mino-<lb/>ri proportione velocius a. quam ſit f. / quod fuit pro­<lb/>bandum. </s>
              <s xml:id="N1A5C7" xml:space="preserve">Sed iam ꝓbatur minor videlicet /  b. nõ <lb/>mouetur velocius in maiori proportione quam ſit <lb/>f. / quod ſic ꝓbatur / quia ſi b. moueretur velocius a. ī <lb/>maiori proportione quam ſit f. ꝓportio a qua mo-<lb/>uetur a. / ſequitur /  continuo reſiſtentie ipſius b. ad <lb/>reſiſtentiam ipſius a. eſt maior proportio quam f. <lb/>et vltra reſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a. <lb/>eſt maior proportio quam f. et ipſius a. ad eandem <lb/>reſiſtentiaꝫ ipſius a. eſt f. proportio adequate ex hy­<lb/>potheſi. </s>
              <s xml:id="N1A5DC" xml:space="preserve">igitur continuo reſiſtentia ipſius b. eſt ma­<lb/>ior a. poña. </s>
              <s xml:id="N1A5E1" xml:space="preserve">Patet conſequentia / quia reſiſtentia ip­<lb/>ſius b. habet maiorem proportionem ad vnū terti­<lb/>um puta ad reſiſtentiam ipſius a. </s>
              <s xml:id="N1A5E8" xml:space="preserve">Et vltra ex con-<lb/>ſequenti continuo reſiſtentia ipſius b. eſt maior a. <lb/>potentia. </s>
              <s xml:id="N1A5EF" xml:space="preserve">et ipſius b. ad a. eſt proportio h. / igitur ip­<lb/>ſius b. ad reſiſtentiam eiuſdem b. eſt minor ꝓportio <lb/>quam h. et ab illa mouetur continuo b. / igitur b. con­<lb/>tinuo mouetur a minori proportione ꝙ̄ h. et h. pro-<lb/>portio eſt maior f. proportione a qua continuo mo­<lb/>uetur a. (in minori tamen ꝓportione quaꝫ ſit f.) / igi­<lb/>tur proportio a qua moueatur b. eſt maior quam f. <lb/>a qua mouetur a. in minori proportione quam f. / et <lb/>per conſequens b. mouetur continuo velocius a. in <lb/>minori ꝓportione quam ſit f. / quod fuit probandū: <lb/></s>
              <s xml:id="N1A605" xml:space="preserve">Patet tamen conſequentia / quia cum aliquid exce­<lb/>dit vnum tertium in aliqua proportione: </s>
              <s xml:id="N1A60A" xml:space="preserve">omne mi­<lb/>nus maius tamen illo tertio excedit idem tertium ī <lb/>minori proportione. </s>
              <s xml:id="N1A611" xml:space="preserve">ſed per te proportio a qua mo­<lb/>uetur b. potentia eſt maior quam ꝓportio f. et mi-<lb/>nor quam h. proportio: igitur. </s>
              <s xml:id="N1A618" xml:space="preserve">Et ſic patet antece-<lb/>dens cum concluſione. </s>
              <s xml:id="N1A61D" xml:space="preserve">¶ Has tres concluſiones pul­<lb/>chras diligenter nota </s>
              <s xml:id="N1A622" xml:space="preserve">Poſſunt enim ex eis inferri <lb/>infinite concluſiones cum multis quas ponit calcu­<lb/>lator in ſecundo capite de medio non reſiſtente.</s>
            </p>
            <note position="left" xml:id="N1A629" xml:space="preserve">1. correl.</note>
            <p xml:id="N1A62D">
              <s xml:id="N1A62E" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. potentia minor mo­<lb/>ueatur ab aliqua proportiõe minore multiplici ra­<lb/>tionali in caſu concluſionis puta ab aliqua propor­<lb/>tione ſuperparticulari aut ſuprapartiente. </s>
              <s xml:id="N1A637" xml:space="preserve">et b. po­<lb/>tentia maior creſcat velocius a. potentia minore in <lb/>alqua proportione multiplici: tunc b. potentia ma­<lb/>ior non mouebitur velocius b. poña minore in pro-<lb/>portione a qua mouetur a. potentia minor. </s>
              <s xml:id="N1A642" xml:space="preserve">ſed in <lb/>maiore vel minore ſecundum tenorem tertie vel q̈r-<lb/>te concluſionis. </s>
              <s xml:id="N1A649" xml:space="preserve">Patet hoc correlarium / quia vt pa­<lb/>tet ex ſuperioribus: nun̄ maior potentia mouetur <lb/>velocius minore mota a ꝓportione rationali in ea <lb/>ꝓportione a qua mouetur minor: niſi quando pro-<lb/>portio in qua maior velocius creſcit ſe habet ad ꝓ­<lb/>portionem a qua mouetur minor in ꝓportione ra-<lb/>tionali: ita  qualis eſt proportio a qua mouetur <lb/>minor talis debet eſſe proportio inter proportiõeꝫ <lb/>in qua maior velocius creſcit, et proportionē a qua <lb/>minor mouetur / vt patet: ſed nulla ꝓportio multi-<lb/>plex ſe habet ad proportionem minorem multipli-<lb/>ci rationalem in aliqua ꝓportione rationali: vt pa­<lb/>tet ex ſecunda et ſexta concluſionibus ſexti capitis <lb/>ſecunde partis / igitur correlarium verum.</s>
            </p>
            <note position="left" xml:id="N1A666" xml:space="preserve">2. correl.</note>
            <p xml:id="N1A66A">
              <s xml:id="N1A66B" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor mouea­<lb/>tur ab aliqua ꝓportione multiplici: et b. potentia <lb/>maior creſcat velocius ipſa a. potentia in aliqua ꝓ­<lb/>portione multiplici ſuperparticulari: aut multipli­<lb/>ci ſuprapartiente. </s>
              <s xml:id="N1A676" xml:space="preserve">tunc b. potentia maior nõ moue­<lb/>tur velocius a. minore in ꝓportione multiplici a q̈ <lb/>mouetur a. potentia minor </s>
              <s xml:id="N1A67D" xml:space="preserve">Probatur / quia ſi ſic iã <lb/>ꝓportio in qua creſcit b. maior potentia velocius <lb/>a. minore ſe haberet ad proportionem a qua moue­               <cb chead="Capitulum vndecimum"/>               tur a. potentia minor in eadem ꝓportione multipli­<lb/>ci a qua mouetur eadē a. poña minor / vt patet ex ſe­<lb/>cunda cõcluſione huius: ſed hoc eſt falſum / quia nul­<lb/>la multiplex eſt cõmenſurabilis ꝓportioni multipli­<lb/>ci ſuperparticulari, aut multiplici ſuprapartienti / <lb/>vt patet ex tertia cõcluſione ſecunde partis: igitur <lb/>illud ex quo ſequitur eſt falſum: et per conſequēs cor­<lb/>relarium verum.               <anchor type="note" xlink:href="note-0107-01" xlink:label="note-0107-01a"/>               </s>
              <s xml:id="N1A69A" xml:space="preserve">¶ Sequitur tertio /  ſi a. poña mi­<lb/>nor moueatur ab aliqua ꝓportione non multipli-<lb/>ci rationali: et b. poña maior creſcat velocius mino­<lb/>re in proportione aliqua multiplici: tunc b. poten-<lb/>tia maior nõ mouetur velocius a. poña minore in ꝓ­<lb/>portione a qua mouetur a. poña minor. </s>
              <s xml:id="N1A6A7" xml:space="preserve">Patet cor­<lb/>relarium / quia alias ſequeretur /  proportio non <lb/>multiplex in qua b. poña maior velocius creſcit a. <lb/>poña minore ſe haberet ad ꝓportionem non multi­<lb/>plicem rationalem a qua mouetur a. poña minor ī <lb/>eadem proportione non multiplici rationali a qua <lb/>mouetur a. potentia minor / vt patet ex ſecunda con­<lb/>cluſione huius: ſed conſequens eſt falſum / vt patet <lb/>ex quarta concluſione ſexti capitis ſecunde partis: <lb/>igitur illud ex quo ſequitur: et per conſequens cor-<lb/>relatium verum.               <anchor type="note" xlink:href="note-0107-02" xlink:label="note-0107-02a"/>               </s>
              <s xml:id="N1A6C3" xml:space="preserve">¶ Sequitur quarto /  ſi a. potētia <lb/>minor moueatur ab aliqua proportione ſuperpar­<lb/>ticulari: et poña b. maior creſcat velocius a. poten-<lb/>tia minore in aliqua ꝓportione ſuperparticulari: <lb/>tunc b. potentia maior nõ mouetur velocius a. potē­<lb/>tia minore in ea ꝓportione ſuperparticulari a qua <lb/>mouetur a. poña minor. </s>
              <s xml:id="N1A6D2" xml:space="preserve">Probatur / quia alias ſe-<lb/>queretur ex ſecunda concluſione cum aliis  ꝓpor-<lb/>tio ſuperparticularis in qua b. poña maior velociꝰ <lb/>creſcit minore ſe haberet ad ꝓportionem ſuperpar­<lb/>ticularem a qua mouetur a. poña minor in eadem <lb/>ꝓportione ſuperparticulari a qua mouetur eadem <lb/>a. poña minor: ſed hoc eſt falſum. </s>
              <s xml:id="N1A6E1" xml:space="preserve">quia nulla ꝓpor-<lb/>tio ſuperparticularis eſt cõmenſurabilis alicui ſu­<lb/>perparticulari / vt patet ex quinta concluſione ſexti <lb/>capitis ſecunde partis: igitur illud ex quo ſequitur / <lb/>et per conſequens correlarium verum.</s>
            </p>
            <div xml:id="N1A6EC" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0107-01a" xlink:label="note-0107-01" xml:id="N1A6F0" xml:space="preserve">3. correl.</note>
              <note position="right" xlink:href="note-0107-02a" xlink:label="note-0107-02" xml:id="N1A6F6" xml:space="preserve">4. correl.</note>
            </div>
            <note position="right" xml:id="N1A6FC" xml:space="preserve">5. correl.</note>
            <p xml:id="N1A700">
              <s xml:id="N1A701" xml:space="preserve">¶ Sequitur quinto /  nūquam poña maior poteſt <lb/>moueri velocius minore in ꝓportione multiplici a <lb/>qua mouetur minor. </s>
              <s xml:id="N1A708" xml:space="preserve">niſi ipſa maior creſcat conti-<lb/>nuo velocius minore in alia ꝓportione multiplici. <lb/></s>
              <s xml:id="N1A70E" xml:space="preserve">Patet hoc correlarium / quia ſola multiplex eſt pro­<lb/>portioni multiplici cõmenſurabilis / vt patet ex ſex­<lb/>ta concluſione ſexti capitis ſecunde partis.</s>
            </p>
            <note position="right" xml:id="N1A715" xml:space="preserve">6. correl.</note>
            <p xml:id="N1A719">
              <s xml:id="N1A71A" xml:space="preserve">¶ Sequitur ſexto /  ſi in caſu huius quarte conclu-<lb/>ſionis a. poña minor cõtinuo moueatur ab aliqua <lb/>proportione multiplici: et b. poña maior creſcat ve­<lb/>locius a potentia minore in aliqua ꝓportione mul­<lb/>tiplici ſuperparticulari vel multiplici ſuprapartiē­<lb/>te compoſita ex proportione multiplici a qua mo-<lb/>uetur minor: et aliqua ſuperparticulari, vel ſupra-<lb/>partiente (vt oportet): tunc illa b. potentia maior <lb/>mouetur velocius a. potentia minore in minori pro­<lb/>portione quam ſit proportio a qua mouetur a. po-<lb/>tentia minor: et etiam in minori ꝓportione quaꝫ ſit <lb/>ea in qua velocius creſcit a. poña minore. </s>
              <s xml:id="N1A733" xml:space="preserve">Proba-<lb/>tur prima pars ex hac quarta concluſione / quia om­<lb/>nis ꝓportio multiplex ſuperparticularis, aut mul­<lb/>tiplex ſuprapartiens eſt minor quam multiplex ad <lb/>totum reſiduum eius dempta proportione ſupra-<lb/>partiente aut ſuperparticulari quam vltra illam <lb/>multiplicem continet / vt patet / quoniam ipſa nõ cõ-<lb/>tinet talem multiplicem niſi ſemel: ergo non exce-<lb/>dit illam in aliqua ꝓportione multiplici ſed in mi-<lb/>nori. </s>
              <s xml:id="N1A748" xml:space="preserve">Et ſic ex concluſione ſequitur /  mouetur ī mi­<lb/>nori proportione velociꝰ ꝙ̄ ſit talis proportio mul­<lb/>tiplex a qua mouetur potentia minor. </s>
              <s xml:id="N1A74F" xml:space="preserve">Sed ſecūda               <pb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato." file="0108" n="108"/>               pars correlarii patet ex prima parte eiuſdem, et ex <lb/>prima concluſione huius. </s>
              <s xml:id="N1A759" xml:space="preserve">Et ſic patet correlarium. <lb/></s>
              <s xml:id="N1A75D" xml:space="preserve">¶ Innumera poteris ſtudio ſe lector proprio labo-<lb/>re his ſimilia inferre correlaria.</s>
            </p>
            <note position="left" xml:id="N1A762" xml:space="preserve">Octaua <lb/>cõcluſio <lb/>calcula.</note>
            <p xml:id="N1A76A">
              <s xml:id="N1A76B" xml:space="preserve">Quinta cõcluſio. </s>
              <s xml:id="N1A76E" xml:space="preserve">Duabus potentiis <lb/>aliquod medium vniformiter difforme ad nõ gra-<lb/>dum terminatum tranſeundo vniformiter cõtinuo <lb/>mouentibus, vna altera velocius continuo creſcē­<lb/>te in ea proportione que proportionem a qua mo-<lb/>uetur altera per proportionem duplam excedit: po­<lb/>tentia que velocius continuo creſcit velocius conti-<lb/>nuo mouetur in proportione dupla ipſa potentia <lb/>minore. </s>
              <s xml:id="N1A781" xml:space="preserve">Probatur / ſit a. potentia que c. mediū .etc̈. <lb/>tranſeundo continuo mouetur ab f. proportione ꝑ <lb/>ſui a non gradu potentie continuū et vniforme cre-<lb/>mentum: ſit h. proportio que f. proportionem ex-<lb/>cedat per proportionem duplam, et ſit b. potentia <lb/>que idem c. medium tranſeundo a nõ gradu poten-<lb/>tie cõtinuo in h. proportione velocius creſcat quaꝫ <lb/>a. potentia: tunc dico /  b. potentia continuo in du­<lb/>plo velocius mouetur a. potētia minore. </s>
              <s xml:id="N1A794" xml:space="preserve">Quod ſic <lb/>probatur / quia b. mouetur velocius a. / vt conſtat, et <lb/>non mouetur velocius in maiori proportione quã <lb/>dupla, nec in minori: igitur b. mouetur adequate ī <lb/>duplo velocius: quod fuit probandū. </s>
              <s xml:id="N1A79F" xml:space="preserve">Conſequen-<lb/>tia ptꝫ cum maiore, et prima pars minoris proba-<lb/>tur / quia ſi b. mouetur in maiori proportiõe quam <lb/>dupla velocius ipſa potentia a. / ſequitur /  reſiſten­<lb/>tie ipſius b. ad reſiſtentiã ipſius a. eſt maior quam <lb/>dupla et proportio ipſius b. ad reſiſtentiam ipſius <lb/>a. componitur adequate ex duplici f. et proportiõe <lb/>dupla: igitur demendo a proportione ipſius b. ad <lb/>reſiſtentiam ipſius a. proportionem que eſt reſiſten­<lb/>tie ipſius b. ad reſiſtentiam ipſius a. non manet du­<lb/>plex f. ſed minus. </s>
              <s xml:id="N1A7B6" xml:space="preserve">Patet cõſequētia / quia per te pro­<lb/>portio reſiſtentie ipſius b. ad reſiſtentiã ipſius a. eſt <lb/>maior quam ſit proportio dupla: et vltra demendo <lb/>a proportione ipſius b. ad reſiſtentiã ipſius a. pro-<lb/>portionē que eſt reſiſtentie ipſius b. ad reſiſtentiaꝫ <lb/>ipſius a. nõ manet duplex f. ſed minus, et demendo <lb/>a proportione ipſius b. ad reſiſtentiã ipſius a. pro-<lb/>portionem que eſt reſiſtentie ipſius b. ad reſiſtentiã <lb/>ipſius a. non manet niſi proportio que eſt ipſius b. <lb/>ad reſiſtentiam eiuſdem b. / igitur proportio que eſt <lb/>ipſius b. ad reſiſtentiam eiuſdem b. nõ eſt duplex f. <lb/>ſed minus, et ab illa proportione continuo b. poten­<lb/>tia mouetur: igitur continuo b. mouetur a propor-<lb/>tione que nõ eſt duplex f. ſed minus: et a. potentia cõ­<lb/>tinuo mouetur ab f. proportione: igitur b. potētia <lb/>mouetur velocius a. in minori proportione quam <lb/>dupla: et per conſequens nõ in maiori proportione <lb/>quam dupla: quod fuit probandū. </s>
              <s xml:id="N1A7DB" xml:space="preserve">Sed  propor-<lb/>tio ipſius b. ad reſiſtentiam ipſius a. componitur <lb/>adequate ex duplici f. et proportione dupla: patet / <lb/>quia proportio ipſius b. ad reſiſtentiam ipſius a. <lb/>cõponitur adequate ex proportione h. que eſt ipſiꝰ <lb/>b. ad ipſum a. et ex proportiõe f. que eſt ipſius a. ad <lb/>reſiſtentiam ipſius a. / vt conſtat. </s>
              <s xml:id="N1A7EA" xml:space="preserve">et proportio h. eſt <lb/>vnū f. et proportio dupla adequate / vt ptꝫ: q2 h. exce­<lb/>dit f. per duplam proportionem adequate ex hypo­<lb/>theſi: igitur proportio ipſius b. ad reſiſtentiam ip-<lb/>ſius a. cõponitur adequate ex duplici f. et ex propor­<lb/>tione dupla / quod fuit probandum. </s>
              <s xml:id="N1A7F7" xml:space="preserve">Et ſic patet pri­<lb/>ma pars minoris. </s>
              <s xml:id="N1A7FC" xml:space="preserve">Iam probatur ſecunda pars mi­<lb/>noris videlicet /  b. nõ mouetur velocius a. in mino­<lb/>ri proportione quam dupla: quia ſi b. mouetur ve-<lb/>locius a. in minori proportione quam dupla: ſequi­<lb/>tur /  continuo reſiſtentie ipſius b. ad reſiſtentiam <lb/>ipſius a. eſt minor preportio ꝙ̄ dupla proportio, et               <cb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato."/>               vltra reſiſtentie ipſius b. ad reſiſtentiam ipſius a. cõ­<lb/>tinuo eſt minor proportio ꝙ̄ dupla: et proportio ip­<lb/>ſius b. ad reſiſtentiam ipſius a. cõponitur adequa-<lb/>te ex duplici f. et ex proportione dupla / vt ſupra ar-<lb/>gutum eſt: igitur demendo a proportione ipſius b. <lb/>ad reſiſtentiam ipſius a. proportionem que eſt reſi­<lb/>ſtentie ipſius b. ad reſiſtentiam ipſius a. manet ma­<lb/>gis quam duplex f. </s>
              <s xml:id="N1A81A" xml:space="preserve">Patet cõſequentia / quia per te <lb/>proportio que eſt reſiſtentie ipſius b. ad reſiſtentiã <lb/>ipſius a. eſt minor proportio quam dupla: et vltra <lb/>demendo a proportione ipſius b. ad reſiſtentiã ip-<lb/>ſius a. proportionem que eſt reſiſtentie ipſius b. ad <lb/>reſiſtentiam ipſius a. manet magis quam duplex f. <lb/>et demendo a proportione ipſius b. ad reſiſtentiam <lb/>ipſius a. proportionem que eſt reſiſtentie ipſius b. <lb/>ad reſiſtentiam ipſius a. manet proportio ipſius b. <lb/>ad reſiſtentiam eiuſdem b. / igitur proportio b. ad re­<lb/>ſiſtentiam eiuſdem b. eſt maior quam duplex f. et ab <lb/>illa proportione b. potentia continuo mouetur: igi­<lb/>tur b. continuo mouetur a maiori proportione quã <lb/>dupla ad f. et a. potentia cõtinuo mouetur ab f. pro­<lb/>portione: igitur b. continuo mouetur velocius a. in <lb/>maiori proportione quam dupla: et per conſequēs <lb/>non mouetur velocius in minori proportione quaꝫ <lb/>dupla / quod fuit probanduꝫ. </s>
              <s xml:id="N1A83F" xml:space="preserve">Et ſic patet concluſio / <lb/>que eſt octaua concluſio calculatoris in ſecundo ca­<lb/>pite de medio non reſiſtente.               <anchor type="note" xlink:href="note-0108-01" xlink:label="note-0108-01a"/>               </s>
              <s xml:id="N1A84B" xml:space="preserve">¶ Ex quo ſequitur pri-<lb/>mo /  ſi in caſu cõcluſionis a. potentia cõtinuo mo-<lb/>ueatur a proportione ſexquialtera: et b. potētia ma­<lb/>ior creſcat in triplo velocius continuo ipſa a. potē-<lb/>tia minore: ipſa potentia b. mouetur cõtinuo in du-<lb/>plo velocius a. potētia minore. </s>
              <s xml:id="N1A858" xml:space="preserve">Probatur / quia tri­<lb/>pla excedit ſexquialteram per duplam / vt patet ex <lb/>quarta concluſione quarti capitis ſecunde partis / <lb/>igitur ex hac concluſione ſequitur /  ſi a. potentia <lb/>minor moueatur a proportione ſexquialtera, et b. <lb/>potentia maior creſcat in triplo velocius  b. potē­<lb/>tia maior mouetur cõtinuo in duplo velocius a. po­<lb/>tentia minore / quod fuit probandum.               <anchor type="note" xlink:href="note-0108-02" xlink:label="note-0108-02a"/>               </s>
              <s xml:id="N1A86E" xml:space="preserve">¶ Sequitur <lb/>ſecundo /  ſi a. potentia minor moueatur a. propor­<lb/>tione dupla, et b. potentia maior creſcat in quadru­<lb/>plo velocius continuo: ipſa potentia b. mouetur cõ­<lb/>tinuo in duplo velocius a. potentia minore. </s>
              <s xml:id="N1A879" xml:space="preserve">Patet / <lb/>quia quadrupla excedit duplam per duplam / vt ptꝫ <lb/>ex quarta concluſione preallegata igitur               <anchor type="note" xlink:href="note-0108-03" xlink:label="note-0108-03a"/>               </s>
              <s xml:id="N1A885" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio /  ſi a. potētia minor moueatur a proportiõe <lb/>quadrupla et b. potentia maior creſcat in octuplo <lb/>velocius: tunc b. potentia maior mouetur continuo <lb/>in duplo velocius. </s>
              <s xml:id="N1A890" xml:space="preserve">Patet / quia octupla quadruplã <lb/>per duplam excedit / vt patet ex quarta concluſione <lb/>preallegata.               <anchor type="note" xlink:href="note-0108-04" xlink:label="note-0108-04a"/>               </s>
              <s xml:id="N1A89C" xml:space="preserve">¶ Sequitur quarto /  ſi a. potentia <lb/>minor moueatur cõtinuo a proportione ſexquiter-<lb/>tia et b. potentia maior continuo creſcat in propor­<lb/>tione dupla ſuprabipartiēte tertias velociꝰ b. potē­<lb/>tia maior mouetur cõtinuo in duplo velocius. </s>
              <s xml:id="N1A8A7" xml:space="preserve">Ptꝫ / <lb/>quia dupla ſuprabipartiens tertias ſexquitertiaꝫ <lb/>per duplam excedit / vt patet ex quarta concluſione <lb/>preallegata. </s>
              <s xml:id="N1A8B0" xml:space="preserve">Et iſto modo infinita talia correlaria <lb/>poteris inferre,</s>
            </p>
            <div xml:id="N1A8B5" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0108-01a" xlink:label="note-0108-01" xml:id="N1A8B9" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0108-02a" xlink:label="note-0108-02" xml:id="N1A8BF" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0108-03a" xlink:label="note-0108-03" xml:id="N1A8C5" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0108-04a" xlink:label="note-0108-04" xml:id="N1A8CB" xml:space="preserve">4. correĺ.</note>
            </div>
          </div>
          <div xml:id="N1A8D1" level="4" n="12" type="chapter" type-free="capitulum">
            <head xml:id="N1A8D6" xml:space="preserve">Capitulum duodecimum: aliqui-<lb/>bus predictarum concluſionum pre-<lb/>cedentium capitum obiiciens.</head>
            <p xml:id="N1A8DD">
              <s xml:id="N1A8DE" xml:space="preserve">HIs concluſionibus velocitatē <lb/>motus in medio vniformiter difformi in-<lb/>uariato declarantibus (vt potuimus) ali-<lb/>qua ex parte expeditis: nunc opere precium eſt lima <lb/>diſputationis ea que dicta ſunt polire at limare.</s>
            </p>
            <p xml:id="N1A8E9">
              <s xml:id="N1A8EA" xml:space="preserve">Et ideo ſecūde concluſioni decimi ca-               <pb chead="Primi tractatus" file="0109" n="109"/>               pitis obiicitur ſic. </s>
              <s xml:id="N1A8F2" xml:space="preserve">Si illa cõcluſio eſſet vera: ſeque-<lb/>retur /  due potentie equales continuo manentes <lb/>equales idem medium vel equale tranſeuntes vna <lb/>altera continuo velocius moueretur cõſequens eſt <lb/>falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1A8FD" xml:space="preserve">Falſitas conſe­<lb/>quentis ptꝫ: quia reſiſtentiis equalibus potētiiſ <lb/>equalibus, neceſſe eſt motus eſſe equales / vt ſatis cõ­<lb/>ſtat: quia tunc proportiones equales erūt ex quibꝰ <lb/>equales motus conſurgunt. </s>
              <s xml:id="N1A908" xml:space="preserve">Sed iam ſequela dedu­<lb/>citur / et capio vnū pedale et vnū ſemipedale: et per <lb/>vtrū illorum ſit extenſa latitudo reſiſtētie vnifor-<lb/>miter difformis a nõ gradu vſ ad octauū: et inci-<lb/>piat a. potentia moueri a nõ gradu reſiſtentie in pe­<lb/>dali vniformiter continuo, creſcens vniformiter a <lb/>nõ gradu potentie / vt ſepius dictum eſt: et b. poten-<lb/>tia incipiat moueri a non gradu reſiſtentie in ſemi­<lb/>pedali, continuo vniformiter et eque velociter cre-<lb/>ſcens ſicut a. potentia. </s>
              <s xml:id="N1A91D" xml:space="preserve">Quo poſito ſic argumentor <lb/>illa duo media ſunt equaliter reſiſtentia cum habe­<lb/>ant equalem reſiſtentiam oīno: puta a non gradu <lb/>vſ ad octauum: et a. et b. continuo manentes equa­<lb/>les vniformiter mouentur / vt dicit ſecunda cõcluſio <lb/>quam impugnamus: et a. velocius mouetur quã b. / <lb/>igitur propoſitum. </s>
              <s xml:id="N1A92C" xml:space="preserve">Maior eſt nota et minor proba­<lb/>tur: et ſuppono /  quãdo in duobus mediis inequa­<lb/>libus extenditur eadem latitudo reſiſtentie vnifor-<lb/>miter difformis a non gradu vſ ad certum gradū <lb/>in ea proportione in qua ſe habent media ad inuicē <lb/>quantitatiue, in eadē proportione plus diſtat qui-<lb/>libet punctus a non gradu in medio maiori quam <lb/>conſimilis punctus in medio minori: ita  ſi vnum <lb/>mediū ſit duplum ad alterum: gradus medius per <lb/>duplum maius ſpacium diſtat a non gradu in me-<lb/>dio maiori ꝙ̄ in medio minori. </s>
              <s xml:id="N1A943" xml:space="preserve">Et ſic de quocū a-<lb/>lio puncto. </s>
              <s xml:id="N1A948" xml:space="preserve">Hoc ptꝫ ex diffiniitõe qualitatis vnifor-<lb/>miter difformis quarto tractatu. </s>
              <s xml:id="N1A94D" xml:space="preserve">Quo ſuppoſito <lb/>arguitur ſic minor: quia a. et b. mouentur vniformi­<lb/>ter continuo / vt dicit illa ſecunda concluſio quã im­<lb/>pugnamus: et a. non mouetur ita velociter ſicut b. <lb/>adequate: nec tardius: igitur a. cõtinuo velociꝰ mo-<lb/>uetur quã b. / quod fuit probandū. </s>
              <s xml:id="N1A95A" xml:space="preserve">Cõſequentia ptꝫ <lb/>et arguitur maior: q2 ſi a. mouetur ita velociter ade­<lb/>quate ſicut b. / ſequitur (cū cõtinuo a. et b. ſunt equa-<lb/>les) /  cõtinuo in quocū puncto eſt a. in medio pe-<lb/>dali in conſimili puncto eſt b. in medio ſemipedali. <lb/></s>
              <s xml:id="N1A966" xml:space="preserve">Patet cõſequētia ex ſe et vltra: in quocū puncto <lb/>eſt a. in pedali in ↄ̨ſimili eſt b. in ſemipedali: et quod­<lb/>libet punctū ī pedali in duplo plus diſtat a nõ g̈du <lb/>̄ cõſimile punctū in ſemipedali: igit̄̄ cõtinuo in du­<lb/>plo plus diſtat a. a puncto a quo īcepit moueri ꝙ̄ b. <lb/>cū tam a. quã b. inceperūt moueri a nõ gradu illius <lb/>reſiſtentie: et ꝑ cõſequēs a. ↄ̨tinuo in duplo velocius <lb/>mouetur ꝙ̄ b. et ex hoc nõ ita velociter adequate / qḋ <lb/>eſt ꝓbandū. </s>
              <s xml:id="N1A979" xml:space="preserve">Sed tã probo minorē videlicet /  a. nõ <lb/>mouet̄̄ tardius ꝙ̄ b. q2 ſi mouetur tardiꝰ: ſequit̄̄ /  <lb/>cõtinuo eſt in puncto magis reſiſtente ꝙ̄ b. et ſi cõti-<lb/>nuo eſt in pūcto magis reſiſtente ꝙ̄ b. / ſequit̄̄ /  con-<lb/>tinuo pluſ̄ in duplo velociꝰ mouetur ꝙ̄ b. / et ꝑ ↄ̨ñs <lb/>nõ tardius / qḋ fuit ꝓbandū. </s>
              <s xml:id="N1A986" xml:space="preserve">Patet ↄ̨ña / q2 ſi ↄ̨tinuo <lb/>a. eſſet in pūcto ↄ̨ſimili ſiue equali illi pūcto in quo <lb/>eſt b. cõtinuo a. in duplo velociꝰ moueret̄̄ ipſo b. / vt <lb/>ꝓbatū eſt: igit̄̄ ſi cõtinuo ſit in pūcto adhuc magis <lb/>reſiſtente / ſequitur /  continuo velocius mouetur ̄ <lb/>b. </s>
              <s xml:id="N1A993" xml:space="preserve">Patet conſequentia per locum a maiori.</s>
            </p>
            <p xml:id="N1A996">
              <s xml:id="N1A997" xml:space="preserve">Reſpõdeo cõcedendo quod īfertur / q2 <lb/>illud ſufficienter demõſtrat argumentū: et nego fal­<lb/>ſitatē cõſequētis: et cū ꝓbatur nego /  ille reſiſtētie <lb/>ſint ſimpliciter equales. </s>
              <s xml:id="N1A9A0" xml:space="preserve">Ad equalitatem enim reſi­               <cb chead="Capitulū duodecimū."/>               <anchor type="note" xlink:href="note-0109-01" xlink:label="note-0109-01a"/>               ſtentiarum (quod nota) ſaltem vniformiter diffor-<lb/>mium non ſufficit equalitas intenſionis, ſed etiam <lb/>extenſionum equalitas requiritur / vt probat argu-<lb/>mentum.</s>
            </p>
            <div xml:id="N1A9B1" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0109-01a" xlink:label="note-0109-01" xml:id="N1A9B5" xml:space="preserve">Quid re­<lb/>q̇rit̄̄ ad e­<lb/>q̈litatem <lb/>reſiſtētia­<lb/>rum.</note>
            </div>
            <p xml:id="N1A9C3">
              <s xml:id="N1A9C4" xml:space="preserve">Sed ↄ̨̨tra: q2 ſi ſolutio eſſet vera vide­<lb/>licet /  quãto eadē reſiſtētia vniformiter difformis <lb/>eſt in minori medio tantū plus reſiſtit ſed nõ adeq̈-<lb/>te: ſequeret̄̄ /  hoc ꝓueniret ratiõe dēſitatꝪ: ſed hoc <lb/>eſt falſum: igit̄̄ ſolutio nulla. </s>
              <s xml:id="N1A9CF" xml:space="preserve">Sequela ptꝫ / q2 nõ vi­<lb/>detur alia ratio. </s>
              <s xml:id="N1A9D4" xml:space="preserve">Sed falſitas cõſequētis arguitur / <lb/>q2 volo /  pedale et ſemipedale ſint eq̈liter dēſa ſi-<lb/>cut facile ſit / vt ptꝫ ex primo capite tertii tractatꝰ: et <lb/>eadē latitudo reſiſtētie vniformiter difformis extē-<lb/>datur ꝑ pedale et ſemipedale. </s>
              <s xml:id="N1A9DF" xml:space="preserve">Quo poſito ptꝫ /  il-<lb/>le q̈litates ſūt eque rare: q2 ſūt in ſubiectis eq̈liter <lb/>raris.               <anchor type="note" xlink:href="note-0109-02" xlink:label="note-0109-02a"/>               </s>
              <s xml:id="N1A9EB" xml:space="preserve">(Raritas em̄ vel dēſitas accidētis penes ra-<lb/>ritatē vel dēſitatē ſubiecti cõmenſurari hꝫ) et tamē <lb/>eadē poña velociꝰ mouet̄̄ in reſiſtētia pedali ꝙ̄ in ſe­<lb/>mipedali / vt probatū eſt: igit̄̄ illud non prouenit ex <lb/>parte raritatis aut denſitatis / quod fuit ꝓbandū.</s>
            </p>
            <div xml:id="N1A9F6" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0109-02a" xlink:label="note-0109-02" xml:id="N1A9FA" xml:space="preserve">Raritas <lb/>q̈litatis <lb/>vnde ſu-<lb/>matur.</note>
            </div>
            <p xml:id="N1AA06">
              <s xml:id="N1AA07" xml:space="preserve">Reſpondeo vt michi apparet pro nūc <lb/>concedendo ſequelam: et negando falſitatem conſe­<lb/>quentis: et ab probatione admiſſo caſu nego /  ille <lb/>qualitates ſint eque rare in maiori ſubiecto et in mi­<lb/>nori: et cum probatur / quia ſubiecta ſunt eque rara <lb/>concedo illud: et cum infertur ergo et accidentia: ne­<lb/>go conſequentiam: et ad probationem nego /  ex ra­<lb/>ritate ſubiecti debeat ſumi raritas accidētis in or-<lb/>dine ad aliud accidens: ſed debet ſumi ex multitu-<lb/>dine forme accidentalis ſub proportionali quanti­<lb/>tate. </s>
              <s xml:id="N1AA1E" xml:space="preserve">Credo tamen /  naturaliter loquendo in den-<lb/>ſiori ſubiecto eſt denſius accidens ceteris paribus <lb/></s>
              <s xml:id="N1AA24" xml:space="preserve">Et ſi hec ſolutio tibi non placeat: dicas /  maior re­<lb/>ſiſtentia in medio minori quam in maiori prouenit <lb/>ex minoritate medii: hoc eſt  continuo ibi fiet mo-<lb/>tus minoris velocitatis, prouenit ex parte minoris <lb/>extenſionis conſimilis reſiſtentie illi que eſt in me-<lb/>dio maiori.               <anchor type="note" xlink:href="note-0109-03" xlink:label="note-0109-03a"/>               </s>
              <s xml:id="N1AA36" xml:space="preserve">Quoniam vt placet calculatori in ca-<lb/>pitulo de reactione in primo notabili quod ponit, <lb/>denſitas nõ ſimpliciter auget rei potentiam. </s>
              <s xml:id="N1AA3D" xml:space="preserve">Et cū <lb/>querit̄̄ quare / igitur dēſius fortius agit aut reſiſtit. <lb/>               <anchor type="note" xlink:href="note-0109-04" xlink:label="note-0109-04a"/>               </s>
              <s xml:id="N1AA49" xml:space="preserve">Reſpõdet /  hoc eſt ratiõe melioris applicationis: <lb/>quēadmoduꝫ diuerſitas figure eſt cauſa velocioris <lb/>motus teſtimonio philoſophi .4. ce. et mūdi tex. cõ. <lb/>42. </s>
              <s xml:id="N1AA52" xml:space="preserve">Et ſi hec ſolutio tibi non placeat: quere aliam. <lb/></s>
              <s xml:id="N1AA56" xml:space="preserve">Argumentum em̄ conuīcit concedere illatum.</s>
            </p>
            <div xml:id="N1AA59" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0109-03a" xlink:label="note-0109-03" xml:id="N1AA5D" xml:space="preserve">Calcula. <lb/>de react.</note>
              <note position="right" xlink:href="note-0109-04a" xlink:label="note-0109-04" xml:id="N1AA65" xml:space="preserve">q̈rto ce. et <lb/>mū. tex. <lb/>cõ. 42.</note>
            </div>
            <p xml:id="N1AA6F">
              <s xml:id="N1AA70" xml:space="preserve">Sed cõtra vtrã ſolutionem arguit̄̄ <lb/>ſic: quia ſi hoc eſſet verum videlicet /  in caſu poſito <lb/>eadem potentia vel equalis continuo velocius mo­<lb/>uetur per reſiſtentiã conſimilis intenſionis in me-<lb/>dio maiori quam in minori: ſequeretur /  poſſibile <lb/>eſſet  eadem potentia eque cito pertranſiret me-<lb/>dium duplum ſicut medium ſubduplum per quod <lb/>tardius mouetur: dūmodo illa media eſſent oīno <lb/>eodem modo qualificata per eandem reſiſtentiam <lb/>vniformiter difformem: ſed conſequens eſt falſum: <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N1AA87" xml:space="preserve">Sequela patet quoniã <lb/>ſi ex eo /  medium eſt minus potentia equalis in eo <lb/>tardius mouetur per conſimilem reſiſtentiam vni-<lb/>formiter difformē: ſequitur /  in quacun propor-<lb/>tione medium eſt minus in eadem proportione ea-<lb/>dem potentia tardius illud pertranſit reſiſtentia <lb/>exiſtente eadem vel conſimili. </s>
              <s xml:id="N1AA96" xml:space="preserve">Sed falſitas conſe-<lb/>quentis oſtenditur / quia ſi eque cito potetia a. eſſet <lb/>in fine pedalis ſicut potentia b. in fine medii ſemipe­<lb/>dalis: (cū vtrū illoꝝ medioꝝ terminet̄̄ ad gradum <lb/>octauū) / ſequit̄̄ /  in illo īſtãti (cū ille poñe ſint eq̈les               <pb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato." file="0110" n="110"/>               et reſiſtentie equales) equalem ꝓportionem habe-<lb/>rent: et cum cõtinuo mouentur vniformiter / vt dicit <lb/>concluſio quam impugnamus: ſequitur /  ſemper <lb/>antea habebant equalem ꝓportionem qualem ha­<lb/>bent in termino motus: et per cõſequens ſemꝑ equa­<lb/>liter mouebūtur: quod eſt contra ſolutionem.</s>
            </p>
            <p xml:id="N1AAB0">
              <s xml:id="N1AAB1" xml:space="preserve">Reſpondeo negando ſequelam et ad <lb/>ꝓbationem dico /  quãuis ſemper in medio mino-<lb/>ri ceteris paribus qualificato conſimili reſiſtentia <lb/>vniformiter difformi, eadem vel cõſimilis potētia <lb/>tardius moueatur: nõ tamen tardius in ea ꝓporti-<lb/>one qua eſt minus: immo in minori tardius. </s>
              <s xml:id="N1AABE" xml:space="preserve">Ita  <lb/>ſemper eadem potentia citius pertranſibit minus <lb/>medium quam maius: dummodo talia media ſint <lb/>qualificata eadem vel cõſimili qualitate vniformi-<lb/>ter difformi. </s>
              <s xml:id="N1AAC9" xml:space="preserve">Quod ſic ptꝫ / quia a. potentia nõ põt <lb/>eque cito pertranſire mediū maius ſicut b. medium <lb/>minus: vt nuperrime ꝓbatum eſt, nec citius: q2 tūc <lb/>a minori ꝓportione moueretur a. quam b. et per cõ­<lb/>ſequens tardius quod eſt cõtra principalē ſolutio-<lb/>nē. </s>
              <s xml:id="N1AAD6" xml:space="preserve">Sequela tamen ptꝫ / quia quando a. eſſet cum re­<lb/>ſiſtentia vt .8. potentia b. ei equalis eſſet cum mino­<lb/>ri reſiſtentia cum adhuc nõ eſſet in fine per te. </s>
              <s xml:id="N1AADD" xml:space="preserve">Qua­<lb/>re cõcedendum eſt /  ſemper pertranſitur citius me­<lb/>dium minus quã maius in caſu poſito.</s>
            </p>
            <p xml:id="N1AAE4">
              <s xml:id="N1AAE5" xml:space="preserve">Sed contra / quia tunc ſequeretur hec <lb/>concluſio /  infinite potentie darentur equales po­<lb/>tentie a. que inciperent ſimul moueri cum potentia <lb/>a. per media qualificata eadē vel conſimili qualita­<lb/>te vniformiter difformi: et in infinitum tardius con­<lb/>tinuo moueretur vnū illorum quam a. et tamen que­<lb/>libet aliarum potentiarum citius pertranſibit me­<lb/>dium ſuū ꝙ̄ a. / ſed conſequens videtur impoſſibile: <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N1AAF8" xml:space="preserve">Sequela probatur et <lb/>pono caſum /  ſit vnū pedale / per quod extendatur <lb/>latitudo reſiſtentie vniformiter difformis a nõ gra­<lb/>du vſ ad octauū / vt dictum eſt ſupra: et ſit aliud in <lb/>duplo minus, et aliud in triplo, et aliud in quadru-<lb/>plo, et ſic in infinitum: et per quodlibet illorum extē­<lb/>datur eadem vel conſimilis latitudo reſiſtentie vni­<lb/>formiter difformis a nõ gradu vſ ad octauū: et in <lb/>aliquo inſtanti incipiat a. creſcēdo a nõ gradu po-<lb/>tentie moueri cõtinuo a ꝓportione dupla per me-<lb/>dium pedale: et in quolibet aliorum mediorum inci­<lb/>piat in eodem inſtanti etiam conſimilis potentia <lb/>conſimiliter oīno creſcens moueri a nõ gradu reſi-<lb/>ſtentie: ita  quelibet maneat cõtinuo equalis ipſi <lb/>a. </s>
              <s xml:id="N1AB17" xml:space="preserve">Quo poſito patꝫ ſecunda pars illati videlicet /  <lb/>quelibet aliarum potentiarū ab a. citius pertran-<lb/>ſibit medium ſuū quam a. </s>
              <s xml:id="N1AB1E" xml:space="preserve">Hoc em̄ dicit ſolutio pre­<lb/>cedentis replice. </s>
              <s xml:id="N1AB23" xml:space="preserve">Et arguitur prima pars videlicet / <lb/> in infinitum tardius continuo mouetur aliqua il­<lb/>larum quam a. / quia citius a. preteribit punctū me-<lb/>diū illiꝰ pedalis per quod mouetur hoc eſt punctuꝫ <lb/>vt .4. quam aliqua aliarū potentiarū pertranſibit <lb/>ſuū mediū per quod ipſum mouetur: et in infinituꝫ <lb/>minus eſt aliquod illorū mediorū per quod mouet̄̄ <lb/>aliqua illarū potentiarū, quam eſt medietas peda­<lb/>lis per quod mouetur a. / vt ptꝫ ex caſu: igitur in infi­<lb/>nitū tardius ꝙ̄ a. mouetur aliqua illaꝝ potentiarū / <lb/>quod fuit ꝓbandū. </s>
              <s xml:id="N1AB3A" xml:space="preserve">Cõſequentia ptꝫ cum minore: et <lb/>arguitur maior: q2 nulla aliaruꝫ potentiarū eque <lb/>cito deueniet ad terminū ſui medii ſicut a. deueniet <lb/>ad punctum mediū pedalis per quod mouetur. </s>
              <s xml:id="N1AB43" xml:space="preserve">nec <lb/>citius aliqua illarum deueniet ad terminū ſui me-<lb/>dii ꝙ̄ a. deueniet ad punctum medium pedalis per <lb/>quod mouetur: igitur citius a. preteribit punctum <lb/>medium quam aliqua aliarum deueniet ad finem               <cb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato."/>               medii / per quod mouetur / quod fuit probandū. </s>
              <s xml:id="N1AB51" xml:space="preserve">Cõ­<lb/>ſequentia patet et arguitur maior. </s>
              <s xml:id="N1AB56" xml:space="preserve">quia ſi eque cito <lb/>aliqua illarum deueniret ad terminū ſui medii ſi-<lb/>cut a. deueniet ad punctum mediū: ſignetur illa et ſit <lb/>b. / et arguo ſic / cum primū a. eſt in puncto medio qui <lb/>eſt vt .4.b. eſt in puncto terminatiuo totius latitu-<lb/>dinis qui eſt vt .8. / et a. mouetur a proportiõe dupla / <lb/>vt ponitur: igitur qualis eſt proportio ipſius a. ad <lb/>reſiſtentiam ipſius a. talis eſt proportio reſiſtentie <lb/>ipſius b. ad reſiſtentiam ipſius a. / et per conſequens <lb/>reſiſtentia ipſius b. et ipſa potentia a. ſunt equales <lb/>cum habeant eadem proportionem ad vnū tertiuꝫ: <lb/>et a. et b. ſunt equales ex caſu: igitur reſiſtentia ipſiꝰ <lb/>b. et b. ſunt equales: ſic b. mouetur a proportione <lb/>equalitatis / quod eſt impoſſibile. </s>
              <s xml:id="N1AB73" xml:space="preserve">Patet igitur /  <lb/>nulla illarum poteſt eque cito venire ad punctū ter­<lb/>minatiuū ſui medii, ſicut a. ad punctum medium pe­<lb/>dalis per quod mouetur. </s>
              <s xml:id="N1AB7C" xml:space="preserve">Sed iam probo minorem <lb/>videlicet /  nulla illarum citius deueniet ad termi-<lb/>nū ſui medii quam a. deueniat ad punctum medium <lb/>ſui pedalis per quod mouetur: quia ſi ſic ſit illa b. / <lb/>et arguo ſic, b. potentia equalis ipſi a. eſt in puncto <lb/>terminatiuo ſui medii puta in puncto vt .8. et a. eſt <lb/>in minori puncto quam vt .4. et mouetur a. potentia <lb/>a proportione dupla: igitur maior eſt proportio re­<lb/>ſiſtentie ipſius b. ad reſiſtentiam ipſius a. ꝙ̄ ſit pro­<lb/>portio ipſius a. ad reſiſtentiam ipſius a. et a. et b. <lb/>ſunt equales: igitur maior eſt reſiſtentia b. quam b. / <lb/>et per conſequens b. mouetur a. proportione mino-<lb/>ris inequalitatis / quod eſt impoſſibile. </s>
              <s xml:id="N1AB97" xml:space="preserve">Patet ta-<lb/>men conſequentia / quia pūcti vt .8. ad punctū quod­<lb/>libet minus puncto vt .4. eſt maior proportio quam <lb/>dupla: et ipſius a. ad reſiſtentiam eiuſdē que eſt mi-<lb/>nor puncto vt .4. eſt proportio dupla: igitur reſiſtē­<lb/>tia b. maiorem proportionem habet ad reſiſtentiã <lb/>ipſius a. quaꝫ a. habeat ad reſiſtentiam eiuſdem a. / <lb/>et per conſequens maior eſt reſiſtentia ipſius b. quã <lb/>a. potentia / quod fuit probandum. </s>
              <s xml:id="N1ABAA" xml:space="preserve">Patet conſequē­<lb/>tia per hanc maximam: id quod habet maiorē pro­<lb/>portionem ad vnū tertium eſt maius. </s>
              <s xml:id="N1ABB1" xml:space="preserve">Patet igitur <lb/>totum illatum.</s>
            </p>
            <p xml:id="N1ABB6">
              <s xml:id="N1ABB7" xml:space="preserve">Reſpondeo / igitur concedendo quod <lb/>infertur vt demonſtrat argumentum.               <anchor type="note" xlink:href="note-0110-01" xlink:label="note-0110-01a"/>               </s>
              <s xml:id="N1ABC1" xml:space="preserve">¶ Ex hoc ar-<lb/>gumento et ſolutionibus replicarū eiuſdem / ſequi-<lb/>tur primo:  vbicun ſunt infinite potentie vt po-<lb/>nitur in caſu vltime replice: neceſſe eſt /  potētia que <lb/>mouetur in maximo illorum mediorum pretereat <lb/>punctum ad quod punctum intenſiſſimū illius me-<lb/>dii habet ſimilem proportionem illi proportioni a <lb/>qua mouetur illa potentia, quam aliqua aliarum <lb/>potentiarum equalium deueniat ad extremum ſui <lb/>medii. </s>
              <s xml:id="N1ABD6" xml:space="preserve">Uolo dicere /  ſi potentia in maxima illorū <lb/>mediorum (loquor ſemper incipientibus a nõ gra-<lb/>du) moueatur a proportione quadrupla: citius de-<lb/>ueniat ad punctum ad quem intenſiſſimus punctus <lb/>puta vt .8. (ſi medium terminetur ad illum) habeat <lb/>proportionem quadruplam, quam aliqua aliaruꝫ <lb/>potentiarum pertranſeat ſuum medium. </s>
              <s xml:id="N1ABE5" xml:space="preserve">Ita  in <lb/>tali caſu oportet /  prius veniat ad punctum vt .2. <lb/>et pretereat illum. </s>
              <s xml:id="N1ABEC" xml:space="preserve">Alias enim vel alia potentia mo­<lb/>ueretur a proportione equalitatis vĺ minoris ine-<lb/>qualitatis vt facile eſt inducere               <anchor type="note" xlink:href="note-0110-02" xlink:label="note-0110-02a"/>               </s>
              <s xml:id="N1ABF8" xml:space="preserve">¶ Sequitur ſecūdo / <lb/> ſi ſint duo media inequalia per que extēditur ea-<lb/>deꝫ latitudo reſiſtentie vniformiter difformis a nõ <lb/>gradu vſ ad octauū: et incipiant due potentie mo­<lb/>ueri per illa media a nõ gradu illiꝰ reſiſtentie: et con­<lb/>tinuo creſcãt ille potētie vniformiter īcipiēdo a nõ <lb/>g̈du potētie: illa tñ que mouet̄̄ in medio mīori in ea <lb/>ꝓportione velociꝰ creſcat altera q̄ mouet̄̄ in medio               <pb chead="Primi tractatus" file="0111" n="111"/>               maiori in qua proportione maius medium excedit <lb/>minꝰ: tūc cõtinuo vniformiter et eque velociter oīno <lb/>ille potentie mouētur. </s>
              <s xml:id="N1AC12" xml:space="preserve">Uolo dicere /  ſi ſint duo me­<lb/>dia ſe habentia in proportione dupla, per que ex-<lb/>tenditur cõſimilis latitudo reſiſtentie vniformiter <lb/>difformis terminata ad non gradum: et moueatur <lb/>vna potentia in minori medio incipiendo a nõ gra­<lb/>du medii, et a nõ gradu potentie, continuo creſcen-<lb/>do vniformiter: et in medio maiori moueatur vna <lb/>alia potentia incipiēdo ſimiliter creſcere a nõ gra­<lb/>du potentie, et a non gradu reſiſtentie: quia inter <lb/>illa media eſt proportio dupla creſcat cõtinuo po-<lb/>tentia que mouetur in medio minori in duplo velo-<lb/>cius altera que mouetur in medio maiori: tunc di-<lb/>co  ille potentie mouentur equaliter. </s>
              <s xml:id="N1AC2D" xml:space="preserve">Probatur <lb/>correlariū vniuerſaliter. </s>
              <s xml:id="N1AC32" xml:space="preserve">Et ſuppono /  in quacū <lb/>proportione ſe habent talia media per que extendi­<lb/>tur latitudo eadem vel cõſimilis reſiſtentie vnifor-<lb/>miter difformis terminate ad nõ gradū: in ea pro-<lb/>portione ſe habēt puncta equi diſtantia a nõ gradu <lb/>in illis mediis. </s>
              <s xml:id="N1AC3F" xml:space="preserve">Quod ptꝫ facile ex diffinitione qua­<lb/>litatis vniformiter difformis quarto tractatu. </s>
              <s xml:id="N1AC44" xml:space="preserve">Hoc <lb/>ſuppoſito probatur correlarium. </s>
              <s xml:id="N1AC49" xml:space="preserve">Et ſint duo me-<lb/>dia ſe habentia in f. proportione et moueatur a. po­<lb/>tentia in maiori continuo vniformiter: et b. in mino­<lb/>ri: et creſcat b. cõtinuo in f. proportione velocius a. <lb/></s>
              <s xml:id="N1AC53" xml:space="preserve">Quo poſito ſic argumentor / potentia b. que moue-<lb/>tur in medio minori nõ mouetur velocius a. nec tar­<lb/>dius: igitur cõtinuo equaliter. </s>
              <s xml:id="N1AC5A" xml:space="preserve">Patet conſequētia / <lb/>et probatur maior: quia ſi b. mouetur velocius quã <lb/>a. / ſequitur /  b. eſt in puncto magis diſtante a non <lb/>gradu ſui medii ꝙ̄ a. / igitur mouetur a. minori pro-<lb/>portione ꝙ̄ a. / et per conſequēs tardius. </s>
              <s xml:id="N1AC65" xml:space="preserve">Patet hec <lb/>conſequentia / quia ſi eſſent in punctis equidiſtanti­<lb/>bus mouerentur ab eadem proportione: quoniam <lb/>tunc f. proportio eſſet inter illa puncta / vt patet ex <lb/>ſuppoſitione: et inter potentias etiam eſſet f. pro-<lb/>portio: ergo ſequitur /  ille potentie haberent e-<lb/>quales proportiones ad ſuas reſiſtentias. </s>
              <s xml:id="N1AC74" xml:space="preserve">Patet <lb/>conſequentia / quia ſi inter b. et a. eſt f. proportio: et <lb/>inter reſiſtentiam ipſius b. et reſiſtentiam ipſius a. <lb/>eſt f. proportio: igitur qualis eſt proportio ipſiꝰ b. <lb/>ad a. talis eſt reſiſtentie ipſius b. ad reſiſtentiam <lb/>ipſius a. et ſi talis eſt proportio ipſius b. ad a. qua-<lb/>lis eſt reſiſtentie ipſius b. ad reſiſtentiam ipſius a. / <lb/>ſequitur permutatim ex ſecunda concluſione tertii <lb/>capitis ſecunde partis /  talis eſt proportio ipſius <lb/>b. ad reſiſtentiam ipſius b. qualis eſt ipſiꝰ a. ad re-<lb/>ſiſtentiam ipſius a. / et ſic ptꝫ conſequentia. </s>
              <s xml:id="N1AC8B" xml:space="preserve">Et vltra <lb/>ex ↄ̨ſequēti ille potentie a. et b. / tunc haberent equa-<lb/>les proportiones ad ſuas reſiſtentias: ergo modo <lb/>proportio ipſius b. ad ſuam reſiſtentiam eſt minor <lb/>quam proportio ipſius a. ad ſuam reſiſtentiam: et <lb/>per conſequens mouetur tardius. </s>
              <s xml:id="N1AC98" xml:space="preserve">Patet conſequē­<lb/>tia / quia b. eſt in maiori reſiſtentia quam tunc eſſet. <lb/></s>
              <s xml:id="N1AC9E" xml:space="preserve">Et per hoc ptꝫ minor / quia ſi b. mouetur tardiꝰ quã <lb/>a. / ſequitur /  eſt in minori reſiſtentia quam eſſet ſi <lb/>moueretur equaliter ſicut a. ſed ſi moueret̄̄ equali-<lb/>ter ſicut a. moueretur ab eadem proportione: et mo­<lb/>do mouetur in minori reſiſtentia quam tunc: ergo <lb/>a. maiori proportione/ et per conſequens velocius et <lb/>nõ tardius / quod eſt oppoſitum conceſſi. </s>
              <s xml:id="N1ACAD" xml:space="preserve">Et ſic patꝫ <lb/>antecedens et per conſequens totum correlarium. <lb/>               <anchor type="note" xlink:href="note-0111-01" xlink:label="note-0111-01a"/>               </s>
              <s xml:id="N1ACB9" xml:space="preserve">¶ Sequitur tertio /  ſi ſint duo media ineq̈lia qua­<lb/>lificata eadem vel conſimili reſiſtentia vniformiter <lb/>difformi terminata ad nõ gradum: et incipiant due <lb/>potentie non variate in eodem inſtanti moueri per <lb/>illa media: et talis ſit proportio potentie mouentis <lb/>in medio minori ad reliquam potentiaꝫ qualis eſt               <cb chead="Capitulū duodecimū."/>               proportio medii maioris ad medium minus: tunc <lb/>tales potētie cõtinuo eque velociter mouētur. </s>
              <s xml:id="N1ACCB" xml:space="preserve">Pro­<lb/>batur: et ſint duo media īter que eſt ꝓportio f. et ſint <lb/>due potentie a. et b. et b. ad a. ſit f. proportio: et in-<lb/>cipiat b. moueri in minori medio ad non gradu et <lb/>a. in maiori. </s>
              <s xml:id="N1ACD6" xml:space="preserve">Quo poſito arguo ſic / a. et b. continuo <lb/>ſunt in punctis equidiſtantibus a nõ gradu ſui me-<lb/>dii: ergo continuo eque velociter mouentur. </s>
              <s xml:id="N1ACDD" xml:space="preserve">Patet <lb/>conſequentia / quia pūcta equaliter diſtantia ſe ha­<lb/>bent in f. proportione: vt patet ex ſuppoſitione ſu-<lb/>perioris correlarii: ergo ſequitur /  ſi potētie ſunt <lb/>in punctis eque diſtantibus  ipſe mouentur ab e-<lb/>quali proportione. </s>
              <s xml:id="N1ACEA" xml:space="preserve">Patet conſequentia vt in ſupe­<lb/>riori correlario. </s>
              <s xml:id="N1ACEF" xml:space="preserve">Et ex conſequenti ſequitur:  ſi b. <lb/>eſt in puncto magis propinquo non gradui ꝙ̄ a.  <lb/>iã mouetur a. maiori ꝓportione ꝙ̄ a. q2 eſt in remiſ­<lb/>ſiori puncto quã eſſet ſi eſſet in puncto equidiſtanti <lb/>ſicut a. / et per cõſequens moueretur velocius ꝙ̄ a. </s>
              <s xml:id="N1ACFA" xml:space="preserve">Et <lb/>ſi eſſet in puncto magis diſtanti a nõ gradu ꝙ̄ a. / iã <lb/>ſequitur /  tunc moueretur cū reſiſtentia intenſiori <lb/>quã ſi eſſet in puncto equidiſtãti ſicut pūctus in quo <lb/>eſt a. / et per ↄ̨ſequēs moueret̄̄ tardiꝰ quã a. et ſic nõ ve­<lb/>lociꝰ. </s>
              <s xml:id="N1AD07" xml:space="preserve">Patet cõſequētia / q2 ſi eſſet in puncto equidi-<lb/>ſtanti ſicut a. moueretur ab equali ꝓportione: ergo <lb/>quãdo eſt in intēſiori mouetur a minori. </s>
              <s xml:id="N1AD0E" xml:space="preserve">Et ſic patꝫ <lb/>veritas correlarii / qm̄ ad b. moueri velociꝰ a. / ſequit̄̄ <lb/>ipſum moueri tardius: et ad b. moueri tardius, ſe-<lb/>quitur ipſum moueri velocius. </s>
              <s xml:id="N1AD17" xml:space="preserve">Opus eſt dicere igi­<lb/>tur /  continuo mouetur equaliter cum ipſo a.</s>
            </p>
            <div xml:id="N1AD1C" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0110-01a" xlink:label="note-0110-01" xml:id="N1AD20" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0110-02a" xlink:label="note-0110-02" xml:id="N1AD26" xml:space="preserve">2. correĺ</note>
              <note position="left" xlink:href="note-0111-01a" xlink:label="note-0111-01" xml:id="N1AD2C" xml:space="preserve">3. correĺ.</note>
            </div>
            <note position="right" xml:id="N1AD32" xml:space="preserve">4. correĺ.</note>
            <p xml:id="N1AD36">
              <s xml:id="N1AD37" xml:space="preserve">¶ Sequitur quarto:  dabile eſt medium vniformi­<lb/>ter difforme in reſiſtentia ad nõ gradum termina-<lb/>tum: quod potentia a non gradu potentie creſcens <lb/>vniformiter continuo, nõ valet vniformiter conti-<lb/>nuo mouendo ſuo motu abſoluere ab extremo re-<lb/>miſſiori inchoando. </s>
              <s xml:id="N1AD44" xml:space="preserve">Probatur / et capio vnū mediū <lb/>difforme in quantitate vniformiter difforme in re-<lb/>ſiſtentia terminata ad non gradū: cuius medii pri-<lb/>ma medietas puta remiſſior ſit longior quam ſecū­<lb/>da in ſexquialtero / vt patet in figura.</s>
            </p>
            <figure xml:id="N1AD4F">
              <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0111-01"/>
            </figure>
            <p xml:id="N1AD53">
              <s xml:id="N1AD54" xml:space="preserve">Et incipiat b. potentia ab extremo remiſſiori talis <lb/>medii moueri creſcendo a nõ gradu potentie conti-<lb/>nuo vniformiter inchoando ab extremo remiſſiori <lb/>vt ſepius poſitū eſt: et moueatur quo ad vſ ad ex-<lb/>tremū intenſius deueniat per lineã rectam: tunc di­<lb/>co /  ipſa potentia b. nõ cõtinuo vniformiter moue­<lb/>tur illud medium tranſeundo. </s>
              <s xml:id="N1AD63" xml:space="preserve">Quod ſic probatur / <lb/>q2 ſi b. potentia cõtinuo vniformiter moueretur pu­<lb/>ta a. proportione f. exempli gratia in ſexquialtero <lb/>minori tēpore totam ſecundã medietatē magis re-<lb/>ſiſtentē abſolueret quaꝫ primã quia ipſa eſt in ſex-<lb/>quialtero breuior ex hypotheſi: et ex cõſequenti ſe-<lb/>quitur /  b. potentia tranſeundo ſecundã medieta-<lb/>tem in ſexquialtero minorē potētiam acquirit quã <lb/>tranſeundo primam medietatem: cum vniformiter <lb/>continuo intendatur: et tranſeundo eandē ſecundã <lb/>medietatē ſue reſiſtentie, tantam latitudinē acqui-<lb/>rit adequate ſicut tranſeūdo primã q2 reſiduã me-<lb/>dietatē latitudinis: igitur tranſeundo ſecundã me-<lb/>dietatem inter acquiſitū potentie et acquiſitū reſi-<lb/>ſtentie nõ eſt tanta proportio ſicut tranſeundo pri-<lb/>mam: et tranſeundo primam eſt proportio f. / vt pa-<lb/>tet / quia continuo ab f. proportiõe mouetur per te:               <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0112" n="112"/>               igitur tranſeundo ſecundam medietatem non mo-<lb/>uetur ab f. proportione: ergo non mouetur cõtinuo <lb/>vniformiter / quod fuit probandum. </s>
              <s xml:id="N1AD8F" xml:space="preserve">Conſequentia <lb/>patet ex ſecundo correlario quinte concluſionis ſe-<lb/>cundi capitis ſecunde partis. </s>
              <s xml:id="N1AD96" xml:space="preserve">Nam quod ibi dici-<lb/>tur de rationalibus quantitatibus de quibuſcū <lb/>ex eadem quinta concluſione facile demonſtrari va­<lb/>let. </s>
              <s xml:id="N1AD9F" xml:space="preserve">Et ſic patet correlarium.               <anchor type="note" xlink:href="note-0112-01" xlink:label="note-0112-01a"/>               </s>
              <s xml:id="N1ADA7" xml:space="preserve">¶ Et ex hoc habes do-<lb/>cumentum notandum /  predicte concluſiones duo­<lb/>rum precedentium capitum intelliguntur cum po-<lb/>tentie mouentur in medio vniformiter difformi per­<lb/>fecte q̈drato, vel quadrilatero vniformis latitudi-<lb/>nis et profunditatis continuo. </s>
              <s xml:id="N1ADB4" xml:space="preserve">¶ Utrum autem ta-<lb/>lia media requirantur ad predictas cõcluſiones ve­<lb/>rificandas, ita  cum nullis aliis mediis potentie <lb/>poſſint moueri ſecundum tenorem predictarum cõ-<lb/>cluſionum quam cum illis tu ipſe inquiras.</s>
            </p>
            <div xml:id="N1ADBF" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0112-01a" xlink:label="note-0112-01" xml:id="N1ADC3" xml:space="preserve">quõ ↄ̨clu­<lb/>ſiones de­<lb/>cimi et vn­<lb/>decimi ca­<lb/>pitū dñt <lb/>reſtringi</note>
            </div>
            <note position="left" xml:id="N1ADD3" xml:space="preserve">argumē-<lb/>tū calcu.</note>
            <p xml:id="N1ADD9">
              <s xml:id="N1ADDA" xml:space="preserve">Secundo contra tertium correlariū <lb/>quinte concluſionis decimi capitis arguitur ſic. </s>
              <s xml:id="N1ADDF" xml:space="preserve">q2 <lb/>b. potentia in caſu illius correlarii aliquando vni-<lb/>formiter mouetur dato  motus ille perpetuo con­<lb/>tinuetur: igitur non cõtinuo intendit motum ſuum / <lb/>et per conſequens correlariū falſuꝫ. </s>
              <s xml:id="N1ADEA" xml:space="preserve">Conſequentia <lb/>patet / et arguitur antecedens: quia motus ipſius b. <lb/>quando ſimul incipit moueri ab eodem puncto cuꝫ <lb/>a. ſolum finite diſtat a gradu velocitatis quo mo-<lb/>uetur a. et a. continuo vniformiter mouetur: et b. con­<lb/>tinuo intendit motum ſuum: et ſic perpetuo mouebū­<lb/>tur: ergo velocitas ipſius b. tandem deneniet ad eq̈­<lb/>litatem velocitatis motus a. et b. / tunc vniformiter <lb/>mouebitur / igitur propoſitum. </s>
              <s xml:id="N1ADFD" xml:space="preserve">Patet conſequētia / <lb/>quia non eſt dabilis latitudo inter motum maiorē <lb/>et minorem quin illa per continuam intenſioneꝫ mi­<lb/>noris tandem valeat acquiri vt ſatis cõſtat: igitur <lb/>b. in tempore finito poteſt acquirere latitudinē mo­<lb/>tus per quam motus ipſius a. excedit motum ipſiꝰ <lb/>b. </s>
              <s xml:id="N1AE0C" xml:space="preserve">Sed  tunc b. vniformiter mouebitur probatur. <lb/></s>
              <s xml:id="N1AE10" xml:space="preserve">quia tūc b. mouebitur ab eadē proportione: et ita ve­<lb/>lociter ſicut a. mouetur ī illo puncto quia a. ſemper <lb/>mouetur vniformiter: et per conſequens ſequitur /  <lb/>in illo puncto erit b. potentia tanta quanta fuit a. <lb/>potentia in illo puncto: et creſcit vniformiter conti­<lb/>nuo et eq̄ velociter ſicut a. et ex hoc ſicut a. creſcebat <lb/>ibi / et per conſequens mouetur vniformiter ſicut a. / <lb/>quod fuit probandum.</s>
            </p>
            <p xml:id="N1AE21">
              <s xml:id="N1AE22" xml:space="preserve">Reſpondeo negando antecedens: et <lb/>ad probationem concedo antecedens / et nego conſe­<lb/>quentiam: et cum probatur / quia nulla eſt latitudo <lb/>finita inter duos motus inequales maiorem vide-<lb/>licet et minorem quin illa valeat in tempore finito <lb/>acquiri a minori motu ꝑ continuã eiꝰ maiorationē: <lb/>diſtīguo illud, aut ſi talis minor motus vniformi-<lb/>ter continuo intendatur aut velocius et velocius / et <lb/>ſic ego bene concedo illud: aut ſi continuo intenda-<lb/>tur tardius et tardius, et ſic ego nego. </s>
              <s xml:id="N1AE37" xml:space="preserve">Non em̄ tunc <lb/>oportet. </s>
              <s xml:id="N1AE3C" xml:space="preserve">Poſſibile enim eſt  vnus gradus motus <lb/>ſemper ſit in acquiri per infinitum tempus. </s>
              <s xml:id="N1AE41" xml:space="preserve">Hoc eſt <lb/> vnum mobile continuo per infinitum tempus in­<lb/>tendat motum ſuum: et nun̄ acquirat vnum gradū <lb/>motus per quem exceditur a motu velociori ſed be­<lb/>ne quēlibet motum citra. </s>
              <s xml:id="N1AE4C" xml:space="preserve">Ut ſi in prima hora illius <lb/>infiniti temporis acquirat primaꝫ partem propor­<lb/>tionalem vnius gradus: et in ſecunda ſecundam et <lb/>in tertia tertiam: et ſic cõſequenter.               <anchor type="note" xlink:href="note-0112-02" xlink:label="note-0112-02a"/>               </s>
              <s xml:id="N1AE5A" xml:space="preserve">¶ Ex quo <lb/>ſequitur primo /  potentia a. in infinitum tarde in-<lb/>tenderet motum ſuum eſto  motus eius perpetuo <lb/>duraret. </s>
              <s xml:id="N1AE63" xml:space="preserve">Patet quia alias ſequeretur /  in tempo-<lb/>re finito poſſet venire ad equalitatem motus b.</s>
            </p>
            <div xml:id="N1AE68" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0112-02a" xlink:label="note-0112-02" xml:id="N1AE6C" xml:space="preserve">1. correl.</note>
            </div>
            <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>
            <note position="right" xml:id="N1AE74" xml:space="preserve">2. correl.</note>
            <p xml:id="N1AE78">
              <s xml:id="N1AE79" xml:space="preserve">¶ Sequitur ſecundo /  potentia a. que vniformi-<lb/>ter continuo mouetur non poteſt attingere potētiã <lb/>maiorem precedentem ipſam que eque velociter et <lb/>vniformiter continuo intenditur ſicut ipſa potētia <lb/>a. de qua videlicet ſit mentio ī ſecūdo correlario q̇n­<lb/>te concluſionis preallegate. </s>
              <s xml:id="N1AE86" xml:space="preserve">Probatur / quia a. non <lb/>poteſt incipere moueri eque velociter ſicut illa po-<lb/>tentia precedens ipſam potentiam a. / ergo ſequitur / <lb/> non poteſt attingere ipſam que velocius moue-<lb/>tur et precedit. </s>
              <s xml:id="N1AE91" xml:space="preserve">Conſequentia patet, et arguitur an-<lb/>tecedens: quia ſi mouebitur aliquando eque veloci­<lb/>ter ſicut maior precedens: et illa maior precedens <lb/>continuo remittit motum ſuum: ſequitur /  a. potē-<lb/>tia aliquando cõtinuo certe velocius mouebit̄̄ quã <lb/>illa potentia que continuo remittit motum ſuum: et <lb/>precedit: et ex conſequenti ſequitur /  a. potentia ali­<lb/>quando attinget illam potentiam maiorem prece-<lb/>dentem (dato /  perpetuo duraret motus illarū po­<lb/>tentiarum in tali medio) / et per conſequens eque ci-<lb/>to pertranſiretur aliquod ſpacium a potentia ma­<lb/>iore et a potentia minore / quod eſt impoſſibile (cete-<lb/>ris deductis) </s>
              <s xml:id="N1AEAC" xml:space="preserve">Patet conſequentia / q2 omne mobile <lb/>ſequens alteruꝫ qḋ ab aliqua certa ꝓportione con­<lb/>tinuo velocius eo mouetur (dūmodo perpetuo ſic <lb/>moueantur) tandem attinget illud vt facile demon­<lb/>ſtrari potet.               <anchor type="note" xlink:href="note-0112-03" xlink:label="note-0112-03a"/>               </s>
              <s xml:id="N1AEBC" xml:space="preserve">¶ Sequitur tertio /  illa potentia ma-<lb/>ior precedens continuo tardius remittit motū ſuū: <lb/>et ſi perpetuo moueretur per tale medium in infini-<lb/>tum tarde remitteret motum ſuum. </s>
              <s xml:id="N1AEC5" xml:space="preserve">Probatur hoc <lb/>correlarium / quia ſi velocius et velocius remitteret <lb/>motum ſuum vel vniformiter continuo: tandem de­<lb/>ueniret ad equalitateꝫ motus ipſius a. vniformiter <lb/>continuo mouentis: et tunc tardius moueretur: <lb/>quod ſuperiori correlario improbatum eſt. </s>
              <s xml:id="N1AED2" xml:space="preserve">Patet <lb/>igitur correlarium.               <anchor type="note" xlink:href="note-0112-04" xlink:label="note-0112-04a"/>               </s>
              <s xml:id="N1AEDC" xml:space="preserve">¶ Sequitur quarto /  iſta con-<lb/>ſequentia nihil valet a. in īfinitum modicum diſtat <lb/>ab aliqua iſtarum potentiarum: et a. qualibet iſtaꝝ <lb/>potētiaꝝ verſus eandem differentiam continuo ve­<lb/>locius mouetur: ergo ſequitur /  a. aliquando attī­<lb/>get alquam illarum potentiarum eſto /  perpetuo <lb/>motus eius duraret. </s>
              <s xml:id="N1AEEB" xml:space="preserve">Probatur / et pono /  <lb/>a. potentia ponatur in puncto initiatiuo c. medii <lb/>quod vniformiter continuo mouendo pertranſit ꝑ <lb/>ſue potentie ad non gradu continuuꝫ et vniforme cre­<lb/>mentum: et in quolibet puncto intrinſeco eiuſdem c. <lb/>medii ponatur potentia vna que vniformiter conti­<lb/>nuo a non gradu potentie et eque velociter ſicut a. <lb/>creſcat: mouendo verſus extremum intenſius c. me-<lb/>dii a ꝓportione ſui ad ſuam reſiſtentiam. </s>
              <s xml:id="N1AEFE" xml:space="preserve">Quo po­<lb/>ſito antecedens illius ↄ̨ñe eſt verum: et conſequens <lb/>falſum: igit̄̄ correlariū uꝫ. </s>
              <s xml:id="N1AF05" xml:space="preserve">Q, tunc antecedens il-<lb/>lius conſequētie eſt verum / patet / quia prima pars <lb/>eius eſt ex ſe nota: et ſecunda patet ex quinta conclu­<lb/>ſione decimi capitis. </s>
              <s xml:id="N1AF0E" xml:space="preserve">Sed  conſequens ſit falſum <lb/>probatur / quia ſi a. aliquando attingit aliquam il­<lb/>larum potentiarum: et continuo a. eſt equalis cuili-<lb/>bet aliarum potentiarum ex hypotheſi: et quelibet <lb/>aliarum poñarum continuo intendit motum ſuum / <lb/>ſequitur /  a. aliquando intendit motum ſuum cum <lb/>aliqua illarum poñarum mouendo ab eodem pun­<lb/>cto cum ea continuo eque velociter: ſed conſequens <lb/>eſt falſum / vt patet ex ſecunda cõcluſione decimi ca­<lb/>pitis: igitur et antecedens. </s>
              <s xml:id="N1AF23" xml:space="preserve">Item ſi a. aliquando at-<lb/>tingit aliquam illarum poñarum ſequitur /  eadeꝫ <lb/>poña eque cito pertranſiret totum ſicut eius partē <lb/>ceteris paribus / quod eſt impoſſibile: </s>
              <s xml:id="N1AF2C" xml:space="preserve">Et ſic patet <lb/>correlarium.               <anchor type="note" xlink:href="note-0112-05" xlink:label="note-0112-05a"/>               </s>
              <s xml:id="N1AF36" xml:space="preserve">¶ Sequitur quinto /  ad arguendum <lb/>a. poñam velocius continuo mouentem b. poñam p̄­<lb/>cedentem mouētem tamen tardius aliquando attī­               <pb chead="Primi tractatus" file="0113" n="113"/>               gere. </s>
              <s xml:id="N1AF42" xml:space="preserve">opus ē ſic argumentari a. poña in certa ꝓpor­<lb/>tione adequate vel inadequate velociꝰ continuo mo­<lb/>uetur ꝙ̄ b. poña precedens / igitur a. poña tandeꝫ b. <lb/>poñam attinget (eſto /  ꝑpetuo motus eius dura-<lb/>ret) </s>
              <s xml:id="N1AF4D" xml:space="preserve">Patet hoc correlarium ex ſe. </s>
              <s xml:id="N1AF50" xml:space="preserve">¶ Plura alia ar­<lb/>gumenta contra pleraſ duorum precedentiuꝫ ca-<lb/>pitum concluſiones adducit calculator in ſecundo <lb/>capite de medio non reſiſtente: ſed ea omnia intelle­<lb/>ctis his / que dicta ſunt facile diſſoluuntur. </s>
              <s xml:id="N1AF5B" xml:space="preserve">Poſſet <lb/>hic etiam plures induci concluſiones de velocitate <lb/>motus in medio vniformiter difformi vtrī ad gra­<lb/>dum terminato et de diuerſarum poñarum motuuꝫ <lb/>comparatione in huiuſcemodi medio: ſed ex predi-<lb/>ctis a perpſicaciuſculo ingenio aliquali tamen la-<lb/>bore comprehendi valent </s>
              <s xml:id="N1AF6A" xml:space="preserve">Ideo ſuperſedeo et hec de <lb/>his dixiſſe ſufficiat.</s>
            </p>
            <div xml:id="N1AF6F" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0112-03a" xlink:label="note-0112-03" xml:id="N1AF73" xml:space="preserve">3. correl.</note>
              <note position="right" xlink:href="note-0112-04a" xlink:label="note-0112-04" xml:id="N1AF79" xml:space="preserve">4. correl.</note>
              <note position="right" xlink:href="note-0112-05a" xlink:label="note-0112-05" xml:id="N1AF7F" xml:space="preserve">5. correl.</note>
            </div>
            <p xml:id="N1AF85">
              <s xml:id="N1AF86" xml:space="preserve">¶De motu penes cauſam in medio vni-<lb/>formiter difformi non variato finis.</s>
            </p>
            <p xml:id="N1AF8B">
              <s xml:id="N1AF8C" xml:space="preserve">¶ Sequitur de motu penes cauſam <lb/>in medio non reſiſtente.</s>
            </p>
          </div>
          <div xml:id="N1AF91" level="4" n="13" type="chapter" type-free="capitulum">
            <head xml:id="N1AF96" xml:space="preserve">Capitulum tridecimum / in quo ponū­<lb/>tur alique concluſiones velocitatē mo­<lb/>tus penes cauſam declarãtes in medio <lb/>non reſiſtente in quo eſt progreſſio la-<lb/>titudinis reſiſtentie vniformiter diffor­<lb/>mis: gradu intenſiori quieſcente.</head>
            <p xml:id="N1AFA3">
              <s xml:id="N1AFA4" xml:space="preserve">QUoniam iam ſupereſt ponere <lb/>aliquas concluſiones de velocitate et tar­<lb/>ditate motus penes cauſam in medio nõ <lb/>reſiſtente in quo eſt progreſſio, generatio, ſiue extē­<lb/>ſio latitudinis reſiſteutie partibiliter quo ad ſubie­<lb/>ctum. </s>
              <s xml:id="N1AFB1" xml:space="preserve">Ideo pro hiis concluſionibus īducendis ma­<lb/>thematico ordine aliquas ſuppoſitiones per mo-<lb/>dum terminorum declarationis duximus premit-<lb/>tendas.</s>
            </p>
            <p xml:id="N1AFBA">
              <s xml:id="N1AFBB" xml:space="preserve">Prima ſuppoſitio </s>
              <s xml:id="N1AFBE" xml:space="preserve">Reſiſtentia in pro-<lb/>poſito accipitur pro quadam qualitate diſtincta a <lb/>ſuo ſubiecto cõnotando ipſam natam eſſe impedi-<lb/>re velocitatem motus: ne mobile ita cito pertranſe­<lb/>at ſpacium in quo ipſa eſt: ſicut pertranſiret ſi ipſa <lb/>non eſſet: et loquor de reſiſtentia motus localis.</s>
            </p>
            <p xml:id="N1AFCB">
              <s xml:id="N1AFCC" xml:space="preserve">Secunda ſuppoſitio </s>
              <s xml:id="N1AFCF" xml:space="preserve">Per medium nõ <lb/>reſiſtens in propoſito intelligendum eſt ſpacium ſe­<lb/>paratum a tali qualitate id eſt carens reſiſtentia <lb/>inſtar vacui quod antiqui philoſophãtes ponebãt <lb/>cuius vacui philoſophus quarto de phiſico auditu <lb/>tractatu ſecundo capitibus ſecundo et tertio memi­<lb/>nit.               <anchor type="note" xlink:href="note-0113-01" xlink:label="note-0113-01a"/>               </s>
              <s xml:id="N1AFE3" xml:space="preserve">Quare non ī merito Calcu. in concluſionibꝰ de <lb/>medio non reſiſtente nonnū̄ tale ſpacium vacuuꝫ <lb/>appellat: ſepius vero medium non reſiſtens.</s>
            </p>
            <div xml:id="N1AFEA" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0113-01a" xlink:label="note-0113-01" xml:id="N1AFEE" xml:space="preserve">phūs .4. <lb/>phi. <lb/>cal. ḋ me: <lb/>nõ reſiſ.</note>
            </div>
            <p xml:id="N1AFFA">
              <s xml:id="N1AFFB" xml:space="preserve">Tertia ſuppoſitio. </s>
              <s xml:id="N1AFFE" xml:space="preserve">Qualitas que par­<lb/>tibiliter alicui ſubiecto acquiritur: tripliciter põt <lb/>acquiri: </s>
              <s xml:id="N1B005" xml:space="preserve">Uno modo partibiliter quo ad intenſionē <lb/>tantum. </s>
              <s xml:id="N1B00A" xml:space="preserve">Alio modo partibiliter quo ad intenſionē <lb/>et extenſionem ſimul: </s>
              <s xml:id="N1B00F" xml:space="preserve">Et tertio modo partibiliter <lb/>ſiue ſucceſſiue quo ad extenſionem tãtū ſiue quo ad <lb/>ſubiectum tantum (quod idem eſt in propoſito) pri­<lb/>mi duo modi declarabuntur inferius in quarto tra­<lb/>ctatu. </s>
              <s xml:id="N1B01A" xml:space="preserve">Sed tertius modus nunc venit declarandus <lb/></s>
              <s xml:id="N1B01E" xml:space="preserve">Pro quo aduertendum eſt /  tunc qualitas dicitur <lb/>acquiri: ſiue progredi: ſiue generari: (quod idem ē) <lb/>partibiliter quo ad ſubiectum tantum quando ip-<lb/>ſã continuo efficitur maior: et continuo magis extē­<lb/>ditur per ſubiectum: et nullo pacto efficitur intēſior <lb/>et talis acquiſitio quo ad partes ſubiecti ſit per ac-               <cb chead="Capitulum tridecimum"/>               quiſitionem raritatis ipſi qualitati. </s>
              <s xml:id="N1B02E" xml:space="preserve">Hoc autem fa­<lb/>miliari exemplo poteſt ſic declarari. </s>
              <s xml:id="N1B033" xml:space="preserve">Nam capto <lb/>pedali albo per totum volo /  pedali manente nec <lb/>rarefacto nec condenſato. </s>
              <s xml:id="N1B03A" xml:space="preserve">et diuiſa hora preſenti ꝑ <lb/>partes proportionales proportione dupla maio-<lb/>ribus terminatis verſus inſtans initiatiuum in pri­<lb/>ma parte proportionali illa albedo cõdenſetur ad <lb/>ſubduplum relinquendo primam partem ꝓportio­<lb/>nalem pedalis ꝓportione dupla: et maneat preciſe <lb/>in reſiduis partibus ꝓportionalibus: et in ſecunda <lb/>parte temporis relinquat ſecundam partem ꝓpor­<lb/>portionalem pedalis cõdenſando adhuc ad ſubdu­<lb/>plum: </s>
              <s xml:id="N1B04F" xml:space="preserve">Et in tertia iterum ad ſubduplum / et ſic conſe­<lb/>quenter. </s>
              <s xml:id="N1B054" xml:space="preserve">Et maneat in fine hore illa albedo nõ quã-<lb/>ta in illo ſubiecto indiuiſibiliter in eo exiſtens: dein­<lb/>de diuiſa hora futura per partes proportionales <lb/>ordine prepoſtero puta minoribus verſus initiati-<lb/>uum inſtans terminatis: incipiat illa albedo exten­<lb/>di partibiliter per illud ſubiectum ita rarefiendo ſi­<lb/>cut condēſabatur: ita  in qualibet ꝓportio­<lb/>nali ſequenti efficiatur ī duplo maior / ꝙ̄ fuit in par­<lb/>te proportionali īmediate precedenti. </s>
              <s xml:id="N1B067" xml:space="preserve">Tunc in tali <lb/>caſu illa albedo dicitur in illa ſecunda hora gene-<lb/>rari partibiliter / quo ad ſubiectum tantuꝫ. </s>
              <s xml:id="N1B06E" xml:space="preserve">Et de ta­<lb/>li modo ꝓgreſſionis ſiue generationis latitudinis <lb/>reſiſtentie loquendum eſt in propoſito. </s>
              <s xml:id="N1B075" xml:space="preserve">Et hoc mo-<lb/>do intelligit Calcu. caſum prime concluſionis in ca­<lb/>pitulo de medio non reſiſtente.</s>
            </p>
            <p xml:id="N1B07C">
              <s xml:id="N1B07D" xml:space="preserve">Quarta ſuppoſitio </s>
              <s xml:id="N1B080" xml:space="preserve">Latitudo reſiſten­<lb/>tia vniformiter difformis tripliciter valet progre-<lb/>di ſiue extendi continuo manens vniformiter dif-<lb/>formis ſub eadem intenſione in medio non reſiſten­<lb/>te. </s>
              <s xml:id="N1B08B" xml:space="preserve">Uno modo quieſcente extremo remiſſiori ſiue nõ <lb/>gradu: ceteriſ punctis mouentibus. </s>
              <s xml:id="N1B090" xml:space="preserve">Secundo mo­<lb/>do quieſcente extremo remiſſiori: ceteriſ punctis <lb/>mouentibus. </s>
              <s xml:id="N1B097" xml:space="preserve">Tertio modo neutro extremo totali-<lb/>ter quieſcente: ſed latitudine reſiſtentie a latere ī la­<lb/>tus mouente: vel vna parte extremi mouente: et alte­<lb/>ra quieſcente et ſic mille aliis modis poteſt imagina­<lb/>ri talis reſiſtentie progreſſio. </s>
              <s xml:id="N1B0A2" xml:space="preserve">Sed duo primi modi <lb/>duntaxat preſenti conſiderationi deſeruiunt.</s>
            </p>
            <p xml:id="N1B0A7">
              <s xml:id="N1B0A8" xml:space="preserve">Quinta ſuppoſitio </s>
              <s xml:id="N1B0AB" xml:space="preserve">Latitudine reſiſtē­<lb/>tie manente vniformiter difformi ſic mouente vt di­<lb/>ctum eſt: neceſſe eſt puncta extremo quieſcenti ꝓpin­<lb/>quior a tardius moueri. </s>
              <s xml:id="N1B0B4" xml:space="preserve">Patet / quia alias reſiſten-<lb/>tia non maneret vniformiter difformis / vt patet ex <lb/>diffinitione qualitatis vniformiter difformis.</s>
            </p>
            <p xml:id="N1B0BB">
              <s xml:id="N1B0BC" xml:space="preserve">¶ His adde /  cum dicimus potentiam moueri cum <lb/>huiuſcemodi reſiſtētia progrediente: intelligimus <lb/>ipſam per lineam breuiſſimam moueri ab extremo <lb/>in extremum.</s>
            </p>
            <p xml:id="N1B0C5">
              <s xml:id="N1B0C6" xml:space="preserve">His poſitis ſit prima concluſio </s>
              <s xml:id="N1B0C9" xml:space="preserve">Dato <lb/>medio non reſiſtente a cuius vno extremo incipiat <lb/>progredi partibiliter latitudo reſiſtentie vniformi­<lb/>ter difformis altero extremorum ſiue intenſiori ſi-<lb/>ue remiſſiori quieſcente / vt declaratum eſt in tertia <lb/>ſuppoſitione: ipſa latitudine cõtinuo manēte vni­<lb/>formiter difformiter extenſa: omni gradu eius cõ­<lb/>tinuo vniformiter mouente: ſi aliquod mobile ali-<lb/>quando cum tali reſiſtentia mouetur vniformiter <lb/>ipſum in eo tempore continuo eſt ad idem punctum <lb/>illius reſiſtentie dummodo mobile nõ varietur nec <lb/>reſiſtentia quo ad intenſionem aut remiſſionem.</s>
            </p>
            <p xml:id="N1B0E2">
              <s xml:id="N1B0E3" xml:space="preserve">Probatur hec concluſio / quoniaꝫ ſi tale mobile ali­<lb/>quando mouetur vniformiter cum tali reſiſtētia / ſe­<lb/>quitur /  in illo tempore continuo mouetur ab ea-<lb/>dem proportione ſed nullam eandem proportionē               <pb chead="De motu quo ad cauſã in medio non reſiſtente." file="0114" n="114"/>               habet ad duo diuerſa puncta illius reſiſtentie cum <lb/>ſit vniformiter difformis ex caſu / ergo ſeq̇tur /  nū-<lb/>̄ eſt cum diuerſis punctis in illo tēpore in quo mo­<lb/>uetur vniformiter. </s>
              <s xml:id="N1B0F7" xml:space="preserve">Patet conſequentia /  ſi in eo tē­<lb/>pore eſſet cum diuerſis punctis iam diuerſas ꝓpor­<lb/>tiones haberet maiorem videlicet cum vno quaꝫ cū <lb/>altero / vt patet / quia eiuſdem ad minus maior eſt ꝓ-<lb/>portio ꝙ̄ ad maius. </s>
              <s xml:id="N1B102" xml:space="preserve">Patet igitur concluſio.</s>
            </p>
            <note position="left" xml:id="N1B105" xml:space="preserve">1. correl.</note>
            <p xml:id="N1B109">
              <s xml:id="N1B10A" xml:space="preserve">¶ Ex quo ſequitur /  vbi in tali reſiſtentia ſic ꝓgre­<lb/>diente / vt dictum eſt / aliquod mobile non variatum <lb/>aliquando mouetur vniformiter: ipſum poſt hoc cõ­<lb/>tinuo mouetur vniformiter. </s>
              <s xml:id="N1B113" xml:space="preserve">Probatur / quia ſi tale <lb/>mobile aliquãdo mouetur vniformiter / ſequitur /  <lb/>ipſum in eo tempore cõtinuo eſt in eodem puncto / vt <lb/>patet ex concluſione: et ſi in eo tempore continuo eſt <lb/>in eodem puncto / ſequitur /  illud mobile non ſuffi-<lb/>cit cum illo puncto mouere velocius  punctus ille <lb/>mouet̄̄ et cõtinuo illud mobile habebit eandem pro­<lb/>portionem ad illum punctum (quia non variabitur / <lb/>vt pono) / et continuo punctus ille mouetur vniformi­<lb/>ter et eque velociter ex caſu: igitur ſequitur /  pūctꝰ <lb/>ille nū̄ precedet mobile: nec vn̄ mobile precedet <lb/>punctum: et mouebitur: igitur continuo mouetur cū <lb/>illo puncto eque velociter et vniformiter / quod fuit <lb/>probandum: </s>
              <s xml:id="N1B130" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <note position="left" xml:id="N1B133" xml:space="preserve">2. correl.</note>
            <p xml:id="N1B137">
              <s xml:id="N1B138" xml:space="preserve">¶ Sequitur ſecundo /  vbi in medio non reſiſtente ē <lb/>progreſſio ſine exrenſio latitudinis reſiſtentie vni-<lb/>formiter difformis altero extremoꝝ quieſcente quo­<lb/>libet puucto continuo mouente difformiter potētia <lb/>ꝓgrediens cum tali reſiſtētia nū̄ continuo vnifor­<lb/>miter mouetur. </s>
              <s xml:id="N1B145" xml:space="preserve">Probatur / quia ſi per aliquod tem­<lb/>pus continuo vniformiter moueretur: per illud tem­<lb/>pus continuo eſſet cum eodem puncto: et ſi ſit conti-<lb/>nuo per aliquod tempus cum eodem puncto cuꝫ qui­<lb/>libet punctus difformiter mouetur: ſequitur /  ipſa <lb/>potentia difformiter mouetur. </s>
              <s xml:id="N1B152" xml:space="preserve">Patet igitur corre­<lb/>larium.</s>
            </p>
            <p xml:id="N1B157">
              <s xml:id="N1B158" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N1B15B" xml:space="preserve">Ubi in medio nõ <lb/>reſiſtente fit progreſſio latitudinis vniformiter dif­<lb/>formis vtrim ad gradum terminate quieſcēte ex­<lb/>tremo intenſiori. </s>
              <s xml:id="N1B164" xml:space="preserve">et remiſſiori velocius mouente ̄ <lb/>potentia ſufficit mouere cuꝫ illo et quolibet eius pū­<lb/>cto intrīſeco vniformiter mouente: potentia illa ſi-<lb/>mul et ab eodem puncto incipiens moueri cum tali <lb/>reſiſtentia non valet diuerſi mode moueri: hoc ē ali­<lb/>quando intendendo, et aliquando remittendo, vel <lb/>aliquando intendendo: et aliquando vniformiter <lb/>mouendo: vel aliquando remittendo, et aliquando <lb/>vniformiter mouendo. </s>
              <s xml:id="N1B177" xml:space="preserve">Probatur / quia talis potē-<lb/>tia non poteſt aliquando intendere: motum ſuum et <lb/>aliquando remittere: nec aliquando intendere mo­<lb/>tum ſuum et aliquando vniformiter mouere: nec ali­<lb/>quando remittere motum ſuum: et aliquando vni-<lb/>formiter mouere: igitur concluſio vera. </s>
              <s xml:id="N1B184" xml:space="preserve">Antecedens <lb/>probatur / quia talis poña non poteſt aliquãdo vni­<lb/>formiter moueri et immediate poſt hoc intēdere aut <lb/>remittere motum ſuum: nec poteſt aliquando inten­<lb/>dere motum ſuum: et immediate poſt hoc remittere: <lb/>nec poteſt aliquando remittere: et immediate poſt <lb/>hoc intendere: nec aliquando intendere: et immedia­<lb/>te poſt hoc vniforlter moueri: nec aliquando re-<lb/>mittere: et immediate poſt hoc vniformiter moueri: <lb/>igitur talis poña non poteſt aliquando intendere <lb/>motum ſuum: et aliquando remittere: nec aliquan-<lb/>do intendere motum ſuum, et aliquando vniformi-<lb/>ter moueri: nec aliquando remittere motum ſuum, <lb/>et aliquando vniformiter moueri: quod fuit probã­<lb/>dum. </s>
              <s xml:id="N1B1A3" xml:space="preserve">Conſequentia eſt manifeſta: et maior patet ex <lb/>correlario precedentis concluſionis, et prima pars               <cb chead="De motu quo ad cauſã in medio non reſiſtente."/>               minoris probatur videlicet /  talis poña non po-<lb/>teſt aliquando intendere motum ſuum et immedia-<lb/>te poſt hoc remittere: quia ſi ſic detur inſtans ī quo <lb/>incipit remittere ante quod inſtans immediate in-<lb/>tendebat motum ſuum in quo inſtanti talis poten­<lb/>tia ſit in puncto a. a quo incipit remittere motū ſu­<lb/>um per te continuo cum intenſiori pūcto mouendo <lb/>̄ ſit a. / et capio vnam partem illius reſiſtentie termi­<lb/>natam ad punctum a. per quam mouendo ipſa po-<lb/>tentia continuo intendit motum ſuum: et manifeſtū <lb/>eſt /  ipſa potentia ſic intendens motum ſuum cõti­<lb/>nuo per illam partem velocius mouetur cum quoli­<lb/>bet puncto illius reſiſtentie quam ille punctus mo-<lb/>uetur: </s>
              <s xml:id="N1B1C5" xml:space="preserve">Alias enim non continuo intenderet per illã <lb/>partem mouendo: </s>
              <s xml:id="N1B1CA" xml:space="preserve">Et ex alia parte per te ipſa poña <lb/>cõtinuo remittit motum ſuum per illam reſiſtentiã <lb/>vel aliquam eius partem mouendo: igit̄̄ ipſa poña <lb/>non continuo per illam partem velocius mouetur <lb/>cum quolibet puncto illius reſiſtentie quam ille pū­<lb/>ctus mouetur: </s>
              <s xml:id="N1B1D7" xml:space="preserve">Et ſic ſequitur contradictio </s>
              <s xml:id="N1B1DA" xml:space="preserve">(Quãdo­<lb/>quidem omnia illa puncta vniformiter ↄ̨tinuo mo-<lb/>uētur ex caſu concluſionis.) </s>
              <s xml:id="N1B1E1" xml:space="preserve">Iam probo ſecūdam ꝑ­<lb/>tem minoris videlicet /  illa poña non poteſt aliqñ <lb/>remittere motum ſuum, et immediate poſt hoc intē-<lb/>dere: quia ſi ſic: detur inſtans in quo incipit intēde-<lb/>re ante quod inſtans immediate remittebat motuꝫ <lb/>ſuū in quo inſtanti talis poña ſit in puncto a. a quo <lb/>incipit intendere motum ſuum per te continuo cum <lb/>remiſſiori puncto mouēdo ꝙ̄ ſit a. / et capio vnam ꝑ-<lb/>tem illius reſiſtentie terminatam ad a. punctum per <lb/>quam mouendo continuo remittebat motum ſuum / <lb/>et manifeſtum eſt /  ipſa ſic remittens motum ſuum <lb/>cõtinuo per illam partem mouendo tardius moue­<lb/>tur cum quolibet puncto illius partis quam ille pū­<lb/>ctus mouetur. </s>
              <s xml:id="N1B1FE" xml:space="preserve">Alias enim non continuo remitteret <lb/>motum ſuum per illam partem mouēdo. </s>
              <s xml:id="N1B203" xml:space="preserve">Et ex alia <lb/>parte ipſa poña per te continuo intendit motuꝫ ſu­<lb/>um per illam reſiſtentiam vel aliquam eius partem <lb/>mouendo: igitur ipſa poña non cõtinuo per illam <lb/>partem velocius mouetur cum quolibet puncto illi­<lb/>us partis ꝙ̄ ille punctus mouetur. </s>
              <s xml:id="N1B210" xml:space="preserve">Et ſic ſequitur cõ­<lb/>tradictio: cum omnia illa puncta vniformiter con­<lb/>tinuo mouētur ex caſu concluſionis. </s>
              <s xml:id="N1B217" xml:space="preserve">Sed iam ꝓba-<lb/>tur tertia pars minoris vcꝫ /  illa poña non poteſt <lb/>aliquando intendere motum ſuum: et īmediate poſt <lb/>hoc vniformiter moueri: quia ſi ſic detur inſtans in <lb/>quo incipit vniformiter moueri ante quod inſtans <lb/>immediate intendebat motum ſuum. </s>
              <s xml:id="N1B224" xml:space="preserve">in quo inſtan­<lb/>ti talis poña ſit in puncto a. a quo incipit vniformi­<lb/>ter moueri per te: et ſequitur /  tunc incipit moueri <lb/>cum a. velocius ꝙ̄ vn̄ antea mouebatur: et ita velo­<lb/>citer ſicut a. mouetur per te, cum in a. incipiat vni-<lb/>formiter moueri. </s>
              <s xml:id="N1B231" xml:space="preserve">et ſic continuo eē in eodē puncto a. <lb/>ex prima cõcluſione: igitur ipſa poña non eſt in pū­<lb/>cto a. / quod eſt oppoſitum dati. </s>
              <s xml:id="N1B238" xml:space="preserve">Patet conſequētia / <lb/>quia a. punctus et ipſa poña inceperūt ab eodem in­<lb/>ſtanti moueri ex caſu concluſionis: ergo ſi vſ ad ī­<lb/>ſtans datum continuo poña mouetur tardius ꝙ̄ a. <lb/>punctus / ſequitur /  ipſa poña in inſtãti dato nõ eſt <lb/>in puncto a. / quod eſt probandum. </s>
              <s xml:id="N1B245" xml:space="preserve">Probatur tamē <lb/>maior videlicet /  in inſtanti dato incipit illa poña <lb/>cum a. velocius moueri ꝙ̄ vn̄ antea mouebatur q2 <lb/>per aliquod tempus per te cõtinuo illa poña ante-<lb/>̄ attingat a. eſt in maiori reſiſtentia quã ſit a. ſeq̄n­<lb/>do ipſum a. / igitur ſemper antea ꝙ̄ attīgat a. / ſequi-<lb/>tur ipſum a. cum nõ ſit poſſibile cum caſu cõcluſio-<lb/>nis  aliquando precedat et aliquãdo ſequatur a. <lb/>punctum cum quo ſufficit mouere ita velociter ſicut <lb/>punctus a. mouetur / vt patet intuenti: quia alias ſe­               <pb chead="Primi tractatus" file="0115" n="115"/>               queretur cum ipſa poña non ſaltet a puncto ī pun­<lb/>ctum (vt ſemper ſuppono) /  aliquando fuit in pun­<lb/>cto a: et ſi ſic ſequitur /  ſemper mãſit ī pūcto a. qm̄ <lb/>per te ita velociter ſufficit mouere cum puncto a. ſi-<lb/>cut punctus a. mouetur. </s>
              <s xml:id="N1B267" xml:space="preserve">Et ex conſequenti ſequitur / <lb/> ſemper ante̄ attingat a. eſt in maiori reſiſten-<lb/>tia quã ſit a. / et ſic in inſtanti dato incipit illa poten­<lb/>tia cum a. velocius moueri quã vn̄ antea moueba­<lb/>tur / quod fuit probandum. </s>
              <s xml:id="N1B272" xml:space="preserve">Sed iam probo quartã <lb/>partem minoris videlicet /  illa poña nõ poteſt ali­<lb/>quando remittere motum ſuum, et immediate poſt <lb/>hoc vniformiter moueri: quia ſi ſic detur inſtans in <lb/>quo incipit vniformiter moueri ante quod inſtans <lb/>immediate remittebat motum ſuum in quo inſtan-<lb/>ti talis poña ſit in puncto a. a quo incipit vniformi­<lb/>ter moueri per te: et ſequitur /  tunc incipit moueri <lb/>cum a. tardius quã vn̄ antea mouebatur, quoniã <lb/>ſemper antea preceſſit a. mouens cum remiſſiori re­<lb/>ſiſtentia / vt patet ex probatione precedentis partis <lb/>et incipit ita velociter moueri per te ſicut a. (cum ī a. <lb/>incipiat vniformiter moueri) et ſic continuo eſſe ī eo­<lb/>dem puncto a. ex prima concluſione / igitur ipſa po-<lb/>tentia in inſtanti dato non eſt in puncto a. / quod eſt <lb/>oppoſitum dati. </s>
              <s xml:id="N1B293" xml:space="preserve">Patet conſequētia / quia ipſa po-<lb/>tentia et a. pūctus inceperūt in eodem inſtanti mo-<lb/>ueri ex caſu cõcluſionis: ergo ſi vſ ad inſtans da-<lb/>tum illa poña mouetur velocius cõtinuo quã a. pun­<lb/>ctus ſequitur /  illa poña in inſtanti dato non eſt in <lb/>puncto a. / quod eſt probandum. </s>
              <s xml:id="N1B2A0" xml:space="preserve">Et ſic patet quarta <lb/>pars minoris et per conſequens concluſio.</s>
            </p>
            <note position="left" xml:id="N1B2A5" xml:space="preserve">1. correl.</note>
            <p xml:id="N1B2A9">
              <s xml:id="N1B2AA" xml:space="preserve">¶ Ex quo ſequirur /  vbi progreditur latitudo reſi-<lb/>ſtentie etc. / vt ponitur in cõcluſione: et potentia ſiue <lb/>mobile incipit ab eodem puncto in eodem inſtan-<lb/>ti moueri cum tali reſiſtentia: neceſſe eſt /  tale mo-<lb/>bile continuo vniformiter moueatur vel  cõtinuo <lb/>intendat motum ſuum: vel continuo remittat. </s>
              <s xml:id="N1B2B7" xml:space="preserve">Pa-<lb/>tet hoc correlarium facile ex concluſione.</s>
            </p>
            <note position="left" xml:id="N1B2BC" xml:space="preserve">.2correl.</note>
            <p xml:id="N1B2C0">
              <s xml:id="N1B2C1" xml:space="preserve">¶ Sequitur ſecundo /  vbi in medio nõ reſiſtente fit <lb/>progreſſio latitudinis difformis cuius nulla pars <lb/>eſt vniformis cuiuſ omnes partes immediate ſe-<lb/>cundum extenſionem ſunt immediate ſecundum in-<lb/>tenſionem: vtrim ad gradum terminate, quieſcē-<lb/>te extremo intenſiori: et remiſſiori velocius cõtinuo <lb/>mouente ꝙ̄ poña data ſufficit moueri cum illo, om­<lb/>ni puncto eius intrinſeco vniformiter continuo <lb/>mouente: talis poña incipiens ſimul moueri a pun­<lb/>cto a quo incipit talis latitudo progredi non valet <lb/>diuerſi mode moueri, puta aliquando intendendo <lb/>aliquando remittendo, vel aliquando intendendo <lb/>et aliquando vniformiter mouendo etc. </s>
              <s xml:id="N1B2DC" xml:space="preserve">Hoc correla­<lb/>rium eadem qua concluſio demonſtratione oſten-<lb/>ditur.</s>
            </p>
            <p xml:id="N1B2E3">
              <s xml:id="N1B2E4" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N1B2E7" xml:space="preserve">Ubi in medio nõ re-<lb/>ſiſtente eſt progreſſio ſiue extēſio latitudinis reſiſtē­<lb/>tie vniformiter difformis in vtro extremo ad gra­<lb/>dum terminate, quolibet puncto intrinſeco conti-<lb/>nuo mouente vniformiter, quieſcente extremo īten­<lb/>ſiori: et remiſſiori velocius mouente quã mobile qḋ <lb/>in tali reſiſtentia mouetur ſufficit moueri cum illo: <lb/>tale mobile habens ꝓportionem maioris inequali­<lb/>tatis ad extremum intenſius. </s>
              <s xml:id="N1B2FA" xml:space="preserve">incipiens ſimul ab eo­<lb/>dem puncto moueri cum tali reſiſtentia cõtinuo vni­<lb/>formiter mouetur. </s>
              <s xml:id="N1B301" xml:space="preserve">Probatur / et ſit talis poña b. / et <lb/>arguo ſic / b. poña in caſu cõcluſionis vel cõtinuo in­<lb/>tendit motum ſuum, vel continuo remittit motū ſu­<lb/>um, vel cõtinuo vniformiter mouetur: vt patet ex ſe­<lb/>unda concluſione et ſuo primo correlarioi: ſed b. po­<lb/>tentia nõ cõtinuo intendit motum ſuum: nec ↄ̨tinuo               <cb chead="Capitulum tridecimum"/>               remittit motum ſuum: igitur continuo vniformiter <lb/>mouetur: quod fuit probandum. </s>
              <s xml:id="N1B313" xml:space="preserve">Conſequentia pa­<lb/>tet cum maiore: et prima pars minoris probatur vi­<lb/>delicet /  b. poña non cõtinuo intendit motum ſuuꝫ <lb/>quia ſi ſic detur ꝓportio a qua incipit moueri cõti-<lb/>nuo intendendo motum ſuum que ſit f. quam habet <lb/>ad punctum a. illius reſiſtentie a quo īcipiendo mo­<lb/>ueri continuo per te intendit motum ſuum: et ille pū­<lb/>ctus a. moueatur cõtinuo a .g. proportione minore <lb/>f. (vt oportet) </s>
              <s xml:id="N1B326" xml:space="preserve">Non enim incipit b. poña moueri a. ꝓ­<lb/>portione quam habet ad extremuꝫ quieſcens: quia <lb/>tunc per aliquod tempus infinita puncta precede-<lb/>rent b. poñam quorum quodlibet cõtinuo a minori <lb/>ꝓportione mouetur ꝙ̄ ſit proportio quam habet b. <lb/>poña ad extremum quieſcens / vt patet ex caſu cõclu­<lb/>ſionis: quandoquidem ab infinite modica ꝓportio­<lb/>ne aliquod punctum illius reſiſtentie moueatur / qḋ <lb/>tamen eſſe nequit: cum ab eodem puncto in eodē in­<lb/>ſtãti incipiat quodlibet illorum pūctorum moueri <lb/>cum illa poña b. </s>
              <s xml:id="N1B33D" xml:space="preserve">Capio igitur / tunc c. punctum re-<lb/>miſſius ipſo a. puncto quod moueatur ab h. ꝓpor-<lb/>tione minore f. ꝓportione a qua mouet̄̄ poña b. ma­<lb/>iore tamen ꝓportione g. a qua mouetur a. punctum / <lb/>et arguo ſic / b. poña incipit intendere motum ſuum <lb/>incipiendo moueri ab a. puncto ſucceſſiue verſus c. <lb/>punctum et alia puncta remiſſiora: igitur per aliqḋ <lb/>tempus c. pūctum precedit ipſam b. poñam: ſed con­<lb/>ſequens eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1B350" xml:space="preserve">Cõ­<lb/>ſequentia patet / et falſitas conſequentis arguitur: <lb/>quia b. poña et c. punctum incipiunt in eodem inſtã-<lb/>ti ab eodem puncto verſus eãdem differētiam mo-<lb/>ueri etc. et ipſa poña b. continuo mouetur a maiori <lb/>ꝓportione quam punctum c. / igitur cõtinuo ipſa b. <lb/>poña precedit punctum c. / et per conſequens pūctum <lb/>c. nū̄ precedit eam / quod eſt oppoſitum conſequē-<lb/>tis: </s>
              <s xml:id="N1B363" xml:space="preserve">Et ſic patet prima pars minoris. </s>
              <s xml:id="N1B366" xml:space="preserve">Sed ſecunda <lb/>ꝓbatur videlicet /  b. poña nõ cõtinuo remittit mo-<lb/>tum ſuum: quia ſi ſic detur proportio a qua incipit <lb/>moueri continuo remittendo motum ſuum que ſit f. <lb/>quam habet ad punctum a. illius reſiſtentie a quo ī­<lb/>cipiendo moueri continuo per te remittit motum ſu­<lb/>um: et illud punctum a. moueatur continuo a g. pro­<lb/>portione maiore f. / vt oportet </s>
              <s xml:id="N1B377" xml:space="preserve">(Non enim incipit b. <lb/>potentia moueri a proportione quam habet ad ex­<lb/>tremum quieſcens / vt ſupra argutum eſt) </s>
              <s xml:id="N1B37E" xml:space="preserve">Capio igi­<lb/>tur / tunc c. punctuꝫ ītenſius ipſo a. puncto quod mo­<lb/>ueatur ab h. proportione maiore f. a qua mouetur <lb/>poña b. minore tamen ꝓportione g. a qua mouetur <lb/>a. punctuꝫ: et arguo ſic / b. poña incipit remittere mo­<lb/>tum ſuum incipiendo moueri ab a. puncto ſucceſſi-<lb/>ue c. puncto et aliis punctis intenſioribus mouenti-<lb/>bus verſus poñam et eam ſequentibus: igitur ꝑ ali-<lb/>quod tempus b. poña precedit c. punctum. </s>
              <s xml:id="N1B391" xml:space="preserve">ſed conſe­<lb/>quens eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1B396" xml:space="preserve">Cõſe-<lb/>quentia eſt nota, et falſitas conſequentis arguitur / <lb/>quia b. poña et c. punctum incipiunt in eodem inſtã-<lb/>ti ab eodem puncto etc. et ipſa poña b. cõtinuo moue­<lb/>tur a minori ꝓportione ꝙ̄ punctum c. / igitur cõtinuo <lb/>c. punctum precedit b. poñam: et ꝑ conſequens b. po­<lb/>tentia nun̄ precedit c. punctum / quod eſt oppoſitū <lb/>conſequentis. </s>
              <s xml:id="N1B3A7" xml:space="preserve">Et ſic patet ſecunda pars minoris et <lb/>ex hoc tota concluſio.               <anchor type="note" xlink:href="note-0115-01" xlink:label="note-0115-01a"/>               </s>
              <s xml:id="N1B3B1" xml:space="preserve">¶ Ex quo ſequitur /  vbi ī me­<lb/>dio non reſiſtente eſt progreſſio ſiue extenſio latitu­<lb/>dis reſiſtentie difformis cuius nulla pars eſt vnifor­<lb/>mis: cuiuſ omnes partes īmediate ſecundum extē­<lb/>ſionem ſunt immediate ſecundum intenſionem vtrū­<lb/> ad gradum terminate: quolibet puncto eius ītrī­<lb/>ſeco mouente cõtinuo vniformiter quieſcente extre-<lb/>mo intenſiori: et remiſſiori velocius continuo mouē­               <pb chead="De motu locali quo ad cauſam in medio non reſiſte." file="0116" n="116"/>               te quã mobile quod in tali reſiſtentia mouetur ſuf-<lb/>ficit moueri cū illo: tale mobile habens ꝓportionē <lb/>maioris inequalitatis ad extremū intenſius inci-<lb/>piens ſimul ab eodem puncto progredi ſiue moue-<lb/>ri cum tali reſiſtentia, vniformiter continuo moue-<lb/>tur. </s>
              <s xml:id="N1B3D1" xml:space="preserve">Patet cdrrelariū ex ꝓbatione concluſionis.</s>
            </p>
            <div xml:id="N1B3D4" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0115-01a" xlink:label="note-0115-01" xml:id="N1B3D8" xml:space="preserve">correla.</note>
            </div>
            <p xml:id="N1B3DE">
              <s xml:id="N1B3DF" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N1B3E2" xml:space="preserve">Ubi in medio non <lb/>reſiſtentie eſt ꝓgreſſio ſiue extenſio latitudinis vni-<lb/>formiter difformis vtrim ad gradū terminate, <lb/>quolibet puncto eius intrinſeco continuo intendē-<lb/>te motum ſuū, quieſcente extremo intenſiori: et re-<lb/>miſſiori velocius continuo mouente quam mobile <lb/>quod in tali reſiſtentia mouetur ſufficit moueri cū <lb/>illa: tale mobile habens ꝓportionē maioris īequa­<lb/>litatis ad extremū intenſius incipiens ſimul ab eo­<lb/>dem puncto progredi ſiue moueri cum tali reſiſten­<lb/>tia continuo remittit motum ſuū. </s>
              <s xml:id="N1B3F9" xml:space="preserve">Probatur et ſit <lb/>illi b. potentia: et arguo ſtc / b. potentia nun̄ vnifor­<lb/>miter mouetur, cū caſu concluſionis / vt patet er ſe-<lb/>cundo correlario prime concluſionis: nec continuo <lb/>intendit motum ſuum: nec aliquando remittit et im­<lb/>wediate poſtea intendit, aut econtra: igitur b. po-<lb/>tentia continuo remittit motum ſuum. </s>
              <s xml:id="N1B408" xml:space="preserve">Conſequen­<lb/>tia patet cnm maiore, et probatur prima pars mi-<lb/>noris, quia ſi ſic detur proportio a qua incipit mo-<lb/>ueri b. potentia continuo intendendo motum ſuum <lb/>que ſit f. quã habet ad punctum a. illius reſiſtentie <lb/>a quo incipiendo moueri continuo per te intendit <lb/>motum ſuū: et illud punctū a. incipiat moueri a pro­<lb/>portione g. minori ꝓportione f. (vt oportet per te) <lb/></s>
              <s xml:id="N1B41A" xml:space="preserve">Non em̄ incipit aliquod punctū illius reſiſtētie a nõ <lb/>gradu moueri, cum extremū remiſſius continuo ve­<lb/>locius mouetur quaꝫ potentia ſufficit mouere cum <lb/>illo ex caſu cõcluſionis: quia alias potentia ſubito <lb/>abſolueret totum illud mediū nõ reſiſtēs, cū ſubito <lb/>eſſet extra reſiſtentiam. </s>
              <s xml:id="N1B427" xml:space="preserve">Capio igitur / tunc c. punctū <lb/>remiſſius ipſo a. quod incipit moueri ab h. ꝓpor-<lb/>tione minore f. ꝓportione a qua incipit mouere b. <lb/>potentia, maiore tamen ꝓportiõe g. a qua incipit <lb/>moueri a. punctū: et arguo ſic / b. potentia incipit in­<lb/>tendere motum ſuū incipiendo moueri ab a. pūcto <lb/>verſus c. punctū et alia puncta intenſiora: igitur ꝑ <lb/>aliquod tempus per qḋ c. punctū mouetur a ꝓpor-<lb/>tione minori f.c punctum ꝓcedit b. potentiam: ſed <lb/>conſequens eſt falſum: igitur illud ex quo ſequitur. <lb/></s>
              <s xml:id="N1B43D" xml:space="preserve">Conſequentia eſt nota, et falſitas conſequentis ar-<lb/>guitur / quia b. potentia et c. punctū incipiūt in eodē <lb/>inſtanti ab eodem pūcto moueri verſus eandē dif-<lb/>ferentiã etc̈. et ipſa b. potentia per illud tempus per <lb/>quod c. punctū mouetur continuo a minori ꝓpor-<lb/>tione quã ſit f. mouetur cõtinuo a maiori ꝓportiõe <lb/>quã c. punctū cum a maiori f. / igitur per illud tēpus <lb/>per quod c. punctum mouetur a proportione mi-<lb/>nori f.b. potentia precedit punctum c. / et per conſe-<lb/>quens per nullum tale tempus per quod c. punctuꝫ <lb/>mouetur a proportione minori f.c. punctum prece-<lb/>dit b. potentiam / quod eſt oppoſitum conſequentis <lb/></s>
              <s xml:id="N1B457" xml:space="preserve">Et ſic patet prima pars minoris. </s>
              <s xml:id="N1B45A" xml:space="preserve">Sed iam proba-<lb/>tur ſecunda videlicet /  b. potentia non aliquando <lb/>remittit motum ſuum, et immediate poſtea intēdit, <lb/>quia ſi ſic det̄̄ inſtans in quo incipit intendere an-<lb/>te quod inſtans immediate remittebat motum ſu-<lb/>um in quo inſtanti b. potentia ſit in puncto a. a quo <lb/>incipit intendere motum ſuum per te continuo cum <lb/>remiſſiori puncto mouendo quam ſit a. </s>
              <s xml:id="N1B46B" xml:space="preserve">Capio igi-<lb/>tur vnam partem illius reſiſtentie terminatam ad <lb/>punctum a. per quam b. potentia mouēdo cõtinuo               <cb chead="De motu locali quo ad cauſam in medio non reſiſte."/>               remittebat motum ſuum, et manifeſtum eſt /  ipſa <lb/>potentia b. ſic continuo remittēs motum ſuum per <lb/>illam partē mouēdo tardius mouetur cum quoli-<lb/>bet puucto illius partis quam ille punctus moue-<lb/>tur. </s>
              <s xml:id="N1B47D" xml:space="preserve">Alias enim non cõtinuo b. potentia remitteret <lb/>motum ſuū illam partē tranſeundo. </s>
              <s xml:id="N1B482" xml:space="preserve">Et ex alia par­<lb/>te ipſa potentia b. per te continuo intendit motum <lb/>ſuū per illam reſiſtentiã vel aliquã eius partē mo-<lb/>uendo: igitur tunc ipſa potentia b. nõ continuo per <lb/>illam partē velocius mouetur cum quolibet puncto <lb/>illius partis ꝙ̄ ille punctus mouetur / qḋ eſt falſum: <lb/>q2 antea quilibet pūctus illius partis velocius mo­<lb/>uebatur ꝙ̄ potentia ſufficit moueri cum illo: igitur <lb/>etiã modo (cū quilibet pūctus cõtinuo intēdat mo-<lb/>tum ſuū). </s>
              <s xml:id="N1B497" xml:space="preserve">Et ſic ptꝫ ſecūda pars minoris. </s>
              <s xml:id="N1B49A" xml:space="preserve">Sed iam <lb/>ꝓbo tertiã partc̈ vcꝫ  b. potētia nõ aliquãdo intē-<lb/>dit motum ſuū, et īmediate poſtea remittit, q2 ſi ſic <lb/>detur inſtans in quo incipit remittere poſt̄ inten-<lb/>debat: et arguo ſic, quia tūc vel b ↄ̨tinuo antea intē­<lb/>debat, vel aliquãdo remittebat et īmediate poſtea <lb/>intendebat: nõ primū (vt ptꝫ) ex prima parte mino-<lb/>ris: nec ſcḋm (vt ptꝫ) ex ſecūda: igitur b. potentia nõ <lb/>aliquãdo intendit motū ſuū, et īmediate poſtea re-<lb/>mittit / quod fuit ꝓbandū. </s>
              <s xml:id="N1B4AF" xml:space="preserve">Et ſic ptꝫ tertia pars mi­<lb/>noris: et ex tota cõcluſio.               <anchor type="note" xlink:href="note-0116-01" xlink:label="note-0116-01a"/>               </s>
              <s xml:id="N1B4B9" xml:space="preserve">¶ Ex quo ſequitur /  ſi illa <lb/>reſiſtentia ꝑpetuo ſic ꝓgrederetur vt dicitur in con­<lb/>cluſione, et potentia duraret ꝑpetuo, et nõ depone-<lb/>retur violēter ab illa reſiſtentia: ipſa potentia per­<lb/>petuo ibi remitteret motū ſuū et data certa ꝓpor-<lb/>tione ipſa continuo moueretur a maiori illa. </s>
              <s xml:id="N1B4C6" xml:space="preserve">Pro­<lb/>batur prima pars correlarii / q2 talis potētia nū̄ <lb/>deueniet ad punctū velociſſime motū (cū tale pun-<lb/>ctū cõtinuo moueatur velocius ꝙ̄ ipſa potētia) qm̄ <lb/>tale incipipit moueri a maiori ꝓportione ꝙ̄ poten­<lb/>tia ex caſu cõcluſionis: et continuo intēdit motū ſuū <lb/>potētia ſuū motū continuo remittente: nec etiã vn̄ <lb/>talis potentia ꝑueniet ad extremū quieſcēs: cū con­<lb/>tinuo magis recedat ab eo mouēdo a maiori ꝓpor­<lb/>tione cõtinuo ꝙ̄ ſit ꝓportio quã habet ad extremū) / <lb/>igr̄ talis potentia cõtinuo erit in pūcta intrinſeca <lb/>illiꝰ reſiſtētie cõtinuo remittens motū ſuū ex cõclu-<lb/>ſione. </s>
              <s xml:id="N1B4E1" xml:space="preserve">Et ex hoc ptꝫ ſecūda pars: nã illa potētia cõ-<lb/>tinuo mouetur a maiori ꝓportione ꝙ̄ ſit ꝓportio <lb/>quã habet eadē potentia ad extremū quiſcens (cum <lb/>ipſa potentia ſit continuo in puncto intrinſeco re-<lb/>miſſiori puncto intenſiori illius reſiſtentie quieſcē-<lb/>te: igitur data certa ꝓportione talis potentia mo­<lb/>uetur a maiori illa / quod fuit probandum.</s>
            </p>
            <div xml:id="N1B4F0" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0116-01a" xlink:label="note-0116-01" xml:id="N1B4F4" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="right" xml:id="N1B4FA" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N1B4FE">
              <s xml:id="N1B4FF" xml:space="preserve">¶ Nec hoc pretereas  idem dici queat de reſiſten-<lb/>tia difformi cuius nulla pars eſt vniformis, cuiuſ <lb/>omnes partes immediate ſecundum extenſionem <lb/>ſunt immediate ſecundum intenſionem vtrin ad <lb/>gradum terminata quod de reſiſtentia vniformiter <lb/>difformi in vtro extremo terminata ad gradum / <lb/>in hac concluſione et ſuo correlario dictum eſt.</s>
            </p>
            <p xml:id="N1B50E">
              <s xml:id="N1B50F" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N1B512" xml:space="preserve">Ubi in medio non <lb/>reſiſtente eſt progreſſio ſiue extenſio latitudinis re­<lb/>ſiſtentie vniformiter difformis in vtro extremo <lb/>ad gradum terminate, quolibet eius puncto intrin­<lb/>ſeco continuo remittente motum ſuum, et extremo <lb/>intenſiori quieſcente, remiſſiori vero velocius in-<lb/>cipiente moueri quam mobile quod in tali reſiſten­<lb/>tia mouetur ſufficit moueri cū illo: tale mobile ha-<lb/>bens proportionem maioris inequalitatis ad ex-<lb/>tremum intenſius incipiens ſimul ab eodem pun-<lb/>cto progredi ſiue moueri cum tali reſiſtentia con-<lb/>tinuo intendit motum ſuum.</s>
            </p>
            <pb chead="Primi tractatus" file="0117" n="117"/>
            <p xml:id="N1B52F">
              <s xml:id="N1B530" xml:space="preserve">Probatur / et ſit illa b. potentia: et arguo ſic / b. potē­<lb/>tia nun̄ vniformiter mouetur / vt ptꝫ ex ſecūdo cor­<lb/>relario prime concluſionis: nec continuo remittit <lb/>motū ſuū: nec aliquãdo intendit et īmediate poſtea <lb/>remittit: aut econtra: igitur b. potentia cõtinuo in-<lb/>tendit motū ſuū / quod ruit ꝓbandū. </s>
              <s xml:id="N1B53D" xml:space="preserve">Cõſequētia ptꝫ <lb/>cū maiore, et ꝓbatur prima pars minoris / q2 ſi ſic <lb/>detur ꝓportio a qua incipit moueri b. potentia cõ-<lb/>tinuo remittendo motum ſuū que ſit f. quã habeat ad <lb/>a. punctū illius reſiſtentie a quo incipiendo moue-<lb/>ri continuo per te remittit motū ſuū et illud punctū <lb/>a. incipiat moueri a ꝓportione g. maiore f. / vt opor­<lb/>tet </s>
              <s xml:id="N1B54E" xml:space="preserve">(Alias em̄ b. potentia nõ remitteret motum ſuū) / et <lb/>capio / tunc c. punctū intenſius a. puncto / quod inci-<lb/>pit moueri ab h. ꝓportione maiore f. / a qua incipit <lb/>moueri b. potentia minori tamen g. proportione a <lb/>qua incipit moueri a. punctū: et arguo ſic / b. poten-<lb/>tia incipit remittere motum ſuū incipiendo moue-<lb/>ri ab a. puncto ſucceſſiue: a. puncto et aliis punctis <lb/>intenſioribus verſus potentiã mouentibus et ſequē­<lb/>tibus eam: igitur per aliquod tempus b. potentia <lb/>precedit c. punctū: ſed cõſequens eſt falſum: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N1B565" xml:space="preserve">Cõſequentia eſt nota, et falſi-<lb/>tas conſequentis arguitur, q2 b. potentia et c. pun-<lb/>ctum incipiunt in eodē inſtanti moueri ab eodē pū-<lb/>cto etc̈. et ipſa b. potentia continuo mouetur a mino­<lb/>ri ꝓportione quã punctū c: quia a minori f. cõtinuo <lb/>cū remittat continuo motum ſuū per te: igitur per <lb/>illud tempus continuo c. punctū precedit b. poten-<lb/>tiam, et per cõſequens b. potentia nõ ꝑ illud tēpus <lb/>precedit c. punctū / quod eſt oppoſitū conſequentis. <lb/></s>
              <s xml:id="N1B579" xml:space="preserve">Et ſic patet prima pars minoris. </s>
              <s xml:id="N1B57C" xml:space="preserve">Sed ſecūda ꝓba­<lb/>tur videlicet /  b. potentia nõ aliquãdo intendit, et <lb/>īmediate poſtea remittit, quia ſi ſic detur inſtans / <lb/>in quo incipit remittere ante quod īmediate inten-<lb/>debat motum ſuū in quo inſtanti b. potentia ſit in <lb/>puncto a. / a quo incipit remittere motum ſuū per te <lb/>continuo cū intenſiori puncto mouendo quã ſit a. <lb/></s>
              <s xml:id="N1B58C" xml:space="preserve">Capio igitur / vnã partem illiꝰ reſiſteutie termina-<lb/>tam ad a. punctū per quã b. potentia mouendo con­<lb/>tinuo intendebat motum ſuū, et manifeſtū eſt /  ip-<lb/>ſa potentia b. ſic continuo intendens motum ſuum <lb/>per illam partem mouendo velocius mouetur cum <lb/>quolibet puncto illius partis ꝙ̄ ille punctus moue­<lb/>tur. </s>
              <s xml:id="N1B59B" xml:space="preserve">Alias em̄ non continuo b. potentia intenderet <lb/>motum ſuū illam partē tranſeundo. </s>
              <s xml:id="N1B5A0" xml:space="preserve">Et ex alia par­<lb/>te ipſa potentia b. per te continuo remittit motum <lb/>ſuū per illam reſiſtentiã vel aliquã eius partē mo-<lb/>uendo: igitur tunc ipſa potentia b. nõ continuo per <lb/>illam partē mouendo tardius mouetur cum quoli­<lb/>bet puncto illius partis quã ille punctus mouetur: <lb/>ſed cõſequens eſt falſum. </s>
              <s xml:id="N1B5AF" xml:space="preserve">q2 antea quilibet punctus <lb/>illius partis tardius mouebatur quã potentia b. <lb/>ſufficit moueri cū illo: igitur etiam modo cū conti-<lb/>nuo quilibet punctus motum ſuum remittat. </s>
              <s xml:id="N1B5B8" xml:space="preserve">Et ſic <lb/>ptꝫ ſecunda pars minoris. </s>
              <s xml:id="N1B5BD" xml:space="preserve">Sed iam tertia ꝓbatur <lb/>videlicet /  b. potentia nõ aliquãdo remittit motū <lb/>ſuū, et immediate poſtea intendit, quia ſi ſic detur <lb/>inſtans in quo incipit intendere poſt̄ remittebat / <lb/>et arguo ſic, quia tunc vel b. potentia continuo an-<lb/>tea remittebat, vel aliquando intendebat et īmedia­<lb/>te remittebat (cum nun̄ poſſit vniformiter moueri <lb/>ex ſecundo correlario prime concluſionis) non pri-<lb/>mū / vt ptꝫ ex prima parte minoris nec ſecundum / vt <lb/>patet ex ſecunda: igitur b. potentia nõ aliquãdo re­<lb/>mittit motum ſuum, et immediate poſtea intendit / <lb/>quod fuit probandum. </s>
              <s xml:id="N1B5D6" xml:space="preserve">Et ſic patet tertia pars mi-<lb/>noris et ex hoc tota concluſio.               <anchor type="note" xlink:href="note-0117-01" xlink:label="note-0117-01a"/>               </s>
              <s xml:id="N1B5E0" xml:space="preserve">¶ Ex quo ſequitur               <cb chead="Capitulū quartūdecimū."/>               primo /  vbi in medio non reſiſtente eſt progreſſio <lb/>ſiue extenſio latitudinis reſiſtentie vniformiter dif­<lb/>formis in vtro extremo ad gradum terminate, <lb/>quolibet eius puncto intrinſeco continuo remitten­<lb/>te motum ſuum, quieſcente extremo intenſiori: et re­<lb/>miſſiori velocius incipiente moueri quã mobile qḋ <lb/>in tali reſiſtentia mouetur ſufficit mouere cum illo <lb/>et extremo remiſſiori remittente motum ſnū ad non <lb/>gradum vel vſ ad motum prouenientē a propor-<lb/>tione a qua incipit tale mobile moueri continuo in­<lb/>tendēs motū ſuū īcluſiue, vel ad minorē: tandē mo-<lb/>bile illud ad eodem puncto cum tali reſiſtentia in-<lb/>cipiens progredi deueniet ad extremum remiſſiſſi-<lb/>mum eiuſdeꝫ latitudinis: dummodo ipſum mobile <lb/>continuo / quo ad vſ reſiſtentiã inuenerit moueat̄̄. <lb/></s>
              <s xml:id="N1B603" xml:space="preserve">Probatur correlarium / quoniam ſi extremum re-<lb/>miſſius illius reſiſtentie remittat motum ſuum ad <lb/>non gradum, vel ad motum illum a quo incipit b. <lb/>potentia in caſu concluſionis moueri intendendo <lb/>motum ſuum, vel ad minorē ſequitur / cum b. poten-<lb/>tia a motu a quo incipit moueri continuo intendit <lb/>motum ſuum  cum extremum remiſſius illius re-<lb/>ſiſtentie remiſerit ſuum motum ad motum a quo b. <lb/>potentia incipit moueri, vel ad minorem, b. poten-<lb/>tia in certa proportione continuo velocius moue-<lb/>tur ꝙ̄ extremum remiſſius illius reſiſtentie cõtinuo <lb/>illud extremum inſequendo, et per conſequens tan-<lb/>dem in tempore finito illud extremū attinget / quod <lb/>fuit probandum. </s>
              <s xml:id="N1B620" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <div xml:id="N1B623" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0117-01a" xlink:label="note-0117-01" xml:id="N1B627" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="right" xml:id="N1B62D" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N1B631">
              <s xml:id="N1B632" xml:space="preserve">¶ Sequitur ſecundo /  illud idem dici poteſt de re-<lb/>ſiſtentia difformi cuius nulla pars eſt vniformis, <lb/>cuiuſ omnes partes īmediate ſecundum extenſio­<lb/>nem ſunt immediate ſeundum intenſionem, vtrin <lb/>ad gradum terminata / quod de reſiſtentia vnifor-<lb/>miter difformi etc̈. dictum eſt in hac concluſione et <lb/>ſuo correlario. </s>
              <s xml:id="N1B641" xml:space="preserve">Hoc patet ex probatione cõcluſiõis <lb/>et ſui correlarii.               <anchor type="note" xlink:href="note-0117-02" xlink:label="note-0117-02a"/>               </s>
              <s xml:id="N1B64B" xml:space="preserve">¶ Ex his omnibus concluſionibus <lb/>ſequitur tertio /  quãuis ita ſit vt in concluſiõibus <lb/>ponitur quando ſimul ab eodem puncto in eodem <lb/>inſtanti per eandem lineam potentia et talis latitu­<lb/>do reſiſtentie incipiūt progredi ſiue moueri verſus <lb/>idem punctum: nõ tamen quando potentia incipe-<lb/>ret moueri quãdo illa latitudo iam mouetur. </s>
              <s xml:id="N1B65A" xml:space="preserve">Tunc <lb/>enim in caſu quarte concluſionis poſſet ipſa poten­<lb/>tia intendere motum ſuum, et in caſu quinte conclu­<lb/>ſionis remittere. </s>
              <s xml:id="N1B663" xml:space="preserve">Patet hoc facile / quoniam poſſet <lb/>pro aliquo inſtanti poni violenter in aliquo pūcto <lb/>quod velocius mouetur quã potentia ſufficiat mo-<lb/>ueri cum illo, vel in puncto quod tardius mouetur <lb/>quam potentia ſufficit adequate mouere cum illo <lb/>et ſic indifferenter intendet motum ſuū vel remittet</s>
            </p>
            <div xml:id="N1B670" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0117-02a" xlink:label="note-0117-02" xml:id="N1B674" xml:space="preserve">3. correĺ.</note>
            </div>
          </div>
          <div xml:id="N1B67A" level="4" n="14" type="chapter" type-free="capitulum">
            <head xml:id="N1B67F" xml:space="preserve">Quartumdecimum capitulum: in <lb/>quo ponuntur concluſiones de velo-<lb/>citate motus in medio non reſiſtente, <lb/>in quo eſt progreſſio ſiue extenſio la-<lb/>titudinis reſiſtentie nõ gradu aut ex­<lb/>tremo remiſſiori quieſcente inſequē-<lb/>do ordinem et modum calculatoris.</head>
            <p xml:id="N1B68E">
              <s xml:id="N1B68F" xml:space="preserve">Expeditis concluſionibus de ve-<lb/>locitate motus in medio non reſiſtente in <lb/>quo eſt progreſſio latitudinis reſiſtentie <lb/>vniformiter difformis quieſcente extremo intenſio­<lb/>ri. </s>
              <s xml:id="N1B69A" xml:space="preserve">Iam reſtat inducere concluſiones de eadem ma­<lb/>teria quieſcente non gradu aut extremo remiſſiori <lb/></s>
              <s xml:id="N1B6A0" xml:space="preserve">Quibus inducendis aliquas ſolito more ſuppoſi-<lb/>tionis premittam.</s>
            </p>
            <pb chead="De motu locali quo ad cauſam in medio non reſiſte." file="0118" n="118"/>
            <p xml:id="N1B6A9">
              <s xml:id="N1B6AA" xml:space="preserve">Prima ſuppoſitio. </s>
              <s xml:id="N1B6AD" xml:space="preserve">Latitudine reſiſtē­<lb/>tie vniformiter difformis ad nõ gradū terminate, <lb/>cõtinuo mouēte ſiue ꝓgrediente ꝑ mediū nõ reſiſtēs <lb/>ipſa cõtinuo vniformiter difformi manēte et nõ gra­<lb/>du eius cõtinuo quieſcēte: quodlibet eiꝰ punctū in-<lb/>trinſecū in ea ꝓportione cõtinuo quolibet altero re­<lb/>miſſiori velocius mouetur in qua eſt ipſo intenſius <lb/></s>
              <s xml:id="N1B6BD" xml:space="preserve">Probat̄̄: ſit a. latitudo reſiſtentie vniformiter dif-<lb/>formis ad nõ gradū terminate, q̄ cõtinuo vniformi­<lb/>ter difformis manēs ꝓgrediat̄̄ ſucceſſiue ꝑ mediuꝫ <lb/>nõ reſiſtēns nõ gradu eiꝰ quieſcēte eo modo quo ſu-<lb/>periꝰ declaratū eſt in tertia et quarta ſuppoſitioni­<lb/>bus p̄cedentis capitis: ſit b. punctꝰ intrinſecꝰ intē­<lb/>ſior c. vero etiã intrinſecꝰ et remiſſior inter q̄ puncta <lb/>ſit proportio f. </s>
              <s xml:id="N1B6CE" xml:space="preserve">Tūc dico /  b. pūctus continuo in f. <lb/>ꝓportione velocius mouet̄̄ ipſo c. pūcto. </s>
              <s xml:id="N1B6D3" xml:space="preserve">Quod ſic <lb/>oſtendēt̄̄: q2 intēſionis ipſiꝰ b. pūcti ad intēſioni c. <lb/>puncti cõtinuo eſt proportio f. ex hypotheſi: et con-<lb/>tinuo a. latitudo reſiſtentie manet vniformiter dif-<lb/>formis ad nõ gradū terminata: igitur cõtinuo di-<lb/>ſtantie quãtitate ipſius b. a nõ gradu ad diſtantiã <lb/>ipſius c. a non gradu eſt proportio f. </s>
              <s xml:id="N1B6E2" xml:space="preserve">Patet conſe-<lb/>quentia ex diffinitione qualitatis vniformiter dif-<lb/>formis quarto tractatu: et continuo diſtantia ipſiꝰ <lb/>b. a nõ gradu et diſtantia ipſius c. a nõ gradu maio­<lb/>rantur per cõtinuū motū ipſius b. et ipſius c. / igitur <lb/>cõtinuo diſtantie acquiſite per motum ipſius b. ad <lb/>diſtantiã acquiſitã per motū ipſius c. eſt proportio <lb/>f. </s>
              <s xml:id="N1B6F3" xml:space="preserve">Patet cõſequentia ex primo et ſecūdo correlario <lb/>quīte cõcluſionis ſecūdi capitis ſecūde partis: et ꝑ <lb/>cõſequens cõtinuo b. punctus in f. proportione ve-<lb/>locius mouetur c. puncto / quod fuit probandum. </s>
              <s xml:id="N1B6FC" xml:space="preserve">Et <lb/>ſic patet ſuppoſitio.</s>
            </p>
            <p xml:id="N1B701">
              <s xml:id="N1B702" xml:space="preserve">Secūda ſuppoſitio. </s>
              <s xml:id="N1B705" xml:space="preserve">Latitudine reſi-<lb/>ſtentie vniformiter difformis vtrī ad gradū ter-<lb/>minate, cõtinuo mouēte ſiue ꝓgrediente pēr mediū <lb/>nõ reſiſtens, ipſa cõtinuo manente vniformiter dif-<lb/>formi et extremo eius remiſſiori quieſcente: quodli-<lb/>bet punctū eius intrinſecū in maiori ꝓportione cõ­<lb/>tinuo quolibet altero intrinſeco remiſſiori velociꝰ <lb/>mouetur quã ſit proportio in qua eſt ipſo intenſius <lb/></s>
              <s xml:id="N1B717" xml:space="preserve">Probatur: ſit a latitudo reſiſtētie vniformiter dif-<lb/>formis vtrin ad gradum terminate que cõtinuo <lb/>manens vniformiter difformis ꝓgrediatur ſucceſſi­<lb/>ue per medium nõ reſiſtens extremo remiſſiori eius <lb/>quieſcente / vt ſepe ſupra dictū eſt. </s>
              <s xml:id="N1B722" xml:space="preserve">ſit b. punctus ex­<lb/>trinſecus intenſior .c. vero etiã intrinſecus et remiſ­<lb/>ſior, inter que puncta ſit ꝓportio f. </s>
              <s xml:id="N1B729" xml:space="preserve">Tunc dico /  b. <lb/>punctus ↄ̨tinuo in maiore ꝓportione quã f. velociꝰ <lb/>continuo mouet̄̄ c. pūcto. </s>
              <s xml:id="N1B730" xml:space="preserve">Qḋ ſic oñdit̄̄ / et capio / d. la­<lb/>titudinē reſiſtentie vniformiter difformis cõtinuo <lb/>eiuſdē extenſionis oīno cū a. incipientē in extremo <lb/>intenſiori ab eadē gradu cū a. terminatã tamen ad <lb/>nõ gradū: et ſit h. punctus qui tantū diſtat continuo <lb/>ab extremo remiſſiori d. latitudinis adequate quã­<lb/>tum b. diſtat ab extremo remiſſiori ipſius a. latitu-<lb/>dinis: et ſit k. pūctus remiſſior h (vt oportet) / qui cõ­<lb/>tinuo tantū diſtat adequate ab extremo remiſſiori <lb/>d. latitudinis quãtū c. diſtat ab extremo remiſſiori <lb/>ipſius a. </s>
              <s xml:id="N1B747" xml:space="preserve">Et ſit l. ꝓportio h. puncti ad ipſum k. </s>
              <s xml:id="N1B74A" xml:space="preserve">Et ar­<lb/>guo ſic / cõtinuo h. punctus in l. ꝓportione mouetur <lb/>velocius k. puncto / vt ptꝫ ex precedenti ſuppoſitiõe. <lb/></s>
              <s xml:id="N1B752" xml:space="preserve">Et cõtinuo in eadē l. ꝓportione b. punctus mouetur <lb/>velocius ipſo c. puncto (vt patꝫ intuenti caſum). </s>
              <s xml:id="N1B757" xml:space="preserve">Et <lb/>intenſionis ipſius h. puncti ad intenſionem ipſius <lb/>k. puncti eſt maior ꝓportio quã intenſionis ipſius <lb/>b. ad intenſionem ipſius c. puncti que eſt f. ex hypo-               <cb chead="De motu locali quo ad cauſam in medio non reſiſte."/>               theſi: ergo k. ꝓportio eſt maior quã f. ꝓportio et k. <lb/>eſt ꝓportio a qua velocius mouetur b. quã c. et f. eſt <lb/>ꝓportio intenſionis ipſius b. puncti ad ipſum c. po­<lb/>tentiarū: ergo b. punctus cõtinuo in maiori ꝓpor-<lb/>tione quam f. velocius mouetur c. puncto: quod fuit <lb/>ꝓbandū. </s>
              <s xml:id="N1B76D" xml:space="preserve">Cõſequentia ptꝫ cū maiore cū prima par­<lb/>te minoris. </s>
              <s xml:id="N1B772" xml:space="preserve">Et ſecūda pars minoris ꝓbatur videli­<lb/>cet / ꝙ̄ intenſionis ipſius h. puncti ad intenſionē etc̈. <lb/>quia b. et c. ſunt pūcta intenſiora quã h. et k. / vt ↄ̨ſtat / <lb/>et b. minori exceſſu excedit c. quã h. ipſum k. (cum to­<lb/>tus exceſſus inter extrema d. latitudinis ſit maior <lb/>toto exceſſu inter extēa ipſiꝰ a. latitudīs: et ſic inter <lb/>extrema partiū equaliū ipſius d. eſt maior exceſſus <lb/>quã inter cõſimiles partes ipſius a) / ergo intenſio-<lb/>nis ipſius h. puncti ad intenſionē ipſius k. pūcti eſt <lb/>maior ꝓportio quã intenſionis ipſius b. puncti ad <lb/>intenſionē ipſius c. puncti que eſt f. / quod fuit infe-<lb/>rendum. </s>
              <s xml:id="N1B78B" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
            </p>
            <p xml:id="N1B78E">
              <s xml:id="N1B78F" xml:space="preserve">Tertia ſuppoſitio. </s>
              <s xml:id="N1B792" xml:space="preserve">Quandocun ali­<lb/>que potentie que continuo inequaliter mouetur in­<lb/>cipiūt in eodem inſtanti moueri / vt attingant eque <lb/>cito / et in eodem inſtanti duo mobilia precedētia ta­<lb/>les potentias que mobilia etiam continuo mouen-<lb/>tur recedendo ab ipſis potentiis: et in principio <lb/>motus diſtat potentia velocius mota a mobili / qḋ <lb/>ipſa inſequitur pluſ̄ reliqua tardius mota a ſuo <lb/>in ea ꝓportione qua velocius continuo mouetur: <lb/>oportet ſi eque cito debeat vtra potentia ſuū mo­<lb/>bile attingere:  in ꝓportione in qua potentia ve-<lb/>locior velociꝰ mouetur potentia tardiore in ea pro­<lb/>portione mobile quod debet attingi a potētia tar-<lb/>diore tardius moueatur quam mobile quod debet <lb/>attigi a potentia velociore. </s>
              <s xml:id="N1B7B1" xml:space="preserve">Uolo dicere:  ſi ſortes <lb/>et plato incipiant in eodem inſtanti moueri perſe-<lb/>quendo ſuos equos fugientes: et ↄ̨tinuo ſortes mo­<lb/>ueatur in duplo velocius platone: et in inſtanti ini-<lb/>tiatiuo motus equus ſortis in duplo plus diſtet a <lb/>ſorte quã equꝰ platonis a platone: oportet /  equꝰ <lb/>platonis (cū plato tardiꝰ moueatur) in duplo tar-<lb/>dius moueatur ꝙ̄ equus ſortis: ſi vter ſuū equum <lb/>eque cito debeat attingere. </s>
              <s xml:id="N1B7C4" xml:space="preserve">Probatur / ſit a. poten-<lb/>tia velocius continuo mota inſequens c. mobile cõ-<lb/>tinuo ab ea recedens: et b. potentia continuo tardiꝰ <lb/>mota inſequens d. mobile continuo ab ea recedens <lb/>diſtet in principio motus a. potētia plus in f. pro­<lb/>portiõe a c. quã b. ab ipſo d. et in eadem f. ꝓportiõe <lb/>a. potētia continuo velocius moueatur ipſa b. po-<lb/>tentia: et ſic moueantur continuo vt tandē in eodem <lb/>inſtanti quod ſit e. attingant ſua mobilia preceden­<lb/>tia. </s>
              <s xml:id="N1B7D9" xml:space="preserve">Tunc dico /  oportet d. in f. ꝓportione cõtinuo <lb/>tardiꝰ moueri ipſo c. </s>
              <s xml:id="N1B7DE" xml:space="preserve">Quod ſic oſtendit̄̄ / q2 cõtinuo <lb/>a. mouetur in f. ꝓportione velociꝰ ipſa b. potentia <lb/>inſequendo mobilia precedentia vſ ad inſtans e. <lb/>ex hypotheſi: igitur ſpacii pertranſiti ab a. poten-<lb/>tia vſ ad inſtans e. ad ſpaciū pertranſitū a b. po-<lb/>tentia vſ ad idem e. inſtans eſt ꝓportio f. / ptꝫ con-<lb/>ſequētia ex ſe: et vltra ſpacii ꝑtrãſiti ab a. potentia <lb/>vſ ad inſtãs e. ad ſpaciū ꝑtrãſitū a b. potētia vſ <lb/>ad idē inſtãs eſt f. ꝓportio: igr̄ demēdo ab illis ſpa­<lb/>ciis partes ſe ſi abētes in f. ꝓportione, puta ſpaciū <lb/>ꝑ qḋ a principio motꝰ a. diſtat a c. et ſpaciū ꝑ qḋ a <lb/>principio motus b. poña diſtat a d. q̄ ex hypotheſi <lb/>ſe hñt in f. ꝓportiõe reſidua ſpacia ſe hñt in f. ꝓpor­<lb/>tione: ptꝫ conſequentia ex ſeptimo correlario quar­<lb/>te concluſionis oceaui capitis ſecunde partis.</s>
            </p>
            <p xml:id="N1B7FD">
              <s xml:id="N1B7FE" xml:space="preserve">Sed reſidua ſpacia puta reſiduum ſpacii maioris <lb/>pertranſiti ab a. et reſiduū ſpacii minoris pertran­<lb/>ſiti a b. potentia ſunt ſpacia pertranſita a c. mobi­               <pb chead="Primi tractatus" file="0119" n="119"/>               li et a d. mobili: igitur ſpacii pertranſiti a c. mobili <lb/>ad ſpacium pertrãſitū a d. mobili eſt f. ꝓportio: et <lb/>per conſequens d. mouetur tardiꝰ c. in f. ꝓportione / <lb/>qḋ fuit ꝓbandū: ptꝫ ergo ſuppoſito.               <anchor type="note" xlink:href="note-0119-01" xlink:label="note-0119-01a"/>               </s>
              <s xml:id="N1B815" xml:space="preserve">¶ Ex hac ſup-<lb/>poſitiõe ſequitur /  ſi mobile quod debet attingi a <lb/>potentia tardius mota moueatur in maiori ꝓpor-<lb/>tione tardius alio ꝙ̄ ſit proportio diſtantiaꝝ: tunc <lb/>citius attingetur a ſua potētia. </s>
              <s xml:id="N1B820" xml:space="preserve">Et ſi velociꝰ tardiꝰ <lb/>attingetur: patet facile.</s>
            </p>
            <div xml:id="N1B825" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0119-01a" xlink:label="note-0119-01" xml:id="N1B829" xml:space="preserve">1. correĺ.</note>
            </div>
            <p xml:id="N1B82F">
              <s xml:id="N1B830" xml:space="preserve">Quarta ſuppoſitio / latitudine reſiſtē-<lb/>tie vniformiter difformis mouente modo dicto per <lb/>mediū nõ reſiſtens: potentia que cū tali reſiſtentia <lb/>mouetur nun̄ preterit partē vel punctū illius re-<lb/>ſiſtentie qui velocius mouetur quã potentia ſufficit <lb/>moueri cum illo. </s>
              <s xml:id="N1B83D" xml:space="preserve">Nec vn̄ punctus qui tardius mo­<lb/>uetur quã potentia ſufficit moueri cū illo preterit <lb/>potentiã. </s>
              <s xml:id="N1B844" xml:space="preserve">Nec etiã punctus qui ita velociter mouet̄̄ <lb/>ſicut potentia ſufficit moueri cū illo preterit poten­<lb/>tiã aut preteritur ab ea. </s>
              <s xml:id="N1B84B" xml:space="preserve">Patet hec ſuppoſitio faci­<lb/>le intelligenti modum ſe habendi illius latitudinis <lb/>ſic progredientis in illo medio non reſiſtente.</s>
            </p>
            <p xml:id="N1B852">
              <s xml:id="N1B853" xml:space="preserve">His ſuppoſitis. </s>
              <s xml:id="N1B856" xml:space="preserve">Sit prima concluſio <lb/></s>
              <s xml:id="N1B85A" xml:space="preserve">Progrediente in medio nõ reſiſtente latitudine re­<lb/>ſiſtentie vniformiter difformis a nõ gradu vſ ad <lb/>certū gradū: quieſcente nõ gradu: et quolibet pun-<lb/>cto eius continuo vniformiter moto: potentia in-<lb/>cipiens ſimul moueri cū tali reſiſtētia continuo vni­<lb/>formiter mouebitur: dūmodo extremū intenſiꝰ ta-<lb/>lis reſiſtentie velocius cõtinuo moueatur quã talis <lb/>potentia ſufficit mouere cum illo aut equaliter. </s>
              <s xml:id="N1B86B" xml:space="preserve">Et <lb/>intelligo in oībus cõcluſionibus  ipſa latitudo cõ­<lb/>tinuo maneat vniformiter difformis. </s>
              <s xml:id="N1B872" xml:space="preserve">Probatur <lb/>hec cõcluſio. </s>
              <s xml:id="N1B877" xml:space="preserve">Et ſit illa potentia in caſu cõcluſionis <lb/>b. </s>
              <s xml:id="N1B87C" xml:space="preserve">Et arguo ſic / b. potentia nun̄ intendit: nec vn̄ <lb/>remittit motū ſuū cõtinuo mouendo cū tali reſiſtē-<lb/>tia in caſu dicto: et mouebitur cum tali reſiſtētia in <lb/>caſu cõcluſionis / igitur b. continuo vniformiter mo­<lb/>uebitur / quod fuit ꝓbandū. </s>
              <s xml:id="N1B887" xml:space="preserve">Patet cõſequētia ex ſe <lb/></s>
              <s xml:id="N1B88B" xml:space="preserve">Et probatur maior / q2 ſi per aliquod tēpus b. potē­<lb/>tia intēdit motū ſuū ſignetur pūctus / in q̊ eſt in in-<lb/>ſtanti medio talis tēporis qui ſit a. / et arguo ſic / vel <lb/>ipſe punctus a. mouetur ita velociter ſicut potentia <lb/>ſufficit mouere cū illo: vel velociꝰ vel tardiꝰ. </s>
              <s xml:id="N1B896" xml:space="preserve">Si ita <lb/>velociter iam ſequitur /  nõ intēdit motum ſuū per <lb/>illud tēpus: ſed vniformiter poſt illud inſtans con-<lb/>tinuo mouebitur (cū ſemꝑ erit ī illo pūcto / vt ptꝫ ex <lb/>quarta ſuppoſitione huiꝰ). </s>
              <s xml:id="N1B8A1" xml:space="preserve">Et ſi tardius ſequitur / <lb/> iã potentia remittit motū ſuū: q2 mouebitur ver-<lb/>ſus puncta intēſiora. </s>
              <s xml:id="N1B8A8" xml:space="preserve">Si vero velocius ipſe punctꝰ <lb/>a. moueatur quã ipſa potentia b. / ſequit̄̄ (cū ſemper <lb/>a. moueat̄̄ vniformiter) /  potētia b. nun̄ p̄teriuit <lb/>a. punctū. </s>
              <s xml:id="N1B8B1" xml:space="preserve">Ptꝫ cõſequētia eſt quarta ſuppoſitione: <lb/>et vltra b. potentia nū̄ preteriuit a. punctū et īme-<lb/>diate ante inſtans in quo eſt in illo pūcto a. p̄cede-<lb/>bat illud: igr̄ ſemꝑ ante illud inſtans p̄ceſſit illud: et <lb/>per cõſequens ſemꝑ ante illud inſtans mouebat̄̄ cū <lb/>maiori reſiſtētia quã modo et tardius, et modo mo-<lb/>uetur a. punctus velocius quam b. potentia / ergo <lb/>ſemꝑ ante illud inſtans a. pūctus mouebat̄̄ velociꝰ <lb/>quã b. potētia, et inceperūt b. potētia et a. punctꝰ in <lb/>eodē inſtãti et ab eodē pūcto ſus eandē differentiã <lb/>moueri. </s>
              <s xml:id="N1B8C8" xml:space="preserve">ergo modo a. p̄cedit b. et ꝑ ↄ̨ñs nõ ſūt ſimĺ / <lb/>qḋ eſt oppoſitū dati. </s>
              <s xml:id="N1B8CD" xml:space="preserve">Sed iam ꝓbat̄̄ minor vcꝫ /  per <lb/>nullū tēpus remittit motum ſuū ſtante caſu:  ſi ſic <lb/>detur punctꝰ in quo talis poña eſt in īſtanti medio <lb/>talis tꝑis qui ſit a. </s>
              <s xml:id="N1B8D6" xml:space="preserve">Et arguo ſic / ipſa poña b. remit­<lb/>tit motū ſuū ꝑ te: ergo ipſa modo continuo ꝓcedit <lb/>ſus pūcta intēſiora veniēdo ad a. punctū quomo­               <cb chead="Capitulū quartūdecimū."/>               do velociꝰ mouet̄̄ ꝑ te: ergo ſemꝑ ãtea poña b. ſeque­<lb/>batur a. punctū mouēs cõtiuuo cū minori reſiſtētia <lb/>quã modo: ptꝫ ↄ̨ña / q2 nõ poteſt cū caſu priꝰ p̄cedere <lb/>et poſtea ſequi (vt facile deducit̄̄ ex quarta ſuppoſi-<lb/>tioue) / et ex cõſequēti ſequit̄̄ /  cõtinuo antea moue-<lb/>bat̄̄ velociꝰ quã modo cū a. pūcto, et modo etiã velo­<lb/>cius quã a. punctꝰ motꝰ cõtinuo vniformiter: ergo <lb/>ſemꝑ p̄ceſſit b. poña a. punctū, et modo etiã p̄cedit: et <lb/>ꝑ ↄ̨ñs ſunt ſimĺ et ꝑ te ſunt ſimĺ / ergo cõtradictio / <lb/>et ſic ptꝫ totū antecedens: et per cõſequēs concluſio.</s>
            </p>
            <p xml:id="N1B8F2">
              <s xml:id="N1B8F3" xml:space="preserve">Secunda concluſio / latitudine vni-<lb/>formiter difformi ſic ꝓgrediente (vt dictū eſt) ꝑ me-<lb/>diū nõ reſiſtens quolibet puncto intrīſeco cõtinuo <lb/>intēdente motū ſuū: quieſcēte nõ gradu vĺ extremo <lb/>remiſſiori, extremo intēſiori velociꝰ cõtinuo mouē­<lb/>te quã poña q̄ mouet̄̄ cū tali reſiſtētia ſufficiat mo-<lb/>ueri cū illo: talis poña incipiens moueri ab eodem <lb/>pūcto, et in eodē inſtãti cū tali reſiſtētia cõtinuo in-<lb/>tēdit motū ſuū quãdiu cū tali reſiſtētia mouet̄̄ ſtan-<lb/>te caſu. </s>
              <s xml:id="N1B908" xml:space="preserve">Probat̄̄ / q2 talis poña ꝑ nullū tēpus moue­<lb/>tur vniformiter: nec ꝑ aliqḋ tēpus remittit motum <lb/>ſuū cū tali reſiſtētia ſtante caſu: et mouet̄̄ (vt pono) / <lb/>igr̄ cõtinuo intēdit motū ſuū: ↄ̨ña eſt nota / et maior <lb/>ptꝫ manifeſte ex ſcḋo correlario prime cõcluſionis <lb/>p̄cedentis capitis. </s>
              <s xml:id="N1B915" xml:space="preserve">Sed minor ꝓbat̄̄ videlicet /  per <lb/>nullū tēpus remittit motū ſuū ſtante caſu: q2 ſi ſic <lb/>detur aliqḋ tēpus per qḋ cõtinuo remittit motum <lb/>ſuū, et ſigno punctū in quo poña eſt in īſtãti medio <lb/>illiꝰ tēporis: et ſit a. </s>
              <s xml:id="N1B920" xml:space="preserve">Et arguit̄̄ ſic / in illo inſtãti po-<lb/>tētia eſt in a. pūcto: et remittit motū ſuū ꝑ te / igr̄ ve­<lb/>locius mouet̄̄ ipſo a. ꝓcedēdo cõtinuo ſus pūcta <lb/>intēſiora. </s>
              <s xml:id="N1B929" xml:space="preserve">Et vltra velociꝰ mouet̄̄ ipſo a. pūcto ꝓce­<lb/>dendo ↄ̨tinuo ſus pūcta intēſiora: et ipſe a. pūctꝰ <lb/>ſemꝑ ãte tardiꝰ mouebat̄̄ quã modo: cū cõtinuo ex <lb/>caſu intēdat motū ſuū: et poña ſemꝑ antea velociꝰ <lb/>mouebat̄̄ ꝙ̄ modo cū ↄ̨tinuo ãtea eſſet in remiſſiori <lb/>reſiſtētia ſiue pūcto quã eſt a. ī quomodo eſt (nõ em̄ <lb/>priꝰ p̄ceſſit ipſa poña a. punctū, et deinde ipſe a. pū­<lb/>ctus p̄teriuit ipſã potētiã / vt ptꝫ ex q̈rta ſuppoſiti-<lb/>one) / igr̄ ſemꝑ ãtea velociꝰ mouebat̄̄ poña ꝙ̄ a. pū-<lb/>ctꝰ: et ꝑ ↄ̨ñs modo p̄cedit ipſa ponã a. pūctū cū īci-<lb/>piūt ab eodē pūcto in eodē inſtãti moueri et ſic non <lb/>eſt modo in ipſo a. pūcto: et nūc eſt in illo ꝑ te: igit̄̄ <lb/>ↄ̨tradictio: et ſic ptꝫ /  nõ eſt dicendū illã potentiaꝫ <lb/>per aliquod tempus remittere motum ſuum: quod <lb/>fuit probandum. </s>
              <s xml:id="N1B948" xml:space="preserve">Patet ergo concluſio.</s>
            </p>
            <p xml:id="N1B94B">
              <s xml:id="N1B94C" xml:space="preserve">Tertia concluſio. </s>
              <s xml:id="N1B94F" xml:space="preserve">Progrediēte latitu­<lb/>dine vniformiter difformis reſiſtētie etc̈. / vt dictū eſt <lb/>quieſcēte nõ g̈du, aut extremo remiſſiori, quolibet <lb/>pūcto ītrīſeco ↄ̨tinuo remittēte motū ſuū, intēſiori <lb/>extremo īcipiēte velociꝰ moueri ꝙ̄ poña q̄ mouet̄̄ cū <lb/>tali reſiſtentia ſufficiat moueri ad illo: talis poña <lb/>īcipiēs moueri cū tali reſiſtētia in eodē inſtanti ab <lb/>eodē pūcto ↄ̨tinuo ̄diu ſic mouet̄̄ cū tali reſiſtētia <lb/>ſtãte caſu remittit motū ſuū. </s>
              <s xml:id="N1B962" xml:space="preserve">Probat̄̄: qm̄ talis po­<lb/>tētia mouet̄̄ cū tali reſiſtētia / vt ptꝫ. </s>
              <s xml:id="N1B967" xml:space="preserve">Et ꝑ nullū tēpꝰ <lb/>vniformiṫ mouet̄̄ ſtate caſu (vt ptꝫ ex ſcḋo correla-<lb/>rio ṗme ↄ̨cluſiõis p̄cedētis capitis. </s>
              <s xml:id="N1B96E" xml:space="preserve">Nec ꝑ aliqḋ tē-<lb/>pus intēdit motū ſuū mouēdo cū tali reſiſtētia: igr̄ <lb/>ↄ̨tinuo remittit motū ſuū mouēdo cū tali reſiſtētia <lb/>ſtãte caſu / qḋ fuit ꝓbandū </s>
              <s xml:id="N1B977" xml:space="preserve">Ptꝫ ↄ̨ña, et ꝓbat̄̄ ſcḋa ꝑs <lb/>maioris vcꝫ /  ꝑ nullū tēpꝰ intendit motū ſuū: q2 ſi <lb/>ſic detur punctꝰ in quo potētia eſt in inſtãti medio <lb/>talis temporis, et ſit a. </s>
              <s xml:id="N1B980" xml:space="preserve">Et arguitur ſic / per illud tem­<lb/>pus potentia intendit motum ſuū per te, et in inſtã-<lb/>ti medio illius eſt in a. puncto: igitur ille pūctus a. <lb/>precedet ipſam potentiam immediate poſt illud in­<lb/>ſtans, et potentia erit cum remiſſiori puncto: patet               <pb chead="De motu quo ad cauſam in medio non reſiſte." file="0120" n="120"/>               cõſequentia intelligenti modum procedendi talis <lb/>reſiſtentie: et vltra precedet ipſam: igitur velocius <lb/>mouetur ꝙ̄ potētia: et ſemper antea velocius a. mo-<lb/>uebatur ꝙ̄ modo cum cõtinuo remittat motum ſuū <lb/>ex caſu: et potētia ſemper antea mouebatur tardiꝰ <lb/>̄ modo: quia cõtinuo precedebat ipſum a. mouen-<lb/>do cum maiori reſiſtētia quã a. non em̄ aliquando <lb/>ſequebatur potentia ipſum a. punctū et poſtea pre-<lb/>ceſſit ipſum a. patet ex quarta ſuppoſitione. </s>
              <s xml:id="N1B9A0" xml:space="preserve">Nam <lb/>ſemper antea a. velocius mouetur quam potentia: <lb/>igitur ſemper a. precedit potentiam et ſic modo in <lb/>inſtanti dato nõ ſunt ſimul (incipiunt enim ab eodē <lb/>inſtanti et puncto) et ſunt in eodem inſtanti ſimul <lb/>per te: ergo cõtradictio, non eſt igitur dicendum  <lb/>aliquando potentia intendit motum ſuū / qudd fuit <lb/>probandum: patet ergo concluſio.</s>
            </p>
            <p xml:id="N1B9B1">
              <s xml:id="N1B9B2" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N1B9B5" xml:space="preserve">Ubicun in me-<lb/>dio nõ reſiſtente fit progreſſio latitudinis reſiſten-<lb/>tie vniformiter difformis partibiliter quo ad ſub-<lb/>iectum modo expoſito quolibet puncto eius intrin­<lb/>ſeco cõtinuo vniformiter intendente motum ſuum <lb/>non gradu, aut extremo remiſſiori quieſcente: po-<lb/>tentia ſimul incipiens moueri in eodem inſtanti et <lb/>ab eodem puncto cum tali reſiſtentia continuo in-<lb/>tendit motum ſuum. </s>
              <s xml:id="N1B9C8" xml:space="preserve">Et ſi pro aliquo inſtanti pro <lb/>quo intendit motum ſuum ad aliquod punctum <lb/>hoc eſt exiſtens in aliquo puncto, poneretur in <lb/>puncto minus reſiſtente illius reſiſtentie. </s>
              <s xml:id="N1B9D1" xml:space="preserve">Ipſa tar­<lb/>dius intenderet motum ſuum. </s>
              <s xml:id="N1B9D6" xml:space="preserve">Prima pars huius <lb/>cõcluſionis patet ex immediate precedente. </s>
              <s xml:id="N1B9DB" xml:space="preserve">Et pro-<lb/>batur ſecūda. </s>
              <s xml:id="N1B9E0" xml:space="preserve">Latitudine reſiſtētie vniformiter dif-<lb/>formis ad nõ gradum terminate procedente / vt po-<lb/>nitur in caſu cõcluſionis. </s>
              <s xml:id="N1B9E7" xml:space="preserve">Sit b. potentia in aliquo <lb/>inſtanti in c. puncto ſit e. punctus in g. ꝓportione <lb/>remiſſior c. puncto in quo e. puncto b. potentia pro <lb/>eodem inſtanti ponatur. </s>
              <s xml:id="N1B9F0" xml:space="preserve">Tunc dico /  b. potentia <lb/>tardius intendit motum ſuum ad e. punctum ꝙ̄ ad <lb/>c. </s>
              <s xml:id="N1B9F7" xml:space="preserve">Quod ſic oſtenditur: quia potentia b. poſita ad <lb/>punctum c. per cõtinuam acquiſitionem minoris re­<lb/>ſiſtentie: citius acquirit aliquam proportionem <lb/>̄ ipſa poſita ad punctum e. acquirat eandem: igit̄̄ <lb/>b. potentia tardius intendit motum ſuum ad e. pū-<lb/>ctum ꝙ̄ ad c. / quod fuit probandum. </s>
              <s xml:id="N1BA04" xml:space="preserve">Cõſequētia ptꝫ <lb/>ex ſe / et ꝓbatur antecedens quia poſito /  pro eodeꝫ <lb/>inſtanti pro quo b. eſt ad c. punctū potentia ei equa­<lb/>lis ponatur ad punctū e. illa potentia equalis ipſi <lb/>b. tardius aliquam ꝓportionem acquirit ꝙ̄ ſit pro­<lb/>portio quam acquirit ad punctum c.b. potētia / igr̄ <lb/>b. potentia poſita ad punctum c. per acquiſitioneꝫ <lb/>minoris reſiſtentie citius acquirit aliquã propor-<lb/>tionem quã ipſa poſita ad punctū e. acquirat ean-<lb/>dem. </s>
              <s xml:id="N1BA19" xml:space="preserve">Cõſequentia patet: et ꝓbatur antecedens. </s>
              <s xml:id="N1BA1C" xml:space="preserve">Et <lb/>pono /  cū b. eſt ad punctū c. potentia ei equalis a. <lb/>ponatur ad punctū e. et ſit d. punctus in quo b. potē­<lb/>tia debet acquirere ꝓportionē h. ad quem (vt opor­<lb/>tet) c. punctus habet ꝓportionem h. et ſit f. punctus <lb/>in quo a. potentia debet acquirere eandem ꝓpor-<lb/>tionem h. inter que puncta e. et f. eſt etiam ꝓportio <lb/>h. (vt oportet). </s>
              <s xml:id="N1BA2D" xml:space="preserve">Et tunc a. potentia tardiꝰ acquirit <lb/>h. ꝓportionem quã b. / igitur ꝓpoſittū. </s>
              <s xml:id="N1BA32" xml:space="preserve">Probatur. <lb/></s>
              <s xml:id="N1BA36" xml:space="preserve">autecedēs q2 f. punctꝰ tardius attinget a. ꝙ̄ d. ipſã <lb/>potentiã b. et in illis pūctis debent a. et b. acquirere <lb/>ꝓportionē h. / ergo tardius acquiret ꝓportionē h. <lb/>̄ b. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N1BA3F" xml:space="preserve">Sed iam ꝓbo añs videlicet /  <lb/>tardius f. attinget a. etc̈. quia f. a principio motꝰ in <lb/>g. proportiõe minꝰ diſtat a mobili / quod inſequit̄̄ / <lb/>quã d. diſtet a b. et continuo f. mouetur in g. proportio­<lb/>tione tardius quã d. / et tamen a. nõ mouetur in g. ꝓ-<lb/>portione nec in maiori proportione tardius quã b. /               <cb chead="De motu quo ad cauſam in medio non reſiſte."/>               igit̄̄ nõ ita cito nec citius f. attinget a. quã d. ipſam <lb/>potētiam b. ſed tardius / quod erat inferendū. </s>
              <s xml:id="N1BA51" xml:space="preserve">Ptꝫ <lb/>cõſequentia ex tertia ſuppoſitione huiꝰ cū ſuo cor-<lb/>relario (applica vtpotes). </s>
              <s xml:id="N1BA58" xml:space="preserve">Iam ꝓbo primã parteꝫ <lb/>maioris: q2 ſicut ſe habet c. ad d. ita e. ad f. ex caſu: <lb/>igitur permutatim ſicut ſe habet c. ad e. (puta in g. <lb/>proportione ex hypotheſi) ita ſe habet d. ad f. puta <lb/>in g. proportione. </s>
              <s xml:id="N1BA63" xml:space="preserve">Et vltra c. ad e. eſt g. proportio et <lb/>latitudo eſt vniformiter difformis ad non gradum <lb/>terminata quieſcente nõ gradu: igitur cõtinuo di-<lb/>ſtantie quantitatiue ipſius c. a nõ gradu ad diſtan-<lb/>tiam ipſius e. ab eodem non gradu eſt g. proportio <lb/></s>
              <s xml:id="N1BA6F" xml:space="preserve">Patet conſequentia ex prima ſuppoſitione hu-<lb/>ius. </s>
              <s xml:id="N1BA74" xml:space="preserve">et vltra diſtantie ipſius c. a non gradu ad diſtã­<lb/>tiam ipſius e. etc̈. eſt proportio g. et etiam diſtantie <lb/>ipſius d. ad diſtantiam ipſius f. eadem ratione eſt <lb/>ꝓportio g. / igitur demendo / a diſtantia c. a nõ gra-<lb/>du diſtantiam d. a nõ gradu, et demendo / a diſtãtia <lb/>c. a nõ gradu diſtãtiam f. a nõ gradu que (vt cõſtat) <lb/>ſunt partes aliarū diſtantiarū puta c. et e. a nõ gra­<lb/>du: remanentes diſtantie ſe habent in eadem g. pro­<lb/>proportione, et ſic reſidui diſtantie ipſius c. a non <lb/>gradu ad reſiduū diſtantie ipſius e. a nõ gradu eſt <lb/>g. proportio: ptꝫ cõſequentia ex ſeptimo correlario <lb/>quarte cõcluſionis octaui capitis ſecunde partis. <lb/></s>
              <s xml:id="N1BA8E" xml:space="preserve">Sed reſiduū diſtantie ipſius c. a nõ gradu eſt diſtã­<lb/>tia ipſius c. a d. et reſiduum diſtantie ipſius e. a non <lb/>gradu eſt diſtantia ipſius e. ab f. (vt conſtat) / igitur <lb/>diſtãtie ipſius c. a d. ad diſtantiã ipſius e. ab f. eſt g. <lb/>proportio. </s>
              <s xml:id="N1BA99" xml:space="preserve">Et a principio motus a. eſt in e. et b. in c. / <lb/>igitur f. in g. proportione a principio motus minꝰ <lb/>diſtat ab a. mobili / quod īſequitur / quã d. diſtat ab <lb/>b. / que fuit prima pars maſoris inferenda. </s>
              <s xml:id="N1BAA2" xml:space="preserve">Sed ꝓ-<lb/>batur ſecunda pars maioris: quia f. punctus in g. <lb/>proportione eſt remiſſior d. puncto (vt ꝓbatum eſt) / <lb/>igitur continuo in g. proportiõe tardius mouetur <lb/>ipſo puncto d. / quod fuit ꝓbandū. </s>
              <s xml:id="N1BAAD" xml:space="preserve">Patet cõſequē-<lb/>tia ex prima ſuppoſitione huiꝰ / et ſic ptꝫ totū antece­<lb/>dens. </s>
              <s xml:id="N1BAB4" xml:space="preserve">Et eodē modo ꝓbabis cū latitudo ad gradū <lb/>in vtro extremo terminat̄̄, auxiliãtibꝰ loco a ma-<lb/>iori: et ſecunda ſuppoſitione huius et etiam tertia. <lb/></s>
              <s xml:id="N1BABC" xml:space="preserve">Et ſic patet concluſio.</s>
            </p>
            <p xml:id="N1BABF">
              <s xml:id="N1BAC0" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
              <s xml:id="N1BAC3" xml:space="preserve">Data potētia intēdēte <lb/>motū ſuū modo dicto ad aliquē gradū reſiſtētie in <lb/>latitudine / vt diximus mota: oīs potentia maior q̄ <lb/>ad eūdem punctū intederet motū ſuū, tardiꝰ intēde­<lb/>ret. </s>
              <s xml:id="N1BACE" xml:space="preserve">Et oīs minor velocius.               <anchor type="note" xlink:href="note-0120-01" xlink:label="note-0120-01a"/>               </s>
              <s xml:id="N1BAD6" xml:space="preserve">Hec eſt ſeptīa cal. quã ſic <lb/>ꝓbo primo quo ad primã partē: q2 data aliqua po­<lb/>tentia q̄ ad aliquē gradū intēdit motū ſuū ꝑ acqui­<lb/>ſitionē minoris reſiſtētie. </s>
              <s xml:id="N1BADF" xml:space="preserve">oīs maior ad eundē pun-<lb/>ctū intēdens motū ſuū tardiꝰ illã minorē reſiſtētiã <lb/>acquiret cõtinuo: igit̄̄ oīs maior tardiꝰ ibi intēde-<lb/>ret motū ſuū. </s>
              <s xml:id="N1BAE8" xml:space="preserve">Ptꝫ ↄ̨ña / q2 nõ aliter ibi aliq̈ potētia <lb/>intēdit motū ſuū ꝙ̄ ꝑ cõtinuã minoris reſiſtētie ac-<lb/>quiſitionē: vt patet: añs tñ ꝓbatur: quia oīs maior <lb/>velocius mouet̄̄ recedendo a tali reſiſtētia et īcipiūt <lb/>ab eodē pūcto ī eodē īſtãti: igit̄̄ illa reſiſtētia tardiꝰ <lb/>attīget illã maiorē potentiã ꝙ̄ minorē: et ꝑ ↄ̨ñs tar-<lb/>dius illa potentia maior acquiret illã minorē reſi-<lb/>ſtentiã / qḋ fuit ꝓbandū. </s>
              <s xml:id="N1BAF9" xml:space="preserve">Et eadē oīno eſt ꝓbatio ſe-<lb/>cūde partis: qm̄ minor citius acquirit minorē reſi-<lb/>ſtentiã quã maior acq̇rat eandē / ptꝫ ergo concluſio. <lb/>               <anchor type="note" xlink:href="note-0120-02" xlink:label="note-0120-02a"/>               </s>
              <s xml:id="N1BB07" xml:space="preserve">¶ Ex hac cõcluſiõe ſeq̇t̄̄ ṗmo /  latitudīe ſic mota / vt <lb/>dictū eſt: quocū gradu illiꝰ dato, dabit̄̄ vna poña <lb/>q̄ ita tarde ſufficit ibi intendere motū ſuū,  nulla <lb/>alia poteſt ita tarde intendere ſtante caſu. </s>
              <s xml:id="N1BB10" xml:space="preserve">latitu-<lb/>dine ſic mota. </s>
              <s xml:id="N1BB15" xml:space="preserve">Probatur / q2 ad oēm reſiſtentiã fini­<lb/>tã quãlibet ꝓportionē maioris īeq̈litatꝪ hꝫ aliqua <lb/>poña (vt patet ex ſe) / igr̄ nulla eſt dabilis reſiſtentia               <pb chead="Primi tractatus" file="0121" n="121"/>               aliqua proportione mota quin detur potentia que <lb/>ſufficit moueri eadem velocitate, et proportione <lb/>cū illa. </s>
              <s xml:id="N1BB25" xml:space="preserve">Signetur / igitur in illa latitudine ſic mota <lb/>vnus punctus / et ponatur ad illum in hoc inſtanti <lb/>potentia b. que ita velociter ſufficit mouere cum il-<lb/>lo ſicut pro tali inſtanti mouetur talis pūctus: quo <lb/>poſito, arguitur ſic / b. intendet motum ſuum, cum <lb/>punctus ille in quo nunc ponitur īmediate poſt hoc <lb/>precedet b. quia punctus intendit continuo motum <lb/>ſuum et incipit velocius mouere ꝙ̄ b. ſufficit moue-<lb/>ri cum illo. </s>
              <s xml:id="N1BB38" xml:space="preserve">Et nulla alia potentia ſufficit cum tali <lb/>gradu exiſtens in tali inſtanti tardius intēdere mo­<lb/>tum ſuum: igitur propoſitum, conſequentia patet <lb/>cum maiore, et minor probatur, quia ſi aliqua ſuf-<lb/>ficit tardiꝰ intēdere motū ſuū detur illa et ſit a. / et ar­<lb/>guo ſic / a. ſufficit tardius intendere motum ſuum ̄ <lb/>b. / igitur ipſa eſt maior b. vel minor, vel equalis. </s>
              <s xml:id="N1BB47" xml:space="preserve">Si <lb/>equalis iam non ſufficit tardius ſed equaliter. </s>
              <s xml:id="N1BB4C" xml:space="preserve">Si <lb/>minor ſequitur /  non ſufficit tardius, ſed velocius / <lb/>vt patet ex quinta concluſione precedēti. </s>
              <s xml:id="N1BB53" xml:space="preserve">Si maior <lb/>ſequitur /  talis potentia non intendit motum ſuū <lb/>ſed remittit q2 velociꝰ ſufficit moueri cū puncto da­<lb/>to ꝙ̄ datus punctus incipiat moueri et per aliquod <lb/>tempus cõtinuo remittet a. motum ſuū / quo ad vſ <lb/>ſit in aliquo puncto qui incipit ita velociter moue-<lb/>ri ſicut a. ſufficit moueri cum illo: et ſic nõ poteſt di­<lb/>ci /  a. tardius remittit motum ſuum ꝙ̄ b. cum non <lb/>remittat incipiendo moueri ab illo puncto: patet <lb/>ergo minor, et per conſequens correlarium.</s>
            </p>
            <div xml:id="N1BB68" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0120-01a" xlink:label="note-0120-01" xml:id="N1BB6C" xml:space="preserve">7. cõclu. <lb/>Calcu.</note>
              <note position="right" xlink:href="note-0120-02a" xlink:label="note-0120-02" xml:id="N1BB74" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N1BB7A" xml:space="preserve">2. correĺ</note>
            <p xml:id="N1BB7E">
              <s xml:id="N1BB7F" xml:space="preserve">¶ Sequitur ſecundo /  latitudine ſic mota / vt dictū <lb/>eſt in quarta concluſione: ſignato quouis puncto <lb/>talis latitudinis ſic mote dabitur vna potētia que <lb/>poſita in illo aliqualiter velociter intendit motum <lb/>ſuum: et nulla non equalis ei ſufficit ita velociter in­<lb/>tendere motum ſuum poſita in illo puncto pro eo-<lb/>dem inſtanti. </s>
              <s xml:id="N1BB8E" xml:space="preserve">Probatur facile / quia quocun pun-<lb/>cto dato dabitur vna potentia habens ad eū pro-<lb/>portionem equalitatis: ponatur ergo talis poten-<lb/>tia in illo puncto ſic intendente motum ſuum: et ma­<lb/>nifeſtum eſt /  talis punctus incipiet precedere po-<lb/>tentiã, cū potentia nõ ſufficiat moueri cum illo aut <lb/>illum precedere / vt conſtat, et ſic illa potentia conti-<lb/>nuo poſt illud inſtans intendet motum ſuū. </s>
              <s xml:id="N1BB9F" xml:space="preserve">Et nul-<lb/>la alia potentia ſufficit velocius intendere motum <lb/>ſuum exiſtens pro eodem inſtanti in tali puncto ̄ <lb/>illa data: igitur correlarium verum. </s>
              <s xml:id="N1BBA8" xml:space="preserve">Conſequentia <lb/>patet cum maiore, et minor probatur: quia vel illa <lb/>q̄ ſufficit (ſi ſit aliqua .etc̈.) eſt maior data potētia vĺ <lb/>minor, vel equalis. </s>
              <s xml:id="N1BBB1" xml:space="preserve">Si maior iam tardius intendit <lb/>ex quinta concluſione. </s>
              <s xml:id="N1BBB6" xml:space="preserve">Si equalis illa non intēdet <lb/>velocius ſed equaliter. </s>
              <s xml:id="N1BBBB" xml:space="preserve">Si minor ipſa nec intendit <lb/>nec remittit motum ſuum / quia ad infinita puncta <lb/>remiſſiora habet proportionem minoris inequali­<lb/>tatis / vt ptꝫ intelligenti naturam qualitatis vnifor­<lb/>miter difformis: patꝫ igitur /  nulla alia potentia <lb/>ſufficit velocius intendere motum exiſtens pro eo-<lb/>dem inſtanti in tali puncto ꝙ̄ alia data. </s>
              <s xml:id="N1BBCA" xml:space="preserve">Patet er-<lb/>go minor: et per conſequens correlariū               <anchor type="note" xlink:href="note-0121-01" xlink:label="note-0121-01a"/>               </s>
              <s xml:id="N1BBD4" xml:space="preserve">¶ Sequitur <lb/>tertio /  latitudine ſic mota / vt dictū eſt in ↄ̨cluſione <lb/>quouis puncto illius reſiſtentie dato dabiles ſunt <lb/>infinite potentie que in eodem inſtanti poſite in il-<lb/>lo puncto continuo intenderent motum ſuum. </s>
              <s xml:id="N1BBDF" xml:space="preserve">Et in­<lb/>ter illas dabilis eſt vna que ita tarde incipit inten­<lb/>dere motum ſuum  nulla tardius. </s>
              <s xml:id="N1BBE6" xml:space="preserve">Et datur vna <lb/>que ita velociter /  nulla velocius ſufficit intendere <lb/>in eodē inſtanti ab eodem puncto procedendo. </s>
              <s xml:id="N1BBED" xml:space="preserve">Hoc <lb/>correlarium ex duobus precedentibus ſuam oſten-<lb/>ſionem accipit.               <anchor type="note" xlink:href="note-0121-02" xlink:label="note-0121-02a"/>               </s>
              <s xml:id="N1BBF9" xml:space="preserve">¶ Sequitur quarto /  latitudine ſic <lb/>nota / vt dictum eſt in quinta concluſione: quocun               <cb chead="Capitulū quartūdecimū."/>               pūcto illius dato in quouis inſtanti temporis: da­<lb/>bitur minima velocitas a qua potentia certa in-<lb/>cipiens moueri a tali puncto pro eodē inſtanti ſuf-<lb/>ficit intendere motum ſuum. </s>
              <s xml:id="N1BC07" xml:space="preserve">Patet facile hoc cor-<lb/>relariū ex primo correlario et ex eiꝰ caſu. </s>
              <s xml:id="N1BC0C" xml:space="preserve">De b. em̄ <lb/>potentia verificatur preſens correlariū. </s>
              <s xml:id="N1BC11" xml:space="preserve">¶ Et ſimi-<lb/>liter dabilis eſt maxima velocitas a qua potentia <lb/>certa incipiens moueri a tali puncto ſufficit inten-<lb/>dere motus ſuū: vt patet ex caſu ſecundi correlarii</s>
            </p>
            <div xml:id="N1BC1A" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0121-01a" xlink:label="note-0121-01" xml:id="N1BC1E" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0121-02a" xlink:label="note-0121-02" xml:id="N1BC24" xml:space="preserve">4. correĺ.</note>
            </div>
            <p xml:id="N1BC2A">
              <s xml:id="N1BC2B" xml:space="preserve">Sexta concluſio. </s>
              <s xml:id="N1BC2E" xml:space="preserve">Datis duobus me-<lb/>diis non reſiſtentibus inequalibus per que exten-<lb/>dantur due reſiſtentie equales intenſiue reſiſten-<lb/>tie vniformiter difformis quieſcente non gradu vĺ <lb/>remiſſiori extremo: et quilibet punctus latitudinis <lb/>que per maius medium extenditur in certa propor­<lb/>tione continuo velocius moueatur ꝙ̄ ſibi correſpõ­<lb/>dens punctus in medio minori: potentia poſita in <lb/>maiori medio ad vnum puuctum continuo velocius <lb/>mouebitur ꝙ̄ ſibi equalis poſita ad punctū ſibi cor­<lb/>reſpondens in minori medio: et hoc dūmodo tales <lb/>potentie intendãt motus ſuos. </s>
              <s xml:id="N1BC47" xml:space="preserve">Probatur / quia po­<lb/>tentia in medio minori exiſtens non incipit moueri <lb/>equaliter cum potentia in maiori exiſtente, nec ve-<lb/>locius: igitur tardius: et per conſequens potentia <lb/>mouēs in maiori medio incipit velocius moueri ̄ <lb/>potentia mouens in minori medio. </s>
              <s xml:id="N1BC54" xml:space="preserve">Et poſt̄ velo-<lb/>cius mouetur ſemper velocius mouetur: ergo con-<lb/>tinuo potentia mota in maiori medio velocius mo­<lb/>uetur ꝙ̄ potentia mota in minori medio: quod fuit <lb/>probandum </s>
              <s xml:id="N1BC5F" xml:space="preserve">Conſequentia ptꝫ: et probatur /  potē­<lb/>tia in minore medio exiſtēs nõ incipit moueri equa­<lb/>liter cum potentia in maiori medio exiſtente: quia <lb/>ſi incipit moueri equaliter per aliquod tempus ſe­<lb/>quitur /  per illud tempus continuo eque cito at-<lb/>tinget eam equalis reſiſtentia illi que attigit aliaꝫ <lb/>in medio maiori. </s>
              <s xml:id="N1BC6E" xml:space="preserve">Sed conſequens eſt falſum: igitur <lb/>et antecedens. </s>
              <s xml:id="N1BC73" xml:space="preserve">Cõſequentia patet: ſed falſitas cõſe-<lb/>quentis probatur / quia in aliqua certa ꝓportione <lb/>quilibet punctus inſequens potentiã in medio mi-<lb/>nori minus diſtat ab illa potētia quam inſequitur: <lb/>et in eadem proportione tardius mouetur cõtinuo <lb/>̄ pūctus ſibi correſpõdens in medio maiori diſtet <lb/>a potentia quam inſequitur et etiam moueatur (vt <lb/>patet caſum intuēti) / et potētia in medio minori ita <lb/>velociter mouetur recedendo a tali puncto ſicut po­<lb/>tentia in medio maiori fugit cõſimile punctū per te / <lb/>igitur talis punctus citius attinget potentiam in <lb/>medio maiori ꝙ̄ cõſimilis punctus attingat aliam <lb/>potentiam in medio minori: et per cõſequens nõ cõ­<lb/>tinuo eque cito: quod eſt oppoſitum cõſequentis et <lb/>ſic illud cõſequens eſt falſum. </s>
              <s xml:id="N1BC92" xml:space="preserve">Cõſequētia tamē ptꝫ <lb/>ex tertia ſuppoſitiõe: et eius correlario. </s>
              <s xml:id="N1BC97" xml:space="preserve">Et per ideꝫ <lb/>ꝓbatur /  nõ incipit moueri velocius: quia tunc ſe-<lb/>queretur /  certus punctus citius attingeret eam ̄ <lb/>ſibi ſimilis in maiori medio attingeret aliam. </s>
              <s xml:id="N1BCA0" xml:space="preserve">Sed <lb/>hoc eſt falſum: quia quãdo potētia mouetur in mi-<lb/>nori medio equaliter cum alia mouente in maiori: <lb/>adhuc citius attingeret punctus potentiam in ma-<lb/>iori medio ꝙ̄ cõſimilis pūctus attingeret potentiã <lb/>in minori medio (vt ptꝫ ex probatione precedentis <lb/>partis) ergo per locum a maiori multo citius attin­<lb/>get potentiam in maiori medio quando potentia <lb/>in minori mouetur velocius ꝙ̄ potentia in maiori <lb/>medio. </s>
              <s xml:id="N1BCB5" xml:space="preserve">Sed iam probo /  poſt̄ velocius mouetur <lb/>ſemper velocius mouetur quia iam nõ poteſt inci-<lb/>pere moueri equaliter ꝓcedendo ab equalibus pū­<lb/>ctis / vt ꝓbatū eſt: et modo mouetur velociꝰ et nõ põt <lb/>moueri tardiꝰ niſi prius moueat̄̄ equaliter: et nõ po­<lb/>teſt incipere moueri equaliter / vt ꝓbatum eſt: ergo               <pb chead="De motu quo ad cauſã in medio non reſiſtente." file="0122" n="122"/>               poſt̄ mouetur velocius: ſemper mouetur velocius / <lb/>quod fuit probandum. </s>
              <s xml:id="N1BCC9" xml:space="preserve">Patet ergo concluſio.</s>
            </p>
            <note position="left" xml:id="N1BCCC" xml:space="preserve">1. correl.</note>
            <p xml:id="N1BCD0">
              <s xml:id="N1BCD1" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  datis dua-<lb/>bus latitudinibus equalibus reſiſtentie vniformi-<lb/>ter difformis inequaliter extenſis per inequales ꝑ­<lb/>tes mediorum non reſiſtentium: et quilibet punctus <lb/>reſiſtentie minus extenſe in aliqua proportione in-<lb/>cipiat vniformiter intendere motum ſuum cõtinuo <lb/>velocius puncto ſibi correſpondente in latitudine <lb/>magis extenſa: poña poſita in reſiſtentia minus ex­<lb/>tenſa in aliquo puncto cū quo incipit intendere mo­<lb/>tum ſuum velocius continuo mouebitur poña equa­<lb/>li poſita in conſimili puncto in latitudine magis ex­<lb/>tenſa dūmodo ibi intendat motum ſuum. </s>
              <s xml:id="N1BCEA" xml:space="preserve">Proba-<lb/>tur correlarium / quia talis poña poſita in latitudi­<lb/>ne minus extenſa incipit velocius moueri: et poſt̄ <lb/>ſic mouetur ſemper velocius mouetur ſtante caſu: <lb/>igitur correlarium verum: </s>
              <s xml:id="N1BCF5" xml:space="preserve">Arguitur maior / q2 ſi in­<lb/>ciperet tardius vel equaliter moueri: et quilibet pū­<lb/>ctus minoris reſiſtentie minus diſtat ab eã ꝙ̄ pun-<lb/>ctus conſimilis diſtat a potentia mota in latitudi-<lb/>ne magis extenſa: et quilibet punctus velocius mo-<lb/>uebitur immediate poſt hoc: ergo citius immedia-<lb/>te poſt hoc aliquis punctus minoris reſiſtentie at-<lb/>tinget in latitudine minus extenſa poñam ibi mo-<lb/>tam quã conſimilis attingat poñam in latitudine <lb/>magis extenſa. </s>
              <s xml:id="N1BD0A" xml:space="preserve">Patet conſequentia ex tertia ſup-<lb/>poſitione: et per conſequens immediate poſt hoc ve­<lb/>locius mouebitur alia (cum moueatur cum minori <lb/>reſiſtentia.) </s>
              <s xml:id="N1BD13" xml:space="preserve">Sed minor eãdem cum minori precedē­<lb/>tis concluſionis demonſtrationem exigit. </s>
              <s xml:id="N1BD18" xml:space="preserve">Et ſic pa­<lb/>tet correlarium.               <anchor type="note" xlink:href="note-0122-01" xlink:label="note-0122-01a"/>               </s>
              <s xml:id="N1BD22" xml:space="preserve">¶ Sequitur ſecundo /  datis dua-<lb/>bus: vel quotcū latitudinibus reſiſtētie vniformi­<lb/>ter difformis equalis reſiſtentie inequalitater exten-<lb/>ſis et quilibet punctus vnius moueatur eque veloci­<lb/>ter ſicut punctus correſpondens in alia: et hoc conti­<lb/>nuo vniformiter: poña que mouetur in medio mino­<lb/>ri / hoc eſt in minus extenſa reſiſtentia continuo tar-<lb/>dius mouetur ꝙ̄ poña ei equalis que mouetur in la­<lb/>titudine magis extenſa et hoc dūmodo ille potētie <lb/>incipiant a conſimilibus punctis. </s>
              <s xml:id="N1BD37" xml:space="preserve">Probatur cor-<lb/>relarium / quia talis potentia in latitudine minus <lb/>extenſa incipit tardius mouere ꝙ̄ alia in latitudi-<lb/>ne magis extenſa: et poſt̄ mouetur tardius non po­<lb/>teſt incipere equaliter moueri: nec velocius: igitur <lb/>continuo tardius mouetur. </s>
              <s xml:id="N1BD44" xml:space="preserve">Patet conſequentia: et <lb/>tam maior ꝙ̄ minor probantur eodem modo ſicut <lb/>probantur in concluſione precedenti.</s>
            </p>
            <div xml:id="N1BD4B" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0122-01a" xlink:label="note-0122-01" xml:id="N1BD4F" xml:space="preserve">2. correl.</note>
            </div>
            <note position="left" xml:id="N1BD55" xml:space="preserve">3. correl. <lb/>decīa cõ-<lb/>clu. cal.</note>
            <p xml:id="N1BD5D">
              <s xml:id="N1BD5E" xml:space="preserve">¶ Sequitur tertio /  tam in caſu concluſionis quã <lb/>correlariorum continuo in quolibet tempore ade-<lb/>quate terminato ad inſtans initiatiuum motus: ve­<lb/>locius intendit motum ſuum poña mota in maiori <lb/>medio ꝙ̄ in minori. </s>
              <s xml:id="N1BD69" xml:space="preserve">Probatur / quia dato quocū <lb/>tali tempore ſemper in inſtanti terminatiuo illius <lb/>potentia que eſt in maiori medio in caſu concluſio-<lb/>nis eſt cū puncto minus intenſo ſiue mouetur a ma-<lb/>iori ꝓportione ꝙ̄ alia poña in medio maiori / vt pa­<lb/>tet ex concluſione: et inceperunt ab equali velocita-<lb/>te: ergo in illo tempore adequate maiorem veloci-<lb/>tatem acquiſiuit potentia mota in maiori medio ̄ <lb/>alia mota in minori: et per conſequens velocius ī ta­<lb/>li tempore adequate intendit motum ſuum. </s>
              <s xml:id="N1BD7E" xml:space="preserve">Et ſic ꝓ­<lb/>batur de alia poñe / que eſt in latitudine minus intē­<lb/>ſa in caſu precedentis correlarii reſpectu potentie <lb/>que in caſu eiuſdem correlarii eſt in latitudine ma-<lb/>gis extenſa. </s>
              <s xml:id="N1BD89" xml:space="preserve">Et ſic patet correlariū. </s>
              <s xml:id="N1BD8C" xml:space="preserve">Et hec ſub aliis <lb/>verbis tamen: eſt decima concluſio calculatoris ̄­<lb/>uis eam ſic non probet. </s>
              <s xml:id="N1BD93" xml:space="preserve">¶ Multe alie concluſiones <lb/>poſſent in hac materia adduci, et ex predictis euidē­               <cb chead="De motu quo ad cauſã in medio non reſiſtente."/>               ter inferri, nihilominus breuitatis cauſa ſuperſe-<lb/>deo in ſequenti capite aliquas ex eis in deductioni­<lb/>bus argumentorum probaturus.</s>
            </p>
          </div>
          <div xml:id="N1BD9F" level="4" n="15" type="chapter" type-free="capitulum">
            <head xml:id="N1BDA4" xml:space="preserve">Quindecimum caput / quod obiicit ali-<lb/>quibus que dicta ſunt in precedentibꝰ duo­<lb/>bus capitibus: inferendo aliquas conclu-<lb/>ſiones de velocitate motus in reſiſtētia dif­<lb/>formiter difformi progrediente per medi-<lb/>um non reſiſtens: et in latitudine vniformi­<lb/>ter difformi condenſante ſe ad non quãtū <lb/>in medio non reſiſtente.</head>
            <p xml:id="N1BDB5">
              <s xml:id="N1BDB6" xml:space="preserve">IAm aggredior impugnare ali-<lb/>qua eorum que dicta ſunt in tridecimo: et <lb/>quarto decimo capitibus: et ſignanter ter-<lb/>tiam ſuppoſitionem tridecimi capitis baſim / et fun­<lb/>damentum omnium dictorum in predictis capiti-<lb/>bus.</s>
            </p>
            <p xml:id="N1BDC3">
              <s xml:id="N1BDC4" xml:space="preserve">Et ideo cõtra eam primo arguitur ſic <lb/></s>
              <s xml:id="N1BDC8" xml:space="preserve">Non eſt poſſibile latitudinem reſiſtentie acq̇ri par-<lb/>tibiliter quo ad ſubiectum tantum / vt dicit ſuppoſi­<lb/>tio / igitur illa falſa. </s>
              <s xml:id="N1BDCF" xml:space="preserve">Conſequentia patet et argui-<lb/>tur antecedens / quoniam ſi illud eſſet poſſibile: ſe-<lb/>queretur /  ab inequalibus proportionibus equa-<lb/>les velocitates prouenirent: ſed hoc eſt falſum: et cõ­<lb/>tra baſim totius huius operis: igitur illḋ ex quo ſe­<lb/>quitur: </s>
              <s xml:id="N1BDDC" xml:space="preserve">Falſitas conſequentis eſt nota, et probatur <lb/>ſequela, et pono caſum /  ſint duo media non reſiſtē­<lb/>tia equalia: et per vnum illorum extendatur parti-<lb/>biliter quo ad ſubiectuꝫ dūtaxat vna reſiſtentia dif­<lb/>formiter difformis cuius prīa medietas ſit vnifor-<lb/>mis continuo vt .2. et ſecunda vt .6. et moueatur qui­<lb/>libet punctus eius vniformiter ↄ̨tinuo: puncto ve-<lb/>lociſſime moto, continuo moto a proportione qua­<lb/>drupla: et puncto medio a dupla (vt oportet) / et ꝑ ali­<lb/>ud medium extendatur a non quanto vna latitudo <lb/>vniformis per totum vt .4. quolibet puncto eius in­<lb/>trinſeco mouente vniformiter: et puncto velociſſime <lb/>moto: continuo moto a proportione quadrupla ita­<lb/> continuo tales latitudines maneant equales, et <lb/>equaliter moueantur: moueatur cum vtra illa­<lb/>rum vna poña vt .8. in eodem inſtanti, ab eodē pun­<lb/>cto: per eandem lineam inchoando: </s>
              <s xml:id="N1BDFF" xml:space="preserve">Quo poſito ſic <lb/>argumentor. </s>
              <s xml:id="N1BE04" xml:space="preserve">poña que mouetur cum latitudine vni­<lb/>formi mouetur equaliter omnino: et continuo eque­<lb/>velociter cum potentia que mouetur cum latitudi-<lb/>ne difformiter difformi: et tales potentie non poſ-<lb/>ſunt continuo moueri ab eadem proportione cum <lb/>nullus punctus in latitudine difformiter difformi <lb/>ſit equalis reſiſtentie adequate cum aliquo puncto <lb/>reſiſtentie vniformis (quandoquidem quodlibet in <lb/>reſiſtentia vniformi ſit vt .4. et in difformiter diffor­<lb/>mi quodlibet eſt vt .2. vel vt .6. adequate) / igitur ab <lb/>inequalibus proportionibus equales velocitates <lb/>proueniunt / quod fuit probandum: </s>
              <s xml:id="N1BE1D" xml:space="preserve">Conſequentia <lb/>patet cum minore: et maior probatur. </s>
              <s xml:id="N1BE22" xml:space="preserve">quia potētia <lb/>que mouetur cum reſiſtentia vniformi continuo eſt <lb/>in puncto medio illius reſiſtentie: et poña que moue-<lb/>tur cum reſiſtētia difformi ſimiliter ē in medio eiuſ­<lb/>dem reſiſtentie difformis: et eque velociter continuo <lb/>mouetur mediuꝫ vnius ſicut medium alterius / vt pa­<lb/>tet ex caſu: igitur eque velociter continuo mouetur <lb/>cum reſiſtentia vniformi ſicut alia poña cum diffor­<lb/>mi / quod fuit probandum. </s>
              <s xml:id="N1BE35" xml:space="preserve">Conſequentia patet cuꝫ <lb/>minore: et arguitur prima pars maioris / q2 poña <lb/>cū reſiſtentia vniformi vt .4. ↄ̨tinuo mouet̄̄ a ꝓpor-<lb/>tione dupla cum ipſa ſit vt .8. et punctus medius ta­<lb/>lis latitudinis etiam continuo mouetur a propor-<lb/>tione dupla ex caſu: et incipiunt moueri ab eodē pū-               <pb chead="Primi tractatus" file="0123" n="123"/>               cto per eandem lineam in eodem inſtanti: ergo con­<lb/>tinuo ſunt ſimul / quod fuit probandum </s>
              <s xml:id="N1BE49" xml:space="preserve">Iam probo <lb/>ſecundam partem maioris / quia potentia que mo­<lb/>uetur cum reſiſtentia difformi non poteſt in caſu eē <lb/>citra punctū medium in medietate remiſſiori: nec vl­<lb/>tra mediū ī medietate intenſiori: et mouetur conti-<lb/>nuo cum latitudine: igitur continuo eſt in medio ta­<lb/>lis latitudinis. </s>
              <s xml:id="N1BE58" xml:space="preserve">Conſequentia patet, et minor ꝓba-<lb/>tur / quia ſi aliquando poſſet in caſu eſſe citra pun-<lb/>ctum medium ī medietate remiſſiori capio inſtans ī <lb/>quo eſt in illa, et arguitur ſic / vel continuo potentia <lb/>illa a principio motus eſt citra punctum medium <lb/>īmedietate remiſſiori vel continuo vltra punctū me­<lb/>dium immediate intenſiori: vel aliquando citra pū­<lb/>ctum medium: et aliquando vltra: nullum iſtorum ē <lb/>dicendum: igitur: </s>
              <s xml:id="N1BE6B" xml:space="preserve">Non primum quia tunc ſequere-<lb/>tur /  a principio motus talis poña mouetur conti­<lb/>nuo a proportione quadrupla cum tota illa medie­<lb/>tas ſit vniformis vt .2. et poña vt .8. et continuo po­<lb/>tentia eſt citra punctum medium per te: igitur (cum <lb/>poña et punctus medius ſuum motum inchoant ab <lb/>eodem puncto in eodem inſtanti) / ſequitur /  maior <lb/>velocitas prouenit a proportione dupla ꝙ̄ a qua-<lb/>drupla quod eſt tantum vel maius inconueniens ̄ <lb/>illud quod inferre intendimus: </s>
              <s xml:id="N1BE80" xml:space="preserve">Nec dicendum ē ſe-<lb/>cundum / quia tunc ſequeretur /  a principio motus <lb/>talis potentia cõtinuo mouetur a proportione ſex-<lb/>quitertia cum tota illa medietas ſit vniformis vt 6 <lb/>et poña vt .8. et continuo poña eſt vltra punctū me-<lb/>dium per te: igitur (cuꝫ poña et punctus mediꝰ ſuum <lb/>motum inchoant ab eodem puncto in eodem inſtã-<lb/>ti et per eandeꝫ lineam) ſequitur /  maior velocitas <lb/>prouenit a proportione ſexquitertia ꝙ̄ a dupla qḋ <lb/>eque magnum inconueniens eſt ſicut illud quod in-<lb/>ferre intendimus: </s>
              <s xml:id="N1BE97" xml:space="preserve">Sed  non ſit dicendum tertium <lb/>probatur / quia ſi aliquando eſt citra punctum medi­<lb/>um, et aliquando vltra capio inſtans in quo ē citra <lb/>punctum medium: et arguitur ſic / vel a principio mo­<lb/>tus ſemper fuit citra punctum medium in medieta­<lb/>te remiſſiori: vel aliquando vltra punctum medium <lb/>in medietate intenſiori: et deinde in medietate remiſ­<lb/>ſiori: </s>
              <s xml:id="N1BEA8" xml:space="preserve">Non primum quia tunc ſequeretur /  cõtinuo <lb/>moueretur per totum illud tempus a proportione <lb/>quadrupla, et tamen moueretur tardius per te quã <lb/>punctus medius qui mouetur a ꝓportione dupla: <lb/>ſed hoc eſt impoſſibile, igitur illud ex quo ſequitur: <lb/></s>
              <s xml:id="N1BEB4" xml:space="preserve">Nec dicendum eſt ſecundum / quia ſi tranſit per pun­<lb/>cta intenſioris medietatis ad puncta medietatis re­<lb/>miſſioris / neceſſe eſt /  tranſeat per punctum mediū / <lb/>vt conſtat: et ſi venerit ad punctum medium nū̄ ab <lb/>eo diſcedet: igit̄̄ illa poña nū̄ eſt vltra pūctū medi­<lb/>um in medietate intenſiori et deinde in medietate re­<lb/>miſſiori. </s>
              <s xml:id="N1BEC3" xml:space="preserve">Conſequentia patet cum maiore / et proba-<lb/>tur minor / quia ſi illa poña venerit ad punctū medi­<lb/>um: nullus punctus medietatis remiſſioris vn̄ po­<lb/>tentiam precedet / quia cum quolibet tali poña ſuffi­<lb/>cit mouere velocius quam ipſe mouetur, nec ip̄a po­<lb/>ctentia aliquem punctum intenſioris medietatis p̄-<lb/>cedet vn̄ (cuꝫ quodlibet tale velocius mouatur ̄ <lb/>potentia ſufficit mouere cum illo) / igitur ſi talis po­<lb/>tentia venerit ad punctum medium nū̄ ab eo diſce­<lb/>det / quod fuit probandum.</s>
            </p>
            <p xml:id="N1BED8">
              <s xml:id="N1BED9" xml:space="preserve">Reſpondeo ad argumentum negan-<lb/>do antecedens: et ad probationem nego ſequelam: <lb/>et ad probationem admiſſo caſu concedo maiorem / <lb/>et nego minorem, et ad probationem minoris con-<lb/>cedo /  nullus eſt ibi punctus ad quem adequate ta­<lb/>lis poña habet proportionem duplam, et cum infer­               <cb chead="Capitulum quindecimum"/>               tur / ergo non poteſt continuo moueri a proportiõe <lb/>dupla negatur conſequentia / et ratio eſt / quoniã quã­<lb/>uis ad nullum punctum habeat ꝓportionem duplã <lb/>adequate habet tamē ad duo ſimul videlicet ad ex-<lb/>tremum prime medietatis et ad initium ſecunde.</s>
            </p>
            <p xml:id="N1BEF1">
              <s xml:id="N1BEF2" xml:space="preserve">Sed contra / quia extremum prime <lb/>medietatis eſt vt .2. et principium ſecunde vt: 6. </s>
              <s xml:id="N1BEF7" xml:space="preserve">Mo­<lb/>do duo et ſex ſunt octo, et poña eſt vt octo. </s>
              <s xml:id="N1BEFC" xml:space="preserve">ergo ad <lb/>illa habet talis poña proportionem equalitatis et <lb/>non duplam: et per conſequens ſolutio nulla.</s>
            </p>
            <p xml:id="N1BF03">
              <s xml:id="N1BF04" xml:space="preserve">Reſpondeo /  difficile eſt mihi ſoluere <lb/>argumentum et in eo diu cogitaui. </s>
              <s xml:id="N1BF09" xml:space="preserve">Dico tamen ad <lb/>replicam negando conſequentiam. </s>
              <s xml:id="N1BF0E" xml:space="preserve">Et ratio ē / quia <lb/>illa puncta vt .2. et vt .6. non faciunt reſiſtentiam vt <lb/>8. </s>
              <s xml:id="N1BF15" xml:space="preserve">Imo dico /  illa duo puncta principium ſecunde <lb/>medietatis et finis prime ita ſe habent  in reſiſten­<lb/>do equiualent puncto reſiſtentie reſiſtentis vt .4.</s>
            </p>
            <note position="right" xml:id="N1BF1C" xml:space="preserve">regula</note>
            <p xml:id="N1BF20">
              <s xml:id="N1BF21" xml:space="preserve">Unde pono talem regulam.</s>
            </p>
            <p xml:id="N1BF24">
              <s xml:id="N1BF25" xml:space="preserve">Ubicun aliqua potentia mouetur <lb/>cum aliqua reſiſtentia difformi: et eſt in parte illius <lb/>reſiſtentie que tardius mouetur quam poña ſufficit <lb/>moueri cuꝫ illa adequate: et pars immediate ſeq̄ns <lb/>velocius mouetur quã potentia ſufficit mouere cum <lb/>illi vel eque velociter: tunc talis reſiſtentia reſiſtit <lb/>ille poñe tantum adequate quantum reſiſteret vna <lb/>reſiſtentia ad quam haberet illa poña adequa-<lb/>te talem proportionem a quali mouetur illa reſiſtē­<lb/>ſtentia cui potentia continuo eſt proxima. </s>
              <s xml:id="N1BF3A" xml:space="preserve">Et ideo / <lb/>tunc talis reſiſtentia equiualet alteri ad quam po-<lb/>tentia talem proportionem habet. </s>
              <s xml:id="N1BF41" xml:space="preserve">Hac regula pre <lb/>ſuppoſita.</s>
            </p>
            <p xml:id="N1BF46">
              <s xml:id="N1BF47" xml:space="preserve">Reſpondeo ad argumentum diſtīguē­<lb/>do minorem: aut  talis poña non poteſt in caſu cū <lb/>illis reſiſtentiis moueri cum eadē proportione quã <lb/>vtra illarum habeat formaliter ad aliquam illa­<lb/>rum reſiſtētiarum: et ſic conceditur: aut quã habeat <lb/>equiualenter: et ſic negatur.</s>
            </p>
            <p xml:id="N1BF54">
              <s xml:id="N1BF55" xml:space="preserve">Sed cõtra q2 ſi hec ſolutio eſſet bona <lb/>ſequeretur /  eadem potentia nõ variata mouetur <lb/>eque velociter adequate cū reſiſtentia maiori ſicut <lb/>cū minori: ſed hoc videtur impoſſibile: igitur illud <lb/>ex quo ſequitur. </s>
              <s xml:id="N1BF60" xml:space="preserve">Sequela ꝓbatur, et volo /  in caſu <lb/>argument&lt;/gap&gt; tota ſecunda medietas illius reſiſtentie <lb/>perdat per totum vniformiter vnū gradum ita  <lb/>maneat vniformis vt .5. moueatur tamen eadē ve-<lb/>locitate qua antea mouebatur. </s>
              <s xml:id="N1BF6B" xml:space="preserve">Quo poſito iã po-<lb/>tentia vt .8. cõtinuo erit in puncto medio illius reſi­<lb/>ſtentie qui mouetur eque velociter ſicut antea: ergo <lb/>talis potentia mouetur eque velociter adequate ſi-<lb/>cut antea et reſiſtentia ſua eſt minor quã antea: igit̄̄ <lb/>aſſumptum verum.</s>
            </p>
            <p xml:id="N1BF78">
              <s xml:id="N1BF79" xml:space="preserve">Reſpondeo concedendo / quod īfertur <lb/>dūmodo talis potentia nõ moueatur a proportiõe <lb/>quam formaliter habet ad talem reſiſtentiam, ſed <lb/>a proportione quam habet ad illam equiualenter <lb/>               <anchor type="note" xlink:href="note-0123-01" xlink:label="note-0123-01a"/>               </s>
              <s xml:id="N1BF89" xml:space="preserve">¶ Ex quo ſequitur primo /  etiam ſi ſecunda me-<lb/>dietas in infinitum intederetur: et prima in infini-<lb/>tum remitteretur potentia tamen ſemper vniformi­<lb/>ter mouetur. </s>
              <s xml:id="N1BF92" xml:space="preserve">Quod nihilomiuꝰ mirabile apparet. <lb/>               <anchor type="note" xlink:href="note-0123-02" xlink:label="note-0123-02a"/>               </s>
              <s xml:id="N1BF9C" xml:space="preserve">¶ Sequitur ſecundo /  vbicuuq aliqua reſiſtentia <lb/>difformiter difformis cuius vtra medietas eſt et <lb/>manet vniformis incipit progredi a non quanto in <lb/>medio non reſiſtente: quolibet puncto eius intrinſe­<lb/>co continuo vniformiter mouente: omnis poña que <lb/>ſimul incipit moueri cum illa cõtinuo mouetur vni­<lb/>formiter. </s>
              <s xml:id="N1BFAB" xml:space="preserve">Probatur / quia cū ea medietate cum qua               <pb chead="De motu quo ad cauſã in medio non reſiſtente." file="0124" n="124"/>               incipit moueri continuo mouebitur et talis medie-<lb/>tas eſt vniformis: igitur continuo vniformiter mo-<lb/>uebitur: </s>
              <s xml:id="N1BFB7" xml:space="preserve">Patet conſequentia cum minore. </s>
              <s xml:id="N1BFBA" xml:space="preserve">et argui-<lb/>tur maior: et capio punctum / in quo eſt in medietate <lb/>in qua incipit moueri in aliquo inſtanti temporis <lb/>terminati ad inſtans initiatiuum motus per quod <lb/>mouetur in illa medietate </s>
              <s xml:id="N1BFC5" xml:space="preserve">(Totalis enim motꝰ quo <lb/>illa potentia mouetur incipit ab aliqua velocitate <lb/>proueniente a proportione quam habet potentia <lb/>ad aliquem punctum intrinſecum illius medietatis <lb/>vt ↄ̨ſtat e)x dictis / et arguo ſic / vel talis pūctus velo­<lb/>cius mouetur quam potentia: vel tardius: vel eque­<lb/>velociter: </s>
              <s xml:id="N1BFD4" xml:space="preserve">Si primum ſequitur /  talis potentia nõ <lb/>eſt in illo puncto quia inceperunt poña et talis pun­<lb/>ctus ab eodem puncto in eodem inſtanti etc. et poña <lb/>mouebatur tardius puncto in quo ponitur eſſe: et <lb/>potentia et punctus mouentur vniformiter: igitur. <lb/></s>
              <s xml:id="N1BFE0" xml:space="preserve">Nec ſecundum puta  tardius / quia tunc ſequere-<lb/>tur /  non eſt in illo puncto quoniam continuo ta-<lb/>lis punctus mouetur tardius ꝙ̄ potentia, et incepe­<lb/>runt in eodem inſtanti ab eodem puncto etc. / igitur <lb/>dicendum eſt tertium puta /  mouetur equaliter: et <lb/>per conſequens ſemper mouebitur cum illo pūcto <lb/>et ſic ſemper erit in eadem medietate: quod fuit pro­<lb/>bandum. </s>
              <s xml:id="N1BFF1" xml:space="preserve">Patet igitur correlarium.</s>
            </p>
            <div xml:id="N1BFF4" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0123-01a" xlink:label="note-0123-01" xml:id="N1BFF8" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0123-02a" xlink:label="note-0123-02" xml:id="N1BFFE" xml:space="preserve">.2correl.</note>
            </div>
            <note position="left" xml:id="N1C004" xml:space="preserve">3. correl.</note>
            <p xml:id="N1C008">
              <s xml:id="N1C009" xml:space="preserve">¶ Sequitur tertio /  vbicun aliqua latitudo reſi­<lb/>ſtētie difformiter difformis cuiꝰ multe ꝑtes ſūt vni­<lb/>formes et nulla difformis ſecundum ſe et quodlibet <lb/>ſui a non quanto incipiat progredi partibiliter ꝑ <lb/>medium non reſiſtens, quolibet eius puncto intrin­<lb/>ſeco continuo vniformiter mouente: omnis potētia <lb/>que cum tali reſiſtentia ab eodeꝫ puncto incipit mo­<lb/>ueri continuo vniformiter mouebitur. </s>
              <s xml:id="N1C01A" xml:space="preserve">Probatur / <lb/>quia cum quacun illarum partium vniformium <lb/>talis poña īcipit moueri: cū ea ſemꝑ mouebit̄̄: igit̄̄ <lb/>cõtinuo vniformiter mouebitur. </s>
              <s xml:id="N1C023" xml:space="preserve">Conſequentia pa-<lb/>patet arguitur antecedens / quoniam in quacū <lb/>parte vniformi prīo mouetur cum illa continuo mo­<lb/>uetur: igitur propoſitum. </s>
              <s xml:id="N1C02C" xml:space="preserve">Probatur antecedens / q2 <lb/>dato aliquo inſtanti temporis per quod mouetur <lb/>in tali parte in qua primo mouetur / arguitur ſic / vel <lb/>punctus in quo in illo īſtanti eſt: mouetur velocius <lb/>quam potentia: vel tardius: vel equaliter: </s>
              <s xml:id="N1C037" xml:space="preserve">Nõ pri-<lb/>mum nec ſecundum / quod probatur ſicut in precedē­<lb/>ti correlario: igitur dicendum eſt tertium videlicet / <lb/> equaliter / et per conſequens /  continuo mouebi-<lb/>tur in illa parte et in illo puncto et ſic continuo vni­<lb/>formiter / quod fuit probandum. </s>
              <s xml:id="N1C044" xml:space="preserve">¶ Intelligatur cor­<lb/>relarium dūmodo talis potētia ab aliqua certa ꝓ­<lb/>portione incipiat moueri. </s>
              <s xml:id="N1C04B" xml:space="preserve">Quia alias dabitur vna <lb/>latitudo reſiſtentie in qua non dabitur (ſaltem di-<lb/>ceret aduerſarius) pars cum qua potentia incipit <lb/>moueri </s>
              <s xml:id="N1C054" xml:space="preserve">Imo quacun data dabitur aliqua magis <lb/>reſiſtens cum qua antea mouebatur (vt diceret ad-<lb/>uerſarius) vt puta ſi alicuius latitudinis quelibet <lb/>pars proportionalis certa proportione ſit vnifor-<lb/>mis alia et alia vniformitate vſ ad equalitatē po­<lb/>tentie aſcendendo excluſiue.</s>
            </p>
            <note position="left" xml:id="N1C061" xml:space="preserve">4. correl.</note>
            <p xml:id="N1C065">
              <s xml:id="N1C066" xml:space="preserve">¶ Sequitur quarto /  vbi potētia mouetur vt poni­<lb/>tur in caſu precedentis correlarii ipſa continuo eſt <lb/>in eodem puncto </s>
              <s xml:id="N1C06D" xml:space="preserve">Probatur / quia non poteſt dici /  <lb/>punctus in quo potentia eſt moueatur velocius aut <lb/>tardius ipſa / vt patet eſt probatione precedētis cor­<lb/>relarii / ergo mouetur equaliter / et per conſequens <lb/>continuo eſt in illo / quod fuit probandum.</s>
            </p>
            <note position="left" xml:id="N1C078" xml:space="preserve">5. correl.</note>
            <p xml:id="N1C07C">
              <s xml:id="N1C07D" xml:space="preserve">¶ Sequitur quinto /  ſi in medio non reſiſtēte a nõ <lb/>quanto progrediatur latititudo reſiſtentie ſic ſe ha­<lb/>bens /  cuiuſlibet partis eius proportionalis pro-<lb/>portione dupla minoribus terminatis verſus pun­               <cb chead="De motu quo ad cauſã in medio non reſiſtente."/>               ctum quieſcens prima medietas ſic reſiſtat poñe vt <lb/>8.  quilibet eius punctus tardius moueatur ꝙ̄ po­<lb/>tentia ſufficit adequate moueri cum illo: et ſecunda <lb/>medietas ſic eidem potentie reſiſtat  quilibet eius <lb/>punctus velociꝰ moueatur quã potentia ſufficit mo­<lb/>ueri cum illo: talis poña in eodem inſtanti cum illa <lb/>reſiſtentia ab eodem puncto progrediens continuo <lb/>cum tali reſiſtentia mouetur vniformiter. </s>
              <s xml:id="N1C097" xml:space="preserve">Probatur / <lb/>q2 talis poña cum illa reſiſtentia mouetur / vt patet / <lb/>quia ad quemlibet punctum illius habet proportio­<lb/>nem maioris inequalitatis: et ab aliquo puncto ali­<lb/>cuius partis proportionalis incipit moueri (vt con­<lb/>ſtat) et continuo eſt ad punctum medium eiuſdeꝫ par­<lb/>tis proportionalis qui continuo mouetur vniformi­<lb/>ter: ergo continuo talis poña mouetur vniformiter / <lb/>quod fuit probandum: </s>
              <s xml:id="N1C0AA" xml:space="preserve">Patet cõſequentia cum ma­<lb/>iore: et minor videlicet /  continuo eſt ad punctū me­<lb/>dium talis partis proportionalis probatur eodeꝫ <lb/>modo ſicut probatur in argumento potentiã ſemꝑ <lb/>eſſe in puncto medio reſiſtentie de qua fit mentio in <lb/>caſu eiuſdem argumenti. </s>
              <s xml:id="N1C0B7" xml:space="preserve">eadem enim eſt probatio: <lb/>patet ergo correlarium. </s>
              <s xml:id="N1C0BC" xml:space="preserve">¶ Et ſi dicas non eſt maior <lb/>ratio /  continuo ſit in puncto medio vnius partis <lb/>proportionalis illius reſiſtētie quã alterius. </s>
              <s xml:id="N1C0C3" xml:space="preserve">quia ī <lb/>cuiuſlibet partis proportionalis puncto medio po­<lb/>terit ſic vniformiter moueri: ergo continuo eſt cum <lb/>cuiuſlibet partis proportionalis puncto medio vel <lb/>nullius. </s>
              <s xml:id="N1C0CE" xml:space="preserve">Dico negando antecedens: imo deus illud <lb/>determinat  potius ſit in puncto medio vnius par­<lb/>tis proportionalis quam alteriꝰ: et volūtas ſua eſt <lb/>ratio in propoſito.               <anchor type="note" xlink:href="note-0124-01" xlink:label="note-0124-01a"/>               </s>
              <s xml:id="N1C0DC" xml:space="preserve">Oportet enim ſupponere hanc <lb/>regulam in philoſophia.</s>
            </p>
            <div xml:id="N1C0E1" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0124-01a" xlink:label="note-0124-01" xml:id="N1C0E5" xml:space="preserve">regula.</note>
            </div>
            <p xml:id="N1C0EB">
              <s xml:id="N1C0EC" xml:space="preserve">Ubicun aliqua potentia naturalis <lb/>ex ſe eſt omnino indifferens ad aliqua multa, et nõ <lb/>poteſt omnia illa ſimul:               <anchor type="note" xlink:href="note-0124-02" xlink:label="note-0124-02a"/>               prima cauſa omnium rerū <lb/>naturalium a qua dependet celuꝫ et natura tota (vt <lb/>ait philoſophus duodecimo methaphiſices) illam <lb/>potentiam ad alterum illorum ſua voluntate deter­<lb/>minat, et hoc ſecundum ordinem nature et concurſu <lb/>generali operatur ipſe rerum omnium opifex. </s>
              <s xml:id="N1C102" xml:space="preserve">Nec <lb/>hec ſolutio extranea videatur quoniaꝫ oportet ita <lb/>ſoluere argumentum defractione fili equalis forti­<lb/>tudinis in omnibus partibus ſuis:               <anchor type="note" xlink:href="note-0124-03" xlink:label="note-0124-03a"/>               cuius meminit <lb/>philoſophus ſecundo celi et mundi in calce. et argu­<lb/>mentum de introductione graduum caliditatis: et <lb/>de productiõe luminis a cãdela: quare videlicet pri­<lb/>us produxit lumen a. in vna camera quã in altera <lb/>cum prius illuminat vnam cameram, et poſtea alte­<lb/>ram. </s>
              <s xml:id="N1C11C" xml:space="preserve">Et hec ē comunis ſolutio in philoſophia: et p̄-<lb/>cipue apud parrhiſienſes.</s>
            </p>
            <div xml:id="N1C121" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0124-02a" xlink:label="note-0124-02" xml:id="N1C125" xml:space="preserve">phūs .12. <lb/>met. tex. <lb/>co. 38.</note>
              <note position="right" xlink:href="note-0124-03a" xlink:label="note-0124-03" xml:id="N1C12F" xml:space="preserve">pḣs 2. ce. <lb/>et mun.</note>
            </div>
            <p xml:id="N1C137">
              <s xml:id="N1C138" xml:space="preserve">Secundo ad idem arguitur ſic. </s>
              <s xml:id="N1C13B" xml:space="preserve">Si la­<lb/>titudo reſiſtentie vniformiter difformis poſſet ſic ꝓ­<lb/>gredi partibiliter quo ad ſubiectum tantum / vt di-<lb/>citur in prīa ſuppoſitione: ſequeretur /  etiam ipſa <lb/>manens vniformiter difformis continuo poſſet cõ-<lb/>denſari ad non quantum ſubiecto eius quieſcente: <lb/>ſed conſequens eſt falſum: igitur illud ex quo ſequi­<lb/>tur. </s>
              <s xml:id="N1C14C" xml:space="preserve">Conſequentia eſt nota. </s>
              <s xml:id="N1C14F" xml:space="preserve">Et arguitur falſitas cõ­<lb/>ſequentis / quia ſi ita poſſet condenſari manens con­<lb/>tinuo vniformiter difformis. </s>
              <s xml:id="N1C156" xml:space="preserve">ſequeretur /  eadē po­<lb/>tentia vel equalis citius pertranſiret eandeꝫ vel eq̈­<lb/>lem reſiſtentiam magis extenſam quam minꝰ exten­<lb/>ſam: ſed conſequēs eſt falſum / igitur illud ex quo ſe­<lb/>quitur </s>
              <s xml:id="N1C161" xml:space="preserve">Sequela tamen probatur: et capio duas la-<lb/>titudines vniformiter difformes equales extenſiue <lb/>et intenſiue omnino puta a quarto vſ ad non gra-<lb/>dum extenſas per duo pedalia gratia exempli: et vo­<lb/>lo /  in inſtanti a. ponatur vna potentia vt .8. in ex­               <pb chead="Primi tractatus" file="0125" n="125"/>               tremo intenſiori vnius et alia etiam vt .8. in extremo <lb/>intenſiori alterius: et moueantur ille potentie conti­<lb/>nuo verſus non gradum illarum latitudinum vna <lb/>illarum continuo quieſcente: et manente pedali: et <lb/>altera illarum continuo ſe cõdenſante ſubiecto eiꝰ <lb/>manente pedali: moueatur tamen punctus vt .4. in <lb/>latitudine que mouetur a minori ꝓportione ꝙ̄ ſit <lb/>proportio a qua potentia ſufficit moueri cum illo. <lb/></s>
              <s xml:id="N1C180" xml:space="preserve">Quo poſito ſic argumentor illa latitudo / que mo-<lb/>uetur continuo erit minor ꝙ̄ illa que quieſcit per to­<lb/>tum tempus motus: et tamen poña que mouetur in <lb/>illa tardius pertranſibit illam ꝙ̄ potentia que mo­<lb/>uetur in reſiſtentia maiori quieſcente: igitur. </s>
              <s xml:id="N1C18B" xml:space="preserve">Ma-<lb/>ior eſt nota ex caſu: et minor probatur / quia continuo <lb/>poña que mouetur cū reſiſtentia ſe condenſante mo­<lb/>uetur tardius ꝙ̄ potentia que mouetur cum alia re­<lb/>ſiſtentia quieſcente: et tandē per continuum motum <lb/>deuenient ad non gradum illarum reſiſtentiarum / <lb/>vt ponitur in caſu: igitur citius poña que mouetur ī <lb/>reſiſtentia quieſcente deueniet ad non gradum illi-<lb/>us reſiſtentie in qua mouetur ꝙ̄ poña que mouet̄̄ cū <lb/>reſiſtentia ſe condenſante. </s>
              <s xml:id="N1C1A0" xml:space="preserve">Conſequentia patet cuꝫ <lb/>minore: et maior probatur / quia illa potentia q̄ mo­<lb/>uet̄̄ cū reſiſtētia ſe ↄ̨denſãte in q̇libet pūcto medii pe­<lb/>dalis ꝑ qḋ extēdebat̄̄ illa reſiſtētia cū maiori reſiſtē­<lb/>tia mouetur quam alia potentia q̄ mouetur in reſi­<lb/>ſtentia quieſcente in conſimili puncto ſiue correſpõ­<lb/>dente: igitur illa poña que mouetur cum reſiſtentia <lb/>ſe condenſante continuo tardius mouetur quã alia <lb/>potentia que mouetur cum reſiſtentia quieſcente.</s>
            </p>
            <p xml:id="N1C1B3">
              <s xml:id="N1C1B4" xml:space="preserve">Conſequentia patet et arguitur antecedens: q2 con­<lb/>tinuo in quolibet puncto illius medii pedalis ꝑ qḋ <lb/>a principio extendebatur reſiſtentia ſe condenſans <lb/>eſt maior et maior reſiſtentia quovſ in illo puncto <lb/>nõ ſit aliq̈ reſiſtentia: et in quolibet puncto medii pe­<lb/>dalis / per quod extenditur reſiſtentia quieſcēs ma-<lb/>net eadem reſiſtentia continuo: igitur potentia que <lb/>mouetur cum reſiſtentia ſe condenſante in quolib3 <lb/>puncto medii pedalis / per quod extendebatur a prī­<lb/>cipio eadem reſiſtentia ſe condenſans cum maiori <lb/>reſiſtentia mouetur ꝙ̄ alia poña que mouetur cum <lb/>reſiſtentia quieſcente in conſimili puncto ſiue cor-<lb/>reſpondente: </s>
              <s xml:id="N1C1CF" xml:space="preserve">Patet conſequētia / quia in prīcipio <lb/>in punctis correſpondentibus illorum mediorum ē <lb/>eadem reſiſtentia omnino / vt patet: et maior proba­<lb/>tur / quia ex caſu continuo puncta intenſiora illiꝰ re­<lb/>ſiſtentie ſe condenſantis mouentur verſus pūcta re­<lb/>miſſiora eiuſdem reſiſtentie: igitur continuo in quo­<lb/>libet puncto medii pedalis / per quod in prīcipio ex­<lb/>tendebatur latitudo ſe condenſans eſt maior et ma­<lb/>ior reſiſtentia: dummodo in illo puncto ſit aliqua <lb/>reſiſtentia.</s>
            </p>
            <p xml:id="N1C1E4">
              <s xml:id="N1C1E5" xml:space="preserve">Reſpondeo concedendo quod infer-<lb/>tur et negando falſitatem conſequentis: et ad pro-<lb/>bationem concedo illud quod infertur / vt probat ar­<lb/>gumentum: </s>
              <s xml:id="N1C1EE" xml:space="preserve">Nec illud eſt inconueniens ſignanter <lb/>quando vna illarum latitudinum reſiſtentiaruꝫ ſic / <lb/>condenſatur vt ponitur in caſu argumenti et altera <lb/>quieſcit.               <anchor type="note" xlink:href="note-0125-01" xlink:label="note-0125-01a"/>               </s>
              <s xml:id="N1C1FC" xml:space="preserve">¶ Ex quo ſequitur primo:  ſtat eandē po-<lb/>tentiam velocius moueri continuo tranſeundo ali-<lb/>quam reſiſtentiam minus extenſam quam tranſeū­<lb/>do eandem magis extenſam. </s>
              <s xml:id="N1C205" xml:space="preserve">Probatur et capio / <lb/>duas latitudīes vniformiter difformes equales ex­<lb/>tenſiue et intenſiue omnino puta ab octauo vſ ad <lb/>quartum extenſas per duo pedalia exempli gratia / <lb/>et volo /  in eodem inſtanti ponatur vna potentia. <lb/></s>
              <s xml:id="N1C211" xml:space="preserve">vt .8. vel vt .10. (non eſt cura) in extremo remiſſiori               <cb chead="Capitulum quindecimum"/>               vnius: et alia ei equalis in extremo remiſſiori alte-<lb/>rius: et moueantur ille potentie continuo verſus ex­<lb/>tremum intenſius illarum latitudinum: vna illarū <lb/>continuo qnieſcente et manente pedali, et altera il-<lb/>larum continuo ſe condenſante (ſubiecto tñ eiꝰ ma­<lb/>nente pedali) verſus extremū ſui intēſius quieſcēs: <lb/>moueatur tamen punctat .4. in latitudine que con-<lb/>denſatur a minori proportione ꝙ̄ ſit ꝓportio a qua <lb/>potentia ſufficiat moueri cum illo. </s>
              <s xml:id="N1C227" xml:space="preserve">Quo poſito ſic <lb/>argumentor illa latitudo / que mouetur cõtinuo erit <lb/>minor ꝙ̄ illa que quieſcit: et poña que mouetur cum <lb/>illa velocius mouetur illam reſiſtentiam tranſeun-<lb/>do quam potentia que mouetur in reſiſtentia ſibi <lb/>equali quieſcente: igitur correlarium verum. </s>
              <s xml:id="N1C234" xml:space="preserve">Ma-<lb/>ior eſt nota ex caſu et minor probatur: quia potētia <lb/>que mouetur cum reſiſtentia ſe condenſante in quo­<lb/>libet puncto medii pedalis per qḋ in prīcipio extē­<lb/>debat illa reſiſtētia cū mīori reſiſtētia mouet̄̄ ꝙ̄ alia <lb/>poña q̄ mouetur in reſiſtetia q̇eſcente in cõſimili pū­<lb/>cto ſiue correſpondente: igitur illa potentia q̄ mo-<lb/>uetur cum reſiſtentia ſe condenſante velocius moue­<lb/>tur ꝙ̄ alia potentia que mouetur cum reſiſtentia q̇e­<lb/>ſcente. </s>
              <s xml:id="N1C249" xml:space="preserve">Conſequentia patet / et arguitur antecedens / <lb/>quia continuo in quolibet puncto illius medii pe-<lb/>dalis / per quod in principio extendebatur reſiſten-<lb/>tia ſe condenſaus eſt minor et minor reſiſtentia: cum <lb/>ex caſu continuo puncta remiſſiora illius reſiſtētie <lb/>ſe condenſantis moueantur verſus puncta intenſio­<lb/>ra et extremum intenſius eiuſdem reſiſtentie: et ī quo­<lb/>libet puncto medii pedalis / per quod extenditur re­<lb/>ſiſtentia quieſcens manet eadem reſiſtentia vtpote <lb/>que erat in illo in principio: igitur poña que moue-<lb/>tur cum reſiſtentia ſe condenſante in quolibet pun-<lb/>cto medii pedalis / per quod extendebatur in princi­<lb/>pio eadem reſiſtentia ſe condenſans cum minori re­<lb/>ſiſtentia mouetur quam alia potentia que moue-<lb/>tur cum reſiſtentia quieſcente in conſimili puncto ſi­<lb/>ue correſpondente. </s>
              <s xml:id="N1C26A" xml:space="preserve">Conſequentia patet / quia in prī­<lb/>cipio in punctis correſpondentibus illoruꝫ medio­<lb/>rum eſt eadem reſiſtentia omnino. </s>
              <s xml:id="N1C271" xml:space="preserve">Q, ſi volueris <lb/>demonſtrare ipſam poñam cum reſiſtentia ſe con-<lb/>denſate continuo velocius moueri: ideo modo pro­<lb/>bes quo probabitur ſequens correlarium. </s>
              <s xml:id="N1C27A" xml:space="preserve">Patet <lb/>igitur correlarium.               <anchor type="note" xlink:href="note-0125-02" xlink:label="note-0125-02a"/>               </s>
              <s xml:id="N1C284" xml:space="preserve">¶ Sequit̄̄ ſecundo /  datis dua­<lb/>bus latitudinibus vniformiter difformibus equa-<lb/>libus intenſiue et inequalibꝰ extenſiue: et captis dua­<lb/>bus potentiis equalibus quarum vna incipit mo-<lb/>ueri per minus extenſam et altera per magis extēſã <lb/>ab extrēo remiſſiori: q̇eſcētibꝰ ↄ̨tinuo latitudinibꝰ: <lb/>potentiis non variatis: poña que mouetur cum re-<lb/>ſiſtentia minus extenſa tardius continuo mouetur <lb/>quam altera que mouebitur cum reſiſtentia magis <lb/>extenſa. </s>
              <s xml:id="N1C299" xml:space="preserve">Probatur. </s>
              <s xml:id="N1C29C" xml:space="preserve">Sit a. potentia que mouetur <lb/>cum reſiſtentia magis extenſa: et b. cum reſiſtentia <lb/>minus extenſa </s>
              <s xml:id="N1C2A3" xml:space="preserve">Tunc dico /  b. continuo mouetur <lb/>tardius ip̄a a. potentia. </s>
              <s xml:id="N1C2A8" xml:space="preserve">Quod ſic oſtenditur: quia <lb/>b. non continuo mouetur velocius ꝙ̄ a. </s>
              <s xml:id="N1C2AD" xml:space="preserve">Nec per <lb/>aliquod tempus mouetur equeuelociter: </s>
              <s xml:id="N1C2B2" xml:space="preserve">Nec ꝑ ali-<lb/>quod tempus mouetur velocius et immediate ante <lb/>mouetur per aliquod tempus tardius: </s>
              <s xml:id="N1C2B9" xml:space="preserve">Nec ecõtra / <lb/>ergo continuo b. mouetur tardius ipſa potentia a. / <lb/>quod fuit probandum. </s>
              <s xml:id="N1C2C0" xml:space="preserve">Conſequentia eſt nota. </s>
              <s xml:id="N1C2C3" xml:space="preserve">Et <lb/>probatur maior: vcꝫ /  b. non continuo mouetur ve­<lb/>locius quam a. quia ſi continuo mouetur velocius <lb/>quam a. / ſequitur /  continuo b. eſt in puncto magis <lb/>diſtante a principio ſui medii ꝙ̄ a. </s>
              <s xml:id="N1C2CE" xml:space="preserve">Et per conſeq̄ns <lb/>ſequitur /  continuo eſt in maiori reſiſtentia: et con­<lb/>tinuo mouetur tardius: quod eſt oppoſitum dati.</s>
            </p>
            <div xml:id="N1C2D5" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0125-01a" xlink:label="note-0125-01" xml:id="N1C2D9" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0125-02a" xlink:label="note-0125-02" xml:id="N1C2DF" xml:space="preserve">.2correl.</note>
            </div>
            <pb chead="De motu quo ad cauſã in medio non reſiſtente." file="0126" n="126"/>
            <p xml:id="N1C2E9">
              <s xml:id="N1C2EA" xml:space="preserve">quod etiam probare intēdimus. </s>
              <s xml:id="N1C2ED" xml:space="preserve">Iam probatur pri­<lb/>ma pars minoris: videlicet /  non per aliquod tem­<lb/>pus mouetur eque velociter: quia ſi ſic capio inſtãs <lb/>initiatiuum talis temporis: in quo (vt oportet ꝑ te) <lb/>a. et b. ſunt inequalibus reſiſtentiis: </s>
              <s xml:id="N1C2F8" xml:space="preserve">Et arguo ſic / ꝑ <lb/>aliqḋ tempus poſt tale inſtans b. poña ↄ̨tinuo mo­<lb/>uetur eque velociter ſicut a. per te: ergo cõtinuo ꝑ il­<lb/>lud tempus b. poña eſt in puncto equaliter diſtante <lb/>a pūcto in quo ipſa eſt in principio talis temporis <lb/>ſicut a. potentia ab eque reſiſtēte puncto in ſuo ma­<lb/>iori medio ſiue reſiſtentia magis extenſa: et quilib3 <lb/>punctus eq̈liter diſtans a pūcto ↄ̨ſimilis intēſiõis <lb/>in minori medio et in maiori: ī mīori ſiue ī reſiſtētia <lb/>minus extenſa eſt intenſior puncto ſibi correſꝑõdē­<lb/>te in reſiſtentia magis extenſa / vt patet: ergo per il­<lb/>lud tempus continuo b. eſt in maiori reſiſtentia: et ꝑ <lb/>conſequens continuo mouetur tardius: et non eque­<lb/>velociter / quod probare intendimus. </s>
              <s xml:id="N1C315" xml:space="preserve">Pro-<lb/>batur ſecunda pars minoris: videlicet /  non per <lb/>aliquod tempus mouetur velocius: et īmediate poſt <lb/>etc. / quia ſi ſic ſignetur inſtans / in quo b. incipit mo-<lb/>ueri per aliquod tempus velocius ante quod īmedi­<lb/>ate continuo per aliquod tempus tardius moueba­<lb/>tur. </s>
              <s xml:id="N1C324" xml:space="preserve">Et ſequitur /  in tali inſtanti a. et b. habēt equa­<lb/>les proportiones ad puncta in quibus ſunt quia ſi <lb/>b. habeat maiorem ſequitur /  īmediate antea ha-<lb/>bebat maiorem, et ſic non īmediate antea mouebat̄̄ <lb/>tardius ꝙ̄ a. / et ſi minorem ſequitur /  īmediate poſt <lb/>illud inſtans datum mouetur tardius et ſic non tūc <lb/>incipit velocius moueri ꝙ̄ a. </s>
              <s xml:id="N1C333" xml:space="preserve">Tunc igitur ſic arguo / <lb/>a. et b. in inſtanti dato ſunt ad puncta eque intenſa <lb/>et b. incipit continuo velocius moueri recedendo a <lb/>ſuo puncto ꝙ̄ a. / ergo b. incipit continuo magis di-<lb/>ſtare ab illo puncto ꝙ̄ a. a conſimili: et per conſeq̄ns <lb/>īcipit continuo eſſe in maiori reſiſtentia quã a. / et ex <lb/>hoc ſeq̇tur incipit continuo tardius moueri et non <lb/>velocius / quod eſt oppoſitum dati. </s>
              <s xml:id="N1C344" xml:space="preserve">Sed probatur <lb/>tertia pars minoris videlicet /  non per aliquod <lb/>tempus b. potentia velocius mouetur et immediate <lb/>poſt continuo per aliquod tempus tardius moue-<lb/>tur: quia ſi ſic. </s>
              <s xml:id="N1C34F" xml:space="preserve">Capio inſtans / in quo b. incipit mo-<lb/>ueri tardius quã a. per aliquod tempꝰ īmediate an­<lb/>te quod per aliquod tempus continuo velociꝰ mo-<lb/>uebatur quã a. </s>
              <s xml:id="N1C358" xml:space="preserve">Et arguo ſic / vel continuo ante illud <lb/>inſtans b. mouetur velocius quã a. vel aliquando <lb/>tardius et īmediate poſt velocius: </s>
              <s xml:id="N1C35F" xml:space="preserve">Sed neutrū iſtoꝝ <lb/>eſt dicendum: ergo non per aliquod tempus b. potē­<lb/>tia velocius mouetur et īmediate poſt per aliquod <lb/>tewpus continuo tardius mouetur. </s>
              <s xml:id="N1C368" xml:space="preserve">Patet conſeq̄n­<lb/>tia / quia b. nū̄ eque velociter mouetur ſicut a. ex ṗ-<lb/>ma parte minoris </s>
              <s xml:id="N1C36F" xml:space="preserve">Sed probatur minor / quia nõ ē <lb/>dicendum primum / vt patet ex maiore: nec ſecunduꝫ / <lb/>vt patet ex ſecunda parte minoris: ergo propoſitū <lb/></s>
              <s xml:id="N1C377" xml:space="preserve">Et ſic patet tota minor et per conſequens correla-<lb/>rium / quod fuit ꝓbandum.               <anchor type="note" xlink:href="note-0126-01" xlink:label="note-0126-01a"/>               </s>
              <s xml:id="N1C381" xml:space="preserve">¶ Sequitur tertio /  vbi­<lb/>cun in latitudinibus ſic vniformiter difformibus <lb/>equalibus intenſiue et inequalibus extenſiue / vt po-<lb/>nitur in caſu precedentis correlarii alique potentie <lb/>incipiunt moueri procedendo ab extremis remiſſio­<lb/>ribus: poña que mouetur in reſiſtentia minus exten­<lb/>ſa ſemper citius deueniet ad finem ſue reſiſtentie</s>
            </p>
            <div xml:id="N1C390" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0126-01a" xlink:label="note-0126-01" xml:id="N1C394" xml:space="preserve">3. correl.</note>
            </div>
            <p xml:id="N1C39A">
              <s xml:id="N1C39B" xml:space="preserve">Hoc eſt citius pertranſibit totam ſuam reſiſtentiaꝫ <lb/>quam altera pertranſeat ſuam reſiſtentiam magis <lb/>extenſam ̄uis ipſa tardius continuo moueant̄̄ eã <lb/>adequate pertranſeundo. </s>
              <s xml:id="N1C3A4" xml:space="preserve">Probatur correlarium / <lb/>qui potentia que mouetur cum reſiſtentia minꝰ ex­<lb/>tenſa continuo mouetur tardius ex precedenti cor-<lb/>relario. </s>
              <s xml:id="N1C3AD" xml:space="preserve">igitur continuo eſt in intenſiori reſiſtentia: <lb/>et continuo citius deueniet ad aliquem punctum re­               <cb chead="De motu quo ad cauſã in medio non reſiſtente."/>               ſiſtentie quam poña que mouetur in reſiſtentia ma­<lb/>gis extenſa deueniat ad conſimile punctum. </s>
              <s xml:id="N1C3B7" xml:space="preserve">Conſe­<lb/>quentia patet ex probatione precedentis correlarii / <lb/>et per conſequens citius deueniet ad punctum extre­<lb/>mum reſiſtentie minus extenſe ꝙ̄ poña ei equalis de­<lb/>ueniat ad idem punctum in reſiſtentia magis exten­<lb/>ſa et ex hoc citius pertranſibit illam / quod fuit pro-<lb/>bandum.               <anchor type="note" xlink:href="note-0126-02" xlink:label="note-0126-02a"/>               </s>
              <s xml:id="N1C3CB" xml:space="preserve">¶ Sequitur quarto /  datis duabus lati­<lb/>tudinibus reſiſtentie vniformiter difformis equali­<lb/>bus intenſiue: et inequalibus extenſiue: et captis dua­<lb/>bus potentiis equalibus quarum vna incipit mo-<lb/>ueri per minus extenſam: et altera per magis exten­<lb/>ſam ab extremo intenſiori quieſcentibus continuo <lb/>latitudinibus et potentiis non variatis: poña que <lb/>mouetur cuꝫ reſiſtentia minus extenſa continuo ve­<lb/>locius mouetur quã altera que mouetur cum reſiſtē­<lb/>tia magis extenſa: </s>
              <s xml:id="N1C3E0" xml:space="preserve">Hoc correlariuꝫ facile ex proba­<lb/>tione precedentis demonſtratur: hoc premiſſo /  oī­<lb/>um punctorum equaliter diſtantium in illis latitu-<lb/>dinibus ab extremo intenſiori punctus in latitudi­<lb/>ne minus extenſa minus reſiſtit ꝙ̄ punctus ſibi cor­<lb/>reſpondens in latitudine magis extenſa </s>
              <s xml:id="N1C3ED" xml:space="preserve">Quod pa­<lb/>tet intuenti.               <anchor type="note" xlink:href="note-0126-03" xlink:label="note-0126-03a"/>               </s>
              <s xml:id="N1C3F7" xml:space="preserve">¶ Sequitur quinto /  latitudine reſiſtē­<lb/>tie vniformiter difformi ſic ſe condenſante / vt po-<lb/>nitur in caſu argumenti: quolibet eius puncto ītrin­<lb/>ſeco continuo vniformiter mouente, quieſcente gra­<lb/>du remiſſiori: et intenſiori tardius mouente quã po­<lb/>tentia que incipit moueri cum illo mouetur cum eo­<lb/>dem, potentia et omni pūcto verſus intenſius extre­<lb/>mum quieſcens mouentibus: omnis talis poña que <lb/>ſic mouetur continuo intendit motum ſuum. </s>
              <s xml:id="N1C40A" xml:space="preserve">Pro-<lb/>batur / quia talis poña continuo velocius mouetur <lb/>quã punctus in quo pro tunc eſt: et continuo moue-<lb/>tur verſus minorem reſiſtentiam: igitur propoſitū <lb/></s>
              <s xml:id="N1C414" xml:space="preserve">Conſequentia patet cum minori ex caſu: et maior ꝓ­<lb/>batur / quia talis potentia velocius mouetur quam <lb/>punctus velociſſime motus / vt patet ex caſu: ergo ̄­<lb/>quicun alter eiuſdem latitudinis </s>
              <s xml:id="N1C41D" xml:space="preserve">Patet con-<lb/>ſequentia / quia quilibet aliorum qui mouetur tar-<lb/>dius mouetur: et ad ipſum habet potentia maioreꝫ <lb/>proportionem / igitur etc.               <anchor type="note" xlink:href="note-0126-04" xlink:label="note-0126-04a"/>               </s>
              <s xml:id="N1C42B" xml:space="preserve">¶ Sequitur ſexto /  ſi q̇li­<lb/>bet punctus intrinſecus talis reſiſtentie ↄ̨tinuo mo­<lb/>ueretur verſus extremum remiſſius quieſcens: conti­<lb/>nuo remittendo motum ſuum: potentia etiam con-<lb/>tinuo intenderet motum ſuuꝫ: dūmodo incipiat po­<lb/>tentia velocius moueri ꝙ̄ punctus qui velociſſime <lb/>mouetur. </s>
              <s xml:id="N1C43A" xml:space="preserve">Patet hoc correlarium ex precedenti iun­<lb/>cto loco a fortiori.               <anchor type="note" xlink:href="note-0126-05" xlink:label="note-0126-05a"/>               </s>
              <s xml:id="N1C444" xml:space="preserve">¶ Sequitur ſeptimo /  latitudi-<lb/>ne reſiſtentie vniformiter difformis ſic ſe condenſã­<lb/>te: vt poſitum eſt quolibet puncto eius intrinſeco cõ­<lb/>tinuo ſucceſſiue intendente motum ſuum, et potētia <lb/>velocius incipiat moueri a puncto velociſſime mo-<lb/>to quã talis punctus incipit moueri: ipſis mouen-<lb/>tibus verſus extremum remiſſius / non oportet /  <lb/>talis potentia continuo intendat motum ſuum: nec <lb/>oportet /  continuo remittat motū ſuum / nec opor­<lb/>tet /  aliquando intendat et aliquando remittat: ſꝫ <lb/>poteſt aliquando intendere, et aliquando remitte-<lb/>rē: oportet tamen /  incipiat intendere. </s>
              <s xml:id="N1C45D" xml:space="preserve">Probatur <lb/>quia caſu poſito /  ſit vna latitudo r̄ſiſtētie ab octa­<lb/>uo vſ ad non gradum: et incipiat poña vt .12. mo-<lb/>ueri cum illa ſe condenſante / vt poſitum eſt: quoli-<lb/>bet puncto intrinſeco continuo intendente motum <lb/>ſuum taliter  quando poña deuenerit ad punctuꝫ <lb/>vt ſex / tunc primo punctum vt ſex incipiat moueri a <lb/>proportione dupla. / et iam ſequitur (cum ille pūctus <lb/>continuo intendat motum ſum) /  poña non ſufficit <lb/>ipſum precedere: ſed ipſe precedet potentiam: et ſic <lb/>poña manebit cum intenſiori reſiſtentia et remittit               <pb chead="Primi tractatus" file="0127" n="127"/>               motum ſuum. </s>
              <s xml:id="N1C479" xml:space="preserve">Et ſic iam patet /  non oportet /  ſem­<lb/>per intendat nec  ſemper remittat </s>
              <s xml:id="N1C47E" xml:space="preserve">Sed  nõ opor­<lb/>tet  aliquado intendat: et aliquando remittat pa­<lb/>tet, ponēdo /  nū̄ punctus vt ſex moueatur a pro-<lb/>portione dupla īmo ſemper a minori imo  maxi-<lb/>ma proportio a qua mouebitur punctus vt .8. ſit mi­<lb/>nor ſexquialtera continuo tamen moueatur a ma-<lb/>iori et maiori. </s>
              <s xml:id="N1C48D" xml:space="preserve">Quo poſito iam patet /  poña conti­<lb/>nuo intendit motum ſuum. </s>
              <s xml:id="N1C492" xml:space="preserve">Ultima vero pars cor-<lb/>relarii patet ex caſu correlarii. </s>
              <s xml:id="N1C497" xml:space="preserve">¶ Illam tamen par­<lb/>ticulam que dicit /  aliquando poteſt intendere et <lb/>aliquaudo remittere tan̄ probaliter poſitã re-<lb/>linquo </s>
              <s xml:id="N1C4A0" xml:space="preserve">Non enim eam ſufficienter demonſtraui / q2 <lb/>non probo poſſibilitatem caſus / in quo illam dico <lb/>eſſe veram </s>
              <s xml:id="N1C4A7" xml:space="preserve">Diſcutiat igitur eam alter.</s>
            </p>
            <div xml:id="N1C4AA" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0126-02a" xlink:label="note-0126-02" xml:id="N1C4AE" xml:space="preserve">4. correl.</note>
              <note position="right" xlink:href="note-0126-03a" xlink:label="note-0126-03" xml:id="N1C4B4" xml:space="preserve">5. correl.</note>
              <note position="right" xlink:href="note-0126-04a" xlink:label="note-0126-04" xml:id="N1C4BA" xml:space="preserve">6. correl.</note>
              <note position="right" xlink:href="note-0126-05a" xlink:label="note-0126-05" xml:id="N1C4C0" xml:space="preserve">7. correl.</note>
            </div>
            <note position="left" xml:id="N1C4C6" xml:space="preserve">8. correl.</note>
            <p xml:id="N1C4CA">
              <s xml:id="N1C4CB" xml:space="preserve">¶ Sequitur octauo /  latitudine reſiſtentie vnifor-<lb/>miter difformis ſic ſe condenſante ſubiecto eius q̇e­<lb/>ſcente et quolibet puncto illius dempto remiſſiori <lb/>continuo mouente vniformiter: potentia incipiens <lb/>moueri ab extremo intenſiori verſus remiſſius ve-<lb/>locius et velocius intendit motum ſuum: dummodo <lb/>velocius incipiat moueri quã gradus a quo īcipit <lb/>moueri moueatur. </s>
              <s xml:id="N1C4DC" xml:space="preserve">Probatur correlarium / quia di­<lb/>diuiſo totali tempore in quo pertinget extremū re­<lb/>miſſius in duas partes equales manifeſtum eſt /  <lb/>plus reſtabit tranſeundum de reſiſtentia in ſecūda <lb/>medietate quã pertranſitum ſit quia plus reſtabit <lb/>de ſubiecto pertranſeundum quã pertranſitum. </s>
              <s xml:id="N1C4E9" xml:space="preserve">igi­<lb/>tur plus de reſiſtentia. </s>
              <s xml:id="N1C4EE" xml:space="preserve">Probatur antecedens / quia <lb/>in prima medietate illius temporis potentia nõ de­<lb/>ueniet ad medium illius ſubiecti: et per conſeq̄ns nec <lb/>ad medium illius reſiſtentie cum medium illius reſi­<lb/>ſtentie iam ſit vltra medium illius ſubiecti: igitur <lb/>plus tam de ſubiecto quã de reſiſtentia reſtabit trã­<lb/>ſeundum in ſecunda medietate quã in prima. </s>
              <s xml:id="N1C4FD" xml:space="preserve">Pa-<lb/>tet antecedens clare / q2 velocius talis poña moue-<lb/>bitur in ſecunda medietate quã in prima: ergo plus <lb/>pertranſibit in ſecunda quam in prima: et ſic in pri­<lb/>ma non pertranſibit medietatem </s>
              <s xml:id="N1C508" xml:space="preserve">Et ſic probabi-<lb/>tur diuiſa ſecūda medietate in duas partes equa-<lb/>les  plus pertranſeundum eſt in ſecunda quã per­<lb/>tranſitur in prima. </s>
              <s xml:id="N1C511" xml:space="preserve">Et iterum illa in duas / et ſic con­<lb/>ſequenter velocius in quolibet tēpore ſequenti quã <lb/>in precedenti: et ſic velocius ꝓportionabiliter ſibi <lb/>decreſcit reſiſtentia in ſecunda medietate quam in <lb/>prima / vt patet intuenti cunabula huius materie: et <lb/>per conſequens velocius et velocius intendit motū <lb/>ſuum / qund fuit probandum.               <anchor type="note" xlink:href="note-0127-01" xlink:label="note-0127-01a"/>               </s>
              <s xml:id="N1C525" xml:space="preserve">¶ Sequitur nono /  <lb/>vbicun poña in latitudine ſic cõdenſante cõtinuo <lb/>intendit motum ſuum, ſiue quolibet puncto qui mo­<lb/>uetur mouente vniformiter: ſiue continuo remitten­<lb/>te: ſiue intendente talis poña velocius et velocius in­<lb/>tendit motum ſuum. </s>
              <s xml:id="N1C532" xml:space="preserve">Patet correlarium ex dictis. <lb/>               <anchor type="note" xlink:href="note-0127-02" xlink:label="note-0127-02a"/>               </s>
              <s xml:id="N1C53C" xml:space="preserve">¶ Sequitur decimo /  vbicū extremum intenſius <lb/>quieſcit quolibet puncto alio continuo vniformiter <lb/>mouente et condenſante: poña incipiens velociꝰ mo­<lb/>ueri quam extremū remiſſius a quo incipit mouea­<lb/>tur mouendo verſus extremnm intenſius continuo <lb/>remittit motum ſuum dūmodo nullum punctuꝫ ita <lb/>velociter moueatur ſicut poña ſufficit moueri cū il-<lb/>lo imo tardius </s>
              <s xml:id="N1C54D" xml:space="preserve">Correlarium hoc facile patet intel-<lb/>ligenti ea que dicta ſunt. </s>
              <s xml:id="N1C552" xml:space="preserve">¶ Cir materiam huiꝰ ar-<lb/>gumenti poſſent multc alie concluſiones induci po­<lb/>nendo  extremū intenſius quieſcat et verſus illud <lb/>continuo alia puncta condenſentur:  aliquando <lb/>condenſentur: et aliquando rarefiant: et quando <lb/>vniformiter: quando tardius et tardius qñ ve-<lb/>locius et velocius. </s>
              <s xml:id="N1C561" xml:space="preserve">Sed q2 ex dictis facile tales con­<lb/>cluſiones poſſent induci ideo ſuperſedeo.</s>
            </p>
            <div xml:id="N1C566" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0127-01a" xlink:label="note-0127-01" xml:id="N1C56A" xml:space="preserve">.9 correl.</note>
              <note position="left" xlink:href="note-0127-02a" xlink:label="note-0127-02" xml:id="N1C570" xml:space="preserve">10. corre.</note>
            </div>
            <cb chead="Capitulum quindecimum"/>
            <p xml:id="N1C578">
              <s xml:id="N1C579" xml:space="preserve">Tertio contra primam concluſionem <lb/>quartidecimi capitis arguitur ſic argumento cal-<lb/>culatorio. </s>
              <s xml:id="N1C580" xml:space="preserve">Quia aliquando in caſu illius concluſio­<lb/>nis poña non mouetur vniformiter / igitur concluſio <lb/>falſa. </s>
              <s xml:id="N1C587" xml:space="preserve">Probatur antecedens / et pono /  poña vt .8. q̄ <lb/>ſit a. incipiat moueri cuꝫ latitudine reſiſtentie vni­<lb/>formiter defformis a non gradu vſ ad octauū / vt <lb/>ponitur in caſu illius cõcluſionis: et ſit mediū ī quo <lb/>adequate illa latitudo extenditur a non quanto b. / <lb/>et ſint infinita media equalia ipſi b. / et per primã me­<lb/>dietatem primi adequate ſit extenſa illa latitudo q̄ <lb/>extenditur a non quanto in b. / et in ſecundo medio il­<lb/>lorum ſit extenſa eadem latitudo in duplo minori <lb/>parte adequate / et in tertio in quadruplo minori / et <lb/>in quarto in octuplo minori / et ſic conſequenter / et in <lb/>inſtanti in quo incipit poña vt 8. moueri ī b. medio <lb/>cum latitudine progrediente a non quanto in quo-<lb/>libet aliorum mediorum incipiat moueri poña eq̄-<lb/>lis ipſi potentie vt: 8. ipſa latitudine in quolibet il­<lb/>lorum mediorū continuo acquirendo equalem quã­<lb/>titatem quantitati quam acquirit eadem latitudo <lb/>in b. / ita  quilibet punctus in quolibet illorum me­<lb/>diorum moueatur equaliter in vno ſicut in altero et <lb/>ſicut in b. </s>
              <s xml:id="N1C5B0" xml:space="preserve">Quo poſito arguitur ſic / īmediate pꝰ hoc <lb/>demonſtrato inſtanti īitiatiuo motus in infinitum <lb/>tarde in equali tempore mouebit̄̄ aliquod illorum <lb/>mobiliū et tardius a. poña in b. medio quã aliquod <lb/>illorū: ergo in infinitū tarde incipit a. moueri: et per <lb/>conſequens nõ vniformiter: et ſic cõcluſio falſa. </s>
              <s xml:id="N1C5BD" xml:space="preserve">Cõ­<lb/>ſequentia patet / et probat̄̄ maior / q2 īmediate pꝰ hoc <lb/>inſtans in equali tempore infinite modicum ſpaciū <lb/>pertranſibit aliquod iſtorum mobilium. </s>
              <s xml:id="N1C5C6" xml:space="preserve">ergo īme-<lb/>diate poſt hoc inſtãs in equali tempore in infinitum <lb/>tarde meubit̄̄ aliquod illorū mobiliū in aliquo il­<lb/>lorū mediorū. </s>
              <s xml:id="N1C5CF" xml:space="preserve">Conſequentia eſt nota, et antecedens <lb/>probatur / q2 īmediate poſt hoc inſtans in equali tē­<lb/>pore in infinitū modicū ē aliquod illorū medioruꝫ: <lb/>et nullum illorum poña ſufficit pertranſire cum ha­<lb/>beat ad extremum eius ꝓportionem equalitates: <lb/>ergo īmediate poſt hoc inſtans initiatiuū in equali <lb/>tempore in infinitum modicū ſpacium pertranſibit <lb/>aliquod illorum infinitorū mobilium. </s>
              <s xml:id="N1C5E0" xml:space="preserve">Conſequen-<lb/>tia patet / q2 ſi in infinite modico ſpacio mouetur ali­<lb/>quod illorum: in infinitum modicum ſpacium per-<lb/>tranſit. </s>
              <s xml:id="N1C5E9" xml:space="preserve">Sed minor videlicet /  a. tardius mouetur <lb/>quã aliqḋ illorū infinitoꝝ mobiliū </s>
              <s xml:id="N1C5EE" xml:space="preserve">Probatur / quia <lb/>a. continuo eſt in minus extenſa reſiſtentia equali ī­<lb/>tenſiue reſiſtentie in qua mouetur quodlibet alterū / <lb/>igitur continuo tardius mouetur </s>
              <s xml:id="N1C5F7" xml:space="preserve">Patet conſeqnē­<lb/>tia ex ſecundo correlario ſexte concluſionis prece-<lb/>dentis capitis. </s>
              <s xml:id="N1C5FE" xml:space="preserve">¶ Et confirmatur etiam / q2 ſi a. equa­<lb/>liter vel velociꝰ continuo mouet̄̄ ipſū eſſet ↄ̨tinuo in­<lb/>equali vel mininori teſiſtentia: ſed quelibet equalis <lb/>vel minor reſiſtentia in latitudine in qua mouetur <lb/>a. minus diſtat a puncto initiatiuo motus quã con­<lb/>ſimilis diſtet in aliquo aliorum mediorum in quoꝝ <lb/>quolibet eſt magis extenſa ipſa latitudo: igitur ſi <lb/>continuo a. eſt in minori reſiſtentia vel inequali ip̄a <lb/>poña a. continuo eſt propinquior puncto initiati-<lb/>uo motus / et per conſequens tardius continuo mo-<lb/>uetur </s>
              <s xml:id="N1C615" xml:space="preserve">Et ſic ſi mouet̄̄ equaliter vel velocius ſeq̇tur /  <lb/>continuo tardius mouetur.</s>
            </p>
            <p xml:id="N1C61A">
              <s xml:id="N1C61B" xml:space="preserve">Reſpondeo negando antecedens /  ad <lb/>probationem admiſſo caſu concedendo minorē / q2 <lb/>argumentum bene probat eam concedendam / et ne­<lb/>go maiorem / et ad probarionem nego /  immediate <lb/>poſt hoc demonſtrato inſtanti initiatiuo motus in <lb/>infinitum tarde moueatnr aliquod illorum / et ad ꝓ-               <pb chead="De motu quo ad cauſam in medio nõ reſiſtente." file="0128" n="128"/>               bationē negãdo añs vcꝫ  īmediate poſt hoc in eq̈li <lb/>tēpore in īfinitū paruū ſpaciū ꝑtranſibit aliqḋ illo­<lb/>rum mobiliū equaliū ipſi a. et cū ꝓbat̄̄ / q2 īmediate <lb/>poſt hoc in aliquo tꝑe in īfinitū modicū erit mediū <lb/>in quo mouet̄̄ aliqḋ illoꝝ nego illud: īmo quocnu <lb/>tꝑe dato poſt hoc in illo latitudo in qua mouet̄̄ a. <lb/>erit extēſa per aliquã partē medii: et in eodē tēpore <lb/>ꝑ maiorē partē medii erit extenſa eadē latitudo iu <lb/>quolibet alioꝝ medioꝝ / vt ptꝫ ex caſu: qm̄ quantãcū­<lb/> extenſionē acquirit illa latitudo in medio b. in q̊ <lb/>mouetur a. tantã adequate in eodē tēpore acquirit <lb/>eadē latitudo in quolibet alioꝝ medioꝝ ſupra extē­<lb/>ſionē quã iam habet in quolibet illoꝝ: et ſic cõtinuo <lb/>in quolibet alioꝝ medioꝝ erit magis extēſa illa la­<lb/>titudo quã in b. medio in quo mouetur a.</s>
            </p>
            <p xml:id="N1C649">
              <s xml:id="N1C64A" xml:space="preserve">Sed contra / q2 ſi latitudo in quolibet <lb/>illoꝝ medioꝝ a b. ſtaret tūc in infinitū tarde moue-<lb/>tur aliquod illoꝝ mobiliū in aliquo illoꝝ mediorū <lb/>in aliquo tempore poſt inſtans initiatiuū motus / et <lb/>tunc a. moueretur adhuc quolibet illoꝝ tardiꝰ: igr̄ <lb/></s>
              <s xml:id="N1C656" xml:space="preserve">Maior ꝓbato eſt ſuperius / qm̄ īmedietate poſt in-<lb/>ſtans initiatiuū motus in equali tēpore in infinitū <lb/>modicū erit ſpaciū pertranſitū ab aliquo illoꝝ cū <lb/>in infinitū modicū ſit aliquod illoꝝ mediorū. </s>
              <s xml:id="N1C65F" xml:space="preserve">Sed <lb/>iam ꝓbatur minor / q2 quãdo ille latitudines mouē­<lb/>tur in illis mediis / vt poſitū eſt in argumento a. mo­<lb/>uetur quolibet illoꝝ mobiliū tardius / vt ptꝫ ex ar-<lb/>gumento et in nulla ꝓportione incipit aliquod illo­<lb/>rum mobiliū velocius moueri mouente latitudine <lb/>quã quieſcente: ergo a. quolibet illoꝝ medioꝝ quie-<lb/>ſcente et latitudine in eis ſimiliter incipit quolibet <lb/>illoꝝ tardius moueri. </s>
              <s xml:id="N1C672" xml:space="preserve">Minor ꝓbatur / quia ſi nõ de­<lb/>tur aliquod illoꝝ quod ſit d. quod in aliqua ꝓpor-<lb/>tione puta dupla incipiat velocius moueri latitu-<lb/>dine mota quã latitudine quieſcente / et arguitur ſic / <lb/>d. in duplo velociꝰ incipit moueri latitudine ſic mo­<lb/>uente / vt ponitur in caſu argumenti quã ſic quieſcē­<lb/>te, ponatur igitur /  incipiat moueri ſimul in quie­<lb/>ſcente latitudine et in mouente: et arguitur ſic / in du­<lb/>plo velocius per te incipit moueri d. in latitudine <lb/>mouente quã quieſcente: ergo immediate poſt hoc <lb/>demonſtrato inſtanti initiatiuo motus d. in latitu­<lb/>dine mota in duplo plus diſtabit a puncto initia-<lb/>tiuo motus quã in latitudine non mota et erit in la­<lb/>titudine mota in puncto in duplo remiſſiori: et in <lb/>latitudine non mota in puncto in dnplo intenſiori / <lb/>igitur īmediate poſt hoc latitudo mota erit in du-<lb/>plo maior in loco vbi mouetur quã in loco vbi quie­<lb/>ſcit: ſed conſequens eſt falſum / quia ſucceſſiue in ca­<lb/>ſu ſit extenſior vbi mouetur quã eſt in loco vbi quie-<lb/>ſcit / vt ponitur igitur. </s>
              <s xml:id="N1C69B" xml:space="preserve">Ultima conſequentia proba­<lb/>tur / quia ſi tantum diſtaret a puncto initiatiuo mo­<lb/>tus in latitudine non mota punctus in quo poten-<lb/>tia eſt in inſtanti in quo ſic mouetur in duplo tar-<lb/>dius quantum diſtat punctus ſubduplus in quo eſt <lb/>potentia in latitudine mota: manifeſtum eſt /  illa <lb/>latitudo mota eſſet in duplo extenſior latitudine <lb/>quieſcente in loco in quo quieſcit: quia tantum di-<lb/>ſtaret in latitudine mota aliquis punctus ab extre­<lb/>mo remiſſiori quantum duplus punctus diſtaret in <lb/>latitudine non mota: et ſic manifeſtum eſt /  in loco <lb/>in quo mouetur eſt in duplo extēſior quã in loco in <lb/>quo quieſcit. </s>
              <s xml:id="N1C6B6" xml:space="preserve">Et ſic probabitur quacun alia pro-<lb/>portione data /  īmediate poſt hoc in eadem pro-<lb/>portione latitudo in quo mouetur erit maior lati-<lb/>tudine vbi quieſcit. </s>
              <s xml:id="N1C6BF" xml:space="preserve">Dico in eadē vel maiori: et ſem-<lb/>ꝑ ſuppono latitudīes manere vniformiṫ difformes</s>
            </p>
            <p xml:id="N1C6C4">
              <s xml:id="N1C6C5" xml:space="preserve">Reſpondeo ad replicam concedendo               <cb chead="De motu quo ad cauſam in medio nõ reſiſtente."/>              maiorem, et negando mnorem, et ad probationem <lb/>nego /  in nulla proportione incipit aliquod illo-<lb/>rum velocius mouere latitudine mouente quã ipſa <lb/>quieſcente: immo do oppoſitum puta /  in aliqua <lb/>proportione incipit aliquod illorum velocius mo-<lb/>ueri latitudine mouente quam ipſa quieſcente. </s>
              <s xml:id="N1C6D5" xml:space="preserve">Et <lb/>cum petitur /  detur / quod illorū ſic in aliqua pro-<lb/>portiõe velociꝰ īcipit moueri latitudīe mouēte quã <lb/>quieſcente. </s>
              <s xml:id="N1C6DE" xml:space="preserve">Dico /  ly aliquod illorū ſupponit con­<lb/>fuſe tantum. </s>
              <s xml:id="N1C6E3" xml:space="preserve">Et ideo non debet ſignari: quãuis ſi-<lb/>gnetur proportio quia ly proportiõe ſupponit de-<lb/>terminate.               <anchor type="note" xlink:href="note-0128-01" xlink:label="note-0128-01a"/>               </s>
              <s xml:id="N1C6EF" xml:space="preserve">¶ Ex quo ſequitur /  in aliqua propor-<lb/>tione incipit aliquod illorum velocius moueri la-<lb/>titudine mota quam quieſcente et tamen in nulla <lb/>proportione aliquod illorum incipit velocius mo-<lb/>ueri latitudine mota quam quieſcente. </s>
              <s xml:id="N1C6FA" xml:space="preserve">Patet cor-<lb/>relarium ex logica et ex improbatione oppoſiti hu­<lb/>ius propoſitionis aſſumpte in nulla proportione <lb/>incipit aliquod illorum etc̈.               <anchor type="note" xlink:href="note-0128-02" xlink:label="note-0128-02a"/>               </s>
              <s xml:id="N1C708" xml:space="preserve">¶ Sequitur ſecundo /  <lb/>in infinitum tarde incipit aliquod illorum moueri <lb/>quieſcentibus illis latitudinibus et tamen nullum <lb/>illorum aliqua proportione incipit tardius moue­<lb/>ri altero. </s>
              <s xml:id="N1C713" xml:space="preserve">Prima pars huiꝰ correlarii patet ex ſu-<lb/>perioribus: et ſecunda probatur / quia quodlibet il­<lb/>lorū ab eadem reſiſtentia vel ab equali incipit mo-<lb/>ueri: ergo nullum illorum aliqua proportione in-<lb/>cipit moueri velociꝰ altero: q2 alias ſeq̄ret̄̄ /  illam <lb/>maiorē ꝓportionē ſubito acq̇reret / quod eſt falſuꝫ.</s>
            </p>
            <div xml:id="N1C720" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0128-01a" xlink:label="note-0128-01" xml:id="N1C724" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0128-02a" xlink:label="note-0128-02" xml:id="N1C72A" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N1C730">
              <s xml:id="N1C731" xml:space="preserve">Quarto contra quartam concluſio-<lb/>nem quartidecimi capitis arguitur ſic.               <anchor type="note" xlink:href="note-0128-03" xlink:label="note-0128-03a"/>               </s>
              <s xml:id="N1C73B" xml:space="preserve">Si illa con­<lb/>cluſio eſſet vera / ſequeretur in caſu /  a. potētia quo­<lb/>cun gradu intrinſeco alicuius reſiſtentie per quã <lb/>mouetur dato: incipit velocius intendere motum <lb/>ſuum et moueri: quolibet illorum punctorum inci-<lb/>piente motum ſuum intendere a non gradu et po-<lb/>tentia ſimul: ſed conſequens eſt falſum / igitur illud <lb/>ex quo ſequitur. </s>
              <s xml:id="N1C74C" xml:space="preserve">Sequela probatur / et pono /  ſit <lb/>vna latitudo a non gradu vſ ad octauum vnifor-<lb/>miter difformis progrediens a non quanto quoli-<lb/>bet eius puncto intrinſeco incipiente a nõ gradu <lb/>intendere motum ſuum: et tncipiat ſimul cum tali <lb/>latitudine moueri potentia vt .8. / quo poſito argui­<lb/>tur ſic / quilibet punctus intrinſecus incipit vnifor-<lb/>miter intendere motum ſuū a non gradu / vt ptꝫ ex <lb/>caſu: et potētia ſimiliter (qm̄ ſi potētia inciperet a <lb/>gradu: iam quolibet pūcto inciperet velociꝰ moue­<lb/>ri et ſic quodlibet inciperet p̄cedere: et per cõſequēs <lb/>nõ moueret̄̄ cū illa latitudine: ſed ſubito pertrãſi-<lb/>ret totū mediū nõ reſiſtēs) et in illo caſu a quolibet <lb/>pūcto intrīſeco illiꝰ latitudīs īcipit velociꝰ moueri: <lb/>et velociꝰ ītēdere motū ſuū: igr̄ ꝓpoſitū. </s>
              <s xml:id="N1C76B" xml:space="preserve">Ptꝫ ↄ̨ña cū <lb/>maiore: et ꝓbat̄̄ mīor / qm̄ qḋlibet punctū intrīſecū <lb/>īcipit p̄cedere: g̊ q̊libet pūcto intrīſeco īcipit velociꝰ <lb/>intendere motū ſuū et moueri. </s>
              <s xml:id="N1C774" xml:space="preserve">Probat̄̄ añs / q2 ipſa <lb/>īcipit a nõ g̈du: g̊ īcipit a pūcto ſibi eq̈li ꝓcedēdo cõ­<lb/>tinuo ſus pūcta minꝰ intēſa: g̊ ſequit̄̄ /  qḋlibet in­<lb/>trīſecū īcipit p̄cedere.               <anchor type="note" xlink:href="note-0128-04" xlink:label="note-0128-04a"/>               </s>
              <s xml:id="N1C782" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi nõ det̄̄ / igit̄̄ <lb/>pūctꝰ ītrīſecꝰ illiꝰ latitudinis quē nõ p̄ceſſit a. et ma­<lb/>nifeſtū eſt /  a. hꝫ ad illū certã ꝓportionē: et ſemꝑ ꝑ­<lb/>te mouebat̄̄ cū remiſſiori pūcto a prīcipio motꝰ: g̊ <lb/>ſequit̄̄ /  talis poña ab aliq̈ certa ꝓportiõe incipit <lb/>moueri: et nõ īcipit a nõ g̈du qḋ eſt ↄ̨tra caſū. </s>
              <s xml:id="N1C78F" xml:space="preserve">Patꝫ <lb/>ↄ̨ña / q2 ↄ̨tinuo mouet̄̄ a maiori ꝓportiõe ꝙ̄ ſi ꝓpor­<lb/>tio quã hꝫ ad illū pūctū quē nū̄ p̄ceſſit etc̈. </s>
              <s xml:id="N1C796" xml:space="preserve">Sꝫ iã ꝓ­<lb/>bat̄̄ falſitas ↄ̨ñtis / q2 ſi a poña īcipit q̊libet puncto <lb/>intrīſeco velociꝰ moueri / ſequit̄̄ /  inſtãti qḋ eſt pñs <lb/>et initiatiuo motꝰ ip̄a poña nõ mouet̄̄ velociꝰ q̊libet <lb/>pūcto ītrīſeco: et īmediate poſt inſtãs / qḋ eſt pñs mo­<lb/>uebit̄̄ velociꝰ quolibet pūcto intrinſeco: ſed ↄ̨ñs eſt               <pb chead="Finis de motu locali quo ad cauſã." file="0129" n="129"/>               falſū: igr̄ illud ex quo ſeq̇tur. </s>
              <s xml:id="N1C7A8" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄: <lb/>qm̄ īmediate poſt inſtãs qḋ eſt p̄ſens cõtinuo infini­<lb/>ta puncta intrīſeca velociꝰ mouebūtur ipſa poten-<lb/>tia a. / igr̄ nõ īmediate poſt inſtãs / qḋ eſt p̄ſens moue­<lb/>bitur velociꝰ quolibet pūcto intrīſeco / qḋ eſt oppo-<lb/>ſitū cõſequētis illati. </s>
              <s xml:id="N1C7B5" xml:space="preserve">Cõſequētia ptꝫ, et ꝓbat̄̄ añs, <lb/>qm̄ īmediate poſt inſtãs / qḋ eſt p̄ſens īfinita pūcta <lb/>p̄cedēt ipſã potentiã / vt ptꝫ, q2 illa potentia erit in <lb/>aliquo pūcto intrīſeco cū intēdat ꝑ te ↄ̨tinuo motū <lb/>ſuū: ergo īmediate poſt hoc cõtinuo īfinita puncta <lb/>velociꝰ mouebūtur ipſa a: poña / qḋ fuit ꝓbandum.</s>
            </p>
            <div xml:id="N1C7C2" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0128-03a" xlink:label="note-0128-03" xml:id="N1C7C6" xml:space="preserve">Senariꝰ <lb/>tñ puto cõfūdere <lb/>ly aliq̄ ꝓ­<lb/>portione</note>
              <note position="right" xlink:href="note-0128-04a" xlink:label="note-0128-04" xml:id="N1C7D2" xml:space="preserve">ↄ̨firmat̄̄.</note>
            </div>
            <p xml:id="N1C7D8">
              <s xml:id="N1C7D9" xml:space="preserve">Reſpõdeo cõcedēdo / qḋ infert̄̄  negã-<lb/>do falſitatē ↄ̨ſequētis, et ad ꝓbationē falſitatis cõ­<lb/>ſequētis, cõcedo ↄ̨ſequētiã, et negãdo añs: nec illud <lb/>añs eſt ꝓpoſitio q̄ infert̄̄ in argumēto: ſꝫ ꝓpoſitio <lb/>q̄ infert̄̄ eſt iſta quolibet g̈du intrīſeco illiꝰ reſiſtētie <lb/>dato incipit a. poña velociꝰ moueri: et velociꝰ inten­<lb/>dere motū ſuū q̄ vera et ꝓbata eſt ſufficienter.               <anchor type="note" xlink:href="note-0129-01" xlink:label="note-0129-01a"/>               </s>
              <s xml:id="N1C7ED" xml:space="preserve">¶ Ex <lb/>quo ſeq̇tur /  quolibet gradu ſiue pūcto ītrīſeco il-<lb/>lius reſiſtentie īcipit a. potētia velociꝰ moueri: et tñ <lb/>nõ īcipit moueri quolibet gradu ſiue pūcto intrīſe-<lb/>co illiꝰ reſiſtentie velociꝰ. </s>
              <s xml:id="N1C7F8" xml:space="preserve">Patet correlariū ex lo-<lb/>gica et caſu. </s>
              <s xml:id="N1C7FD" xml:space="preserve">Unã illaꝝ ꝓpoſitionū eſt īmediate ex-<lb/>ponibilis: et alia nõ.               <anchor type="note" xlink:href="note-0129-02" xlink:label="note-0129-02a"/>               </s>
              <s xml:id="N1C807" xml:space="preserve">¶ Sequit̄̄ ſecūo /  in caſu ar-<lb/>gumenti quocū gradu ſiue pūcto intrīſeco illius <lb/>reſiſtētie īcipit a. velociꝰ moueri: et tñ ãte quodlibet <lb/>īſtãs futuꝝ poſt īſtãs / qḋ eſt p̄ſens velociꝰ īfiniti g̈dꝰ <lb/>ſiue pūcti intrinſeci mouebūtur. </s>
              <s xml:id="N1C812" xml:space="preserve">Patet hoc corre-<lb/>lariū ex deductione argumēti.               <anchor type="note" xlink:href="note-0129-03" xlink:label="note-0129-03a"/>               </s>
              <s xml:id="N1C81C" xml:space="preserve">Et eſt duodecima cõ­<lb/>cluſio calculatoris in primo capite de medio nõ re­<lb/>ſiſtente.               <anchor type="note" xlink:href="note-0129-04" xlink:label="note-0129-04a"/>               </s>
              <s xml:id="N1C828" xml:space="preserve">¶ Seq̇tur tertio /  ſi poſt̄ latitudo illa re­<lb/>ſiſtentie mouet̄̄ cõtinuo vniformiter cū poña incipi­<lb/>ente moueri cū illa: quilibet pūctus eiꝰ intrinſecus <lb/>incipiat moueri velociꝰ vniformiter quã antea: mo­<lb/>tus illiꝰ potētie incipiet eſſe retrogradꝰ quo ad reſi­<lb/>ſtentiã. </s>
              <s xml:id="N1C835" xml:space="preserve">Incipiet em̄ intēdere motū ſuū. </s>
              <s xml:id="N1C838" xml:space="preserve">Et ſi poſtea <lb/>quilibet punctꝰ reſtitueret̄̄ priſtine velocitati vnifor­<lb/>miter: poña iteꝝ incipiet ꝑtrãſire eandē reſiſtentiã <lb/>remittendo motū ſuū. </s>
              <s xml:id="N1C841" xml:space="preserve">Et poteſt hoc fieri infinities <lb/>ſi motus latitudinis īfinities variet̄̄. </s>
              <s xml:id="N1C846" xml:space="preserve">Probat̄̄ cor-<lb/>relariū / et pono /  in latitudīe data a nõ gradu vſ <lb/>ad octauū moueat̄̄ pūctus vt .4. a ꝓportiõe dupla <lb/>vniformiṫ ꝑ aliqḋ tēpꝰ: et ꝑ idē tēpꝰ moueat̄̄ poña vt <lb/>octo cū illo pūcto vt .4. etiã a ꝓportiõe dupla: et de-<lb/>inde in īſtãti a. īcipiat ſubito ille pūctꝰ vt .4. moueri <lb/>a ꝓportiõe q̈drupla. </s>
              <s xml:id="N1C855" xml:space="preserve">Quo poſito manifeſtū ē /  ille <lb/>pūctꝰ īcipiet p̄cedere poñaꝫ īcipiet intēdere <lb/>motū ſuū: intēdat igr̄ motū ſuū / quo ad vſ veniat <lb/>ad punctū a. vel b. (nõ eſt cura) et cū ꝑuenerit ad il-<lb/>lud punctū incipiat latitudo iteꝝ moueri eo modo <lb/>q̊ mouebat̄̄ ãtea vniformiṫ puta g̈dus vt .4. īcipiat <lb/>moueri a ꝓportiõe dupla: et g̈dꝰ vt .8. a q̈drupla vni­<lb/>formiṫ ↄ̨tinuo. </s>
              <s xml:id="N1C866" xml:space="preserve">Quo poſito iã poña iteꝝ incipit re-<lb/>mittere motū ſuū q̊ ad vr ſit ī pūcto vt .4. qm̄ q̇lꝫ <lb/>pūctꝰ citra .4. / tunc tardiꝰ mouet̄̄ / tūc ꝙ̄ poña ſufficit <lb/>moueri cū illo, qm̄ cū pūcto vt .4. ſufficit moueri po­<lb/>tētia a ꝓportiõe dupla et ab eadē mouet̄̄ punctꝰ vt <lb/>4. et q̇lꝫ pūctꝰ remiſſiora minori, et ipſa poña cū q̇lꝫ <lb/>remiſſiori a maiori ꝙ̄ dupla ſufficit moueri: igr̄ qḋ­<lb/>lꝫ remiſſiꝰ cū q̊ eſt īcipit ꝑtrãſire et ꝑ ↄ̨ñs ãtea ꝙ̄ deue­<lb/>niet ad pūctū vt .4. ↄ̨tinuo remittet motū ſuū. </s>
              <s xml:id="N1C879" xml:space="preserve">Et ſic <lb/>ptꝫ correlariū. </s>
              <s xml:id="N1C87E" xml:space="preserve">¶ Hec igr̄ ꝓ īgenioli mei tenuitate <lb/>de velocitate motꝰ penes cauſã ī medio difformiter <lb/>difformi variato, et q̇eſcēte poña ſiĺr variata et q̇eſcē­<lb/>te, itidē ī medio vniformiter difformiter reſiſtēte et <lb/>īuariato, etiã in medio nõ reſiſtente in quo fit parti­<lb/>bilis acquiſitio reſiſtentie vniformiter et difformi-<lb/>ter difformis / dicta ſint tanta.</s>
            </p>
            <div xml:id="N1C88D" level="5" n="10" type="float">
              <note position="left" xlink:href="note-0129-01a" xlink:label="note-0129-01" xml:id="N1C891" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0129-02a" xlink:label="note-0129-02" xml:id="N1C897" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0129-03a" xlink:label="note-0129-03" xml:id="N1C89D" xml:space="preserve">Duodeci­<lb/>ma ↄ̨cĺo <lb/>calcu.</note>
              <note position="left" xlink:href="note-0129-04a" xlink:label="note-0129-04" xml:id="N1C8A7" xml:space="preserve">3. correĺ.</note>
            </div>
            <cb chead="Seq̇t̄̄ de motu locali quo ad effectū."/>
          </div>
        </div>
        <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
          <p xml:id="N1C8B4">
            <s xml:id="N1C8B5" xml:space="preserve">¶ Seq̇tur tractatꝰ ſecūdꝰ huiꝰ tertie ꝑtis in q̊ de-<lb/>termīat̄̄ de velocitate et tarditate motꝰ penes effe-<lb/>ctū, exordiendo primo a motu locali tan̄ a priori</s>
          </p>
          <div xml:id="N1C8BC" level="4" n="1" type="chapter" type-free="capitulum">
            <head xml:id="N1C8C1" xml:space="preserve">Capitulū ṗmū / in quo ponūtur aliq̈ cõia elemēta <lb/>ī hac materia definitiões vcꝫ diuiſionibꝰ adiunctis</head>
            <p xml:id="N1C8C6">
              <s xml:id="N1C8C7" xml:space="preserve">PHiloſophorū prīcipis ariſtote­<lb/>lis pleriſ in locis ſue pḣie huic nr̄o inii-<lb/>tio a pṗme accõmoda extat ſententia.               <anchor type="note" xlink:href="note-0129-05" xlink:label="note-0129-05a"/>               </s>
              <s xml:id="N1C8D3" xml:space="preserve">Ait <lb/>em̄ ꝓhemio phiſicoꝝ, et ī prīcipio moralis pḣie īdu­<lb/>cēdo platõis teſtīoniū, duplicē reꝝ cognoſcēdi eſſe <lb/>viã a ṗori vcꝫ / et ꝑ cauſas vſ ad elemēta reſoluēdo <lb/>et ꝑ effectū q̊s duos cognoſcēdi tramites ṗmo poſte­<lb/>rioꝝ capite illo in quo demouſtrationē ipſã partit̄̄ <lb/>q2 et ꝓpṫ quid appellat: ſuapte tñ natura ītellectui <lb/>nr̄o vt eidē pḣo placet p̄allegato ꝓhemio īnata at-<lb/> congenita eſt via ꝑ effectū rē dinoſcendi: tam et ſi <lb/>vtro tramite ipſaꝝ reꝝ cognitionē attīgere vale-<lb/>at. </s>
              <s xml:id="N1C8EA" xml:space="preserve">Exacta igr̄ at tradita / vt potuimꝰ velocitatꝪ et <lb/>tarditatꝪ motꝰ noticia penes ṗmū modū ꝓpter q̇d <lb/>vcꝫ / et ꝑ cauſã q̄ cauſa ꝓportiõalitas geometrica eſt <lb/>iã nūc p̄ſens opus nos īducit at admonet ad tra-<lb/>dendã noticiã velocitatis et tarditatis motꝰ penes <lb/>m modū cognoſcēdi hoc ē peues effectū. </s>
              <s xml:id="N1C8F7" xml:space="preserve">Proceda­<lb/>mus igr̄ / a motū locali ꝓpṫ ſui dignitatē at ṗori-<lb/>tatē exordiū ſumētes. </s>
              <s xml:id="N1C8FE" xml:space="preserve">Suppoſita igr̄ definitiõe mo­<lb/>tus localis dico /  biꝑtitꝰ eſt motꝰ localis. </s>
              <s xml:id="N1C903" xml:space="preserve">Nã q̇dã <lb/>eſt motꝰ localis vniformis, quidam vero difformis</s>
            </p>
            <div xml:id="N1C908" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0129-05a" xlink:label="note-0129-05" xml:id="N1C90C" xml:space="preserve">pḣs in ꝓ­<lb/>hemio <lb/>phiſicoꝝ</note>
            </div>
            <note position="right" xml:id="N1C916" xml:space="preserve">Diuiſio <lb/>motꝰ lo-<lb/>calis.</note>
            <p xml:id="N1C91E">
              <s xml:id="N1C91F" xml:space="preserve">Motꝰ localis vniformis ē / quo ī equa­<lb/>libꝰ tꝑis eq̈lia ſpacia ꝑtrãſeūtur rarefactiõe et cõ-<lb/>dēſatiõe deductis, deductis etiã aliis paruis q̇ſqui­<lb/>liis cuiuſmodi eſt ↄ̨tra mutatio ſpacii vĺ qḋ non ſit <lb/>aliqḋ ſpaciū: ſufficit em̄ veꝝ vĺ ymaginaꝝ ſpacium <lb/></s>
              <s xml:id="N1C92B" xml:space="preserve">Exēplū / vt ſi mobile ī hora adeq̈te ꝑtrãſeat leucã. </s>
              <s xml:id="N1C92E" xml:space="preserve">Et <lb/>ī ṗma parte ꝓportiõali hore ṗmã ꝑtē ꝓportiõalē leu-<lb/>ce in ſcḋa ſcḋaꝫ / et ſic ↄ̨ñter. </s>
              <s xml:id="N1C935" xml:space="preserve">¶ Motꝰ o difformis eſt <lb/>qñ ī eq̈libꝰ ꝑtibꝰ tꝑis nõ eq̈lia ſpacia ꝑtrãſeūtur ce-<lb/>teris paribꝰ, deductꝪ deducēdis: vt ſi mobile ꝑtrã-<lb/>ſeat in hora adeq̈te leucã, in ṗma medietate vnam <lb/>q̈rtã et in ſcḋa tres q̈rtas talis motus eſt difformis <lb/>               <anchor type="note" xlink:href="note-0129-06" xlink:label="note-0129-06a"/>               </s>
              <s xml:id="N1C947" xml:space="preserve">¶ Motꝰ difformis diuidit̄̄ / q2 q̇dã eſt vniformiṫ dif-<lb/>formis, q̇dã o difformiṫ difformis. </s>
              <s xml:id="N1C94C" xml:space="preserve">Motꝰ vnifor-<lb/>miter difformis (vt cõiter definit̄̄) eſt triplex q̇dã eſt <lb/>vniformiṫ difformis q̊ ad ſubiectū tm̄, q̇dã q̊ ad tē-<lb/>pꝰ tm̄, q̇dã o q̊ ad ſubiectū et tēpꝰ ſiĺ. </s>
              <s xml:id="N1C955" xml:space="preserve">¶ Motꝰ vni-<lb/>formiṫ difformis q̊ ad ſubiectū vt cõiter definit̄̄ eſt <lb/>qñ cuiꝰcū ꝑtis ſubiecti dimidiū tm̄ excedit̄̄ ī velo-<lb/>citate ab extremo velociori illiꝰ ̄tū excedit extre-<lb/>mū tardiꝰ motū ī velocitate. </s>
              <s xml:id="N1C960" xml:space="preserve">Exēplū / vt motꝰ rote fi­<lb/>guli: et ꝑ dimidiū ītelligas pūctū ī medio vĺ q̇ yma­<lb/>gīarie ē ibi ṫmīſãdo. </s>
              <s xml:id="N1C967" xml:space="preserve">¶ Motꝰ o vniformiṫ diffor-<lb/>mis q̊ ad tēpꝰ ē qñ cuiꝰcū ꝑtꝪ / accepte m tēpꝰ .i. q̄ <lb/>adeq̈te ē ī aliq̈ ꝑte tꝑis g̈dꝰ mediꝰ q̇ ē ī medio taĺ ꝑtꝪ <lb/>tãto excedit extremū remiſſiꝰ ̄to excedit̄̄ ab intēſio­<lb/>ri. </s>
              <s xml:id="N1C972" xml:space="preserve">Exēplū / vt ſi aliqḋ mobile incipiat moueri a non <lb/>g̈du cõtinuo intendendo vniformiter motū ſuū per <lb/>aliqḋ tēpꝰ: tūc talis motꝰ eſt vniformiter difformis <lb/>q̊ ad tēpꝰ. </s>
              <s xml:id="N1C97B" xml:space="preserve">¶ Motꝰ aūt vniformiter difformis quo <lb/>ad tēpꝰ, et quo ad ſubiectū: definit̄̄ ↄ̨iūgēdo definiti­<lb/>ones motꝰ vniformiṫ difformis quo ad tēpꝰ, et quo <lb/>ad ſubiectū.               <anchor type="note" xlink:href="note-0129-07" xlink:label="note-0129-07a"/>               </s>
              <s xml:id="N1C989" xml:space="preserve">¶ Motꝰ aūt difformiṫ difformis cõſi-<lb/>militer diuidi poteſt: videlicet motuū difformiter <lb/>difformiū alius eſt difformiter difformis quo ad <lb/>tempus, alius quo ad ſubiectum, alius quo ad tem­<lb/>pus et ſubiectū ſimul. </s>
              <s xml:id="N1C994" xml:space="preserve">Et ſimiliter poteſt diuidi mo­<lb/>tus vniformis, quãuis proprie ſecundum definiti-<lb/>onem datam ille motus ſit vniformis, quo in equa­<lb/>libus partibus temporis equalia ſpacia pertran-<lb/>ſeūtur: et in nullis equalibus inequalia, ſiue talis               <pb chead="De motu locali quo ad effectum." file="0130" n="130"/>               motꝰ ſit vniformis quo ad ſubiectū ſiue difformis. <lb/></s>
              <s xml:id="N1C9A5" xml:space="preserve">¶ Sed qm̄ definitio motꝰ vniformiter difformis q̊ <lb/>ad ſubiectū q̄ cõiter dat̄̄ michi ſufficiēs nõ videtur. <lb/></s>
              <s xml:id="N1C9AB" xml:space="preserve">Ideo vt definitio motꝰ vniformiter difformis adī-<lb/>ueniat̄̄ vt poſſibile erit.               <anchor type="note" xlink:href="note-0130-01" xlink:label="note-0130-01a"/>               </s>
              <s xml:id="N1C9B5" xml:space="preserve">Querit̄̄ an definitio illa mo­<lb/>tus vniformiṫ difformis q̊ ad ſubiectū ſit bñ aſſig̈ta</s>
            </p>
            <div xml:id="N1C9BA" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0129-06a" xlink:label="note-0129-06" xml:id="N1C9BE" xml:space="preserve">Diuiſio <lb/>motꝰ dif­<lb/>formis.</note>
              <note position="right" xlink:href="note-0129-07a" xlink:label="note-0129-07" xml:id="N1C9C8" xml:space="preserve">Diuiſio <lb/>motꝰ lo-<lb/>calis dif­<lb/>formiter <lb/>diffor-<lb/>mis.</note>
              <note position="left" xlink:href="note-0130-01a" xlink:label="note-0130-01" xml:id="N1C9D8" xml:space="preserve">Queſtio <lb/>vtrū defi­<lb/>nitio mo­<lb/>tus vni-<lb/>formiter <lb/>difforīs <lb/>q̊ ad ſub­<lb/>iectuꝫ ſit <lb/>bene aſſi­<lb/>gnata.</note>
            </div>
            <p xml:id="N1C9F0">
              <s xml:id="N1C9F1" xml:space="preserve">Et arguit̄̄ primo /  non q2 ſcḋ3 illã nul­<lb/>lus ē motꝰ vniformiter difformis q̊ ad ſubiectū igr̄ <lb/></s>
              <s xml:id="N1C9F7" xml:space="preserve">Argr̄ añs / q2 ſi eſſet aliq̇s motꝰ vniformiter diffor-<lb/>mis quo ad ſubiectū maxīe effet motꝰ rote quo mo-<lb/>uet̄̄ circulariter: ſꝫ talis motꝰ nõ eſt vniformitēr dif-<lb/>formis q̊ ad ſubiectū: igr̄ ↄ̨ña ptꝫ cū maiore: et argr̄ <lb/>mīor / q2 ſi talis motꝰ ē vniformiter difformis capio <lb/>vnã rotã q̄ moueat̄̄ vniformiṫ difformiṫ a nõ g̈du in <lb/>cētro vſ ad octauū in circūferētia: et arguo ſic / taĺ <lb/>motꝰ ꝑ te ē vniformiṫ difformis a nõ gradu vſ adu <lb/>octauū / g̊ velocitas eius corrñdet g̈dui medio puta <lb/>vt .4. q̇ mediꝰ g̈dus vt .4. eſt in pūcto medio taĺ rote / <lb/>ſꝫ ↄ̨ñs eſt falſū: igr̄ illud ex quo ſeq̇tur, ↄ̨ña ptꝫ ſup-<lb/>poſita opinione tenēte motū vniformiter difformē <lb/>corrñdere motui exiſtēti in medio corporis mobilis <lb/></s>
              <s xml:id="N1CA13" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄ / q2 aliq̇s pūctus qui tardiꝰ mo­<lb/>uet̄̄ ꝙ̄ punctꝰ exiſtēs in medio illiꝰ rote mouet̄̄ veloci­<lb/>tate vt .4. / g̊ ſeq̇tur /  alter pūctꝰ puta medius talis <lb/>rote velociꝰ mouet̄̄ ꝙ̄ vt .4. </s>
              <s xml:id="N1CA1C" xml:space="preserve">Cõſequentia ptꝫ, et argr̄ <lb/>añs, q2 pūctus exiſtēs in medio ſemidiametri inter <lb/>centrū et circūferētiã mouet̄̄ velocitate vt .4. et talis <lb/>pūctꝰ tardiꝰ mouet̄̄ ꝙ̄ pūctus exiſtēs in medio rote: <lb/>igr̄ ꝓpoſitū. </s>
              <s xml:id="N1CA27" xml:space="preserve">Argr̄ maior capio vnã rotã a.b.c. / et vo­<lb/>lo /  ītra illã deſcribat̄̄ vnꝰ circulꝰ ei cõcētricꝰ cuiꝰ <lb/>diameter ſit ſubdupla ad diametrū totius rote, et <lb/>trãſeat talis circulꝰ ꝑ mediū pūcti ſemidiametri, q̇ <lb/>circulꝰ ſit f.gh. / vt ſcribit̄̄ in figura. </s>
              <s xml:id="N1CA32" xml:space="preserve">Quo poſito ſic <lb/>               <anchor type="figure" xlink:href="fig-0130-01" xlink:label="fig-0130-01a"/>               argumētor pūctꝰ mediꝰ <lb/>ſemidiametri deſcribit <lb/>circulū f.g.h. et talis cir­<lb/>culꝰ ſiue talis linea cir-<lb/>cularꝪ eſt ſubdupla ad <lb/>circulū a.b.c. ſiue ad li-<lb/>neã circūferētialē talis <lb/>rote / q̄ deſcribit̄̄ a pun-<lb/>cto velociſſime moto ta­<lb/>lis rote, q2 circūferētia <lb/>circuli cuiꝰ diameter eſt <lb/>dupla ad diametrū alteriꝰ circuli mīoris eſt dupla <lb/>ad circūferentiã mīoris circuli. </s>
              <s xml:id="N1CA54" xml:space="preserve">Modo ſic eſt ī ꝓpo­<lb/>ſito de diametrꝪ, et ꝑ ↄ̨ñs de circūferētiis illoꝝ duo­<lb/>rū circuloꝝ: igr̄ ille pūctꝰ ſemidiametri mouet̄̄ velo­<lb/>citate vt .4. </s>
              <s xml:id="N1CA5D" xml:space="preserve">Probat̄̄ hec ↄ̨ña / q2 ſubduplã lineã de-<lb/>ſcribit ad lineã deſcriptã a pūcto velociſſime moto <lb/>et talis pūctꝰ mouet̄̄ velocitate vt .8. vt poſitū ē: igr̄ <lb/>ille pūctꝰ mediꝰ ſemidiametri (qm̄ mouet̄̄ ſubdupla <lb/>velocitate) mouet̄̄ vt .4. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N1CA68" xml:space="preserve">Sꝫ iã ꝓbat̄̄ <lb/>mīor vcꝫ /  talis pūctꝰ tardiꝰ mouet̄̄ ꝙ̄ pūctꝰ exiſtēs <lb/>in medio rote (et nõ loquor hic de medio centrali q2 <lb/>tale mediū nõ mouet̄̄: ſꝫ de medio qḋ eſt īter cētrū et <lb/>circūferētiã) / et arguo ſic / talis pūctꝰ mediꝰ ſemidia-<lb/>metri eſt in fine tertie q̈rte totiꝰ corporis illiꝰ rote et <lb/>in prīcipio vltīe q̈rte ꝓcedendo ſus cētrū: igr̄ pū-<lb/>ctus exiſtēs in medio totiꝰ magnitudinis ipſiꝰ rote <lb/>eſt ꝓximior circūferētie ꝙ̄ ille pūctꝰ mediꝰ ſemidia-<lb/>metri / et ꝑ ↄ̨ñs mouet̄̄ velociꝰ ꝙ̄ ille pūctꝰ mediꝰ ſemi­<lb/>diametri / qḋ fuit ꝓbãdu. </s>
              <s xml:id="N1CA7F" xml:space="preserve">Ptꝫ ↄ̨ña ītelligēti naturã <lb/>motꝰ vniformiṫ difformis.               <anchor type="note" xlink:href="note-0130-02" xlink:label="note-0130-02a"/>               </s>
              <s xml:id="N1CA89" xml:space="preserve">¶ Dices forte / et bene ne-<lb/>gãdo añs, et ad ꝓbationē ↄ̨cedēdo maiorē, et negã-<lb/>do mīorē, et cū ꝓbat̄̄ admitto caſū cū his q̄ ibi ſup-<lb/>ponūtur, et ↄ̨cedo añs et ↄ̨ñam, et diſtīguo ↄ̨ñs ̄tuꝫ <lb/>ad illã particulã in qua dr̄ /  talis g̈dus mediꝰ eſt ī               <cb chead="De motu locali quo ad effectum."/>               pūcto exiſtēti in medio talis rote, q2 aut tu ītelligꝪ <lb/>de medio magnitudīs illiꝰ rote qḋ quidē mediū eſt <lb/>in medio īter cētrū et circūferētiã talis rote diuidē-<lb/>do illã rotã in duas rotas cõcētricas eq̈lis magni-<lb/>tudinis ̄uis ſint īeq̈lis ãbitꝰ et circūferētie / vt ptꝫ in <lb/>figura: et ſic nego, aut loqueris de pūcto exiſtēte in <lb/>medio lõgitudinis īter cētrū et circūferetiã, et ſic bñ <lb/>ↄ̨cedo /  ibi eſt gradꝰ mediꝰ / vt bene ꝓbat argumētū <lb/></s>
              <s xml:id="N1CAA6" xml:space="preserve">Unde dico /  ̄uis in q̈litate vniformiter difformi <lb/>mediꝰ gradꝰ debeat eſſe in medio corporis ̄tū ad <lb/>magnitudinē </s>
              <s xml:id="N1CAAD" xml:space="preserve">In motu tñ vniformiter difformi nõ <lb/>oportet /  g̈dus mediꝰ ſit in medio corporis ̄tū ad <lb/>magnitudinē: ſꝫ oportet /  ſit in medio corꝑis ̄tū <lb/>ad lõgitudinē (ſumēdo lõgitudinē eius a puncto nõ <lb/>moto ſiue tardiſſime moto vſ ad punctū velociſſi-<lb/>me motū) q2 ſcḋm illū modū p̄cedit ille motꝰ vnifor­<lb/>miter difformis.</s>
            </p>
            <div xml:id="N1CABC" level="5" n="3" type="float">
              <figure xlink:href="fig-0130-01a" xlink:label="fig-0130-01" xml:id="N1CAC0">
                <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0130-01"/>
              </figure>
              <note position="left" xlink:href="note-0130-02a" xlink:label="note-0130-02" xml:id="N1CAC6" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1CACC">
              <s xml:id="N1CACD" xml:space="preserve">Sed ↄ̨̨tra arguit̄̄ ſic / q2 aliqua pars il­<lb/>liꝰ rote nõ mouet̄̄ vniformiter difformiter: g̊ ſequit̄̄ / <lb/> ipſa tota rota nõ mouet̄̄ vniformiter difformiter <lb/></s>
              <s xml:id="N1CAD5" xml:space="preserve">Cõſequētia ptꝫ ſcḋm hãc opinionē / q2 oportet /  in <lb/>motu vniformiter difformi cuiuſlꝫ partꝪ g̈dꝰ mediꝰ <lb/>(id eſt q̇ eſt in medio lõgitudinis / vt dictū eſt) / tm̄ ex-<lb/>cedat īfimū ̄tū excedit̄̄ a ſūmo (vt ptꝫ ex definitõe) / <lb/>ꝓbat̄̄ añs / q2 datur ibi vna pars in illa rota cuius <lb/>pūctꝰ mediꝰ ſcḋm lõgitudinē nõ tm̄ excedit vnū ex-<lb/>tremã ̄tū excedit̄̄ ab altero in velocitate: igr̄ talis <lb/>pars nõ mouet̄̄ vniformiter difformiter. </s>
              <s xml:id="N1CAE6" xml:space="preserve">Probat̄̄ <lb/>añs, et ſigno in tali rota vnū q̈dratū nõ equaliū la-<lb/>teꝝ cuiꝰ pūctꝰ mediꝰ ſit pūctꝰ mediꝰ ſemidiametri in­<lb/>ter cētrū et circūferētiã et tangat tale q̈dratū extre-<lb/>mitates circunferentie ex vtro latere / vt patuit in <lb/>ī figura ſupra poſita: ſit illud quadratū .a.b.c.d. / <lb/>et arguo ſic / pūctꝰ exiſtēs in medio illiꝰ q̈drati moue­<lb/>tur vt .4. cū ſit pūctꝰ mediꝰ ſemidiametri īter centrū <lb/>et circūferentiã illiꝰ rote quē ſuperiꝰ ꝓbauimꝰ moue­<lb/>ri velocitate vt .4. et pūcta extrema q̄ tãgūt extremi­<lb/>tates rote mouetur velocitate vt .8. </s>
              <s xml:id="N1CAFD" xml:space="preserve">Ergo g̈dus me­<lb/>dius neutrū extremoꝝ excedit, et ꝑ ↄ̨ñs nõ tm̄ q̈tum <lb/>excedit̄̄ ab vno excedit reliquū / qḋ fuit ꝓbãdū               <anchor type="note" xlink:href="note-0130-03" xlink:label="note-0130-03a"/>               </s>
              <s xml:id="N1CB09" xml:space="preserve">¶ Di-<lb/>ces forte negãdo añs: et ad probationē negãdo iteꝝ <lb/>añs / et cū probat̄̄ ↄ̨cedo /  pūctꝰ mediꝰ illiꝰ q̈drati mo-<lb/>uetur velocitate vt q̈tuor, et ↄ̨cedo etiã /  duo pūcta <lb/>extrema talis quadrati applicata circūferētie rote <lb/>mouētur velocitate vt .8. </s>
              <s xml:id="N1CB16" xml:space="preserve">Sed nõ debēt capi extre-<lb/>ma motꝰ illiꝰ partꝪ ſcḋm talē lõgitudinē ̄uis de fa­<lb/>cto illa ſit lõgitudo talis partis: ſed d3 ſumi in tali <lb/>parte ꝓcedēdo m latitudinē ꝑ lineã rectã a centro <lb/>rote ꝓcedentē ꝑ mediū talis partis vſ ad circūfe-<lb/>tiã / vt ptꝫ in figura ſuperiꝰ poſita. </s>
              <s xml:id="N1CB23" xml:space="preserve">Modo poteſt dici <lb/>īmo de facto ita eſt /  quãto gradꝰ mediꝰ excedit̄̄ a <lb/>g̈du velociſſime moto illiꝰ ꝑtis exiſtētis in tali linea <lb/>tantū excedit tardiſſimum exiſtentem in tali parte.</s>
            </p>
            <div xml:id="N1CB2C" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0130-03a" xlink:label="note-0130-03" xml:id="N1CB30" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1CB36">
              <s xml:id="N1CB37" xml:space="preserve">Sed cõtra q2 vtra medietas illius <lb/>q̈drati a.b.c.d. mouet̄̄ velociꝰ ꝙ̄ vt .4. / g̊ ſeq̇tur /  to-<lb/>tū illud q̈dratū mouet̄̄ velociꝰ ꝙ̄ vt .4. / ↄ̨ña ptꝫ / q2 to-<lb/>tius velocitas cõficit̄̄ ex partiū velocitatibꝰ, et velo-<lb/>citatis denoīatio ex vtriuſ medietatis denoīatio­<lb/>nibus cõſtat̄̄. </s>
              <s xml:id="N1CB44" xml:space="preserve">Sed ꝓbat̄̄ añs / q2 vtra medietas il-<lb/>lius q̈drati equaliter mouet̄̄ puta medietas e. et me­<lb/>dietas f. cum equaliter diſtent a centro illiꝰ rote, et <lb/>vtra illaꝝ velociꝰ mouetur ꝙ̄ vt .4. / igitur ꝓpoſi-<lb/>tum. </s>
              <s xml:id="N1CB4F" xml:space="preserve">Cõſquētia ptꝫ / et arguit̄̄ minor / q2 vtriuſ me-<lb/>dietatis pūctus mediꝰ mouet̄̄ velocius ꝙ̄ vt .4. cum <lb/>vtriuſ medietatis tam e. ꝙ̄ f. punctus mediꝰ plus <lb/>diſtet a centro quã punctus medius totius: vt patꝫ <lb/>in figura: igit̄̄ vtra illaꝝ medietatū f. et e. velocius <lb/>mouetur quam vt quatuor / quod fuit probandum.</s>
            </p>
            <pb chead="Secūdi tractatus" file="0131" n="131"/>
            <note position="left" xml:id="N1CB60" xml:space="preserve">1. confir-<lb/>matio.</note>
            <p xml:id="N1CB66">
              <s xml:id="N1CB67" xml:space="preserve">¶ Et confirmatur / quia cuiuſlibet motus vniformi-<lb/>ter difformis gradꝰ velociſſimꝰ .i. quo mouet̄̄ pun-<lb/>ctus velociſſime motꝰ tm̄ excedit gradū mediū ̄tū <lb/>gradꝰ mediꝰ excedit gradū quo mouet̄̄ pūctus tar-<lb/>diſſime motꝰ vt cõcedit hec opinio et cõis ſcola: ſed <lb/>motꝰ talis q̈drati a.b.c.d. nõ eſt huiuſmodi, igr̄ ta-<lb/>lis motꝰ nõ eſt vniformiter difformis. </s>
              <s xml:id="N1CB76" xml:space="preserve">Minor ꝓbat̄̄ / <lb/>q2 gradꝰ velociſſimꝰ illiꝰ partis eſt gradus octauꝰ <lb/>cū quadratū illud applicet̄̄ circūferētie rote: et me-<lb/>dius eſt vt quatuor, et motꝰ illiꝰ nõ terminat̄̄ ad nõ <lb/>gradū: ergo ſeq̇tur /  gradus velociſſimꝰ ꝑ maiorē <lb/>latitudinem excedit mediuꝫ quam medius excedat <lb/>infimum / quod fuit probandum.</s>
            </p>
            <note position="left" xml:id="N1CB85" xml:space="preserve">2. confir-<lb/>matio.</note>
            <p xml:id="N1CB8B">
              <s xml:id="N1CB8C" xml:space="preserve">¶ Confirmatur ſecundo principale argumentum / <lb/>q2 ſi motꝰ talis rote eſſet vniformiter difformis a <lb/>nõ gradū vſ ad octauū / ſeq̄ret̄̄ /  adequata velo-<lb/>citas illiꝰ rote eſſet vt quatuor: ſed ↄ̨ñs eſt falſū: igr̄ <lb/>illud ex quo ſeq̇tur. </s>
              <s xml:id="N1CB97" xml:space="preserve">Cõſequētia eſt nota, et falſitas <lb/>ↄ̨ñtis argr̄ / q2 velocitas totiꝰ illiꝰ partis q̄ claudit̄̄ <lb/>circulo minori .d.e.f. eſt vt duo cuꝫ ſit a quarto vſ <lb/>ad nõ gradū, et velocitas totiꝰ reſidui eſt vt ſex cum <lb/>ſit a quarto vſ ad octauum, et ſi eſſet in medietate <lb/>adequate faceret ad denoīationē totiꝰ motꝰ vt tria. <lb/>modo eſt in ſexquialtero maiori parte medietate: g̊ <lb/>ſeq̇tur /  motꝰ eiꝰ facit ad denoīationē totiꝰ in ſex-<lb/>q̇altero magis: et ꝑ ↄ̨ñs / vt quatuor cū dimidio (cum <lb/>quatuor cū dimidio ad tria ſit ꝓportio ſexq̇altera) / <lb/>g̊ ſeq̇tur /  talis motus adequate eſt velocior quã vt <lb/>quatuor cū dimidio, et ꝑ ↄ̨ñs velocior quã vt quatu­<lb/>tor / qḋ fuit ꝓbandū. </s>
              <s xml:id="N1CBB2" xml:space="preserve">Sed iã ꝓbo /  illa pars rote q̄ <lb/>eſt totū reſiduū a minori circulo eſt in ſexquialtero <lb/>maior medietate, q2 illa pars eſt tres quarte totiꝰ <lb/>rote: igr̄ in ſexq̇altero eſt maior medietate </s>
              <s xml:id="N1CBBB" xml:space="preserve">Probat̄̄ / <lb/>q2 medietas eſt due q̈rte: mõ triū quartaꝝ ad duas <lb/>q̈rtas eſt ꝓportio ſexq̇altera. </s>
              <s xml:id="N1CBC2" xml:space="preserve">Sed iã ꝓbo añs vcꝫ /  <lb/>reſiduū illius rote a minori circulo ſit tres quarte <lb/>illius rote quia totius rote ad minorem totum cir-<lb/>culū eſt ꝓportio quadrupla: g̊ totū reſiduū a mīori <lb/>circulo qui eſt vna quarta eſt tres q̈rte: ſꝫ illa ꝑs eſt <lb/>totū reſiduū a mīori circulo / vt notū eſt: g̊ illa ē tres <lb/>q̈rte totiꝰ rote / qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0131-01" xlink:label="note-0131-01a"/>               </s>
              <s xml:id="N1CBD6" xml:space="preserve">Sꝫ iã ꝓbo /  totius <lb/>rote ad mīorē circulū ei cõcētricū ſit ꝓportio q̈dru-<lb/>pla, q2 vt demõſtrat brauardinꝰ ī tractatu ꝓporti-<lb/>onū capite q̈rto ſēꝑ īter duos circulos īeq̈les eſt du­<lb/>plicata ꝓportio ad ꝓportionē q̄ eſt īter diametros <lb/>eorūdē circuloꝝ. </s>
              <s xml:id="N1CBE3" xml:space="preserve">ita  ꝓportio circuloꝝ eſt ꝓportio <lb/>diametroꝝ duplicata / vt etiã facile poteſt intueri in <lb/>               <anchor type="figure" xlink:href="fig-0131-01" xlink:label="fig-0131-01a"/>               figura ſuppoſita <lb/>ſꝫ diametri totiꝰ <lb/>rote ad diametꝝ <lb/>circĺi d.e.f. ē ꝓpor­<lb/>tio dupla: g̊ totiꝰ <lb/>rote ad circulū .d <lb/>e.f. eſt ꝓportio q̈-<lb/>drupla q̄ ē dupla <lb/>ad duplã / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N1CC01" xml:space="preserve">Qḋ o <lb/>diametri ad dia­<lb/>metꝝ ſit ꝓportio <lb/>dupla / ptꝫ ex caſu <lb/>prīcipalis argu-<lb/>mēti. </s>
              <s xml:id="N1CC0E" xml:space="preserve">Et ſic ex hac deductiõe ptꝫ /  totꝰ ille motꝰ eſt <lb/>vt quī q2 ille tres q̈rte denominã vt q̈tuor cū di-<lb/>midio, et alia q̈rta  eſt mīor circulꝰ denoīat vt di-<lb/>midiū (cū ſit vt duo) / igr̄ totꝰ motꝰ eſt vt quī et ſic nõ <lb/>eſt adequate vt quatuor / quod fuit probandum.</s>
            </p>
            <div xml:id="N1CC19" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0131-01a" xlink:label="note-0131-01" xml:id="N1CC1D" xml:space="preserve">Brauar-<lb/>dinꝰ ī tra­<lb/>ctatu ꝓ-<lb/>portio-<lb/>nū capi-<lb/>te .4.</note>
              <figure xlink:href="fig-0131-01a" xlink:label="fig-0131-01" xml:id="N1CC2D">
                <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0131-01"/>
              </figure>
            </div>
            <p xml:id="N1CC33">
              <s xml:id="N1CC34" xml:space="preserve">Scḋo prīcipaliṫ arguit̄̄ ſic </s>
              <s xml:id="N1CC37" xml:space="preserve">Si illa dif­<lb/>finitio eſſet bona ſeq̄ret̄̄ /  motꝰ celi nõ eſſet vnifor-               <cb chead="Capitulū primū."/>               miter difformis q̊ ad ſubiectū: ſꝫ ↄ̨ñs eſt falſū / et ↄ̨tra <lb/>cõiṫ opinãtes / ir̄ illḋ ex q̊ ſeq̇tur. </s>
              <s xml:id="N1CC41" xml:space="preserve">Seq̄la ꝓbat̄̄ / et diuido <lb/>ṗmū mobile in duas medietates ꝑ coluꝝ vcꝫ ꝓcedē­<lb/>tē a polo artico ꝑ polū antarticū et ꝑ capita arietꝪ <lb/>et libre / q̊ poſito arguo ſic / nulla illaꝝ medietatū mo­<lb/>uet̄̄ vniformiṫ difformiṫ: igr̄ nec celū mouet̄̄ vnifor-<lb/>miṫ difformiṫ. </s>
              <s xml:id="N1CC4E" xml:space="preserve">Cõſequētia ptꝫ, et argr̄ añs / qm̄ neu-<lb/>triꝰ illaꝝ medietatū pūctꝰ q̇ eſt ī medio tãtū excedi-<lb/>tur in velocitate a pūcto velociſſime moto ̄tū exce-<lb/>dit pūctū tardiſſime motū ſiue nõ g̈dū cū pūctꝰ exi-<lb/>ſtēs in medio ſit pūctꝰ exñs in circulo eq̇noctiali q̇ ē <lb/>pūctꝰ velociſſime motꝰ: igr̄ a nullo excedit̄̄ in veloci­<lb/>tate / et ꝑ ↄ̨ñs nõ tm̄ excedit a pūcto velociſſime moto <lb/>quantum excedit punctū tardiſſime motum vel nõ <lb/>gradum velocitatis / quod fuit probandum.</s>
            </p>
            <p xml:id="N1CC61">
              <s xml:id="N1CC62" xml:space="preserve">¶ Et confirmat̄̄ / q2 ſi eſſet aliquis motus vniformi-<lb/>ter difformis q̊ ad ſubiectū maxīe eſſet motꝰ localis <lb/>q̊ ꝑ rarefactionē mouet̄̄ vnū q̈dratū qḋ rarefit vni-<lb/>formiter a nõ g̈du in extremo q̇eſcēte vſ ad octauū <lb/>in altero extremo: ſꝫ hec nõ, igr̄. </s>
              <s xml:id="N1CC6D" xml:space="preserve">Maior eſt nota cū <lb/>ↄ̨ña, et ꝓbat̄̄ mīor / q2 nõ cuiuſlꝫ ꝑtis illiꝰ g̈dus mediꝰ <lb/>tm̄ excedit̄̄ a velociſſimo quãto excedit g̈dū tardiſſi­<lb/>mū illiꝰ ꝑtis vĺ nõ g̈dū: igr̄ totū illud q̈dratū nõ mo­<lb/>uet̄̄ vniformiṫ difformiṫ q̊ ad ſubiectū. </s>
              <s xml:id="N1CC78" xml:space="preserve">Cõſequētia <lb/>ptꝫ ex definitiõe, et argr̄ añs, et ſigno vnã partē ī me­<lb/>dietate illiꝰ q̈drati q̄ velociꝰ rarefit: et ſit illa pars <lb/>figurata ꝑ modū duoꝝ lateꝝ vniꝰ triãguli faciētis <lb/>vnū angulū ſupra punctū mediū ex vno latere et ex <lb/>alio infra vt apparet in figura hic infra ſcripta.</s>
            </p>
            <figure xml:id="N1CC85">
              <image file="0131-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0131-02"/>
            </figure>
            <p xml:id="N1CC89">
              <s xml:id="N1CC8A" xml:space="preserve"><reg norm="Tunc" type="context">Tūc</reg> ſic <reg norm="arguitur" type="wordlist">argr̄</reg> / illa <reg norm="pars" type="wordlist">ꝑs</reg> eſt <reg norm="pars" type="wordlist">ꝑs</reg> <reg norm="illius" type="simple">illiꝰ</reg> q̈dra-<lb/>ti: et <reg norm="tamen" type="wordlist">tñ</reg> ipſa <reg norm="non" type="wordlist">nõ</reg> <reg norm="mouetur" type="simple">mouet̄̄</reg> <reg norm="vniformiter" type="simple">vniformiṫ</reg> <reg norm="dif- formiter" type="simple">dif-<lb/>formiṫ</reg>: <reg norm="igitur" type="wordlist">igr̄</reg> <reg norm="propoſitum" type="simple context">ꝓpoſitū</reg>. </s>
              <s xml:id="N1CC91" xml:space="preserve"><reg norm="Arguitur" type="wordlist">Argr̄</reg> <reg norm="antecedens" type="wordlist">añs</reg> / <reg norm="quia(?)" type="wordlist">q2</reg> <reg norm="pun­ ctus" type="context">pū­<lb/>ctus</reg> <reg norm="exiſtens" type="wordlist">exñs</reg> in medio <reg norm="illius" type="simple">illiꝰ</reg> <reg norm="partis" type="wordlist">ꝑtis</reg> in linea <lb/><reg norm="procedente" type="simple context">ꝓcedēte</reg> a <reg norm="puncto" type="context">pūcto</reg> <reg norm="non" type="wordlist">nõ</reg> moto <reg norm="vſque" faithful="vſ" type="simple">vſqꝫ</reg> ad <reg norm="pun­ ctum" type="context context">pū­<lb/>ctū</reg> velociſſime <reg norm="motum" type="context">motū</reg> <reg norm="ipſius" type="simple">ipſiꝰ</reg> q̈drati eſt <lb/><reg norm="punctus" type="context">pūctus</reg> <reg norm="medius" type="simple">mediꝰ</reg> <reg norm="totius" type="simple">totiꝰ</reg> q̈drati qui <reg norm="mouetur" type="simple">mouet̄̄</reg> vt quatuor / vt <lb/><reg norm="patet" type="wordlist">ptꝫ</reg> in figura: <reg norm="igitur" type="wordlist">igr̄</reg> ſi talis <reg norm="mouetur" type="simple">mouet̄̄</reg> vniformiter diffor-<lb/>miter <reg norm="ſequitur" type="simple">ſequit̄̄</reg> / <reg norm="quae" type="wordlist"></reg> <reg norm="totus" type="simple">totꝰ</reg> <reg norm="motus" type="simple">motꝰ</reg> <reg norm="eius" type="simple">eiꝰ</reg> eſt vt quatuor / ſed <reg norm="conſequens" type="wordlist">ↄ̨ñs</reg> <lb/>eſt <reg norm="falſum" type="context">falſū</reg>: <reg norm="igitur" type="wordlist">igr̄</reg> illud ex quo <reg norm="ſequitur" type="simple">ſequit̄̄</reg>. </s>
              <s xml:id="N1CCA2" xml:space="preserve">Falſitas ↄ̨ñtis <reg norm="pro­ batur" type="simple">pro­<lb/>bat̄̄</reg> / <reg norm="quia(?)" type="wordlist">q2</reg> <reg norm="vtraque" faithful="vtra" type="simple">vtraqꝫ</reg> medietas talis partis <reg norm="velocius" type="simple">velociꝰ</reg> <reg norm="mouetur" type="simple">mouet̄̄</reg> <lb/><reg norm="per" type="wordlist">ꝑ</reg> <reg norm="rarefactionem" type="context">rarefactionē</reg> <reg norm="quam" type="context">quã</reg> vt quatuor <reg norm="quia(?)" type="wordlist">q2</reg> <reg norm="vtriuſque" faithful="vtriuſ" type="simple">vtriuſqꝫ</reg> <reg norm="illarum" type="simple">illaꝝ</reg> <reg norm="pun- ctus" type="context">pū-<lb/>ctus</reg> <reg norm="medius" type="simple">mediꝰ</reg> eſt <reg norm="intenſior" type="context">intēſior</reg> <reg norm="quam" type="wordlist">ꝙ̄</reg> vt .4. <reg norm="cum" type="context">cū</reg> <reg norm="vtriuſque" faithful="vtriuſ" type="simple">vtriuſqꝫ</reg> <reg norm="illarum" type="simple">illaꝝ</reg> <reg norm="me- dietatum" type="context">me-<lb/>dietatū</reg> <reg norm="punctus" type="context">pūctus</reg> <reg norm="medius" type="simple">mediꝰ</reg> ſit ſupra <reg norm="punctum" type="context">punctū</reg> <reg norm="exiſtentem" type="context">exiſtentē</reg> in <lb/>medio <reg norm="illius" type="simple">illiꝰ</reg> q̈drati: et ſic <reg norm="vtraque" faithful="vtra" type="simple">vtraqꝫ</reg> <reg norm="illarum" type="simple">illaꝝ</reg> <reg norm="mouetur" type="simple">mouet̄̄</reg> <reg norm="velocius" type="simple">velociꝰ</reg> <lb/>̄ vt quatuor: <reg norm="ergo" type="wordlist">g̊</reg> <reg norm="per" type="wordlist">ꝑ</reg> <reg norm="conſequens" type="wordlist">ↄ̨ñs</reg> tota illa pars <reg norm="cuius" type="simple">cuiꝰ</reg> ille <reg norm="ſunt" type="context">ſūt</reg> me­<lb/>dietates <reg norm="mouetur" type="simple">mouet̄̄</reg> <reg norm="velocius" type="simple">velociꝰ</reg> <reg norm="quam" type="wordlist">ꝙ̄</reg> vt <reg norm="quatuor" type="wordlist">q̈tuor</reg> / <reg norm="quod" type="simple">qḋ</reg> eſt <reg norm="oppoſitum" type="simple">oppoſituꝫ</reg> <lb/>aut <reg norm="ſaltem" type="context">ſaltē</reg> <reg norm="infert" type="context">īfert</reg> <reg norm="oppoſitum" type="context">oppoſitū</reg> <reg norm="conſequentis" type="wordlist">ↄ̨ñtis</reg> / <reg norm="quod" type="simple">qḋ</reg> erat <reg norm="probandum" type="simple context context">ꝓbãdū</reg> <reg norm="falſum" type="context">falſū</reg>.</s>
            </p>
            <p xml:id="N1CCB5">
              <s xml:id="N1CCB6" xml:space="preserve">In oppoſitū tñ arguit̄̄ / ꝑ cõmunē au-<lb/>ctoritatem recentiū pḣoꝝ hãc definitionē ponentiū</s>
            </p>
            <p xml:id="N1CCBB">
              <s xml:id="N1CCBC" xml:space="preserve">Pro ſolutiõe  enodatiõe huiꝰ q̄ſtiõis <lb/>pono aliquas cõcluſiones quibꝰ mediantibꝰ adīue­<lb/>niatur definitio motus vniformiter difformis quo <lb/>ad ſubiectum.</s>
            </p>
            <p xml:id="N1CCC5">
              <s xml:id="N1CCC6" xml:space="preserve">Prima ↄ̨̨cluſio. </s>
              <s xml:id="N1CCC9" xml:space="preserve">Motꝰ vniformiṫ dif-<lb/>formis quo ad ſubiectū nõ bene definit̄̄ iſto modo. <lb/></s>
              <s xml:id="N1CCCF" xml:space="preserve">Motus vniformiter difformis quo ad ſubiectū eſt <lb/>cuiꝰ oēs partes īmediate ſcḋm extenſionē ſunt īme-<lb/>diate ſcḋm intenſionē motus ſiue velocitatū ita  <lb/>remiſſiſſimus gradus velocitatis qui eſt in intēſio-<lb/>ri ſit remiſſiſſimus qui non eſt in remiſſiori illarum <lb/>duarum partium ſibi immediatarum. </s>
              <s xml:id="N1CCDC" xml:space="preserve">Probatur <lb/>hec concluſio: quia pono caſum /  ſit vna rota que <lb/>que mouetur a non gradu vſ ad certum gradum <lb/>ita  a centro eius q̇eſcente vſ ad mediū ſemidia­<lb/>metri ſit motus vniformiter difformis a nõ gradu <lb/>vſ ad quatuor et a pūcto medio ſemidiametri vſ-<lb/> ad circūferentiã ſit motus vniformiter difformis               <pb chead="De motu locali quo ad effectum." file="0132" n="132"/>               a quarto vſ ad duodecimū (volo enim /  talis ro­<lb/>ta ſit flexibilis q2 alias non video quomodo / hoc eſ­<lb/>ſet poſſibile) / quo poſito arguitur ſic / motus ille nõ <lb/>eſt vniformiter difformis et tamen omnes partes ī-<lb/>mediate ſecundū extenſionem ſunt īmediate ſecun-<lb/>dū intēſionē: igitur illa definitio cõuenit aliis a dif­<lb/>finito / et per ↄ̨ñs non eſt bona. </s>
              <s xml:id="N1CCFC" xml:space="preserve">Minor eſt nota ex ca-<lb/>ſu: et maior probatur / quia ſi eſſet vniformiter dif-<lb/>formis cū incipiat a. duodecim et terminat̄̄ ad non <lb/>gradū pūctꝰ mediꝰ ſemidiametri moueret̄̄ velocita­<lb/>te q̄ eſt gradus medius inter duodecim et nõ gradū: <lb/>ſed hoc eſt falſum / vt patet ex caſu qm̄ talis punctus <lb/>mouetur vt quatuor vt ponitur:</s>
            </p>
            <p xml:id="N1CD0B">
              <s xml:id="N1CD0C" xml:space="preserve">Secunda cõcluſio </s>
              <s xml:id="N1CD0F" xml:space="preserve">Motus vniformi­<lb/>ter difformis quo ad ſubiectum nõ bene definitur <lb/>iſto modo </s>
              <s xml:id="N1CD16" xml:space="preserve">Motꝰ vniformiter difformis quo ad ſub­<lb/>iectum eſt quando cuiuſcun partis ſubiecti pun-<lb/>ctus qui eſt in medio (loquor de puncto vero vel ima­<lb/>ginario) tanto exceditur in velocitate ab extremo il­<lb/>lius partis velociſſime moto quantuꝫ excedit extre­<lb/>mum remiſſiſſime motum eiuſdem partis ſiue non <lb/>motum (quod dico propter motum terminatum ad <lb/>non gradum) </s>
              <s xml:id="N1CD27" xml:space="preserve">Hec concluſio bene probatur per pri­<lb/>mum argumentum principale ante oppoſitum et ꝑ <lb/>ſecundam confirmationem eius. </s>
              <s xml:id="N1CD2E" xml:space="preserve">Illud em̄ argumē­<lb/>tum et confirmatio oſtendunt /  non oportet mediū <lb/>gradum motus vniformiter difformis / quo ad ſub-<lb/>iectum eſſe in medio magnitudinis corporis moti <lb/>vniformiter difformiter quo ad ſubiectum: ſed bene <lb/>oportet /  ſit in medio longitudinis talis corporis <lb/>modo expoſito in argumento.</s>
            </p>
            <p xml:id="N1CD3D">
              <s xml:id="N1CD3E" xml:space="preserve">Tertia cõcluſio </s>
              <s xml:id="N1CD41" xml:space="preserve">Motus vniformiter <lb/>difformis quo ad ſubiectum non bñ definitur ſic.</s>
            </p>
            <p xml:id="N1CD46">
              <s xml:id="N1CD47" xml:space="preserve">Motus vniformiter difformis quo ad ſubiectū eſt <lb/>quando cuiuſcun partis ſubiecti dimidium ſiue <lb/>punctus qui eſt in medio talis partis (in medio in-<lb/>quã ſecundum longitudinem) tantum exceditur ī ve­<lb/>locitate a puncto ſiue ab extremo velociſſime moto <lb/>quantum excedit punctum ſiue extremuꝫ tardiſſime <lb/>motum in velocitate ſiue extremum nõ motuꝫ (quod <lb/>dico propter motum terminatum ad non gradum) <lb/></s>
              <s xml:id="N1CD59" xml:space="preserve">Probatur hec concluſio per vltimam replicam pri­<lb/>mi argumenti huius dubitatiõis: et per ſecundū ar­<lb/>gumentum: </s>
              <s xml:id="N1CD60" xml:space="preserve">Nam ſi illa definitio eſſet bona / ſeque-<lb/>retur /  quelibet pars illius quod vniformiter dif-<lb/>formiter mouetur quo ad ſubiectum etiam vnifor-<lb/>miter difformiter moueretur quo ad ſubiectū vt fa­<lb/>cile deducitur ex illa definitione: ſed tenendo illã de­<lb/>finitionem / ſequitur oppoſitum videlicet /  non que­<lb/>libet pars illius quod vniformiter difformiter mo­<lb/>uetur etc. / vt probat vltima replica primi argumēti <lb/>et ſecūdum argumentum.</s>
            </p>
            <note position="left" xml:id="N1CD73" xml:space="preserve">definitio <lb/>motꝰ vni­<lb/>formiter <lb/>diffor-<lb/>mis q̊ ad <lb/>ſubiectū.</note>
            <p xml:id="N1CD81">
              <s xml:id="N1CD82" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N1CD85" xml:space="preserve">Motus vniformi­<lb/>ter difformis quo ad ſubiectum / vt pro nūc mihi ap­<lb/>paret bene definitur ſic </s>
              <s xml:id="N1CD8C" xml:space="preserve">Motus vniformiter diffor­<lb/>mis quo ad ſubiectum eſt quando quilibet punctus <lb/>ſubiecti intrinſecus et etiam extrinſecus velociſſime <lb/>motus in ea proportione velocius mouetur in qua <lb/>magis diſtat a centro talis motus. </s>
              <s xml:id="N1CD97" xml:space="preserve">Exemplum / vt ſi <lb/>rota moueatur vniformiter difformiter: requiri-<lb/>tur /  in quacun ꝓportione puncta magis diſtãt <lb/>a centro ipſius rote in ea ꝓportione velocius moue­<lb/>antur </s>
              <s xml:id="N1CDA2" xml:space="preserve">Et per centrū in propoſito ego intelligo pū-<lb/>ctum quieſcens exiſtens in illo corpore quod ſic mo­<lb/>uetur vniformiter difformiter vel a quo imagina-<lb/>rie ꝓcedit talis motus. </s>
              <s xml:id="N1CDAB" xml:space="preserve">Et volo dicere /  ſi corpus <lb/>moueatur vniformiter difformiter quo ad ſubiectū <lb/>a non gradu vſ ad certum gradum, oportet /  in               <cb chead="De motu locali quo ad effectum."/>               quacun proportione puncta magis diſtant a pū-<lb/>cto illius ſubiecti in quo eſt non gradus motus in <lb/>ea velocius moueantur. </s>
              <s xml:id="N1CDB9" xml:space="preserve">Si vero tale corpus qḋ mo­<lb/>uetur vniformiter difformiter quo ad ſubiectū ita <lb/>ſe habeat /  quilibet punctus eius moueatur ita  <lb/>motus eius incipiat a certo gradu remiſſiori et ter-<lb/>minetur ad certum gradum intenſiorē vt verbi gra­<lb/>tia incipiat a quarto et terminetur ad octauuꝫ ſicut <lb/>eſt de motu totius reſidui a circulo minori exiſtente <lb/>intra rotam in caſu primi argumenti: tunc ad inue­<lb/>niendum centruꝫ talis motus oportet addere cor-<lb/>pori aliquod corpus quod moueatur vniformiter <lb/>difformiter a non gradu ad gradum vt quatuor vĺ <lb/>remiſſimum quo mouetur aliud corpus cuius mo-<lb/>tus vtrim terminatur ad gradum: et ſi tunc omīa <lb/>puncta illius corporis cuius motus in vtro extre­<lb/>mo terminatur ad gradum in ea ꝓportione velociꝰ <lb/>moueantur in qua plus diſtant a puncto non moto <lb/>corporis dati qui quidem punctus tunc eſt centrum <lb/>illius motus tunc tale corpus vniformiter difformi­<lb/>ter mouetur quo ad ſubiectum. </s>
              <s xml:id="N1CDE0" xml:space="preserve">Probatur hec con-<lb/>cluſio / quia illa definitio cõuenit omni et ſoli etc. / igi­<lb/>tur eſt bona: et antecedens pro nunc alio modo non <lb/>probatur niſi quia omni motui q̇ cõmuniter cõcedi­<lb/>tur vniformiter difformis quo ad ſubiectum con-<lb/>uenit illa definitio, et ſoli tali: igitur propoſitum.</s>
            </p>
            <note position="right" xml:id="N1CDED" xml:space="preserve">1. correl.</note>
            <p xml:id="N1CDF1">
              <s xml:id="N1CDF2" xml:space="preserve">¶ Ex hac concluſione et predictis ſequitur /  cuiuſli­<lb/>bet quod vniformiter difformiter mouetur quo ad <lb/>ſubiectum quelibet pars quantitiua vniformiter <lb/>difformiter mouetur quo ad ſubiectum. </s>
              <s xml:id="N1CDFB" xml:space="preserve">Probatur / <lb/>quia cuiuſlibet talis partis quilibet punctus in ea <lb/>proportione velocius mouetur in qua plus diſtat a <lb/>centro illius motus / ergo ſequitur /  quelibet pars <lb/>quantitatiua illius quod vniformiter difformiter <lb/>mouetur quo ad ſubiectum etiam vniformiter dif-<lb/>formiter mouetur quo ad ſubiectum </s>
              <s xml:id="N1CE0A" xml:space="preserve">Conſequentia <lb/>patet ex definitione: et antecedens patet / quoniam ſi­<lb/>cut illa puncta mouentur in toto ita etiam in illa ꝑ­<lb/>te totius in qua ſunt / vt notū eſt.               <anchor type="note" xlink:href="note-0132-01" xlink:label="note-0132-01a"/>               </s>
              <s xml:id="N1CE18" xml:space="preserve">¶ Sequitur ſecūdo / <lb/> non oportet /  motus vniformiter difformis quo <lb/>ad ſubiectum correſpondeat gradui motus exiſten­<lb/>ti in medio magnitudinis talis corporis: nec in me­<lb/>dio longitudinis. </s>
              <s xml:id="N1CE23" xml:space="preserve">Probatur hoc correlarium / quo <lb/>ad primam partem ex primo argumento et eius ſe­<lb/>cunda confirmatione: </s>
              <s xml:id="N1CE2A" xml:space="preserve">Et quo ad ſecundam partem <lb/>ex confirmatione ſecundi argumenti.</s>
            </p>
            <div xml:id="N1CE2F" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0132-01a" xlink:label="note-0132-01" xml:id="N1CE33" xml:space="preserve">.2correl.</note>
            </div>
            <note position="right" xml:id="N1CE39" xml:space="preserve">3. correl.</note>
            <p xml:id="N1CE3D">
              <s xml:id="N1CE3E" xml:space="preserve">¶ Sequitur tertio /  motus vniformiter difformis <lb/>quo ad ſubiectum cõmenſurari habet penes gradū <lb/>medium inter ſummã et infimū vel non gradum vbi­<lb/>cun ſit talis gradus. </s>
              <s xml:id="N1CE47" xml:space="preserve">Patet / quia non videtur aliꝰ <lb/>modus cognoſcendi totalem velocitatem motꝰ vni­<lb/>formiter difformis quo ad ſubiectuꝫ. </s>
              <s xml:id="N1CE4E" xml:space="preserve">Et per hoc pa­<lb/>tet concluſio reſponſiua ad dubitationem / q̄ talis ē.</s>
            </p>
            <p xml:id="N1CE53">
              <s xml:id="N1CE54" xml:space="preserve">Definitio illa / que cõmuniter dat̄̄ de <lb/>motu vniformiter difformi quo ad ſubiectum non <lb/>eſt ſufficienter aſſignata: quoniã nec valet ſi intelli­<lb/>gatur de medio magnitudinis nec ſi ītelligatur de <lb/>medio longitudinis / vt declaratum eſt in ſecūdo cor­<lb/>relario. </s>
              <s xml:id="N1CE61" xml:space="preserve">His poſitis.</s>
            </p>
            <p xml:id="N1CE64">
              <s xml:id="N1CE65" xml:space="preserve">Reſpondeo ad argumenta ante oppo­<lb/>ſitum /  illa ſunt pro concluſione reſpoſiua. </s>
              <s xml:id="N1CE6A" xml:space="preserve">Quia <lb/>tamen in primo argumēto queritur an in motu vni­<lb/>formiter difformi quo ad ſubiectum gradus mediꝰ <lb/>debeat eſſe in medio corporis quo ad magnitudinē <lb/>vel quo ad longitudinem / dico /  neuter illoruꝫ me­<lb/>diorum requiritur /  ſit in medio corporis / vt dicit <lb/>ſecundum correlarium. </s>
              <s xml:id="N1CE79" xml:space="preserve">¶ Ad replicam tamen reſ-<lb/>pondetur negando antecedens / vt ibi dicitur / quam­               <pb chead="Secundi tractatus" file="0133" n="133"/>               uis talis replica ſit pro concluſione. </s>
              <s xml:id="N1CE83" xml:space="preserve">Quia tamē in­<lb/>quirit penes quē punctum debeat ibi attendi motꝰ <lb/>illius quadrati / dico /  debet attendi penes punctū <lb/>qui mouetur gradu medio inter gradum octauum <lb/>quo mouetur punctus velociſſime motus illius par­<lb/>tis et gradum quo mouetur punctus tardiſſime mo­<lb/>tus eiuſdem quadrati vbicun talis punctus fue-<lb/>rit: de ſitu enim eius non eſt curandum. </s>
              <s xml:id="N1CE94" xml:space="preserve">Sed ad vi-<lb/>dendum an tale quadratum moueatur vniformiter <lb/>difformiter oportet aſpicere an in quacū propor­<lb/>tione quilibet punctus eius magis diſtet a centro ī <lb/>ea velociꝰ moueatur. </s>
              <s xml:id="N1CE9F" xml:space="preserve">Et hoc ſufficit et requiritur ad <lb/>motum vniformiter difformem / vt ibi dictum eſt: et <lb/>quia ſic eſt de illo quadrato. </s>
              <s xml:id="N1CEA6" xml:space="preserve">Ideo dico illud moue-<lb/>ri vniformiter difformtter. </s>
              <s xml:id="N1CEAB" xml:space="preserve">¶ Ad ſecundam confir-<lb/>mationem concedo ſequelam / et nego falſitatem cõ-<lb/>ſequentis: et ad probationem dico /  denominatio <lb/>motus non debet attendi penes denominationem <lb/>partium ita  quantocun motus fuerit in maiori <lb/>parte ſubiecti tanto plus denominat. </s>
              <s xml:id="N1CEB8" xml:space="preserve">vt bene pro-<lb/>bat argumentum / quãuis hoc oporteat in qualita-<lb/>te / vt poſtea dicetur. </s>
              <s xml:id="N1CEBF" xml:space="preserve">Sed quomodo debeat cogno-<lb/>ſci velocitas talis motus dictum eſt: et poſtea latiꝰ. <lb/></s>
              <s xml:id="N1CEC5" xml:space="preserve">dicetur.</s>
            </p>
            <p xml:id="N1CEC8">
              <s xml:id="N1CEC9" xml:space="preserve">Ad ſecundū argumentū / cum ſua con­<lb/>firmatione dico /  ſunt pro concluſione reſpcnſiua <lb/>quia impugnant definitionem communeꝫ </s>
              <s xml:id="N1CED0" xml:space="preserve">Dico ta­<lb/>men /  motus celi eſt vniformiṫ difformis / vt poſtea <lb/>dicetur / quia quodlibet punctum eius in ea propor­<lb/>tione in qua plus diſtat a polo proximiori vel eque <lb/>propinquo in ea velocius mouetur </s>
              <s xml:id="N1CEDB" xml:space="preserve">Dico / eque pro­<lb/>pinquo ꝓpter puncta exiſtentia in equinoctiali: de <lb/>hoc poſtea dicetur. </s>
              <s xml:id="N1CEE2" xml:space="preserve">¶ Quantū ad confirmationem <lb/>dico /  illud quadratū vniformiter difformiter mo­<lb/>uetur per rarefactionem et ſimiliter illa pars que ſi­<lb/>gnatur in eo. </s>
              <s xml:id="N1CEEB" xml:space="preserve">Et cum probatur /  non dico /  illa ꝓ­<lb/>batio eſt pro me et contra definitionem quam īpug-<lb/>gno. </s>
              <s xml:id="N1CEF2" xml:space="preserve">Et hec de dubitatione.               <anchor type="note" xlink:href="note-0133-01" xlink:label="note-0133-01a"/>               </s>
              <s xml:id="N1CEFA" xml:space="preserve">¶ Sed de velocitate <lb/>motꝰ penes effectū eſt difficultas per quid habeat <lb/>attendi </s>
              <s xml:id="N1CF01" xml:space="preserve">Ideo recitãde ſunt opiniones in hac mate­<lb/>ria cõmuniter occurrentes. </s>
              <s xml:id="N1CF06" xml:space="preserve">Unde duplex eſt opinio <lb/>cõmunis tam de motu vniformiter difformi quo ad <lb/>tempus quaꝫ de motu vniformiter difformi quo ad <lb/>ſubiecum et quo ad ſubiectum et tempus ſimul.</s>
            </p>
            <div xml:id="N1CF0F" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0133-01a" xlink:label="note-0133-01" xml:id="N1CF13" xml:space="preserve">penes q̇d <lb/>velocitaſ <lb/>penes ef-<lb/>fectū hē-<lb/>at attēdi</note>
            </div>
            <p xml:id="N1CF21">
              <s xml:id="N1CF22" xml:space="preserve">Prima opinio eſt guillermi hentiſbe-<lb/>ri qui dicit /  velocitas motus vniformiter diffor-<lb/>mis quo ad ſubiectū d3 attēdi penes punctū velociſ­<lb/>ſime motuꝫ </s>
              <s xml:id="N1CF2B" xml:space="preserve">De vniformiter autē difformi quo ad tē­<lb/>pus coincidit cum ſecunda opinione / que dicit /  mo­<lb/>tus vniformiter difformis quo ad tempus debet at­<lb/>tendi penes gradum medium quo ad tempus id eſt <lb/>penes gradum quo mouetur mobile in medio ta-<lb/>lis temporis: et motus vniformiter difformis quo <lb/>ad ſubiectum debet attendi penes gradum mediuꝫ <lb/>totius latitudinis vniformiter difformis. </s>
              <s xml:id="N1CF3C" xml:space="preserve">Et hec eſt <lb/>communior opinio:</s>
            </p>
            <p xml:id="N1CF41">
              <s xml:id="N1CF42" xml:space="preserve">¶ Aduertendum tamen /  quando dicimus /  velo­<lb/>citas motus vniformiter difformis debet attēdi pe­<lb/>nes gradum mediuum voluminis dicere /  tale mo­<lb/>bile vniformiter difformiter motum mouetur ade-<lb/>quate ita velociter ſicut mouetur punctus in quo eſt <lb/>gradus medius talis latitudinis </s>
              <s xml:id="N1CF4F" xml:space="preserve">Et quãdo dicitur / <lb/> motus vniformiter difformis quo ad tempus ve-<lb/>locitas debet attendi penes gradum mediū qui eſt <lb/>in medio temporis volumus dicere /  tam veloci-<lb/>ter mouetur in illo tempore adequate illud mobile: <lb/>ac ſi per totum illud tempus moueretur illo gradu <lb/>quem habet in medio illius temporis.</s>
            </p>
            <cb chead="Capitulum primum"/>
            <p xml:id="N1CF60">
              <s xml:id="N1CF61" xml:space="preserve">¶ Aduertendum eſt vlterius /  velocitas motꝰ quo <lb/>ad effectum debet attendi penes ſpacium pertranſi­<lb/>tum: ita  quanto ſpacium pertranſitum fuerit ma­<lb/>ius in equali tēpore tanto motus erit velocior. </s>
              <s xml:id="N1CF6A" xml:space="preserve">Di-<lb/>co tamen /  non debet attendi velocitas motus lo-<lb/>calis penes ſpacium corporale nec penes ſpacium <lb/>ſuperficiale ſed penes ſpacium lineale deſcriptum <lb/>a certo puncto / q2 tunc ſi vnus equus traheret duas <lb/>trabes inequales eque velociter tamen ſequeretur / <lb/> maior velocius moueretur / cum deſcribat maius <lb/>ſpacium corporale et ſuperficiale quam minor: qḋ <lb/>tamen falſum / quia equaliter mouentur cū in vtra-<lb/> punctus medius equale ſpacium deſcribat. </s>
              <s xml:id="N1CF7F" xml:space="preserve">Et <lb/>ſic etiam dicendum eſt de motu circulari vniformi-<lb/>ter difformi quo ad ſubiectum /  velocitas eius ha­<lb/>bet attendi penes lineam circularem deſcriptam a <lb/>puncto / in quo eſt gradus medius illius latitudinis <lb/>motus vniformiter difformis. </s>
              <s xml:id="N1CF8C" xml:space="preserve">Uelocitas motꝰ vni­<lb/>formiter difformis quo ad tempus et quo ad ſubie-<lb/>ctum debet attendi penes lineaꝫ deſcriptam a pun­<lb/>cto / in quo eſt medius gradus talis latitudinis. </s>
              <s xml:id="N1CF95" xml:space="preserve">Et <lb/>ſimiliter dicenduꝫ eſt de motu difformiter difformi <lb/>quo ad tempus. </s>
              <s xml:id="N1CF9C" xml:space="preserve"> velocitas eius debet attendi penes <lb/>ſpacium pertranſitum in tali tempore: </s>
              <s xml:id="N1CFA1" xml:space="preserve">Qualiter <lb/>autem quantitas talis ſpacii debeat cognoſci / quia <lb/>ibi eſt huius materie precipua inquiſitio in fequent­<lb/>tibus ſuo loco declarabitur.               <anchor type="note" xlink:href="note-0133-02" xlink:label="note-0133-02a"/>               </s>
              <s xml:id="N1CFAF" xml:space="preserve">¶ Ex his tamen īfer-<lb/>tur iſtam conſequentiam non valere. </s>
              <s xml:id="N1CFB4" xml:space="preserve">Iſta rota vni­<lb/>formiter difformiter mota quo ad ſubiectuꝫ deſcri­<lb/>bit maiorem lineam quam punctus in quo eſt gra-<lb/>dus medius totius latitudinis motus: igitur moue­<lb/>tur velocius quam ille punctus quia antecedens eſt <lb/>verum cum punctus exiſtens in circunferentia ſiue <lb/>peripheria ipſius rote deſcribat maiorem lineam <lb/>quam punctus in quo eſt gradus medius latitudi­<lb/>nis motus et vtra illarum linearum per motuꝫ ro­<lb/>te deſcribitur </s>
              <s xml:id="N1CFC9" xml:space="preserve">Similiter arguendo de celo dabitur <lb/>antecedens verum et cõſequens falſum / vt aliquali-<lb/>ter viſum eſt et poſtea videbitur.               <anchor type="note" xlink:href="note-0133-03" xlink:label="note-0133-03a"/>               </s>
              <s xml:id="N1CFD5" xml:space="preserve">¶ Secundo ſequi-<lb/>tur /  iſta conſequentia non valet iſta rota vnifor-<lb/>miter difformiter mouetur quo ad ſubiectum / et ci-<lb/>tius trãſibit lineam circularem equalem linee de-<lb/>ſcripte a puncto / in quo eſt medius gradus latitudi­<lb/>nis quam talis punctus / in quo eſt gradus medius <lb/>latitudinis motus deſcribat ſuam lineam: ergo ro­<lb/>ta citius mouetur quam talis punctus </s>
              <s xml:id="N1CFE6" xml:space="preserve">Manifeſtū <lb/>eſt enim /  rota ſecundum ſe totam quantocun ꝑ­<lb/>tio tempore moueatur deſcribit talem lineam: pun­<lb/>ctus vero nõ. </s>
              <s xml:id="N1CFEF" xml:space="preserve">Et ideo dictum eſt /  debet attendi pe­<lb/>nes lineam ab vno puncto continuo deſcriptam de <lb/>quo tamen latius in ſequentibus.               <anchor type="note" xlink:href="note-0133-04" xlink:label="note-0133-04a"/>               </s>
              <s xml:id="N1CFFB" xml:space="preserve">¶ Tertio ſequi-<lb/>tur /  iſta conſequcntia non valet: iſtud lignum ma­<lb/>ius ſpatium pertranſibit quam illud in eodem tem­<lb/>pore: igitur velocius mouebitur in eodem tempore <lb/></s>
              <s xml:id="N1D005" xml:space="preserve">Probatur captis / vt iam dictum eſt duobus lignis <lb/>in equalis craſſitudinis et longitudinis / que ab vno <lb/>equo equaliter trahãtur / et manifeſtum eſt /  maius <lb/>ſpacium corporale ſuperficiale et etiam lineale (nõ <lb/>tamen ab eodem puncto continuo deſcriptum) per­<lb/>tranſit quam aliud lignum minus: nihilominus ta­<lb/>men talia ligna equaliter mouentur. </s>
              <s xml:id="N1D014" xml:space="preserve">¶ Hiis ſuper-<lb/>ficie tenꝰ dictꝪ / vt intelligat̄̄ ordo ꝓcedendi ī hac ma­<lb/>teria. </s>
              <s xml:id="N1D01B" xml:space="preserve">primo diſceptabo penes / quid habeat atten-<lb/>di velocitas motus difformis qno ab ſubiectū hoc <lb/>eſt tam vniformiter difformis quã difformiter dif-<lb/>formis quo ad ſubiectum. </s>
              <s xml:id="N1D024" xml:space="preserve">Et ſecundo diſputabo pe­<lb/>nes / quid habeat attendi velocitas motꝰ difformis <lb/>quo ad tempus tam vniformiter difformis ꝙ̄ dif-<lb/>formiter difformis quãtū ingenioli nr̄i capacitas               <pb chead="De motu locali quo ad effectum ſubiecto difformi." file="0134" n="134"/>               ſe extendit </s>
              <s xml:id="N1D032" xml:space="preserve">In ea em̄ parte eſt abyſſus multa et huiꝰ <lb/>materie laborynthus a capacitate intellectus fini-<lb/>ta in extricabilis et incomprehenſibilis: vt ibi vide-<lb/>bitur in poſitione variorum caſuum varia mõſtra <lb/>et difformitates motuum difformiter difformiū ad <lb/>tempus ponentium. </s>
              <s xml:id="N1D03F" xml:space="preserve">Et poſtremo aliquid quam bre­<lb/>uiſſime potero de velocitate motus difformis quo <lb/>ad tp̄s et quo ad ſubiectū ſimul et ēt motꝰ mixti deter­<lb/>minabo </s>
              <s xml:id="N1D048" xml:space="preserve">Et ſic trimembris dūtaxat erit huius mate­<lb/>rie diſceptatio, et inquiſitio quibus determinatis <lb/>abſoluta fere erit.</s>
            </p>
            <div xml:id="N1D04F" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0133-02a" xlink:label="note-0133-02" xml:id="N1D053" xml:space="preserve">.1. correl.</note>
              <note position="right" xlink:href="note-0133-03a" xlink:label="note-0133-03" xml:id="N1D059" xml:space="preserve">2. correl.</note>
              <note position="right" xlink:href="note-0133-04a" xlink:label="note-0133-04" xml:id="N1D05F" xml:space="preserve">.3. corre.</note>
            </div>
          </div>
          <div xml:id="N1D065" level="4" n="2" type="chapter" type-free="capitulum">
            <head xml:id="N1D06A" xml:space="preserve">Capitulum ſecundum / in quo inueſtiga­<lb/>tur diſputatiue et per modum queſtionis <lb/>penes quid attendi habeat motus loca-<lb/>lis difformis quo ad ſubiectum velocitas</head>
            <p xml:id="N1D073">
              <s xml:id="N1D074" xml:space="preserve">COnſequenter ad primi puncti <lb/>expeditionem accedens </s>
              <s xml:id="N1D079" xml:space="preserve">Queritur penes <lb/>quid tam̄ penes effectum motus diffor-<lb/>mis quod ad ſubiectum velocitas attendi habeat: <lb/>an videlicet penes lineam deſcriptam a puncto ve­<lb/>lociſſime moto: an penes lineam deſcriptam a pun­<lb/>cto in quo eſt gradus medius: an penes reductionē <lb/>ad vniformitatem.</s>
            </p>
            <note position="left" xml:id="N1D088" xml:space="preserve">opinio <lb/>hētiſberi</note>
            <p xml:id="N1D08E">
              <s xml:id="N1D08F" xml:space="preserve">Et arguitur primo /  non debeat attē­<lb/>di penes primum / vt opinatur hentiſber in tracta-<lb/>tu de motu locali capite primo: quia ſi ſic ſequeret̄̄ <lb/>pari ratione /  deberet attendi penes punctum tar­<lb/>diſſime motum: ſed hoc eſt falſum cum aliquãdo nõ <lb/>detur: igitur. </s>
              <s xml:id="N1D09C" xml:space="preserve">Patet conſequentia / quia non vide-<lb/>tur maior ratio de vno ꝙ̄ de altero. </s>
              <s xml:id="N1D0A1" xml:space="preserve">¶ Dices /  ar-<lb/>guens dat rationem dicens /  plerum non datur <lb/>punctus tardiſſime motus: et ideo non poterit con-<lb/>tinuo velocitas motus penes talem punctū attēdi.</s>
            </p>
            <p xml:id="N1D0AA">
              <s xml:id="N1D0AB" xml:space="preserve">Sꝫ ↄ̨̨tra q2 etiã vt inferiꝰ videbit̄̄ da-<lb/>tur aliquis motus difformis quo ad ſubiectum cu-<lb/>ius non datur punctus continuo velociſſime motus / <lb/>vt patebit in rota rarefiente: igitur etiam non po-<lb/>teſt continuo attendi penes talem punctum: et ſi ta-<lb/>lis punctus continuo maneat non tamen linea quã <lb/>diſcribit adequate.               <anchor type="note" xlink:href="note-0134-01" xlink:label="note-0134-01a"/>               </s>
              <s xml:id="N1D0BF" xml:space="preserve">¶ Et confirmatur / quia tunc ſe­<lb/>queretur /  rota vniformiter difformiter mota mo­<lb/>ueretur continuo ita velociter ſicut medietas eius <lb/>que velocius mouetur: ſed hoc eſt falſum: igitur </s>
              <s xml:id="N1D0C8" xml:space="preserve">Cõ­<lb/>ſequentia patet et falſitas conſequentis oſtenditur / <lb/>quoniam cum vtra medietas ſit equalis non va-<lb/>let ratio ſufficiens aſſignari quare potius ita velo­<lb/>citer mouetur tota rota ſicut medietas vna et non ſi­<lb/>cut altera (et volo /  ly ita et ſicut diſtribuat): igitur <lb/>ſi ita velociter ſicut vna etiam ſicut et altera vel ſi-<lb/>cut neutra. </s>
              <s xml:id="N1D0D9" xml:space="preserve">¶ Dices /  ideo dicitur moueri ita velo-<lb/>citer ſicut medietas eius que velociꝰ mouetur: et nõ <lb/>ſicut illa que tardius mouetur:               <anchor type="note" xlink:href="note-0134-02" xlink:label="note-0134-02a"/>               quia iuxta dictū phi­<lb/>loſophi ſecundo de anima dignum eſt vnumquod-<lb/> a digniori denominari. </s>
              <s xml:id="N1D0E9" xml:space="preserve">Tum etiam quia illd qḋ <lb/>deſcribitur a medietate / que velocius mouetur de-<lb/>ſcribitur a tota rota cathegorematice: et nullū ma-<lb/>ius ſpacium a tota rota deſcribitur: ſed quodlibet <lb/>minus vſ ad non gradum vel ad certum gradum <lb/></s>
              <s xml:id="N1D0F5" xml:space="preserve">Non autem ſic eſt de ſpacio deſcripto a medietate <lb/>tardius mota.</s>
            </p>
            <div xml:id="N1D0FA" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0134-01a" xlink:label="note-0134-01" xml:id="N1D0FE" xml:space="preserve">cõfirma-<lb/>tio.</note>
              <note position="left" xlink:href="note-0134-02a" xlink:label="note-0134-02" xml:id="N1D106" xml:space="preserve">phūs .2. <lb/>de aīa.</note>
            </div>
            <p xml:id="N1D10E">
              <s xml:id="N1D10F" xml:space="preserve">Sed contra / quia plerum nõ datur <lb/>punctus extremus: vt poſito /  deus corrumpat in <lb/>rota omnia puncta extrema. </s>
              <s xml:id="N1D116" xml:space="preserve">Item etiam nominali­<lb/>ſando non datur punctum extremum / quia termini­<lb/>ſta omnia talia indiuiſibilia negat: et ſigmentum re­<lb/>putat: igitur ſaltem ſecundum viam nominaliū nõ <lb/>poteſt ſumi velocitas motus difformis / quo ad ſub­               <cb chead="De motu locali quo ad effectum ſubiecto difformi."/>               iectum penes lineam a puncto velociſſime moto de­<lb/>ſcriptam.               <anchor type="note" xlink:href="note-0134-03" xlink:label="note-0134-03a"/>               </s>
              <s xml:id="N1D12B" xml:space="preserve">¶ Dices /  in tali caſu velocitas illiꝰ mo-<lb/>tus debet attendi penes lineam deſcriptam a pun-<lb/>cto imaginario poſito in peripheria / hoc eſt tota ro­<lb/>ta tantam lineam deſcribit et tam velociter moue-<lb/>tur / quam velociter mouetur vnus punctum qui eſſet <lb/>in peripheria talis rote.</s>
            </p>
            <div xml:id="N1D138" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0134-03a" xlink:label="note-0134-03" xml:id="N1D13C" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N1D142">
              <s xml:id="N1D143" xml:space="preserve">Sed contra capio vnam rotam / q̄ dif-<lb/>formiter mouetur quo ad ſubiectum / et cum incipit <lb/>moueri incipiat maiorari per rarefactionem ita  <lb/>punctus eius extremus continuo magis ac mgis di­<lb/>ſtat a centro ita  in principio totius rote diame-<lb/>ter ſit pedalis et in fine bipedalis. </s>
              <s xml:id="N1D150" xml:space="preserve">quo poſito ſic ar­<lb/>guitur velocitas talis motus non poteſt attendi pe­<lb/>nes lineam deſcriptam a puncto velociſſime moto: <lb/>igitur propoſitum. </s>
              <s xml:id="N1D159" xml:space="preserve">Arguitur antecedens / quia ta-<lb/>lis punctus nullam lineam deſcribit: quod proba-<lb/>tur ſic / quia nullam circularem vt notum eſt cū non <lb/>redeat ad idem punctum / a quo receſſit ſed ad pun-<lb/>ctum in duplo magis diſtans a centro. </s>
              <s xml:id="N1D164" xml:space="preserve">nec etiam li­<lb/>neam rectam aliquam deſcribit: et non videtur quã <lb/>aliam lineam deſcribat: igitur non datur ibi linea <lb/>deſcripta a tali pnncto penes / quam poſſit veloci-<lb/>tas motus illius rote commenſurari               <anchor type="note" xlink:href="note-0134-04" xlink:label="note-0134-04a"/>               </s>
              <s xml:id="N1D174" xml:space="preserve">¶ Et confirma­<lb/>tur / qua illa rota non mouetur ita velociter ſicut pū­<lb/>ctus eius extremus mouetur in principio motus / vt <lb/>notum eſt / cum maiorem lineam deſcribat per totū <lb/>tempus / quam ſi rota maneret īuariata quo ad ma­<lb/>gnitudinem, nec tanta velocitate quanta mouetur <lb/>in fine motus nec in medio inſtanti motus / quia tūc <lb/>hoc eſſet coincidere cum alia opinione que commen­<lb/>ſurat penes gradum medium: igitur non videt̄̄ pe-<lb/>nes / quid attendi habeat velocitas talis motus. </s>
              <s xml:id="N1D189" xml:space="preserve">Et <lb/>ſic habetur /  non omnis velocitas motus diffor-<lb/>mis quo ad ſubiectum attendi habeat penes veloci­<lb/>tatem puncti velociſſime moti.</s>
            </p>
            <div xml:id="N1D192" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0134-04a" xlink:label="note-0134-04" xml:id="N1D196" xml:space="preserve">2. confir.</note>
            </div>
            <p xml:id="N1D19C">
              <s xml:id="N1D19D" xml:space="preserve">Secundo principaliter contra eandē <lb/>partem arguitur: quia ſi illud eſſet verum ſequere-<lb/>tur hec concluſio /  aliquod mobile continuo vnifor­<lb/>miter moueretur et tamen quilibet punctus eius in­<lb/>trinſecus continuo intenderet motum ſuuꝫ / ſed hoc <lb/>videtur impoſſibile / igitur illud ex quo ſequitur.</s>
            </p>
            <p xml:id="N1D1AA">
              <s xml:id="N1D1AB" xml:space="preserve">Sequela tamen probatur: et capio vnam rotã quaꝫ <lb/>diuido in duas medietates circulares concentricas / <lb/>vt patet ſupra in figura et rarefiat continuo vnifor­<lb/>miter dum talis rota mouetur circulariṫ medietas <lb/>interior verſus circunferentiam condenſando me-<lb/>dietatem ſuperiorem verſus circunferentiam quieſ­<lb/>centibus continuo punctis circunferentialibus: ita <lb/> continuo equaliter diſtant a centro. </s>
              <s xml:id="N1D1BC" xml:space="preserve">quo poſito il­<lb/>la rota continuo vniformiter mouetur / vt notum eſt <lb/>ex opinione et tamen quilibet punctus eius intrin-<lb/>ſecus continuo intendit motum ſuum (cum con-<lb/>tinuo magis ac magis diſtet a centro et ↄ̨tinuo ma­<lb/>iorem lineam deſcribat) igitur. </s>
              <s xml:id="N1D1C9" xml:space="preserve">Poteſt vniuerſali-<lb/>ter inferri talis concluſio ſi in tali rota corrumpan­<lb/>tur extrema puucta. </s>
              <s xml:id="N1D1D0" xml:space="preserve">¶ Dices /  hoc non eſt inconue­<lb/>niens / vt beue probat argumentum: </s>
              <s xml:id="N1D1D5" xml:space="preserve">Imo etiã alia <lb/>opinio idem tenetur concedere.</s>
            </p>
            <p xml:id="N1D1DA">
              <s xml:id="N1D1DB" xml:space="preserve">Contra quia tunc pari pacto ſequere-<lb/>tur /  aliquod mobile continuo vniformiter moue-<lb/>retur: et tamen quilibet punctus eius intrinſecus cõ­<lb/>tinuo remitteret motum ſuum: ſed hoc videtur incõ­<lb/>ueniēs: igitur </s>
              <s xml:id="N1D1E6" xml:space="preserve">Sequela probatur caſu poſito /  me­<lb/>dietas rote ſuperior rarefiat verſus medietatē in-<lb/>tenſiorem eam condenſando punctis extremis q̇e-<lb/>ſcentibus / quo poſito facile apparet propoſitum.</s>
            </p>
            <pb chead="Secundi tractatus" file="0135" n="135"/>
            <note position="left" xml:id="N1D1F3" xml:space="preserve">dicitur.</note>
            <p xml:id="N1D1F7">
              <s xml:id="N1D1F8" xml:space="preserve">¶ Dices /  iſte due concluſiones tam illate: et ab iſta <lb/>opinione / et altera ſunt concedende. </s>
              <s xml:id="N1D1FD" xml:space="preserve">Et ideo ſunt cor­<lb/>relaria et non inconuenientia.</s>
            </p>
            <p xml:id="N1D202">
              <s xml:id="N1D203" xml:space="preserve">Contra quia tunc ſequeretur /  a qua­<lb/>libet parte proportionali alicuius mobilis ſecun-<lb/>dum certam diuiſionem procedendo demeretur ali­<lb/>qua velocitas: ita  quelibet ſecundum talem diui­<lb/>ſionem moueatur minori velocitate ꝙ̄ antea mo-<lb/>uebatur: et tamen totum mobile mouetur continuo <lb/>vniformiṫ et eq̄ velociṫ ſicut ãtea: ſꝫ ↄ̨ſeq̄ns eſt falſū: <lb/>igitur illud ex quo ſequitur: </s>
              <s xml:id="N1D214" xml:space="preserve">Falſitas conſequentis <lb/>oſtenditur / quia alias ſequeretur /  tota velocitas <lb/>poteſt demi a partibus proportionalibus manen­<lb/>te tamen ſemper velocitate totius equali / quod eſt <lb/>mere impoſſibile. </s>
              <s xml:id="N1D21F" xml:space="preserve">Patet hoc poſito /  in hora con-<lb/>tinue cuiuſlibet partis proportionalis ſecundum / <lb/>hanc diuiſionem remittatur motus quo ad vſ ve-<lb/>niat ad non gradum / tunc continuo per illam horã <lb/>tale mobile per te mouebitur equaiiter et vniformi-<lb/>ter: ergo adhuc poſt illud inſtans terminatiuum po­<lb/>terit ſic moueri motu partium ad non gradum re-<lb/>miſſo: </s>
              <s xml:id="N1D230" xml:space="preserve">Sed iam probo ſequelam: et pono caſum /  <lb/>vna rota diuidatur per partes proportionales cir­<lb/>culares concentricas minoribus terminatis verſus <lb/>peripheriam rote: et a prima dematur medietas ſue <lb/>velocitatis et a ſequenti eam puta a ſecunda demat̄̄ <lb/>medietas vnius gradus et a tertia quarta vniꝰ gra-<lb/>dus: et ſic conſequenter procedendo per partes ſub­<lb/>duplas quo poſito a puncto extremo nulla veloci-<lb/>tas demitur: et mouetur: igitur continuo mouet̄̄ vni­<lb/>formiter </s>
              <s xml:id="N1D245" xml:space="preserve">Patet conſequentia et tamen quelibet ꝑs <lb/>eius proportionalis ſecundum certam diuiſionem <lb/>mouetur velocitate minori / ꝙ̄ mouebatur antea <lb/></s>
              <s xml:id="N1D24D" xml:space="preserve">Sed ad inferendum  quelibet pars proportiona­<lb/>lis ſecundum talem diuiſioneꝫ moueatur ſubdupla <lb/>velocitate oportet ponere in caſu /  a qualibet illa­<lb/>rum dematur medietas velocitatis qua antea mo-<lb/>uebatur: et ſic habebitur propoſitum. </s>
              <s xml:id="N1D258" xml:space="preserve">Et ſi tibi caſꝰ <lb/>appareat difficilis / vt nunc michi videor facile erit <lb/>verificare illum caſum in rota flexibili puta aque vĺ <lb/>alterius liquoris exiſtentis intra ſperam rotundaꝫ <lb/>et quilibet punctus eius moueatur quieſcente cētro <lb/>motu circulari: partibus eius mouentibus eodē mo­<lb/>do quo ponitur in caſu:</s>
            </p>
            <p xml:id="N1D267">
              <s xml:id="N1D268" xml:space="preserve">Tertio principaliter contra ſecundaꝫ <lb/>partem queſtionis videlicet /  non debet attēdi pe-<lb/>nes gradum medium arguitur ſic: quia ſi illud eſſet <lb/>veruꝫ ſequeretur /  ſi vna rota moueretur difformi­<lb/>ter quo ad ſubiectum a non gradu vſ ad certū gra­<lb/>dum ita  pars illa que eſt a centro vſ ad medie-<lb/>tatem ſemidiametri moueatur a non gradu vſ ad <lb/>quartum: et reſidua pars vſ ad circunferentiã mo­<lb/>ueatur a quarto vſ ad duodecimum / tunc talis ro­<lb/>ta moueretur velocitate vt ſex: ſed conſequens ē fal­<lb/>ſum / igitur illud ex quo ſequitur </s>
              <s xml:id="N1D27F" xml:space="preserve">Sequela probatur / <lb/>quia ille eſt gradus medius inter duodecimū et non <lb/>gradum. </s>
              <s xml:id="N1D286" xml:space="preserve">Sed iam arguitur falſitas conſequentis / <lb/>quia tunc ſequeretur /  illa rota eque velociter mo­<lb/>ueretur ſicut ſi motus eius eſſet vniformiter diffor-<lb/>mis a non gradu vſ ad duodecimum. </s>
              <s xml:id="N1D28F" xml:space="preserve">Sed conſe-<lb/>quens eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1D294" xml:space="preserve">Con-<lb/>ſequentia apparet: et falſitas conſequentis argui-<lb/>tur / quia ſi illa rota moueretur vniformiter diffor-<lb/>miter a non gradu vſ ad duodecimum: tunc pun-<lb/>ctus medius ſemidiametri moueretur velocitate vt <lb/>ſex / et per conſequēs maiori velocitate quam modo <lb/>et quilibet punctus intrinſecꝰ maiori velocitate quã <lb/>modo / vt ſatis patet intueti: ergo ſequitur /  illa ro­               <cb chead="Capitulum ſecundum"/>               ta mouetur / tunc maiori velocitate quã modo. </s>
              <s xml:id="N1D2A8" xml:space="preserve">Pro­<lb/>batur hec conſequentia / quia modo videlicet quan-<lb/>do vna pars eius que incipit a centro rote et termi-<lb/>natur ad medium ſemidiametri mouetur a nõ gra-<lb/>du vſ ad quartum et reliqua pars a quarto vſ <lb/>ad duodecimum: a velocitate vel penes velocitatem <lb/>alicuius puncti intrinſeci eius commēſuratur et at­<lb/>tenditur motus illius rote, et ab eodem poſtea deb3 <lb/>attendi quando velocius mouetur: igitur propoſi-<lb/>tum: quia rota manet: nec rarefacta: nec condenſa­<lb/>ta: et idem continuo manet punctus eius mediꝰ quã­<lb/>do mouetur ſic motu difformiter difformi et quam­<lb/>do mouetur motu vniformiter difformi.</s>
            </p>
            <note position="right" xml:id="N1D2C3" xml:space="preserve">dicitur.</note>
            <p xml:id="N1D2C7">
              <s xml:id="N1D2C8" xml:space="preserve">¶ Dices negando ſequelam: et ad probationem: di­<lb/>ces /  non eſt cõtra te: quia tu vis dicere /  / debet at­<lb/>tendi motus difformis quo ad ſubiectum penes gra­<lb/>dum mediuꝫ quando talis motus eſt vniformiṫ dif­<lb/>formis quo ad ſubiectum: ſed non quando eſt diffor­<lb/>miter difformis: qnia tunc ſequenda eſt tertia pars <lb/>queſtionis videlicet penes reductionem ad vnifor-<lb/>mitatem.</s>
            </p>
            <p xml:id="N1D2D9">
              <s xml:id="N1D2DA" xml:space="preserve">Sed contra / quia ſi in omni motu vni­<lb/>formiter difformi quo ad ſubiectum debeat veloci-<lb/>tas attendi penes gradum medium / vel igitur ꝑ gra­<lb/>dum medium intelligitur gradus qui eſt medio ta-<lb/>lis ſubiecti quo ad magnitudinem: vel ī medio quo <lb/>ad longitudinem, vel in medio quo ad magnitudi-<lb/>nem et longitudinem ſimul / ſed nullum iſtorum ē di­<lb/>cendum: igitur non debet motus vniformiter diffor­<lb/>mis quo ad ſubiectum velocitas penes gradum me­<lb/>dium commenſurari et attendi. </s>
              <s xml:id="N1D2EF" xml:space="preserve">Maior quo ad pri-<lb/>mam partem videlicet /  non debeat attendi penes <lb/>gradum medium hoc eſt exiſtentem in medio ſubie-<lb/>cti / quo ad magnitudinem patet ex primo argumē-<lb/>to: et ſecunda confirmatione eius in dubitatiõe for-<lb/>mata in priori capite / et quo ad ſecundam partē pa­<lb/>tet ex confirmatione ſecundi argumenti eiuſdem du­<lb/>bitationis prioris capitis. </s>
              <s xml:id="N1D300" xml:space="preserve">Sed quantum ad tertiã <lb/>partem patet manifeſte / quia quãdo rota mouetur <lb/>ſic vniformiter difformiter quo ad ſubiectum a nõ <lb/>gradu in centro vſ ad certum gradum in circunfe­<lb/>rentia procedendo a centro vſ ad circunferentiaꝫ <lb/>nullus idem punctus eſt in medio magnitudinis et <lb/>longitudinis ſignanter quando  rota eſt vbi eq̈­<lb/>lis craſſitudinis </s>
              <s xml:id="N1D311" xml:space="preserve">Tamen volo efficatiori argumēto <lb/>meo iudicio confirmare ſecundam partem minoris <lb/>videlicet /  non debeat velocitas motus vniformi-<lb/>ter difformis quo ad ſubiectum attendi penes pun­<lb/>ctum exiſtentem in medio mobilis quantum ad lon-<lb/>gitudinem. </s>
              <s xml:id="N1D31E" xml:space="preserve">Et in predicta rota de qua ſepe mentio <lb/>facta eſt a centro eius vſ ad circunferētiam ſigno <lb/>vnam colūnã ex cuius baſi in centro rote educo line­<lb/>am giratiuam girantem omnes partes proportio­<lb/>nales talis columne / vt ↄ̨muniter ponitur et volo /  <lb/>talis rota moueat̄̄ vniformiṫ difformiter q̊ ad ſub-<lb/>iectum a non gradu vſ ad octauum / quo poſito ſic <lb/>argumentor illa linea giratiua mouetur vniformi­<lb/>ter difformiter cum ſit pars corporis vniformiter <lb/>difformiter moti et tamen motus eius non correſpõ­<lb/>det gradui exiſtenti in medio corporis quantuꝫ ad <lb/>longitudinem cum nullum tale ſit / vt notum eſt: igi-<lb/>tur aliquod mouetur vniformiter difformiter quo <lb/>ad ſubiectum cuius motus velocitas non attendi-<lb/>tur penes gradum motus exiſtentem in medio eius <lb/>quantum ad longitudinem. </s>
              <s xml:id="N1D33F" xml:space="preserve">Simile argumentum <lb/>fierit / ſi a centro rote educeretur vna linea que circū­<lb/>daret primo primam partem proportionalem cir­<lb/>cularem illius rote, et ſecundam et tertiam et quartã               <pb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi." file="0136" n="136"/>               et ſic cõſequēter: et manifeſtū eſt /  talis linea erit in­<lb/>finita habens cõtinuo circuitiones maiores, et mo­<lb/>uetur vniformiter difformiter: et nullã eſt eius me-<lb/>diū quantū ad longitudinē. </s>
              <s xml:id="N1D353" xml:space="preserve">et per ↄ̨ñs nõ poteſt mo­<lb/>tus eius cõmenſurari penes gradū exiſtentē in me-<lb/>dio eiꝰ quantū ad lõgitudinē. </s>
              <s xml:id="N1D35A" xml:space="preserve">Preterea cõſimile ar­<lb/>gumentū eſſet oīno ſi ſignaretur vnū quadratum a <lb/>centro illiꝰ rote vſ ad circūferentiã: et ꝓtraheret̄̄ <lb/>vna linea girans oēs partes ꝓportionales eiꝰ per <lb/>modum cuiuſdam diametri infinite / vt philoſophi <lb/>oſtendunt communiter in materia de infinito. </s>
              <s xml:id="N1D367" xml:space="preserve">Illa <lb/>enim mouetur vniformiter difformiter quo ad ſub-<lb/>iectuꝫ cum ſit pars corporis vniformiter difformi-<lb/>ter moti quo ad ſubiectum: tamen in eo non repe-<lb/>ritur punctus medius.</s>
            </p>
            <p xml:id="N1D372">
              <s xml:id="N1D373" xml:space="preserve">Quarto principaliter contra eandem <lb/>ſecundã partē cõcluſionis argr̄: q2 ſi illa pars eſſet <lb/>vera / ſequeretur /  celū nõ mouetur ita velociter ſi-<lb/>cut linea equinoctialis (et loquor de primo mobili) / <lb/>ſed cõſequēs eſt falſum: igitur et antecedēs. </s>
              <s xml:id="N1D37E" xml:space="preserve">Conſe-<lb/>quētia ptꝫ et coloratur falſitas cõſequētis: q2 ſi nõ <lb/>mouet̄̄ ita velociter ſicut linea eq̇noctialis, et linea <lb/>eq̇noctialis eſt linea exiſtens in medio eiꝰ: ergo mo­<lb/>bile motū vniformiter difformiter quo ad ſubiectū <lb/>nõ mouetur ita velociter ſicut pūctus exiſtēs in me-<lb/>dio eiꝰ.               <anchor type="note" xlink:href="note-0136-01" xlink:label="note-0136-01a"/>               </s>
              <s xml:id="N1D392" xml:space="preserve">¶ Dices negando falſitatē conſequentis: et <lb/>ad ꝓbationē dices /  in celo, et in quolibet corpore <lb/>ſperico motꝰ velocitas debet attendi penes lineaꝫ <lb/>deſcriptã a pūcto exiſtente in medio inter polum et <lb/>punctū velociſſime motū: et ſic motꝰ primi mobilis <lb/>cõmenſurari hꝫ penes lineã deſcriptã a pūcto / q̇ eſt <lb/>in medio inter polum ſiue articum ſine autarticum <lb/>et lineam equinoctialem.</s>
            </p>
            <div xml:id="N1D3A3" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0136-01a" xlink:label="note-0136-01" xml:id="N1D3A7" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D3AD">
              <s xml:id="N1D3AE" xml:space="preserve">Sed cõtra. </s>
              <s xml:id="N1D3B1" xml:space="preserve">Q2 vel debet attēdi penes <lb/>lineã deſcriptã a pūcto medio in ſuperficie cõcaua <lb/>vel in ſuperficie cõuexa: ſed nullū iſtoꝝ eſt dicendū: <lb/>igr̄. </s>
              <s xml:id="N1D3BA" xml:space="preserve">Antecedens argr̄ / q2 punctus exiſtens in medio <lb/>quãtū ad ſuperficiē cõuexã nõ eſt ſimpliciter in me-<lb/>dio nec punctꝰ exiſtens in ſuꝑficie cõcaua: igr̄. </s>
              <s xml:id="N1D3C1" xml:space="preserve">Item <lb/>tale mobile nõ mouetur ita velotiter ſicut ſuꝑficies <lb/>cõuexa nec ita tarde ſicut ſuꝑficies cõcaua: ergo ſe-<lb/>quitur /  velocitas eiꝰ nõ habet attendi penes pun­<lb/>ctū hoc eſt penes lineã deſcriptã a puncto exiſtente <lb/>in ſuperficie conuexa: nec in ſuperficie concaua.</s>
            </p>
            <note position="left" xml:id="N1D3CE" xml:space="preserve">Dicitur.</note>
            <p xml:id="N1D3D2">
              <s xml:id="N1D3D3" xml:space="preserve">¶ Dices /  velocitas illius primi mobilis menſu-<lb/>randa eſt a puncto exiſtente in medio inter ſuperfi­<lb/>ciem concauam et conuexam inter polum et punctū <lb/>velociſſime motum totius orbis.</s>
            </p>
            <p xml:id="N1D3DC">
              <s xml:id="N1D3DD" xml:space="preserve">Contra. </s>
              <s xml:id="N1D3E0" xml:space="preserve">Quia tunc ſequeret̄̄ hec con-<lb/>cluſio /  ſi primum mobile condenſaretur verſus <lb/>ſuperficiem conuexam quieſcentem ipſum cõtinuo <lb/>velocius et velociꝰ moueretur: et ſi rarefieret verſus <lb/>concauam quieſcente etiam conuexa ipſum mobi-<lb/>le cõtinuo tardius et tardius moueretur / ſed conſe-<lb/>quens eſt falſum: q2 tunc ſequeret̄̄ /  ̄tocū illud <lb/>mobile efficeret̄̄ maiꝰ tardius moueretur, et quãto <lb/>minus velociꝰ quod videtur abſurdū. </s>
              <s xml:id="N1D3F3" xml:space="preserve">cū ceteris pa-<lb/>ribus videatur /  corpus maius maiorē lineã de-<lb/>ſcribat quã minꝰ. </s>
              <s xml:id="N1D3FA" xml:space="preserve">Sed ſequela probatur / q2 quãto <lb/>punctus medius magis accedat ad ſuperficiē con-<lb/>uexã per condenſationē tanto magis recedit a cen­<lb/>tro, et per cõſequens maiorē lineã deſcribit, et quã­<lb/>to magis recedit a ſuperficie cõuexa magis accedit <lb/>ad centrū ſpere vel ad axem: et per cõſequens mino­<lb/>rem lineam circularem deſcribit, et ſic tardius mo­<lb/>uetur / quod fuit probandū.               <anchor type="note" xlink:href="note-0136-02" xlink:label="note-0136-02a"/>               </s>
              <s xml:id="N1D410" xml:space="preserve">¶ Dices ↄ̨cedēdo cõclu-               <cb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi."/>               ſionem ſicut concedenda eſt.</s>
            </p>
            <div xml:id="N1D416" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0136-02a" xlink:label="note-0136-02" xml:id="N1D41A" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D420">
              <s xml:id="N1D421" xml:space="preserve">Sed cõtra. </s>
              <s xml:id="N1D424" xml:space="preserve">Quia tunc ſequeretur /  <lb/>ſi omnes ſpere intermedie corrumperentur, et pri-<lb/>mum mobile quieſcente conuexa ſuperficie rarefie-<lb/>ret verſus axem quo ad vſ ex orbe efficiat̄̄ ſpera <lb/>ſolida vnicam ſuperficiem dumtaxat habens: tūc <lb/>illud mobile iam factum ſpera ſolida longe tardi­<lb/>us moueretur quam antea, et etiam moueretur vni­<lb/>formiter difformiter quo ad ſubiectum: ſed conſe-<lb/>quens eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1D437" xml:space="preserve">Se-<lb/>quela patet ex opinione et ſolutiõibus datis. </s>
              <s xml:id="N1D43C" xml:space="preserve">Sed <lb/>falſitas conſequentis quo ad primam partem ar-<lb/>guitur / quia tunc ſequeretur /  ab equali propor-<lb/>tione inequales motus prouenirēt: ſed conſequēs <lb/>eſt falſum: et contra baſim et fundamentum totius <lb/>huius operis: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1D449" xml:space="preserve">Seque-<lb/>la tamen probatur / quia modo intelligentia mouet <lb/>primum mobile ab aliqua proportione, et tunc ip-<lb/>ſū ſic rarefactū / vt ponitur ab eadem proportione <lb/>mouetur ad eadem intelligentia / quia volo /  nullo <lb/>pacto plus reſiſtet quam antea reſiſtebat, et tamen <lb/>tardius mouetur vt dicis: igitur ab eadem propor­<lb/>tione inequales velocitates proueniunt / quod fuit <lb/>probandum. </s>
              <s xml:id="N1D45C" xml:space="preserve">¶ Et ſi dicas /  in celo nulla eſt reſi-<lb/>ſtentia nec ibi proprie motus factus a certa pro­<lb/>portione inter actiuitatem et reſiſtentiam: ponamꝰ <lb/>caſum ſimilem de quodam orbe habente grauita-<lb/>tē facto ex aliquo mixto vel aliquo elemento quod <lb/>ſic rarefiat <reg norm="quoaduſque" type="simple">quoaduſ</reg> efficiatur ſpera ſolida nul-<lb/>la addita grauitate vel leuitate: et moueatur ab ea­<lb/>dem virtute a qua antea mouebatur / quo poſito ſe-<lb/>quitur illam: igitur. </s>
              <s xml:id="N1D46F" xml:space="preserve">Sed falſitas ſecunde par-<lb/>tis conſequentis arguitur / quia talis motus non <lb/>ita ſe habet  quanto punctus magis diſtat a cen­<lb/>tro tanto velocius moueatur / vt patet de punctis <lb/>terminatibus axem / qui maxime diſtant a centro <lb/>et tamen nõ mouent̄̄: igitur talis motꝰ nõ eſt vnifor-<lb/>miter difformis quo ad ſubiectū. </s>
              <s xml:id="N1D47E" xml:space="preserve">Patet conſequē-<lb/>tia a definitione ad definitum negatiue. </s>
              <s xml:id="N1D483" xml:space="preserve">Nec valet <lb/>dicere /  per centrū in tali motu debet ītelligi po-<lb/>lus / quia etiam contra illud procedit ratio. </s>
              <s xml:id="N1D48A" xml:space="preserve">Nõ em̄ <lb/>quanto punctus in illa ſpera ſolida magis diſtat <lb/>a polo tanto velocius mouetur / vt patet de punctis <lb/>exiſtentibus prope centrum ſpere circa axem que <lb/>puncta ita tarde mouentur ſicut aliqua que ſunt ꝓ­<lb/>pinquiora polo: ergo nec centrum ſphere eſt cen-<lb/>trum talis motus nec polus               <anchor type="note" xlink:href="note-0136-03" xlink:label="note-0136-03a"/>               </s>
              <s xml:id="N1D49E" xml:space="preserve">¶ Et confirmatur / quia <lb/>ſi illa opinio eſſet vera / ſequeretur /  ſi aliqua rota <lb/>continuo condenſaretur verſus centrū mouente e-<lb/>tiam ſuperficie conuexa et motore non mouente a <lb/>maiori conamine: tunc continuo illa rota tardius <lb/>et tardius moueretur: ſed conſequens eſt falſum: <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N1D4AD" xml:space="preserve">Sequela ꝓbatur / quia <lb/>continuo punctus medius minorem lineam deſcri-<lb/>bit: igitur tardius mouetur. </s>
              <s xml:id="N1D4B4" xml:space="preserve">Falſitas tamen con-<lb/>ſequētis arguitur / quia illa rota eque velociter cir­<lb/>cuit ſicut ãtea: g̊ eque velociter mouetur ſicut antea <lb/></s>
              <s xml:id="N1D4BC" xml:space="preserve">Patꝫ ↄ̨ña / q2 circuitio talis rote nihil aliud eſt quã <lb/>motus circularis talis rote. </s>
              <s xml:id="N1D4C1" xml:space="preserve">Item hec circuitio eſt <lb/>ita velox ſicut antea et hec circuitio eſt hic motur <lb/>circularis: igitur hic motus circularis eſt ita velox <lb/>ſicut antea / et per conſequens illa rota tunc non tar­<lb/>dius mouetur / quod fuit probandum.               <anchor type="note" xlink:href="note-0136-04" xlink:label="note-0136-04a"/>               </s>
              <s xml:id="N1D4D1" xml:space="preserve">¶ Dices for-<lb/>te negando falſitatem conſequentis, et ad probati­<lb/>onem concedo /  ita velociter circuit ſicut antea, et <lb/>negando /  ita velociter mouetur, et cum probatur <lb/>per ſyllogiſmum expoſitorum: dico / quod male cõ­<lb/>cluditur ſed oportet inferre: ergo hic motus circu-               <pb chead="Secundi tractatus" file="0137" n="137"/>               laris eſt ita velox circulatio ſicut antea vt conclu-<lb/>datur maior extremitas de minori. </s>
              <s xml:id="N1D4E5" xml:space="preserve">Quãuis enim <lb/>idē ſit circulatio et motus circularis nõ tamen pe-<lb/>nes idem iudicari debet velocitas circuitiõis et ve-<lb/>locitas motus localis circularis / vt poſtea dicetur.</s>
            </p>
            <div xml:id="N1D4EE" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0136-03a" xlink:label="note-0136-03" xml:id="N1D4F2" xml:space="preserve">Confir-<lb/>matio.</note>
              <note position="right" xlink:href="note-0136-04a" xlink:label="note-0136-04" xml:id="N1D4FA" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D500">
              <s xml:id="N1D501" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N1D504" xml:space="preserve">Q2 ſi illa ſolutio eſſet bona <lb/>ſeq̄ret̄̄ /  ab eadē ꝓportione potētie ad ſuã reſiſtē-<lb/>tiã ꝓuenirēt īequales motꝰ, et equales circuitiones / <lb/>qḋ eſt falſū. </s>
              <s xml:id="N1D50D" xml:space="preserve">Seq̄la ptꝫ facile ex ſolutiõe. </s>
              <s xml:id="N1D510" xml:space="preserve">Poſitum <lb/>eſt em̄ /  poña moueret ab eodē conamine rotã cõti­<lb/>nuo equaliter reſiſtentē / et dictū eſt /  a tali ꝓporti-<lb/>one ꝓueniebãt īequales motꝰ. </s>
              <s xml:id="N1D519" xml:space="preserve">eq̈les aūt circuitiões <lb/>               <anchor type="note" xlink:href="note-0137-01" xlink:label="note-0137-01a"/>               </s>
              <s xml:id="N1D523" xml:space="preserve">¶ Dices forte /  iã / tūc nõ eſt eadē ꝓportio īter mo-<lb/>uēs et mobile ſed eſt mīor. </s>
              <s xml:id="N1D528" xml:space="preserve">Sed hoc nõ põt dici qm̄ <lb/>volo /  poña ſit naturalis: et maneat in rota tanta <lb/>reſiſtētia ſicut ãtea erat vt poſitū eſt. </s>
              <s xml:id="N1D52F" xml:space="preserve">Et ſi hoc non <lb/>admittas equa lance currit ↄ̨tra te argumentū de <lb/>circuitiõibꝰ q2 tūc ex īequalibꝰ ꝓportiõibꝰ ꝓuenirēt <lb/>equales circuitiões et īequales motꝰ / qḋ tã incõueni­<lb/>ens videt̄̄ ſicut reliquū. </s>
              <s xml:id="N1D53A" xml:space="preserve">¶ Et ideo dices forte / vt di-<lb/>cūt alii  nõ eſt incõueniēs ab eq̈li ꝓportiõe eq̈les <lb/>circuitiões īequales autē motꝰ ꝓuenire / vt dictū eſt.</s>
            </p>
            <div xml:id="N1D541" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0137-01a" xlink:label="note-0137-01" xml:id="N1D545" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D54B">
              <s xml:id="N1D54C" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N1D54F" xml:space="preserve">Q2 hoc dato iã deſtruit̄̄ fū­<lb/>damentū totiꝰ materie: et iã pari facilitate ꝓteruus <lb/>phiſicꝰ cõcederet  a ꝓportiõe dupla, et a ꝓportio-<lb/>ne quadrupla equales velocitates nate ſunt ꝓueni­<lb/>re. </s>
              <s xml:id="N1D55A" xml:space="preserve">et multa ſimilia q̄ ſunt abſona calculatori pḣo <lb/>               <anchor type="note" xlink:href="note-0137-02" xlink:label="note-0137-02a"/>               </s>
              <s xml:id="N1D564" xml:space="preserve">¶ Qua ꝓpter dicūt alii ad argumētū concedendo <lb/>conſequentiã, et negãdo falſitatē ↄ̨ñtis: et ad pun-<lb/>ctū ꝓbationis negant /  talis rota ãtea et poſt mo­<lb/>uebat̄̄ ab equali ꝓportione / q2 vt dicūt magnitudo <lb/>rote tenet ſe ex ꝑte poñe. </s>
              <s xml:id="N1D56F" xml:space="preserve">Mõ manēte eodē conamīe <lb/>poñe rota tardiꝰ mouet̄̄ et a minore ꝓportione quia <lb/>ãtea magnitudo iṗiꝰ rote iuuabat poñaꝫ ad deſcri­<lb/>bendã lineã. </s>
              <s xml:id="N1D578" xml:space="preserve">Mõ vero cū ipſa rota cõtinuo efficiat̄̄ <lb/>minor nõ ita iuuat poñam ſicut añ </s>
              <s xml:id="N1D57D" xml:space="preserve">Qḋ facile exem­<lb/>plo declarart põt. </s>
              <s xml:id="N1D582" xml:space="preserve">Manifeſtū eſt em̄ /  ſi in ſuꝑficie <lb/>alicuiꝰ rote addat̄̄ aliq̇d eiuſdē ſpeciei cõtinuatū cū <lb/>rota nulliꝰ grauitatis: et ſortes giret totū illud ab <lb/>eodē conamine illa totalis rota velociꝰ mouet̄̄ quã <lb/>mouebat̄̄ ãtea pars eiꝰ et tñ poña manet eq̈lis et re-<lb/>ſiſtentia rote: ſed totalis proportio eſt maior quia <lb/>iuuatur ibi poña ſortis a magnitudine rote.</s>
            </p>
            <div xml:id="N1D591" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0137-02a" xlink:label="note-0137-02" xml:id="N1D595" xml:space="preserve">Reſpon­<lb/>ſio cõis.</note>
            </div>
            <p xml:id="N1D59D">
              <s xml:id="N1D59E" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N1D5A1" xml:space="preserve">Q2 magnitudo tenet ſe ex <lb/>parte reſiſtētie: g̊ nõ ex parte potētie etiã manente <lb/>eq̈li g̈uitate oīno. </s>
              <s xml:id="N1D5A8" xml:space="preserve">Probat̄̄ añs de orbe / qui maio-<lb/>ratur ꝑ rarefactionē quovſ fiat ſpera ſolida qui <lb/>tūc tardiꝰ mouet̄̄ quã qñ erat minor / vt patꝫ ex ſcḋa <lb/>replica huiꝰ quarti argumēti.               <anchor type="note" xlink:href="note-0137-03" xlink:label="note-0137-03a"/>               </s>
              <s xml:id="N1D5B6" xml:space="preserve">¶ Dices ſicut dicēdū <lb/>eſt /  nec magnitudo, nec paruitas in talibꝰ tenet <lb/>ſe ex parte poñe vt ſatis ꝓbat replica: ſed diſtãtia <lb/>pūcti a cētro penes cuiꝰ motū d3 attēdi velocitas to­<lb/>tiꝰ mobilis puta ipſiꝰ pūcti ī q̊ eſt g̈dꝰ mediꝰ totiꝰ la-<lb/>titudīs motꝰ tenet ſe ex ꝑte poñe. </s>
              <s xml:id="N1D5C3" xml:space="preserve">CeterꝪ em̄ paribꝰ <lb/>iuuat poñaꝫ ad velociꝰ deſcribēdū lineã / ꝙ̄ deſcribit <lb/>qñ recedit a cētro: et ꝑ contrariū iuuat ad deſcribē-<lb/>dam tardiꝰ qñ magis accedit ad centrū a quo exori­<lb/>tur motus. </s>
              <s xml:id="N1D5CE" xml:space="preserve">Et ſic dico /  qñ rota rarefit verſus cir-<lb/>cunferentiam mouente circūferentia: tota ꝓportio <lb/>efficitur maior, et quando condenſatur ordine con-<lb/>uerſo tota ꝓportio efficitur minor.</s>
            </p>
            <div xml:id="N1D5D7" level="5" n="9" type="float">
              <note position="left" xlink:href="note-0137-03a" xlink:label="note-0137-03" xml:id="N1D5DB" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D5E1">
              <s xml:id="N1D5E2" xml:space="preserve">Sed ↄ̨̨tra </s>
              <s xml:id="N1D5E5" xml:space="preserve">Q2 iſta ſolutio nõ ſatiſfacit <lb/>adhuc em̄ ſequit̄̄ /  ab īeq̈libꝰ ꝓportiõibꝰ eq̈les cir-<lb/>cuitiões ꝓueniūt / qḋ eſt īpoſſibile. </s>
              <s xml:id="N1D5EC" xml:space="preserve">Ptꝫ ↄ̨ña / q2 ſorte <lb/>cū eq̈li cõamīe ↄ̨tinuo girante ſiue rota rarefiat ſi-<lb/>ue ↄ̨dēſet̄̄ ipſe eque velociter ↄ̨tinuo circuit et tñ ꝑ te <lb/>ꝓportio eſt continuo maior vel minor: igr̄ ꝓpoſitū.</s>
            </p>
            <cb chead="Capitulū ſecundū."/>
            <p xml:id="N1D5F7">
              <s xml:id="N1D5F8" xml:space="preserve">Quīto ↄ̨̨tra eandē partē arguit̄̄ ſic / ali­<lb/>q̇s motꝰ eſt vniformiṫ difformis q̊ ad ſubiectū: et tñ <lb/>eiꝰ velocitas nõ corrñdet g̈dui medio: igr̄. </s>
              <s xml:id="N1D5FF" xml:space="preserve">Añs ꝓba­<lb/>tur et ſuppono /  rarefactio ſit motꝰ localis diffor-<lb/>mis q̊ ad ſubiectū. </s>
              <s xml:id="N1D606" xml:space="preserve">q̊ ſuppoſito pono /  ſint duo pe-<lb/>dalia ſcḋm oēm dimēſionē puta a.b. / et volo /  a ra-<lb/>refiat vniformiṫ quovſ efficiat̄̄ in duplo longiꝰ et <lb/>in duplo latiꝰ vniformiṫ, et b. rarefiat vniformiter <lb/>q̊vſ efficiat̄̄ in ſexq̇altero lõgiꝰ, et in ſexq̇altero la­<lb/>tius vniformiṫ ita  a. in fine ſit vnū q̈dratū cuiꝰ co­<lb/>ſta ſit dupla ad coſtã eiuſdē in prīcipio rarefactõis <lb/>et b. ſit aliud q̈dratū cuiꝰ coſta in fine rarefactionis <lb/>ſit ſexq̇altera ad coſtã eiꝰ in prīcipio rarefactiõis / q̊ <lb/>poſito ſic argr̄: ſi ille motꝰ q̊ mouet̄̄ a. et etiã q̊ mouet̄̄ <lb/>b. debeãt ↄ̨mēſurari penes pūctū mediū / ſequit̄̄ /  a <lb/>adeq̈te in duplo velociꝰ moueret̄̄ quã b. / ſed ↄ̨ñs eſt <lb/>falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1D621" xml:space="preserve">Seq̄la ꝓbatur / <lb/>quia pūctus medius ipſius a. in toto illo tempore <lb/>rarefactionis pertrãſibit vnū ſemipedale q2 pūctꝰ <lb/>extremius mouet̄̄ ꝑ pedale: et pūctus medius ipſius <lb/>b. mouet̄̄ ꝑ quartã pedalis cū pūctꝰ extremꝰ eiuſdeꝫ <lb/>b. moueat̄̄ ꝑ ſemipedale: ſed ſemipedalis ad quar-<lb/>tã pedalis eſt ꝓportio dupla / vt ptꝫ: igitur in duplo <lb/>velociꝰ mouet̄̄ a. quã b. / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N1D632" xml:space="preserve">Sed falſitas <lb/>ↄ̨ñtis arguitur ſuppoſita illa concluſione geome-<lb/>trica vcꝫ  ſemꝑ quadrata ꝑfecta equalis craſſitu-<lb/>dinis ſe habent in proportione duplicata ad ꝓpor­<lb/>tionē ſuarū cõſtarū / vt poſtea dicetur ī capitulo de <lb/>augmentatione. </s>
              <s xml:id="N1D63F" xml:space="preserve">ſi vero ſint vndiqua quadrata <lb/>ꝑfecta tunc ſe habēt in ꝓportione triplicata ad pro­<lb/>portionē ſuarū coſtarū. </s>
              <s xml:id="N1D646" xml:space="preserve">Quo ſuppoſito ſic arguit̄̄ / <lb/>pedale a. in duplo ſuprabipartiente quintas velo­<lb/>cius rarefit quã pedale b. et ipſa rarefactio eſt motꝰ <lb/>localis vt ſuppoſitū eſt: ergo in duplo ſuprabipar­<lb/>tiente quintas velocius mouetur a. quã b. / et per cõ-<lb/>ſequēs nõ in duplo adequate / quod fuit probandū. <lb/></s>
              <s xml:id="N1D654" xml:space="preserve">Conſequentia apparet, et arguitur maior / quia pe­<lb/>dale a. efficitur quadruplū in fine rarefactionis ad <lb/>ipſum in principio quia in principio rarefactionis <lb/>coſte ipſius a. ad coſtam eius in fine rarefactionis <lb/>eſt proportio dupla cū ceteris poſitis in caſu: ergo <lb/>ipſius quadrati a. in fine ad ipſum in principio eſt <lb/>proportio quadrupla que eſt duplicata proportio <lb/>coſtarū, et antea erat illud pedale adequate: ergo <lb/>acquiſiuit tria pedalia: et aliud puta b. acquiſiuit <lb/>pedale cum quarta preciſe: igitur quantitatis ac-<lb/>acquiſite ipſi a. ad quãtitatē acquiſitã ipſi b. eſt pro­<lb/>portio dupla ſuꝑbipartiēs q̇ntas: et tãta ē ꝓportio <lb/>rarefactionis ipſius a. ad rarefactionē ipſiꝰ b. igit̄̄ <lb/></s>
              <s xml:id="N1D670" xml:space="preserve">Sed iã ꝓbo /  b. acq̇ſiuit pedale cū quarta q2 coſte <lb/>ipſiꝰ b. in fine ad coſtã eiuſdē in prīcipio rarefactio­<lb/>nis eſt ꝓportio ſexq̇altera. </s>
              <s xml:id="N1D677" xml:space="preserve">g̊ totiꝰ quadrati b. in fi-<lb/>ne ad ipſū in prīcipio eſt ꝓportio dupla ſexquiq̈rta <lb/>q̄ eſt dupla ad ſexq̇alterã. </s>
              <s xml:id="N1D67E" xml:space="preserve">Ptꝫ ↄ̨ña ex ſuppoſitione <lb/>et antea b. erat pedale: g̊ acq̇ſiuit pedale cū quarta / <lb/>qḋ fuit ꝓbandū. </s>
              <s xml:id="N1D685" xml:space="preserve">Simile argumētū poſſet fieri de ra­<lb/>refactione duarū ſperarū ſolidarū equaliū in ṗnci­<lb/>pio rarefactiõis: et in fine ita ſe habētiū  diametri <lb/>vnius ad diameirum alterius eſſet ꝓportio dupla.</s>
            </p>
            <p xml:id="N1D68E">
              <s xml:id="N1D68F" xml:space="preserve">Sexto prīcipaliṫ arguit̄̄  hoc ↄ̨̨tra ter­<lb/>tiã ꝑtē q̄ſtionis vcꝫ /  debet attēdi motꝰ localis dif-<lb/>formis velocitas quo ad ſubiectū penes reductiõeꝫ <lb/>ad vniformitatē. </s>
              <s xml:id="N1D698" xml:space="preserve">q2 motus circularis in ſubiecto cir­<lb/>culari nõ p̄t reduci ad vniformitatē: igitur nõ debet <lb/>attendi penes reductionē ad vniformitatē.               <anchor type="note" xlink:href="note-0137-04" xlink:label="note-0137-04a"/>               </s>
              <s xml:id="N1D6A4" xml:space="preserve">¶ Et cõ-<lb/>firmatur / q2 ſi reduceretur ad vniformitateꝫ motus <lb/>circularis alicuiꝰ rote a non gradu vſ ad octauū <lb/>vel oporteret reducēdo ab aliqua parte capere ali­               <pb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi." file="0138" n="138"/>               quã certam velocitatē et ponere ī equali parte ſicut <lb/>fit in reductione qualitatis vniformiter difformis <lb/>vel capiendo ab aliq̈ parte et ponēdo in minori vel <lb/>a mīori et ponēdo in maiori. </s>
              <s xml:id="N1D6B8" xml:space="preserve">Nõ tertiū / q2 tūc facile <lb/>reducēdo ad vniformitatē ꝓbaret̄̄ /  velocitas illiꝰ <lb/>rote ſit īfinita q2 caperet̄̄ a prima parte ꝓportiõali <lb/>vnꝰ g̈dus, et a ſcḋa tm̄, et a tertia tm̄: et poneret̄̄ per <lb/>totã rotã: et ſic eſſet īfinita velocitas. </s>
              <s xml:id="N1D6C3" xml:space="preserve">Nec ſcḋm / quia <lb/>tūc ſeq̄ret̄̄ /  tota velocitas eſſet minor quã vt q̈tu-<lb/>or vt ſi velocitas totiꝰ rote poneret̄̄ īmedietate eiꝰ <lb/>et ibi eſſet vniformis vt quatuor: deinde accipiendo <lb/>medietatē illiꝰ latitudinis motꝰ reducta ad vnifor-<lb/>mitatē puta duos g̈dus. </s>
              <s xml:id="N1D6D0" xml:space="preserve">et ponēdo eos in alia me-<lb/>dietate et ſic tota velocitas maneret vt duo: </s>
              <s xml:id="N1D6D5" xml:space="preserve">Nec eſt <lb/>dicendū primū / q2 diuiſa illa rota in duas partes <lb/>cõcentricas quaꝝ vna ſit quarta pars totiꝰ rote, et <lb/>reſidua ſus circūferentiã ſit tres quarte / vt pone-<lb/>batur in p̄cedēti capite in ſcḋa cõfirmatiõe puta vl­<lb/>tima primi argumēti. </s>
              <s xml:id="N1D6E2" xml:space="preserve">Deinde volo /  ille tres q̈rte <lb/>reducant̄̄ ad vniformitatē / et ptꝫ /  erūt vniformis <lb/>in motu g̈du ſexto cū totalis motꝰ illiꝰ partis q̄ cõ-<lb/>ponit̄̄ ex illis tribꝰ quartis ſit vniformiter diffor-<lb/>mis a quarto vſ ad octauū: et volo etiã /  reducat̄̄ <lb/>alia pars ꝓpe centū ad vniformitatē: et manifeſtū <lb/>eſt /  erit vt duo motꝰ eiꝰ: cū ſit vniformiter diffor-<lb/>mis a non gtadū vſ ad quartū. </s>
              <s xml:id="N1D6F3" xml:space="preserve">Deinde volo /  a <lb/>q̄libet triū quartaꝝ magis intēſaꝝ remoueat̄̄ vnꝰ <lb/>g̈dusꝰ / et ponat̄̄ in quarta minꝰ intēſēſa / q̄ eſt vt duo / <lb/>et manifeſtū eſt /  oēs quarte manebūt vt quī vni-<lb/>formes: et ꝑ ↄ̨ñs tota illa velocitas talis motꝰ vni-<lb/>formiter difformis reducendo ad vniformitatē re-<lb/>mouēdo a parte equali et ponēdo ſibi in equali erit <lb/>vt quin / quod eſt falſum: quia eſt vt quatuor cum <lb/>eſt a non gradu vſ ad octauū: igr̄ velocitas mo-<lb/>tus vniformiter difformis quo ad ſubiectū nõ de-<lb/>bet cõmenſari penes reductionē ad vniformitatē. <lb/>               <anchor type="note" xlink:href="note-0138-01" xlink:label="note-0138-01a"/>               </s>
              <s xml:id="N1D711" xml:space="preserve">¶ Dices forte cõcedēdo /  motꝰ circularis nõ poteſt <lb/>reduci ad vniformitatē ipſo manēte in ſubiecto cir­<lb/>culariter moto q2 hoc repugnat et ītellige ſicut ītel­<lb/>ligendum eſt: ſed bene talis velocitas reduceret̄̄ ad <lb/>vniformitatē qua tale mobile moueat̄̄ vniformiter <lb/>motu recto quolibet pūcto deſcribente tantã lineã <lb/>quantã deſcribit pūctꝰ mediꝰ. </s>
              <s xml:id="N1D720" xml:space="preserve">Et hoc loquendo de <lb/>motu circulari / vt loquūtur terminiſte. </s>
              <s xml:id="N1D725" xml:space="preserve">Si autē lo-<lb/>quimur / vt reales credo /  dicendū eſſet ſcḋm eoruꝫ <lb/>viã /  motꝰ circularis eſſentialiter eſſet circularis <lb/>ita  talis motꝰ nõ põt eſſe quin ſit motꝰ circularis <lb/>q2 differt ſpecie eſſentiali a motu recto. </s>
              <s xml:id="N1D730" xml:space="preserve">Et ideo / vt <lb/>modꝰ reſpõdendi huic argumēto et etiã cognoſcē-<lb/>di velocitatem motus difformis quo ad ſubiectum <lb/>ſit vtri vie communis.</s>
            </p>
            <div xml:id="N1D739" level="5" n="10" type="float">
              <note position="right" xlink:href="note-0137-04a" xlink:label="note-0137-04" xml:id="N1D73D" xml:space="preserve">Confir-<lb/>matio.</note>
              <note position="left" xlink:href="note-0138-01a" xlink:label="note-0138-01" xml:id="N1D745" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1D74B">
              <s xml:id="N1D74C" xml:space="preserve">Reſpõdeo alter  de facto motꝰ diffor­<lb/>mis quo ad ſubiectū velocitas nequa̄ cõmēſura-<lb/>ri debet ꝑ reductionē ad vniformitatē: ſed cõmēſu-<lb/>randa eſt penes denoīationē partiū nõ ̄tū ad ma­<lb/>gnitudinē: ſed ̄tū ad lõgitudinē </s>
              <s xml:id="N1D757" xml:space="preserve">Uolo dicere /  nõ <lb/>in ea ꝓportionē qua pars eſt maior altera in ea ꝓ-<lb/>porõe velocitas motꝰ exiſtēs in ea plus facit ad de-<lb/>noīationē totiꝰ velocitatis. </s>
              <s xml:id="N1D760" xml:space="preserve">Sꝫ volo dicere /  in ea <lb/>ꝓportiõe in qua eſt lõgior ceteris paribꝰ in ea plus <lb/>facit ad denoīationē totiꝰ ita  tm̄ adequate mo-<lb/>uet̄̄ vna rota ̄tū vna linea ꝓcedēs a cētro illiꝰ ro-<lb/>te vſ ad circūferentiã. </s>
              <s xml:id="N1D76B" xml:space="preserve">Et ſi talis linea moueat̄̄ a <lb/>nõ g̈du vſ ad octauū etiã tota rota. </s>
              <s xml:id="N1D770" xml:space="preserve">Et põt vena-<lb/>ri velocitas motꝰ illiꝰ linee penes denoīationē iſto <lb/>mõ medietas huiꝰ linee q̄ velociua mouet̄̄, mouet̄̄ vt <lb/>ſex: igr̄ denoīat totū moueri vt tria: et alia medietas <lb/>totius vt vnū: et ſic tota linea mouetur vt quatuor.</s>
            </p>
            <cb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi."/>
            <p xml:id="N1D77D">
              <s xml:id="N1D77E" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N1D781" xml:space="preserve">Q2 ſi talis modꝰ cognoſcē-<lb/>di velocitatē motꝰ difformis q̊ ab ſubiectū eſſet vĺr <lb/>validꝰ ſeq̄ret̄̄ /  dabilis eēt vna ꝑs rote vniformiter <lb/>difformiṫ mote q̄ nõ vniformiṫ difformiṫ moueret̄̄ <lb/>īmo nõ eēt dabilis g̈dꝰ q̊ adeq̈te moueret̄̄: ſꝫ q̊libet <lb/>īadeq̈te citra ſūmū / et ↄ̨ñs oī opiniõi aduerſat̄̄: igr̄ <lb/>illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N1D790" xml:space="preserve">Seq̄la ꝓbat̄̄ / et capio vnã rotã que <lb/>moueat̄̄ vniformiṫ difformiṫ a nõ g̈du vſ ad octa-<lb/>uū, et ſigno in ea vnã colūnã cuiꝰ vnū extremū tãgat <lb/>cētrū et aliud circūferētiã. </s>
              <s xml:id="N1D799" xml:space="preserve">Deīde educo lineã girati­<lb/>uã ꝓcedentē a cētro talis rote et girantē oēs partes <lb/>ꝓportiõales taĺ colūne (et loquor de linea giratiua <lb/>ſicut loquūtur noīales ̄uis idē eſſet ſi loq̄rer ſcḋm <lb/>reales) / q̊ poſito ſic arguitur talis linea eſt. ꝑs illius <lb/>colūne: et hꝫ īfinitas ꝑtes eq̈les quaꝝ q̄libet mouet̄̄ <lb/>maiori et velociori g̈du quã q̈tuor, et hꝫ īfinitas eq̈-<lb/>les quaꝝ q̄libet mouet̄̄ velociꝰ quã quī, et ſic ↄ̨ñter <lb/>vſ ad octauū g̈dū excluſiue: et reſidue partes ſolū <lb/>ſūt finite vt facile eſt ītueri: igr̄ talis linea mouetur <lb/>maiori vtlocitate quã vt quatuor quã vt quī ꝙ̄ vt <lb/>ſex etc̈. vſ ad octauū g̈dū excluſiue / qḋ fuit ꝓbãdū</s>
            </p>
            <p xml:id="N1D7B2">
              <s xml:id="N1D7B3" xml:space="preserve">In oppoſitū tamē eſt coīs ſchola aſſe­<lb/>rens velocitatē motꝰ difformis quo ad ſubiectū ali­<lb/>quo illorū modorū attendi debere ſiue cõmēſurari</s>
            </p>
            <p xml:id="N1D7BA">
              <s xml:id="N1D7BB" xml:space="preserve">Pro deſciſioue huiꝰ q̄ſtionis ſupponē­<lb/>da eſt diffinitio motus vniformiter difformis quo <lb/>ad ſubiectū. </s>
              <s xml:id="N1D7C2" xml:space="preserve">Et etiã diffinitio motꝰ difformiter dif-<lb/>formis quo ad ſubiectū q̄ ſuꝑiori capite poſite ſunt <lb/></s>
              <s xml:id="N1D7C8" xml:space="preserve">¶ Item aduertendū eſt /  in motu circulari duo cõ-<lb/>ſiderãda ſunt: puta ipſa circuitio: et ipſe motus cir-<lb/>cularis: quãuis eī idē ſit motꝰ circularis et circuitio <lb/>penes aliud tñ cõmenſurari habet velocitas circui­<lb/>tionis: et velocitas motus circularis: ſicut idē eſt al­<lb/>bedo et ſiĺitudo: et penes aliḋ cognoſci hꝫ intēſio al­<lb/>bedinis: et ītenſio ſiĺitudinls qḋ facile ex dialecticis <lb/>ꝑcipi põt. </s>
              <s xml:id="N1D7D9" xml:space="preserve">In iſtis eī aſpicienda eſt appellatio ne in <lb/>ea fallamur: </s>
              <s xml:id="N1D7DE" xml:space="preserve">Uelocitas em̄ motꝰ circularis attendi­<lb/>tur penes lineam deſcriptam a certo puncto vt infe­<lb/>riꝰ declarabit̄̄.               <anchor type="note" xlink:href="note-0138-02" xlink:label="note-0138-02a"/>               </s>
              <s xml:id="N1D7EA" xml:space="preserve">Sed velocitas circuitionis attēdi hꝫ <lb/>penes angulū deſcriptū in tãto vel tanto tp̄e circa <lb/>centrū: ita  ſi in eq̈li tp̄e duo mobilia ſiue eq̈lia ſi-<lb/>ue ineq̈lia circulariter mota eq̈les angulos circa cē­<lb/>trū deſcribūt ipſa eq̈liter circueūt et circūgyrãt: </s>
              <s xml:id="N1D7F5" xml:space="preserve">Si <lb/>vero in eodē tp̄e ineq̈les deſcribãt circa cētrū angu­<lb/>los: notū euadet eorū circuitiones ineq̈les eē.               <anchor type="note" xlink:href="note-0138-03" xlink:label="note-0138-03a"/>               </s>
              <s xml:id="N1D801" xml:space="preserve">Et hec <lb/>opinio eſt cõiter loq̄ntiū: et ſignãter Pauli veneti ī <lb/>ſua ſūma in libro phiſicoꝝ capitulo .35. vide eū ibi. <lb/></s>
              <s xml:id="N1D809" xml:space="preserve">Poſſet tñ facile attēdi velocitas circuitiõis penes <lb/>velocitatē motꝰ alicuiꝰ pūcti equaliter diſtãtis a cē­<lb/>tro: hoc eſt dicere /  ſi in duobus mobilibꝰ circulari­<lb/>ter ſiue eq̈lia ſint ſiue īequalia duo pūcta eq̈liter di­<lb/>ſtãtia a cētro equaliter moueant̄̄: talia mobilia eq̈­<lb/>liter circueūt. </s>
              <s xml:id="N1D816" xml:space="preserve">Nõ tñ arbitreris  quãto pūctū ē pro­<lb/>pinquiꝰ cētro tãto velociꝰ circuit: qm̄ qḋlibet eq̄ve-<lb/>lociter circuit cū altero dūmõ corꝑis motꝰ ſit vnifor­<lb/>miter difformis quo ad ſubiectū </s>
              <s xml:id="N1D81F" xml:space="preserve">Quare ꝑſpicuū ē <lb/>videre diſtãtiã pūctorū nullo pacto conferre ad ve­<lb/>locitatē circuitiõis (loquor de diſtãtia a cētro) quã­<lb/>uis plurimū ad velocitatē motꝰ circularis vt ſupe-<lb/>rius tactū eſt in quodã argumēto: et inferius tange­<lb/>tur. </s>
              <s xml:id="N1D82C" xml:space="preserve">His ſuppoſitis ſit.</s>
            </p>
            <div xml:id="N1D82F" level="5" n="11" type="float">
              <note position="right" xlink:href="note-0138-02a" xlink:label="note-0138-02" xml:id="N1D833" xml:space="preserve">Penes <lb/>q̇d hꝫ at-<lb/>tēdi velo­<lb/>citas cir­<lb/>caitiõis.</note>
              <note position="right" xlink:href="note-0138-03a" xlink:label="note-0138-03" xml:id="N1D841" xml:space="preserve">paulꝰ ve­<lb/>netꝰ ī ſū. <lb/>phiſi. ca. <lb/>35.</note>
            </div>
            <p xml:id="N1D84D">
              <s xml:id="N1D84E" xml:space="preserve">Prīa ↄ̨̨cluſio. </s>
              <s xml:id="N1D851" xml:space="preserve">Uelocitas motꝰ vnifor-<lb/>miṫ difformis quo ad ſubiectū nõ d3 attēdi aut cõ-<lb/>menſurari penes velocitatē pūcti exiſtētis in medio <lb/>corporis quãtū ad magnitudinē vt bene probat ter­<lb/>tium argumentum huius capitis</s>
            </p>
            <p xml:id="N1D85C">
              <s xml:id="N1D85D" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
              <s xml:id="N1D860" xml:space="preserve">Uelocitas motus vni-               <pb chead="Secundi tractatus" file="0139" n="139"/>               miter difformis q̊ ad ſubiectū nõ d3 attendi penes <lb/>velocitatē pūcti exiſtētis in medio mobilis quãtū <lb/>ad lõgitudinē. </s>
              <s xml:id="N1D86C" xml:space="preserve">Ptꝫ hec ↄ̨cluſio ex eodē argumēto.</s>
            </p>
            <p xml:id="N1D86F">
              <s xml:id="N1D870" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N1D873" xml:space="preserve">Uelocitas motꝰ vni­<lb/>formiter difformis quo ad ſubiectū cõmēſurari d3 <lb/>penes gradū mediū totiꝰ latitudinis talis motus <lb/>vniformiter difformis vbicū fuerit talis gradus <lb/>ſiue in medio corꝑis ̄tū ad magnitudinē ſiue non <lb/>(non eſt cura) </s>
              <s xml:id="N1D880" xml:space="preserve">Probat̄̄ hec cõcluſio / qm̄ ceteri modi <lb/>cognoſcēdi velocitatē motꝰ vniformiter difformis <lb/>quo ad ſubiectū ſuperioribꝰ argumētis īprobãtur <lb/>reſtat / igitur vt penes modum datum cognoſcatur</s>
            </p>
            <p xml:id="N1D889">
              <s xml:id="N1D88A" xml:space="preserve">Quarta cõcluſio. </s>
              <s xml:id="N1D88D" xml:space="preserve">Uelocitas motꝰ dif-<lb/>formiter difformis quo ad ſubiectum cognoſci põt <lb/>penes denoīationē partiū quantū ad longitudinē <lb/></s>
              <s xml:id="N1D895" xml:space="preserve">Intelligēdo ꝑ lõgitudinē diſtantiã a nõ gradu ta-<lb/>lis motꝰ vel a g̈du tardiſſimo ſus g̈dus velociores / <lb/>vt declaratū eſt in vltimo argumēto. </s>
              <s xml:id="N1D89C" xml:space="preserve">Probat̄̄ hec <lb/>ↄ̨cluſio / q2 nõ occurrit alter modꝰ facilior ad cogno­<lb/>ſcendū huiuſmodi velocitatem per denominationē / <lb/>igr̄ tali modo īueſtiganda eſt motꝰ difformiter dif-<lb/>formis quo ad ſubiectū velocitas. </s>
              <s xml:id="N1D8A7" xml:space="preserve">Nec replica fa-<lb/>cta de linea giratiua in vltīo argumēto huiꝰ capitꝪ <lb/>hãc ↄ̨cluſionē valet vllo pacto infirmare / vt patebit <lb/>ex ſolutione eiuſdem replice.</s>
            </p>
            <p xml:id="N1D8B0">
              <s xml:id="N1D8B1" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N1D8B4" xml:space="preserve">Probabile eſt ve-<lb/>locitatē motꝰ difformis quo ad ſubiectū attēdi de-<lb/>bere penes gradū ſummū.               <anchor type="note" xlink:href="note-0139-01" xlink:label="note-0139-01a"/>               </s>
              <s xml:id="N1D8C0" xml:space="preserve">Ptꝫ / q2 ad illã opinionē <lb/>q̄ eſt hentiſberi nullū incõueniēs ſequit̄̄: īmo oīa ar­<lb/>gumēta q̄ in eū adducūiur facillime diſſoluūtur.</s>
            </p>
            <div xml:id="N1D8C7" level="5" n="12" type="float">
              <note position="left" xlink:href="note-0139-01a" xlink:label="note-0139-01" xml:id="N1D8CB" xml:space="preserve">Opinio hentiſbe­<lb/>ri.</note>
            </div>
            <p xml:id="N1D8D3">
              <s xml:id="N1D8D4" xml:space="preserve">Sexta cõcluſio. </s>
              <s xml:id="N1D8D7" xml:space="preserve">Diſtantia punctorū <lb/>a cētro a q̊ ꝓcedit motꝰ difformis q̊ ad ſubiectū te-<lb/>net ſe ex ꝑte potētie: et auget ꝓportionē poñe ad re­<lb/>ſiſtentiã. </s>
              <s xml:id="N1D8E0" xml:space="preserve">necnõ eidē potētie eſt adiumento. </s>
              <s xml:id="N1D8E3" xml:space="preserve">et ꝑ op-<lb/>poſitū ꝓpinq̇tas. </s>
              <s xml:id="N1D8E8" xml:space="preserve">nec magnitudo aut paruitans a-<lb/>liq̇d facit. </s>
              <s xml:id="N1D8ED" xml:space="preserve">Probat̄̄ facile hec cõcluſio ex deductiõe <lb/>q̈rti argumēti huiꝰ capitis.               <anchor type="note" xlink:href="note-0139-02" xlink:label="note-0139-02a"/>               </s>
              <s xml:id="N1D8F7" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  nõ ſtat <lb/>aliquã rotã q̄ mouet̄̄ a tute ſortis vt q̈tuor rare-<lb/>fieri et maiorari ꝑ ↄ̨tinuã elõgationē pūctoꝝ a cētro <lb/>et ipſã cõtinuo ab eadē ꝓportiõe moueri ceteris pa­<lb/>ribꝰ. </s>
              <s xml:id="N1D902" xml:space="preserve">Ptꝫ correlariū hoc, q2 diſtãtia pūctoꝝ. </s>
              <s xml:id="N1D905" xml:space="preserve">adau-<lb/>get ꝓportionē. </s>
              <s xml:id="N1D90A" xml:space="preserve">Similiter dicendū eſt / ſi cõdenſaret̄̄ <lb/>rota ſorte cõtinuo mouēte a tute vt q̈tuor. </s>
              <s xml:id="N1D90F" xml:space="preserve">tunc em̄ <lb/>totalis ꝓportio cõtinuo diminuit̄̄ ꝓpṫ deꝑditionē <lb/>diſtante punctorum a centro.</s>
            </p>
            <div xml:id="N1D916" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0139-02a" xlink:label="note-0139-02" xml:id="N1D91A" xml:space="preserve">correĺ.</note>
            </div>
            <p xml:id="N1D920">
              <s xml:id="N1D921" xml:space="preserve">Septima cõcluſio. </s>
              <s xml:id="N1D924" xml:space="preserve">Propīquitas aut <lb/>diſtãtia pūctoꝝ a cētro nichil cõducit ceterꝪ paribꝰ <lb/>ad velocitatē circūgiratiõis ſiue circuitiõis / qḋ idē <lb/>eſt. </s>
              <s xml:id="N1D92D" xml:space="preserve">Probat̄̄ / q2 eq̄ velociter oīa pūcta cõplēt circu-<lb/>los ſuos / vt ptꝫ ī rota in ſpera lune ſolis, et ſic ↄ̨ñter <lb/>ꝓcedēdo et eq̈les ãgulos faciūt circa centrū: igr̄ eq̄ <lb/>velociter circueūt / et ꝑ ↄ̨ñs diſtãtia nichil ↄ̨fert               <anchor type="note" xlink:href="note-0139-03" xlink:label="note-0139-03a"/>               </s>
              <s xml:id="N1D93B" xml:space="preserve">¶ Ex <lb/>q̊ ſequit̄̄ /  nū̄ ↄ̨cēdendū eſt ab eq̈libꝰ ꝓportiõibꝰ <lb/>īeq̈les motꝰ circulares ꝓuenire, aut ab ineq̈libꝰ ꝓ-<lb/>portiõibꝰ eq̈les circuitiões / vt ſolutio q̈rti argumēti <lb/>oñdit.               <anchor type="note" xlink:href="note-0139-04" xlink:label="note-0139-04a"/>               </s>
              <s xml:id="N1D94B" xml:space="preserve">¶ Sequit̄̄ ex hac ſolutiõe ſcḋo /  ſi in eodem <lb/>axe ponant̄̄ īfinite rote ↄ̨tinuo mīores et mīores ita <lb/> diametri prime ſit dupla ad diametrū ſecūde, et <lb/>ſcḋe ad diametrū tertie, et ſic ↄ̨ñter: et ſortes moue-<lb/>at oēs illas rotas mediãte illo axe: in īfinitū tarde <lb/>mouet̄̄ ibi aliqua rota: nichilominꝰ tñ q̄libet rota <lb/>ita velociter circuit ſicut prima. </s>
              <s xml:id="N1D95A" xml:space="preserve">Patꝫ prima pars / <lb/>q2 īfinite modicū circulū deſcribit aliqua illaꝝ ro-<lb/>tarū in eodē tꝑe: igr̄. </s>
              <s xml:id="N1D961" xml:space="preserve">Scḋa pars ꝓbat̄̄ / q2 eque cito <lb/>q̄libet circuitionē ſuã ſicut prima cõplet: igr̄ q̄libet <lb/>eque velociter circuit ſicut prima. </s>
              <s xml:id="N1D968" xml:space="preserve">Ite ↄ̨tinuo cuiuſli­               <cb chead="Capitulū ſecundū."/>               bet illaꝝ ãguīus deſcriptꝰ circa cētrū eſt eq̈lis ãgu-<lb/>lo deſcripto a ṗma rota: igr̄ quelibet illaꝝ cõtinuo <lb/>equaliter circuit cū prima </s>
              <s xml:id="N1D972" xml:space="preserve">Ex quo facile apparet  <lb/>magnitudo ſiue diſtãtia pūctoꝝ nihil facit ad velo­<lb/>citatē circuitiõis: ſed bene ad velocitatē motꝰ circu-<lb/>laris.               <anchor type="note" xlink:href="note-0139-05" xlink:label="note-0139-05a"/>               </s>
              <s xml:id="N1D980" xml:space="preserve">¶ Sequit̄̄ vlteriꝰ /  in caſu p̄dicto nõ ab eadē <lb/>proportiõe adequate ſortes mouet primam rotã et <lb/>ſcḋam: ſed a maiori primã quã ſcḋam. </s>
              <s xml:id="N1D987" xml:space="preserve">q2 diſtantia <lb/>pūctoꝝ medioꝝ eſt adiumēto potētie ſortis. </s>
              <s xml:id="N1D98C" xml:space="preserve">¶ Hic <lb/>tñ tu aduerte  nõ volo dicere / quãlibet illaꝝ rotaꝝ <lb/>moueri adeq̈te a certa ꝓportiõe: ſed bene q̄libet il-<lb/>larū mouet̄̄ a certa ꝓportiõe inadequate. </s>
              <s xml:id="N1D995" xml:space="preserve">Nec volo <lb/>dicere / ̄libet illaꝝ circūgirare ſiue ꝓpriã circuitio­<lb/>nē efficere a certa ꝓportiõe adeq̊te: ſed bene īadeq̈-<lb/>te. </s>
              <s xml:id="N1D99E" xml:space="preserve">Qḋ ideo dixerim / qm̄ ſi cõcedat̄̄ ſortē potētie vt <lb/>4. circūgirare rotã in octuplo minorē prima a cer­<lb/>ta ꝓportiõe adequate cū oporteat talē ꝓportionē <lb/>eſſe maiorē ꝓportiõe a qua ſortes circūducit primã <lb/>rotã (cū maior rota magis reſiſtit ſue circūgiratiõi <lb/>quã mīor) / tã ſeq̄ret̄̄ /  ab īeq̈libꝰ ꝓportiõibꝰ equa-<lb/>les circuitiões ꝓuenirēt qḋ vitare intēdit ſeptīa cõ­<lb/>cluſio. </s>
              <s xml:id="N1D9AF" xml:space="preserve">Et ideo in ꝓpoſito ymaginandū eſt de illis <lb/>rotis ſicut de īfinitis rotis partialibꝰ cõcētricis ro­<lb/>te alicui cuiꝰ ſūt partes. </s>
              <s xml:id="N1D9B6" xml:space="preserve">Manifeſtū eſt em̄ /  q̄libet <lb/>illaꝝ rotaꝝ eque velociter circuit cū qualꝫ aliarū: et <lb/>cuiuſlꝫ illaꝝ circuitio ꝓuēit ab eadē ꝓportiõe inade­<lb/>quate ſiue partialiter qm̄ ꝓuenit ab eadē ꝓportiõe <lb/>a qua circuitio totalis rote efficit̄̄ ſicut em̄ dicere-<lb/>mus ſortē potētie / vt .4. mouentē põdus reſiſtentie <lb/>vt .2. velocitate vt .4. mouere quãlibet partē illiꝰ põ­<lb/>deris velocitate vt q̈tuor et a ꝓportione dupla: ſed <lb/>hoc īadequate. </s>
              <s xml:id="N1D9C9" xml:space="preserve">¶ Ad īducēdã octauã ↄ̨cluſionē ſolu­<lb/>tiuam quinti argumenti preſentis queſtiõis pono <lb/>aliquas ſuppoſitiones geometricas.</s>
            </p>
            <div xml:id="N1D9D0" level="5" n="14" type="float">
              <note position="left" xlink:href="note-0139-03a" xlink:label="note-0139-03" xml:id="N1D9D4" xml:space="preserve">1. correĺ:</note>
              <note position="left" xlink:href="note-0139-04a" xlink:label="note-0139-04" xml:id="N1D9DA" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0139-05a" xlink:label="note-0139-05" xml:id="N1D9E0" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N1D9E6">
              <s xml:id="N1D9E7" xml:space="preserve">Prima ſuppoſitio  </s>
              <s xml:id="N1D9EA" xml:space="preserve">Si ſūt due quãtita­<lb/>tes equalis ꝓfunditatis vniformiter, et eq̄ late vni-<lb/>formiter, et vna lõgior allera in q̈cū ꝓportiõe eſt <lb/>lõgior in eadē eſt maior. </s>
              <s xml:id="N1D9F3" xml:space="preserve">Exēplū / vt ſi ſit vnū pedale <lb/>pedaliter latū, et pedaliter ꝓfundū, et ſit alia quã-<lb/>titas eq̄ ꝓfunda et eq̄ lata vniformiter, et in duplo <lb/>longior: manifeſtū eſt /  illa eſt in duplo maior q2 <lb/>cõtinet duo pedalia. </s>
              <s xml:id="N1D9FE" xml:space="preserve">Probat̄̄ hec ſuppoſitio facile / <lb/>qm̄ cū tales latitudines ſint vniformes in latitudī­<lb/>ne et ꝓfūditate illud qḋ maior plꝰ cõtinet ē eque la-<lb/>tū et eque ꝓfundū vniformiter ſicut mīor: ergo alia <lb/>quãtitas maior cõtinet totã minorē et illud vltra: et <lb/>illḋ ē eq̄ magnū adeq̈te ſicut tã lõga ꝑs mīoris quã­<lb/>tatis: igr̄ in q̈cū ꝓportiõe lõgitudo maioris ex­<lb/>cedit longitudinem minoris in eadeꝫ proportione <lb/>magnitudo maioris excedit magnitudinis mīoris</s>
            </p>
            <p xml:id="N1DA11">
              <s xml:id="N1DA12" xml:space="preserve">Secūda ſuppoſitio </s>
              <s xml:id="N1DA15" xml:space="preserve">Si due quantita­<lb/>tes ineq̈les ſint eq̄ profunde vniformiter et eq̄ longe <lb/>vniformiter et vna latior altera: in q̈cū ꝓportiõe <lb/>vna eſt latior in eadē eſt maior. </s>
              <s xml:id="N1DA1E" xml:space="preserve">Exēplū / vt ſi ſit vna <lb/>quãtitas bipedalis ſcḋm lõgitudinē pedalis ſcḋ3 la­<lb/>titudinē et ꝓfūditatē vniformiter et alia vniformiṫ <lb/>eque lõga et eq̄ ꝓfunda et ī ſexquialtero latior: erit <lb/>ī ſexquialtero maior. </s>
              <s xml:id="N1DA29" xml:space="preserve">Ptꝫ hec ſuppoſitio ſicut ṗor.</s>
            </p>
            <p xml:id="N1DA2C">
              <s xml:id="N1DA2D" xml:space="preserve">Tertia ſuppoſitio </s>
              <s xml:id="N1DA30" xml:space="preserve">Si ſint due quan-<lb/>titates eq̄ longe eque late vniformiter: et vna ſit in <lb/>aliq̈ ꝓqortione ꝓfundior altera: in eadē ꝓportione <lb/>in q̈ eſt ꝓfundior ē maior. </s>
              <s xml:id="N1DA39" xml:space="preserve">Exemplū / vt ſi ſit vna ma-<lb/>gnitudo bipedaliter lõga pedaliter lata et pedali-<lb/>ter ꝓfunda et vna alia bipedaliter lõga et pedaliter <lb/>lata et ſemipedaliter profunda / tūc dico /  alia quã­<lb/>titas maior in ea ꝓportione in q̈ eſt ꝓfundior ī ea ē <lb/>maior puta in dupla. </s>
              <s xml:id="N1DA46" xml:space="preserve">Patet etiam hec ſicut prima <lb/></s>
              <s xml:id="N1DA4A" xml:space="preserve">His ſuppoſitionibus premiſſis ſit hec.</s>
            </p>
            <pb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi." file="0140" n="140"/>
            <p xml:id="N1DA51">
              <s xml:id="N1DA52" xml:space="preserve">Octaua ↄ̨̨cluſio ꝓportio quadratorū <lb/>ꝑfectoꝝ et eque ꝓfundoꝝ vniformiter eſt ꝓp̄ortio co­<lb/>ſtaꝝ duplicata. </s>
              <s xml:id="N1DA59" xml:space="preserve">Et voco quadratū pērfectū cuiꝰ oēs <lb/>coſte ſunt eq̈les et oēs anguli recti eq̈les. </s>
              <s xml:id="N1DA5E" xml:space="preserve">Nõ intelli-<lb/>gas tñ /  velim dicere /  oēs coſte debent eſſe eq̈les <lb/>ſcḋm oēm dimēſionē: ſed ſatis eſt ſcḋm latitudinem <lb/>et lõgitudinē. </s>
              <s xml:id="N1DA67" xml:space="preserve">Exēplū / vt ſi ſit vnū q̈dratū pedaliter <lb/>longū, pedaliter latū et pedaliter ꝓfundū: et aliud <lb/>bipedaliter longū bipedaliter latū et ſolū pedali-<lb/>ter ꝓfundū / tūc dico /  vnū eſt q̈druplū ad alteꝝ: qm̄ <lb/>coſte ſe habēt in proportio dupla et magnitudi-<lb/>nes ſe habebãt in ꝓportiõe dupla ad duplã cuiuſ-<lb/>modi eſt q̈drupla ꝓportio. </s>
              <s xml:id="N1DA76" xml:space="preserve">Probat̄̄ hec cõcluſio et <lb/>capio duo q̈drata ꝑfecta eq̈liter ꝓfunda vniformiṫ / <lb/>q̇ꝝ minꝰ ſit a. et maiꝰ c. et habeat ſe coſta ipſius c. ad <lb/>coſtã ipſiꝰ a. in ꝓportione f. / tūc dico /  ipſiꝰ c. ad ip­<lb/>ſum a. eſt ꝓportio duplicata ad ꝓportionē ipſiꝰ f. <lb/></s>
              <s xml:id="N1DA82" xml:space="preserve">Quod ꝓbo ſic et capio vnū aliud corpꝰ puta b. /  ſit <lb/>eque ꝓfundū et eque latū ſicut a. vniformiter et in f. <lb/>ꝓportiõe lõgiꝰ et manifeſtū eſt /  ipſiꝰ b. ad ipſuꝫ a. <lb/>eſt ꝓportio f. / vt ptꝫ ex prima ſuppoſitiõe: et ipſius c. <lb/>ad ipſum b. eſt etiã f. ꝓportio: vt ptꝫ ex ſcḋa ſuppo-<lb/>ſitione: qm̄ cū ipſū c. (vt ponit̄̄ in caſu) ſit in f. ꝓpor-<lb/>tione latiꝰ quã ipſum b. et eſt eque longū et eque ꝓ-<lb/>fundū ſicut ipſum b. / igr̄ eſt in f. ꝓportiõe maiꝰ ipſo <lb/>b. / vt oſtēdit p̄dicta ſcḋa ſuppoſitio: igr̄ ipſius c. ad <lb/>ipſuꝫ a. eſt ꝓportio duplicata ad ꝓportionē f. </s>
              <s xml:id="N1DA97" xml:space="preserve">Ptꝫ <lb/>hec ↄ̨ña ex cõcluſione octaua ſexti capitis ſcḋe par­<lb/>tis / qm̄ ibi ſunt .3. termini cõtinuo ꝓportiõales f. ꝓ-<lb/>portionē / qm̄ b. ad a. eſt ꝓportio f. et c. ad b. eſt ꝓpor­<lb/>tio f. / igr̄ c. ad a. eſt proportio duplicata ſiue dupla <lb/>ad ꝓportionē f. / vt clare oſtendit p̄dicta octaua con­<lb/>cluſio allegata.               <anchor type="note" xlink:href="note-0140-01" xlink:label="note-0140-01a"/>               </s>
              <s xml:id="N1DAAB" xml:space="preserve">¶ Ex hac cõcluſione ſequit̄̄ tale cor-<lb/>relariū /  ꝓportio duoꝝ corpoꝝ cuboꝝ ſiue ꝑfecte <lb/>quadratoruꝫ ſimpliciter cuiuſmodi ſunt data ſiue <lb/>taxilli quoꝝ lõgitudo eſt eq̈lis latitudini et ꝓfūdi-<lb/>tati: ē ꝓportio coſtaꝝ triplicata. </s>
              <s xml:id="N1DAB6" xml:space="preserve">Exēplū / vt ſi fuerit <lb/>vnū corpꝰ cubū pedaliṫ ꝓfundū et aliud corpꝰ cubū <lb/>bipedaliter ꝓfundū dico /  illud bipedalittr ꝓfun­<lb/>dū eſt octuplū ad illud pedaliter ꝓfundū / qm̄ coſte <lb/>ad coſtã ē ꝓportio dupla / igr̄ ex correlario oꝫ ꝓpor­<lb/>tionē magnitudīs eē triplã ad ꝓportionē duplã: et <lb/>illa ē octupla / vt pꝫ ex ſcḋa ꝑte: igr̄. </s>
              <s xml:id="N1DAC5" xml:space="preserve">Probat̄̄ hoc cor­<lb/>relariū et capio duo corꝑa cuba quoꝝ latera ſiue co­<lb/>ſte ſe habeãt in f. ꝓportiõe et ſit minꝰ illoꝝ a. et maiꝰ <lb/>illoꝝ d. / deīde capio b. corpꝰ /  ſit eq̄ ꝓfnndū et eque <lb/>latū ſicut a. et in f. ꝓportiõe lõgiꝰ: deīde capio q̈rtū <lb/>corpꝰ puta c. / qḋ ſit eq̄ longū et eq̄ ꝓfundū ſicut b. et ī <lb/>f. ꝓportiõe latiꝰ: et arguo ſic / d. ad c. eſt f. ꝓportio / vt <lb/>pꝫ ex ſcḋa ſuppõe et b. ad a. ē f. ꝓportio / vt pꝫ ex ṗma / <lb/>igr̄ d. ad a. eſt triplicata ꝓportio ſiue tripla ad ꝓ-<lb/>portionē f. / vt ptꝫ ex .8. ↄ̨cluſiõe ſexti capitꝪ ſcḋe ꝑtꝪ / <lb/>qḋ fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0140-02" xlink:label="note-0140-02a"/>               </s>
              <s xml:id="N1DAE1" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  datꝪ duobꝰ q̈drãgu­<lb/>lis cubis quoꝝ coſte ſe hñt in ꝓportiõe ſexq̇altera: <lb/>maiorꝪ q̈drãguli ad mīorē ē ꝓportio tripla ſuꝑtri­<lb/>partiēs octauas q̈lis .27. ad .8. </s>
              <s xml:id="N1DAEA" xml:space="preserve">Probat̄̄ qm̄ / vt ptꝫ <lb/>ex p̄cedēti correlario ꝓportio duoꝝ cuboꝝ ſiue q̈dra­<lb/>toꝝ perfectorū ē ꝓportio coſtaꝝ triplata: ſꝫ ꝓpor-<lb/>tio tripla ſuꝑtriꝑtiēs .8. eſt tripla ad ꝓportionē ſex­<lb/>q̇alterã / q̄ ē īter coſtas datoꝝ q̈dratoꝝ: igr̄ talia q̄-<lb/>drata cuba ſe hñt ī ꝓportiõe tripla ſuꝑtriꝑtiēte .8. <lb/></s>
              <s xml:id="N1DAF8" xml:space="preserve">Maior ptꝫ cū ↄ̨ña: et ꝓbat̄̄ minor / qm̄ ꝓportior .27. <lb/>ad .8. ↄ̨ponit̄̄ ex tribꝰ ſexq̇alterꝪ. </s>
              <s xml:id="N1DAFD" xml:space="preserve">Sint em̄ īter illos <lb/>nūeros .4. termini cõtinuo ꝓportiõales ꝓportione <lb/>ſexq̇altera. </s>
              <s xml:id="N1DB04" xml:space="preserve">Nã .27. ad .18. eſt ꝓportio ſexq̇altera et <lb/>18. ad .12. eſt ꝓportio ſexq̇altera et .12. ad .8. ſexq̇alte­<lb/>ra.               <anchor type="note" xlink:href="note-0140-03" xlink:label="note-0140-03a"/>               </s>
              <s xml:id="N1DB10" xml:space="preserve">¶ Seq̇tur vlteriꝰ /  datis duobꝰ q̈dratis cubicis <lb/>quoꝝ latera ſe hñt in ꝓportiõe tripla: īter maius et               <cb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi."/>               minꝰ reperit̄̄ ꝓportio vicecupla ſeptupla: qualis eſt <lb/>ꝓportio .27. ad vnū. </s>
              <s xml:id="N1DB1A" xml:space="preserve">Ptꝫ hoc correlariū ex primo <lb/>correlario hoc addito /  proportio vicecupla ſe-<lb/>ptupla ex tribꝰ triplis cõponit̄̄ / qḋ facile eſt ꝓſpice­<lb/>re. </s>
              <s xml:id="N1DB23" xml:space="preserve">Nã .27. ad .9. eſt ꝓportio tripla: et .9. ad .3. eſt pro­<lb/>portio tripla: et .3. ad vnū ſimiliter tripla ꝓportio <lb/></s>
              <s xml:id="N1DB29" xml:space="preserve">Iſto modo ꝓcedēdo aliquãtula primeditatiõe et cõ­<lb/>ſideratione cõpoſitionis ꝓportionū: īfinita corre-<lb/>laria ex p̄dicto primo correlario īferri valent et ſi-<lb/>militer ex cõcluſione. </s>
              <s xml:id="N1DB32" xml:space="preserve">ſed differantur vſ ad mate-<lb/>riam de augmentatione.</s>
            </p>
            <div xml:id="N1DB37" level="5" n="15" type="float">
              <note position="left" xlink:href="note-0140-01a" xlink:label="note-0140-01" xml:id="N1DB3B" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0140-02a" xlink:label="note-0140-02" xml:id="N1DB41" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0140-03a" xlink:label="note-0140-03" xml:id="N1DB47" xml:space="preserve">3. correĺ.</note>
            </div>
            <note position="right" xml:id="N1DB4D" xml:space="preserve">Cõcluſio <lb/>brauarḋ</note>
            <p xml:id="N1DB53">
              <s xml:id="N1DB54" xml:space="preserve">Nona cõcluſio. </s>
              <s xml:id="N1DB57" xml:space="preserve">Scḋm opinionē q̄ po­<lb/>nit velocitatē motus difformiter difformis quo ad <lb/>ſubiectū attendi debere penes gradū ſummū: ꝓpor­<lb/>tio motus duaꝝ ſperaꝝ ſiue duoꝝ orbiū: pariter <lb/>duoꝝ circuloꝝ in equali tēpore ceteris paribꝰ circū­<lb/>giratoꝝ eſt ſicut ꝓportio ſuoꝝ diametroꝝ. </s>
              <s xml:id="N1DB64" xml:space="preserve">Proba­<lb/>tur hec cõcluſio / qm̄ ꝓportio perimetroꝝ circulorū <lb/>eſt ſicut ꝓportio diametroꝝ: et quãto vna diameter <lb/>eſt maior altera tanto maiorē lineã deſcribit eius <lb/>punctꝰ maxime a centro diſtans: igr̄ cõcluſio vera. <lb/></s>
              <s xml:id="N1DB70" xml:space="preserve">¶ Hic tñ aduerte /  ad inducendã hanc concluſionē <lb/>proceſſu mathematico oportet maiori apparatu <lb/>vti quã p̄ſens exigat opus: ſatis eſt em̄ in iſtis. </s>
              <s xml:id="N1DB77" xml:space="preserve">Eu-<lb/>clidi et mathematicoꝝ ṗmoribꝰ fidē exhibere. </s>
              <s xml:id="N1DB7C" xml:space="preserve">In <lb/>hac em̄ cõſideratione phiſica mathematice ſcien­<lb/>tie ſubalternari nõ dedignatur: quēadmodū in ſci­<lb/>entia de iride ſubalternata perſpectiue dinoſcitur <lb/>teſte philoſopho primo poſteriorum.</s>
            </p>
            <note position="right" xml:id="N1DB87" xml:space="preserve">Pḣs pri-<lb/>mo po-<lb/>ſteriorū.</note>
            <p xml:id="N1DB8F">
              <s xml:id="N1DB90" xml:space="preserve">Decima cõcluſio. </s>
              <s xml:id="N1DB93" xml:space="preserve">Proportio motuū <lb/>duaꝝ ſpheraꝝ ſolidaꝝ eſt ſicut ꝓportio diametro-<lb/>rum. </s>
              <s xml:id="N1DB9A" xml:space="preserve">Et hoc ſcḋm oēm opinionē. </s>
              <s xml:id="N1DB9D" xml:space="preserve">Probat̄̄ ex priori <lb/>̄tum ad opinionē / q̄ dicit velocitatē attendi debe-<lb/>re penes punctū velociſſime motū. </s>
              <s xml:id="N1DBA4" xml:space="preserve">Sed ̄tū ad aliã <lb/>opinionē ptꝫ / qm̄ ſcḋm aliã velocitas ſpere ſolide <lb/>debet attendi ſcḋm lineã deſcriptã a pūcto medio <lb/>ſemidiametri īter centrū et circūferentiã: et ꝑ ↄ̨ñs a <lb/>puncto deſcripto ab vna quarta ſemidiametri: ſed <lb/>in quacū ꝓportione vna diameter eſt maior alte­<lb/>ra in eadē vna quarta eſt maior vna quarta alteriꝰ / <lb/>ergo ſcḋm hãc opinionē in quacū ꝓportionē dia­<lb/>meter vniꝰ ſpere ſolide erit maior diametro alteriꝰ <lb/>in eadē ꝓportiõe maiorē lineã deſcribet punctꝰ me­<lb/>dius ſemidiametri: et per ↄ̨ñs ꝓportio motus erit <lb/>ſicut ꝓportio diametrorum / quod fuit probandū.</s>
            </p>
            <p xml:id="N1DBBD">
              <s xml:id="N1DBBE" xml:space="preserve">Undecima ↄ̨̨cluſio </s>
              <s xml:id="N1DBC1" xml:space="preserve">Proportio motuū <lb/>duaꝝ ſperaꝝ īequaliū in eode tēpore circūgirataꝝ <lb/>dūmodo ſint ſolide eſt ſubtripla ad ꝓportionē ſpe­<lb/>raꝝ īter ſe. </s>
              <s xml:id="N1DBCA" xml:space="preserve">Probat̄̄ hec cõcluſio / qm̄ ꝓportio mo-<lb/>tuū duaꝝ ſperaꝝ eſt ꝓportio diametroꝝ taliū ſpe­<lb/>raꝝ / vt ptꝫ ex priori: ſꝫ ꝓportio ſperaꝝ īequaliū eſt <lb/>ꝓportio diametroꝝ triplata ſiue eſt tripla ad pro­<lb/>portionē diametroꝝ / qḋ idē eſt / vt patꝫ ex vltīa decī <lb/>elemētoꝝ. </s>
              <s xml:id="N1DBD7" xml:space="preserve">Euclidis <gap/> g̊ ꝓportio diametroꝝ eſt ſubtri­<lb/>pla ad ꝓportionē ſperaꝝ et talis ē ꝓportio motuū / <lb/>igr̄ ꝓportio motuuū duaꝝ ſperaꝝ ineq̈liū etc. ē ſub­<lb/>tripla ꝓportio ad proportionem ſperarū inter ſe. <lb/>               <anchor type="note" xlink:href="note-0140-04" xlink:label="note-0140-04a"/>               </s>
              <s xml:id="N1DBE9" xml:space="preserve">¶ Ex quo ſequit̄̄ /  ſi vna ſpera eſt in octuplo maior <lb/>altera /  mouet̄̄ preciſe in duplo velociꝰ altera: et ſi <lb/>vna ſpera fuerit in triplo ſupertripartiēti octauas <lb/>maior altera ipſa mouet̄̄ in ſexq̇altero velociꝰ alte­<lb/>ra. </s>
              <s xml:id="N1DBF4" xml:space="preserve">Ptꝫ hoc correlariū / q̊ ad primã ꝑtē qm̄ ꝓportio <lb/>octupla eſt tripla ad duplã: g̊ ſi ſpere ſe habēt ī octu­<lb/>pla ꝓportione motꝰ earū ſe habebūt in dupla q̄ eſt <lb/>ſubtripla ad octuplã: ptꝫ ↄ̨ña ex immediate prece-<lb/>dēte ↄ̨cluſione. </s>
              <s xml:id="N1DBFF" xml:space="preserve">Eodē mõ ptꝫ / q̄ ad ſcḋaꝫ partē qm̄ ſi <lb/>ſpere ſe habent in ꝓportione tripla ſuꝑtripartiēti               <pb chead="Secundi tractatus" file="0141" n="141"/>               octauas / ↄ̨ñs eſt motus eaꝝ ſe habere in ꝓportione <lb/>ſubtripla ad ꝓportionē triplã ſuꝑtripartiētē octa­<lb/>nas / vt ptꝫ ex ↄ̨cluſiõe: et talis eſt ꝓportio ſexq̇alte-<lb/>ra / vt oſtenſū eſt in ſcḋo correlario octaue ↄ̨cluſiõis <lb/>huiꝰ capitis / igr̄ ꝓpoſitū: de ꝓportiõe autē ſperaꝝ et <lb/>de motuū eaꝝ ꝓportiõe videas theodoſiū deſperꝪ et <lb/>pulchrã doctinã necnõ ſubtile artificiū cõcluſionū <lb/>qua in hac materia thomas brauardibꝰ et in capi-<lb/>tulo quarto et vltimo tractatꝰ ꝓportionū / quas edi­<lb/>dit mathematico apparatu īducit: his poſitis ſit.</s>
            </p>
            <div xml:id="N1DC1B" level="5" n="16" type="float">
              <note position="right" xlink:href="note-0140-04a" xlink:label="note-0140-04" xml:id="N1DC1F" xml:space="preserve">1. correĺ.</note>
            </div>
            <p xml:id="N1DC25">
              <s xml:id="N1DC26" xml:space="preserve">Duodecima ↄ̨̨cluſio reſpõſiua ad q̄ſti­<lb/>onē. </s>
              <s xml:id="N1DC2B" xml:space="preserve">Quēadmodū ꝓbabile eſt velocitatē motus de <lb/>quo eſt p̄ſens inq̇ſitio attēdi debere penes lineã de-<lb/>ſcriptã a pūcto in quo eſt g̈dus mediꝰ aut penes re-<lb/>ductionē ad vniformitatē denoīatiõis: ita ꝓbile eſt <lb/>talē motū attēdi debere penes lineã a pūcto velo-<lb/>ciſſime moto deſcriptã ſiue talis punctꝰ velociſſime <lb/>motꝰ ſit verꝰ ſiue ymaginariꝰ: prima pars huiꝰ ↄ̨clu­<lb/>ſionis aliq̈liter ptꝫ ex p̄dictīs et et declabit̄̄ ꝑ ãplius <lb/>in argumētoꝝ ſolutiõibꝰ. </s>
              <s xml:id="N1DC3E" xml:space="preserve">Scḋa o pars ptꝫ ex cõ-<lb/>cluſiõe quīta huiꝰ.               <anchor type="note" xlink:href="note-0141-01" xlink:label="note-0141-01a"/>               </s>
              <s xml:id="N1DC48" xml:space="preserve">Si tñ plus affectas hãc ſecundã <lb/>partē ↄ̨cluſiõis īueſtigare p̄ſto erit tibi guillermus <lb/>hentiſber in ſuo tractatu de motu locali capite pri­<lb/>mo illã cū ſuis ↄ̨mētariis ad extremū vſ diſcutiēs</s>
            </p>
            <div xml:id="N1DC51" level="5" n="17" type="float">
              <note position="left" xlink:href="note-0141-01a" xlink:label="note-0141-01" xml:id="N1DC55" xml:space="preserve">hētiſber</note>
            </div>
            <p xml:id="N1DC5B">
              <s xml:id="N1DC5C" xml:space="preserve">Ad rationes ante oppoſitū q2 vtrã <lb/>opinionē ſuſtinemꝰ oꝑe p̄ciū eſt oēs illas rõnes ſol-<lb/>uere: ̄uis ille q̄ ſūt ↄ̨tra vnã opinione ſint ꝓ altera</s>
            </p>
            <p xml:id="N1DC63">
              <s xml:id="N1DC64" xml:space="preserve">Ad prṫmã dico / vt dictū eſt ibi cū dice-<lb/>bat̄̄ /  ideo velocitas motꝰ difformis quo ad ſubie-<lb/>ctū attendi d3 penes punctū velociſſime motū q2 di­<lb/>gnū eſt vnūqḋ a digniori denoīri. </s>
              <s xml:id="N1DC6D" xml:space="preserve">Itē q2 aliqñ <lb/>nõ datur punctꝰ tardiſſime motus vt ibi dr̄: et ad re-<lb/>plicã reſpõdeo /  ̄uis nõ detur aliqñ pūctꝰ qui ve-<lb/>lociſſime mouet̄̄ verꝰ: datur tñ ymaginariꝰ / qḋ ſuffi­<lb/>cit: et ſimiliter nõ detur linea vera datur tñ ymagi-<lb/>naria quã deſcribit: et loquor in ꝓpoſito de o vel <lb/>ymaginario vt ad ꝓpoſitū cõducit. </s>
              <s xml:id="N1DC7C" xml:space="preserve">Et ꝑ hoc ptꝫ ad <lb/>primã cõfirmationē cū ſua replica prima. </s>
              <s xml:id="N1DC81" xml:space="preserve">Et ad ſe-<lb/>cundã replicã / q̄ ponit rotã cõtinuo rarefieri ita  <lb/>cõtinuo magis diſtent pūcta extra a centro admit-<lb/>to caſum et nego añs: et ad ꝓbationē nego /  nullaꝫ <lb/>lineã deſcribat: et cū ꝓbat̄̄ / q2 nec rectã nec circularē <lb/>cõcedo añs: et nego cõſequētiã. </s>
              <s xml:id="N1DC8E" xml:space="preserve">Multe em̄ linee ſunt <lb/>que nec recte nec circulares ſunt / vt patꝫ de linea pro <lb/>media parte recta et ꝓ media circulari. </s>
              <s xml:id="N1DC95" xml:space="preserve">Hoc idē ptꝫ <lb/>de linea giratiua et de filio ad globum redacto. </s>
              <s xml:id="N1DC9A" xml:space="preserve">Et <lb/>ideo dico /  talis linea habet ſe quaſi ad modum <lb/>linee giratiue vel curue.</s>
            </p>
            <p xml:id="N1DCA1">
              <s xml:id="N1DCA2" xml:space="preserve">Ad ſecūdã cõfirmationē dico breuiṫ / <lb/> talis rota mouet̄̄ ita velociter ſicut pūctꝰ eiꝰ extre­<lb/>mꝰ mouet̄̄ in toto tꝑe adequate. </s>
              <s xml:id="N1DCA9" xml:space="preserve">Et ſi queras cui cor­<lb/>reſpõdet velocitas illiꝰ pūcti ī toto illo tꝑe adeq̈te.</s>
            </p>
            <p xml:id="N1DCAE">
              <s xml:id="N1DCAF" xml:space="preserve">Reſpõdeo / vt michi videt̄̄ ꝓ nūc /  cor­<lb/>reſpõdet velocitati quã talis pūctꝰ hꝫ in inſtanti me-<lb/>dio totiꝰ tꝑis. </s>
              <s xml:id="N1DCB6" xml:space="preserve">Nã ymaginor illū punctū moueri vni­<lb/>formiter quo ad tēpꝰ cõtinuo vniformiter intēden-<lb/>do motū: et cū dicis / qḋ hoc eſt cõicidere cū alia opi­<lb/>nione, nego tibi illud, et ratio eſt / q2 alia opinio di-<lb/>ceret in illo caſu rotã illã moueri cõtinuo ita velo-<lb/>cīter ſicut pūctꝰ / qui eſt in medio ſemidiametri inter <lb/>centrū et circūferentiã q̇ lõge tardiꝰ moue^ quã pū-<lb/>ctus peripherie: et ↄ̨ñter diceret /  velocitas motus <lb/>totiꝰ rote corrñdet velocitati motꝰ qua hꝫ ille pūctꝰ <lb/>qui eſt in medio illius ſemidiametri mouetur in me­<lb/>dio totius temporis in quo mouetur.</s>
            </p>
            <p xml:id="N1DCCD">
              <s xml:id="N1DCCE" xml:space="preserve">Ad ſcḋm argumentū reſponſum eſt               <cb chead="Capitulū tertiū."/>               ibi vſ ad vltimã replicã ad quã reſpõdeo ↄ̨ceden­<lb/>do / qḋ īfert̄̄, et negãdo falſitatē ↄ̨ñtis, et cū ꝓbat̄̄ fal­<lb/>ſitas ↄ̨ñtis nego ſeq̄lã vcꝫ /  ſtabit punctū extremū <lb/>moueri ita velociṫ ſicut ãtea mouebat̄̄ q̈libet parte <lb/>ꝓportiõali carēte velocitate ſiue q̇eſcēte. </s>
              <s xml:id="N1DCDC" xml:space="preserve">Sꝫ dico /  <lb/>cū aliq̈ pars ꝓportiõalis deuenerit ad nõ graduꝫ <lb/>velocitatꝪ tota rota q̇eſcit.               <anchor type="note" xlink:href="note-0141-02" xlink:label="note-0141-02a"/>               </s>
              <s xml:id="N1DCE8" xml:space="preserve">Utrū aūt poſſet fieri / qḋ <lb/>in calce argumēti ponit̄̄ vcꝫ /  a q̈libet ꝑ parte ꝓpo-<lb/>tionali ſcḋm certã diuiſionē demat̄̄ medietas velo-<lb/>citatis abſ hoc /  demat̄̄ aliq̇d a pūcto exiſtēte in <lb/>peripheria rote nõ eſt michi certū: nichilominꝰ vi­<lb/>detur /  pari ratione concedendum ſit ſicut conce-<lb/>ditur procedens illatum.</s>
            </p>
            <div xml:id="N1DCF7" level="5" n="18" type="float">
              <note position="right" xlink:href="note-0141-02a" xlink:label="note-0141-02" xml:id="N1DCFB" xml:space="preserve">Dubiū.</note>
            </div>
            <p xml:id="N1DD01">
              <s xml:id="N1DD02" xml:space="preserve">Ad tertiã rationē reſpõdēt priores cõ­<lb/>cluſiões huiꝰ capitis poſite in corꝑe huiꝰ queſtiõis.</s>
            </p>
            <p xml:id="N1DD07">
              <s xml:id="N1DD08" xml:space="preserve">Ad quartū argumentū dictum eſt ibi <lb/>vſ ad vltimã replicã ad quã reſpõdet ſeptīa ↄ̨clu-<lb/>ſio cū ſuo correlario: diſtãtia em̄ pūctoꝝ vĺ ꝓpinq̇-<lb/>tas nichil cõfert ad velocitatē circūgirationis, nec <lb/>auget, nec minuit ꝓportionē ſꝫ dūtaxat īpedimētū <lb/>circūgirandi / qḋ forte eſt g̈uitas exiſtēs in corꝑe cir­<lb/>cunducto. </s>
              <s xml:id="N1DD17" xml:space="preserve">Si nulla em̄ eſſet g̈uitas aut aliqḋ aliud <lb/>īpedimentū eque cito giraretur magna rota ſicut <lb/>parua: et ſi potentia circungirans eſſet naturalis <lb/>ſubito circungiraretur.</s>
            </p>
            <p xml:id="N1DD20">
              <s xml:id="N1DD21" xml:space="preserve">Ad quintū negat̄̄ añs:  ad ꝓbationē <lb/>admiſſo caſu et ſuppoſitiõe ↄ̨cedo illatū vcꝫ /  a. ade­<lb/>quate in duplo velociꝰ mouet̄̄ ꝙ̄ b. / et nego falſitateꝫ <lb/>ↄ̨ñtis, et ad ꝓbationē admiſſa ↄ̨cluſiõe geometrica / <lb/>q̄ ibi ſupponit̄̄ cõcedo /  a. pedale in duplo ſuꝑbi-<lb/>partiēti quītas velociꝰ rarefit quã pedale b. et  ra­<lb/>refactio eſt motꝰ localis et cū infert̄̄ / g̊ in duplo ſuꝑ-<lb/>bipartiēti quãtas velociꝰ mouet̄̄ a. ꝙ̄ b. / nego ↄ̨ñam <lb/>̄uis em̄ idē ſit rarefactio et motꝰ: penes tñ aliud cõ­<lb/>mēſurari habet velocitas rarefactiõis et motus lo­<lb/>calis ſicut dictū eſt de circuitione et motu circulari.</s>
            </p>
            <p xml:id="N1DD38">
              <s xml:id="N1DD39" xml:space="preserve">Ad ſextã rõnē dictū eſt ibi vſ ad re-<lb/>plicã de linea girãte columnã: ad quã dico /  motꝰ <lb/>talis linee giratiue nõ d3 reduci ad vniformitatē vt <lb/>ſupponit replica: ſed totū reſiduū illius linee qḋ <lb/>eſt ſupra pūctū in quo eſt mediꝰ g̈dus motꝰ quo mo­<lb/>uet̄̄ totalis rota d3 capi ac ſi eſſet medietas totius <lb/>linee. </s>
              <s xml:id="N1DD48" xml:space="preserve">Tã velociter em̄ mouet̄̄ illa linea giratiua ſi-<lb/>cut vna linea recta exiēs a cētro rote vſ ad circū-<lb/>feretiã eiꝰ. </s>
              <s xml:id="N1DD4F" xml:space="preserve">Et ideo velocitas illiꝰ linee giratiue cõ-<lb/>mēſurari hꝫ penes velocitatē talis linee recte. </s>
              <s xml:id="N1DD54" xml:space="preserve">Et ſi <lb/>hec ſolutio tibi nõ placet vexes īteīlectū ad cõperiē-<lb/>dã aliã. </s>
              <s xml:id="N1DD5B" xml:space="preserve">Nõ em̄ ꝓ nūc alia michi occurit. </s>
              <s xml:id="N1DD5E" xml:space="preserve">Argumē­<lb/>tū in oppoſitū nõ eſt magis ꝓ vna opiniõe quã pro <lb/>reliqua. </s>
              <s xml:id="N1DD65" xml:space="preserve">Et ideo queſtio noſtra his paucis contēta <lb/>terminum ſumat.</s>
            </p>
          </div>
          <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
            <head xml:id="N1DD6F" xml:space="preserve">Capitulū tertiū / in quo oſtendit̄̄ modꝰ cogno-<lb/>ſcendi ſiue cõmenſurandi motū vniformieer diffor-<lb/>mem et difformiter difformem quo ad tempus quo <lb/>ad velocitatem et tarditatem in omni ſpecie .etc̈. <lb/>In oī ſpecie ꝓportiõis rõnalis et irrõalis <lb/>per modū q̄ſtiõis ꝓcedendo.</head>
            <p xml:id="N1DD7C">
              <s xml:id="N1DD7D" xml:space="preserve">Exactis vt potuimus difficulta-<lb/>tibus circa motꝰ difformis quo ad ſubiectū ↄ̨tingē­<lb/>tibꝰ: iã reſtat accedere ad difficultates circa cogno­<lb/>dã et ↄ̨mēſurandã velocitatē motꝰ difformis quo ad <lb/>tēpꝰ occureētes. </s>
              <s xml:id="N1DD88" xml:space="preserve">Circa qḋ talē q̄ro q̄ſtionē. </s>
              <s xml:id="N1DD8B" xml:space="preserve">¶ Utrum <lb/>oīs motus vniformiter difformis quo ad tempus <lb/>menſurari habet penes gradum medium: et omīs <lb/>difformiter difformis quo ad tēpus penes reducti­<lb/>onē ad vniformitatē ſiue pēnes cõmenſurationem <lb/>denoīatiõis q̈ denoīatiõe denoīat mobile moueri.</s>
            </p>
            <pb chead="De motu locali quo ad effectum ſubiecto difformi." file="0142" n="142"/>
            <p xml:id="N1DD9C">
              <s xml:id="N1DD9D" xml:space="preserve">Et arguitur primo /  motus vnifor-<lb/>miter difformis velocitas no eſt gradn illiꝰ medio <lb/>ↄ̨menſurãda / q2 ſeq̄retur /  omne quod mouetur in <lb/>aliquo tempore vniformiter diffõrmiter a non gra­<lb/>du vſ ad certum gradum id eſt a non gradu vſ <lb/>ad duo decimum moueretur in duplo tardius quã <lb/>mobile motum per idem tempus gradu duo deci-<lb/>mo continuo / ſed conſequens eſt falſum: igitur illḋ <lb/>ex q̊ ſeq̇t̄̄. </s>
              <s xml:id="N1DDB0" xml:space="preserve">Cõſeq̄ntia pꝫ / q2 in toto illo tp̄e tale mobi­<lb/>le motū vniformiṫ difformiṫ mouet̄̄ ita velociṫ ac ſi <lb/>moueretur motu vt ſex ſi talis motus debeat correſ­<lb/>pondere gradui medio cum ſex ſit gradus mediꝰ in­<lb/>ter duodecim et non gradū: ſed ſi continuo per ideꝫ <lb/>tempus moueretur gradu ſexto in duplo tardiꝰ mo­<lb/>ueretur mobili moto gradu duodecimo vniformi-<lb/>ter: igitur. </s>
              <s xml:id="N1DDC1" xml:space="preserve">Sed falſitas conſequentis oſtenditur / q2 <lb/>ſi in illo tempore moueretur in duplo tardius quaꝫ <lb/>mobile motum gradu duodecimo: vel igitur ī vtra­<lb/> medietate moueretur in duplo tardius, vel in ali­<lb/>qua: vel in aliqua non: ſed neutrum iſtorum eſt dicē­<lb/>dum: igitur. </s>
              <s xml:id="N1DDCE" xml:space="preserve">Non primum / quia in prima mouetur <lb/>in quadruplo minus: igitur non in duplo minꝰ nec <lb/>ſecundum: quoniam in ſecunda medietate non mo-<lb/>uetur in duplo minus ſed in ſexquitertio </s>
              <s xml:id="N1DDD7" xml:space="preserve">Uelocitas <lb/>enī ſecunde medietatis temporis correſpondet gra­<lb/>dui nouo: vt ptꝫ ex iſto mõ dicendi. </s>
              <s xml:id="N1DDDE" xml:space="preserve">¶ Forte dices et be­<lb/>ne ad illud quod querit argumentum /  in toto tem­<lb/>pore adequate mouetur in duplo minus quam mo­<lb/>bile motum vniformiter vt duodecim: tamē per nul­<lb/>lam partem temporis mouetur adequate in duplo <lb/>minus. </s>
              <s xml:id="N1DDEB" xml:space="preserve">Et ideo illa conſequentia non valet: moue-<lb/>tur in iſto tempore in duplo minus. </s>
              <s xml:id="N1DDF0" xml:space="preserve">ergo in vtra <lb/>medietate: vel in aliqua: vel in aliqua non. </s>
              <s xml:id="N1DDF5" xml:space="preserve">Nam in <lb/>prima mouetur in quadruplo minus quam mobile <lb/>gradu duodecimo et in ſecunda in ſexquitertio.</s>
            </p>
            <p xml:id="N1DDFC">
              <s xml:id="N1DDFD" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>omne mouens vniformiter a non gradu vſ ad cer­<lb/>tum gradum in triplo velocius moueretur in ſecun­<lb/>da medietate temporis quam in prima: ſed conſe-<lb/>quens eſt falſum: igitur. </s>
              <s xml:id="N1DE08" xml:space="preserve">Sequela patet / quoniã ī ſe­<lb/>cunda medietate / vt dicis mouetur velocitate ſubſex­<lb/>quitertia ad gradum intenſiorem: et in prima medi­<lb/>etate mouetur velocitate ſubquadrupla ad eundeꝫ <lb/>gradum intenſiorem: ſed omne ſubſexquitertiū ad <lb/>aliquod eſt triplum ad quartam eius vel ad ſubqua­<lb/>druplum illius / quod idem eſt: igitur gradus mediꝰ <lb/>prime medietatis eſt triplus ad gradum medium <lb/>ſecunde medietatis. </s>
              <s xml:id="N1DE1B" xml:space="preserve">¶ Dices et bene concedendo / qḋ <lb/>infertur / vt poſtea oſtendetur in quadam propoſi-<lb/>tione.</s>
            </p>
            <p xml:id="N1DE22">
              <s xml:id="N1DE23" xml:space="preserve">Sed contra / quia ſi illa ſolutio eēt bo-<lb/>na ſequeretur /  in ſecunda medietate prime medie­<lb/>tatis in triplo velocius moueretur illud mobile quã <lb/>in prima eiuſdem medietatis: et diuiſa illa medieta­<lb/>te adhuc in duas in ſubtriplo moueretur: ſed conſequens <lb/>eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N1DE30" xml:space="preserve">Falſitas con­<lb/>ſequentis probatur / quia tunc ſequeretur / quodlib3 <lb/>mobile incipiens moueri a non gradu vſ ad certū <lb/>gradum infinita tarditate moueri per aliquod tem­<lb/>pus: ſed conſequens eſt falſum: igitur illud ex quo <lb/>ſequitur: ſequela probatur / quoniã in mediate poſt <lb/>inſtans initiatiuum motus tale mobile mouebitur <lb/>aliquantula velocitate: et in duplo minori et in tri-<lb/>plo minori et in quadruplo / et ſic conſequenter: igi-<lb/>tur infinita tarditate mouebitur / quodlibet tale mo­<lb/>bile: </s>
              <s xml:id="N1DE47" xml:space="preserve">Antecedens patet ex ſolutione. </s>
              <s xml:id="N1DE4A" xml:space="preserve">Sed falſitas cõ­               <cb chead="De motu locali quo ad effectum ſubiecto difformi."/>               ſequentis arguitur / quia alias ſequeretur mobile / <lb/>quod continuo infinite velociter intendit motum ſu­<lb/>um infinitum tarde moueri: ſed conſequens videtur <lb/>implicare / igitur illud ex quo ſequitur: </s>
              <s xml:id="N1DE56" xml:space="preserve">Et ſequela <lb/>ꝓbatur pono caſum /  ſint īfinita mobilia .a.b.c. <lb/>etc. que moueantur per horaꝫ vniformiter difformi­<lb/>ter incipiendo a non gradu et a. moueatur per ean-<lb/>dem a non gradu vſ ad octauum: et b. a non gra-<lb/>du vſ ad ſextumdecimum: et c. a non gradu vſ ad <lb/>triceſimum ſecundum et conſequenter ꝓcedendo ꝑ <lb/>numeros duplos: et hoc in eadem hora: quo poſito <lb/>ſic argumentor / quodlibet iſtorum mobilium infini­<lb/>ta tarditate per aliquod tempus mouebitur. </s>
              <s xml:id="N1DE6B" xml:space="preserve">ſed in <lb/>ta velocitate aliquod iſtorum per idem tempus in-<lb/>tendet motum ſuum. </s>
              <s xml:id="N1DE72" xml:space="preserve">ergo aliquod iſtorum quod in­<lb/>finita tarditate per aliquod tempus mouebitur in­<lb/>finita velocitate per aliquod tempus intendit mo-<lb/>tum ſuum / quod fuit probaudum.</s>
            </p>
            <note position="right" xml:id="N1DE7B" xml:space="preserve">cõfirma-<lb/>tio.</note>
            <p xml:id="N1DE81">
              <s xml:id="N1DE82" xml:space="preserve">¶ Et confirmatur / quia ſi quilibet motus vniformi­<lb/>ter difformis commenſurari debeat penes graduꝫ <lb/>medium ſequeretur /  motus a certo gradu vſ ad <lb/>non gradum vt exempli gratia quo aliquod mobi­<lb/>le mouetur a quarto vſ ad non gradum remitten­<lb/>do motum ſuum in hora: et motus quo aliquod mo­<lb/>bile mouetur vniformiter difformiter a non gradu <lb/>vſ ad quartum in eadem hora eſſent omnino eq̈-<lb/>les / ſꝫ hoc eſt falſum: igr̄ illud ex quo ſeq̇tur. </s>
              <s xml:id="N1DE95" xml:space="preserve">Seque-<lb/>la probatur vtriuſ eī motus illorū duorum motu­<lb/>um gradus medius eſt vt duo / et per conſequens illi <lb/>motus ſunt equales. </s>
              <s xml:id="N1DE9E" xml:space="preserve">Sed iam oſtenditur falſitas <lb/>contequentis: quia tunc ſequeretur /  ſi aliquis mo­<lb/>tus intenderetur a gradu vt .4. vſ ad gradū du-<lb/>plum in hora et alter motus equalis illi puta vt .4. <lb/>ab eodem gradu quarto ln eadem hora vniformi-<lb/>ter et eque velociter remittatur vſ ad quietem ſiue <lb/>ad non gradum motus: tunc talis motus qui remit­<lb/>titur non dumtaxat vniformiter et eqne velociter re­<lb/>mitteretur ſicut alter motus equalis ei intendere-<lb/>tur in eodem tempore: ſed hoc eſt falſum / quia quã-<lb/>tam latitudineꝫ acquirit ille motus qui intenditur <lb/>tantam adequate deperdit ille motus qui remitti-<lb/>tur in eodem tempore. </s>
              <s xml:id="N1DEB9" xml:space="preserve">Naꝫ ille q̇ intenditur cum ſit <lb/>vt .4. acquirit .4. gradus ſupra ſe: et in eodeꝫ tempo­<lb/>re ille qui remittitur vſ ad non gradum cum ſic vt <lb/>quatuor perdit etiam quatuor gradus in eodē tem­<lb/>pore. </s>
              <s xml:id="N1DEC4" xml:space="preserve">Sed iam probo ſequelam / quoniam ille motꝰ <lb/>vt .4. qui remittitur in hora vſ ad non gradum re­<lb/>mittitur in eadem hora ad ſuum ſubduplum, et ad <lb/>ſuum ſubquadruplum: et ad ſuum ſuboctuplum: et <lb/>ſic in infinitum </s>
              <s xml:id="N1DECF" xml:space="preserve">Motus vero alter qui intendit̄̄ pre­<lb/>ciſe intenditur ad ſuum duplum. </s>
              <s xml:id="N1DED4" xml:space="preserve">igitur in infinituꝫ <lb/>maiorem proportionem deperdit motus qui remit­<lb/>titnr quam acquirat motus qui intenditur: et ꝑ con­<lb/>ſequens non ita velociter ſicut vnus remittitur al-<lb/>ter intenditur / quod fuit probandum.</s>
            </p>
            <p xml:id="N1DEDF">
              <s xml:id="N1DEE0" xml:space="preserve">¶ Dices forte ad punctum argumenti diſtinguen-<lb/>do illatum aut  in eadem hora non remittat̄̄ eque­<lb/>velociter vnus motus ſicut alter intenditur equali­<lb/>tate geometrica / et ſic conceditur / vt bene probat ar-<lb/>gumentum, aut equalitate arithmetica / et ſic nega-<lb/>tur: </s>
              <s xml:id="N1DEED" xml:space="preserve">Ad hoc enim  eque velociter vnus motus re-<lb/>mittatur ſicut alter intenditur equalitate arithme­<lb/>tica ſufficit  quantancū latitudinem vnus acq̇-<lb/>rat in aliquo tempore, tantam alter deperdat ī eo­<lb/>dem tempore: et ita ſit in caſu poſito: ſed ad hoc  <lb/>aliquis motus intendatur equeuelociter geometri­<lb/>ce ſicut alter remittitur geometrice: oportet /  quã-<lb/>tãcun proportionem vnus acquirat ſupra ſe ī ali­<lb/>quo tempore tantaꝫ alter qui remittitur deperdat               <pb chead="Secundi tractatus" file="0143" n="143"/>               in eodem tempore. </s>
              <s xml:id="N1DF05" xml:space="preserve">Modo non ſit ſic in propoſito:</s>
            </p>
            <p xml:id="N1DF08">
              <s xml:id="N1DF09" xml:space="preserve">Sed contra / quia tunc ſequeretur /  ſi <lb/>motus vt .4. vel aliquis alter intendatur ad ſuum <lb/>duplum vniformiter / et alter motus ei equalis remi­<lb/>tatur in eadem hora ad non gradum ſiue ad quietē / <lb/>tunc ille qui remittitur in infinitum velocius remit­<lb/>titur quam alter qui intenditur intendatur </s>
              <s xml:id="N1DF16" xml:space="preserve">Quod <lb/>tamen eſt falſum cum tantam latitudinem vnus ac­<lb/>quirat ſicut alter deperdat.</s>
            </p>
            <note position="left" xml:id="N1DF1D" xml:space="preserve">dicitur.</note>
            <p xml:id="N1DF21">
              <s xml:id="N1DF22" xml:space="preserve">¶ Dices et bene diſtinguendo illatum aut  ī infini­<lb/>tum velocius remittatur in eodem tempore veloci-<lb/>tate geometrica: et ſic conceditur aut arithmetica: et <lb/>ſic negatur.</s>
            </p>
            <p xml:id="N1DF2B">
              <s xml:id="N1DF2C" xml:space="preserve">Sed cõtra quia tunc ſequeretur /  nõ <lb/>eſſet poſſibile /  ita velociter geometrice intendere­<lb/>tur vnus motus in tempore finito vniformiter ſicut <lb/>motus ei eq̈lis remitteretur vniformiter ad nõ gra­<lb/>dū in eodē tꝑe: ſed conſequens videtur falſum (cum <lb/>equalem latitudineꝫ vnus motus deperdat ſicut al­<lb/>ter acquirit) / igitur illud ex quo ſequitur. </s>
              <s xml:id="N1DF3B" xml:space="preserve">Sequela <lb/>tamen probatur quoniam / vt patet ex reſponſione <lb/>motus qui remittitur ad non gradum infinitam ꝓ-<lb/>portionem deperdit, et motus qui intenditur ſoluꝫ <lb/>finitam: igitur non eque velociter geometrice vnus <lb/>motus intenditur ſicut alter ei equalis remittitur ī <lb/>eodem tempore.               <anchor type="note" xlink:href="note-0143-01" xlink:label="note-0143-01a"/>               </s>
              <s xml:id="N1DF4F" xml:space="preserve">¶ Confirmatur ſecundo / quo­<lb/>niam ſi motus vniformiter difformis correſponde­<lb/>ret ſuo gradui medio ſequeretur / quando duo mo-<lb/>tus equales vniformiter difformes remitterentur ī <lb/>hora vnus ī duplo velocius altero ille qui tardiꝰ re­<lb/>mittitur / quando eſt remiſſus ad ſubduplum: alter <lb/>eſſet remiſſus ad ſubquadruplum et non ad quieteꝫ <lb/>ſiue ad non gradum: ſed conſequens falſum / vt pa-<lb/>tet intuenti: igitur illud ex quo ſequitur: </s>
              <s xml:id="N1DF62" xml:space="preserve">Sequela <lb/>tamen probatur quoniam / ſi in eodem tempore vnꝰ <lb/>continuo in duplo velocius altero remittitur ſeq̄re­<lb/>tur / quando vnus deperdit proportionem duplam <lb/>alter deperdit proportionem quadruplam / et in tē-<lb/>pore quo vnus quadruplam alter ſexdecuplaꝫ que <lb/>eſt dupla ad quadruplam. </s>
              <s xml:id="N1DF71" xml:space="preserve">vt patet ex ſecunda par­<lb/>te capite ſexto.               <anchor type="note" xlink:href="note-0143-02" xlink:label="note-0143-02a"/>               </s>
              <s xml:id="N1DF7B" xml:space="preserve">¶ Confirmatur tertio / qm̄ ſi mo-<lb/>tus vniformiter difformis correſponderet gradui <lb/>medio ſequeretur /  ſi eſſent duo motus vniformi-<lb/>ter difformes equales incipientes ab eodem gra-<lb/>du terminati ad eundem vel ad non gradum et vnꝰ <lb/>illorum puta a. in duplo velocius continuo intende­<lb/>retur quam alter puta b. / et talis intenſio duraret ī <lb/>infinitum /  aliquando a. eſſet motus duplus ad b. / <lb/>ſed conſequens eſt falſuꝫ: igitur illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N1DF8F" xml:space="preserve">Seq̄la probatur / q2 qñcū b. acq̇rit aliquã latitudi­<lb/>nē a. acq̇rit duplã: et ſꝑ in duplo velociꝰ a. acq̇ret ali­<lb/>quem gradum / quam eundem acquirit b. / et hec inten­<lb/>ſio procedit in infinitum: igitur aliquãdo a. erit mo­<lb/>tus duplus ad b. </s>
              <s xml:id="N1DF9A" xml:space="preserve">Probatur hec conſequentia / quo­<lb/>niam per infinitam latitudinem excedet latitudo ac­<lb/>quiſita ipſi a. latitudinem acquiſitam ipſi b. / igitur <lb/>aliquando totus motus a. erit duplus ad totuꝫ mo­<lb/>tuꝫ b. </s>
              <s xml:id="N1DFA5" xml:space="preserve">Cõſequētia apparet nota et arguit̄̄ añs / q2 ī in­<lb/>finitum maior erit latitudo acquiſita ipſi a. quã la-<lb/>titudo acquiſita ipſi b. / quia per infinitos gradꝰ la-<lb/>titudo acquiſita ipſi a. excedet latitudinem ipſiꝰ b. / <lb/>igitur ꝑ infinitã latitudinē excedit latitudo acquiſi­<lb/>ta ipſi a. latitudinē acquiſitã ipſi b. </s>
              <s xml:id="N1DFB2" xml:space="preserve">Probat̄̄ ante­<lb/>cedens / quoniam latitudo acquiſita ipſi a. cum ſem­<lb/>per erit dupla ad latitudinem acquiſitam ipſi b. / qñ <lb/>erit vt .4. excedit latitudineꝫ ipſius b, per duos gra­<lb/>dus et quando vt .8. per .4. et quando vt centum per <lb/>50. et quando vt .1000. per .500. / et ſic in infinitum: igi­               <cb chead="Capitulum tertium"/>               tur per infinitos gradus latitudo acquiſita ipſi a. <lb/>excedet latitudinem acquiſitam ipſi b. / quod fuit ꝓ­<lb/>bandum. </s>
              <s xml:id="N1DFC6" xml:space="preserve">Sed iam probatur falſitas conſequentis <lb/>quoniam / ſi aliquando totus motus a. ad totuꝫ mo­<lb/>tum b. erit duplus. </s>
              <s xml:id="N1DFCD" xml:space="preserve">ſignetur illud inſtans / in quo ita <lb/>erit / et arguitur ſic / totus motus a. ad totum motum <lb/>b. eſt duplus / ergo ſi vna pars ipſius a. eſt dupla ad <lb/>vnam partem b. totum reſiduum de a. eſt dupluꝫ ad <lb/>reſiduum de b. / ſed conſequens eſt falſum: igitur illḋ <lb/>ex quo ſequitur. </s>
              <s xml:id="N1DFDA" xml:space="preserve">Falſitas conſequētis probatur / q2 <lb/>in illo inſtanti totum acquiſitum a. eſt duplū ad to­<lb/>tum acquiſitum b. / et tamen reſidua pars de a. non <lb/>eſt dupla ad reſiduam partem de b. / ſed ille partes <lb/>ſunt equales ſicut erant in principio: et ſic ſequitur / <lb/> quando vna pars a. eſt dupla ad vnam partem <lb/>b. totum reſiduum a. non eſt duplum ad totum reſi-<lb/>duum b. / et ſic a. non eſt duplum ad b. </s>
              <s xml:id="N1DFEB" xml:space="preserve">Patet hec con­<lb/>ſequentia ex ſeptimo correlario q̈rte concluſionis <lb/>octaui capitis ſecunde partis.</s>
            </p>
            <div xml:id="N1DFF2" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0143-01a" xlink:label="note-0143-01" xml:id="N1DFF6" xml:space="preserve">2. confir.</note>
              <note position="left" xlink:href="note-0143-02a" xlink:label="note-0143-02" xml:id="N1DFFC" xml:space="preserve">.3. confir.</note>
            </div>
            <p xml:id="N1E002">
              <s xml:id="N1E003" xml:space="preserve">¶ Et confirmatur quarto et vltimo / quia ſi oīs mo-<lb/>tus vniformiter difformis commenſurari hꝫ gradu <lb/>medio: vel igitur in quolibet tali motu ille gradus <lb/>medius eſt ſubduplus adequate ad intenſius extre­<lb/>mum talis motus vel maior ſubduplo: vel minor: <lb/>nullum iſtorum eſt dicendum igitur. </s>
              <s xml:id="N1E010" xml:space="preserve">Probatur mi­<lb/>nor / quia capto motu vniformiter difformi ab octa­<lb/>uo vſ ad quartum gradus medius eius eſt vt .6. / <lb/>et talis eſt dumtaxat ſubſexquitertius ad gradum ī­<lb/>tenſiorem: et non ſubduplus: igitur non in omni mo­<lb/>tu vniformiter difformi gradus medius eſt ſubdu-<lb/>plus ad gradum intenſiorem. </s>
              <s xml:id="N1E01F" xml:space="preserve">Item capto motu <lb/>vniformiter difformi ab octauo vſ ad non gradū <lb/>medius gradus eius eſt ſubduplus ad extremū in-<lb/>tenſius: igitur non in omni motu vniformiter dif-<lb/>formi gradus medius eſt maior quam ſubduplus. <lb/></s>
              <s xml:id="N1E02B" xml:space="preserve">Item nullus gradus medius alicuius motꝰ vnifor-<lb/>miter difformis eſt minor quam ſubduplus ad ex-<lb/>tremum intenſius / vt facile eſt intueri: igitur illa mi­<lb/>nor vera.               <anchor type="note" xlink:href="note-0143-03" xlink:label="note-0143-03a"/>               </s>
              <s xml:id="N1E039" xml:space="preserve">¶ Dices ſicut dicendum eſt negando illaꝫ <lb/>minorem: immo in aliquibus motibus vniformiter <lb/>difformibus gradus medius eſt preciſe ſubduplus <lb/>ad gradum ſummū eiuſdem motus / vt patet in om­<lb/>ni motu vniformiter difformi terminato ad nõ gra­<lb/>dum. </s>
              <s xml:id="N1E046" xml:space="preserve">In omni motu vero vniformiter difformi ter-<lb/>minato vtrim ad gradum. </s>
              <s xml:id="N1E04B" xml:space="preserve">gradus medius eſt ma­<lb/>ior quam ſubduplus ad extremum intenſius / vt po­<lb/>ſtea oſtenditur.</s>
            </p>
            <div xml:id="N1E052" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0143-03a" xlink:label="note-0143-03" xml:id="N1E056" xml:space="preserve">dicitur.</note>
            </div>
            <p xml:id="N1E05C">
              <s xml:id="N1E05D" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>aliquando gradus medius alicuius motus vnifor­<lb/>miter difformis vtrim terminati ad gradum eēt <lb/>ſubſexquitertius ad gradum ſummum: aliquando <lb/>ſubſexquialterius: aliquando ſubſexquiquartus: <lb/>et ſic in infinitum. </s>
              <s xml:id="N1E06A" xml:space="preserve">Quod ſi concedis ſicut conceden­<lb/>dum eſt ſequitur /  nulla poteſt inueniri certa regu­<lb/>la et vniuerſalis ad ſciendum in quolibet motu vni­<lb/>formiter difformi quanto plus pertranſitur per to­<lb/>tum motum in medietate intenſiori quam in medie­<lb/>tate remiſſiori: quod videtur ſatis inconueniens.</s>
            </p>
            <p xml:id="N1E077">
              <s xml:id="N1E078" xml:space="preserve">Secundo principaliter tangendo ve­<lb/>locitatem, motus difformiṫ difformis cuius nulla <lb/>pars eſt vniformis comparando ipſum ad vnifor­<lb/>miter difformem: arguitur ſic. </s>
              <s xml:id="N1E081" xml:space="preserve">quia ſi prima pars et <lb/>ſecunda queſtionis eſſent vere: ſequeretur /  aliqui <lb/>duo motus ſunt modo equales: et in tempore equa-<lb/>li equales latitudines deperdent ſucceſſiue ita  in <lb/>fine illius temporis erunt equales: et tamen ꝑ vnuꝫ <lb/>illorum motuum maius ſpacium continuo pertrã-<lb/>ſitur quã per alium: hoc videtur īpoſſibile: igitur               <pb chead="De motu locali quo ad effectum tempore difformi." file="0144" n="144"/>               illud ex quo ſequitur. </s>
              <s xml:id="N1E095" xml:space="preserve">Impoſſibilitas conſequētis <lb/>arguitur quoniam / ſi illi motus ſunt equales in prī­<lb/>cipio: et manent equales in fine: et in toto tempore re­<lb/>miſſionis illorum equales latitudines deperdunt <lb/>adequate: ſequitur /  in toto illo tempore cathego­<lb/>reumatice illi motus ſunt equales: et per conſequens <lb/>non maius ſpacium in eodeꝫ tempore pertranſitur <lb/>per vnum quam per reliquum: et per te eſt oppoſitū / <lb/>igitur contradictio. </s>
              <s xml:id="N1E0A8" xml:space="preserve">Sequela tamen probatur et ca­<lb/>pio duos motus equales gratia exempli vt .8. puta <lb/>a.b. / et volo /  a. vniformiter iu hora ſequenti deper­<lb/>dat .4. gradus: ita  medietas illorum: .4. deperda­<lb/>tur ī medietate illius tꝑis, et vna q̈rta in quarta ꝑte <lb/>et quinta in quinta, et ſic confequenter: ita  cõtinuo <lb/>in equali tempore ſit equalis deperditio .b. vero in <lb/>hora illa deperdat .4. gradus ſucceſſiue non vnifor­<lb/>miter ſed continuo velocius: ita  in qualibet par-<lb/>te temporis ſequentis velocius quã in precedenti ſi­<lb/>bi equali / quod facile poteſt fieri iſto modo: ſi dini-<lb/>ſa illa hora per partes proportionales proportio­<lb/>ne quadrupla, in prima illarum deperdat medie-<lb/>tatem illius medietatis deperdēde, et ī ſecunda par­<lb/>te proportionali proportiõe quadrupla ſubduplū <lb/>et in tertia ſubquadruplum / et ſic in infinitum: et ma­<lb/>nifeſtum eſt /  iam illo latitudo continuo deperdi-<lb/>tur: continuo velocius et velocius / vt facile eſt intue­<lb/>ri </s>
              <s xml:id="N1E0CF" xml:space="preserve">Quo poſito ſic arguitur per motum b. / cõtinuo ꝑ <lb/>totam horam pertranſibitur maius ſpacium quaꝫ <lb/>per motum a. / et in fine et in principio ſunt equales, <lb/>et in eodem tempore equalem latitudinem deperdēt <lb/>adequate: igitur intentum. </s>
              <s xml:id="N1E0DA" xml:space="preserve">Conſequentia patet cuꝫ <lb/>minore: ſed arguitur maior videlicet /  continuo ꝑ <lb/>motum b. tranſibitur maius ſpacium quam ꝑ mo-<lb/>tum a. / quia continuo motus b. eſt maior et intenſior <lb/>motu a. / igitur continuo per illum maius ſpacium <lb/>pertranſibitur in eodem tempore </s>
              <s xml:id="N1E0E7" xml:space="preserve">Conſequentia ſe <lb/>manifeſtat et arguitur antecedens / quia b. motus in <lb/>nullo inſtanti intrinſeco illius hore erit equalis a. <lb/>nec miuor: ergo continuo maior. </s>
              <s xml:id="N1E0F0" xml:space="preserve">Probatur antece­<lb/>dens / quia ſi in aliquo inſtanti motus b. erit equa-<lb/>lis aut minor ipſi a. ſignetur illud: et ſit c. inſtãs in-<lb/>trinſecū / et arguitur ſic / in iſto inſtanti a. motus et b. <lb/>ſunt equales: ergo ex caſu equalem perdiderunt la­<lb/>titudinem: et equales reſtat deperdenda ipſi a. et ip­<lb/>ſi b. et a. / continuo vniformiter deperdet illam deper­<lb/>dendam ex caſu: et b. velocius quam antea deperde­<lb/>bat. </s>
              <s xml:id="N1E103" xml:space="preserve">et antea deperdebat equaliter cum a: ergo velo­<lb/>cius deperdet modo totam latitudinem deperden-<lb/>dam ꝙ̄ a. / et per conſequens citius tota latitudo de­<lb/>perdenda erit deperdita iꝑſi b. quam ipſi a. / quod ē <lb/>cõtra caſum: </s>
              <s xml:id="N1E10E" xml:space="preserve">Et per locum a maiori probabitur ſi-<lb/>militer /  pro nullo inſtanti motus b. eſt minor mo-<lb/>tu.               <anchor type="note" xlink:href="note-0144-01" xlink:label="note-0144-01a"/>               </s>
              <s xml:id="N1E11A" xml:space="preserve">¶ Et confirmatur ſuppoſito / quia vna pars pro­<lb/>portionalis proportiõe quadrupla eſt due partes <lb/>proportione dupla: et per conſequens due partes ꝓ­<lb/>portionales ꝓportione quadrupla ſunt .4. propor­<lb/>tione dupla: et ſic conſequenter procedendo per nu­<lb/>meros pariṫ pares: quod poteſt patere intuenti q̇n­<lb/>tum caput prīe partis </s>
              <s xml:id="N1E129" xml:space="preserve">Quo ſuppoſito ſic argumē-<lb/>tor ex caſu in fine prime partis proportionalis pro­<lb/>portione quadrupla b. perdet primam partem pro­<lb/>portionalem proportione dupla latitudinis deper­<lb/>dende / et tunc a. deperdit duas partes proportiona­<lb/>les proportione dupla latitudinis deperdende: q2 <lb/>tunc ſunt tranſacte due partes proportionales tē-<lb/>poris proportione dupla / vt patet ex ſuppoſito: et <lb/>a. motus remittitur vniformiter / vt patet ex caſu.</s>
            </p>
            <div xml:id="N1E13C" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0144-01a" xlink:label="note-0144-01" xml:id="N1E140" xml:space="preserve">cõfirma-<lb/>tio.</note>
            </div>
            <p xml:id="N1E148">
              <s xml:id="N1E149" xml:space="preserve">In fine vero ſecunde partis proportionalis tempo­<lb/>ris proportione quadrupla b. deperdit duas par-               <cb chead="De motu locali quo ad effectum tempore difformi."/>               tes proportionales latitudinis deperdende ꝓpor-<lb/>tione dupla: et a .4. qm̄ ille due partes ꝓportõe qua­<lb/>drupla ſunt quatuor partes preportionales ꝓpor­<lb/>tione dupla: igitur continuo maior latitudo eſt de­<lb/>perdita a. quam ipſi b. vſ ad inſtans terminatiuū <lb/>et ſic ſemper in quolibet inſtanti intrinſeco illiꝰ ho-<lb/>re motus b. eſt velocior motu a. / quod fuit proban-<lb/>dum.               <anchor type="note" xlink:href="note-0144-02" xlink:label="note-0144-02a"/>               </s>
              <s xml:id="N1E164" xml:space="preserve">¶ Dices et bene ad argumentum concedendo / <lb/>quod infertur vt bene probat argumentum, et negã­<lb/>do falſitatem conſequentis: et cum aſtruitur illa fal­<lb/>ſitas conſequentis negatur conſequenria </s>
              <s xml:id="N1E16D" xml:space="preserve">Immo cõ­<lb/>ceditur /  in principio illi motus ſunt equales, et in <lb/>fine equales, et equalem latitudinem adequate de-<lb/>perdunt in eodem tempore et tamen in toto illo tem­<lb/>pore vnus eſt intenſior altero / vt pulchre probat ar­<lb/>gumentum.</s>
            </p>
            <div xml:id="N1E17A" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0144-02a" xlink:label="note-0144-02" xml:id="N1E17E" xml:space="preserve">dicitur.</note>
            </div>
            <p xml:id="N1E184">
              <s xml:id="N1E185" xml:space="preserve">Sed contra ſi ſolutio veritati eſſet cõ­<lb/>ſona talis ex ea duceretur concluſio:  videlicet ali­<lb/>qui duo motus ſe habent modo in proportione du­<lb/>pla et per idem tempus vniformiter et eque velociter <lb/>remitterentur adequate: et tamen ſemper in illo tē-<lb/>pore ſpacium pertranſitum a maiori erit pluſ̄ du­<lb/>plū ad ſpaciū pertranſituꝫ a minori: ſꝫ cõſeq̄ns vr̄ <lb/>falſū: cū illo mõ ſe hñt ī ꝓportiõe dupla et ſꝑ equali­<lb/>ter remittūtur. </s>
              <s xml:id="N1E198" xml:space="preserve">apparet igitur /  cõtinuo manebūt <lb/>ſe habētes in ꝓportione dupla: et ſic ſpaciū ꝑtran-<lb/>ſitum a maiori nõ eſt pluſquam duplū ad ſpacium <lb/>pertranſitū a minori: et ſic illud conſequens eſt fal­<lb/>ſum: et per conſequēs illud ex quo ſequitur ꝓbatur <lb/>tamē ſequela et pono caſum /  ſint .a. et .b. motus: et <lb/>a. ſit duplus ad .b. / et remittantur continuo eque ve­<lb/>lociter et vniformiter a. et b. perdendo equalē lati­<lb/>tudinē omnino per totū tempus. </s>
              <s xml:id="N1E1AB" xml:space="preserve">quo poſito ſic ar-<lb/>gumentor in toto illo tēpore remiſſionis motus a. <lb/>erit pluſquã duplus ad motum b. et modo a. ſe ha­<lb/>bet ad b. in ꝓportione dupla: et continuo in illo tē-<lb/>pore eque velociter remittentur .etc. / igitur cõcluſio <lb/>vera. </s>
              <s xml:id="N1E1B8" xml:space="preserve">Conſequentia patet cū minore / et arguit̄̄ ma­<lb/>ior: et volo /  ſit c. equale ipſi a. in principio / et con-<lb/>tinuo remittatur taliter /  coutinuo ſe habeat in ꝓ­<lb/>portione dupla ad b. / et arguitur ſic. </s>
              <s xml:id="N1E1C1" xml:space="preserve">continuo c. ꝑ-<lb/>det maiorē latitudinē quã b. q2 continuo duplam / <lb/>vt patet ex primo et ſecūdo correlariis quinte con-<lb/>cluſionis ſecūdi capitis ſecūde partis / igitur conti­<lb/>nuo maiorem quã a. cū a. et b. deperdant equales <lb/>latitudines continuo / vt patet per caſum: et in prin­<lb/>cipio a. et c. ſunt equalia: igitur continuo a. motus <lb/>erit maior c. motu et c. continuo adequate eſt duplꝰ <lb/>ad b. / ergo continuo a. erit maior motus quã duplꝰ <lb/>ad b. / quod fuit ꝓbanduꝫ </s>
              <s xml:id="N1E1D6" xml:space="preserve">Patet hec conſequentia <lb/>per hanc maximam. </s>
              <s xml:id="N1E1DB" xml:space="preserve">Quando duo inequalia ha-<lb/>bent aliquas ꝓportiones ad vnū et idem tertium <lb/>maiorem proportionem ad idem tertiū habet ma­<lb/>ius illorū quam minus: vt ſatis conſtat.</s>
            </p>
            <p xml:id="N1E1E4">
              <s xml:id="N1E1E5" xml:space="preserve">Tertio principaliter tangendo mate­<lb/>riam principaliter intentam in hoc capite de com­<lb/>menſuratione motus difformiter difformis cuius <lb/>difformitas in infinitum procedit ſecundum nume­<lb/>rum partium proportionalium: arguitur ſiic. </s>
              <s xml:id="N1E1F0" xml:space="preserve">Si <lb/>motus difformiter difformis commēſurari habe-<lb/>ret penes reductionem ad vniformitatē aut penes <lb/>denominationē ſue intēſionis ſequeretur hec con-<lb/>cluſio:  videlicet aliquis eſſet motꝰ difformis qui <lb/>non poſſet ad vniformitatem reduci et cuius non <lb/>poſſet dari certa intenſio: conſequens eſt falſū / igit̄̄ <lb/>illud ex quo ſequitur: </s>
              <s xml:id="N1E201" xml:space="preserve">Falſitas conſequentis patet <lb/>et arguitur ſequela et diuido horam in duas par-<lb/>tes inequales quarum vtra ſe habet ad totã ho-               <pb chead="Secundi tractatus" file="0145" n="145"/>               ram in proportione irrationali / et volo /  in maio­<lb/>ri illarum moueatur a. mobile gradu octauo et in <lb/>minori illarū moueatur idem mobile gradu quar­<lb/>to </s>
              <s xml:id="N1E213" xml:space="preserve">(Semper in iſtis argumentis ſuppono /  vni gra­<lb/>dui velocitatis in hora correſpondeat pedanea per­<lb/>tranſitio) quo poſito ſic argumentor talis motus <lb/>eſt difformiter difformis: et tamen non poteſt redu-<lb/>ci ad vniformitatem: </s>
              <s xml:id="N1E21E" xml:space="preserve">Nec eius valet dari ſiue aſſi-<lb/>gnari determinata intenſio: igitur. </s>
              <s xml:id="N1E223" xml:space="preserve">Maior eſt nota / <lb/>et minor probatur ſupponēdo /  quanto aliq̈ pars <lb/>motus totalis eſt tn minori parte temporis tãto mi­<lb/>nus facit ad denominationem intenſionis totiꝰ mo­<lb/>tus ceteris aliis paribus: et tanto minus de ſpacio <lb/>per talem motum tranſitur: vt motus vt vnum par-<lb/>tialis in vna quarta hore facit ad intenſionem to-<lb/>tius motus vt vna quarta, et per illum in illa quar-<lb/>ta pertranſitur quarta pars pedalis. </s>
              <s xml:id="N1E236" xml:space="preserve">Et generali-<lb/>ter obſeruandum eſt /  in quacun proportione ſe <lb/>habet pars temporis ad totuꝫ tempus in eadem ſe <lb/>habet velocitas motus in llla parte ad velocitateꝫ <lb/>totalis motus in toto tempore. </s>
              <s xml:id="N1E241" xml:space="preserve">Quo poſito argui-<lb/>tur aſſumptum / quia motus vt .8. in illa parte tem-<lb/>poris non ſe habet in aliqua proportione rationa­<lb/>li ad totalem motum, nec etiam vt quatuor: et penes <lb/>tales proportiones debet inueſtigari eius intenſio <lb/>et reductio ad vniformitatem: igttur non poteſt da­<lb/>ri eius determinata intenſio aut reductio ad vnifor­<lb/>mitatem. </s>
              <s xml:id="N1E252" xml:space="preserve">Conſequentia patet cum minore: et argui­<lb/>tur maior / quia partes temporis in quibus ſunt illi <lb/>motus ſe habent ad totum tempus in proportione <lb/>irrationali / vt poſitum eſt: igitur etiam motus illa­<lb/>rum partium ad totalem motum. </s>
              <s xml:id="N1E25D" xml:space="preserve">Conſequentiã de­<lb/>clarat ſuppoſitio.               <anchor type="note" xlink:href="note-0145-01" xlink:label="note-0145-01a"/>               </s>
              <s xml:id="N1E267" xml:space="preserve">¶ Dices forte et bene concedendo / <lb/> talis motus non poteſt dari determinata inten-<lb/>ſio et rationalis reductio ad vniformitatem: ita  ī­<lb/>tenſio illius motus ſe habeat ad motum alicuius il­<lb/>larum partium in proportione aliqua rationali: <lb/>nec hoc eſt inconueniens, nec contra tituluꝫ queſtio­<lb/>nis: quia intelligitur titulus queſtionis dūmodo ꝑ­<lb/>tes in quibus tales motus ponūtur ſe habeãt in ꝓ-<lb/>portione rationali. </s>
              <s xml:id="N1E27A" xml:space="preserve">Unum tamen eſt / quod poſtea <lb/>oſtendetur /  talis motus totalis eſt intenſior quã <lb/>motus vt ſex.</s>
            </p>
            <div xml:id="N1E281" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0145-01a" xlink:label="note-0145-01" xml:id="N1E285" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1E28B">
              <s xml:id="N1E28C" xml:space="preserve">Sed contra ſolutionem arguitur ſic / <lb/>quia aliquis eſt motus difformis cuius partes ſūt <lb/>in partibus temporis rationalē ꝓportionē haben­<lb/>tibus ad totū tempus: et tamē talis motꝰ nõ valet <lb/>reduci ad vniformitatē, nec valet inueniri certa eiꝰ <lb/>intenſio: igit̄̄ ſolutio nulla. </s>
              <s xml:id="N1E299" xml:space="preserve">Arguitur antecedēs et <lb/>pono caſum /  diuidatur hora per partes ꝓportio­<lb/>nales proportione dupla: et in prima a. mobile mo­<lb/>ueatur aliquatulū velociter exempli gratia vt .2. et <lb/>in ſecunda in duplo velocius quã in prima. et in ter­<lb/>tia in triplo: et ſic conſequenter aſcendendo per om­<lb/>nes numeros. </s>
              <s xml:id="N1E2A8" xml:space="preserve">quo poſito ſic arguitur / talis mo-<lb/>tus eſt difformiter difformis cuius partes ſunt in <lb/>partibus temporis habentibꝰ proportionē ratio-<lb/>nalem in ordine ad totum: et tamē non inuenit̄̄ nec <lb/>dabilis eſt certa intenſio eiꝰ nec reductio ad vnifor­<lb/>mitatem: igitur propoſitū: tota ratio patet dem-<lb/>pta minore / que ſic arguit̄̄ / q2 ille motus videtur eſſe <lb/>infinitus: igitur nõ valet dari determinata eiꝰ intē­<lb/>tio ſaltem finita de qua loquimur. </s>
              <s xml:id="N1E2BB" xml:space="preserve">Probatur añs / <lb/>quia in infinitū intēſus eſt ille motus in illa hora: <lb/>igitur apparet /  ſit īfinitus.               <anchor type="note" xlink:href="note-0145-02" xlink:label="note-0145-02a"/>               </s>
              <s xml:id="N1E2C7" xml:space="preserve">¶ Dices forte /  tota-<lb/>lis ille motus eſt ita intenſus ſicut motus qui fit in <lb/>ſecunda parte ꝓportionali temporis: ita  talis <lb/>motus eſt ī duplo ītenſior motu facto ī prima par­<lb/>te ꝓportionali tēporis: et reduciter ad vniformita­               <cb chead="Capitulum tertium"/>               tem ſupponendo /  per quamlibet partē illius ho­<lb/>re eſt motus vt duo et per totū reſiduū a prima par­<lb/>te ꝓportionali eſt motꝰ vt .4. et per totū reſiduum <lb/>a ſecunda eſt motꝰ vt .6. et per totū reſiduū a tertia <lb/>eſt motus vt .8. / vt facile patet ex caſu: ita  queli-<lb/>bet pars ſequens alterã cū oībus ſequētibus eam <lb/>excedit immediate precedentem per duos gradus. <lb/></s>
              <s xml:id="N1E2E2" xml:space="preserve">Quo ſuppoſito arguitur reductio vniformitatis <lb/>talis motus: et volo /  capiãtur duo gradus extēſi <lb/>per totū reſiduū a. prīa ꝑte ꝓportionali: et ponan­<lb/>tur in prima ſibi equali. </s>
              <s xml:id="N1E2EB" xml:space="preserve">Diuidendo em̄ proportio­<lb/>ne dupla totū aggregatū ex oībus immediate ſe-<lb/>quentibus aliquã eſt equalis illi / vt patet ex quinto <lb/>capite prime partis) / deinde capiantur duo gradꝰ <lb/>a toto a ſecunda / et ponãtur in ſecunda: et nichil po­<lb/>natur vlterius in prima: aut ſecunda: deinde a ſe-<lb/>quentibus tertiam capiantur duo gradus / qui po­<lb/>nantur in tertia: et ſic cõſequenter. </s>
              <s xml:id="N1E2FC" xml:space="preserve">quo poſito in fi­<lb/>ne totus ille motus erit vniformis vt .4. / igit̄̄ dabi-<lb/>lis eſt eius intēſio et ad vniformitateꝫ reductio ha­<lb/>betur em̄ /  velocitas totalis motus eſt dupla ad <lb/>velocitatem eiꝰ que eſt in prima parte proportio-<lb/>nali hore.</s>
            </p>
            <div xml:id="N1E309" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0145-02a" xlink:label="note-0145-02" xml:id="N1E30D" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N1E313">
              <s xml:id="N1E314" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>ſi hora diuidatur per partes ꝓportionales ꝓpor-<lb/>tione tripla et per primã illarū moueat̄̄ aliquod <lb/>mobile aliquantula velocitate: et ꝑ ſecundam du­<lb/>pla velocitate: et per tertiam tripla: et ſic in infini­<lb/>tuꝫ vt in priori caſu. </s>
              <s xml:id="N1E321" xml:space="preserve">tale mobile etiã moueret̄̄ in to­<lb/>tali hora adequate dupla velocitate ad velocitatē <lb/>qua mouetur in prima parte proportionali hore / <lb/>ſed cõſequens eſt falſum / igitur illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N1E32B" xml:space="preserve">Sequela probatur / quia non videtur maior ratio­<lb/>ni iſto caſu quam in p̄cedenti: falſitas tamē conſe­<lb/>quentis arguitur / quia talis motus eſt dūtaxat in <lb/>ſexquialtero velocior motu prime partis propor-<lb/>tionalis temporis: igitur non eſt ī duplo velocior. <lb/></s>
              <s xml:id="N1E337" xml:space="preserve">Conſequentia patet: et arguitur añs: et volo gra-<lb/>tia argumēti /  motus prime partis proportiona­<lb/>lis ſit vt .2. / quo poſito ſic argumētor motus vt duo <lb/>eſt per totam horã. </s>
              <s xml:id="N1E340" xml:space="preserve">ergo talis motus denominat <lb/>totū moueri vt duo in tota hora motꝰ vero vt duo <lb/>ſuperadditus in ſecunda parte ꝓportionali et in <lb/>oībus ſequentibus eſt in ſubtriplo tempore: et eſt <lb/>equalis intenſionis cñ aliis duobꝰ gradibꝰ per to­<lb/>tum: igitur in triplo minus denominat. </s>
              <s xml:id="N1E34D" xml:space="preserve">Duo vero <lb/>gradus extenſi per tertiã partē ꝓpottionalē et to­<lb/>tum reſiduū ſunt in triplo minori ſubiecto / ergo ad­<lb/>huc in triplo minꝰ denominãt: et ſic conſequenter <lb/>ꝓcedendo per ſubtriplam proportionē: ergo tota­<lb/>lis denominatio talis motꝰ facti in illa hora con-<lb/>flatur ex infinitis cõtinuo ſe habentibꝰ in ꝓportio­<lb/>ne ſubtripla: igitur reſiduū a prima eſt ſubdupluꝫ <lb/>ad primū / vt patet ex correlario prīe ↄ̨cluſionis q̇nti <lb/>capitis prime partis et primū illoꝝ erat vt duo hoc <lb/>eſt prima denomīatio erat vt .2. / igitur oēs alie de­<lb/>nominatiões ſunt vt vnū: modo duo et vnū ſūt tria / <lb/>igit̄̄ totalis motꝰ velocitas eſt vt .3. et velocitas in <lb/>prima parte ꝓportionali eſt vt .2. / ergo velocitas to­<lb/>talis motus ſe habet in ꝓportiõe ſexquialtera ad <lb/>velocitatem eiuſdē motꝰ in prima parte ꝓportio-<lb/>nali temporis / quod fuit ꝓbandū: patet tamen con­<lb/>ſequentia / q2 triū ad duo eſt ꝓportio ſexquialtera.</s>
            </p>
            <p xml:id="N1E372">
              <s xml:id="N1E373" xml:space="preserve">Quarto principaliter tangēdo motꝰ <lb/>difformiter difformis quorū partes diuerſis con-<lb/>tinuo ꝓportionibus ſe habent: arguitur ſic: q2 ali­<lb/>quis eſt motus difformiter difformis cuius nõ eſt <lb/>dabilis vniformitas nec denoīationis intēſio: igit̄̄               <pb chead="De motu locali quo ad effectum tempore difformi." file="0146" n="146"/>               titulus queſtiõis falſus. </s>
              <s xml:id="N1E383" xml:space="preserve">Arguitur añs: et pono ca-<lb/>ſum /  a. mobile in prima parte proportionali ꝓ-<lb/>portione dupla huius hore moueat̄̄ aliquantuluꝫ <lb/>velociter: et in ſecunda in ꝓportione ſexquialtera <lb/>velocius ꝙ̄ in prima et in tertia in ꝓportione ſexq̇­<lb/>quarta velocius quã in ſcḋa: et ſic conſequenter ꝓ-<lb/>cedendo per omnes ſpecies proportionis ſuꝑparti­<lb/>cularis: quo poſito talis motus eſt vniformiter dif­<lb/>formis: et non eſt dabilis eius intenſio: nec reductio <lb/>ad vniformitatem: igitur. </s>
              <s xml:id="N1E398" xml:space="preserve">Arguitur minor / quia nõ <lb/>apparet cuius intenſionis ſit ille motus niſi fuerit <lb/>infinite: cum in infinitum velociter moueatur a. mo­<lb/>bile in aliqua parte proportionali temporis: igit̄̄ <lb/>non repertiur eius certa intenſio.</s>
            </p>
            <note position="left" xml:id="N1E3A3" xml:space="preserve">dicitur.</note>
            <p xml:id="N1E3A7">
              <s xml:id="N1E3A8" xml:space="preserve">¶ Dices et bene negando minorem: et quoniam ar-<lb/>gumentum nihil aliud petit niſi intenſionem talis <lb/>motus, et vniformitatem, et quomodo cognoſci de-<lb/>beat: et inueſtigari. </s>
              <s xml:id="N1E3B1" xml:space="preserve">Ideo dico /  totalis illius mo-<lb/>tus velocitas correſpondet velocitati ſecunde par-<lb/>tīs ꝓportionalis: et ſic illud mobile a. in totali tem­<lb/>pore mouetur in ſexq̇altero velociꝰ quã in prīa ꝑte <lb/>proportionali temporis. </s>
              <s xml:id="N1E3BC" xml:space="preserve">Quod ſic oſtenditur ſup­<lb/>poſito gratia argumenti /  in prīa parte ꝓportio-<lb/>nali moueatur vt duo: et  quelibet pars ſequēs al­<lb/>teram cum toto reſiduo ſequenti eã excedit īmedia-<lb/>te precedentem ſe per vnum ſemper equaliter (vt fa­<lb/>cile eſt intueri) illis ſuppoſitis ſic argumētor duo <lb/>gradus velocitatis qui ſunt per totam horam de-<lb/>nominant totuꝫ a. moueri vt duo in illa hora: et vnꝰ <lb/>gradus extenſus ſiue continuatus per totum reſi-<lb/>duum a prima parte ꝓportiõali / quod eſt ſubduplū <lb/>ad totum tempus denominat vt dimidium: quoniã <lb/>ſi eſſet per totum denominaret vt vnum: ergo ī ſub­<lb/>duplo denominat quia eſt in ſubduplo tēpore. </s>
              <s xml:id="N1E3D7" xml:space="preserve">Itē <lb/>alter gradus qui eſt in toto reſiduo a. ſecunda par­<lb/>te proportionali denominat in ſubduplo minꝰ quã <lb/>ille qui eſt in toto reſiduo a prima: cum illa tempo-<lb/>ra ſe habeant in proportione ſubdupla: et ſic conſe­<lb/>quenter: igitur totalis denominatio omnium illo-<lb/>rum motuum demptis duobus gradibus extenſis <lb/>per totam horam componitur ex infinitis cõtinuo <lb/>ſe habentibus in proportione ſubdupla: ergo reſi-<lb/>duum a primo eſt equale primo </s>
              <s xml:id="N1E3EC" xml:space="preserve">Patet conſequen-<lb/>tia ex correlario preallegato: et primum eſt vt dimi­<lb/>dium: ergo totus ille motus vt eſt vt vnū: et veloci-<lb/>tas proueniens a duobus gradibus per totam ho­<lb/>ram eſt vt duo: ergo totus motus adequatus illius <lb/>hore eſt vt tria: et velocitas prime partis id eſt quaꝫ <lb/>habet in prima parte ꝓportionali temporis eſt vt <lb/>duo: et trium ad duo eſt ꝓportio ſexquialtera: ergo <lb/>velocitas illius totalis motꝰ ſe habet in ꝓportiõe <lb/>ſexquialtera ad velocitatē quã habet in prima ꝑte <lb/>ꝓportionali: et ſic ſe habet velocitas ſecunde par-<lb/>tis ꝓportionalis ad velocitatem prime / quod fuit <lb/>probandum.</s>
            </p>
            <p xml:id="N1E407">
              <s xml:id="N1E408" xml:space="preserve">Sed contra mutando paululum ca-<lb/>ſum: volo /  a. in prima ꝓportionali hore ꝓportio­<lb/>ne dupla aliquantulū velociter moueat̄̄: et in ſecū-<lb/>da in ſexquialtero velociꝰ quã in prima: et in tertia <lb/>in ſexquitertio velocius quã in prima: et in quarta <lb/>in ſexquiquarto velocius quã in prima: et ſic conſe-<lb/>quenter procedēdo per oēs ſpecies ꝓportionis ſu-<lb/>perparticularis ſemꝑ referēdo ad primã partem. <lb/></s>
              <s xml:id="N1E41A" xml:space="preserve">Quo poſito arguitur ſic / talis motus eſt difformiṫ <lb/>difformis quo ad tempꝰ: et non valet ad vniformi-<lb/>tatē reduci, aut certa eius intēſio eiꝰ inueniri: igit̄̄ <lb/>minor patet / q2 nõ apparet modus quo ille motus <lb/>poſſet ad vniformitatē reduci: et ſi aduerſariꝰ hoc <lb/>neget, det illum modū: et in dubie facile erit calcu-               <cb chead="De motu locali quo ad effectum tempore difformi."/>               latori philoſopho illum impugnare.               <anchor type="note" xlink:href="note-0146-01" xlink:label="note-0146-01a"/>               </s>
              <s xml:id="N1E42F" xml:space="preserve">¶ Et confir-<lb/>matur / quia ſi aliquod mobile moueat̄̄ ī prima ꝑte <lb/>ꝓportionali huiꝰ hore aliq̈ ꝓportiõe aliquantuluꝫ <lb/>velociter: et in ſecūda in duplo velocius et in tertia <lb/>in ſexquitertio velocius quã in prima et in quarta <lb/>in ſexquiquīto velocius quã in prima: et in quinta <lb/>in ſexquioctauo velociꝰ: et inſequēti in ſexquiduo-<lb/>decimo velociꝰ: et ſic in infinitū ꝓcedendo interſca­<lb/>lariter ꝑ ſpēs ꝓportionis ſuꝑparticularis ↄ̨tinuo <lb/>vna pĺes omittēdo: tūc taĺ motꝰ ē difformiṫ diffor­<lb/>mis quo ad temdus: et nõ poteſt eius certa intenſio <lb/>dari. </s>
              <s xml:id="N1E448" xml:space="preserve">igit̄̄. </s>
              <s xml:id="N1E44B" xml:space="preserve">Et ſic poteſt etiam formari caſus vbi inṫ <lb/>ſcalariter ꝓcedat̄̄ per eaſdē ſpecies ꝓportiõis ſuꝑ­<lb/>particularis cõtinuo plures omittēdo duas dicen­<lb/>do ī ſexquialtero, in ſexquiquīto: ī ſexquidecīo, in <lb/>ſexquidecimo ſeptimo. </s>
              <s xml:id="N1E456" xml:space="preserve">Item ꝓcedendo per eaſdem <lb/>ſpecies cõtinuo dimittendo plures ꝑ tres vel q̈tuor <lb/>vel per .5. vel per .6. et ſic in īfinitū: et dabunt̄̄ motꝰ <lb/>difformes quo ad tēpus: et tamē ipſi non poſſūt ad <lb/>vniformitatē reduci: igitur:               <anchor type="note" xlink:href="note-0146-02" xlink:label="note-0146-02a"/>               </s>
              <s xml:id="N1E466" xml:space="preserve">¶ Cõfirmat̄̄ ſecundo et <lb/>pono caſum /  in prima parte ꝓportiõali aliquod <lb/>mobile moueat̄̄ aliquantulū velociter et in ſecūda <lb/>ī ſexquialtero velocius quã in prima: et in tertia in <lb/>ſuperbipartiēte tertias velocius quã in prima: et <lb/>in quarta in ſexquitertio velocius ꝙ̄ in prima: et in <lb/>quinta in ſuꝑpartiente quartas velocius quam in <lb/>prima: et in ſexta in ſexquiquarto velocius ꝙ̄ in pri­<lb/>ma: et ſic cõſequenter ꝓcedēdo per oēs ſpecies pro­<lb/>portiõis ſuperparticularis interſerēdo ſpecies ꝓ­<lb/>portiõis ſuprapartientis: tūc tale mobile mouet̄̄ <lb/>difformiter quo ad tempus: et tamē motꝰ illiꝰ vni­<lb/>formitas nõ poteſt venari: igit̄̄ titulꝰ q̄ſtiõis ē falſꝰ <lb/>               <anchor type="note" xlink:href="note-0146-03" xlink:label="note-0146-03a"/>               </s>
              <s xml:id="N1E488" xml:space="preserve">¶ Confirmatur tertio / et pono caſū /  a. mobile in <lb/>prima parte ꝓportiõali moueat̄̄ aliquãtulū: et in <lb/>ſecunda in duplo plus: et in tertia in ſexquialtero <lb/>plus quã in prima: et in quarta in ſuperbipartien­<lb/>te tercias plus quã in prima: et in quinta in duplo <lb/>ſexquialtero plus quã in prima: et in ſexta in duplo <lb/>ſuperbipartiēte tertias velocius quã ī prima et in <lb/>ſeptima in triplo velocius quã in prima: et ſic cõſe-<lb/>quenter capiēdo primoquin: et conſequen-<lb/>ter alias .5. et ſic in infinitū. </s>
              <s xml:id="N1E49D" xml:space="preserve">Quo poſito illoꝝ motꝰ <lb/>eſt difformiter difformis: et tamē illius velocitas <lb/>non valet perſcrutari igitur.</s>
            </p>
            <div xml:id="N1E4A4" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0146-01a" xlink:label="note-0146-01" xml:id="N1E4A8" xml:space="preserve">.1. confir.</note>
              <note position="right" xlink:href="note-0146-02a" xlink:label="note-0146-02" xml:id="N1E4AE" xml:space="preserve">2. confir.</note>
              <note position="right" xlink:href="note-0146-03a" xlink:label="note-0146-03" xml:id="N1E4B4" xml:space="preserve">.3. conur.</note>
            </div>
            <p xml:id="N1E4BA">
              <s xml:id="N1E4BB" xml:space="preserve">In oppoſitum tamen eſt vniuerſalis <lb/>opinio cõmuniter philoſophantiū / q̄ in hac parte <lb/>multū vigoris acroboris habet </s>
              <s xml:id="N1E4C2" xml:space="preserve">Preterea ꝑ quēli­<lb/>bet talē motū difformem in totali tēpore adequate <lb/>ꝑtranſitur aliquod ſpaciū adequate: et tale ſpaciū <lb/>in tali tēpore ab aliqua velocitate vniformi natum <lb/>eſt pertranſiri: igit̄̄ illa velocitas vniformis eſt tan­<lb/>ta quanta eſt velocitas illius motꝰ difformis quo <lb/>illud ſpaciū in eodē tempore pertrãſitur adequate <lb/></s>
              <s xml:id="N1E4D2" xml:space="preserve">Quod patet per diffinitionē motꝰ eque velocis: igi­<lb/>tur quilibet motꝰ difformis alicui vniformi corre-<lb/>ſpondet cui equiualet / quod fuit probandum.</s>
            </p>
            <p xml:id="N1E4D9">
              <s xml:id="N1E4DA" xml:space="preserve">Pro deciſione huius queſtionis tria <lb/>faciemus. </s>
              <s xml:id="N1E4DF" xml:space="preserve">Primo aliqua notabimꝰ, ſecundo non­<lb/>nullas cõcluſiones quibꝰ facilis erit ad queſitum <lb/>reſponſio eliciemus. </s>
              <s xml:id="N1E4E6" xml:space="preserve">Proſtremo vero reſpondebi­<lb/>mus ad argumenta in oppoſitum.</s>
            </p>
            <p xml:id="N1E4EB">
              <s xml:id="N1E4EC" xml:space="preserve">Pro primi expeditione repetētes quo­<lb/>dãmodo ea que ſuperius iam tacta ſunt dicamus / <lb/> duplex eſt motus difformis quod ad tempus puta <lb/>difformiter difformis et vniformiter difformis.</s>
            </p>
            <p xml:id="N1E4F5">
              <s xml:id="N1E4F6" xml:space="preserve">Utriuſ membri definitio ſuperiꝰ data eſt. </s>
              <s xml:id="N1E4F9" xml:space="preserve">Sꝫ mo­<lb/>tus vniformiter difformis quo ad tempꝰ adhuc du­               <pb chead="Secundi tractatus" file="0147" n="147"/>               plex eſt: </s>
              <s xml:id="N1E503" xml:space="preserve">Nam quidam eſt vniformiter difformis ter­<lb/>minatus ad non gradum in altero extremo. </s>
              <s xml:id="N1E508" xml:space="preserve">Alter <lb/>vero eſt vniformiter difformis vtrobi ad graduꝫ <lb/>terminatus. </s>
              <s xml:id="N1E50F" xml:space="preserve">Et de vtro iſtorum dicitur /  gradui <lb/>ſuo medio correſpondet: id eſt gradui motus quem <lb/>habet in medio temporis. </s>
              <s xml:id="N1E516" xml:space="preserve">Nam quanto velociꝰ mo­<lb/>uetur mobile motum vniformiter difformiter medi­<lb/>ante medietate talis motus intenſiori tanto tardiꝰ <lb/>mouetur mediãte medietate remiſſiori, et ſic eque ve­<lb/>lociter mouetur ac ſi moueretur gradu medio. </s>
              <s xml:id="N1E521" xml:space="preserve">Et <lb/>ad cognitionem talis gradus medii pono aliq̈s ꝓ­<lb/>poſitiones.</s>
            </p>
            <p xml:id="N1E528">
              <s xml:id="N1E529" xml:space="preserve">Prima propoſitio </s>
              <s xml:id="N1E52C" xml:space="preserve">In omni latitudīe <lb/>vniformiter difformi incipiente a gradu a termina­<lb/>ta ad non gradum: gradus medius eſt ſubduplus <lb/>ad extremuꝫ intenſius: ita  ſi latitudo incipiat ad <lb/>octauo et terminatur ad nõ gradū: gradus medius <lb/>eſt gradus quartus q2 quartus gradꝰ eſt ſnbduplꝰ <lb/>ad octauum. </s>
              <s xml:id="N1E53B" xml:space="preserve">Ad quam ꝓpoſitionem oſtendendam <lb/>ſupponendum eſt /  quandocun ſunt iufiniti ter­<lb/>mini cõtinuo ꝓportionales ꝓportione dupla / tūc to­<lb/>tum aggregatum ex eis eſt duplum ad totuꝫ aggre­<lb/>gatū ex oībus ſequētibus primū. </s>
              <s xml:id="N1E546" xml:space="preserve">Secūdo ſupponē­<lb/>dum eſt /  medium eſt illḋ quod equaliter dlſtat ab <lb/>extremis </s>
              <s xml:id="N1E54D" xml:space="preserve">Hee ſuppoſitiones ſatis aperte ſunt ex ṗ­<lb/>ma et ſecunda partibus. </s>
              <s xml:id="N1E552" xml:space="preserve">His ſuppoſitis arguitur ꝓ­<lb/>poſitio: et volo /  diuidatur latitudo vniformiter <lb/>difformis a nõ gradu vſ ad certum gradum ī par­<lb/>tes ꝓportionales continuo ſe habentes ī ꝓportio­<lb/>ne dupla: et arguo ſic / gradus initians aggregatuꝫ <lb/>ex omnibus latitudinibus ſequentibus primam eſt <lb/>medius: et talis eſt ſubduplus ad gradum intenſio­<lb/>rem illius latitudinis / igitur talis latitudinis vni-<lb/>formiter difformis terminate ad non gtadum: gra­<lb/>dus medius eſt ſubduplus ad extremum intenſius <lb/>eiuſdem latitudinis: et ſic ꝓbabis de qualibet alia <lb/></s>
              <s xml:id="N1E56A" xml:space="preserve">Conſequentia patet, et arguitur maior / q2 talis gra­<lb/>dus equaliter diſtat ab extremis illius latitudinis / <lb/>vt patet ex prima ſuppoſitione </s>
              <s xml:id="N1E571" xml:space="preserve">Nam initiat ſecun­<lb/>dam medietatem latitudinis: et terminat primam: <lb/>igitur eſt medius gradus: </s>
              <s xml:id="N1E578" xml:space="preserve">Patet conſequentia ex <lb/>ſecunda ſuppoſitione. </s>
              <s xml:id="N1E57D" xml:space="preserve">Sed  iſte ſit ſubduplus ad <lb/>extremum intenſius probatur: quia ipſe bis ſūptꝰ <lb/>conſtituit extremum intenſius adequate: igitur.</s>
            </p>
            <p xml:id="N1E584">
              <s xml:id="N1E585" xml:space="preserve">Alio modo Hentiſber deducit hanc concluſionem <lb/>in ſuo tractatu de motu locali capite primo.</s>
            </p>
            <p xml:id="N1E58A">
              <s xml:id="N1E58B" xml:space="preserve">Secunda propoſitio </s>
              <s xml:id="N1E58E" xml:space="preserve">Gradus mediꝰ <lb/>motus vniformiter difformis vtrobi ad gradum <lb/>terminati eſt intenſior quaꝫ ſubduplus ad extremū <lb/>intenſius. </s>
              <s xml:id="N1E597" xml:space="preserve">Probatur hec ꝓpoſitio / quia omnis gra­<lb/>dus ſubduplus ad extremum intenſius tantum di-<lb/>ſtat ab extremo intenſiori quantum a nõ gradu: ſꝫ <lb/>uullus gradus medius latitudinis vtrobi ad gra­<lb/>dum terminate tantum diſtat ab extremo intenſio-<lb/>ri eius quantum a non gradu: igitur nullus gradꝰ <lb/>medius latitudinis vtrobi ad gradum terminate <lb/>eſt ſubduplus ad extremum intenſius eiuſdem lati-<lb/>tudinis: nec remiſſior / vt ꝓbabītur: ergo intenſior.</s>
            </p>
            <p xml:id="N1E5AA">
              <s xml:id="N1E5AB" xml:space="preserve">Conſequentia patet in ſecundo ſecunde. </s>
              <s xml:id="N1E5AE" xml:space="preserve">Et maior <lb/>patet ex precedēti propoſitione: et minor probatur / <lb/>quia tantum talis gradus diſtat ab extremo inten­<lb/>ſiori quantū diſtet adequate ab extremo remiſſiori <lb/>ſed non tantum talis gradus medius diſtat ab ex-<lb/>tremo intenſiori quantum diſtat a non gradu / vt ſa­<lb/>tis patet de ſe: igitur non tantuꝫ diſtat ab extremo <lb/>intenſiori quãtum a non gradu </s>
              <s xml:id="N1E5BF" xml:space="preserve">Patet conſequētia <lb/>per hanc maximam </s>
              <s xml:id="N1E5C4" xml:space="preserve">Quando aliqua duo ſunt eq̈-               <cb chead="Capitulum tertium"/>               lia q̇cq̇d eſt maius vno eſt maius altero. </s>
              <s xml:id="N1E5CA" xml:space="preserve">Et per hoc <lb/>patet facile /  talis gradꝰ ē intenſior gradu ſudu-<lb/>plo ad extremum intenſius. </s>
              <s xml:id="N1E5D1" xml:space="preserve">q2 magis diſtat a non <lb/>gradu quam gradus ſubduplus ad extremum in-<lb/>tenſius / et ſic patet propoſitio.</s>
            </p>
            <p xml:id="N1E5D8">
              <s xml:id="N1E5D9" xml:space="preserve">Tertia proportio </s>
              <s xml:id="N1E5DC" xml:space="preserve">Cuiuſlibet latitudi­<lb/>nis motus vniformiter difformis terminati ad nõ <lb/>gradum: medietas intenſior eſt in triplo intenſior <lb/>medietate remiſſiori. </s>
              <s xml:id="N1E5E5" xml:space="preserve">Probatur hec ꝓpoſitio ſup-<lb/>ponendo /  quando ſunt tres termini continuo ꝓ-<lb/>portionabiles ꝓportione dupla / tūc extremi ad ex-<lb/>tremū eſt proportio duplicata / et per conſequens q̈­<lb/>drupla. </s>
              <s xml:id="N1E5F0" xml:space="preserve">Hoc ſuperius oſtenſum eſt in ſecunda par-<lb/>te ſexti capitis octaua concluſione. </s>
              <s xml:id="N1E5F5" xml:space="preserve">Secundo ſup-<lb/>ponendum eſt /  in qualibet tali latitudine motus <lb/>vniformiter difformis terminati ad non gradum <lb/>gradus initians ſecundam partem proportionalē <lb/>ꝓportione dupla eſt ſubduplus ad extremum inten­<lb/>ſius: et gradus initians tertia tem proportio­<lb/>nalem eſt ſubduplus ad gradum initiantē ſecundã: <lb/>et ſic conſequenter (loquor de partibus proportiõa­<lb/>libus quantitatiuis) </s>
              <s xml:id="N1E608" xml:space="preserve">Suppono vlterius /  ſubſexq̇­<lb/>tertium ad quadruplum alicuius eſt triplum ad il-<lb/>lud ſubquadruplum. </s>
              <s xml:id="N1E60F" xml:space="preserve">Quod probatur facile / quia ſi <lb/>eſt ſubſexquitertium ad illud eſt tres quarte eius: et <lb/>ſubquadruplum ad illud quadruplum eſt vna quar­<lb/>ta: igitur illud ſubſexquitertium erit triplum ad il­<lb/>lud ſubquadruplum. </s>
              <s xml:id="N1E61A" xml:space="preserve">Patet conſequentia / q2 triuꝫ <lb/>quartarum ad vnam quartam eſt ꝓportio tripla. <lb/></s>
              <s xml:id="N1E620" xml:space="preserve">His ſuppoſitis probatur ꝓpoſitio: et diuido vnam <lb/>talem latitudinem per partes ꝓportionales ꝓpor­<lb/>tione dupla: quo poſito arguitur ſic / gradus mediꝰ <lb/>medietatis intenſioris eſt triplus ad graduꝫ medi­<lb/>um medietatis remiſſioris et penes tales gradꝰ me­<lb/>tri habent velocitates illarum medietatū / vt dictū <lb/>eſt. </s>
              <s xml:id="N1E62F" xml:space="preserve">igitur medietas intenſior eſt triple intenſionis <lb/>ad medietatem remiſſiorem / quod fuit probandum <lb/></s>
              <s xml:id="N1E635" xml:space="preserve">Patet conſequentia cuꝫ minore / et arguitur maior / <lb/>quia vt patet ex ſecunda ſuppoſitione gradus ini-<lb/>tians tertiã partem proportionalem eſt ſubduplꝰ <lb/>ad initiantem ſecundam: et intians ſecundam ad in­<lb/>itiantiantem primam: igitur initians primaꝫ eſt q̈­<lb/>druplus ad initiantem tertiam / vt patet ex prīa ſup­<lb/>poſitione: et ille eſt gradus medius ſecunde medie-<lb/>tatis puta remiſſioris: igitur gradus medius me-<lb/>dietatis remiſſioris ē ſubquadruplus ad extremuꝫ <lb/>intenſius medietatis intenſioris: et gradus mediꝰ <lb/>medietatis intenſioris eſt ſubſexquitertius ad ex-<lb/>tremum intenſius: ergo eſt triplus ad gradum me­<lb/>dium medietatis remiſſioris qui eſt ſubquadruplꝰ <lb/>ad extremum intenſius latitudinis. </s>
              <s xml:id="N1E652" xml:space="preserve">Patet conſe-<lb/>quentia ex tertia ſuppoſitione. </s>
              <s xml:id="N1E657" xml:space="preserve">Sed reſtat ꝓbare / <lb/> gradus medius medietatis ītenſioris eſt ſubſex­<lb/>quitertius ad extremum intenſius eiuſdcm medie­<lb/>tatis: </s>
              <s xml:id="N1E660" xml:space="preserve">Quod probatur ſic / quia talis gradus ē me-<lb/>dius inter duplum et ſubduplum puta inter extre-<lb/>mum intenſius illius medietatis et extremuꝫ remiſ­<lb/>ſius eiuſdem qui eſt ſubduplus ad illum: igitur ta-<lb/>lis gradus medius eſt ſubſexquitertius ad illū du­<lb/>plum puta ad illud extremum intenſius / quod fuit <lb/>probandum. </s>
              <s xml:id="N1E66F" xml:space="preserve">Patet conſequētia per hanc maximã <lb/></s>
              <s xml:id="N1E673" xml:space="preserve">Omnis gradus medius inter duplum et ſubduplū <lb/>eſt ſexquialterꝰ ad ſubduplum et ſexquitertius ad <lb/>duplum / vt patet de ſenario mediãte inter .4. et .8. <lb/>de ternario mediante inter binarium et quarterna­<lb/>rium et de nouenario mediante inter ſenariū et duo­<lb/>denarium: et vniuerſaliter in omnibus.</s>
            </p>
            <p xml:id="N1E680">
              <s xml:id="N1E681" xml:space="preserve">Quarta ꝓpoſitio / que ſequit̄̄ ex priori <lb/></s>
              <s xml:id="N1E685" xml:space="preserve"><pb chead="De motu locali quo ad effectū ſcḋm tempus difformi." file="0148" n="148"/>               Oīs potentia mouēs vniformiter difformiter lati­<lb/>tudine terminata ad nõ gradū: in triplo plus ꝑtrã­<lb/>ſit ī medietate in qua mouet̄̄ intēſius ꝙ̄ ī medietate <lb/>tēporis in qua mouetur remiſſius: vt ſi in medieta-<lb/>te in qua mouetur remiſſius ꝑtranſit vnū pedale: in <lb/>alia ꝑtranſit tripedale. </s>
              <s xml:id="N1E696" xml:space="preserve">Probatur hec propoſitio <lb/>facile ex priori: qm̄ motꝰ fluens in medietate in qua <lb/>mouetur velocius eſt triplus ad motū factū in me-<lb/>dietate tēporis in qua mouetur remiſſiꝰ / vt dicit pre­<lb/>cedens: igit̄̄ ꝑtrãſitū in medietate in qua mouetur <lb/>velocius erit triplū ad ꝑtranſitū in reliqua medie-<lb/>tate. </s>
              <s xml:id="N1E6A5" xml:space="preserve">Cõſequentia ptꝫ / q2 tēporibꝰ exiſtentibus equa­<lb/>libus et velocitatibus in equalibus ſpacia ꝑtranſi-<lb/>ta ſe habent in ea ꝓportione in qua ſe habent velo­<lb/>citates: vt facile induci poteſt ex definitione velocio­<lb/>ris et tardioris data ſexto phiſicoꝝ </s>
              <s xml:id="N1E6B0" xml:space="preserve">¶ Ex quo ſequi­<lb/>tur /  ſi a. mobile moueatur ꝑ horam vniformiter <lb/>difformiter incipiendo a non gradu vſ ad certum <lb/>gradū et in prima medietate vnã leucã ꝑtranſit: in <lb/>ſecūda medietate triū leucarū ſpaciū abſoluet. </s>
              <s xml:id="N1E6BB" xml:space="preserve">Et <lb/>ſi ordine prepoſtero moueri incepiſſet puta ab illo <lb/>dato gradu vſ ad nõ gradū in prima medietate <lb/>hore tribus abſolutis leucis: vna dumtaxat reſta-<lb/>ret tranſeunda in ſecunda tēporis medietate.</s>
            </p>
            <p xml:id="N1E6C6">
              <s xml:id="N1E6C7" xml:space="preserve">Quinta ꝓpoſitio. </s>
              <s xml:id="N1E6CA" xml:space="preserve">Si aliquod mobile <lb/>moueatur vniformiter difformiter a nõ gradu vſ <lb/>ad certū gradū in aliquo tēpore: ipſum adequate <lb/>ſubduplū ſpaciū ꝑtranſit ad ſpaciū natū ꝑtranſiri <lb/>illo gradu intenſiori ꝑ idem tēpus cõtinuato. </s>
              <s xml:id="N1E6D5" xml:space="preserve">Pro­<lb/>batur / q2 totalis velocitas illius motus eſt ſubdu-<lb/>pla ad velocitatē illius gradus iutenſioris eiuſdē <lb/>latitudinis: igitur ſubduplū ſpaciū ꝑtranſibitur <lb/>mediante vna illaꝝ ad ſpaciū ꝑtranſitū ab illa que <lb/>eſt in duplo intenſior dūmodo tēpora ſint equalia <lb/>ſi ſpaciorum proportio proportionem velocitatū <lb/>eodem tempore ſequitur / vt oportet. </s>
              <s xml:id="N1E6E6" xml:space="preserve">Ex hac ſequit̄̄.</s>
            </p>
            <p xml:id="N1E6E9">
              <s xml:id="N1E6EA" xml:space="preserve">Sexta ꝓpoſitio que talis eſt. </s>
              <s xml:id="N1E6ED" xml:space="preserve">Omne <lb/>mobile motū vniformiter difformiter a certo gra-<lb/>du vſ ad certū gradū in aliquo tēpore maiꝰ ſpa-<lb/>ciū quã ſubduplū ꝑtranſit in eodem tēpore ad ſpa­<lb/>ciū natū ꝑtranſiri mediante extremo intenſiori il-<lb/>lius latitudinis ꝑ idem tēpus cõtinuato. </s>
              <s xml:id="N1E6FA" xml:space="preserve">Probat̄̄ / <lb/>quia ſi talis latitudo inctperet a gradu ſuo inten-<lb/>ſiori et terminaretur ad nõ gradū: p̄ciſe illud mobi­<lb/>le ꝑtranſiret in illo tēpore ſubduplū ſpaciū ad ſpa­<lb/>ciū natū ꝑtranſiri mediante extremo intenſiori il­<lb/>lius latitudinis ꝑ idem tēpus cõtinuato / vt patꝫ ex <lb/>priori: ſed modo illa latitudo ab illo gradu incipi­<lb/>ens et ad gradū terminata eſt intenſior / vt ptꝫ ex ſe­<lb/>cunda / ergo in equali tēpore maiꝰ ſpaciū quã illud <lb/>ſubduplum pertranſibit / quod fuit probandum.</s>
            </p>
            <p xml:id="N1E70F">
              <s xml:id="N1E710" xml:space="preserve">Septima ꝓpoſitio. </s>
              <s xml:id="N1E713" xml:space="preserve">Si aliqḋ mobile <lb/>vniformiter difformiter moueat̄̄ a certo gradu in-<lb/>tēſiori ad cetū gradū remiſſiorē ī hora: ipſū in pri­<lb/>ma medietate hore minus quã triplū ſpaciū ꝑtran­<lb/>ſit ad ſpaciū ꝑtranſitū in ſecunda medietate hore <lb/>in qua tardiꝰ mouetur. </s>
              <s xml:id="N1E720" xml:space="preserve">Probatur / quia ſi talis la-<lb/>titudo motus diuidatur ꝑ partes proportionales <lb/>ꝓportione dupla ſecundū partes tēporis: ille par-<lb/>tes nõ cõtinue ſe habebūt in ꝓportione dupla ſicut <lb/>ſe habent tales partes in latitudine terminata ad <lb/>nõ gradū: igr̄ reſiduū oīm partiū a prima non eſt <lb/>ſubtriplū ad velocitatē prime ſed maius quã ſub-<lb/>triplū: et ꝑ conſequens ſpaciū ꝑtranſitum in oībus <lb/>partibus a prima puta in ſecūda medietate eſt ma­<lb/>ius quã ſubtriplum ad ſpacium pertranſitū in pri­               <cb chead="De motu locali quo ad effectū ſcḋm tempus difformi."/>               ma. </s>
              <s xml:id="N1E738" xml:space="preserve">Antecedens patet intuenti et conſequentia pro­<lb/>batur / quia quanto proportio aliqua in qua ſe ha­<lb/>bent cõtinuo aliqua infinita eſt minor tanto aggre­<lb/>gatum ex omnibus ſequentibus primū eſt maius. <lb/></s>
              <s xml:id="N1E742" xml:space="preserve">Item patet predicta propoſitio exemplariter / qm̄ <lb/>capta latitudine incipiente a duodecim et termina­<lb/>ta ad quatuor gradus medius medietatis intenſi­<lb/>oris eſt vt decem: et gradus medius medietatis re-<lb/>miſſioris eſt vt .6. modo gradus ſextus nõ eſt ſub-<lb/>triplus ad duodenarium: et ſic in omni alia lati-<lb/>tudine inuenies predicte propoſitionis certitudinē <lb/>               <anchor type="note" xlink:href="note-0148-01" xlink:label="note-0148-01a"/>               </s>
              <s xml:id="N1E758" xml:space="preserve">¶ Et ſi queras quomodo cognoſcēdum ſit in omni <lb/>latitudine motus vtrim ad graduꝫ terminata in <lb/>qua proportione ſe habeat extremuꝫ intenſius ad <lb/>gradum mediuꝫ eiuſdem latitudinis: et in qua pro-<lb/>portione plus pertrãſitur mediante medietate in-<lb/>tenſiori talis latitudinis quam mediante medieta­<lb/>te remiſſiori.</s>
            </p>
            <div xml:id="N1E767" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0148-01a" xlink:label="note-0148-01" xml:id="N1E76B" xml:space="preserve">Queſtio</note>
            </div>
            <p xml:id="N1E771">
              <s xml:id="N1E772" xml:space="preserve">Rſpõdeo /  in hac materia nulla põt <lb/>dari certa et vniuerſalis regula. </s>
              <s xml:id="N1E777" xml:space="preserve">Quoniã ſecundū / <lb/>quod extremum intenſius et remiſſius ſe habent in <lb/>alia et alia ꝓportiõe ad īuicē: ita ſe habet gxadꝰ me­<lb/>dius ad extremū intenſius talis latitudinis in alia <lb/>et alia ꝓportiõe: tamen poſſent ſiguari peculiares <lb/>regule certis ſpeciebus proportionum accõmode <lb/></s>
              <s xml:id="N1E785" xml:space="preserve">Si enim extrema ſe habeant in proportiõe dupla <lb/>gradus medius eſt ſubſexquitertius ad extremum <lb/>intenſius. </s>
              <s xml:id="N1E78C" xml:space="preserve">Si vero extrema ſe habent in proporti-<lb/>one tripla: tunc gradus medius erit ſubſexquial-<lb/>terus ad extremum intenſius. </s>
              <s xml:id="N1E793" xml:space="preserve">Si vero ſe habent in <lb/>proportione quadrupla: tunc gradus medius eſt <lb/>ſubſupertripartiens quintas ad extremum inten-<lb/>ſius. </s>
              <s xml:id="N1E79C" xml:space="preserve">Si vero ſe habeant in proportione ſextupla: <lb/>gradus medius eſt ſuperquintipartiens ſeptimas <lb/>ad gradum intenſiorem. </s>
              <s xml:id="N1E7A3" xml:space="preserve">et ſic diuerſis proportioni­<lb/>bus diuerſe regule aſſignatur.               <anchor type="note" xlink:href="note-0148-02" xlink:label="note-0148-02a"/>               </s>
              <s xml:id="N1E7AD" xml:space="preserve">¶ Quereret tamē <lb/>aliquis vlterius quo tramite et menſura poſſet fa-<lb/>cile inueſtigari gradus medius in omni latitudīe.</s>
            </p>
            <div xml:id="N1E7B4" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0148-02a" xlink:label="note-0148-02" xml:id="N1E7B8" xml:space="preserve">Queſtio</note>
            </div>
            <p xml:id="N1E7BE">
              <s xml:id="N1E7BF" xml:space="preserve">Reſpondeo /  per hanc regulam quia <lb/>aut latitudo illa terminatur ad nõ gradū / tūc diui­<lb/>datur extremum intenſius per medium: et vna me-<lb/>dietas eſt gradus medius. </s>
              <s xml:id="N1E7C8" xml:space="preserve">Si vero incipit a gradu <lb/>et terminatur ad gradum: tunc ſubduplum ad ag-<lb/>gregatum ex extremo intenſiori et remiſſiori eſt gra­<lb/>dus medius inter illa extrema. </s>
              <s xml:id="N1E7D1" xml:space="preserve">Exemplum primi / <lb/>vt ſi aliqua latitudo incipiati ab octauo et termina­<lb/>tur ad non gradum: quoniam medietas ipſorum <lb/>8. eſt .4. ideo gradus quartus eſt gradus medius. <lb/></s>
              <s xml:id="N1E7DB" xml:space="preserve">Exemplum ſecundi / vt ſi aliqua latitudo incipiat <lb/>ab octauo et terminatur ad quartum. </s>
              <s xml:id="N1E7E0" xml:space="preserve">dico /  gra-<lb/>dus ſextus eſt gradus mediꝰ qui eſt ſubduplus ad <lb/>aggregatum ex 8. et .4. </s>
              <s xml:id="N1E7E7" xml:space="preserve">Illud enim aggregatum eſt <lb/>vt duodecim: et ſic vniuerſaliter reperies omni ſe-<lb/>cluſa exceptione.</s>
            </p>
            <p xml:id="N1E7EE">
              <s xml:id="N1E7EF" xml:space="preserve">Notandum eſt ſecundo /  motum ve-<lb/>locitates quando ſunt equales quãdo inequa-<lb/>les intenſiue: et ſi equales, aut coextenſe partibus <lb/>temporis equalibus, aut inequalibus. </s>
              <s xml:id="N1E7F8" xml:space="preserve">Si vero in­<lb/>equales idem etiam contingit, quia aut extendun-<lb/>tur per tempora equalia, aut per inequalia. </s>
              <s xml:id="N1E7FF" xml:space="preserve">Si <lb/>ſint inequales inequalibus coextenſe temporibus / <lb/>hoc contingit dupliciter quia aut maior velocitas <lb/>coextenditur tempori maiori aut minori. </s>
              <s xml:id="N1E808" xml:space="preserve">Exemplū <lb/>primi / vt ſi velocitas vt .4. coextendatur vni hore: <lb/>hoc eſt mobile moueatur vt .4. per vnam horam et <lb/>vt duo per dimidiam. </s>
              <s xml:id="N1E811" xml:space="preserve">Exemplum ſecundi / vt ſi <lb/>aliquod mobile moueatur velocitate vt quatuor               <pb chead="Secundi tractatus" file="0149" n="149"/>               per mediam horam, et velocitate vt duo per horam <lb/></s>
              <s xml:id="N1E81C" xml:space="preserve">Item ſi maior velocitas coextendatur tēpori mīori <lb/>et minor maiori. </s>
              <s xml:id="N1E821" xml:space="preserve">hoc coutingit tripliciter / quia aut <lb/>ꝓportio tempoꝝ excedit ꝓportionē velocitatū aut <lb/>ꝓportio velocitatū excedit ꝓportionē tempoꝝ aut <lb/>ꝓportiones tempoꝝ et velocitatū ſunt equales. </s>
              <s xml:id="N1E82A" xml:space="preserve">Exē-<lb/>plum primi / vt ſi aliquod mobile in hora moueatur <lb/>vt duo, et in quarta hore vt quatuor: tunc ꝓportio <lb/>tempoꝝ excedit proportionē velocitatū. </s>
              <s xml:id="N1E833" xml:space="preserve">Nam ipſa <lb/>tēpoꝝ proportio quadrupla eſt: velocitatū vero du­<lb/>pla / vt patet aſpicienti. </s>
              <s xml:id="N1E83A" xml:space="preserve">Exemplū ſecundi / vt ſi mo-<lb/>bile moueatur vt vnū per horã, et in media vt .3. / tūc <lb/>proportio tempoꝝ eſt dupla, velocitatū o tripla: <lb/>exuperat igitur velocitatū proportio tempoꝝ pro-<lb/>portionē. </s>
              <s xml:id="N1E845" xml:space="preserve">Exemplū tertii / vt ſi aliquod mobile mo-<lb/>ueatur in hora vt vnū, et aliud in media vt duo: con­<lb/>ſtat ꝓportionē tempoꝝ ꝓportioni velocitatū equa­<lb/>ri: vtra em̄ dupla eſt: et velocitatū, et tempoꝝ. </s>
              <s xml:id="N1E84E" xml:space="preserve">Hac <lb/>longa diuiſione velocitatū exacta: ipſa velocita­<lb/>te fruſtrat ī conciſa: opere preciū eſt cuilibet huiꝰ di-<lb/>uiſionis fruſto et membro peculiarē propoſitioneꝫ <lb/>aſſcriberet. </s>
              <s xml:id="N1E859" xml:space="preserve">Sit igitur.</s>
            </p>
            <p xml:id="N1E85C">
              <s xml:id="N1E85D" xml:space="preserve">Capitalis propoſitio. </s>
              <s xml:id="N1E860" xml:space="preserve">Si velocitates <lb/>ſint equales equalibus coextenſe temporibus: mo-<lb/>bilia in eiſdem mota equalia ſpacia in eiſdē tēpo-<lb/>ribus abſoluūt (ceteris aliis deductis) vt puta ra-<lb/>refactione condenſatione ſpacii et prepoſtera mo-<lb/>tione / vt concluſiones ſexto phiſicoꝝ oſtendunt. </s>
              <s xml:id="N1E86D" xml:space="preserve">Si <lb/>vero velocitates equales per īequalia labantur tē­<lb/>pora: tunc in ea ꝓportione mobile in maiori tēpo-<lb/>re maius ſpaciū pertranſit quam in minori: in qua <lb/>ipſū maius tēpus ſe habet ad minus. </s>
              <s xml:id="N1E878" xml:space="preserve">Prima pars <lb/>huiꝰ ꝓpoſitionis patet ex ſe: et ſecunda ꝓbatur: ſup­<lb/>poſito /  quando aliquid mobile mouetur vnifor-<lb/>miter per aliquod tēpus in quacū ꝓportione ſe <lb/>habent partes tēporis ad totū: in ea ꝓportione ſe <lb/>habent ſpacia pertranſita in illis temporibus ad <lb/>ad ſpaciū pertranſitū in toto tēpore: quo ſuppoſi-<lb/>to arguitur ſic mobile quod mouetur in maiori tē-<lb/>pore et mobile motū in minori tēpore mouētur vni-<lb/>formiter et eque velociter. </s>
              <s xml:id="N1E88D" xml:space="preserve">ergo in eq̈libꝰ tēporibus <lb/>equalia ſpacia ꝑtranſeunt / vt patet ex priori parte: <lb/>ergo quantū ſpaciū mobile motū in minori tēpore <lb/>ꝑtranſit in totali ſuo tēpore: tantū adequate per-<lb/>trãſit mobile motū in maiori tēpore in tēpore ſibi <lb/>equali: ergo qualis eſt ꝓportio illius tēporis ma-<lb/>ioris ad tēpus minus talis eſt ꝓportio ſpacii ꝑtrã­<lb/>ſiti in tēpore maiori ad ſpaciū ꝑtranſitū in tēpore <lb/>minori / quod fuit ꝓbandū: et cõſequentia patet ex <lb/>ſuppoſito hoc adiecto /  qualis eſt ꝓportio totius <lb/>tēporis ad illam ſuã partem equalē tēpori minori <lb/>talis eſt proportio ipſius maioris temporis ad il-<lb/>lud minus tempus / vt patet de ſe.</s>
            </p>
            <p xml:id="N1E8A8">
              <s xml:id="N1E8A9" xml:space="preserve">Secūda ꝓpoſitio. </s>
              <s xml:id="N1E8AC" xml:space="preserve">Quãdo inequales <lb/>velocitates equalibus tēporibus coextendūtur: tūc <lb/>mobile quod maiore velocitate mouetur in ea pro­<lb/>portione maius ſpaciū ꝑtranſit ꝙ̄ alterum / mobile <lb/>in qua ſe habet velocitas maior ad minorē. </s>
              <s xml:id="N1E8B7" xml:space="preserve">Pro-<lb/>batur hec ꝓpoſitio (̄uis facilis ſit) / quia ſi mobile <lb/>motū velocitate maiori in tēpore a. moueretur ade­<lb/>quate equali velocitate ſicut mouetur aliud mobile <lb/>motū velocitate minori in eodē a. tempore / tūc illa <lb/>duo mobilia equalia ſpacia ꝑtranſirent in a. tēpo­<lb/>re / vt ptꝫ ex priori parte p̄cedentis ꝓpoſitionis: ſed <lb/>modo illud mobile mouetur in aliqua proportione <lb/>puta in f. velocius quã tunc: ergo in f. proportione <lb/>maius ſpaciū pertranſit quã tunc: et per conſequēs <lb/>maius ſpaciū ꝑtranſit in eodem tēpori in f. ꝓpor-               <cb chead="Capitulū tertiū."/>               tione quã alterū mobile motum in eodem tempore <lb/>velocitate in f. proportione minori.</s>
            </p>
            <p xml:id="N1E8D3">
              <s xml:id="N1E8D4" xml:space="preserve">Tertia ꝓpoſitio. </s>
              <s xml:id="N1E8D7" xml:space="preserve">Si inequales velo-<lb/>citates in equalibus tēporibus coextendunt̄̄, et ma­<lb/>ior velocitas maiori tempori coextendatur: et mīor <lb/>minori: tunc mobile quod mouetur in maiori tem-<lb/>pore maius ſpaciū ꝑtranſit in ꝓportione cõpoſita <lb/>temporis maioris ad tempus minus: et velocitatis <lb/>maioris ad velocitatē minorē. </s>
              <s xml:id="N1E8E6" xml:space="preserve">Exemplū / vt ſi mobi­<lb/>le a. moueatur per horã vt quatuor, et b. per mediã <lb/>horã, vt .2. / tunc dico /  a ꝑtranſit maius ſpacium <lb/>quã b. in ꝓportione cõpoſita ex ꝓportione hore ad <lb/>mediã horam: et velocitatis vt .4. ad velocitatem vt <lb/>duo. / et cū vtra illaꝝ ꝓportionū ſit dupla: conſe-<lb/>quens eſt /  cõpoſita ex eis ſit quadrupla / vt patet <lb/>ex ſecunda parte: et per conſequens in quadruplo <lb/>maius ſpaciū ꝑtranſit a. in hora quam b. in media <lb/>hora. </s>
              <s xml:id="N1E8FB" xml:space="preserve">Probatur hec concluſio / quia ſi a. et b. moue-<lb/>rentur equaliter in illis duobus temporibus ine-<lb/>qualibus: tunc a. ꝑtranſit maius ſpaciū quam b. in <lb/>illa ꝓportione in qua ſe habent tēpora / vt patet ex <lb/>ſecunda parte prime ꝓpoſitionis: et modo a. in ali-<lb/>qua proportione que ſit f. maiori velocitate mouet̄̄ <lb/>quã tunc: ergo in f. proportione maius ſpaciū per-<lb/>tranſit quã tunc. </s>
              <s xml:id="N1E90C" xml:space="preserve">Patet conſequētia / quia quanto <lb/>in eodem tempore velocitas eſt maior: tanto in eo-<lb/>dem tempore per eandeꝫ maius ſpaciū ꝑtranſitur. <lb/></s>
              <s xml:id="N1E914" xml:space="preserve">Ergo proportio ſpacii ꝑtranſiti a mobili quod ve-<lb/>lociꝰ mouetur ad ſpaciū ꝑtranſitū a mobili / quod <lb/>tardius mouetur componitur adequate ex propor­<lb/>tione tēporū: et ex proportione velocitatū que eſt f. / <lb/>quod fuit probandū. </s>
              <s xml:id="N1E91F" xml:space="preserve">Patet / quia inter terminos il­<lb/>lius proportionis reperiūtur iſti termini puta ſpa­<lb/>ciū ꝑtranſitum ab illa velocitate maiori in maiori <lb/>tempore et ſpaciū pertranſitū in eodem maiori tē-<lb/>pore a velocitate equali velocitate minoris tempo­<lb/>ris: et ſpacium ꝑtranſitum a velocitate minoris tē-<lb/>poris in minori tempore: ſed primi termini ad ſe-<lb/>cundū eſt proportio f. que eſt proportio velocitatū <lb/>et ſecundi ad tertiū eſt proportio tempoꝝ: et totalis <lb/>illa ꝓportio q̄ cõponit̄̄ ex illis duabꝰ eſt proportio <lb/>ſpacii ad ſpaciū: g̊ ꝓportio ſpacii ꝑtrãſiti a mobi­<lb/>li velociori ad ſpaciū ꝑtrãſitū a mobili tardiori cõ-<lb/>ponitur ex ꝓportiꝰe velocitatis ad velocitatē: et tꝑs <lb/>ad tēpus / quod fuit probandū: et ſic ptꝫ propoſitio <lb/>               <anchor type="note" xlink:href="note-0149-01" xlink:label="note-0149-01a"/>               </s>
              <s xml:id="N1E943" xml:space="preserve">¶ Ex hac propoſitione ſequitur primo /  ſi a. mo-<lb/>ueatur per vnã horã velocitate vt .6. et b. ꝑ mediam <lb/>horã velocitate vt .4. /  ſpaciū ꝑtranſitū ab a. erit <lb/>triplū ad ſpaciū ꝑtranſitū a.b. </s>
              <s xml:id="N1E94C" xml:space="preserve">Ptꝫ / qm̄ ex propor­<lb/>tione tēporis ad tēpus, et velocitatis ad velocitatē <lb/>quaꝝ prima eſt dupla: et ſecūda ſexq̇altera cõponit̄̄ <lb/>tripla proportio / vt ptꝫ in his terminis .6. ad .4. et <lb/>4. ad .2. et in illa proportione a. mouet̄̄ velociꝰ b. / vt <lb/>ptꝫ ex precedenti propoſitione: igitur propoſitum.</s>
            </p>
            <div xml:id="N1E959" level="5" n="10" type="float">
              <note position="right" xlink:href="note-0149-01a" xlink:label="note-0149-01" xml:id="N1E95D" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N1E963">
              <s xml:id="N1E964" xml:space="preserve">Sequit̄̄ ſcḋo /  ſi a. mobile moueat̄̄ ꝑ <lb/>horã velocitate vt .6. et b. ꝑ duas tertias hore velo-<lb/>citate vt .4. /  in minori proportione maiꝰ ſpacium <lb/>ꝑtrãſit a. ꝙ̄ b. ꝙ̄ in priori caſu. </s>
              <s xml:id="N1E96D" xml:space="preserve">Ptꝫ / q2 tūc ſpaciū ꝑ-<lb/>trãſitū ab a. erit duplū ſexquiq̈rtū ad ſpaciū ꝑtrã-<lb/>ſitū a.b. et in priori caſu erat triplū: g̊ in minori pro­<lb/>portione maiꝰ ſpaciū ꝑtraſit a. quã b. in iſto caſu ̄ <lb/>in priori. </s>
              <s xml:id="N1E978" xml:space="preserve">Ptꝫ ↄ̨ña / q2 tripla eſt maior ꝙ̄ dupla ſex-<lb/>quiquarta proportio. </s>
              <s xml:id="N1E97D" xml:space="preserve">Probo tamen maiorē / quia <lb/>proportio tēporis ad tēpus eſt ſexq̇altera: et ſimili­<lb/>ter velocitatis ad velocitatē: ergo ſpaciū ꝑtrãſitū <lb/>ab a. eſt maiꝰ ſpacio ꝑtrãſito a b. in proportione cõ­<lb/>poſita ex duabꝰ ſexq̇alteris, q̄ eſt dupla ſexquiq̈rta / <lb/>vt patet in his terminis: 9.6.4. auxiliantibus his               <pb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi." file="0150" n="150"/>               que dicta ſunt in ſecunda parte huius operis capi­<lb/>te quarto. </s>
              <s xml:id="N1E991" xml:space="preserve">Infinita alia correlaria poſſūt ex hac ꝓ­<lb/>poſitione inferri. </s>
              <s xml:id="N1E996" xml:space="preserve">Sed iſta ſufficiant pro praxi pro­<lb/>poſitionis habenda.</s>
            </p>
            <p xml:id="N1E99B">
              <s xml:id="N1E99C" xml:space="preserve">Quīta ꝓpoſitio. </s>
              <s xml:id="N1E99F" xml:space="preserve">Si maior velocitas <lb/>tēpori minori coextendat̄̄ et minor maiori, et ꝓpor-<lb/>tio velocitatis maioris ad velocitatem minoris ſit <lb/>equalis ꝓportioni tēporis maioris ad tēpus minꝰ <lb/>tūc illa mobilia equalia ſpacia ꝑtranſeūt. </s>
              <s xml:id="N1E9AA" xml:space="preserve">Exēplū / <lb/>vt ſi a. mobile per mediã horã moueatur velocitate <lb/>vt .4. et b. mobile per horã velocitate vt .2. tunc quia <lb/>proportio tēporis ad tēpus eſt dupla / et velocitatis <lb/>etiã ad velocitatē dupla ſequitur /  a. et b. equalia <lb/>ſpacia ꝑtranſeūt. </s>
              <s xml:id="N1E9B7" xml:space="preserve">Probat̄̄ hec ꝓpoſitio: ſit a. mo-<lb/>bile qḋ moueatur ꝑ aliqḋ tēpus: et b. mouetur ꝑ tē-<lb/>pus in f. ꝓportione maius: et in f. ꝓportione minori <lb/>velocitate: tūc ibi ꝓportio velocitatū et tēpoꝝ ſunt <lb/>equales q2 vtra f. / igit̄̄ ſi a. moueat̄̄ equali veloci-<lb/>tate cū b. tunc in f. ꝓportione b. maius ſpaciū per-<lb/>tranſit quã a. q2 in ꝓportiõe tēporis / vt ptꝫ ex ſcḋa <lb/>parte prime propoſitionis: ſed modo a. mouet̄̄ in f. <lb/>ꝓportione velocius quã tunc: ergo in f. ꝓportione <lb/>maius ſpacium ꝑtranſit quã tunc in eodē tēpore: vt <lb/>ptꝫ ex ſecūda ꝓpoſitione: ergo tantū ſicut b. </s>
              <s xml:id="N1E9CE" xml:space="preserve">Patet <lb/>ↄ̨ña per hanc maximã quãdo aliqua duo ſe habent <lb/>in aliqua ꝓportione vt puta f. </s>
              <s xml:id="N1E9D5" xml:space="preserve">Si minꝰ illoꝝ acqui­<lb/>rit illã ꝓportionē f. ſupra ſe, efficitur equale alteri / <lb/>quod erat maius: vt ſi quaternariꝰ ad quē octona-<lb/>rius habet ꝓportionē duplã acquirat ſupra ſe ꝓ-<lb/>portionē duplã efficiet̄̄ equalis octauario / vt ptꝫ de <lb/>ſe: et ſic ptꝫ ꝓpoſitio.               <anchor type="note" xlink:href="note-0150-01" xlink:label="note-0150-01a"/>               </s>
              <s xml:id="N1E9E7" xml:space="preserve">¶ Ex hac ꝓpoſitione ſequitur / <lb/> ſi a. mobile moueatur per horã velocitate vt .4. <lb/>et b. mobile per duas tertias hore velocitate vt ſex <lb/>b. et a. equalia ſpacia ꝑtranſeūt. </s>
              <s xml:id="N1E9F0" xml:space="preserve">Probatio / q2 qua­<lb/>lis eſt ꝓportio tꝑis maioris ad tempus minꝰ: talis <lb/>eſt ꝓportio velocitatis fluentis per tēpus minꝰ ad <lb/>velocitatem per maius tēpus labentem. </s>
              <s xml:id="N1E9F9" xml:space="preserve">(Utrobi <lb/>enim ſexquialtera proportio reperitur.</s>
            </p>
            <div xml:id="N1E9FE" level="5" n="11" type="float">
              <note position="left" xlink:href="note-0150-01a" xlink:label="note-0150-01" xml:id="N1EA02" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N1EA08">
              <s xml:id="N1EA09" xml:space="preserve">Quīta ꝓpoſitio. </s>
              <s xml:id="N1EA0C" xml:space="preserve">Si maior velocitas <lb/>tēpori et extendatur minori, et minor velocitas ma­<lb/>iori tēpori: ꝓportio velocitatis tēporis ꝓportio­<lb/>nē exuperet: tūc mobile minori tēpore motū maius <lb/>ſpaciū deſcribet ꝙ̄ mobile motū in maiori tēpore <lb/>in ea ꝓportione per quã velocitatū ꝓportio tēpoꝝ <lb/>ꝓportionē excedit. </s>
              <s xml:id="N1EA1B" xml:space="preserve">Exemplū / vt ſi a. mobile moueat̄̄ <lb/>per horã velocitate vt .2. et b. mobile per mediã ho-<lb/>ram velocitate vt .8. tunc b. mobile maius ſpacium <lb/>ꝑtranſit quã a. mobile in ea ꝓportione per quã pro­<lb/>portio quadrupla velocitatū excedit ꝓportitioneꝫ <lb/>duplã tēpoꝝ. </s>
              <s xml:id="N1EA28" xml:space="preserve">Et q2 quadrupla velocitatū duplam <lb/>tēpoꝝ per duplã antecedit notū euadet ſpaciū a b. <lb/>mobili pertrãſitū ad ſpaciū ab a. mobili ꝑtranſi-<lb/>tū duplū eſſe. </s>
              <s xml:id="N1EA31" xml:space="preserve">Uniuerſalitcr tamen mathematico <lb/>ordine hanc quintã ꝓpoſitiouē inducamus. </s>
              <s xml:id="N1EA36" xml:space="preserve">Sit em̄ <lb/>a. mobile quod per aliquod tēpus aliqua velocita­<lb/>te moueatur: et b. mobile moueatur per tēpus in f. <lb/>ꝓportione minus: et velocitate in g. ꝓportione ma-<lb/>iori quã velocitas qua mouetur a. ſit g. ꝓportio <lb/>maior f. excedat g. ꝓportio ꝓportionē f. per h. ꝓ-<lb/>portionē. </s>
              <s xml:id="N1EA45" xml:space="preserve">quibꝰ ſtructis ſic argr̄: ſi ꝓportio veloci-<lb/>tatis b. ad velocitatē a. eſſet equalis ꝓportiõi tēpo-<lb/>ris tn quo mouet̄̄ a. ad tēpus in quo mouetur b. que <lb/>eſt f.a. et b. equalia ſpacia ꝑtranſirent in illis tēpo-<lb/>ribus in equallbꝰ / vt p̄cedens ꝓpoſitio demonſtrat <lb/>puta quarta. </s>
              <s xml:id="N1EA52" xml:space="preserve">Sed modo velocitas qua mouet̄̄ b. eſt <lb/>in h. ꝓportione mãior velocitate / qua tunc moueret̄̄ / <lb/>ergo in h. ꝓportione maius ſpaciū pertranſit mo-               <cb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi."/>               do b. quã tunc: qm̄ ſicut ſe habent velocitates in a-<lb/>liquo tēpore: ita ſpacia pertranſita in eodē / vt ptꝫ <lb/>ex ſecūda ꝓpoſitione: et ex conſequenti ſequitur / ­<lb/>modo b. in h. proportione maius ſpaciū pertrãſit ̄ <lb/>a. qm̄ a. et b. tunc equalia ſpacia pertranſirent: et h. <lb/>ꝓportio eſt ꝓportio per quã g. ꝓportio velocitatū <lb/>excedit f. proportionē tēpoꝝ: igr̄ b. mouetur velocius <lb/>ipſo a. in ꝓportione per quã ꝓportio velocitatum <lb/>temporum proportionem excedit: quod fuit ꝓban-<lb/>dum: et ſic patet propoſitio.</s>
            </p>
            <note position="right" xml:id="N1EA6E" xml:space="preserve">Correĺ.</note>
            <p xml:id="N1EA72">
              <s xml:id="N1EA73" xml:space="preserve">¶ Ex hac propoſitione ſequitur /  ſi a. mobile mo-<lb/>ueatur per horã velocitate vt duo: et b. mobile per <lb/>mediã horam, velocitate vt .6.  b. mobile in ſexqui­<lb/>altero maius ſpaciū pertranſit quã a. vt ſi a. per-<lb/>trãſit bipedale b. tripedale ꝑtrãſit. </s>
              <s xml:id="N1EA7E" xml:space="preserve">Probat̄̄ / q2 ibi <lb/>velocitates inequales in equalibus temporibus co­<lb/>extenduntur: et mbior velocitas maiori tempori co­<lb/>extenditur / vt notū eſt: et proportio velocitatū que <lb/>tripla eſt, proportionē tēporum duplã per ꝓporti-<lb/>onem ſexquialterã antecedit. </s>
              <s xml:id="N1EA8B" xml:space="preserve">Hec igitur ſignum eſt <lb/>et fidem facit auxilio precedentis propoſitionis b. <lb/>mobile in ſuo tēpore quo mouetur ſexquialterum <lb/>ſpaciuꝫ ad ſpaciū ab a. exactū abſoluiſſe: quod ab <lb/>iniitio ꝓpoſitū fuit </s>
              <s xml:id="N1EA96" xml:space="preserve">¶ Inferas tuo marte mĺta huic <lb/>ſimilia correlaria que ex hac quīta propoſitiõe <lb/>ſuã demonſtrationem facile ſortiūtur. </s>
              <s xml:id="N1EA9D" xml:space="preserve">Hoc em̄ cor-<lb/>relariū: ideo poſitū eſt: quia neceſſe intelligentem <lb/>particularia fantaſmata ſpeculari.               <anchor type="note" xlink:href="note-0150-02" xlink:label="note-0150-02a"/>               </s>
              <s xml:id="N1EAA9" xml:space="preserve">teſte philoſo-<lb/>pho ſecūdo de aīa: nichil eſt in īteliectu quin priꝰ <lb/>quodammodo ſingulariter preceſſerit in ſenſu de <lb/>ſenſu et ſeaſato aſſerente philoſopho.</s>
            </p>
            <div xml:id="N1EAB2" level="5" n="12" type="float">
              <note position="right" xlink:href="note-0150-02a" xlink:label="note-0150-02" xml:id="N1EAB6" xml:space="preserve">phdot;us .2. <lb/>de aīa</note>
            </div>
            <p xml:id="N1EABE">
              <s xml:id="N1EABF" xml:space="preserve">Sexta ꝓpoſitio. </s>
              <s xml:id="N1EAC2" xml:space="preserve">Ubicun maior ve­<lb/>locitas tꝑri coaſſiſtit mīori, mīor o maiori eſt ꝓ­<lb/>portio velocitatū tp̄m ꝓportiõe īferior et mīor, tūc <lb/>mobile qḋ maiori velocitate mouent̄̄ mīori tp̄e mīo­<lb/>rem magnitudinē deſcribet quã mobile motū ma-<lb/>iori tēpore in ea ꝓportione per quã temporū ꝓpor­<lb/>tio velocitatū ꝓportioni effertur. </s>
              <s xml:id="N1EAD1" xml:space="preserve">Exemplū / vt ſi a. <lb/>mobile per horan moueatur velocitate vt duo ade-<lb/>quate, et b. per mediã horam moueatur velocitate <lb/>vt .3. tunc b. minꝰ ſpaciū pertranſit quã a (minꝰ in-<lb/>quam) in ꝓportione ſexquitertia per quã ſexquiter­<lb/>tiam ꝓportio dupla tēporuꝫ ꝓportionē ſexq̇alterã <lb/>velocitatū excedit: ſi igitur a. pedale pertrãſeat: b. <lb/>tres quartas deſcribet. </s>
              <s xml:id="N1EAE2" xml:space="preserve">Generaliṫ tñ iudicat̄̄ ↄ̨clu-<lb/>ſio iſto modo. </s>
              <s xml:id="N1EAE7" xml:space="preserve">Sit a. mobile per aliquod tēpus mo­<lb/>tum aliqua velocitate, b. vero per tēpus in g. ꝓpor-<lb/>tione minus, et moueatur b. in f. ꝓportione minori <lb/>tamen g. velocius ipſo a. excedat g. ꝓportio pro-<lb/>portionē f. per h. ꝓportionē: tunc a. maius ſpaciuꝫ <lb/>pertranſit in h. ꝓportione ꝙ̄ b. </s>
              <s xml:id="N1EAF4" xml:space="preserve">Quod ꝓbatur ſic. <lb/></s>
              <s xml:id="N1EAF8" xml:space="preserve">quia ſi proportio velocitatis qua moueatur b. mobi­<lb/>le per tempus minus eſſet equalis proportioni tē-<lb/>porum: tunc b: equale ſpaciū pertranſiret adequa-<lb/>te in tempore in quo mouetur ſpacio pertrãſito ab <lb/>a. in tempore in quo a. mouetur, vt patet ex quarta <lb/>prppoſitione: ſed modo mouetur b. velocitate in h. <lb/>proportione minori quam tunc: igitur b. pertran-<lb/>ſit modo ſpacium in eodem tempore in h. propor-<lb/>tione minus quam tunc / vt patet ex ſecunda propo-<lb/>ſitione, et ex conſequenti ſequitur /  medo pertran­<lb/>ſit b. ſpacium in h. proportione minus quam a. qm̄ <lb/>a. pertranſit tantum ſicut tūc pertranſibat b. / quod <lb/>fuit probandum. </s>
              <s xml:id="N1EB13" xml:space="preserve">Sed iam probo illam minorem: <lb/>videlicet  b. modo mouetur velocitate in h. ꝓpor-<lb/>tione minori quam tunc, per hanc maximã. </s>
              <s xml:id="N1EB1A" xml:space="preserve">Quan­<lb/>docun duo numeri inequales habent duas pro-<lb/>portiones ad vnum tertium: tunc in               <pb chead="Secundi tractatus" file="0151" n="151"/>               ea proportione minor illorū eſt minor maiore per <lb/>quã maior ꝓportio excedit minorē: id eſt per quam <lb/>ꝓportio maioris numeri ad illud tertiū excedit ꝓ-<lb/>portionē minoris numeri ad idem tertiū. </s>
              <s xml:id="N1EB2C" xml:space="preserve">Quoniã <lb/>ꝓportio maioris ad idē tertiū cõponit̄̄ ex ꝓportio­<lb/>ne illius ad numeꝝ minorem, et numeri minoris ad <lb/>idem tertiū. </s>
              <s xml:id="N1EB35" xml:space="preserve">Hoc eſt primū correlariū quarte cõclu­<lb/>ſionis quartis capitis ſcḋe partis. </s>
              <s xml:id="N1EB3A" xml:space="preserve">Sed ita eſt in ꝓ-<lb/>poſito /  ſi ꝓportio velocitatis maioris ad veloci-<lb/>tatē minorē eſſet equalis g. ꝓportioni tēpoꝝ: tunc <lb/>ipſa iam excederet ꝓportionē quã modo habet pu­<lb/>ta f. per h. ꝓportionē / vt ptꝫ ex caſu: ergo modo illa <lb/>velocitas maior eſt in h. ꝓportione minor quã tūc / <lb/>qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0151-01" xlink:label="note-0151-01a"/>               </s>
              <s xml:id="N1EB4E" xml:space="preserve">¶ Et vt hec theoretica non ſit expers <lb/>practice tale infero correlariū. </s>
              <s xml:id="N1EB53" xml:space="preserve">Si equꝰ a. moueret̄̄ <lb/>velocitate vt .4. in hora adequate, et equus b. velo-<lb/>citate vt .6. adequate in media hora, et ipſe equꝰ b. <lb/>6. leucas pertranſeat in illa media hora: neceſſe eſt <lb/>equū a. ad extremū .8. leucarum in hora deuenire. <lb/></s>
              <s xml:id="N1EB5F" xml:space="preserve">Probat̄̄ / qm̄ in p̄dicto caſu equus b. motꝰ in mino-<lb/>ri tēpore maiore velocitate mouet̄̄ ipſo equo a. mo­<lb/>to in maiore tēpore et ꝓportio dupla tēpoꝝ excedit <lb/>ꝓportionē velocitatū ꝑ ſexquitertiã ꝓportionē: igr̄ <lb/>auxilio p̄cedentis ꝓpoſitiõis ꝑſpicuū euadit equū <lb/>a. in ſexquitertio maius ſpaciū ꝑtranſire quã equꝰ <lb/>b. ꝑtranſeat. </s>
              <s xml:id="N1EB6E" xml:space="preserve">Sed equus b. ex caſu ſex leucarū ſpa-<lb/>ciū ꝑtranſit in illa media hora: igitur a. ſpaciū .8. <lb/>leucaꝝ in hora cõpleuit (quãdoquidē .8. ad .6. ſexq̇-<lb/>tertia eſt ꝓportio) </s>
              <s xml:id="N1EB77" xml:space="preserve">¶ Hoc ſenario numero ꝓpoſiti-<lb/>onū lata illa diſtinctio velocitatum fimbrias ſuas <lb/>colligat, ſiquidem ſenarius perfectus eſt.</s>
            </p>
            <div xml:id="N1EB7E" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0151-01a" xlink:label="note-0151-01" xml:id="N1EB82" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N1EB88">
              <s xml:id="N1EB89" xml:space="preserve">Notandū eſt tertio tãgendo materiã <lb/>ſecūdi argumēti pricipalis ante oppoſitū /  aliud <lb/>eſt latitudinē motꝰ vniformiter intendi aut vnifor-<lb/>miter remitti: aliud vero mobile vniformiter mo-<lb/>ueri. </s>
              <s xml:id="N1EB94" xml:space="preserve">Unde cum latitudo motus vniformiter inten-<lb/>ditur a nõ gradu vel a gradu ad certū gradū ſemꝑ <lb/>mobile vniformiter difformiter mouetur. </s>
              <s xml:id="N1EB9B" xml:space="preserve">Et ſimi-<lb/>liter quãdo vniformiter remittitur aliquis motus <lb/>a gradu vſ ad nõ gradū vel certū gradū / tunc mo­<lb/>bile vniformiter difformiter mouetur. </s>
              <s xml:id="N1EBA4" xml:space="preserve">Nã latitudo <lb/>motus ſi acquiſita aut deꝑdita coextendit̄̄ vnifor­<lb/>miter difformiter tēporis partibꝰ, ita  illiꝰ motꝰ <lb/>cuiuſlibet partis gradus mediꝰ tanto exceditur a <lb/>ſūmo quantū excedit infimū vel nõ gradū. </s>
              <s xml:id="N1EBAF" xml:space="preserve">Quare <lb/>definitiue arguendo relinquit̄̄ oēm talē motum ſic <lb/>vniformiter acquiſitū vel deperditū eſſe vniformi-<lb/>ter difformē. </s>
              <s xml:id="N1EBB8" xml:space="preserve">Hanc materiã latiꝰ īquiras recurren­<lb/>do ad hentiſberū in ſuo tractatu de motu locali ca­<lb/>pite primo in fine adiūctis eiuſdē hentiſberi cõmē-<lb/>tariis. </s>
              <s xml:id="N1EBC1" xml:space="preserve">Inſuꝑ aduerte /  latitudo motꝰ tripliciter <lb/>acquiri põt vt ad ꝓpoſitū noſtrū ſufficit vel deꝑdi <lb/></s>
              <s xml:id="N1EBC7" xml:space="preserve">Quod ideo dixerim / qm̄ multis aliis modis et re-<lb/>mitti et intendi põt motꝰ latitudo: ſed hii tres dūta­<lb/>xat nr̄o quadrant ꝓpoſito. </s>
              <s xml:id="N1EBCE" xml:space="preserve">Primo modo latitudo <lb/>motꝰ põt acq̇ri vel deꝑdi cõtinuo vniformiter, vt pu­<lb/>ta qñ mobile in partibꝰ equalibꝰ tꝑis eq̈les gradꝰ <lb/>velocitatis acq̇rit vel deꝑdit cõtinue. </s>
              <s xml:id="N1EBD7" xml:space="preserve">Scḋo põt lati­<lb/>tudo motꝰ acq̇ri vel deꝑdi cõtinuo velociꝰ et velociꝰ <lb/>vt puta qñ mobile in q̈libet parte ſequēti tꝑis con-<lb/>tinuo maiorē latitudinē motꝰ deꝑdit quã in equali <lb/>p̄cedenti. </s>
              <s xml:id="N1EBE2" xml:space="preserve">Tertio modo poteſt latitudo motus ſiue <lb/>velocitas acquiri vel deperdi cõtinuo tardiꝰ et tar-<lb/>dius: vt puta quãdo mobile ↄ̨tinuo in qualibet par­<lb/>te ſequēti tēporis minorē latitudinē motꝰ deperdit <lb/>quam in equali precedente. </s>
              <s xml:id="N1EBED" xml:space="preserve">¶ Qua diuiſione pre-<lb/>miſſa pono aliquas propoſitiones.</s>
            </p>
            <p xml:id="N1EBF2">
              <s xml:id="N1EBF3" xml:space="preserve">Prima propoſitio. </s>
              <s xml:id="N1EBF6" xml:space="preserve">Si aliquis motus               <cb chead="Capitulū tertiū."/>               vniformiter cõtinuo intendatur vel remittat̄̄ a cer-<lb/>to gradu vſ ad certū gradū vel ad nõ gradū eius <lb/>velocitas gradui medio correſpõdet. </s>
              <s xml:id="N1EC00" xml:space="preserve">Probat̄̄ hec <lb/>ꝓpoſitio / q2 talis motꝰ ſic intenſſus aut remiſſus eſt <lb/>vniformiter difformis / vt ptꝫ ex principio huiꝰ nota­<lb/>bilis auxiliante definitione motꝰ vniformiter dif-<lb/>formis: igitur eiꝰ velocitas gradui ſuo medio corre­<lb/>ſpondet. </s>
              <s xml:id="N1EC0D" xml:space="preserve">Patet hec conſequentia ex notabili pri-<lb/>mo huius capitis.</s>
            </p>
            <p xml:id="N1EC12">
              <s xml:id="N1EC13" xml:space="preserve">Secūda ꝓpoſitio. </s>
              <s xml:id="N1EC16" xml:space="preserve">Oīs motꝰ cõtinuo <lb/>velocius et velocius intenſus correſpondet quantū <lb/>ad velocitatē gradui remiſſiori medio gradu inter <lb/>extremū intēſionis eiꝰ in principio motꝰ et īter extre­<lb/>mū intēſionis in fine motꝰ. </s>
              <s xml:id="N1EC21" xml:space="preserve">Exemplū / vt ſi motus vt <lb/>4. cõtinuo intēdat̄̄ ꝑ horã quovſ ſit vt .8. ita  ac-<lb/>quirat quatuor gradꝰ in hora et illã latitudinē .4. <lb/>graduū cõtinuo velocius et velociꝰ acquirat in ipſa <lb/>hora: tūc tota eiꝰ velocitas correſpõdet minori gra­<lb/>dui ſexto gradu qui eſt gradus mediꝰ inter .4. et .8. <lb/>hoc eſt illud mobile nõ tã velociter mouetur in illa <lb/>hora adequate quã velociter moueretur ſi cõtinuo <lb/>vniformiter moueret̄̄ gradu ſexto medio. </s>
              <s xml:id="N1EC34" xml:space="preserve">Probat̄̄ <lb/>hec ꝓpoſitio. </s>
              <s xml:id="N1EC39" xml:space="preserve">Sit a. motꝰ et b. motꝰ equalis ei in prī­<lb/>cipio: et volo /  a. ꝑ horã cõtinuo vniformiter inten­<lb/>dat̄̄ vſ ad c. gradū acquirendo certã latitudinē, et <lb/>b. cõtinuo in eadē hora adequate intendat̄̄ etiã vſ <lb/>ad c. gradū acq̇rendo eandem latitudinē adequate <lb/>quã acq̇rit a. ita  in fine tēporis a. et b. erūt equa-<lb/>les c. gradu ſicut etiã in principio ſunt equales: ac-<lb/>quirat tamē b. illa in latitudinē cõtinuo velocius et <lb/>velociꝰ quã a. acquirit cõtinuo vniformiter. </s>
              <s xml:id="N1EC4C" xml:space="preserve">Et ar-<lb/>guit̄̄ ſic / velocitas ipſiꝰ a. correſpõdet gradui medio <lb/>inter c. gradū et gradū in quo eſt a. et b. in principio / <lb/>vt patꝫ ex p̄cedēte ꝓportione. </s>
              <s xml:id="N1EC55" xml:space="preserve">et velocitas motus b. <lb/>correſpondet minori gradui quam gradui medio / <lb/>igr̄ oīs motus cõtinuo velocius et velociꝰ intenſus <lb/>correſpondet gradui remiſſiori medio gradu inter <lb/>extremū eiꝰ intēſius et remiſſius. </s>
              <s xml:id="N1EC60" xml:space="preserve">Ptꝫ hec cõſeq̄ntia / <lb/>q2 idē eſt gradus mediꝰ vĺ equalis inter extrema a. <lb/>motꝰ et b. motus, vt ponit caſus. </s>
              <s xml:id="N1EC67" xml:space="preserve">Et ſicut ꝓbatur de <lb/>b. in ꝓpoſito, ita arguendū eſt de quocū alio mo­<lb/>tu cõtinuo velociꝰ et velociꝰ intenſo. </s>
              <s xml:id="N1EC6E" xml:space="preserve">Sed iam reſtat <lb/>ꝓbare minorē / q2 motus b. in quolibet inſtãti intrī-<lb/>ſeco erit minor motu a. / ergo velocitas eiꝰ in toto tē­<lb/>pore adequate minori gradui correſpõdebit quaꝫ <lb/>velocitas ipſiꝰ a. </s>
              <s xml:id="N1EC79" xml:space="preserve">Sed velocitas ipſiꝰ a. correſpon-<lb/>det gradui medio inter extrema ipſius b. / vt ꝓbatū <lb/>eſt: ergo velocitas b. correſpõdet gradui remiſſiori <lb/>gradu medio inter extrema eiuſdē b. / quod fuit pro­<lb/>bandū. </s>
              <s xml:id="N1EC84" xml:space="preserve">Sed iã ꝓbo illud añs vcꝫ /  motus b. in quo­<lb/>libet inſtanti intrinſeco eſt minor et remiſſior motu <lb/>a. q2 ſi nõ detur aliquod inſtans in quo ſit maior vĺ <lb/>equalis et ſit c. tale inſtans illiꝰ hore: et argr̄ ſic / in c. <lb/>inſtãti b. motꝰ eſt eq̈lis a. motu cū caſu poſito: g̊ eq̈-<lb/>les latitudīes acq̇ſiuerūt adeq̈te in tꝑe termīato ad <lb/>illud inſtãs, et eq̈les reſtãt acq̇rēde vſ ad c. gradū, <lb/>et ↄ̨tinuo b. velocius acq̇ret latitudinē illã acq̇rendã <lb/>poſt illud inſtãs quã ãtea idē b. acq̇ſiuerit, et ãtea a. <lb/>et b. acq̇ſiuerūt eq̈liter, et ↄ̨tinuo a. poſt illud inſtans <lb/>acq̇ret vniformiter: g̊ velociꝰ et citius b. acquiret c. <lb/>gradum quã a. / quod eſt contra caſum. </s>
              <s xml:id="N1EC9D" xml:space="preserve">Et eodē mo-<lb/>do probabitur /  in illo inſtanti motus b. nõ eſt in-<lb/>tenſior motu a. / quia iã ſequeretur /  ante illud in-<lb/>ſtans velociꝰ acq̇rebat b. latitudinē motus quã a. et <lb/>poſt illud inſtãs velociꝰ acq̇ret ex caſu reſiduū lati-<lb/>tudinis acq̇rende quã antea, et ꝑ ↄ̨ñs poſt illud in-<lb/>ſtãs velociꝰ et citiꝰ acq̇ret reſiduū latitudinis acq̇rē-<lb/>de quã a. / et ſic citiꝰ habebit c. gradū quã a. / quod eſt <lb/>contra caſum. </s>
              <s xml:id="N1ECB0" xml:space="preserve">Et ſic patet illa minor probata.</s>
            </p>
            <pb chead="De motu locali quo ad effectum tempore difformi." file="0152" n="152"/>
            <p xml:id="N1ECB7">
              <s xml:id="N1ECB8" xml:space="preserve">¶ Et confirmatur </s>
              <s xml:id="N1ECBB" xml:space="preserve">Quia a. et b. in principio ſūt mo­<lb/>tus equales: et in toto tempore debent acquirere eq̈­<lb/>les latitudines: et in quolibet inſtanti intrinſeco eſt <lb/>plus acquiſitum ipſi a. quã b. illius latitudinis ac-<lb/>quirende. </s>
              <s xml:id="N1ECC6" xml:space="preserve">igitur continuo a. motus eſt maior b. </s>
              <s xml:id="N1ECC9" xml:space="preserve">Cõ­<lb/>ſequentia eſt ſatis manifeſta. </s>
              <s xml:id="N1ECCE" xml:space="preserve">et minor patet / q2 con­<lb/>tinuo in quolibet inſtanti intrinſeco maior pars re­<lb/>ſtat acquirenda talis latitudinis ipſi b. quã ipſi a. <lb/>cum b. continuo velocius et velocius acquirat. </s>
              <s xml:id="N1ECD7" xml:space="preserve">et a. <lb/>vniformiter:               <anchor type="note" xlink:href="note-0152-01" xlink:label="note-0152-01a"/>              igitur in quolibet inſtanti intriuſeco <lb/>maior pars latitudinis eſt acquiſita ipſi a. quã ip-<lb/>ſi b. et hec eſt quinquageſima quarta concluſio cal-<lb/>culatoris in capitulo de motu locali.</s>
            </p>
            <div xml:id="N1ECE7" level="5" n="14" type="float">
              <note position="left" xlink:href="note-0152-01a" xlink:label="note-0152-01" xml:id="N1ECEB" xml:space="preserve">54. ↄ̨clu. <lb/>cal. in c: ḋ <lb/>mo. lo.</note>
            </div>
            <p xml:id="N1ECF5">
              <s xml:id="N1ECF6" xml:space="preserve">Tertia propoſitio </s>
              <s xml:id="N1ECF9" xml:space="preserve">Omnis motus ve-<lb/>lociꝰ et velociꝰ deꝑditꝰ quãtū ad tranſitioneꝫ ſpacii <lb/>inteuſiori gradui gradu medio correſpondet hoc ē <lb/>tale mobiie motum illo motu maius ſpacium in il-<lb/>lo tempore pertrãſit adequate quã ſi gradu medio <lb/>inter extrema illius motus continuo vniformiter <lb/>moueretur in illo tempore. </s>
              <s xml:id="N1ED08" xml:space="preserve">Hec propoſitio proba-<lb/>ta eſt in ſecundo argumento prīcipali ante oppoſi­<lb/>tum in hoc capite.               <anchor type="note" xlink:href="note-0152-02" xlink:label="note-0152-02a"/>               </s>
              <s xml:id="N1ED14" xml:space="preserve">Et hec eſt quinquageſima ſecun-<lb/>da ↄ̨cluſio calculatoris in predicto capitulo de mo­<lb/>tu locali               <anchor type="note" xlink:href="note-0152-03" xlink:label="note-0152-03a"/>               </s>
              <s xml:id="N1ED20" xml:space="preserve">¶ Ex hac concluſione ſequitur /  ſi a. mobi­<lb/>le moueatur in hora incipiendo ab octauo vſ ad <lb/>quartum continuo vniformiter remittendo motum <lb/>ſuum, et b. mobile moueatur etiam in hora ab octa­<lb/>uo vſ ad quartum continuo velocius et velociꝰ re­<lb/>mittēdo motum ſuum et a. pertranſit .6. pedalia b. <lb/>pertranſibit pluſ̄ ſex pedalia. </s>
              <s xml:id="N1ED2F" xml:space="preserve">Probatur / q2 mo-<lb/>tus a. correſpondet gradui medio qui eſt ſextus. </s>
              <s xml:id="N1ED34" xml:space="preserve">vt <lb/>patet ex prima propoſitione: motus vero b. correſ-<lb/>pondet gradui intenſiori medio / vt patet ex tertia ꝓ­<lb/>poſitione.               <anchor type="note" xlink:href="note-0152-04" xlink:label="note-0152-04a"/>               </s>
              <s xml:id="N1ED42" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. incipiat mo-<lb/>ueri ab octauo vſ ad quartum vniformiter et b. in <lb/>eodem tempore moueatur incipiendo a decimo ſex­<lb/>to vſ ad duodecimum perdendo latitudinem .4. <lb/>graduum velocius et velocius: tunc continuo b. mo-<lb/>uebitur pluſ̄ in duplo velocius a. et continuo per-<lb/>tranſibit pluſ̄ duplum ſpacium ad ſpacium in eo­<lb/>dem tempore pertranſitum ab a. </s>
              <s xml:id="N1ED53" xml:space="preserve">Probatur / q2 qñ <lb/>a. et b. continue et vniformiter remitterentur perdē­<lb/>do .4. gradus continuo inter a. et b. ſſet maior ꝓpor­<lb/>tio quã dupla, īmo continuo maior et maior: qm̄ ꝑ <lb/>equalem remſſionem maioris et minoris: maiorē ꝓ­<lb/>portionem deperdit minus quã maius / vt patet ex <lb/>octaua ſuppoſitione quartis capitis ſecunde partis <lb/>et quando ſunt duo numeri ſe habentes in aliqua ꝓ­<lb/>portione, et continuo equaliter remittuntur: conti-<lb/>nuo ſe habent in maiori et maiori ꝓportione: igitur <lb/>ſequitur / ſi ille velocitates a. et b. que ſe habent in ꝓ­<lb/>portione dupla eque velociter remittantur cõtinuo <lb/>ſe habebunt in maiori ꝓportione quã dupla: et ſic <lb/>b. coutinuo ſe haberet in maiori ꝓportione quã du­<lb/>pla ad ipſum a. ſed modo continuo eſt minus deꝑ-<lb/>ditum ipſi b. quam ipſi a. cum cõtinuo reſtat ei plus <lb/>deperdendum / vt facile patet ex caſu / igitur per locū <lb/>a maiori continuo b. motus erit pluſ̄ in duplo ve­<lb/>locior ipſo a. motu. </s>
              <s xml:id="N1ED7A" xml:space="preserve">Ex quo ſequitur alia pars cor-<lb/>relarii /  videlicet pluſ̄ duplum ſpacium pertran­<lb/>ſibit b. quam a. in eodē tempore.               <anchor type="note" xlink:href="note-0152-05" xlink:label="note-0152-05a"/>               </s>
              <s xml:id="N1ED86" xml:space="preserve">¶ Sequitnr tertio / <lb/> ſi tam. </s>
              <s xml:id="N1ED8B" xml:space="preserve">quã b. remitterentur ad ſuum ſubduplum <lb/>in hora: ita  a. deperdat in hora continuo vnifor-<lb/>miter quatuor gradus et b. octo continuo velocius <lb/>et velocius: ſequitur /  b. pluſ̄ duplum ſpacium in <lb/>hora pertranſibit quã a. </s>
              <s xml:id="N1ED96" xml:space="preserve">Probatur / quia ſi b. motꝰ <lb/>vniformiter remitteretur ꝑ totam illam horam ꝑ-<lb/>dendo vniformiter .8. gradus ſicut a. perdit vnifor­               <cb chead="De motu locali quo ad effectum tempore difformi."/>               miter quatuor: tunc motus eius correſpõderet gra­<lb/>dui medio duplo ad gradum medium motus a. / vt <lb/>patet / q2 gradus medius inter .16. et .8. eſt .12. et gra­<lb/>dus medius inter .8. et .4. eſt vt .6: modo .12: ad .6. eſt <lb/>proportio dupla: ſed modo quando ſic velocius et <lb/>velocius et velocius remittitur ſua velocitas correſ­<lb/>pondet intenſiori gradui quã tunc: vt patet ex ter-<lb/>tia propoſitione: igit̄̄ in noſtro caſu b. motus ī illa <lb/>hora ꝑtranſibit pluſ̄ duplū ſpaciū ad ſpaciū ꝑtrã­<lb/>ſitum ab a. in eodem tempore. </s>
              <s xml:id="N1EDB2" xml:space="preserve">Quod tamen prima <lb/>fronte videtur mirabile quia in principio motꝰ b. <lb/>eſt duplus ad motum a. adequate et in toto tempo­<lb/>re perdit motum duplum ad motum quē perdit a. <lb/>tamen bene aſpicienti materiam proportionū ap-<lb/>parebit neceſſarium.</s>
            </p>
            <div xml:id="N1EDBF" level="5" n="15" type="float">
              <note position="left" xlink:href="note-0152-02a" xlink:label="note-0152-02" xml:id="N1EDC3" xml:space="preserve">.52. ↄ̨clu. <lb/>cal. in c. ḋ <lb/>mo. lo.</note>
              <note position="left" xlink:href="note-0152-03a" xlink:label="note-0152-03" xml:id="N1EDCD" xml:space="preserve">.1. correl.</note>
              <note position="left" xlink:href="note-0152-04a" xlink:label="note-0152-04" xml:id="N1EDD3" xml:space="preserve">2. correl.</note>
              <note position="left" xlink:href="note-0152-05a" xlink:label="note-0152-05" xml:id="N1EDD9" xml:space="preserve">3. correl.</note>
            </div>
            <note position="right" xml:id="N1EDDF" xml:space="preserve">quītage-<lb/>ſimaquī­<lb/>ta calcu.</note>
            <p xml:id="N1EDE7">
              <s xml:id="N1EDE8" xml:space="preserve">Quarta propoſitio </s>
              <s xml:id="N1EDEB" xml:space="preserve">Omnis motꝰ tar-<lb/>dius et tardius intenſius quantum ad pertranſitio­<lb/>nem ſpacii gradui intenſiori medio correſpondet. <lb/></s>
              <s xml:id="N1EDF3" xml:space="preserve">Probatur / quia ſi continuo vniformiter talis mo-<lb/>tus (qui ſit a) intenderetur: ipſe preciſe correſpõde-<lb/>ret gradui medio quantum ad pertranſitionē ſpa­<lb/>cii / vt patet ex prima propoſitione: ſed modo in quo­<lb/>libet inſtanti intrinſeco temporis per quod a. mobi­<lb/>le mouetur: mouetur velocius quã tunc: ergo: veloci­<lb/>tas eius modo correſpondet gradui intenſiori me-<lb/>dio: quia intenſiori quã tunc. </s>
              <s xml:id="N1EE04" xml:space="preserve">Conſequentia patet <lb/>et arguitur minor: et volo /  b. ſit motus in prīcipio <lb/>hore equalis ipſi a. qui in eadem hora vniformiter <lb/>continuo acquirit equalem latitudinem illi quã ac­<lb/>quirit a. adequate ipſo tamē a. tardius et tardius <lb/>continuo acquirente ita  ſicut ſunt equales in prī­<lb/>cipio ita ſunt equales in fine. </s>
              <s xml:id="N1EE13" xml:space="preserve">Quo poſito ſic argu-<lb/>mentor / continuo b. motus erit remiſſior ipſo a. mo­<lb/>tu et a. motus intenſior: igitur continue a. motꝰ erit <lb/>intenſior quã tunc quãdo continuo vniformiter in-<lb/>tenderetur ſicut b. quia b. et a: tunc ſemper eēnt eq̈-<lb/>les. </s>
              <s xml:id="N1EE20" xml:space="preserve">Sed iam probo /  continuo a. motus erit inten­<lb/>ſior b. motu: quia ſi non detur aliqḋ inſtans in quo <lb/>non ſed in illo ſit equalis vel remiſſior ipſo b. et ſit <lb/>tale inſtans c. terminans vnam quartam gratia ar­<lb/>gumenti vel quintam: vel ſextam non eſt cura. </s>
              <s xml:id="N1EE2B" xml:space="preserve">Et ar­<lb/>guo ſic / in illo inſtanti a. motus et b. motus ſunt eq̈-<lb/>les per te: et in principio erant equales ex caſu et in <lb/>tota hora adequate equales latitudīes ſunt eis ac­<lb/>quiſite: et equales reſtant acquirende poſt illud in-<lb/>ſtans c. et quãtam latitudinem b. acquiſiuit in illa <lb/>quarta tantam acquiret in qualibet ſequenti ade-<lb/>quate: quia vniformiter intenditur et a. ex caſu in q̈­<lb/>libet quarta ſequenti minus acquirit ꝙ̄ in illa pre-<lb/>cedenti c. / vt patet ex caſu quoniã continuo tardius <lb/>et tardius acquiret illam latitudinem acquirendã / <lb/>igitur in toto tempore ſequenti c. minorem latitudi­<lb/>nem acquiret quã b. et antea acquiſiuerat equalem: <lb/>igitur in toto tempore adequate minorem latitudi­<lb/>nē acquiret a. quã b. / quod eſt contra caſum: </s>
              <s xml:id="N1EE4A" xml:space="preserve">Et ſic <lb/>probabitur ꝑ locum a maiori /  in nullo inſtãti mo­<lb/>tus a. eſt remiſſior motu b. </s>
              <s xml:id="N1EE51" xml:space="preserve">Et ſicut argutum eſt ſu-<lb/>umndo quartam temporis argui poteſt ſumendo <lb/>quãcun partem aliquotam vel non aliquotam vĺ <lb/>quotcū: et ſic patet proportio. </s>
              <s xml:id="N1EE5A" xml:space="preserve">Et hec eſt quinqua-<lb/>geſima quinta calculatoris</s>
            </p>
            <p xml:id="N1EE5F">
              <s xml:id="N1EE60" xml:space="preserve">Quinta proportio </s>
              <s xml:id="N1EE63" xml:space="preserve">Omnis motus tar­<lb/>dius et tardius deperditus: gradui remiſſiori me-<lb/>dio correſpondet. </s>
              <s xml:id="N1EE6A" xml:space="preserve">Probatur hec propoſitio. </s>
              <s xml:id="N1EE6D" xml:space="preserve">Sit <lb/>enim a. motus vt .8. qui in hora ſequenti adequate <lb/>perdat aliquaꝫ latitudinem in hora ita  maneat <lb/>in fine minor c. gradu et hoc cõtinuo vniformiter b. <lb/>vero ſit motus equalis ipſi a. et perdat in hora ade­               <pb chead="Secundi tractatus" file="0153" n="153"/>               quate tantam latitudinem ſicut a. ita  in fine a. et <lb/>b. maneant equales. </s>
              <s xml:id="N1EE7F" xml:space="preserve">Quo poſito ſic argumentor / ve­<lb/>locitas ipſius motus a. correſpõdet gradui medio <lb/>inter extremum ipſorum a. et b. in principio et ertre­<lb/>mum eorundem in fine (dico eorundem / quia illi mo­<lb/>tus tam in principio ꝙ̄ in fine ſunt equales / vt po­<lb/>nit caſus) </s>
              <s xml:id="N1EE8C" xml:space="preserve">Sed b. motus in quolibet inſtanti intrin­<lb/>ſeco illius temporis erit remiſſior ipſo a. motu: igi­<lb/>tur b. motus remiſſiori gradui correſpondet quam <lb/>a. motus et a. motus correſpondet gradui medio in­<lb/>ter extrema ipſius b. / igitur b. motus correſpondet <lb/>gradui remiſſiori quam ſit gradus medius inter ex­<lb/>trema eiuſdem b. motus. </s>
              <s xml:id="N1EE9B" xml:space="preserve">Conſequentia patet / <lb/>quia extrema b. motus et a. motus ſunt equalia. </s>
              <s xml:id="N1EEA0" xml:space="preserve">Et <lb/>maior patet ex prima ꝓpoſitione: et minor proba-<lb/>tur ſic: quia ſi non detur oppoſitum illius minoris <lb/>videlicet /  non in quolibet inſtanti etc. ſed in aliquo <lb/>equalis vel intenſior: et et ſit illud c. terminans vnaꝫ <lb/>ſextã gr̄a argumēti / et arguo ſic / ī illo īſtãti c. ꝑ te mo­<lb/>tus a. et motus b. ſunt equales: et in principio erant <lb/>equales et equalem latitudinem debent deperdere: <lb/>ergo equalem latitudinem deperdiderunt: et eq̈les <lb/>reſtant ab eis deperdende, et a. in qualibet ſexta ſe­<lb/>quente c. tantã deperdet ſicut in precedēte quia vni­<lb/>formiter deperdet et b. in qualibet ſequēte ſexta mi­<lb/>nus deperdet quã in precedente quia continuo tar-<lb/>dius et tardius deperdit / vt dicit caſus: et in precedē­<lb/>te deperdet tantum ſicut a: igitur in qualibet ſexta <lb/>ſequente c. inſtans b. minus deperdet quã a. ei ante <lb/>c. inſtans equalem latitudinem deperdit: ergo in to­<lb/>to tempore illius hore b. minorem latitudinem de-<lb/>perdit quã a. / quod eſt contra caſum. </s>
              <s xml:id="N1EEC7" xml:space="preserve">Et eodem mo-<lb/>do probabitur iuuamine tamen loci a maiore  b. <lb/>motus in inſtanti non eſt intenſior a c. motu. </s>
              <s xml:id="N1EECE" xml:space="preserve">Et <lb/>ſic patet minor: et per conſequens tota propoſitio. <lb/>               <anchor type="note" xlink:href="note-0153-01" xlink:label="note-0153-01a"/>               </s>
              <s xml:id="N1EEDA" xml:space="preserve">Et hec eſt quiuq̈geſima tertia ↄ̨cluſio calculatoris <lb/>in dicto capitulo de motu locali.               <anchor type="note" xlink:href="note-0153-02" xlink:label="note-0153-02a"/>               </s>
              <s xml:id="N1EEE4" xml:space="preserve">¶ Ex hac pro-<lb/>poſitione ſequitur /  ſi mobile a. moueatur vnifor-<lb/>miter difformiter ab octauo vſ ad quartum per-<lb/>dendo latitudinem motus vt 4. vniformiter conti-<lb/>nuo ī hora et mobile b. moueatur in eadem hora ab <lb/>octauo vſ ad quartum perdendo etiam latitudi-<lb/>nem vt .4. continuo tardius et tardius: tunc ſi a. per­<lb/>tranſeat .6. pedalia b. pertranſibit minus. </s>
              <s xml:id="N1EEF5" xml:space="preserve">Proba­<lb/>tur / quia ſi a. tranſit .6. pedalia illa .6. pedalia. </s>
              <s xml:id="N1EEFA" xml:space="preserve">ſunt <lb/>ſpacium natum tranſiri a gradu medio ipſius mo­<lb/>tus a. vniformiter difformis, et motus b. correſpon­<lb/>det remiſſiori gradui gradu medio: igitur mobile <lb/>b. minus pertranſit quam ſex pedalia. </s>
              <s xml:id="N1EF05" xml:space="preserve">Minor pa-<lb/>tet ex precedenti propoſitione.</s>
            </p>
            <div xml:id="N1EF0A" level="5" n="16" type="float">
              <note position="left" xlink:href="note-0153-01a" xlink:label="note-0153-01" xml:id="N1EF0E" xml:space="preserve">53. cal. ī c. <lb/>de mo. lo</note>
              <note position="left" xlink:href="note-0153-02a" xlink:label="note-0153-02" xml:id="N1EF16" xml:space="preserve">correlar.</note>
            </div>
            <p xml:id="N1EF1C">
              <s xml:id="N1EF1D" xml:space="preserve">Sexta ꝓpoſitio </s>
              <s xml:id="N1EF20" xml:space="preserve">Omnis latitudo mo­<lb/>tus conſimiliter omnino perdita et acq̇ſita vni gra­<lb/>dui omnino correſpondet. </s>
              <s xml:id="N1EF27" xml:space="preserve">Uolo dicere /  ſi ſit ali-<lb/>quis motus qui gratia exempli incipiat a non gra­<lb/>du et intendatur vſ ad octauum in hora adequate <lb/>vniformiter: et alter motus vel idem remittatur in <lb/>hora vniformiter ſicut intendebatur ab octauo vſ <lb/>ad non gradum: tales motus eidem gradui correſ­<lb/>pondet: et ſic exemplificatu in aliis. </s>
              <s xml:id="N1EF36" xml:space="preserve">Probatio hu-<lb/>ius concluſionis facilis eſt quoniam tanta oīno eſt <lb/>latitudo motus in via intenſionis quanta in via re­<lb/>miſſionis quoniam omnino eodem modo intendi-<lb/>tur ſicut remittitur. </s>
              <s xml:id="N1EF41" xml:space="preserve">igitur eidem gradui correſpon­<lb/>det. </s>
              <s xml:id="N1EF46" xml:space="preserve">Et ſic patet iſta propoſitio / que etiam ſuperius <lb/>probata eſt in tractatu de motu penes cauſam.               <anchor type="note" xlink:href="note-0153-03" xlink:label="note-0153-03a"/>               </s>
              <s xml:id="N1EF50" xml:space="preserve">Et <lb/>hec eſt quinquageſima ſexta concluſio calculatoris <lb/>in capitulo preallegato de motu locali. </s>
              <s xml:id="N1EF57" xml:space="preserve">In quo lo-<lb/>co idem calculator facit paruam obiectionem con-               <cb chead="Capitulum tertium"/>               tra hanc concluſionem </s>
              <s xml:id="N1EF5F" xml:space="preserve">Uide eum ibi.</s>
            </p>
            <div xml:id="N1EF62" level="5" n="17" type="float">
              <note position="left" xlink:href="note-0153-03a" xlink:label="note-0153-03" xml:id="N1EF66" xml:space="preserve">.56. cal. ī <lb/>c. ḋ mo. l.</note>
            </div>
            <p xml:id="N1EF6E">
              <s xml:id="N1EF6F" xml:space="preserve">Notanduꝫ eſt quarto / vt ſuperius ta-<lb/>ctum eſt velocitates motuum dupliciter inueſtigari <lb/>poſſe videlicet ex cõmenſuratione ſpaciorum ꝑtran­<lb/>ſitorum: et hoc ab effectu: et a poſteriori quod in p̄-<lb/>ſenti tractatu inquirimus. </s>
              <s xml:id="N1EF7A" xml:space="preserve">Alio vero modo ex cõ-<lb/>menſuratione et proportionalitate proportionum <lb/>a quibus proueniunt velocitates ille: </s>
              <s xml:id="N1EF81" xml:space="preserve">Et cuꝫ aliqua <lb/>ars ab huius ſcientie primoribus tradita ſit ad in­<lb/>ueſtigandas proportiões a quibus velocitates mo­<lb/>tuum proueniunt. </s>
              <s xml:id="N1EF8A" xml:space="preserve">Ideo non abs re aliquas propo­<lb/>ſitiones huic famulantes inueſtigationi pñti operi <lb/>inſerendas cenſui.</s>
            </p>
            <note position="right" xml:id="N1EF91" xml:space="preserve">ↄ̨cluſiõſe <lb/>horen. <lb/>trac. pro­<lb/>por. c. 4.</note>
            <p xml:id="N1EF9B">
              <s xml:id="N1EF9C" xml:space="preserve">Prima propoſitio </s>
              <s xml:id="N1EF9F" xml:space="preserve">Quauis velocita-<lb/>te data: et quacun proportione propoſita: cuiuſ-<lb/>dam artis ingenio inueſtigari poteſt. </s>
              <s xml:id="N1EFA6" xml:space="preserve">an data ve-<lb/>locitas a propoſita proportione: aut a minori aut <lb/>maiore proueniat. </s>
              <s xml:id="N1EFAD" xml:space="preserve">Exemplum / vt data aliqua velo-<lb/>citate que ſit a. cuius proportionem a qua videlicet <lb/>proueniat talis velocitas a. ignoramus: et propoſi­<lb/>ta quauis proportione videlicet dupla: vel tripla <lb/>vel quadrupla inueſtigare et per artem inuenire  <lb/>videlicet talis velocitas a. proueniat a tali propor­<lb/>tione dupla propoſita (exempli gratia) an a maio­<lb/>ri: an a minorl. </s>
              <s xml:id="N1EFBE" xml:space="preserve">Ad cuius probationem ſit illa velo­<lb/>citas a. qua moueatur c. reſiſtentia a b. potētia cu-<lb/>ius proportionem ad c. ignoro: et ſit proportio ꝓ-<lb/>poſita michi nota dupla exempli gratia: tunc ad ī­<lb/>ueſtigandum: et inueniendum: an illa velocitas a. ꝓ­<lb/>ueniat a maiori proportione quã dupla: an a mino­<lb/>ri: an ab equali: capio vnam aliam potentiam que <lb/>ſit d. que ſe habet in proportione dupla ad b. potē­<lb/>tiam: et moueat vtra illarum potentiarum c. reſi­<lb/>ſtentiam: et manifeſtum eſt /  d. velocius mouet c. re­<lb/>ſiſtentiam quam b. </s>
              <s xml:id="N1EFD5" xml:space="preserve">Tūc his ſic poſitis: arguitur ſic / <lb/>vel d. mouet c. reſiſtentiam in duplo velocius quam <lb/>b. moueat eãdem reſiſtētiã: vel magis quã in duplo <lb/>velocius: vel minus. </s>
              <s xml:id="N1EFDE" xml:space="preserve">Si in duplo velocius ſequitur / <lb/> proportio d. ad c. eſt dupla ad proportionem b. <lb/>ad c. </s>
              <s xml:id="N1EFE5" xml:space="preserve">Patet / quia velocitates ſunt duple et talis ꝓ-<lb/>portio componitur ex ꝓportione d. ad b. et b. ad c. / <lb/>vt patet ex quarto capite ſecunde partis: ergo pro­<lb/>portio b. ad c. eſt medietas proportionis d. ad c. / er­<lb/>go reſiduum puta ꝓportio d. ad b. eſt reliqua medi­<lb/>etas et eſt proportio dupla vt poſitum eū: ergo alia <lb/>proportio b. ad c. eſt etiam proportio dupla cum ſit <lb/>alia medietas. </s>
              <s xml:id="N1EFF6" xml:space="preserve">Modo omnes medie-<lb/>tates ſunt equales. </s>
              <s xml:id="N1EFFB" xml:space="preserve">Et ſic inuentum /  illa ē veloci-<lb/>tas a. prouenit a proportione dupla / quod fuit īue­<lb/>ſtigandum. </s>
              <s xml:id="N1F002" xml:space="preserve">Si vero d. poña maior moueat c. reſi-<lb/>ſtentiam magis quam in duplo velocius quã b. / tūc <lb/>ſequitur /  ꝓportio d. ad c. eſt maior quã dupla ad <lb/>ꝓportionē b. ad c. quia velocitas ꝓueniens a pro-<lb/>portione d. ad c. eſt maior ꝙ̄ dupla ad velocitatem <lb/>prouenientem a proportione b. ad c. et proportio d. <lb/>ad c. componit̄̄ adequate ex ꝓportione d. ad b. et b. <lb/>ad c. / ergo proportio b. ad c. eſt minus ꝙ̄ medietas: <lb/>quia alias tota proportio non eſſet maior ꝙ̄ dupla <lb/>ad illam ſui partem: et totum reſiduum puta ꝓpor-<lb/>tio d. ad b. eſt ꝓportio dupla et eſt maius: igitur il-<lb/>la proportio b. ad c. eſt minor dupla / quod a princi­<lb/>pio fuit inueſtigandum. </s>
              <s xml:id="N1F01D" xml:space="preserve">Si autē d. poña maior mo­<lb/>ueat c. reſiſtentiam minus ꝙ̄ in duplo velocius: tūc <lb/>illa proportio d. ad c. eſt minor qnã dupla ad ꝓpor­<lb/>tionem b. ad c. / patet / quia velocitas eſt minor quam <lb/>dupla: et vltra eſt minor quã dupla ad ꝓportioneꝫ <lb/>b. ad c. / ergo illa proportio b. ad c. eſt maior quã me­<lb/>dietas totius ꝓportionis d. ad c. </s>
              <s xml:id="N1F02C" xml:space="preserve">Conſequentia pa­               <pb chead="De motu locali quo ad effectum tempore difformi." file="0154" n="154"/>               tet de ſe: et vltra eſt magis quã medietas: ergo totū <lb/>reſiduuꝫ (quod eſt ꝓportio d. ad b) eſt minus illa ꝓ­<lb/>portione b. ad c. : et illud reſiduum eſt proportio du­<lb/>pla: ergo illa proportio b. ad c. eſt maior ꝓportio <lb/>quã dupla a qua prouenit illa velocitas a. </s>
              <s xml:id="N1F03C" xml:space="preserve">Et ſic ha­<lb/>betur /  velocitas a. prouenit a maiore ꝓportione <lb/>quã dupla / quod a principio fuerat inueſtigandum <lb/></s>
              <s xml:id="N1F044" xml:space="preserve">Et ſic vniuerſaliter probabis propoſita proportio­<lb/>ne vel tripla vel ſexq̇altera vel quauis mutatis mu-<lb/>tandis.</s>
            </p>
            <p xml:id="N1F04B">
              <s xml:id="N1F04C" xml:space="preserve">Secunda propoſitio. </s>
              <s xml:id="N1F04F" xml:space="preserve">Captis duabus <lb/>potentiis inequalibus mouentibus eandem reſiſtē­<lb/>tiam: et ſcita ꝓportione inter illas potentias: ſcita <lb/>etiam proportione in qua maior potentia velocius <lb/>mouet reſiſtentiam quã minor moueat eandem: ar-<lb/>tificio quodam reperitur quanta eſt ꝓportio maio­<lb/>ris potentie ad reſiſtentiam: et etiam minoris potē­<lb/>tie ad eandem reſiſtentiam: </s>
              <s xml:id="N1F060" xml:space="preserve">Exemplum / vt poſito  <lb/>ſortes ſit duple poñe ad platonē: et moueat tam ſor­<lb/>tes quã plato a. mobile: et moueat ſortes illḋ a. mo­<lb/>bile in ſexquialtero velocius platone / tunc volo in-<lb/>ueſtigare / que ꝓportio ſit ſortis ad illam reſiſtētiã <lb/>a. et platonis ad eandem reſiſtentiam. </s>
              <s xml:id="N1F06D" xml:space="preserve">Quod ſic oñ­<lb/>ditur. </s>
              <s xml:id="N1F072" xml:space="preserve">ſortes mouet ī ſexquialtero velocius a. reſiſtē­<lb/>tiam quã plato: ergo ꝓportio ſortis ad a. eſt ſexq̇-<lb/>altera ad ꝓportionem platonis ad idem a. et vltra <lb/>eſt ſexquialtera ad ꝓportionem platonis ad a. / er-<lb/>go ꝓportio platonis ad a. eſt due tertie ꝓportiõis <lb/>ſortis ad a. quia ſemper ſubſexquialterum ad ali-<lb/>quid eſt due tertie illius: et vltra illa ꝓportio plato­<lb/>nis ad a. eſt due tertie ꝓportiones ſortis ad a. / ergo <lb/>totum reſiduum eſt vna tertia totius ꝓportiõis ſor­<lb/>tis ad a. / vt patet de ſe: et totum reſiduum eſt ꝓpor-<lb/>tio ſortis ad platonem dupla nota / vt poſitum eſt / <lb/>quia totalis ꝓportio ſortis ad a. componitur ex ꝓ­<lb/>portiõe ſortis ad platonem: et platonis ad a. / vt pa­<lb/>tet ex quarto capite ſecunde partis: ergo dupla ꝓ-<lb/>portio eſt vna tertia ꝓportionis ſortis ad a. / et ꝑ cõ­<lb/>ſequens tota ꝓportio ſortis ad a. eſt tripla a ꝓpor­<lb/>tionem duplam que eſt vna tertia eius: et ſic eſt pro-<lb/>portio octupla: cum octupla ſit tripla ad duplam / <lb/>vt patet ex ſecunda parte octaua concluſione ſexti <lb/>capitis </s>
              <s xml:id="N1F09B" xml:space="preserve">Iuter termīos em̄ ꝓportionis octuple re-<lb/>periuntur .4. termini cõputatis extremis ↄ̨tinuo ꝓ­<lb/>portionabiles ꝓportioe dupla. </s>
              <s xml:id="N1F0A2" xml:space="preserve">Et ſic habetur / q̄ ꝓ-<lb/>portio ſit ſortis ad a. reſiſtentiam / quod fuit inueſti­<lb/>gandum: et quia ꝓportio platonis ad a. eſt due ter­<lb/>tie ꝓportionis ſortis ad a. que eſt octupla / cõſequēs <lb/>eſt  ſit quadrupla: qm̄ q̈drupla ē due tertie ꝓpor­<lb/>tionis octuple: et ſic habetur que ꝓportio ſit plato-<lb/>nis ad a. / quod a principio extitit ꝑſcrutandum</s>
            </p>
            <p xml:id="N1F0B1">
              <s xml:id="N1F0B2" xml:space="preserve">Tertia proportio </s>
              <s xml:id="N1F0B5" xml:space="preserve">Data quauis potē-<lb/>tia mouente duas reſiſtentias inequales inter quas <lb/>reſiſtentias eſt proportio nota: notū eſt in qua ꝓ­<lb/>portione velocius data potentia moueat minorem <lb/>̄ maiorem: mathematica induſtria ꝓportiões po­<lb/>tentie ad vtram reſiſtentiam quales videlicet exi­<lb/>ſtant inueſtigare licebit vt ſi ſortes proiiciat in ali­<lb/>quo tempore lapidem a. et in eodem vel equali lapi­<lb/>dem b. minorem inter quos lapides eſt ꝓportio no­<lb/>ta gratia argumenti dupla: moueat ſortes illos <lb/>lapides ab eadem virtute: ſit ſcitū /  moueat ſor­<lb/>tes b. lapidem in triplo velocius quã a. lapidē gra­<lb/>tia exempli </s>
              <s xml:id="N1F0D0" xml:space="preserve">Iam inueſtigare intendimus ingenio <lb/>artis mathematice / que eſt illa proportio a qua ſor­<lb/>tes mouet b. lapideꝫ, et que ſit illa a qua moueat a. <lb/>lapidem vtrum videlicet dupla: an tripla: aut aliq̈ <lb/>alia: quia hoc ignotum eſt. </s>
              <s xml:id="N1F0DB" xml:space="preserve">Non enim ſequtiur mo-               <cb chead="De motu locali quo ad effectum tempore difformi."/>               uet in triplo velocius b. quã a. / ergo a ꝓportione tri­<lb/>pla mouet b. </s>
              <s xml:id="N1F0E3" xml:space="preserve">Quando enim aliquid mouet aliud a <lb/>ꝓportione dupla adhuc dabitur aliquid quod ī tri­<lb/>plo tardius in eodem tempore ab eodem mouetur: <lb/>vt ſuperius dictum eſt. </s>
              <s xml:id="N1F0EC" xml:space="preserve">His ſuppoſitis volo inueſti­<lb/>gare a qua ꝓportione ſortes mouet a. lapidem: et <lb/>a qua b. lapidē: et arguo ſic / ſortes in triplo velociꝰ <lb/>mouet b. quã a. / ergo ſequitur /  ꝓpoſtio ſortis ad <lb/>b. lapidem eſt tripla ad ꝓportionem ſortis ad a. la­<lb/>pidē (ſiq̇dē ꝓportio velocitatū ꝓportionē ꝓportio-<lb/>nū inſequatur: et econtra) et vltra ꝓportio ſortis ad <lb/>b. eſt tripla ad ꝓportionem ſortis ad a. / igitur pro-<lb/>portio ſortis ad a. eſt vna tertia totius ꝓportionis <lb/>ſortis ad b. et ꝓportio ſortis ad b. componitur ex ꝓ­<lb/>portione ſortis ad a. et a. ad b. adequate / vt patet in­<lb/>telligenti quartum caput ſecunde partis: et ꝓpor-<lb/>tio ſortis ad a. eſt vna tertia / vt dictum eſt: ergo reſi­<lb/>duum puta ꝓportio a. ad b. ſunt due tertie: et illa ꝓ-<lb/>portio a. ad b. eſt dupla nota / vt poſitum eſt. </s>
              <s xml:id="N1F10B" xml:space="preserve">ergo ꝓ­<lb/>portio dupla eſt dupla ad ꝓportionem ſortis ad a. <lb/>que eſt vna tertia. et dupla due tertie proportionis <lb/>ſortis ad b. </s>
              <s xml:id="N1F114" xml:space="preserve">Modo duarū tertiarum ad vnam ter-<lb/>tiam eſt ꝓportio dupla: </s>
              <s xml:id="N1F119" xml:space="preserve">Et ſic habetur /  illa ꝓpor­<lb/>tio ſortis ad a. qua ſortes mouet a. lapidem eſt ſub­<lb/>dupla ad duplam. </s>
              <s xml:id="N1F120" xml:space="preserve">Eſt enim medietas duple / quod <lb/>erat inquirendum. </s>
              <s xml:id="N1F125" xml:space="preserve">Et ſic ſimiliter habetur /  illa ꝓ­<lb/>portio ſortis ad b. id eſt qua ſortes mouet b. lapidē <lb/>eſt ſexquialtera ad duplam. </s>
              <s xml:id="N1F12C" xml:space="preserve">componitur ex dupla <lb/>a. ad b. et medietate duple ſortis ad a. / quod fuit al-<lb/>terum inueſtigandum.               <anchor type="note" xlink:href="note-0154-01" xlink:label="note-0154-01a"/>               </s>
              <s xml:id="N1F138" xml:space="preserve">¶ Ex hac ꝓpoſitione ſequi-<lb/>tur /  ſi ſortes moueat b. lapidem per tantum ſpa-<lb/>cium quantus eſt diameter quadrati: et a. lapidem <lb/>per tantum ſpacium quanta eſt coſta eiuſdem qua-<lb/>drati: tunc ꝓportio ſortis ad a. lapidem id eſt a qua <lb/>mouet a. lapidem eſt pluſ̄ dupla ad ꝓportionem <lb/>duplam: et proportio qua ſortes mouet b. lapidem <lb/>eſt pluſ̄ tripla ad duplam. </s>
              <s xml:id="N1F149" xml:space="preserve">Quod ſic ꝓbatur: q2 <lb/>tota ꝓportio ſortis ad b. ſe habet ad ꝓportionem <lb/>ſortis ad a. ſicut diameter ſe habet ad coſtam: ergo <lb/>ꝓportio ſortis ad a. eſt ſicut coſta. </s>
              <s xml:id="N1F152" xml:space="preserve">et ꝓportio ſortis <lb/>ad b. eſt ſicut diameter et ſic ꝓportio a. ad b. eſt ſicut <lb/>exceſſus diametri ad coſtam: ſed ille exceſſus eſt mi­<lb/>nor quã ſubduplus ad coſtam: quia coſta cõtinet il-<lb/>lum exceſſum pluſ̄ bis / vt patet ex ſecunda cõcluſio­<lb/>ne et eiuſdem ꝓbatione quarti capitis prime ꝑtis: <lb/>et illa ꝓportio a. ad b. que eſt ſicut exceſſus diame-<lb/>tri ad coſtam eſt ꝓportio dupla / vt poſitum eſt: et eſt <lb/>minus quã ſubdupla ad proportioneꝫ ſortis ad a. / <lb/>vt dictum eſt: igitur ꝓportio ſortis ad a. eſt maior <lb/>quam dupla / quod fuit vnum ꝓbandum. </s>
              <s xml:id="N1F169" xml:space="preserve">Sed  ꝓ-<lb/>portio ſortis ad b. ſit maior quã tripla ad duplam / <lb/>iam pene argutum eſt. </s>
              <s xml:id="N1F170" xml:space="preserve">Componitur enim illa ex ꝓ-<lb/>portione ſortis ad a. que eſt pluſ̄ due duple vt ꝓ-<lb/>batum eſt: et ex ꝓportione a. ad b. dupla: ergo cõpo­<lb/>nitur ex vna dupla: et duabus maioribus dupla a­<lb/>dequate: et ſic cõtinet pluſ̄ tres duplas: conſeq̄ns <lb/>eſt igitur vt ſit illa proportio ſortis ad b. maior ̄ <lb/>tripla ad duplam: qnod fuit alterum inducendum. <lb/>               <anchor type="note" xlink:href="note-0154-02" xlink:label="note-0154-02a"/>               </s>
              <s xml:id="N1F186" xml:space="preserve">¶ Ex quo ſequitur /  illa ꝓportio ſortis ad b. ē pluſ­<lb/>̄ octupla. </s>
              <s xml:id="N1F18B" xml:space="preserve">Eſt enim octupla adequate tripla ad du­<lb/>plam / vt patet ex octaua concluſione ſexti capitis ſe­<lb/>cunde partis: et illa ſortis ad b. maior quam tripla <lb/>ad duplam / vt ꝓbatum eſt: igitur ꝓpoſitum.</s>
            </p>
            <div xml:id="N1F194" level="5" n="18" type="float">
              <note position="right" xlink:href="note-0154-01a" xlink:label="note-0154-01" xml:id="N1F198" xml:space="preserve">.1. correl.</note>
              <note position="right" xlink:href="note-0154-02a" xlink:label="note-0154-02" xml:id="N1F19E" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N1F1A4">
              <s xml:id="N1F1A5" xml:space="preserve">Quarta propoſitio </s>
              <s xml:id="N1F1A8" xml:space="preserve">Data quauis velo­<lb/>citate: quauiſ ſignata ꝓportione: arithmetico ap­<lb/>paratu an ꝓportio a qua ꝓuenit illa velocitas pro­<lb/>portioni ſignate cõmenſurabilis exiſtat an nõ ope­<lb/>re preciū erit īueſtigare. </s>
              <s xml:id="N1F1B3" xml:space="preserve">vt eſto /  ſortes moueat a. <lb/>lapidem velocitate b. </s>
              <s xml:id="N1F1B8" xml:space="preserve">et ignotum ſit a qua propor-               <pb chead="Secundi tractatus" file="0155" n="155"/>               tiõe mouet ſortes ſiue ꝓueniat illa velocitas b. et ꝓ­<lb/>ponitur ſiue ſignatur proportio ſexquialtera: tunc <lb/>arithmeticis principiis īueſtigare poſſumus an ꝓ­<lb/>portio ſortis ad a. a qua prouenit velocitas b. ſit ꝓ­<lb/>portioni ſexquialtere ꝓpoſite et ſignate cõmenſura­<lb/>bilis nec ne. </s>
              <s xml:id="N1F1CA" xml:space="preserve">Quo inueſtigatur iſto modo: capio <lb/>vnum lapidem qui ſit c. ſubſexquialterum ad a. la-<lb/>pidem: et moueat ſortes in eodem tempore vel equa­<lb/>li ab eadem virtute a. et c. / tunc arguitur ſic / vel ſpaci­<lb/>um per quod ſortes in illo tempore mouet c. eſt com­<lb/>menſurabile ſpacio per quod mouet a. in eodem tē­<lb/>pore, vel nõ. </s>
              <s xml:id="N1F1D9" xml:space="preserve">Si nõ iã illa ſpacia ſe habebunt in ali­<lb/>qua ꝓportione irrationali et ſic proportio ſexqui-<lb/>altera erit irrationalis ꝓportioni a qua prouenit <lb/>velocitas b. que eſt ſortis ad a. </s>
              <s xml:id="N1F1E2" xml:space="preserve">Quod probatur ſic / <lb/>quia ſi illa ſpacia ſint incõmenſnrabilia / conſeq̄ns <lb/>eſt /  proportiones a quibus proueniunt ſint incõ-<lb/>menſurabiles. </s>
              <s xml:id="N1F1EB" xml:space="preserve">ſed proportiones a quibus proueni­<lb/>unt ſunt ſortis ad a. et ſortis ad c. / igitur proportio <lb/>ſortis ad c. eſt incõmenſurabilis ꝓportioni ſortis <lb/>ad a. minori proportione ſortis ad c. / igitur exceſſus <lb/>qua proportio ſortis ad c. excedit ꝓportionem ſor­<lb/>tis ad a. eſt incõmenſurabilis proportiõi ſortis ad <lb/>a. </s>
              <s xml:id="N1F1FA" xml:space="preserve">Probatur hec conſequentia per hanc maximaꝫ. <lb/></s>
              <s xml:id="N1F1FE" xml:space="preserve">Quandocun duo ſunt incõmenſurabilia exceſſus <lb/>quo maius illorum excedit minus eſt etiam incõmē­<lb/>ſurabilis minori / vt ꝓbatuꝫ eſt in prima parte hu­<lb/>ius operis de exceſſu diametri ad coſtam quarto ca­<lb/>pite ſuppoſitione quarta: ſaltem ex modo proban­<lb/>di illius ſuppoſitiõis patet. </s>
              <s xml:id="N1F20B" xml:space="preserve">Sed proportio ſortis <lb/>ad c. eſt incõmenſurabilis proportioni ſortis ad a. <lb/>et excedit proportionem ſortis ad a. per proportio­<lb/>nem a. ad c. ſexquialteram: ergo ꝑ datam maximaꝫ <lb/>proportio ſexquialtera eſt incõmenſurabilis ꝓpor­<lb/>tioni ſortes ad a. a qua prouenit velocitas b. / quod <lb/>fuit vnum inducenduꝫ. </s>
              <s xml:id="N1F21A" xml:space="preserve">Si vero ſpacia illa videlicet <lb/>ꝑ que ſortes mouet c. et mouet a. ſint commenſurabi­<lb/>lia: ſequitur /  propoitio ſexquialtera ꝓpoſita eſt <lb/>cõmenſurabilis proportioni ſortis ad a. a qua pro­<lb/>uenit b. velocitas </s>
              <s xml:id="N1F225" xml:space="preserve">Qḋ ſic probatur / quia ſi illa ſpa-<lb/>cia ſunt cõmenſurabilia ſint illa cõmenſurabilia.</s>
            </p>
            <p xml:id="N1F22A">
              <s xml:id="N1F22B" xml:space="preserve">argumenti gratia proportione dupla. / et ſequitur / <lb/> proportio ſortis ad c. eſt dupla ad proportioneꝫ <lb/>ſortis ad a. </s>
              <s xml:id="N1F232" xml:space="preserve">Cõſequentia ſepius arguta eſt: ergo ſe­<lb/>quitur /  illa ꝓportio ſortis ad a. eſt medietas eius / <lb/>et per conſequens totum reſiduum / quod eſt propor­<lb/>tio a. ad c. eſt alia medietas: ſed totum reſiduum eſt <lb/>proportio ſexquialtera. / ergo proportio ſexquialte­<lb/>ra eſt medietas illius ꝓportionis ſortis ad c. et alia <lb/>medietas eſt proportio ſortis ad a. a qua prouenit <lb/>velocitas b. / ergo ſequitur /  illa ꝓportio ſortis ad <lb/>a. a qua prouenit velocitas b. eſt equalis proportio­<lb/>ni ſexquialtere: et ſic probabis ꝑticulariter in omni­<lb/>bus: </s>
              <s xml:id="N1F249" xml:space="preserve">Sed vniuerſaliter probabitur ſic / proportio <lb/>ſortis ad c. eſt cõmenſurabilis ꝓportioni ſortis ad <lb/>a. a qua prouenit velocitas b. et proportio ſortis ad <lb/>c. excedit proportionem ſortis ad a. etc̈. per propor­<lb/>tionem a. ad c. ſexquialteram adequate: igitur pro­<lb/>portio illa a. ad c. ſexquialtera eſt cõmenſurabilis <lb/>ꝓportioni ſortis ad a. / quod fuit inducendum. </s>
              <s xml:id="N1F258" xml:space="preserve">Con­<lb/>ſequentia patet ꝑ hanc maximam </s>
              <s xml:id="N1F25D" xml:space="preserve">Quotienſcun <lb/>duo inequalia ſunt cõmenſurabilia exceſſus maio-<lb/>ris ſupra minus eſt ipſi minori cõmenſurabilis: qm̄ <lb/>eſt pars aliquota vel ꝑtes aliquote vtriuſ / vt pa-<lb/>tet ex ſexta ſuppoſitione q̈rti capitis ſecunde par-<lb/>tis. </s>
              <s xml:id="N1F26A" xml:space="preserve">Sed in ꝓpoſito ꝓportio illa ſexquialtera a. ad <lb/>c. eſt exceſſus quo proportio ſortis ad c. excedit pro­<lb/>portionem ſortis ad a. a qua prouenit b. velocitas: <lb/>ergo proportio ſexquialtera cõmenſurabilis eſt pro­               <cb chead="Capitulum tertium"/>               portioni ſortis ad a. a qua prouenit velocitas b. / qḋ <lb/>fuit inducendum.               <anchor type="note" xlink:href="note-0155-01" xlink:label="note-0155-01a"/>               </s>
              <s xml:id="N1F27D" xml:space="preserve">¶ Et hee quatuor cõcluſiones (ne <lb/>alienis ſpoliis triumphare videamur) ex officina et <lb/>ꝑſpicaci minerua doctiſſimi magiſtri Nicolai ho-<lb/>horen deprompte ſunt et excerpte quas in ſuo trac-<lb/>tatu proportionum quarto capite ſuis fulcimētis <lb/>et probationibus mathematicis reperies munitas <lb/></s>
              <s xml:id="N1F28B" xml:space="preserve">¶ Exactis notabilibus et ex conſequenti parte huiꝰ <lb/>corporis noſtre queſtionis abſoluta ad ſecundaꝫ ꝑ­<lb/>tem accedendum eſt in qua multe et egregie conclu-<lb/>ſiones (quibus medieantibus queſtio diſſoluetur) ꝓ­<lb/>babūtur: at inducentur</s>
            </p>
            <div xml:id="N1F296" level="5" n="19" type="float">
              <note position="right" xlink:href="note-0155-01a" xlink:label="note-0155-01" xml:id="N1F29A" xml:space="preserve">Nicolaꝰ <lb/>horem.</note>
            </div>
            <p xml:id="N1F2A2">
              <s xml:id="N1F2A3" xml:space="preserve">Prima concluſio </s>
              <s xml:id="N1F2A6" xml:space="preserve">Diuiſo aliquo cor-<lb/>pore ſiue latitudine ꝑ partes ꝓportionales quauis <lb/>libuerit ꝓportione: totum illud corpus ſiue latitu-<lb/>do ſe habet ad reſiduum a prima ꝑte proportionali <lb/>in ea proportione q̈ ipſum ſiue latitudo ipſa diui-<lb/>ditur. </s>
              <s xml:id="N1F2B3" xml:space="preserve">Hec eſt prima et fundamentalis concluſio cui <lb/>innuitur quintum caput prime partis huius ope-<lb/>ris vide eam ibi.</s>
            </p>
            <p xml:id="N1F2BA">
              <s xml:id="N1F2BB" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N1F2BE" xml:space="preserve">Diuiſo aliquo tē­<lb/>pore per partes ꝓportionales quauis ꝓportione: <lb/>et ſit aliquod mobile quod aliquãta velocitate mo-<lb/>ueatur in prima parte ꝓportionali et in ſecunda in <lb/>duplo maiori ꝙ̄ in prima: et in tertia in triplo ma-<lb/>iori ꝙ̄ in prima: et in quarta in quadruplo maiori / <lb/>et ſic conſequenter aſcendendo per omnes ſpecies <lb/>proportionis multiplicis: talis velocitas totius il­<lb/>lius temporis et omnium illarum partium propor­<lb/>tionalium ſe habet ad velocitatem prime partis ꝓ­<lb/>portionalis in ea proportione in qua ſe habet to-<lb/>tum illud tempus ſic diuiſuꝫ in ordine ad primam <lb/>partem proportionalem. </s>
              <s xml:id="N1F2D9" xml:space="preserve">vt ſi illud tp̄s diuiſim fue­<lb/>rit in partes proportionales ꝓportione ſexquial-<lb/>tera: et velocitates illarum partium proportiona-<lb/>lium diſponantur modo quo ponit concluſio: tunc <lb/>dico /  totalis illa velocitas totius illius temporis <lb/>adequate ſe habet ad velocitatem prime partis ꝓ-<lb/>portionalis in proportione tripla. </s>
              <s xml:id="N1F2E8" xml:space="preserve">ex eo  totū tē-<lb/>pus diuiſuꝫ ꝑ partes proportionales proportione <lb/>ſexquialtera ſe habet ad primam proportionalem <lb/>in proportiõe tripla. </s>
              <s xml:id="N1F2F1" xml:space="preserve">Eſt enim ṗma pars vna tertia <lb/>totius / vt oſtendit quarta cõcluſio quinti capituli p̄­<lb/>me partis huius operis. </s>
              <s xml:id="N1F2F8" xml:space="preserve">Probatur tamen vniuer­<lb/>ſaltter hec cõcluſio. </s>
              <s xml:id="N1F2FD" xml:space="preserve">et ſuppono /  quando velocita-<lb/>tes ſe habent eo mõ q̊ textꝰ cõcluſionis pretēdit tūc <lb/>ꝑ totū tp̄s extendit̄̄ illa velocitas / q̄ extendit̄̄ ꝑ ṗmã <lb/>partem proportionalem, et ꝑ totum reſiduū a prīa <lb/>extenditur tanta adequate nõ cõicans cum prima ꝑ <lb/>totum corpus extenſa, et per totum reſiduum a pri-<lb/>ma et ſecunda ꝑte proportionali iterum extenditur <lb/>tanta velocitas adequate nõ cõmunicans cum aliq̈ <lb/>precedeutinm: et ſic cõſequenter. </s>
              <s xml:id="N1F310" xml:space="preserve">Hec ſuppoſitio pa­<lb/>tet manifeſte intuenti: qm̄ ſi velocitas ſecunde par-<lb/>tis ꝓportiõalis ē dupla ad velocitatē prīe et tertie <lb/>tripla etc. ſcḋa ipſa ↄ̨tinet bis tã intenſã velocitatē <lb/>ſicut ē prīa nõ cõmunicãtē: et tertia pars cõtinet ter <lb/>tantam: et ſic cõſequenter. </s>
              <s xml:id="N1F31D" xml:space="preserve">et per conſequens reſidu­<lb/>um a prima continet vniformiter bis tantam velo­<lb/>citatem ſicut eſt prima (quãuis nõ adequate. </s>
              <s xml:id="N1F324" xml:space="preserve">Conti­<lb/>net enim adhuc maiorem) et reſiduum a ſecunda ꝑ-<lb/>te proportionaliter tantaꝫ per totum quamuis in­<lb/>adequate: et ſic conſequenter ſemper ille partes ex-<lb/>cedunt ſe continuo per equalem velocitatem veloci­<lb/>tati prime partis ꝓportionalis. </s>
              <s xml:id="N1F331" xml:space="preserve">Hoc ſuppoſito</s>
            </p>
            <p xml:id="N1F334">
              <s xml:id="N1F335" xml:space="preserve">Probatur cõcluſio et volo /  hora ſit diuiſa ꝑ par-<lb/>tes ꝓportionales aliq̈ proportione (quauis libue-<lb/>rit) que ſit g. et coextēdantur ille velocitates / vt dicit               <pb chead="De motu locali quo ad effectū tempore difformi." file="0156" n="156"/>               caſus concluſionis per illas partes proportiona-<lb/>les et ſit proportio totius hore diuiſe per partes <lb/>proportionales proportione g. ad primam parteꝫ <lb/>proportionalem f. / tunc dico /  tota illa velocitas <lb/>totius hore ſe habet in proportione f. ad propor-<lb/>tionem prime partis proportionalis. </s>
              <s xml:id="N1F34B" xml:space="preserve">Quod pro-<lb/>bo ſic: quia velocitas equalis velocitate prime par­<lb/>tis proportionalis extenſa per illam horam ali-<lb/>quid facit ad intenſionem totius velocitatis: quia <lb/>eſt pars eius / vt oſtendit ſuppoſitio p̄cedens: et tan­<lb/>ta velocitas ſicut illa ſuperaddita preexiſtenti ex-<lb/>tenditur per totum reſiduum a prima parte pro-<lb/>portionali proportione g. / vt etiam dicit ſuppoſi-<lb/>tio: igitur illa in g. proportione minus facit / quia <lb/>eſt equalis alteri extenſe per totum, et eſt in tempo­<lb/>re in g. proportione minori / vt dicit prima conclu-<lb/>ſio, quia tempus diuiditur proportione g. / ergo to­<lb/>tum ſe habet ad reſiduum a prima parte propor-<lb/>tionali in g. proportione. </s>
              <s xml:id="N1F368" xml:space="preserve">Item per totum reſiduū <lb/>a prima parte proportionali et ſecunda extenditur <lb/>iterum tanta velocitas non communicans cum a-<lb/>liqua precedentium: et illud tempus reſiduum a pri­<lb/>ma et ſecunda ſe habet in g. proportione ad totum <lb/>reſiduum a prima: igitur illa velocitas ei coextēſa <lb/>in g. proportione minus denominat quam prece-<lb/>dens velocitas equalis ei coextenſa ſubiecto in g. <lb/>proportione maiori / et ſic conſequenter: igitur de-<lb/>nominatio totius illius velocitatis componitur ex <lb/>infinitis continuo ſe habentibus in proportione g: <lb/>ergo illa denominatio totius velocitatis ſiue illa <lb/>tota velocitas (quod pro eodem capio) ſe habet ad <lb/>primam illarum denominationum ſiue velocitatū <lb/>que eſt prime partis proportiõalis et etiam totius <lb/>reſidui a prima, in proportione f. / quod fuit infercn­<lb/>dum. </s>
              <s xml:id="N1F38B" xml:space="preserve">Patet hec conſequentia: quia ſemper quan-<lb/>do aliquid diuiditur proportione g. ipſum ſe ha-<lb/>bet ad primã partē proportionalem in ꝓportione <lb/>f. / vt poſitum eſt. </s>
              <s xml:id="N1F394" xml:space="preserve">Et ex hoc patet /  in caſu concluſio­<lb/>nis tota velocitas ſe habet ad velocitatē prime par­<lb/>tis proportiõalis in ea proportione in qua habet <lb/>totum tempus in ordine od primam partem pro-<lb/>portionalē proportione qua diuiditur ipſum tem-<lb/>pus / quod fuit probandum.</s>
            </p>
            <p xml:id="N1F3A1">
              <s xml:id="N1F3A2" xml:space="preserve">Tertia cõcluſio. </s>
              <s xml:id="N1F3A5" xml:space="preserve">Diuiſa hora vel tem­<lb/>pore aliquo quauis proportiõe f. volueris: et in pri-<lb/>ma parte proportionali talis proportionis mobi­<lb/>le aliquod moueatur adequate certa velocitate, et <lb/>aliud mobile vĺ idē in tota illa hora vel tēpore mo-<lb/>ueatur eadem velocitate: tunc in quacun propor-<lb/>tione ſe habuerit tempus ad primam partem pro-<lb/>portionalem: in ea proportione ſe habebit ſpaciū <lb/>abſolutum ſiue pertranſitum in toto tempore ad <lb/>ſpacium pertranſitum in prima parte proportio-<lb/>nali: vt ſi aliquod mobile moueatur velocitate vt .2. <lb/>in prima parte proportiõali hore proportione tri-<lb/>pla, et aliud vel idem mobile moueatur in tota ho-<lb/>ra adequate eadem velocitate vt .2. / tūc dico /  illud <lb/>mobile quod mouetur iu tota hora velocitate vt: 2. <lb/>vel correſpondente ei: ſexquialterum ſpacium per-<lb/>tranſit ad ſpacium pertranſitum velocitate vt .2. in <lb/>prima parte proportionali quoniam omne totum <lb/>diuiſum per partes proportionales proportione <lb/>tripla ſe habet ad primam partem proportiona-<lb/>lem in proportione ſexquialtera / vt patet ex primo <lb/>correlario ſecunde concluſionis quinti capitis pri­<lb/>me partis. </s>
              <s xml:id="N1F3D4" xml:space="preserve">Probatur tamen facile hec concluſio: <lb/>quoniam quãdo velocitas eſt vniformis in aliquo <lb/>tempore, ipſa diuiditur in eaſdem partes propor­<lb/>tionales in quas diuiditur tempus / vt patet in phi­               <cb chead="De motu locali quo ad effectū tempore difformi."/>               <anchor type="note" xlink:href="note-0156-01" xlink:label="note-0156-01a"/>               loſopho ſexto phiſicorū vbi inquit ꝓ motus et ma-<lb/>gnitudo pertranſita perinde at tempus diuidi-<lb/>tur: ergo quancun proportionem habebit totum <lb/>tempus ad primam partem proportionalem: ean-<lb/>dem habet velocitas: et per conſequens totum ſpa-<lb/>cium pertranſitum in toto tempore ad ſpaciū per-<lb/>tranſitum in prima parte. </s>
              <s xml:id="N1F3F1" xml:space="preserve">Patet hec conſequen-<lb/>tia ex prima concluſione ſecundi notabilis. </s>
              <s xml:id="N1F3F6" xml:space="preserve">In ca-<lb/>ſu enim velocitas equales inequalibus coexten-<lb/>duntur temporibus / ergo ſpacia ſe habent in pro-<lb/>portione temporum: ſed minus tempus eſt prima <lb/>pars proportionalis, et tempus maius eſt totum <lb/>diuiſum in partes proportionales: ergo ſpacium <lb/>pertranſirum in toto tempore ſe habet ad ſpacium <lb/>pertranſituꝫ in prima parte proportionali ſicut ſe <lb/>habet totum tempus ad primam partem propor-<lb/>tionalem eius / quod fuit probandum.</s>
            </p>
            <div xml:id="N1F40B" level="5" n="20" type="float">
              <note position="right" xlink:href="note-0156-01a" xlink:label="note-0156-01" xml:id="N1F40F" xml:space="preserve">pḣus .6. <lb/>phiſicoꝝ.</note>
            </div>
            <p xml:id="N1F417">
              <s xml:id="N1F418" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N1F41B" xml:space="preserve">Diuiſa hora qua-<lb/>uis proportione volueris in partes proportiona-<lb/>les: et in prima illarum partium proportionalium <lb/>mobile aliquod aliquanta velocitate moueatur, et <lb/>in ſecunda in duplo maiori velocitate ꝙ̄ in prima: <lb/>et in tertia in triplo maiori ꝙ̄ in prima, et ſic con-<lb/>ſequenter: tunc illo caſu totalis velocitas ſe habe-<lb/>bit ad velocitatem prime partis proportionalis <lb/>in ea proportione in qua ſe habebit totum tempus <lb/>ad primam partem proportionalem eius: et ſpa-<lb/>cium in toto tempore adequate pertranſitum ſe <lb/>habebit ad ſpaciū abſolutum in prima parte pro-<lb/>portionali in proportione duplicata. </s>
              <s xml:id="N1F436" xml:space="preserve">Uolo dicere / <lb/> ſi hora diuidatur modo poſito in concluſione et <lb/>exempli gratia diuidatur proportione ſexquialte-<lb/>ra: et moueatur mobile per illas partes propor-<lb/>tionales proportione ſexquialtera / vt dicit caſus <lb/>concluſionis: tunc totalis velocitas talis motus <lb/>ſe habebit ad velocitatem prime partis proporti-<lb/>onalis in proportione tripla: quia ſic ſe habet to-<lb/>tum diuiſum proportione ſexquialtera ad primaꝫ <lb/>partem proportionalem / vt patet ex quarta conclu­<lb/>ſione quinti capitis prime partis: et ſpacium per-<lb/>tranſitum in tota hora ad ſpacium pertranſitum <lb/>in prima parte proportiõali ſe habet in ꝓportio-<lb/>ne dupla ad triplam: quia tripla eſt proportio ve-<lb/>locitatum. </s>
              <s xml:id="N1F455" xml:space="preserve">Modo illa proportio tripla ad duplaꝫ <lb/>eſt noncupla / vt patet ex octaua concluſione ſexti <lb/>capitis ſecūde partis. </s>
              <s xml:id="N1F45C" xml:space="preserve">Et ſic ſi ꝑtranſit vnū pedale <lb/>in ṗma parte ꝓportiõali: nouē ꝑtrãſit in tota hora <lb/></s>
              <s xml:id="N1F462" xml:space="preserve">Demõſtratur concluſio ſic: ſit vnum mobile quod <lb/>adequate moueatur velocitate prime partis pro-<lb/>pprtionalis per primam partem proportionalem <lb/>dumtaxat, et tranſeat ſpacium c. et aliud mobile <lb/>moueatur per totam horam velocitate prime par-<lb/>tis proportionalis. </s>
              <s xml:id="N1F46F" xml:space="preserve">et pertranſeat ſpacium b. et <lb/>tertiū mobile moueatur per totam horam totali <lb/>illa velocitate ſicut ponitur in caſu concluſiõis que <lb/>ſe habet in f. proportione ad velocitatē prime par-<lb/>tis proportionalis: in qua f. proportione ſe habet <lb/>totum tempus ad primam partē eius proportio-<lb/>nalē / vt dicit ſecunda concluſio et prima pars hu-<lb/>ius concluſionis: et pertranſeat ſpacium a. / et argui­<lb/>tur ſic / ſpacii a. ad ſpacium b. eſt f. proportio: quo-<lb/>niã tempora in quibus pertranſeuntur ſunt equa-<lb/>lia: et velocitas qua pertranſitur a. in f. proporti-<lb/>one eſt maior velocitate qua pertraſitur b. / vt patet <lb/>ex caſu. </s>
              <s xml:id="N1F48A" xml:space="preserve">Et etiam ſpaci b. ad ſpacium c. eſt propor-<lb/>tio f. et a. eſt ſpacium pertranſitum in tota hora <lb/>in caſu concluſionis: et c. pertranſitum in prima <lb/>parte proportionali: igitux propoſitum. </s>
              <s xml:id="N1F493" xml:space="preserve">Maior <lb/>patet ex ſecunda propoſitione ſecundi notabilis               <pb chead="Secundi tractatus" file="0157" n="157"/>               huius capitis. </s>
              <s xml:id="N1F49D" xml:space="preserve">Et minor ex ſecunda parte prime <lb/>propoſitionis eiuſdem notabilis.</s>
            </p>
            <p xml:id="N1F4A2">
              <s xml:id="N1F4A3" xml:space="preserve">¶ Alio modo et breuiꝰ demonſtratur concluſio ſic: <lb/>velocitatis totius hore ad velocitatem prime par-<lb/>tis proportionalis eſt proportio f. et temporis to-<lb/>tius hore quod eſt maius ad tempus prime partis <lb/>proportionalis eſt etiam f. proportio: ergo ſpacii <lb/>pertranſiti in tota hora ad ſpacium pertranſitum <lb/>in prima parte proportionali eſt proportio com-<lb/>poſita ex duplici proportione f. / et per conſequens <lb/>ſpacium pertranſitum in tota hora ad ſpaciū per­<lb/>tranſitū in prima parte proportionali eſt propor-<lb/>tio dupla ad proportionem velocitatum que eſt f. <lb/></s>
              <s xml:id="N1F4BB" xml:space="preserve">Patet tamen conſequentia ex tertia propoſitione <lb/>ſecundi notabilis huius capitis.</s>
            </p>
            <note position="left" xml:id="N1F4C0" xml:space="preserve">1. correĺ.</note>
            <p xml:id="N1F4C4">
              <s xml:id="N1F4C5" xml:space="preserve">¶ Ex his concluſionibus ſequitur primo:  diuiſa <lb/>hora per partes proportionales proportione mul­<lb/>tiplici, ſiue dupla, ſiue tripla, ſiue quadrupla, ſiue <lb/>quauis alia multiplici: et in prima parte proporti-<lb/>onali aliquod mobile moueatur aliquantulum, et <lb/>ī ſcḋa in duplo maiori velocitate ꝙ̄ in ṗma: et ī ṫcia <lb/>in triplo ꝙ̄ in prima / vt precedentis theorematis <lb/>caſus oſtendit: totius illius velocitatis ad velo-<lb/>citatem prime partis proportionalis erit propor-<lb/>tio dupla, ſi diuiſio facta fuerit proportiõe dupla: <lb/>et ſexquialtera ſi tripla: et ſexquitertia ſi quadru-<lb/>pla: et ſic in infinitum aſcendendo ſeriatim per ſpe-<lb/>cies proportiõis ſuperparticularis et multiplicis. <lb/></s>
              <s xml:id="N1F4E1" xml:space="preserve">et ſpacli pertranſiti in tota hora ad ſpacium per-<lb/>tranſituꝫ in prima parte eſt proportio quadrupla <lb/>que eſt dupla ad duplam et hoc ſi fiat diuiſio par-<lb/>tium proportionalium proportione dupla: ſi vero <lb/>fiat proportione tripla: ſpacii pertranſiti in tota <lb/>hora ad ſpacium pertranſitum in prima parte erit <lb/>proportio dupla ad ſexquialteram que eſt dupla <lb/>ſexquiquarta: ſi vero fiat diuiſio proportione qua­<lb/>drupla: tunc ſpacii pertranſiti in tota hora ad ſpa­<lb/>cium pertranſitum in prima parte proportionali <lb/>erit proportio dupla ad ſexquitertiam que eſt ſu-<lb/>pra ſeptipartiens nonas: et ſi fiat diuiſio proporti-<lb/>one quintupla: tunc totius ſpacii ad ſpacium per-<lb/>tranſitū in prima parte proportionali eſt propor-<lb/>tio dupla ad proportioneꝫ ſexquiquartam que eſt <lb/>proportio ſupra nonipartiens ſexdecimas: et ſic in <lb/>infinitum duplicando proportionem velocitatum. <lb/></s>
              <s xml:id="N1F505" xml:space="preserve">Prima pars huius correlarii patet ex ſecūda con­<lb/>cluſione manifeſte et ſecunda pars eiuſdem ex quar­<lb/>ta: et applica ſi potes               <anchor type="note" xlink:href="note-0157-01" xlink:label="note-0157-01a"/>               </s>
              <s xml:id="N1F511" xml:space="preserve">¶ Sequitur ſecundo particu-<lb/>lariter /  diuiſa hora per partes proportionales <lb/>proportione ſextupla: et in prima illarū moueatur <lb/>aliquod mobile aliquanta velocitate, et in ſecunda <lb/>in duplo maiori, et in tertia in triplo, modo ſepi-<lb/>us recitato: tunc totius velocitatis ad velocitatem <lb/>prime partis proportionalis eſt proportio ſexqui­<lb/>quinta: et ſpacii pertranſiti in tota hora ad ſpaciū <lb/>pertranſitū in prima parte proportionali eſt pro-<lb/>portio ſupra vndecimpartiens viceſimas quintas <lb/></s>
              <s xml:id="N1F527" xml:space="preserve">Probatur prima pars huius correlarii: quia velo­<lb/>citate ita ſe habente vt ponitur: totalis velocitas <lb/>ex omniū partium velocitatibus conſurgens ſe ha­<lb/>bet ad velocitateꝫ prime partis proportionalis in <lb/>proportione in qua ſe habet totum tempus ad pri­<lb/>mam partem proportionalem / vt patet ex ſecunda <lb/>concluſione: ſed hora diuiſa per partes proporti-<lb/>onales proportione ſextupla ſe habet ad primam <lb/>partem proportionalē in proportione ſexquiquin­<lb/>ta / vt docet quītum capitulum prime partis huius <lb/>operis: igitur tota illa velocitas ſe habet ad velo-               <cb chead="Capitulū tertiū."/>               citatē prime patis proportionalis in proportione <lb/>ſexquiquinta / quod fuit probandum. </s>
              <s xml:id="N1F543" xml:space="preserve">Sed iam pro­<lb/>batur ſecunda pars: quia proportio ſupra vndecī-<lb/>patiēs viceſimas quintas eſt dupla ad proportio-<lb/>nem ſexquiquītam / vt patet in his terminis .36.30. <lb/>25. iuuamine ſexti capitis ſecunde partis huiꝰ ope-<lb/>ris: igitur ſpacium pertranſitum in tota hora ad <lb/>ſpacium pertranſitum in parte ꝓportionali ſe ha-<lb/>bet in proportione ſupra vndecimpartiente viceſi-<lb/>maſquintas. </s>
              <s xml:id="N1F556" xml:space="preserve">Patet hec conſequentia ex quarta cõ­<lb/>cluſione.               <anchor type="note" xlink:href="note-0157-02" xlink:label="note-0157-02a"/>               </s>
              <s xml:id="N1F560" xml:space="preserve">¶ Sequitur tertio /  diuiſa hora per par­<lb/>tes proportionales proportione octupla: et in eiſdē <lb/>moueatur aliquod mobile modo pluries reſūpto <lb/>totius velocitatis ad velocitatē prime partis pro-<lb/>portionalis eſt ꝓportio ſexquiſeptima: et ſpacii ꝑ-<lb/>tranſiti in tota hora ad ſpacium pertranſitum in <lb/>prima parte proportionnali erit proportio dupla <lb/>ad ſexquiſeptima que eſt ſuper quindecimpartiens <lb/>quadrageſimas: cuiuſmodi eſt .9. cū ſeptima ad .7. <lb/>et .64. ad .49. </s>
              <s xml:id="N1F575" xml:space="preserve">Probatur prima pars correlarii: <lb/>quia hora ſic diuiſa per partes proportiõales pro­<lb/>portione octupla ſe habet ad primaꝫ partem pro-<lb/>portionalem in proportione ſexquiſeptima / vt ptꝫ <lb/>ex quīto capite prime partis huiꝰ operis: et in eadē <lb/>proportione ſe debet habere velocitas totiꝰ ad ve-<lb/>locitatem prime partis / vt dicit ſecunda concluſio: <lb/>igitur propoſitum. </s>
              <s xml:id="N1F586" xml:space="preserve">Secunda pars probatur: quia <lb/>proportio ſupra quindecimpartiens quadrageſi-<lb/>maſnonas eſt dupla ad proportionem ſexquiſepti­<lb/>mam / vt patet in his terminis .64.56. et .49. patro­<lb/>cinio ſexti capitis ſecunde partis: igitur in ſupra-<lb/>quīdecimpartiens quadrageſimaſnonas ſe habet <lb/>ſpacium pertranſitū in tota hora ad ſpacium per-<lb/>tranſitum in prima parte proportiõali / quod fuit <lb/>probandum. </s>
              <s xml:id="N1F599" xml:space="preserve">Patet tamen conſequentia: ex quar-<lb/>ta concluſione. </s>
              <s xml:id="N1F59E" xml:space="preserve">¶ Ex hoc modo poteris inferre in-<lb/>nita correlaria ſimilia retento caſu velocitatis et <lb/>variando continuo diuiſionē hore, que omnia cor-<lb/>relaria ſuffragantibus ſeēunda et quarta conclu-<lb/>ſionibus facilem ſortiuntur demonſtrationem.</s>
            </p>
            <div xml:id="N1F5A9" level="5" n="21" type="float">
              <note position="left" xlink:href="note-0157-01a" xlink:label="note-0157-01" xml:id="N1F5AD" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0157-02a" xlink:label="note-0157-02" xml:id="N1F5B3" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N1F5B9">
              <s xml:id="N1F5BA" xml:space="preserve">Quinta concluſio generi proportiõis <lb/>ſuperparticularis ſpeciebuſ eius deſeruiens. </s>
              <s xml:id="N1F5BF" xml:space="preserve">Di­<lb/>uiſa hora per partes proportionales proportiõe <lb/>ſuperparticulari ſexquialtera, ſexquiquarta, ſeu <lb/>quauis alia ſuperparticulari: diſtributa veloci-<lb/>tate partibus illis proportionalibus ita vt mobi-<lb/>le in prima illarum moueatur aliqnantulum, et in <lb/>ſecunda in duplo velocius, et in tertia in triplo ve-<lb/>locius ꝙ̄ in prima, et ſic conſequenter in caſu ſepiꝰ <lb/>repetito: tunc tota velocitas ſe habet ad velocita-<lb/>tem prime partis proportionalis in proportione <lb/>tripla ſi fuerit hora diuiſa in proportione ſexqui-<lb/>altera. </s>
              <s xml:id="N1F5D8" xml:space="preserve">ſi vero fuerit diuiſa in proportione ſexqui-<lb/>tertia: in proportione quadrupla: ſi in proportio-<lb/>ne ſexquiquarta: in proportione quintupla. </s>
              <s xml:id="N1F5DF" xml:space="preserve">et ſic cõ­<lb/>ſequenter aſcendendo ſeriatim per ſpecies propor­<lb/>tionis ſuperparticularis et multiplicis. </s>
              <s xml:id="N1F5E6" xml:space="preserve">Et ſpacia <lb/>pertranſita in totali tempore ad ſpacia prime par­<lb/>tis proportionalis ſe habent in proportione du-<lb/>plicata (duplicata inquam ad triplam ſiue dupla <lb/>ad triplam: ſi fuerit diuiſio facta in proportione <lb/>ſexquialtera: et quadrupla ſi fuerit facta diuiſio <lb/>in proportione ſexquitertia: et ſic conſequenter).</s>
            </p>
            <p xml:id="N1F5F5">
              <s xml:id="N1F5F6" xml:space="preserve">Probatur hec concluſio / que infinitas habet par-<lb/>tes in termino illo / et ſic cõſequenter incluſas et pri­<lb/>mo probatur eius prima pars que eſt de ꝓportiõe <lb/>velocitatum ex ſecunda concluſione: hoc addito /  <lb/>totum diuiſum proportione ſexquialtera ſe habet               <pb chead="De motu locali quo ad effectū ſcḋm tempus difformi." file="0158" n="158"/>               ad primam partcm in proportione tripla: et totuꝫ <lb/>diuiſum proportione ſexquitertia in proportione <lb/>quadrupla: et ſic conſequenter / vt prima pars quin-<lb/>to ſuo capitulo oſtendit. </s>
              <s xml:id="N1F60C" xml:space="preserve">Et ſic patet prima pars. <lb/></s>
              <s xml:id="N1F610" xml:space="preserve">Secunda vero patet ex quarta concluſione hoc ad­<lb/>dito /  in caſu concluſionis proportio ſpacii per-<lb/>tranſiti in tota hora ad ſpacium pertranſitum in <lb/>prima parte eſt dupla ad proportionem totius ve­<lb/>locitatis ad velocitatem prime partis proportio-<lb/>nalis temporis.</s>
            </p>
            <note position="left" xml:id="N1F61D" xml:space="preserve">1. correĺ.</note>
            <p xml:id="N1F621">
              <s xml:id="N1F622" xml:space="preserve">¶ Ex hac ↄ̨cluſione ſequitur primo /  diuiſa hora <lb/>per partes proportionales proportione ſuperpar­<lb/>ticulari quauis libuerit: diſtributa velocitate vt <lb/>in caſu ſecunde concluſionis ponitur, ita videlicet / <lb/> mobile in prima parte proportiõali moueatur <lb/>aliquantulum, et in ſecunda in duplo velocius, et in <lb/>tertio in triplo velocius ꝙ̄ in prima, et in quarta in <lb/>quadruplo velocius ꝙ̄ in prima, et ſic conſequenter / <lb/>tūc tota velocitas erit equalis velocitati tertie par­<lb/>tis proportiõalis ſi fuerit facta diuiſio ꝓportione <lb/>ſexquialtera: et ſi fuerit diuiſio facta ſexquitertia <lb/>tota velocitas erit equalis velocitati quarta par-<lb/>tis proportionalis: et ſi fuerit facta diuiſio propor­<lb/>tione ſexquiquarta erit equalis velocitati quinte <lb/>partis proportionalis: et ſic conſequenter aſcendē­<lb/>do per ſpecies proportionis ſuperparticularis et <lb/>per partes proportionales. </s>
              <s xml:id="N1F645" xml:space="preserve">Probatur correlariū <lb/>facile ex ſecunda concluſione: quoniã facta diuiſio-<lb/>ne hore proportione ſexquialtera: tota hora ſe ha-<lb/>bet ad primam partē in proportione tripla / vt con­<lb/>ſtat: ergo tota velocitas vt dicit concluſio ſe habet <lb/>ad velocitatē prime partis proportionalis in pro-<lb/>portione tripla et in tali proportione ſe habet ve-<lb/>locitas tertie partis proportionalis ad velocitatē <lb/>prime / vt dicit caſus igr̄. </s>
              <s xml:id="N1F658" xml:space="preserve">Itē diuiſiõe facta ꝑ partes <lb/>ꝓportiõales ꝓportiõe ſexquitertia: totū ſic diuiſuꝫ <lb/>ſe habet ad primam partem proportionalem in ꝓ­<lb/>portione quadrupla: ergo totalis velocitas ſe ha-<lb/>bet ad velocitatem prime partis proportiõalis in <lb/>proportione quadrupla / vt patet ex ſecūda conclu-<lb/>ſione: et tanta eſt velocitas quarte partis / igitur. </s>
              <s xml:id="N1F667" xml:space="preserve">Et <lb/>ſic probabis reſiduas partes in infinitum.</s>
            </p>
            <note position="left" xml:id="N1F66C" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N1F670">
              <s xml:id="N1F671" xml:space="preserve">¶ Sequitur ſecūdo /  hora diuiſa per partes pro-<lb/>portionales proportione ſexquialtera et mobile a. <lb/>in prima parte moueatur aliquantulū, et in ſecun-<lb/>da parte in duplo velocius, et in tertia in triplo ve-<lb/>locius q̈ in prima, et ſic conſequenter: vt in prima <lb/>parte proportionali pertranſit vnum pedale: in to­<lb/>ta hora pcriranſit nouē. </s>
              <s xml:id="N1F680" xml:space="preserve">Probatur / quia illo caſu <lb/>poſito velocitatis totius ad velocitatē prime par-<lb/>tis eſt proportio tripla: vt patet ex precedenti: igi-<lb/>tur ſpacii pertraſiti in tota hora ad ſpaciū ꝑtran-<lb/>ſitum in prima parte eſt ꝓportio dupla ad triplam / <lb/>vt ptꝫ ex quarta huius: ſed noncupla eſt dupla ad <lb/>triplam ex ſecūda parte huius operis capite ſexto / <lb/>igitur totius ſpacii pertrãſiti in tota hora ad ſpa­<lb/>cium pertranſitum in prima parte eſt ꝓportio non­<lb/>cupla / quod fuit probandum.               <anchor type="note" xlink:href="note-0158-01" xlink:label="note-0158-01a"/>               </s>
              <s xml:id="N1F69A" xml:space="preserve">¶ Sequitur tertio /  <lb/>diuiſa hora vel tempore aliquo proportione qua-<lb/>uis ſuperparticulari / vt poſitum eſt in primo corre­<lb/>lario: ſpacii pertrãſiti in tota hora ad ſpaciū per-<lb/>tranſitum in prima parte eſt proportio dupla ad <lb/>proportionem quam habet velocitas tertie partis <lb/>ad velocitatem prime partis ſi fuerit diuiſio facta <lb/>proportione ſexquialtera: ſi vero fiat proportione <lb/>ſexquitertia in proportione dupla ad proportio-<lb/>nem velocitatis quarte partis ad velocitatem pri-<lb/>me. </s>
              <s xml:id="N1F6B1" xml:space="preserve">ſi ſexquiquarta in proportione dupla ad pro-<lb/>portionem velocitatis quinte partis ad velocita-               <cb chead="De motu locali quo ad effectū ſcḋm tempus difformi."/>               tem prime / et ſic conſequenter. </s>
              <s xml:id="N1F6B9" xml:space="preserve">Et quia hoc correla-<lb/>rium manifeſte ſequitur ex predictes ꝓbatione non <lb/>indiget.               <anchor type="note" xlink:href="note-0158-02" xlink:label="note-0158-02a"/>               </s>
              <s xml:id="N1F6C5" xml:space="preserve">¶ Ex quo ſequitur quarto /  hora diuiſa <lb/>per partes proportionales proportione aliqua <lb/>ſuperparticulari quauis volueris: et aliquod mo-<lb/>bile moueatur in prima etc̈. / vt poſitū eſt: ſpacii per­<lb/>tranſiti eſt tota hora eſt noncuplum ad ſpaciū per-<lb/>tranſitum in prima parte proportionali ſi fuerit <lb/>diuiſio facta proportione ſexquialtera: ſi vero pro­<lb/>portio eſt ſequitertia: eſt ſexdecuplum: ſi autē pro­<lb/>portione ſexquiquarta: eſt vicecuplum quintuplū. <lb/></s>
              <s xml:id="N1F6D9" xml:space="preserve">ita  in prima parte pertranſit vnum pedale in to­<lb/>ta hora viginti quin pedalia: et ſic conſequenter. <lb/></s>
              <s xml:id="N1F6DF" xml:space="preserve">Patet hoc correlarium ex predictis. </s>
              <s xml:id="N1F6E2" xml:space="preserve">¶ Innumera <lb/>alia correlaria inferre poteris ſi virtutē et robur, <lb/>ſecunde et quarte concluſionis diligenter inſpexe-<lb/>ris: non ſolum in generibus proportionum multi-<lb/>plicis at ſuperparticularis: verū etiam pari faci­<lb/>litate in omnibus aliis generibus puta ſuprapar-<lb/>tiente multiplici ſuperparticulari multiplici ſu-<lb/>perpartiente.</s>
            </p>
            <div xml:id="N1F6F3" level="5" n="22" type="float">
              <note position="left" xlink:href="note-0158-01a" xlink:label="note-0158-01" xml:id="N1F6F7" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0158-02a" xlink:label="note-0158-02" xml:id="N1F6FD" xml:space="preserve">4. correĺ</note>
            </div>
            <p xml:id="N1F703">
              <s xml:id="N1F704" xml:space="preserve">Sexta cõcluſio. </s>
              <s xml:id="N1F707" xml:space="preserve">Diuiſa hora quauis <lb/>proportione libuerit et in quacun proportione ſe <lb/>habuerint due partes immediate in eadem propor­<lb/>tione vel maiori ſe habuerit velocitas minoris par­<lb/>tis ad velocitatem maioris: tota illa velocitas eſt <lb/>infinita: ſpacium pertranſitum pari ratione infi­<lb/>nitum erit. </s>
              <s xml:id="N1F716" xml:space="preserve">Probatur ſecnnda pars concluſionis <lb/>quoniam in illo caſu mobile / quod ſic mouetur tan­<lb/>tum ſpacium pertranſit in ſequenti parte ſicut in <lb/>priori vel maius et ſunt infinite partes proportio-<lb/>nales: ergo in totali hora infinitum pertranſibit. <lb/></s>
              <s xml:id="N1F722" xml:space="preserve">Patet cõſequentia cum minore: et arguitur maior / <lb/>qm̄ qualis eſt proportio prime partis ad ſecundaꝫ <lb/>partē proportionalē talis eſt ꝓportio velocitatis <lb/>ſecunde partis proportionalis ad velocitatem pri­<lb/>me partis vel maior: igitur tantum ſpaciū pertran­<lb/>ſit in ſecūda ſicut in prima vel maius. </s>
              <s xml:id="N1F72F" xml:space="preserve">Item qualis <lb/>eſt proportio ſecunde partis ad tertiam partem ta­<lb/>lis eſt proportio velocitatis tertie partis ad ſecun­<lb/>de / et ſic conſequenter de quibuſcun duabus par-<lb/>tibus proportionalibus immediatis / vt ptꝫ ex caſu <lb/>concluſionis: igitur in qualibet pate immediate ſe­<lb/>quente alteram maiorem, mobile motum tali velo­<lb/>citate pertranſit tantum ſpacium ſicut in īmediate <lb/>precedenti vel maius / quod fuit probãdum. </s>
              <s xml:id="N1F742" xml:space="preserve">Patet <lb/>tamen conſequentia ex quarta et quīta ꝓpoſitioni­<lb/>bus ſecundi notabilis. </s>
              <s xml:id="N1F749" xml:space="preserve">Et ſic patet ſecunda pars et <lb/>per conſequens prima. </s>
              <s xml:id="N1F74E" xml:space="preserve">Si enim mediante illa velo­<lb/>citate mobile pertranſit infinitum ſpacium: conſe­<lb/>quens eſt illam velocitatem infinitam eſſe. </s>
              <s xml:id="N1F755" xml:space="preserve">(Eſt em̄ <lb/>in tempore fiuito) </s>
              <s xml:id="N1F75A" xml:space="preserve">Patet igitur concluſio.</s>
            </p>
            <note position="right" xml:id="N1F75D" xml:space="preserve">1. correĺ.</note>
            <p xml:id="N1F761">
              <s xml:id="N1F762" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi hora diuidatur per <lb/>partes proportionales proportione dupla: vt mo­<lb/>bile moueatur in prima parte aliquantulum, et in <lb/>ſecunda in duplo velocius ꝙ̄ in prima, et in tertia <lb/>in duplo velocius ꝙ̄ in ſecunda, et in quarta in du-<lb/>plo velocius ꝙ̄ in tertia, ſpacium pertranſitum erit <lb/>infinitum. </s>
              <s xml:id="N1F771" xml:space="preserve">Patet correlarium ex concluſione quo-<lb/>niam in quacun proportione ſe habent partes ꝓ­<lb/>portionales īmediate continuo: in eadem propor-<lb/>tione ſe habet velocitas partis minoris ad veloci­<lb/>tatem partis maioris: et per conſequens totum il-<lb/>lud mobile pertranſit in qualibet ſequenti primaꝫ <lb/>tantum quantum iu prima. </s>
              <s xml:id="N1F780" xml:space="preserve">Infinitum igitur ſpa-<lb/>cium tranſcurret / quod fuit probandū.               <anchor type="note" xlink:href="note-0158-03" xlink:label="note-0158-03a"/>               </s>
              <s xml:id="N1F78A" xml:space="preserve">¶ Sequitur <lb/>ſcḋo /  partita hora per partes ꝓportiõales ꝓpor­<lb/>tione ſexquitertia: et in prima parte proportionali               <pb chead="Secundi tractatus" file="0159" n="159"/>               a. mobile moueatur aliqua velocitate, et in ſecunda <lb/>in ſexquialtero velocius ꝙ̄ in prima, et in tertia in <lb/>ſexquialtero velocius ꝙ̄ in ſecunda, et in quarta in <lb/>ſexquialtero velocius ꝙ̄ in tertia, et ſic conſeque-<lb/>ter: ſpacium pertranſitum in tota hora erit infi-<lb/>nitum. </s>
              <s xml:id="N1F7A0" xml:space="preserve">Probatio: quia in qualibet parte ſequen-<lb/>ti primam a. mobile maius ſpacium abſoluet ̄ <lb/>in prima: qm̄ contiuo maior eſt proportio velocita­<lb/>tis minoris ad velocitatē maioris ꝙ̄ ſit temporis <lb/>maiors ad tempus minus: igitur per quintã pro-<lb/>poſitionem ſecundi notabilis in qualibet ſequenti <lb/>primã maius ſpacium ꝑtranſibit ꝙ̄ in prima: et ꝑ <lb/>conſequens in tota hora infinitum ſpacium tranſ-<lb/>curret: quod fuit probandum.               <anchor type="note" xlink:href="note-0159-01" xlink:label="note-0159-01a"/>               </s>
              <s xml:id="N1F7B8" xml:space="preserve">¶ Tertio ſequitur: <lb/> ſi hora fuerit diuiſa per partes proportionales <lb/>proportione aliqua ſuprapartienti: et continuo ve­<lb/>locitates partium proportionaliū immediataruꝫ <lb/>puta velocitas minoris partis ad velocitatem ma­<lb/>ioris ſe habuerit in aliqua proportione multiplici <lb/>vel multiplici ſuperparticulari, vel multiplici ſu-<lb/>perpartienti: ſpaciū ꝑtranſitū in tota hora erit in-<lb/>finitum. </s>
              <s xml:id="N1F7CB" xml:space="preserve">Patet hoc correlarium / quia continuo ma­<lb/>ior erit ibi proportio velocitatum temporum ma-<lb/>iorum et minorum ꝙ̄ proportio maioris temporis <lb/>ad minꝰ tēpus igitur. </s>
              <s xml:id="N1F7D4" xml:space="preserve">Interas ad libitū correlaria</s>
            </p>
            <div xml:id="N1F7D7" level="5" n="23" type="float">
              <note position="right" xlink:href="note-0158-03a" xlink:label="note-0158-03" xml:id="N1F7DB" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0159-01a" xlink:label="note-0159-01" xml:id="N1F7E1" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N1F7E7">
              <s xml:id="N1F7E8" xml:space="preserve">Septima cõcluſio. </s>
              <s xml:id="N1F7EB" xml:space="preserve">Partita hora per <lb/>partes proportionales qua libuerit proportione <lb/>mobile continuo mouente velocius in parte ſequē­<lb/>ti quam in parte p̄cepenti: velocius nihilominus in <lb/>proportiõe minori ꝙ̄ ſit proportio diuiſionis) ſpa­<lb/>cium ꝑtranſitum in tota hora ſe habebit ad ſpaci-<lb/>um ꝑtranſitum in prima parte ꝓportionali in pro­<lb/>portione qua aliquod totum diuiſum proportione <lb/>qua maior proportio temporis excedit proportio-<lb/>nem velocitatum ſe habet in ordine ad primã par-<lb/>tem ꝓportionalem. </s>
              <s xml:id="N1F802" xml:space="preserve">Hoc theorema multiplicibus <lb/>verbis implicitum et intricatū familiarem et exem-<lb/>plarem enucleationem efflagitat. </s>
              <s xml:id="N1F809" xml:space="preserve">Exemplo / igitur <lb/>vtens volo dicere:  ſi hora fuerit diuiſa ꝑ partes <lb/>ꝓportionales ꝓportione quadrupla exempli gra­<lb/>tia: et a. mobile moueatur in prima parte ꝓportio-<lb/>nali aliquanta velocitate, et in ſecūda in duplo ma­<lb/>iori velocitate, et in tertia in duplo maiori ꝙ̄ in ſe-<lb/>cunda, et ſic in qualibet ſequenti in duplo maiori <lb/>velocitate quam in immediate ꝑcedenti (quoniam <lb/>ꝓportio illarum velocitatum que eſt dupla excedi-<lb/>tur a ꝓportione tempoꝝ que eſt quadrupla ꝑ ꝓpor­<lb/>tionem duplam) / dico /  totale ſpacium ꝑtranſituꝫ <lb/>in illa totali hora ſe habet ad ſpaciū ꝑtranſitū in <lb/>prima parte proportionali: ſicut ſe habet aliquod <lb/>corpus diuiſum ꝓportione dupla in ordine ad ſuã <lb/>primam partem / vt poſt modum correlaria fami-<lb/>liariter oſtendent. </s>
              <s xml:id="N1F82A" xml:space="preserve">Probatur tamen concluſio ge-<lb/>neraliter / et ſit hora diuiſa ꝑ partes ꝓportionales <lb/>ꝓportione g. maiore: ſit continuo velocitatis par­<lb/>tis minoris ad velocitatē partis maioris īmedia-<lb/>te p̄cedentis ꝓportio f. minor quã ſit ꝓportio g. ex-<lb/>cedat ꝓportio g. ꝓportionem f. mediante ꝓpor-<lb/>tione h. </s>
              <s xml:id="N1F839" xml:space="preserve">Tunc dicit / theorema ſpacium ꝑtranſitum <lb/>in totali hora ſe habere ad ſpacium ꝑtranſitum in <lb/>prima parte ꝓportionali illius hore, in ea ꝓporti­<lb/>one in qua ſe habet aliquod diuiſum ꝓportione h. <lb/>ad primam partem ꝓportionalem eiuſdem ꝓpor-<lb/>tionis h. </s>
              <s xml:id="N1F846" xml:space="preserve">Quod ſic ꝓbatur / quia prime partis pro-<lb/>portionalis hore ad ſecundã partem ꝓportialē <lb/>eiuſdem eſt ꝓportio g. maior: et velocitatis ſecunde <lb/>partis proportionalis ad velocitatē prime partis <lb/>ꝓportionalis eſt ꝓportio f. minor / vt ponit caſus: et               <cb chead="Capitulū tertiū"/>               g. ꝓportio temporis maioris ad tempus minus ex­<lb/>cedit f. ꝓportionem velocitatis temporis minoris <lb/>ad velocitatem temporis maioris (quod tēpus ma­<lb/>ius eſt prima pars proportionalis et minus ſecun-<lb/>da) per h. ꝓportionem / vt ponitur in caſu: igitur in <lb/>h. ꝓportione maius ſpacium ꝑtranſitur a mobili <lb/>in prima parte proportionali quã in ſecunda. </s>
              <s xml:id="N1F860" xml:space="preserve">Ptꝫ <lb/>hec conſequentia ex ſexta ꝓpoſitione ſecundi nota­<lb/>bilis huius queſtionis. </s>
              <s xml:id="N1F867" xml:space="preserve">Et ſic argumentaberis de <lb/>ſecunda et tertia /  in h. proportione maius ſpaci-<lb/>um pertranſitur in ſecunda quam in tertia: et ſic de <lb/>quibuſcun duabus partibus immediatis argu-<lb/>mentatione exordiri licebit: igitur illa ſpacia per-<lb/>tranſita ſe habent continuo in h. proportiõe ita  <lb/>primi ad ſecundum ſit h. proportio et ſecundi ad ter­<lb/>tium / et ſic conſequenter: igitur aggregatum ex om­<lb/>nibus illis ſpaciis ſe habebit ad ſpacium pertran­<lb/>ſitum in prima parte proportionali in ꝓportione in <lb/>qua ſe habet totum diuiſum in ꝓportione h. ad pri­<lb/>mam partem ꝓportionaleꝫ eiuſdem ꝓportionis <lb/>h. / quod fuit probandū.               <anchor type="note" xlink:href="note-0159-02" xlink:label="note-0159-02a"/>               </s>
              <s xml:id="N1F887" xml:space="preserve">¶ Ex hac concluſione ſequi­<lb/>tur primo:  partitione hore facta per partes pro­<lb/>portionales ꝓportione quadrupla: velocitatibus <lb/>continuo ſe habentibus in ꝓportione dupla: ita  <lb/>velocitatis ſecunde partis ꝓportionalis ad velo-<lb/>citatem prime ſit proportio dupla, et velocitatis <lb/>tertie ad velocitatem ſecunde ſit etiam proportio <lb/>dupla .etc̈. ſpacium pertranſitum in tota hora eſt <lb/>duplum ad ſpacium pertranſitum in prima parte <lb/>proportionali. </s>
              <s xml:id="N1F89C" xml:space="preserve">Probatur / quia proportio illoruꝫ <lb/>temporum quadrupla excedit ꝓportionem duplã <lb/>velocitatum per proportionem duplam / vt patet ex <lb/>quarta concluſioue quarti capitis ſecunde partis: <lb/>igitur totale ſpacium pertranſitum in illa hora eſt <lb/>duplum ad ſpacium pertranſitum in prima parte <lb/>proportionali hore. </s>
              <s xml:id="N1F8AB" xml:space="preserve">Patet conſequentia ex prece-<lb/>denti concluſione: hoc addito /  quodlibet diuiſuꝫ <lb/>per partes proportionales proportione dupla ſe <lb/>habet ad primam partem proportionalem in pro-<lb/>portiõe dupla. </s>
              <s xml:id="N1F8B6" xml:space="preserve">Arguitur tamen et familiarius pro­<lb/>batur correlarium: et volo /  ſpacium pertranſituꝫ <lb/>in prima parte proportionali proportione dupla <lb/>ſit pedale: et arguo ſic / ſpacium pertranſitum in ſe-<lb/>cunda parte proportionali eſt ſubduplum ad ſpa-<lb/>tium pertranſitum in prima, et ſpacium pertranſi-<lb/>tum in tertia ad ſpacium pertranſitum in ſecunda / <lb/>et ſic conſequenter ſe habent illa ſpacia in propor-<lb/>tione ſubdupla: et primuꝫ illorum eſt pedale: igitur <lb/>totum aggregatum ex omnibus ſequentibus pri-<lb/>mum eſt pedale: et per conſequens totum ſpacium <lb/>eſt bipedale: et ſic duplum ad ſpacium pertranſituꝫ <lb/>in prima parte proportiõali quod eſt pedale: quod <lb/>fuit inferendū. </s>
              <s xml:id="N1F8D3" xml:space="preserve">Probatur tamen maior /  illa ſpa­<lb/>cia pertranſita in partibus proportionalibus ſe <lb/>habent in proportione ſubdupla quoniam prime <lb/>partis ad ſecundam eſt proportio quadrupla per <lb/>caſum: et velocitatis ſecunde ad velocitatem prime <lb/>eſt proportio dupla per caſum: igitur ſpacium per­<lb/>tranſitum in ſecunda eſt ſubduplum ad ſpaciū per­<lb/>tranſitū in prima: et ſic argues de ſpacio pertran-<lb/>ſito in tertia ad ſpacium pertranſitum in ſecunda: <lb/>et de quibuſcun ſpaciis pertranſitis in duabus <lb/>partibus īmediatis proportionalibus: igitur illa <lb/>ſpacia continuo ſe habent in proportione ſubdu-<lb/>pla: quod fuit probandum. </s>
              <s xml:id="N1F8EE" xml:space="preserve">Patet conſequentia <lb/>ex ſexta propoſitione ſecundi notabilis: hoc addi-<lb/>to /  proportio quadrupla excedit proportionem <lb/>duplam per ipſammet duplam: vt ſecunda pars <lb/>loco preallegato docet.</s>
            </p>
            <div xml:id="N1F8F9" level="5" n="24" type="float">
              <note position="right" xlink:href="note-0159-02a" xlink:label="note-0159-02" xml:id="N1F8FD" xml:space="preserve">1. correĺ.</note>
            </div>
            <pb chead="Secūdi. De motu locali quo ad effectū ſcḋm tempus difformi." file="0160" n="160"/>
            <p xml:id="N1F907">
              <s xml:id="N1F908" xml:space="preserve">¶ Sequitur ſecūdo /  diuiſa hora ꝑ partes ꝓpor-<lb/>tionales ꝓportiõe ſuꝑtripartienti quartas cuiuſli­<lb/>bet partis velocitate ſe habente ad velocitatē par-<lb/>tis maioris īmediate precedentis in ꝓportione ſex­<lb/>quialtera ſpaciū pertranſitū in tota hora ſe habet <lb/>ad ſpaciū pertranſitū in prima parte proportionali <lb/>in ꝓportione ſeptupla: abſoluto pedali in prima <lb/>parte: ſeptē pedalia in tota hora abſoluētur. </s>
              <s xml:id="N1F919" xml:space="preserve">Pro­<lb/>batur hoc correlariū ex cõcluſione īmediate precedē­<lb/>ti: quia partes ꝓportionales tēporis ſe habent cõ-<lb/>tinuo in ꝓportione ſuꝑtripartienti quartas: et ve-<lb/>locitates partiū īmediatarū ſe habent in ꝓportiõe <lb/>ſexq̇altera / vt ponit caſus: et ꝓportio ſuꝑtripartiēs <lb/>q̈rtas excedit ꝓportionē ſexquialteram ꝑ .4. ꝓpor-<lb/>tionē ſexquiſextaꝫ / vt ptꝫ in his terminis .7.6.4. / igr̄ <lb/>ſpaciū ꝑtranſitū in toto tēpore ſe habebit ad ſpa-<lb/>cium pertranſitū in prima parte proportionali in <lb/>ꝓportione ſeptupla / quod fuit ꝓbandū. </s>
              <s xml:id="N1F930" xml:space="preserve">Patet cõ-<lb/>ſequentia ex cõcluſione ſeptima: hoc adiecto /  cor­<lb/>pus diuiſum proportione ſexquiſexta ſe habet ad <lb/>primã ſui partē in ꝓportione ſeptupla: vt patet ex <lb/>prima parte huiꝰ operis. </s>
              <s xml:id="N1F93B" xml:space="preserve">Familiarius tamen ꝓba­<lb/>tur ſic, et ſuppono /  mobile ꝑtranſit in prima par­<lb/>te proportionali vnum pedale, et arguo ſic / mobile <lb/>pertranſit in prima parte proportionali vnum pe­<lb/>dale: et in ſecunda in ſexquiſexto minus, et in tertia <lb/>in ſexquiſexto minꝰ ꝙ̄ in ſecunda: et ſic conſequēter <lb/>ꝓcedendo per ꝓportiones ſexquiſextas: igitur to-<lb/>tale ſpaciū componitur ex illis infinitis continuo <lb/>ſe habentibus in ꝓportione ſexquiſexta: ergo ag-<lb/>gregatū ex omnibꝰ ſequētibus primã eſt ſextupluꝫ <lb/>ad primū / vt ptꝫ ex prima parte huiꝰ operis capite <lb/>quinto: et primū eſt vnū pedale: ergo totū reſiduum <lb/>eſt ſextupedale, et ꝑ cõſequens totū ſpaciū eſt ſeptē <lb/>pedū / quod ſe habet in proportiõe ſeptupla ad vnū <lb/>pedale ꝑtranſitū in prima parte ꝓportiõali / quod <lb/>fuit ꝓbandum. </s>
              <s xml:id="N1F95C" xml:space="preserve">Probatur tamen antecedens vide­<lb/>licet /  illud mobile in qualibet parte ſequenti per­<lb/>tranſit ſubſexquiſextū ſpaciū ad ſpaciū ꝑtranſitū <lb/>in īmediate p̄cedenti, quia prime partis ꝓportio-<lb/>nalis ad ſecundã eſt ꝓportio ſuꝑtripartiens quar-<lb/>tas, et velocitatis ſecunde partis ꝓportionalis ad <lb/>velocitatē prime eſt ꝓportio ſexquialtera: ſed ꝓpor­<lb/>tio ſuꝑtripartiens quartas tempoꝝ excedit ꝓpor-<lb/>tionē velocitatū ſexquialterã per ꝓportionē ſexqni­<lb/>ſextam / vt notū eſt: igitur ſpaciū pertranſitū in ſe-<lb/>cunda parte ꝓportionali eſt ſubſexquiſextū ad ſpa­<lb/>cium pertranſitū in prima. </s>
              <s xml:id="N1F975" xml:space="preserve">Patet conſequentia / ex <lb/>ſexta ꝓpoſitione ſecundi notabilis ſepius allega-<lb/>ta. </s>
              <s xml:id="N1F97C" xml:space="preserve">Et ſic ꝓbabis de ſpacio pertranſito in tertia ad <lb/>ſpacium ꝑtranſitum in ſecunda, et de ſpaciis ꝑtrã-<lb/>ſitis in duabus partibus īmmediatis quibuſcun <lb/>ſignatis: ergo cõtinuo ſpaciū pertranſitū in aliqua <lb/>parte ꝓportionali ſequente eſt ſubſexquiſextū ad <lb/>ſpacium ꝑtranſiium in parte īmediate precedente: <lb/>quod fuit ꝓbanduꝫ. </s>
              <s xml:id="N1F98B" xml:space="preserve">Inferas tuo ingenio et labore <lb/>ſimilia infinita correlaria. </s>
              <s xml:id="N1F990" xml:space="preserve">Iſta enim ſufficiūt pro <lb/>praxi concluſionis.</s>
            </p>
            <p xml:id="N1F995">
              <s xml:id="N1F996" xml:space="preserve">Octaua cõcluſio. </s>
              <s xml:id="N1F999" xml:space="preserve">Partita hora ꝑ part­<lb/>tes ꝓportionales quauis ꝓportione volueris, et in <lb/>certa ꝓportione continuo velocius mobile moueat̄̄ <lb/>in parte p̄cedente maiore quã in īmediate ſequenti <lb/>minori: ſpaciū ꝑtranſitum in totali hora ſe habe-<lb/>bit ad ſpaciū ꝑtranſitum in prima parte ꝓportio-<lb/>nali in ꝓportione qua ſe habet aliquod totū diui-<lb/>ſum in partes ꝓportionales ꝓportione compoſi-<lb/>ta ex proportione temporis puta partis propor-<lb/>tionalis maioris ad partem immediate ſequenteꝫ <lb/>minorem, et velocitatis partis maioris ad veloci-               <cb chead="Secūdi. De motu locali quo ad effectū ſcḋm tempus difformi."/>               tatem partis minoris ad primam partem prpor-<lb/>tionalem talis diuiſionis. </s>
              <s xml:id="N1F9B5" xml:space="preserve">Hoc inuolutum theo-<lb/>rema exemplari declaratione reſoluatur: volo em̄ <lb/>dicere /  conſciſa hora per partes proportionales <lb/>proportione dupla, et in prima parte proportiõa-<lb/>li aliquod mobile moueatur aliquanta velocitate <lb/>q̄ in ſecunda parte proportionali in ſexquialtero <lb/>minori velocitate, et in tertia in ſexquialtero mīor <lb/>velocitate quã in ſecūda, et ſic cõſequēter  </s>
              <s xml:id="N1F9C6" xml:space="preserve">ita  cu-<lb/>iuſlꝫ ꝑtis p̄cedētis maioris velocitas ad velocitatē <lb/>mīoris īmediate ſequētꝪ ſexq̇alterã ꝓportionē ha-<lb/>beat: tūc dicit theorema poſitū. </s>
              <s xml:id="N1F9CF" xml:space="preserve">ſpaciū ꝑtranſitū in <lb/>totali hora ſe habere ad ſpaciū ꝑtranſitū in prima <lb/>parte proportionali in proportione ſequialtera: <lb/>qm̄ proportio compoſita ex proportione dupla tē­<lb/>porum et ſexquialtera velocitatū eſt tripla: et quod­<lb/>libet totū diuiſum per partes proportione tripla <lb/>ſe habet ad primã proportionalem partem eius in <lb/>proportione ſexquialtera. </s>
              <s xml:id="N1F9E0" xml:space="preserve">Probatur tamen vni-<lb/>uerſaliter cõcluſio: ſit hora diuiſa per partes pro-<lb/>portionales portiõe g. et moueatur mobile in ali-<lb/>qua certa proportione velocius continuo in parte <lb/>p̄cedenti maiore quam in minore ſequente ita  cõ­<lb/>tinuo maior velocitas ſit in parte maiori quam in <lb/>minore īmediate ſequente, ſit proportio cõtinuo <lb/>velocitatis partis maioris ad velocitatem partis <lb/>minoris f. compoſita proportio ex g. et f. ſit h. / tūc <lb/>ſpaciū ꝑtranſitum in totali hora ſe pabet ad ſpa-<lb/>cium ꝑtranſitum in prima parte proportionali in <lb/>ꝓportione in qua ſe habet aliquod totum diuiſum <lb/>in partes proportionales ꝓportione h. ad primaꝫ <lb/>partem ꝓportionalē eiuſdem diuiſionis videlicet <lb/>proportione h. </s>
              <s xml:id="N1F9FF" xml:space="preserve">Quod probatur ſic / quia ſpacii ꝑ-<lb/>tranſiti in prima parte proportionali ad ſpacium <lb/>ꝑtranſitū in ſecunda parte ꝓportionali eſt propor­<lb/>tio h. et ſpacii ꝑtranſiti in ſecunda ad ſpaciū ꝑtran­<lb/>ſiti in tertia eſt etiam proportio h. / et ſic conſequen-<lb/>ter de ſpaciis ꝑtranſitis in duabus partibus pro-<lb/>portionalibus īmediatis quibuſuis demonſtratis / <lb/>ergo totale ſpaciū ꝑtrãſitū in tota hora componit̄̄ <lb/>ex infinitis continuo ſe habentibus in proportione <lb/>h. / igitur totale ſpaciū ſe habet ad primū illoꝝ ſpa­<lb/>ciorum / quod eſt ꝑtranſitū in prima parte propor-<lb/>tionali in proportiõe in qua ſe habet aliquod totū <lb/>diuiſum ꝑ partes ꝓportionales proportione h. ad <lb/>primã eius partē / quod fuit probandū. </s>
              <s xml:id="N1FA1C" xml:space="preserve">Patet con-<lb/>ſequentia / quia eodem modo ſe habent illa ſpacia <lb/>continuo ſe habentia in proportione h. ſicut ſe ha-<lb/>bent partes proportionales alicuiꝰ continui pro-<lb/>portiõe h. </s>
              <s xml:id="N1FA27" xml:space="preserve">Probatur tamen añs videlicet /  ſpacii <lb/>ꝑtranſiti in prima parte ꝓportionali ad ſpaciū ꝑ-<lb/>tranſitū in ſecūda eſt ꝓpertio h. et ſpacii ꝑtrãſiti in <lb/>ſcḋa ad ſpaciū ꝑtranſitum in tertia etc̈. quia prima <lb/>pars proportionalis eſt maius tempus quã ſecun-<lb/>da in g. proportione, et ei coextenditur velocitas in­<lb/>tenſior quam ſeēunde in f. proportione / vt dici hipo­<lb/>teſis: et h. proportio eſt proportio cõpoſita ex g. et f. <lb/>proportionibus ex hypoteſi: igitur ſpaciū ꝑtranſi­<lb/>tum in prima parte ꝓportiõali ſe habet ad ſpaciū <lb/>ꝑtrãſitū in ſecūda in h. ꝓportiõe. </s>
              <s xml:id="N1FA3E" xml:space="preserve">Cõſimili argumē­<lb/>to ꝓbabis de quibuſcū ſpaciis ꝑtranſitis in qui­<lb/>buſcū duabus partibus immediatis: quod erat <lb/>inferendum. </s>
              <s xml:id="N1FA47" xml:space="preserve">Patet tamen conſequentia ꝑ tertiam <lb/>propoſitionem ſecundi notabilis huius queſtiõis. <lb/>               <anchor type="note" xlink:href="note-0160-01" xlink:label="note-0160-01a"/>               </s>
              <s xml:id="N1FA53" xml:space="preserve">¶ Ex hac ſolutione ſequitur primo /  partitiõe ho­<lb/>re facta ꝑ partes proportionales proportione ſu-<lb/>prabipartiēte tertias, et in prima parte ꝓporõali <lb/>moueatur aliquod mobile aliquãta velocitate, et ī <lb/>ſecunda in ſuprabipartiente quintas minore et in <lb/>tertia in eadē proportiõe ſuprabipartiēte quintas               <pb chead="Secundi tractatus" file="0161" n="161"/>               mīore velocitate quã in ſecūda / et ſic cõſequēter: tūc <lb/>ſpaciū ꝑtranſitū in totali hora ſe habet ad ſpaciū <lb/>ꝑtranſitū in prima parte ꝓportionali in ꝓportiõe <lb/>ſuꝑtripartiente quartas, qualis eſt .7. ad .4. </s>
              <s xml:id="N1FA6B" xml:space="preserve">Pro-<lb/>batur / q2 ſpaciū ꝑtranſitū in prima parte ꝓporti-<lb/>onali ſe habet ad ſpaciū ꝑtranſitū in ſecunda in ꝓ­<lb/>portiõe dupla ſexquitertia, et in eadē ꝓportione ſe <lb/>habet ſpaciū ꝑtranſitū in ſeeunda ad ſpaciū ꝑtrã­<lb/>ſitum in tertia, et ſic cõſequenter: igitur totale ſpa-<lb/>ciū ſe habet ad ſpaciū ꝑtranſitū in prima parte ꝓ­<lb/>portiõali in ꝓportione ſupratripartiēte quartas <lb/></s>
              <s xml:id="N1FA7D" xml:space="preserve">Patet hec cõſequentia ex priori cõcluſione: hoc ad­<lb/>dito /  quodlibet corpus diuiſū per partes ꝓpor-<lb/>tionales ꝓportiõe dupla ſexquitertia ſe habet ad <lb/>primã partē ꝓportionalē in ꝓportione ſuꝑtripar­<lb/>tiente quartas: vt facile eſt intueri ex prima parte <lb/>huiꝰ operis. </s>
              <s xml:id="N1FA8A" xml:space="preserve">Probat̄̄ tamen antecedens. </s>
              <s xml:id="N1FA8D" xml:space="preserve">Quia ꝓ-<lb/>portio prime partis tēporis ad ſecundã eſt ſuꝑbi-<lb/>partiens tertias, et velocitatis prime partis ad ve­<lb/>locitatē ſecunde eſt ꝓportio ſuꝑbipartiens quītas / <lb/>igitur totius ſpacii ꝑtranſiti in prima parte ꝓpor­<lb/>tionali que eſt maius tēpus ad ſpaciū ꝑtranſitū in <lb/>ſecunda parte ꝓportionali eſt ꝓportio dupla ſex-<lb/>q̇tertia: et ſic ꝓbabis de ſpaciis ꝑtranſitis in aliis <lb/>partibꝰ quibuſcū īmediatis. </s>
              <s xml:id="N1FAA0" xml:space="preserve">Cõſequentia ꝓbat̄̄ / <lb/>ꝑ tertiã ꝓpoſitionē ſecūdi notabilis huiꝰ q̄ſtionis <lb/>hoc addito /  proportio dupla ſexq̇tertia cõponit̄̄ <lb/>adequate ex ꝓportione ſuꝑbipartiente tertias, et <lb/>ſuꝑbipartiente quintas: vt ptꝫ in his terminis .7. <lb/>.5.3. / et ſic ptꝫ correlariū               <anchor type="note" xlink:href="note-0161-01" xlink:label="note-0161-01a"/>               </s>
              <s xml:id="N1FAB2" xml:space="preserve">¶ Sequitur ſecundo /  diui­<lb/>ſa hora ꝑ partes ꝓportionales ꝓportione dupla <lb/>mobili cõtinuo in duplo tardius mouente in parte <lb/>ſequēti minori quã in parte maiori īmediate prece­<lb/>denti illã: ſpaciū ꝑtranſitū in totali hora ſe habet <lb/>ad ſpaciū ꝑtranſitū in prima parte proportionali <lb/>hore in ꝓportione ſexquitertia. </s>
              <s xml:id="N1FAC1" xml:space="preserve">Probatio / q2 pro­<lb/>portio cõpoſita ex ꝓportione tēporis maioris ad <lb/>tēpus minꝰ dupla, et velocitatis temporis maioris <lb/>ad velocitatē tēporis minoris ſimiliter dupla eſt <lb/>quadrupla, vt ſatis ↄ̨ſtat: et quodlibet totū diuiſū <lb/>ꝑ partes ꝓportionales ꝓportione quadrupla ſe <lb/>habet ad primã partē ꝓportionalē in proportione <lb/>ſexquitertia, vt ptꝫ ex prima parte: igr̄ totale ſpa-<lb/>ciū ꝑtranſitū in illa hora in caſu correlarii ſe ha-<lb/>bet ad ſpaciū ꝑtranſitū in prima parte ꝓportiõali <lb/>in ꝓportione ſexquitertia / quod fuit ꝓbandū. </s>
              <s xml:id="N1FAD8" xml:space="preserve">Cõ-<lb/>ſequentia ptꝫ ex cõcluſione octaua </s>
              <s xml:id="N1FADD" xml:space="preserve">¶ Sequit̄̄ tertio­<lb/> / diuiſa hora in partes ꝓportionales ꝓportione <lb/>tripla, mobili cõtinuo in quadruplo tardiꝰ mo-<lb/>uēte in parte ſequenti minori ꝙ̄ in īmediate p̄ceden­<lb/>ti eã: ſpaciū ꝑtranſitū in totali hora ſe habebit ad <lb/>ſpaciū ꝑtranſitū in prima parte ꝓportionali in ꝓ­<lb/>portione ſexquivndecima: pertranſito pedali in <lb/>prima: duodecim vndecimas pedalis ī totali hora <lb/>abſoluet. </s>
              <s xml:id="N1FAF0" xml:space="preserve">Probatur / q2 ꝓportio cõpoſita ex ꝓpor­<lb/>tione tēporis maioris ad tēpus minꝰ tripla et velo-<lb/>citatis tēporis maioris ad velocitatē tēporis mi-<lb/>noris quadrupla eſt duodecupla, vt patet in his <lb/>terminis .12.4.1. et quodlibet totū diuiſuꝫ ꝑ partes <lb/>ꝓportionales ꝓportione duodecupla ſe habet ad <lb/>primã ſui partē ꝓportionalē in ꝓportione ſexqui <lb/>vndecima, vt ptꝫ ex prima parte: igitur ſpaciū per­<lb/>tranſitū a mobili in totali tēpore ſe habet ad ſpa­<lb/>cium ꝑtranſitum in prima parte proportionali in <lb/>proportione ſexquivndecima. </s>
              <s xml:id="N1FB07" xml:space="preserve">Patet cõſequentia <lb/>ex octaua concluſione.</s>
            </p>
            <div xml:id="N1FB0C" level="5" n="25" type="float">
              <note position="right" xlink:href="note-0160-01a" xlink:label="note-0160-01" xml:id="N1FB10" xml:space="preserve">Correĺ.</note>
              <note position="left" xlink:href="note-0161-01a" xlink:label="note-0161-01" xml:id="N1FB16" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N1FB1C">
              <s xml:id="N1FB1D" xml:space="preserve">Nona concluſio. </s>
              <s xml:id="N1FB20" xml:space="preserve">Diuiſa hora per par­<lb/>tes ꝓportiõales q̈uis ꝓportione, et in certa ꝓpor-<lb/>tiõe ↄ̨tinuo mobile velociꝰ moueat̄̄ ī qualibet parte               <cb chead="Capitulū tertiū."/>               pari ſequenti quã in pari īmediate precedenti eaꝫ <lb/>et ſimiliter in certa proportione equali maiori, vel <lb/>minori, continuo in qualibet parte ſequente impa­<lb/>ri velocius moueatur quã in impari īmediate pre-<lb/>cedenti: ſpaciū pertranſitū in totali hora erit infi-<lb/>nitū dūmodo ꝓportio velocitatū ſit equalis pro-<lb/>portioni tempoꝝ vel maior: et ſi ꝓportio velocita-<lb/>tum partiū pariuꝫ, et ꝓportio velocitatū partium <lb/>impariū fuerit minor ꝓportione tempoꝝ: tunc ſpa­<lb/>cium pertranſitū in omnibus partibus paribus ſe <lb/>habet ad ſpaciū pertranſitū in prima illaꝝ pariū <lb/>in ꝓportione qua ſe habet aliquod totum diuiſuꝫ <lb/>per partes ꝓportionales ꝓportione per quã pro-<lb/>portio tempoꝝ excedit ꝓportionē velocitatum ad <lb/>primã partē ꝓportionale eiuſdē totius. </s>
              <s xml:id="N1FB46" xml:space="preserve">Et ſimili-<lb/>ter dicendū eſt de ſpacio ꝑtranſito in omnibꝰ par-<lb/>tibus imparibus. </s>
              <s xml:id="N1FB4D" xml:space="preserve">Declaratur hec cõcluſio iſto mo­<lb/>do: diuidatur hora per partes proportionales <lb/>proportione dupla, et capiantur ex vno latere oēs <lb/>ꝑtes pares: et ex alio oēs īpares, et in qualibet īpa­<lb/>ri ſequente moueatur a. mobile in quadruplo velo­<lb/>cius quã in impari īmediate precedenti eam: tunc <lb/>dicit prima pars concluſionis /  illud mobile in­<lb/>finitū ſpaciū ꝑtranſit et etiã infinitū ſpaciū tranſi-<lb/>ret ſi in qualibet ſequēti impari moueretur in quī-<lb/>tuplo velocius quã in impari īmediate precedenti <lb/>eam quia ꝓportio velocitatū eſt ibi maior vel equa­<lb/>lis ꝓportioni tempoꝝ. </s>
              <s xml:id="N1FB66" xml:space="preserve">Tēpora em̄ illa continuo ſe <lb/>habent in ꝓportione quadrupla. </s>
              <s xml:id="N1FB6B" xml:space="preserve">Si vero mobile <lb/>in qualibet parte ſequeti impari moueretur in du-<lb/>plo velociꝰ preciſe ꝙ̄ in parte īmediate precedenti <lb/>impari, diuiſione ſic facta in partes ꝓportionales <lb/>ꝓportione dupla: tunc ſpaciū ꝑtranſitū in omnibꝰ <lb/>partibus paribus ſe habet ad ſpaciū ꝑtrauſitū <lb/>in prima pari in ꝓportione dupla: et ſpaciū ꝑtran­<lb/>ſitum in omnibus partibus imparibus etiã ſe ha-<lb/>bet ad ſpaciū pertranſitū in prima impari in pro-<lb/>portione dupla: quia proportio tempoꝝ quadru-<lb/>pla excedit ꝓportionem velocitatū duplam ꝑ du-<lb/>plam: et corpus diuiſum per partes ꝓportionales <lb/>ꝓportione dupla ſe habet ad primã partē propor­<lb/>tionalem etiam in ꝓportione dupla, et etiã veloci-<lb/>tas maior eſt coextenſa tempori minori. </s>
              <s xml:id="N1FB8A" xml:space="preserve">Ideo to-<lb/>tum ſpaciū pertranſitū in omnibus partibus im-<lb/>paribus eſt duplū ad ſpaciū ꝑtranſitū in prima <lb/>illarū impariū. </s>
              <s xml:id="N1FB93" xml:space="preserve">Et conſimiliter dicendum eſt de pa­<lb/>ribus. </s>
              <s xml:id="N1FB98" xml:space="preserve">Probatur hec concluſio ex predictis, et hoc <lb/>generaliter: et primo patet prima pars ex ſexta <lb/>concluſione: et ſecunda ex ſeptima.               <anchor type="note" xlink:href="note-0161-02" xlink:label="note-0161-02a"/>               </s>
              <s xml:id="N1FBA4" xml:space="preserve">¶ Ex hac conclu­<lb/>ſione ſequitur primo /  partita hora per partes ꝓ­<lb/>portionales ꝓportione dupla: et in prima illarum <lb/>mobile moueatur aliquanta velocitate vuiformi-<lb/>ter, et in ſecūda moueat̄̄ vniformiter intēdendo mo­<lb/>tū ſuū a gradu quo mouetur in prima vſ ad gra-<lb/>dum duplū: et in tertia moueatur illo gradu duplo <lb/>vniformiter: et in quarta intendat vniformiter mo-<lb/>tum ſuū ab illo gradu duplo vſ ad gradū duplū <lb/>illius, ita  in omnibus partibus imparibus mo-<lb/>ueatur vniformiter continuo in duplo velocius in <lb/>ſequente impari ꝙ̄ īmediate precedenti impari, et <lb/>in qualibet parte pari moueatur intendendo mo-<lb/>tum ſuum vniformiter a gradu partis imparis im­<lb/>mediate precedentis vſ ad gradum partis paris <lb/>īmediate ſequentis: ita  velocitates partium im-<lb/>parium reducte ad vniformieatem etiam ſi habe-<lb/>ant continuo in proportione dupla: tunc ſpacium <lb/>totale pertranſitum in hora ſe habebit in propor-<lb/>tione tripla ſexquialtera ad ſpacium pertranſi-<lb/>tum in prima parte proportionali impari. </s>
              <s xml:id="N1FBCF" xml:space="preserve">Pro-               <pb chead="De motu locali quo ad effectum tempore difformi." file="0162" n="162"/>               batur correlarium et in prima parte proportiona-<lb/>li ꝑtranſeat illud mobile vnum pedale et arguitur <lb/>ſic </s>
              <s xml:id="N1FBDB" xml:space="preserve">In omnibus partibus tam paribus quam īpa-<lb/>ribus ꝑtranſit illud mobile tria pedalia cum dimi­<lb/>dio: ſed triū pedaliū cum dimidio ad vnum pedale <lb/>eſt ꝓportio tripla ſexquialtera: igitur correlarium <lb/>verum. </s>
              <s xml:id="N1FBE6" xml:space="preserve">Arguitur maior / quia in prima ꝑte impari <lb/>ꝑtranſit vnum pedale et ſpacia pertranſita in om-<lb/>nibus partibus imparibus continuo ſe habent ī ꝓ­<lb/>portione dupla quoniam velocitates cõtinuo ſe ha­<lb/>bent in ꝓportione dupla et tempora in quadrupla: <lb/>et ſic totale ſpacium ꝑtranſitum in omnibus parti­<lb/>bus imparibus erit duplum ad ſpacium ꝑtranſitū <lb/>in prima illarum / vt patet ex ſeptima concluſione. <lb/></s>
              <s xml:id="N1FBF8" xml:space="preserve">ergo ꝑ cõſequens totale ſpacium pertranſitū in om­<lb/>nibus erit bipedale. </s>
              <s xml:id="N1FBFD" xml:space="preserve">Et ſpacium pertranſitum in om­<lb/>nibus paribus eſt pedale cum dimidio. </s>
              <s xml:id="N1FC02" xml:space="preserve">Quod pro­<lb/>batur ſic / quia cõtinuo velocitatis partis paris ad <lb/>velocitatem ꝑtis imparis immediate precedentis <lb/>eſt ꝓportio ſexquialtera: (cum velocitas illius par­<lb/>tis paris correſpondeat gradui medio inter gradū <lb/>velocitatis illius partis imparis immediate prece­<lb/>dentis et gradum duplum) et ſemper gradus mediꝰ <lb/>inter duplum et ſubdupluꝫ eſt ſexquialterus ad ſub­<lb/>duplum / vt conſtat. </s>
              <s xml:id="N1FC15" xml:space="preserve">igitur talis gradus medius erit <lb/>ſexquialterus ad graduꝫ partis imparis immedia­<lb/>te precedentis: igitur ſpacium pertranſitum in pri­<lb/>ma parte ꝓportionali impari ſe habet ad ſpacium <lb/>pertranſituꝫ in prima parte proportionali pari in <lb/>ꝓportiõe ſexquitertia / vt patet ex ſexta propoſitio­<lb/>ne ſecundi notabilis ſed ſubſexquitertium ad peda­<lb/>le ſunt tres quarte et in omnibus ſequentibus pari­<lb/>bus pertranſibit tantum: igitur in omnibus ſimul <lb/>pertranſibit ſex quartas que faciunt pedale cum di­<lb/>midio. </s>
              <s xml:id="N1FC2C" xml:space="preserve">et in imparibus pertrãſibit bipedale: igitur <lb/>in omnibus partibus ſimul paribus et imparibus <lb/>pertranſibit tria pedalia cum dimidio / quod fuit ꝓ­<lb/>bandum. </s>
              <s xml:id="N1FC35" xml:space="preserve">Reſtat tamen probare /  in omnibus par­<lb/>tibus paribus ſequentibus ṗmã tm̄ pertranſit ſicut <lb/>in prima. </s>
              <s xml:id="N1FC3C" xml:space="preserve">Nam ille partes pares cõtinuo ſe habēt <lb/>in proportione quadrupla et velocitates continuo <lb/>ſe habent in proportione dupla aſcendendo / vt pa-<lb/>tet ex caſu correlarii: ergo totale ſpacium pertran-<lb/>ſitum in omnibus paribus eſt duplum ad ſpaci-<lb/>um pertranſitum in prima illarum et ſic illud ſpaci­<lb/>um eſt .6. quarte. </s>
              <s xml:id="N1FC4B" xml:space="preserve">Conſequentia patet ex ſeptima cõ­<lb/>cluſione: hoc addito /  proportio temporis excedit <lb/>ꝓportionem velocitatum ꝑ ꝓportionem duplam: <lb/>et totum diuiſum per partes ꝓportionales propor­<lb/>tione dupla eſt duplum ad primam illarum.</s>
            </p>
            <div xml:id="N1FC56" level="5" n="26" type="float">
              <note position="right" xlink:href="note-0161-02a" xlink:label="note-0161-02" xml:id="N1FC5A" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N1FC60" xml:space="preserve">2. correl.</note>
            <p xml:id="N1FC64">
              <s xml:id="N1FC65" xml:space="preserve">¶ Secundo ſequitur /  diuiſa hora per partes ꝓ-<lb/>portionales proportione quadrupla: et in prima ꝑ­<lb/>te moueatur mobile aliquanta velocitate vniformi­<lb/>ter, et in ſecunda intendat motum ſum vniformiter <lb/>ab illo gradu quo mouetur in prima vſ ad triplū <lb/>et in tertia moueatur vniformiṫ illo triplo gradu et <lb/>in quarta moueatur vniformiter intendendo motū <lb/>ſuum a gradu quo mouebatur in tertia vſ ad tri­<lb/>plum illius: et ſic conſequenter ſemper in qualibet <lb/>pari intendendo gradum īmediate precedentis im­<lb/>paris vſ ad triplum eiuſdem gradus vniformiter <lb/>ſpacium pertranſitum in totali hora ſe habebit ad <lb/>ſpacium pertranſitum in prima parte proportio-<lb/>nali impari in proportione ſupra vndecīpartiente <lb/>tridecimas. </s>
              <s xml:id="N1FC84" xml:space="preserve">Probatur ſupponendo /  medium in­<lb/>ter triplum et ſubtriplum eſt duplum ad ſubtriplū <lb/>vt medium inter vnum et .3. eſt .2. / quod eſt duplū ad <lb/>vnum. </s>
              <s xml:id="N1FC8D" xml:space="preserve">Supponitur ſecūdo /  velocitas ꝑtium īpa-<lb/>rium immediatarum continuo ſe habent in propor­               <cb chead="De motu locali quo ad effectum tempore difformi."/>               tione tripla et etiam partium parium / vt patet aſpi­<lb/>ciēti caſū correlarii </s>
              <s xml:id="N1FC97" xml:space="preserve">His ſuppoſitis eſto /  mobile ī <lb/>prima parte proportionali pertranſit tridecim pe­<lb/>dalia: arguitur ſic in omnibus partibus imparibꝰ <lb/>illud mobile pertranſit ſexdecim pedalia: et in om-<lb/>nibus paribus pertranſit octo: igitur in tota hora <lb/>ꝑtranſibit viginti q̈tuor: et .24. ad .13. pedalia ꝑtrã­<lb/>ſita in prima parte proportionali eſt proportio ſu­<lb/>pra vndecīpartiens tridecimas: igitur propoſituꝫ <lb/></s>
              <s xml:id="N1FCA9" xml:space="preserve">Maior ꝓbatur / quia ꝓportio temporum ꝑtum im-<lb/>parium que eſt ſexdecupla / vt conſtat: excedit ꝓpor­<lb/>tionem velocitatis triplam ꝑ ꝓportionalem quītu­<lb/>plam ſexquitertiam, qualis eſt .16. ad .3. et quodli-<lb/>bet totum diuiſum ꝓportione quintupla ſexquiter­<lb/>tia ſe habet ad primam ꝑtem eius ꝓportionaleꝫ in <lb/>ꝓportione ſupertripartiente tridecimas / vt patet <lb/>ex prima parte capite quinto: igitur in omnibus ꝑ­<lb/>tibus ꝓportionalibus imparibus illud mobile per­<lb/>tranſit .16. pedalia: </s>
              <s xml:id="N1FCBE" xml:space="preserve">Patet conſequentia ex ſeptīa <lb/>concluſione huius: hoc addito /  in prima parte im­<lb/>pari pertranſit .13. pedalia: et .16. ad .13. eſt ꝓportio <lb/>ſupertripartiens tridecimas. </s>
              <s xml:id="N1FCC7" xml:space="preserve">Et ſic patet maior <lb/></s>
              <s xml:id="N1FCCB" xml:space="preserve">Minor ꝓbatur / quia ꝓportio temporum partium <lb/>parium ſexdecupla / vt conſtat excedit proportionē <lb/>velocitatum triplam per ꝓportionem quintuplam <lb/>ſexquitertiam / vt patet ex probatione maioris: et <lb/>quodlibet totum diuiſum ꝓportione quintupla ſex­<lb/>quitertia ſe habet ad primam partem eius propor­<lb/>portionalem in proportione ſupertripartiente tri­<lb/>decimas: vt patet ex prima parte capite quinto: igi­<lb/>tur in omnibus partibus paribus pertranſit illud <lb/>mobile ſpacium ſe habens ad ſpacium pertranſitū <lb/>in prima illarum pariuꝫ in ꝓportione ſupertripar­<lb/>tiente tridecimas: et ſpacium pertranſitum in pri-<lb/>ma parium eſt ſpacium. </s>
              <s xml:id="N1FCE6" xml:space="preserve">ſex pedalium cum dimidio / <lb/>igitur ſpacium pertranſituꝫ in omnibus partibus <lb/>paribus eſt .8. pedum </s>
              <s xml:id="N1FCED" xml:space="preserve">Patet conſequen-<lb/>tia: q2 .8. ad .6. cum dimidio eſt proportio ſupertri­<lb/>partiens tridecimas. </s>
              <s xml:id="N1FCF4" xml:space="preserve">Probatur tamen /  in pri-<lb/>ma parte ꝓportionali illud mobile pertrãſit .6. pe­<lb/>dalia cum dimidio: quia illa pars eſt ſubquadru-<lb/>pla ad primã imparem: et velocitas illius eſt dupla <lb/>ad velocitatem ṗme imparis / vt patet facile ex ṗmo <lb/>ſuppoſito: igitur in illa ꝑte mobile pertranſit .6. pe­<lb/>dalia cum dimidio. </s>
              <s xml:id="N1FD03" xml:space="preserve">Patet conſequentia ex ſexta ꝓ­<lb/>poſitione ſecundi notabilis, addito /  in prima ꝑ-<lb/>te ꝓportionali impari ꝑtranſit .13. pedalia: et ſic pa­<lb/>tet minor: et ꝑ conſequens totum correlarium <lb/>               <anchor type="note" xlink:href="note-0162-01" xlink:label="note-0162-01a"/>               </s>
              <s xml:id="N1FD13" xml:space="preserve">¶ Sequitur tertio /  partita hora ꝑ ꝑtes ꝓportio-<lb/>nales ꝓportione quadrupla: et mobile in qualibet <lb/>parte ſequente impari in quadruplo velocius mo-<lb/>ueatur ꝙ̄ ī immediate p̄cedēti impari: et in qualibet <lb/>ſequenti pari etiam in quadruplo velocius mouea­<lb/>tur ꝙ̄ in immediate p̄cedenti pari: et in duplo velo-<lb/>cius in prima ꝑte pari ꝙ̄ in ṗma impari: tunc tota-<lb/>le ſpacium ꝑtranſitum in hora ſe habet ad ſpaciuꝫ <lb/>ꝑtranſitum in ṗma parte ꝓportionali impari ī ꝓ­<lb/>portione dupla </s>
              <s xml:id="N1FD28" xml:space="preserve">Hoc correlarium ex p̄dictis facile ꝓ­<lb/>bari p̄t </s>
              <s xml:id="N1FD2D" xml:space="preserve">¶ Inferat quilibet ſuopte ingenio ꝓpriiſ <lb/>viribus nõnulla ſimilia correlaria </s>
              <s xml:id="N1FD32" xml:space="preserve">Poſſunt enim <lb/>īfinita inferri. </s>
              <s xml:id="N1FD37" xml:space="preserve">vt puta ſi hora diuidatur ꝓportione <lb/>dupla: et omnium partium parium velocitates con­<lb/>tinuo ſe habeãt in ꝓportione ſexquialtera: omniū-<lb/> imparium ꝓportio velocitatum ſit ſexquitertia <lb/>ſit velocitatis ṗme paris ad velocitatem ṗme im­<lb/>paris ꝓportio ſexquiquarta: tunc calcula totale <lb/>ſpcium ad ſpacium ꝑtranſitum in ṗma parte. </s>
              <s xml:id="N1FD46" xml:space="preserve">Item <lb/>conſciſa hora in partes ꝓportionales ꝓportiõe tri­<lb/>pla: et omnium partium imparium immediatarum               <pb chead="Secundi tractatus" file="0163" n="163"/>               velocitates ſe habeant in ꝓportione ſexquiquarta <lb/>omnium vero parium in ꝓportione ſexquiquinta: <lb/>excedat velocitas ṗme partis paris velocitatem <lb/>ṗme partis imparis in proportiõe ſexquiſexta: tūc <lb/>inueſtiga ꝓportionem totius ſpacii ad ſpaciuꝫ per­<lb/>tranſitū in prima innitendo p̄cedentibus. </s>
              <s xml:id="N1FD5C" xml:space="preserve">Itē parti­<lb/>ta hora in partes ꝓportionales ꝓportiõe quadru­<lb/>pla: mobili in omni īpari ſequente mouēte in ſex­<lb/>quiſexto velocius ꝙ̄ in immediate ꝓcedente impari <lb/>et in omni pari ſequente in ſexquiſeptimo velocius <lb/>quã in pari immediate precedente: ſuperet veloci­<lb/>tas prime partis paris velocitatem prime imparis <lb/>in ꝓportione ſexquioctaua: tunc cõmenſura totale <lb/>ſpacium ſpacio prime partis ꝓportionalis precedē­<lb/>tibus ſuffultus </s>
              <s xml:id="N1FD71" xml:space="preserve">Et ſic aſcendendo per ſpecies ꝓpor-<lb/>tionis multiplicis in diuidenda hora velocitatibꝰ <lb/>ſe habentibus continuo in diuerſis ꝓportionibus <lb/>ſuperparticularibus infinitam multitudinem ſe ſe <lb/>ↄ̨ſequētiū cõcluſionum inferre valebis. </s>
              <s xml:id="N1FD7C" xml:space="preserve">Deinde diui­<lb/>ſa hora aliqua multipli ſimplici vel compoſita ve-<lb/>locitatibus partiuꝫ imparium cõtinuo ſe habētibꝰ <lb/>in ꝓportione aliqua ſuprapartiente: et partium pa­<lb/>riū immediatarum velocitatibus continuo ſe habē­<lb/>tibus in aliqua alia ꝓportione ſuprapartiente: ex-<lb/>cedente velocitate prime partis paris velocita-<lb/>tem prime partis imparis in aliqua alia propor-<lb/>tione ſuperpartiente infinita correlaria inferre po­<lb/>teris. </s>
              <s xml:id="N1FD91" xml:space="preserve">Preterea partita hora per partes pro­<lb/>portionales ꝓportione multipici: quarūcun dua­<lb/>rum ꝑtium ꝑ .4. partes ꝓportionales diſtantiū ve-<lb/>locitatibus ſe habentibus in aliqua ꝓportione ſu­<lb/>perparticulari vel ſuperpartiente ita vt ṗme diſtã­<lb/>tes ꝑ .4. partes ꝓportionales vt puta prima et ſex­<lb/>ta ſe habeant in velocitate in ꝓportione ſexquial-<lb/>tera: et ſeptime velocitas ad velocitatem ſecunde in <lb/>ꝓportione ſexquitertia: et octaue velocitas ad velo­<lb/>citatem tertie in ꝓportione ſexquiq̈rta: et none ve-<lb/>locitas ad velocitatem quarte in ꝓportione ſexqui­<lb/>quinta: et decime velocitas ad velocitatem quinte ī <lb/>ꝓportione ſexquiſexta: et vndecime velocitas ad ve­<lb/>locitatem ſexte in ꝓportione ſexquialtera: et ſic ite-<lb/>rum aſcendendo vſ ad proportionem ſexquiſextã <lb/>et deinde redeundo vſ ad ꝓportionem ſexquial-<lb/>teram / et ſic conſequenter: ita  omnes diſtantes ꝑ <lb/>4. incipiendo a ṗma ſe habeant in ꝓportione ſexq̇­<lb/>altera in velocitate: et incipiendo a ſecunda in ſexq̇­<lb/>tertia: et a tertia in ſexquiquarta: et a quarto in ſex­<lb/>quiquinta: et a quinta in ſexquiſexta: et non plus.</s>
            </p>
            <div xml:id="N1FDBC" level="5" n="27" type="float">
              <note position="right" xlink:href="note-0162-01a" xlink:label="note-0162-01" xml:id="N1FDC0" xml:space="preserve">.3. correl.</note>
            </div>
            <p xml:id="N1FDC6">
              <s xml:id="N1FDC7" xml:space="preserve">Ita poteris facere de partibus inter quas cõtinuo <lb/>mediant octo ꝑtes aſcendendo a prima vſ ad de-<lb/>cimã: et ſic in infinitum poteris variare caſus reten­<lb/>ta ſemper aliqua vniformiter ꝓportionum </s>
              <s xml:id="N1FDD0" xml:space="preserve">Et ſi-<lb/>cut inferuntur multa correlaria quando velocitas <lb/>maior coextenditur ꝑtibꝰ minoribus. </s>
              <s xml:id="N1FDD7" xml:space="preserve">ita plura alia <lb/>poſſunt inferri quando continuo velocitas maior <lb/>coextenditur partibus minoribus que omnia ex ṗ-<lb/>oribus facile inducuntur. </s>
              <s xml:id="N1FDE0" xml:space="preserve">Et quia nimium in iſtis <lb/>immorari vltra modum eis inherere, eſt a melio­<lb/>ribus ſublimioribuſ ꝓſtergari: </s>
              <s xml:id="N1FDE7" xml:space="preserve">Ideo calculator <lb/>his dedaleis laberinthulis implicitꝰ: verbiſ mul­<lb/>tiplicibus multiformibuſ ꝓportionibus implica­<lb/>tus: inflate bucce garritum contineat.</s>
            </p>
            <p xml:id="N1FDF0">
              <s xml:id="N1FDF1" xml:space="preserve">Decima concluſio </s>
              <s xml:id="N1FDF4" xml:space="preserve">Diuiſa hora ꝑ par­<lb/>tes ꝓportionales ꝓportione dupla et a. mobile in <lb/>prima ꝑte ꝓportionali moueatur aliquantula ve-<lb/>locitate: et in ſecunda in ſexquialtero maiori veloci­<lb/>tate: et in tertia in ſexquiquarto maiori velocitate <lb/>̄ in prima: et in quinta in ſexquiſexdecimo maiori <lb/>quã in prima / et ſic conſequenter aſcendendo ꝑ ſpe-               <cb chead="Capitulum tertium"/>               cies ꝓportionis ſuperparticularis denominatas <lb/>a numeris pariter paribus </s>
              <s xml:id="N1FE08" xml:space="preserve">(Meliꝰ tñ diceret̄̄ deſcē­<lb/>dēdo: q2 ꝓportiões ſuꝑparticulares ſūt mīores quã­<lb/>to a maiori numero denominantur hoc eſt a parte <lb/>aliquota denominata a maiori numero) ſpacium ꝑ­<lb/>trauſitum in totali hora ſe habet ad ſpacium per-<lb/>tranſitum in prima ꝑte ꝓportionali in ꝓportione <lb/>dupla ſexquitertia. </s>
              <s xml:id="N1FE17" xml:space="preserve">Probatur et ſit gratia exempli <lb/>velocitas ṗme ꝑtis ꝓportionalis vt duo, ꝑtrãſeat­<lb/> a. mobile mediante illa velocitate in prima ꝑte ꝓ­<lb/>portionali bipedale: et arguitur ſic / illa velocitas vt <lb/>duo coextenditur toti hore, quia in qualibet parte <lb/>ꝓportionali hore velocitas eſt maior quam vt duo <lb/>vt habetur ex caſu et tota hora eſt dupla ad primaꝫ <lb/>partem ꝓportionalem eius in qua mobile pertran­<lb/>ſit bipcdale mediante velocitate vt duo: igitur me-<lb/>diante illa velocitate coextenſa toti hore pertran-<lb/>ſit quadrupedale: et mediantibus exceſſibus parti-<lb/>um ꝓportionalium ſupra illam velocitatem vt duo <lb/>pertranſit duas tertias pedalis que faciūt vnã ter­<lb/>tiam duorum pedalium: igitur totuꝫ ſpacium ſe ha­<lb/>bebit ad ſpacium pertranſitum in prima parte ꝓ-<lb/>portionali in proportione dupla ſexquitertia cuiuſ­<lb/>modi eſt ꝓportio ipſoꝝ quatuor cum duabus ter-<lb/>tiis vnius ad duo </s>
              <s xml:id="N1FE3C" xml:space="preserve">Probo tamen /  mediantibꝰ il-<lb/>lis exceſſibus ꝑtranſeat duas tertias pedalis: quo­<lb/>niam cum velocitas ſecunde ꝑtis ꝓportionalis ſit <lb/>ſexquialtera ad velocitatem prime que eſt vt duo ſe­<lb/>quitur /  exceſſus velocitatis ſecunde ad velocitatē <lb/>prime eſt vnus gradus et quia tertia excedit primã <lb/>in ꝓporeione ſexquiquarta / ſequitur /  exceſſus eius <lb/>eſt medietas vnius gradus quoniam duorum cū di­<lb/>midio ad duo eſt proportio ſexquiquarta, et veloci­<lb/>tas quarte partis ſe habet ad velocitatem prime ī <lb/>ꝓportione ſexquioctaua: igitur exceſſus eius ē vna <lb/>quarta: igitur in illo caſu exceſſus ſecunde ad exceſ­<lb/>ſum tertie eſt ꝓportio dupla et exceſſus tertie ad ex-<lb/>ceſſum quarte dupla ſimiliter: et ſic conſequenter re­<lb/>peries illos exceſſus ſe habere in ꝓportione ſubdu­<lb/>pla et ſubdupla. et coextenduntur partibus cõtinuo <lb/>ſe habentibus in ꝓportione ſubdupla et ſubdupla / <lb/>igitur continuo illa ſpacia mediantibus illis velo­<lb/>citatibus ꝑtranſita ſe habet in ꝓportione ſubqua-<lb/>drupla / et ꝑ conſequens aggregatum ex omnibꝰ eis <lb/>ſe habebit ad primum illorum in ꝓportione ſexqui­<lb/>tertia et ṗmum illorum eſt vnum ſemipedale: ergo <lb/>totum erit vnum ſemipedale cum vna ſexta peda-<lb/>lis: et ꝑ conſequens due tertie vnius pedalis / qḋ fuit <lb/>ꝓbandum. </s>
              <s xml:id="N1FE6F" xml:space="preserve">Sed iam ꝓbo /  p̄mum illorum ſit vnum <lb/>ſemipedale quoniam primum illorum ꝑtranſit̄̄ me­<lb/>diante exceſſu ſecunde ꝑtis ꝓportionalis ſupra pri­<lb/>mam qui exceſſus eſt vnus gradus mediante quo ī <lb/>prima parte ꝓportionali pertranſitur vnum peda­<lb/>le: igitur mediante illo in ſecunda parte ꝓportiõa-<lb/>li ſubdupla ad illam pertranſitur vnum ſemipeda­<lb/>le / quod fuit ꝓbandum. </s>
              <s xml:id="N1FE80" xml:space="preserve">Patet conſequentia ex ſecū­<lb/>da ꝑte prime ꝓpoſitionis ſecundi notabilis.</s>
            </p>
            <p xml:id="N1FE85">
              <s xml:id="N1FE86" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  ſi fuerit ho­<lb/>ra diuiſa ꝓportione dupla: et in prima illarum par­<lb/>tium moueatur aliquod mobile aliquanta velocita­<lb/>te, et in ſecunda in ſupertripartiente quartas maio­<lb/>ri velocitate, et in tertia in ſupertripartiente octa-<lb/>uas maiori velocitate ꝙ̄ in prima: et in quarta in ſu­<lb/>ꝑtripartiente ſexdecimas maiori ꝙ̄ in prima et in <lb/>quinta in ſuꝑtripartiente triceſimas ſecundas ma­<lb/>iori velocitate ꝙ̄ in prima / et ſic conſequenter ꝓcedē­<lb/>do per ſpecies ꝓportionis ſupertripartientis de-<lb/>nominatas a numeris pariter paribus ſiue a par-<lb/>tibus aliquotis denominatis ab illis numeris: ſpa­               <pb chead="De motu locali quo ad effectum tempore difformi." file="0164" n="164"/>               cium ꝑtranſitum in toto tempore eſt dupluꝫ ſexqui­<lb/>alterum ad ſpacium pertranſitum in prima parte <lb/>proportionali </s>
              <s xml:id="N1FEA8" xml:space="preserve">Quod probatur eſto /  velocitas ṗ­<lb/>me partis ſit vt .4. et pertranſeatur quadrupedale <lb/>mediante illa per totam horam exrenſa: et ſic medi­<lb/>ante illa in prima ꝑte ꝓportionali bipedale / et ar-<lb/>guitur ſic / mediãte illa velocitate extenſa ꝑ totã ho­<lb/>ram mobile ꝑtranſit quadrupedale et mediantibꝰ <lb/>exceſſibus quibus velocitates partium proportio-<lb/>nalium aliarum a prima excedunt primam pertrã­<lb/>ſitur vuum: et ſic mediante totali illa velocitate per­<lb/>tranſeuntur quin pedalia in totali illa hora: et q̇n­<lb/>tupedalis ad bipedale pertranſitum in prima par­<lb/>te proportionali hore eſt proportio dupla ſexqui-<lb/>altera. </s>
              <s xml:id="N1FEC3" xml:space="preserve">igitur propoſitum. </s>
              <s xml:id="N1FEC6" xml:space="preserve">Probatur tamen /  me­<lb/>diantibus illis exceſſibus pertranſitur vnum peda­<lb/>le: quia mediante exceſſu quo velocitas ſecunde par­<lb/>tis excedit velocitatem prime pertranſeuntur tres <lb/>quarte et mediante exceſſu quo tertia excedit primã <lb/>pertranſitur ſubquadruplum ſpacium ad tres q̈r-<lb/>tas / et ſic conſequenter (quia illi exceſſus cõtinuo ſe <lb/>habent in proportione ſubdupla / vt facile eſt intue­<lb/>ri: et continuo coextenduntur tempori in duplo mi­<lb/>nori) / igitur aggregatum ex omnibus illis ſpaciis <lb/>pertranſitis mediantibus illis exceſſibus cõponi-<lb/>tur ex infinitis continuo ſe habentibus in propor-<lb/>tione ſubquadrupla et ex hoc illud habet ſe ad pri-<lb/>mum illoruꝫ ī proportione ſexquitertia / vt patet ex <lb/>prima parte capite quinto: et primum illoruꝫ ē tres <lb/>quarte pedalis: ergo totum eſt pedale: </s>
              <s xml:id="N1FEE7" xml:space="preserve">Patet con-<lb/>ſequentia / q2 pedalis ad tres quartas eſt propor-<lb/>tio ſexquitertia. </s>
              <s xml:id="N1FEEE" xml:space="preserve">Sed reſtat probare ſpacium per-<lb/>tranſitum ab illo exceſſu quo ſecunda pars propor­<lb/>tionalis excedit primam eſſe tres quartas quia ve­<lb/>locitas ṗme partis eſt vt .4. et velocitas ſecunde ꝑ-<lb/>tis habet ꝓportionē ſuꝑtripartienteꝫ q̈rtas ad ve-<lb/>locitatē prīe / igit̄̄ eſt vt .7. et ſic exceſſus eſt trium gra­<lb/>duū: ſꝫ mediãte vno gradu in prīa ꝑte ꝓportionali <lb/>mobile ꝑtranſibat dimidium pedale vt habetur ex <lb/>caſu: igitur mediante vno gradu in ſecunda parte <lb/>ꝓportionali que eſt in duplo minor mobile pertrã­<lb/>ſit vnam quartam et ſunt ibi tres gradus exceſſus: <lb/>igitur mediantibus illis ꝑtranſibit tres quartas / <lb/>quod fuit ꝓbandum.               <anchor type="note" xlink:href="note-0164-01" xlink:label="note-0164-01a"/>               </s>
              <s xml:id="N1FF0E" xml:space="preserve">¶ Sequitur ſecundo /  parti-<lb/>ta hora ꝑ partes ꝓportionales proportiõe dupla <lb/>et in prima illarum mobile aliquod moueatur aliq̈ <lb/>velocitate: et in ſecunda illarum in ſexquitertio ma­<lb/>iori: et in tertia in ſexquiſexto maiori ꝙ̄ in prima et <lb/>in quarta in ſexquiduodecuplo maiori ꝙ̄ in prima / <lb/>et ſic conſequenter aſcendo ꝑ numeros pares conti­<lb/>nuo ſe habentes in ꝓportione dupla exordiendo a <lb/>numero ternario: hoc eſt ꝑ ſpecies ꝓportionis ſuꝑ-<lb/>particularis denomīatas a partibus aliquotis de­<lb/>nominatis ab illis numeris: ſpacium pertranſituꝫ <lb/>in totali hora eſt duplum ſuperbipartiens nonas <lb/>ad ſpacium pertranſitum in prima parte ꝓportio­<lb/>nali. </s>
              <s xml:id="N1FF2B" xml:space="preserve">Probatur eſto exempli cauſa /  velocitas pri­<lb/>me partis ꝓportionalis ſit vt .3. et mediante illa mo­<lb/>bile pertranſeat in prima parte ꝓportionali tripe­<lb/>dale: et ꝑ conſequens mediante illa extenſa ꝑ totaꝫ <lb/>horam ſextipedale: et arguitur ſic mediante illa ve­<lb/>locitate vt .3: coextenſa toti hore mobile ꝑtranſibit <lb/>ſextipedale: et mediantibus excrementis quibus ve­<lb/>locitates parttium ꝓportionalium aliarum a pri-<lb/>ma excedunt primam mobile pertranſit duas ter-<lb/>tias pedalis: igitur in totali illa hora pertranſit <lb/>ſextipedale cum duabus tertius: ſed ſextipedalis cū <lb/>duabus tertiis ad tripedale pertranſituꝫ in prima <lb/>parte ꝓportionali eſt proportio dupla ſuperbipar­               <cb chead="De motu locali quo ad effectum tempore difformi."/>               tiens nonas: igitur propoſitum. </s>
              <s xml:id="N1FF49" xml:space="preserve">Sed iam probo /  <lb/>mediantibus exceſſibus velocitatum quibus alie ꝑ­<lb/>tes proportionales excedunt velocitatem ṗme mo-<lb/>bile pertranſit duas tertias. </s>
              <s xml:id="N1FF52" xml:space="preserve">quia velocitas ſecun-<lb/>de partis ꝓportionalis excedit velocitatem prime <lb/>ꝑ vnum gradum (eſt enim velocitas prime vt .3. et ſe­<lb/>cunde ſexquitertia ad illam) et mediante vno gradu <lb/>in prima parte ꝓportionali mobile pertranſit vnū <lb/>pedale: ergo mediante illo gradu mobile ꝑtranſit <lb/>vnum ſemipedale in ſecunda parte proportionali <lb/>ſubdupla ad primam: et mediante exceſſu quo tertia <lb/>pars excedit primam pertranſit ſubquadruplū ad <lb/>illud ſemipedale. </s>
              <s xml:id="N1FF67" xml:space="preserve">et mediante exceſſu quo quarta ex­<lb/>cedit primam adhuc pertranſit ſubquadruplū ad <lb/>precedens / et ſic conſequenter: quia illi exceſſus con-<lb/>tinuo ſe habent in ꝓportione ſubpupla / vt patet ex <lb/>caſu: et continuo extenduntur in duplo minori par­<lb/>te: igitur aggregatum ex omnibus illis ſpaciis per­<lb/>tranſitis mediantibus illis exceſſibus componitur <lb/>ex infinitis continuo ſe habentibus in proportione <lb/>ſubquadrupla. </s>
              <s xml:id="N1FF7A" xml:space="preserve">igitur ſe habet ad primum illorum <lb/>in ꝓportione ſexquitertia. </s>
              <s xml:id="N1FF7F" xml:space="preserve">Conſequentia ſepiꝰ ar-<lb/>guta eſt. </s>
              <s xml:id="N1FF84" xml:space="preserve">et cum primum illorum ſit ſemipedale: con­<lb/>ſequens eſt vt aggregatum ex omnibus illis ſit due <lb/>tertie (ſiquidem duarum tertiarum ad ſemipedale <lb/>ſit ſexquitertia proportio) </s>
              <s xml:id="N1FF8D" xml:space="preserve">Et ſic patet probandum <lb/>et totum correlarium. </s>
              <s xml:id="N1FF92" xml:space="preserve">¶ Innumera talia correlaria <lb/>poſſunt inferri diuidendo horam aliis ſpeciebus ꝓ­<lb/>poportionis: et faciendo exceſſus quibus alie par-<lb/>tes excedunt primam in certa ꝓportiõe continue ſe <lb/>habere: vt ſi hora diuidatur per partes proportio­<lb/>nales ꝓportione tripla: et in prima illaruꝫ aliquod <lb/>mobile moueatur aliquanta velocitate et in ſecun-<lb/>da in duplo ſexquialtero maiori: et in tertia in du-<lb/>plo ſexquiſexto: et in quarta in duplo ſexquidecimo <lb/>octauo maiori ꝙ̄ in prima: et in quinta in duplo ſex­<lb/>quiquīquageſimo quarto maiori ꝙ̄ in prima: et ſic <lb/>conſequenter procedendo ex parte ꝓportionis mul­<lb/>tiplicis ſuperparticularis per numeros ſe haben-<lb/>tes continuo in ꝓportione ſubtripla </s>
              <s xml:id="N1FFAF" xml:space="preserve">Ibi enim ex-<lb/>ceſſus ſe habent in proportione ſubtripla </s>
              <s xml:id="N1FFB4" xml:space="preserve">Itē ſi ho­<lb/>ra partiatur per partes ꝓportionales ꝓportione <lb/>ſuperbipartiente tertias et a. mobile in prima mo-<lb/>ueatur aliquanta velocitate et in ſecunda in triplo <lb/>ſexquiquinto velocius: et in tertia in triplo ſexqui-<lb/>decimo velocius ꝙ̄ in prima: et in quarta in triplo <lb/>ſexqui viceſimo velocius ꝙ̄ in prima: et in quinto in <lb/>triplo ſexquiquadrigeſimo progrediendo per ſpe­<lb/>cies denomīatas a numeris imparibus ſiue ab vni­<lb/>tate et partibus aliquotis denominatis ab illis nu­<lb/>meris continuo ſe habentibus in ꝓportione dupla <lb/>exordiendo a quinario. </s>
              <s xml:id="N1FFCD" xml:space="preserve">Et ſic conſequenter poteris <lb/>infinita ſimilia ponere</s>
            </p>
            <div xml:id="N1FFD2" level="5" n="28" type="float">
              <note position="left" xlink:href="note-0164-01a" xlink:label="note-0164-01" xml:id="N1FFD6" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N1FFDC">
              <s xml:id="N1FFDD" xml:space="preserve">Undecima concluſio </s>
              <s xml:id="N1FFE0" xml:space="preserve">Diuiſa hora per <lb/>partes proportionales quacun libuerit propor-<lb/>tione et in prima mobile moueatur aliquanta velo­<lb/>citate et in ſecunda in ſexquialtero maiori: et in ter-<lb/>tia in ſexquitertia maiori ꝙ̄ in ſecunda: et in quarta <lb/>in ſexquiquarta maiori ꝙ̄ in tertia et in quinta ī ſex­<lb/>quiquinto maiori ꝙ̄ in quarta / et ſic conſequenter. <lb/></s>
              <s xml:id="N1FFF0" xml:space="preserve">et ſi nõ valeat regula vniuerſalis ſignari ad reperi­<lb/>endum ſpacium pertranſitum in totali hora: nichi­<lb/>lominus tamen qualibet ſpecie diuiſionis hore ſi-<lb/>gnata poteſt certitudinaliter inueſtigari ſpaciuꝫ ꝑ­<lb/>tranſitum in tota hora: et ꝓportio eius ad ſpacium <lb/>pertranſitum in prima parte ꝓportionali. </s>
              <s xml:id="N1FFFD" xml:space="preserve">Proba­<lb/>tur hec concluſio / et primo probatur ſecunda ꝑs eiꝰ. <lb/></s>
              <s xml:id="N20003" xml:space="preserve">quia ſit hora fuerit diuiſa per partes proportiona­               <pb chead="Secundi tractatus" file="0165" n="165"/>               les proportione dupla: et moueatur mobile vt dicit̄̄ <lb/>in caſu concluſionis: ſpaeium pertranſitum in to-<lb/>tali hora ſe habebit ad ſpacium pertranſitum in ṗ­<lb/>ma parte proportionali in proportione tripla.</s>
            </p>
            <p xml:id="N20011">
              <s xml:id="N20012" xml:space="preserve">Quod ſic probatur eſto /  velocitas prime partis <lb/>ſit vt duo et ſecunde vt .3. et tertie vt .4. ſicut apparet <lb/>ex caſu cõncluſionis: et mediante illa velocitate pri-<lb/>me partis ꝓportionalis vt duo que etiã coextendi­<lb/>tur toti hore pertranſeat mobile bipedale ī prima <lb/>parte ꝓportionali: et per conſequens quadrupeda­<lb/>le in tota hora / et arguo ſic illud mobile mediante il­<lb/>la velocitate vt duo extenſa per totam horam per-<lb/>tranſit quadrupedale: et mediantibus exceſſibus q̇-<lb/>bus partes ꝓportionales ſe excedunt pertranſit bi­<lb/>pedale: igitur in tota hora ꝑtranſit ſex bipedalia: <lb/>ſed ſex pedalium ad duo pedalia pertranſita in pri­<lb/>ma parte eſt ꝓportio tripla: igitur. </s>
              <s xml:id="N2002D" xml:space="preserve">Patet conſeq̄n­<lb/>tia cum maiore: et arguitur minor: videlicet /  medi­<lb/>antibus illis exceſſibus mobile pertranſit pedale. <lb/></s>
              <s xml:id="N20035" xml:space="preserve">quia mediante illo gradu quo ſecunda pars ꝓpor­<lb/>tionalis excedit primam qui eſt extenſus etiam a to­<lb/>to reſiduo a prima illud mobile pertranſit vnū pe-<lb/>dale quia mediantibus duobus gradibus coexten­<lb/>ſis illi parti id eſt toti reſiduo a prima pertranſit bi­<lb/>pedale / vt ponitur: mediante vno igitur extenſo eidē <lb/>pertranſitur vnum pedale: et mediante etiã vno gra­<lb/>du quo tertia pars excedit ſecundam extenſo ꝑ to-<lb/>tum reſiduum a prima et ſecunda pertranſit ſubdu-<lb/>plum ad pedale quia extenditur ꝑ in duplo minorē <lb/>partem: et mediante exceſſu quo quarta excedit ter-<lb/>tiam qui eſt etiam vnus gradus extenſus per totuꝫ <lb/>reſiduum a prima ſecūda et tertia / quod ē ſub­<lb/>duplum ad totum reſiduum a prima et ſecūda et ter­<lb/>tia pertranſit illud mobile in duplo minus ꝙ̄ medi­<lb/>ante precedente: igitur ſpacium totale pertranſitū <lb/>mediantibus illis exceſſibus componitur ex aliqui­<lb/>bus continuo ſe habentibus in ꝓportiõe ſubdupla <lb/>et ſubdupla: et primum eſt pedale: ergo totum eſt bi-<lb/>pedale / quod fuit ꝓbandum. </s>
              <s xml:id="N2005E" xml:space="preserve">Item partita hora in <lb/>partes proportionales ꝓportiõe ſexquialtera mo­<lb/>bili mouente eodem modo quo ponitur in caſu cõ­<lb/>cluſionis: ſpacium pertranſitum in tota hora ē ſex­<lb/>tuplum ad ſpacium pertranſitum in prima parte ꝓ­<lb/>porionali hore. </s>
              <s xml:id="N2006B" xml:space="preserve">Probatur et ſit gratia argumenti <lb/>velocitas prime partis ꝓportionalis / vt duo et me­<lb/>diante illa coextenſa toti hore pertranſeat mobile <lb/>tripedale: et per conſequens mediante illa in ṗma ꝑ­<lb/>te ꝓportionali ꝑtranſibit pedale qua ṗma ꝑs ꝓpor­<lb/>tionalis eſt ſubtripla ad totum diuiſum tali ꝓpor­<lb/>tione: quo poſito arguitur ſic mediante illa veloci-<lb/>tate / vt duo coextenſo toti hore ꝑtranſit tripedale et <lb/>mediantibus exceſſibus etiam ꝑtranſit tripedale: <lb/>igitur in totali hora ꝑtranſit ſexpedalia: et in prīa <lb/>parte ꝓportionali vnum pedale / vt ponitur: igitur <lb/>totale ſpacium ſe habet ad ſpacium pertranſitum ī <lb/>prima parte ꝓportionali in ꝓportiõe ſextupla / qḋ <lb/>fuit ꝓbandum. </s>
              <s xml:id="N20088" xml:space="preserve">Sed iam probo /  mediantibus ex-<lb/>ceſſibus pertranſit tripepale quia velocitas ſecun-<lb/>de partis ꝓportionalis excedit velocitatem prime <lb/>per totum reſiduum a prima parte proportionali: <lb/>igitur mediante illo mobile pertranſit vnum peda­<lb/>le. </s>
              <s xml:id="N20095" xml:space="preserve">Patet hec conſequentia / quia mediante vno gra­<lb/>du in prima parte proportionali mobile pertranſit <lb/>ſemipedale vt apparet ex caſu: igitur mediante vno <lb/>gradu extenſo per totum reſiduum a prima parte ꝓ­<lb/>portionali vnum pedale cum totum reſiduum a pri­<lb/>ma parte ſit duplum ad illam: et mediante exceſſu <lb/>quo tertia pars excedit ſecundam / qui eſt etiam vnꝰ <lb/>gradus ꝑ totum reſiduum a prima et ſecunda exten­               <cb chead="Capitulum tertium"/>               ſus pertranſibit ſubſexquialterum ad illud peda-<lb/>le: et mediãte exceſſu quo quarta excedit tertiam ex-<lb/>tenſo per totum reſiduum a prima ſecunda et ter-<lb/>tia pertranſit etiam ſubſexquialterum ad precedēs <lb/>cum illi exceſſus continuo ſint equales continuo co­<lb/>extenſis partibus ī ſexquialtero minoribus: igitur <lb/>illud ſpacium pertranſitum mediantibus illis ex-<lb/>ceſſibus componitur ex infinitis continuo ſe haben­<lb/>tibus in proportione ſexquialtera. / igitur totius il­<lb/>lius ſpacii ad primum illorum ſpaciorum eſt ꝓpor­<lb/>tio tripla: et primum eſt pedale: ergo totum eſt tri-<lb/>pedale / quod fuit probandum. </s>
              <s xml:id="N200BF" xml:space="preserve">Et ſic patet /  <lb/>aliquando totale ſpacium eſt ſextuplum aliquan-<lb/>do triplum ad ſpacium pertranſitum in prima par­<lb/>te ꝓportionali </s>
              <s xml:id="N200C8" xml:space="preserve">¶ Et ex his infertur prima pars cõ-<lb/>cluſionis videlicet /  non eſt vna regula certa: quaꝫ <lb/>parteꝫ ꝓbaliter pono / quia forte eſt modus: et cer­<lb/>ta regula: et nõ occurrit mihi </s>
              <s xml:id="N200D1" xml:space="preserve">Apparet etiã veritas <lb/>ſecunde partis / quia quauis ꝓportione propoſita <lb/>qua tempus diuiditur, mobili mouente / vt ponitur <lb/>in caſu concluſionis ex p̄dictis poteſt inueniri ſpa-<lb/>cium pertranſitum in totali tēpore. </s>
              <s xml:id="N200DC" xml:space="preserve">¶ Alio tamen <lb/>modo poterit tale ſpaciū ad inueniri primo imagi­<lb/>nando medietatem velocitatis prime partis eſſe ſe <lb/>motam per totam horam: et tunc inuenitur ſpaciū <lb/>pertranſitum in totali hora mediante reſidua velo­<lb/>citate manente ex quarta concluſione huius. </s>
              <s xml:id="N200E9" xml:space="preserve">q2 tūc <lb/>reſidua velocitas ſe habebit omnino ſicut ponit il­<lb/>la concluſio. </s>
              <s xml:id="N200F0" xml:space="preserve">deinde illo ſpacio ſic ad inuento adiū-<lb/>ge ſpacium natum ꝑertranſiri a velocitate quã ſub­<lb/>traxeris et ſic totum ſpacium erit ad inuentum quo <lb/>relato ad ſpacium pertrãſitum in prima parte pro­<lb/>portionali habebitur queſitum. </s>
              <s xml:id="N200FB" xml:space="preserve">Exemplum / vt par­<lb/>tita hora per ꝑtes ꝓportionales ꝓportione dupla <lb/>mobili moto / vt dictum eſt in caſu concluſionis pre­<lb/>cedētis: et ſit velocitas prīe ꝑtis ꝓportiõalis vt duo <lb/>q̄ velocitas ē coextēſa toti hore: et mediãte illa velo­<lb/>citate vt duo coextenſa toti hore pertranſeat mobi­<lb/>le exēpli gratia bipedale. </s>
              <s xml:id="N2010A" xml:space="preserve">remoueas igitur ad ima­<lb/>ginationem vnum gradum illius velocitatis vt duo <lb/>que extenditur per totam horam. </s>
              <s xml:id="N20111" xml:space="preserve">et tunc manifeſtū <lb/>eſt /  illa ſemota mobile mouebitur aliqua veloci-<lb/>tate in prima: et in ſecunda in duplo maiori et in ter­<lb/>tia in tripla maiori quã in prima etc. / et ſic conſequē­<lb/>ter: igitur totalis velocitas ſe habebit ad velocita­<lb/>tem prime partis ꝓportionalis in ꝓportione du-<lb/>pla ex ſecunda concluſione: et ſpacium pertranſituꝫ <lb/>in totali hora ſe habebit in ꝓportione duplicata <lb/>ad ſpacium pertranſitum in prima parte ꝓportio­<lb/>nali mediante velocitate vt vnum (quia oportet in-<lb/>telligere alium gradum ſemotum mediante cuius <lb/>velocitate vnius videlicet gradus mobile pertran-<lb/>ſit ſemipedale in prima parte ꝓportiõali) / ergo me­<lb/>diante tota velocitate pertranſit bipedale. </s>
              <s xml:id="N2012E" xml:space="preserve">et mediã­<lb/>te illo gradu quē remoueras extenſo per totam ho­<lb/>ram pertranſit vnuꝫ pedale in tota hora: igitur to­<lb/>tale ſpacium eſt tripedale: et in prima parte propor­<lb/>tionali mediantibus illis duobus gradibus ꝑtrã-<lb/>ſibat pedale: igitur totum ſpaciuꝫ eſt triplū ad ſpa­<lb/>cium pertranſitum in prima parte </s>
              <s xml:id="N2013D" xml:space="preserve">Et ſic iudicabis <lb/>de omnibus.</s>
            </p>
            <p xml:id="N20142">
              <s xml:id="N20143" xml:space="preserve">Duodecima cõcluſio: </s>
              <s xml:id="N20146" xml:space="preserve">Si ſit aliquod <lb/>tp̄s diuiſū ꝑ partes ꝓportiõales ꝓportione dupla <lb/>et in prima parte ꝓportiõali mobile moueatur ali-<lb/>quanta velocitate: et in ſecunda in duplo velocius <lb/>quã in prima: et in tertia in ſexquialtero velocius ̄ <lb/>in prima: et in quarta in ſexquitertio velociꝰ quam <lb/>in prima. / et ſic conſequenter procedendo per omēs               <pb chead="De motu locali quo ad effectum tempore difformi." file="0166" n="166"/>               ſpecies proportionis ſuperparticularis: ſpaciū ꝑ-<lb/>tranſitum in totali tempore eſt maius quã duplum <lb/>ad ſpacium pertranſitum in prima parte ꝓportio­<lb/>nali, et minus ꝙ̄ quadruplum. </s>
              <s xml:id="N20160" xml:space="preserve">Probatur prīa ꝑs / <lb/>quia diuiſa ſic hora per partes proportionales ꝓ-<lb/>portione dupla: et mobili moto continuo vniformi­<lb/>ter illo motu quo mouetur in prima parte ꝓportio­<lb/>nali ſpaciū pertrãſitū adequate in tota hora eſſet <lb/>adequate duplum ad ſpacium pertranſitum in pri­<lb/>ma parte proportionali / vt patet ex ſe: ſed mõ mo-<lb/>bile velocius mouetur quam tunc in qualibet ꝑ­<lb/>te proportionali dempta prima modo velociꝰ mo-<lb/>uetur quã tunc / et in prima eque velociter ſicut tunc: <lb/>igitur pertranſit pluſ̄ duplum ſpaciuꝫ ad ſpaciū <lb/>pertranſitum in prima parte proportionali. </s>
              <s xml:id="N20179" xml:space="preserve">Pro­<lb/>batur ſecunda pars: quia ſi illud mobile mouetur ī <lb/>prima parte proportionali aliquantum velociter: <lb/>et in ſecunda in duplo: et in tertia in triplo velocius <lb/>quã in prima: et ſic conſequenter vt ponitur in caſu <lb/>quarte concluſionis: tunc adequate pertranſiret q̈­<lb/>druplum ſpacium ad ſpacium pertranſitum in pri­<lb/>ma parte ꝓportionali: vt patet ex quarta concluſio­<lb/>ne: ſed modo mouetur in totali hora tardius quam <lb/>tunc ꝑ omnes partes proportionales dempta pri-<lb/>ma et ſecunda. / et in prima et ſecunda equaliter ſicut <lb/>tunc: igitur modo pertranſit minus ſpacium quam <lb/>tunc in totali hora: et tunc quadruplum pertranſit <lb/>ad ſpacium pertranſitum in prima parte ꝓportio­<lb/>nali: igitur modo minus quam quadruplū / qḋ fuit <lb/>ꝓbandum. </s>
              <s xml:id="N2019A" xml:space="preserve">Et ſic patet concluſio.               <anchor type="note" xlink:href="note-0166-01" xlink:label="note-0166-01a"/>               </s>
              <s xml:id="N201A2" xml:space="preserve">¶ Ex cuius ꝓba-<lb/>tione ſequitur primo /  ſi fuerit tempus diuiſum ꝑ <lb/>partes ꝓportionales proportione ſexquialtera: et <lb/>mobile moueatur eodem modo quo dictum eſt ī ca-<lb/>ſu concluſionis: ſpacium pertranſitum in totali ho­<lb/>ra erit maius quã triplum ad ſpacium pertranſitū <lb/>in prima parte ꝓportionali: et minus quã non ocu-<lb/>plum. </s>
              <s xml:id="N201B3" xml:space="preserve">Probatur prima pars / quia ſi mobile moue­<lb/>retur vniformiter per totam horam illa velocitate <lb/>qua mouetur in prima parte ꝓportionali adequa-<lb/>te: tunc ſpacium pertranſitū in totali hora eſſet tri­<lb/>plum ad ſpacium pertranſitum in prima parte pro­<lb/>portionali quia tota hora ē tripla ad primã ꝑtē ꝓ-<lb/>portionalem ꝓportione ſexquialtera: ſed modo in <lb/>totali hora mouetur intenſius quã tunc / vt patet: er­<lb/>go ſequitur /  modo pertranſibit maius ſpacium <lb/>quã tunc: et tunc pertranſit triplum ſpacium ad ſpa­<lb/>cium pertranſitum in prima parte ꝓportionali: er­<lb/>go modo maius quã triplum: quod fuit ꝓbandum. <lb/></s>
              <s xml:id="N201CD" xml:space="preserve">Probatur ſecunda pars / quia ſi mobile moueretur <lb/>eodem modo quo ponitur in caſu quarte cõcluſiõis <lb/>diuiſa ſic hora per partes ꝓportionales ꝓportio-<lb/>ne ſexquialtera. / tunc ꝑtranſiret nonocuplam ſpaci­<lb/>um ad ſpacium pertranſitum in prima parte pro-<lb/>portionali: vt patet ex quinta concluſione: et eius ſe­<lb/>cundo correlario: ſed modo tardius mouetur in to-<lb/>tali hora quam tunc: ergo modo tranſit minus ſpa­<lb/>cium quã nonocuplū ad ſpaciū pertranſitum in pri­<lb/>ma parte ꝓportionali: quod fuit ꝓbandum.</s>
            </p>
            <div xml:id="N201E2" level="5" n="29" type="float">
              <note position="left" xlink:href="note-0166-01a" xlink:label="note-0166-01" xml:id="N201E6" xml:space="preserve">.1. correl.</note>
            </div>
            <note position="left" xml:id="N201EC" xml:space="preserve">2. correl.</note>
            <p xml:id="N201F0">
              <s xml:id="N201F1" xml:space="preserve">¶ Sequitur ſecundo /  hora diuiſa per partes pro­<lb/>portionales ꝓportione ſuperbipartiente tertias: <lb/>mobili moto in prima parte proportionali aliquã­<lb/>tula velocitate: et in ſecunda in ꝓportione ſupertri-<lb/>partiēte quartas velocius: et in tertia in proportio­<lb/>ne ſupertripartiente octauas velocius quã in ſecū-<lb/>da: et in quarta in ꝓportione ſupratripartiente de-<lb/>cimas ſextas velocius ꝙ̄ in tertia: et ſic conſequēter <lb/>ſpacium pertranſitum in totali hora erit maius ̄ <lb/>duplum ſexquialterum ad ſpacium ꝑtranſitum in <lb/>prima parte ꝓportionali et minus quã ſexdecuplū               <cb chead="De motu locali quo ad effectum tempore difformi."/>               ſexquiquartum.               <anchor type="note" xlink:href="note-0166-02" xlink:label="note-0166-02a"/>               </s>
              <s xml:id="N20210" xml:space="preserve">¶ Sequitur tertio /  diuiſa hora ꝑ <lb/>partes proportionales tripla proportione: et ī pri­<lb/>ma parte proportionali mobile moueatur aliquã-<lb/>tula velocitate. </s>
              <s xml:id="N20219" xml:space="preserve">et in ſecunda in ſuprabipartiente ter­<lb/>tias maiori velocitate: et in tertia in ſuperbipartiē­<lb/>te quintas maiore velocitate ꝙ̄ in prima: et in quar­<lb/>ta in ſuperbipartiente ſeptimas maiori ꝙ̄ in prīa <lb/>et in quinta in ſuperbipartiente nonas maiori ꝙ̄ in <lb/>prima: et ſic conſequenter procedendo ꝑ ſpecies pro­<lb/>portionis ſuperbipartientis denominatas a nūe-<lb/>ris īparibꝰ vĺ a ꝑtibꝰ aliq̊tis a nūeris īparibꝰ deno­<lb/>minatis: ſpacium ꝑtranſitum in totali hora ē ma-<lb/>ius ꝙ̄ ſexquialterum ad ſpacium pertranſitum in ṗ­<lb/>ma parte proportionali: et minus quã dupluꝫ ſexq̇-<lb/>quartum.               <anchor type="note" xlink:href="note-0166-03" xlink:label="note-0166-03a"/>               </s>
              <s xml:id="N20237" xml:space="preserve">¶ Sequitur quarto /  diuiſa hora ꝑ par-<lb/>tes ꝓportionales ꝓportione quadrupla: et in ṗma <lb/>ꝑte proportionali mobile moueat̄̄ aliquantula ve­<lb/>locitate: et in ſecunda in ſexquialtero velocius: et in <lb/>tertia in ſuperbipartienti tertias velocius ꝙ̄ in pri­<lb/>ma: et in quarta in ſupertripartiente quartas velo­<lb/>cius ꝙ̄ in prima: et in quinta in ſuperbipartiente q̇n­<lb/>tas velocius ꝙ̄ in prima et in ſexta in ſupertripar-<lb/>tiente octauas velocius ꝙ̄ in prima: et ſic conſequen­<lb/>ter in partibus imparibus procedendo per propor­<lb/>tionem ſupertripartientem: et in paribus ꝑ ꝓportio­<lb/>nem ſuperbipartientem: ſpacium pertranſitum in <lb/>totali hora eſt pluſ̄ ſexquitertium ad ſpacium per­<lb/>tranſitum in prima parte ꝓportionali: et minꝰ quã <lb/>ſuperſeptipartiens nonas ad ſpacium pertranſi-<lb/>tum in prima </s>
              <s xml:id="N20258" xml:space="preserve">Iſta tria correlaria eandem cum ſu-<lb/>periori correlario ſortiuntur demonſtrationem.</s>
            </p>
            <div xml:id="N2025D" level="5" n="30" type="float">
              <note position="right" xlink:href="note-0166-02a" xlink:label="note-0166-02" xml:id="N20261" xml:space="preserve">.3. correl.</note>
              <note position="right" xlink:href="note-0166-03a" xlink:label="note-0166-03" xml:id="N20267" xml:space="preserve">4. correl.</note>
            </div>
            <note position="right" xml:id="N2026D" xml:space="preserve">Queſtio</note>
            <p xml:id="N20271">
              <s xml:id="N20272" xml:space="preserve">¶ Sed queret equilibris calculator ad amiſſim om­<lb/>nia coniectans et numerorū quadã ſtatera appen-<lb/>dens adequatam velocitatem qua in tota hora il-<lb/>lud mobile mouetur: et adequatum ſpacium ꝑtran-<lb/>ſitum a tali mobili in caſu duodecime concluſionis <lb/>et quatuor lateralium correlariorum eam ſequenti­<lb/>um. </s>
              <s xml:id="N20281" xml:space="preserve">Hinc curioſe queſtioni (cui queſtioni querente <lb/>proteruo difficilis eſt reſponſio) ei ſilentium impo-<lb/>nens per duas ꝓpoſitiones reſpõdeo.</s>
            </p>
            <p xml:id="N20288">
              <s xml:id="N20289" xml:space="preserve">Prima propoſitio </s>
              <s xml:id="N2028C" xml:space="preserve">Si velocitas in in­<lb/>finitum difformis aliquã coherentiam ſiue ꝓportio­<lb/>nem continuo ſeruat: facile eſt totalem velocitatem <lb/>cõmenſurare: et ſpacium mediante illa tranſitū mē­<lb/>tiri. </s>
              <s xml:id="N20297" xml:space="preserve">Patet hec ꝓpoſitio / quia ſi continuo velocita-<lb/>tes in eadem proportione ſe habeant: et etiam ſpa­<lb/>cia ſe in aliqua ꝓportione continuo ſe habebunt: et <lb/>tunc cognita illa ꝓportione iam totale ſpacium ſe <lb/>habebit ad ſpacium pertranſituꝫ in prima parte ꝓ­<lb/>poſtionali in ea ꝓportione in qua ſe habebit totū <lb/>eadem proportione diuiſum ad primam eius ꝑtem <lb/>ꝓportionalem / vt dictum eſt ſupra.</s>
            </p>
            <p xml:id="N202A8">
              <s xml:id="N202A9" xml:space="preserve">Secunda propoſitio </s>
              <s xml:id="N202AC" xml:space="preserve">Non habentibꝰ <lb/>illis velocitatibus difformibus aliquam cõtinuo ī­<lb/>ter ſe proportionem ſicut ſit in caſu duodecime con­<lb/>cluſionis et ſequentium correlariorum: impoſſibile <lb/>eſt naturaliter intellectum finite capacitatis talem <lb/>velocitatem ſic difformē ad vniformitatem redige­<lb/>re: et adequatum ſpacium pertranſitum infallibili­<lb/>rer aſſignare. </s>
              <s xml:id="N202BD" xml:space="preserve">Probatur hec ꝓpoſitio / quia cū ſint <lb/>ibi iufinite velocitates inequales ſi nullam vnifor-<lb/>mitateꝫ proportionum inter ſe ſeruent ſed cõtinuo <lb/>ſe habeãt in alia et alia proportione oporteret intel-<lb/>lectum infinitas ꝓpoſitiones rimari, et deinde con-<lb/>ſiderare quantum velocitas in vna ꝓportione mi-<lb/>nor altera plus facit ad pertrãſitum ſpacii ꝙ̄ alte­<lb/>ra in eadem proportione minor: ſed impoſſibile eſt / <lb/> intellectus finite capacitatis iſta infinita proſpi­               <pb chead="Secundi tractatus" file="0167" n="167"/>               ciat et ſine tali preſpectione et preſcrutatione nõ po­<lb/>terit ſpacium pertranſitum in totali tempore meti­<lb/>ri: conſequens igitur erit /  in tali caſu nequit certi­<lb/>tudinaliter reſponſionem ferre </s>
              <s xml:id="N202DB" xml:space="preserve">Et ſic patet ꝓpoſi-<lb/>tio. </s>
              <s xml:id="N202E0" xml:space="preserve">Credo tamen animas ſeparatas a corpore et in­<lb/>telligentias in imꝑſpecto tempore omīa iſta cogno­<lb/>ſcere </s>
              <s xml:id="N202E7" xml:space="preserve">Ceſſet / igitur dolor querulantium et non putat <lb/>homo ſua terminus clauſa intelligentia et finita ca­<lb/>pacitate vniuerſalem rerum naturalium amplitu-<lb/>dineꝫ difformes monſtruoſaſ motiones amplecti <lb/>at comprehendere. </s>
              <s xml:id="N202F2" xml:space="preserve">Hoc enim valde difficile eſt ꝑ-<lb/>inde at infinitam magnitudinem finito loco ꝑſtrī­<lb/>gere               <anchor type="note" xlink:href="note-0167-01" xlink:label="note-0167-01a"/>               </s>
              <s xml:id="N202FE" xml:space="preserve">Quare non abs re ſapientiſſimus ille ſalomõ <lb/>rerum naturalium difformes motus animo reuol-<lb/>ueus res naturales quo ad ſui motiones cognitu <lb/>difficiles cenſuit ecclaſiaſtes primo capite inquiēs <lb/></s>
              <s xml:id="N20308" xml:space="preserve">Cunte res difficiles: non poteſt eas homo explica­<lb/>re ſermone quare non ſatiatur oculus viſu nec au­<lb/>ris auditu               <anchor type="note" xlink:href="note-0167-02" xlink:label="note-0167-02a"/>               </s>
              <s xml:id="N20314" xml:space="preserve">Quam ſententiã pertractans hugo car­<lb/>dinalis inquit explicat ecclaſiaſtes quam in explica­<lb/>bilis ſit rerum naturalium mitabilitas dicēs cun-<lb/>ctas res naturales difficiles eſſe tū ad ītelligendū <lb/>tū ēt ad explicãdū </s>
              <s xml:id="N2031F" xml:space="preserve">Nec eī nūerari poſſūt mĺtitudīe <lb/>nec ↄ̨p̄hendi quãtitate: nec inueſtigari queunt ꝓfun­<lb/>ditate </s>
              <s xml:id="N20326" xml:space="preserve">Et ſubdit infirmitati noſtri intellectus cõdo­<lb/>lens. </s>
              <s xml:id="N2032B" xml:space="preserve">Quantis ergo tenebris homo inuoluit̄̄: quan­<lb/>ta ignorantie cecitate humanus ſenſus coartatur / <lb/>vt vix pauca etiam ſecundum ſuperficiem attinge-<lb/>re poteſt qui ſi ſingula ſecundū exteriorē ſpē3 cerne­<lb/>ret: vim lateutem, naturam inuiſibilem rerū nul-<lb/>latenus penetraret. </s>
              <s xml:id="N20338" xml:space="preserve">Uniuerſitas igitur rerum om-<lb/>nino hoī incõp̄hēſibilis et m exteriorē ſpē3 ē et m ī­<lb/>terioreꝫ qualitatē </s>
              <s xml:id="N2033F" xml:space="preserve">Hec ille </s>
              <s xml:id="N20342" xml:space="preserve">Quare non ſolum in p̄-<lb/>dictis caſibus non valet infallibiliter adequatum <lb/>ſpacium tali velocite difformi pertranſitum inue-<lb/>niri (quãuis de facto ſit aliquod adequatum ſpaci­<lb/>um / quod adequate pertranſitur) verumetiam ī no­<lb/>tioribus aliis caſibus talis ſpacii certitudo cecutiē­<lb/>tibus nobis in hoc ſeculo non valet reperiri: et certi­<lb/>tudinaliter metiri: vt ſi quiſpiam ponat /  partita <lb/>hora per partes ꝓportionales proportione dupla <lb/>mobile in prima parte ꝓportionali aliquantū ve-<lb/>lociter mouatur, et in ſecunda in ſexquialtero velo­<lb/>cius et in tertia in ſexquiquinto et in quarta in ſexq̇­<lb/>octauo ꝙ̄ in prima. / et ſic conſequenter procedendo <lb/>per ſpecies proportionis ſuperparticularis inter <lb/>ſcalariter continuo duos omittendo. </s>
              <s xml:id="N20361" xml:space="preserve">Item ſi diui-<lb/>ſa hora per partes ꝓportionales ꝓportione tripla <lb/>a. mobile in prima parte proportionali moueatur <lb/>aliquãtulum: et in ſecunda in ſexquiquinto velocius <lb/>et in tertia in ſexquinono velocius ꝙ̄ in prima, et in <lb/>quarta in ſexquitridecimo velocius ꝙ̄ ī prima et in <lb/>quinta in ſexdecimo ſeptimo velocius ꝙ̄ in prima / <lb/>et ſic conſequenter procedendo per ſpecies propor-<lb/>tionis ſuperparticularis continuo omittendo tres <lb/></s>
              <s xml:id="N20375" xml:space="preserve">Item ſic procedendo continuo omittendo quatuor <lb/></s>
              <s xml:id="N20379" xml:space="preserve">Item omittendo continuo quin et .6. et .7. / et ſic cõ­<lb/>ſequenter: infinite dabuntur velocitates difformes <lb/>quarum vniformitas a nobis nequa̄ naturaliter <lb/>reperiri poteſt. </s>
              <s xml:id="N20382" xml:space="preserve">Deinde diuiſa hora per partes ꝓ-<lb/>portionales ꝓportione quadrupla. </s>
              <s xml:id="N20387" xml:space="preserve">et in prima par­<lb/>te ꝓportionali moueatur a. mobile aliquantū velo­<lb/>citer: et in ſecunda in duplo ſexquialtero velocius: et <lb/>in tertia in ſupertripartiente quartas velocius ꝙ̄ ī <lb/>prima: et in quarta in ſexquialtero velocius ꝙ̄ in ṗ­<lb/>ma et in quinta in triplo velocius ꝙ̄ in prima: et ī ſex­<lb/>ta in dupla ſexquiſexto velocius ꝙ̄ in prima / et ſic cõ­<lb/>ſequenter ꝑmiſcendo ſeriatim ſpecies diuerſorum <lb/>generum proportionis. </s>
              <s xml:id="N2039A" xml:space="preserve">¶ Ex his ſatis facile appa­               <cb chead="Capitulum tertium"/>               ret multa talia nobis incomprehenſibilia eſſe. </s>
              <s xml:id="N203A0" xml:space="preserve">Nec <lb/>tamen propterea hec ars reiicienda eſt: quoniã et ſi <lb/>infinita ſint nobis incomprehēſibilia: infinita etiã <lb/>mathematica demonſtratione valent a nobis infal­<lb/>libiliter demonſtrari. </s>
              <s xml:id="N203AB" xml:space="preserve">puta ea que continuum ordi-<lb/>nem alicuius ꝓportionis obſeruant vt ſuperius di­<lb/>ctum eſt </s>
              <s xml:id="N203B2" xml:space="preserve">Cetera vero ſicut nullum ordinem ſeruant <lb/>ita nullis regulis ſcientie aſtringi valent               <anchor type="note" xlink:href="note-0167-03" xlink:label="note-0167-03a"/>               </s>
              <s xml:id="N203BC" xml:space="preserve">¶Hic ta-<lb/>men vnum aduertendum eſt /  plerun homo arbi­<lb/>trabitur nullam eſſe ſeriem aut ordinem proportio­<lb/>num in aliquo caſu ſibi propoſito: nihilominꝰ ma­<lb/>turius et diutius conſideranti occurret talis ordo. <lb/></s>
              <s xml:id="N203C8" xml:space="preserve">ſicut in caſu quarte concluſionis non apparet ali-<lb/>quis ordo alicuius ꝓportionis continue: nihilomi­<lb/>nus ibi reperitur continuo equalitas velocitatū in <lb/>partibus inequalibus.               <anchor type="note" xlink:href="note-0167-04" xlink:label="note-0167-04a"/>               </s>
              <s xml:id="N203D6" xml:space="preserve">¶ Sed petes / q̇d igitur calcu­<lb/>latori proponenti tales caſus in publica et celebri <lb/>litteraria paleſtra reſpondendum ſit.</s>
            </p>
            <div xml:id="N203DD" level="5" n="31" type="float">
              <note position="left" xlink:href="note-0167-01a" xlink:label="note-0167-01" xml:id="N203E1" xml:space="preserve">cccleſia-<lb/>ſtes .1. ca.</note>
              <note position="left" xlink:href="note-0167-02a" xlink:label="note-0167-02" xml:id="N203E9" xml:space="preserve">hugo car­<lb/>di.</note>
              <note position="right" xlink:href="note-0167-03a" xlink:label="note-0167-03" xml:id="N203F1" xml:space="preserve">nota.</note>
              <note position="right" xlink:href="note-0167-04a" xlink:label="note-0167-04" xml:id="N203F7" xml:space="preserve">Queſtio</note>
            </div>
            <note position="right" xml:id="N203FD" xml:space="preserve">horen.</note>
            <p xml:id="N20401">
              <s xml:id="N20402" xml:space="preserve">Reſpondeo ponendo / quandam ꝓpo-<lb/>ſitionem quã ponit doctiſſimus ꝓportionū indaga­<lb/>tor magiſter nicholaus horen. </s>
              <s xml:id="N20409" xml:space="preserve">¶ Ubicun occurrit <lb/>multiplicitas ꝓportionum inṫ quas facile nõ repe­<lb/>ritur proportio cenſendum eſt multas earum irra-<lb/>tionales eſſe ad inuicem, quare et ſpacia pertranſi­<lb/>ta irrationalia eſſe </s>
              <s xml:id="N20414" xml:space="preserve">Qua propter cuꝫ talis caſus ꝓ­<lb/>ponitur reſpondendum eſt ſpacium pertranſitū in <lb/>tota hora incõmenſurabile eſſe ſpacio pertranſito <lb/>in prima parte ꝓportionali. </s>
              <s xml:id="N2041D" xml:space="preserve">¶ Sed dices īſtabit ta­<lb/>men totis viribus illiberalis at acerrimus calcu­<lb/>lator: grandia verba trutinando inflata bucca: <lb/>ſupercilio eleuato: rugata fronte: at ore tragi-<lb/>co: rationem ſuam inſolubilem perſonabit, multiſ­<lb/> clamoribus reſpondentem vulgo ſuperatum at­<lb/> deuictum nitetur oſtendere.</s>
            </p>
            <p xml:id="N2042C">
              <s xml:id="N2042D" xml:space="preserve">Reſpondeo /  in ſimili negocio dupli-<lb/>ci cautela vtendum cenſeo </s>
              <s xml:id="N20432" xml:space="preserve">¶ Prima pro delubrio et <lb/>ridiculo habeatur argumentum eius tan̄ inutile <lb/>et intelligibile petatur calamus et atramentariū / <lb/>vt ſpecie multiplicationis ceteriſ algoriſmi ſpe-<lb/>ciebꝰ calculari valeat velocitatis ītēſio in caſu ꝑ eū <lb/>poſito. </s>
              <s xml:id="N2043F" xml:space="preserve">¶ Secunda cautela </s>
              <s xml:id="N20442" xml:space="preserve">Dicatur breuiter arguē­<lb/>ti /  talis velocitas non poteſt infallibiliter et certi­<lb/>tudinaliter calculari perinde at multe alie diffor­<lb/>mes velocitates non valent naturaliter ad vnifor-<lb/>mitatem reduci. </s>
              <s xml:id="N2044D" xml:space="preserve">Et ſi clamoribus velit reſponden-<lb/>tem expugnare oppoſitum aſſeuerendo: proponat <lb/>ei reſpondens ſimilem caſum et dicat ei vt certificet <lb/>illi de ſpacio pertranſito adequato mediante tali <lb/>velocitate difformi. </s>
              <s xml:id="N20458" xml:space="preserve">Et ſi dixerit /  non eſt poſſibile <lb/>naturaliter inuenire velocitatem adequatam in ta­<lb/>li caſu: ſubiungat reſpondens /  nec in ſuo ſimiliter <lb/>pari ratione. </s>
              <s xml:id="N20461" xml:space="preserve">Si autem dicat opponens ſe nolle ta­<lb/>le ſpacium aſſignare quauis aſſignabile ſit natura­<lb/>liter: hoc idem dicat ei reſpondens.               <anchor type="note" xlink:href="note-0167-05" xlink:label="note-0167-05a"/>               </s>
              <s xml:id="N2046D" xml:space="preserve">               <anchor type="note" xlink:href="note-0167-06" xlink:label="note-0167-06a"/>               </s>
              <s xml:id="N20475" xml:space="preserve">Et hac cautela <lb/>reſpondendi (ſi fas eſt etiam eam cautelam in ꝓpo­<lb/>ſito appellare) vſus eſt redemptor noſter luce .20. <lb/>cuius oculis omnia nuda et aperta ſūt ad hebreos <lb/>quarto cum interrogantibus principibus ſacerdo­<lb/>tum in qua poteſtate hoc facis: dixit: interrogabo <lb/>vus et ego vnum aliud verbum. </s>
              <s xml:id="N20484" xml:space="preserve">Reſpondente michi <lb/>baptiſmus iohannis de celo erat an ex hominibus <lb/>qui perplexi in reſponſione ne videlicet in igno-<lb/>miniam aut iram populi inciderent: reſpondebant <lb/>ſe neſcire. </s>
              <s xml:id="N2048F" xml:space="preserve">Et rurſum ſubiunxit dominus nec ego di­<lb/>cam vobis in qua poteſtate hec facio </s>
              <s xml:id="N20494" xml:space="preserve">¶ His exactis <lb/>ſecundum noſtri ingenioli capacitatē ſit concluſio <lb/>reſponſiua ad queſtionem.</s>
            </p>
            <div xml:id="N2049B" level="5" n="32" type="float">
              <note position="right" xlink:href="note-0167-05a" xlink:label="note-0167-05" xml:id="N2049F" xml:space="preserve">luce .20.</note>
              <note position="right" xlink:href="note-0167-06a" xlink:label="note-0167-06" xml:id="N204A5" xml:space="preserve">hebre. 4.</note>
            </div>
            <p xml:id="N204AB">
              <s xml:id="N204AC" xml:space="preserve">Oīs motꝰ vniformiter difformis quo               <pb chead="De motu locali quo ad effectū tꝑe difformi" file="0168" n="168"/>               ad tempus menſurari habet penes gradum mediū <lb/></s>
              <s xml:id="N204B5" xml:space="preserve">Omniſ difformiter difformis quo ad tempus pe­<lb/>nes reductionem ad vniformitatem ſiue penes cal-<lb/>culationem denominationis: et ſi in nõ nullis caſi-<lb/>bus difficile ſit aut impoſſibile naturaliter ad admiſ­<lb/>ſim infallibiliter velocitatem menſurare. </s>
              <s xml:id="N204C0" xml:space="preserve">Hec cõ­<lb/>cluſio ſuum colorem apparentiam et probabilita-<lb/>tem ex ſuperioribus ſortitur.</s>
            </p>
            <p xml:id="N204C7">
              <s xml:id="N204C8" xml:space="preserve">Ad rationes ante oppoſitum </s>
              <s xml:id="N204CB" xml:space="preserve">Ad pri-<lb/>mam reſponſum eſt ibi vſ ad vltimam replicã ad <lb/>quã reſpondeo concedendo ſequelam: et negãdo fal­<lb/>ſitatē cõſequentis: et cū ꝓbatur / quia alias ſequere-<lb/>tur mobile qḋ continuo īfinite velociter intēdit mo­<lb/>tū ſuū infinite tarde moueri: nego illã ſequelã et ad <lb/>ꝓbationē admitto caſū: et ad argumentū cõcedo an­<lb/>tecedēs capiēdo ly infinita ī maiore et minore ſin ca­<lb/>thegorematice et nego cõſequētiã.               <anchor type="note" xlink:href="note-0168-01" xlink:label="note-0168-01a"/>               </s>
              <s xml:id="N204E3" xml:space="preserve">¶ Ex quo ſequit̄̄ / <lb/> in caſu poſito quodlibet illoꝝ īmediate poſt hoc <lb/>infinita tarditate mouebit̄̄ et tñ īmediate poſt hoc <lb/>infinita velocitate mouebitur aliquod illorū </s>
              <s xml:id="N204EC" xml:space="preserve">Cor-<lb/>relarium hoc facile patet ex caſu.               <anchor type="note" xlink:href="note-0168-02" xlink:label="note-0168-02a"/>               </s>
              <s xml:id="N204F6" xml:space="preserve">¶ Sequitur ſecun­<lb/>do /  in caſu poſito qḋlibet iſtoꝝ īmediate poſt hoc <lb/>in infinitū modicū ſpacium per aliquod tempus ꝑ-<lb/>tranſibit: et tñ īmediate poſt hoc infinite magnum <lb/>ſpaciū ꝑtrãſibit aliquod illoꝝ ꝑ aliquod tempus.</s>
            </p>
            <div xml:id="N20501" level="5" n="33" type="float">
              <note position="left" xlink:href="note-0168-01a" xlink:label="note-0168-01" xml:id="N20505" xml:space="preserve">.1. correl.</note>
              <note position="left" xlink:href="note-0168-02a" xlink:label="note-0168-02" xml:id="N2050B" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N20511">
              <s xml:id="N20512" xml:space="preserve">Patet correlariū / quia ſpacia velocitatibus cõmē­<lb/>ſurantur.               <anchor type="note" xlink:href="note-0168-03" xlink:label="note-0168-03a"/>               </s>
              <s xml:id="N2051C" xml:space="preserve">¶ Sequitur tertio /  īmediate poſt hoc in­<lb/>finita tarditate mouebitur aliquod illorum: et nul­<lb/>lum iſtorum īmediate poſt hoc mouebitur ita tarde <lb/>ſicut a. et a. mouebitur: et ipſuꝫ a. nõ īmediate pꝰ hoc <lb/>infinita tarditate mouebitur. </s>
              <s xml:id="N20527" xml:space="preserve">Probatur correlari­<lb/>um et pono caſum /  ſint infinita mobilia a. b.c. etc. et <lb/>incipiat a. moueri ab octauo vſ ad non gradum ī <lb/>hora vniformiter difformiter: et b. a gradu duplo <lb/>vſ ad non graduꝫ in prima medietate: et c. adhuc <lb/>a gradu duplo ad illum in prima quarta hore vſ <lb/>ad non gradum. </s>
              <s xml:id="N20536" xml:space="preserve">et d. a gradu duplo a quo incipit c. <lb/>in prima octaua hore vſ ad non gradum et ſic in ī­<lb/>finitum </s>
              <s xml:id="N2053D" xml:space="preserve">Quo poſito ſequitur /  immediate pꝰ hoc <lb/>infinita tarditate mouebitur aliquod iſtoruꝫ: quia <lb/>immediate poſt hoc erit aliquod iſtorum prope nõ <lb/>gradum motus: et aliud in duplo propinquius non <lb/>gradui: et aliud in quadruplo: et ſic conſequenter / et <lb/>nullum iſtorum immediate poſt hoc mouebitur ita <lb/>tarde ſicut a. quoniam quodlibet illorum incipit ve­<lb/>locius moueri quã a. dempto a. et quodlibet illoruꝫ <lb/>immediate poſt hoc per aliquod tempus mouebi-<lb/>tur velocius quã a. / ergo nullum iſtorum immedia-<lb/>te poſt hoc mouebitur ita tarde ſicut a. in eodem tē-<lb/>pore </s>
              <s xml:id="N20556" xml:space="preserve">Et  a. nõ immediate poſt hoc infinita tardi-<lb/>tate mouetur. </s>
              <s xml:id="N2055B" xml:space="preserve">Probatur / quia immediate poſt hoc <lb/>mouetur maiori quã vt .6. / igitur non infinita tardi­<lb/>tate mouebitur. </s>
              <s xml:id="N20562" xml:space="preserve">Et ſic patet correlariū. </s>
              <s xml:id="N20565" xml:space="preserve">¶ Ad ṗmaꝫ <lb/>confirmationē reſponſum eſt ibi vſ ad vltimaꝫ re­<lb/>plicam: ad quã reſpondeo negando ſequelam im-<lb/>mo dico /  poſſibile eſt  eque velociter geometrice <lb/>intendatur vnus motus in tempore finito ſicut al-<lb/>ter remittitur ipſis in principio exiſtentibus equa-<lb/>libus: ſed oportet illum qui intenditur infinitam ve­<lb/>locitatem acquirere in illo tempore finito in quo al­<lb/>ter motus remittitur ad non gradum. </s>
              <s xml:id="N20578" xml:space="preserve">et ad proba-<lb/>tionem ſequele dico /  rñſio loquit̄̄ de motu q̇ vſ <lb/>ad certū gradū finite intenditur: et de tali bene con­<lb/>cedo  nõ eſt poſſibile ipſū eque velociter ꝓportio-<lb/>nabiliter intēdi ſicut alter motus ad non gradū re­<lb/>mittit̄̄. </s>
              <s xml:id="N20585" xml:space="preserve">¶ Ad ſecundã confirmationem que facilis ē: <lb/>rñdeo negãdo ſequelã īmo dico /  qñ vnus eſt remiſ­<lb/>ſus ad ſubduplū alter eſt remiſſus ad nõ gradū. </s>
              <s xml:id="N2058C" xml:space="preserve">Et <lb/>cū ꝓbatur /  non q2 qñ vnus eſt remiſſus ad ſubdu­               <cb chead="De motu locali quo ad effectū tꝑe difformi"/>               plum perdidit proportioneꝫ duplam: et alter remit­<lb/>titur in duplo velocius adequate: ergo debuit per­<lb/>didiſſe proportionem quadruplam preciſe q̄ eſt du­<lb/>pla duple: nego conſequentiam. </s>
              <s xml:id="N2059A" xml:space="preserve">Et ratio eſt / q2 illḋ <lb/>mobile non ſufficit ad illum motum remitti in du-<lb/>plo velocius altero qnia hic non loquimur de velo­<lb/>citate geometrica ſed arithmetica que debet attē-<lb/>di penes latitudinem deperditam: et non penes ꝓ-<lb/>portionem deperditam et ſic debet ſemper capi quã­<lb/>do dicitur eque velociter, ſi non addatur propor-<lb/>tionabiliter aut geometrice. </s>
              <s xml:id="N205AB" xml:space="preserve">¶ Ad tertiam confir-<lb/>mationem reſpondeo negando ſequelam: et cum ꝓ­<lb/>batur / quia ſemper a. in duplo velocius acquiret la­<lb/>titudinem quã b. et hec intenſio procedit in infinituꝫ <lb/>etc. / igitur aliquando a. erit duplus motus ad b. ne-<lb/>go conſequentiam: et cum probatur conſequentia. <lb/></s>
              <s xml:id="N205B9" xml:space="preserve">quia per infinituꝫ latitudo acquiſita ipſi a. excedet <lb/>latitudinem acquiſitam ipſi b. / ergo aliquando mo­<lb/>tus a. erit duplus ad motum b. conceſſo anteceden-<lb/>te nego conſequentiam / vt argumentum probat eã <lb/>negandam eſſe. </s>
              <s xml:id="N205C4" xml:space="preserve">¶ Ad quartam confirmationem reſ­<lb/>ponſum eſt vſ ad vltimam replicam ad quam reſ­<lb/>pondet ſeptima propoſitio primi notabilis huius <lb/>queſtionis cum annotationibus ibi poſitis.</s>
            </p>
            <div xml:id="N205CD" level="5" n="34" type="float">
              <note position="left" xlink:href="note-0168-03a" xlink:label="note-0168-03" xml:id="N205D1" xml:space="preserve">.3. correl:</note>
            </div>
            <p xml:id="N205D7">
              <s xml:id="N205D8" xml:space="preserve">Ad ſecundam rationem reſpondeo cõ­<lb/>cedēdo ſequelã et negando falſitatem conſequentis <lb/>et ad ꝓbationem concedo  illi motus ſunt equales <lb/>in principio et equales in fine et equalem latitudinē <lb/>deperdunt in totali illo tēpore cathegorematice: et <lb/>cū infertur / ergo in toto illo tꝑe ſunt equales: nego <lb/>illã conſequentiam: quia non mediantibus eis eq̈-<lb/>le ſpaciū pertranſitur / vt patet ex tertia concluſiõe <lb/>tertii notabilis: et ex deductione argumēti. </s>
              <s xml:id="N205EB" xml:space="preserve">Et hec ē <lb/>ſolutio ibi poſita. </s>
              <s xml:id="N205F0" xml:space="preserve">Et ad replicam conceditur ſeque­<lb/>la: et negatur falſitas ↄ̨ñtis vt docet argumentum: <lb/>et ſecundum correlarium tertie propoſitionis ter-<lb/>tii notabilis.</s>
            </p>
            <p xml:id="N205F9">
              <s xml:id="N205FA" xml:space="preserve">Ad tertiam rationeꝫ reſpondeo negã­<lb/>do ſequelam. </s>
              <s xml:id="N205FF" xml:space="preserve">immo dico /  dabitur certa intenſio ī <lb/>caſu poſito in argumento. </s>
              <s xml:id="N20604" xml:space="preserve">ſed non erit rationalis <lb/>ad intenſionem velocitatis prime partis: </s>
              <s xml:id="N20609" xml:space="preserve">Nec hoc <lb/>requiritur. </s>
              <s xml:id="N2060E" xml:space="preserve">Quod tamen totalis ille motus ſit intē­<lb/>ſior motu vt ſex vniformi probatur / quia ſi hora eēt <lb/>diuiſa in duas partes equales et in prima illarum <lb/>mobile moueretur vt octo. et in ſecunda vt quatuor <lb/>totus motus eſſet vt ſex (vt notum eſt) ſed motus iſte <lb/>de quo fit mentio in caſu argumenti eſt intenſior: <lb/>cū maior pars quã medietas ſit vt octo et reſidua vt <lb/>4. / ergo ſequitur /  ille motus eſt intenſior quã mo-<lb/>tus vt ſex / quod fuit probandum. </s>
              <s xml:id="N20621" xml:space="preserve">Et ad primam re-<lb/>plicam dictum eſt ibi. </s>
              <s xml:id="N20626" xml:space="preserve">Ad vltimam vero reſpondeo <lb/>negando conſequentiam ſicut docet eam negandã <lb/>ſecunda concluſio huius capitis vide eam ibi.</s>
            </p>
            <p xml:id="N2062D">
              <s xml:id="N2062E" xml:space="preserve">Ad quartam rationem reſponſum eſt <lb/>ibi vſ ad replicam ad quam replicam cum ſuis cõ­<lb/>firmationibus patet reſponſio ex duodecima con-<lb/>cluſione huius capitis cuꝫ ſuis correlariis: </s>
              <s xml:id="N20637" xml:space="preserve">Uide eã <lb/></s>
              <s xml:id="N2063B" xml:space="preserve">Et hec de queſtione et capitulo tertio.</s>
            </p>
          </div>
          <div xml:id="N2063E" level="4" n="4" type="chapter" type-free="capitulum">
            <head xml:id="N20643" xml:space="preserve">Capitulum quartum in <lb/>quo diſputatiue īquiritur <lb/>quõ motus difformis quo <lb/>ad ſubiectū et tp̄s ſimul: pa­<lb/>riter motus mixti veloci­<lb/>tas cognoſci debeat.</head>
            <p xml:id="N20650">
              <s xml:id="N20651" xml:space="preserve">ABſoluta ſuperioribus capiti-<lb/>bus doctrina perſcrutande motus dif-<lb/>mis quo ad ſubiectū et difformis quo ad               <pb chead="Secundi tractatus" file="0169" n="169"/>               tempus velocius: iã nūc reſtat velocitateꝫ motus <lb/>difformis quo ad tempus et quo ad ſubiectū ſimul <lb/>itidē motus mixti inquiramus ſolito per more diſ­<lb/>putatiue ꝓcedētes. </s>
              <s xml:id="N20663" xml:space="preserve">¶ Queritur ergo penes qḋ tan-<lb/>̄ penes effectum motus difformis quo ad tempus <lb/>et ſubiectū ſimul necnõ motus mixti velocitas atten­<lb/>di habeat. </s>
              <s xml:id="N2066C" xml:space="preserve">an vcꝫ motꝰ difformis quo ad tp̄s et ſub-<lb/>iectū ſimul velocitas menſurari debeat penes lineã <lb/>deſcriptam mediante velocitate vniformi ad quaꝫ <lb/>talis velocitas difformis reduci habet: et an motus <lb/>mixti velocitas attendi habeat penes ſpacium com­<lb/>poſitum ex ſpaciis ꝑtranſitis mediantibus pluri-<lb/>bus motibus quibus ſimul moueatur mobile motū <lb/>motu mixti.</s>
            </p>
            <p xml:id="N2067D">
              <s xml:id="N2067E" xml:space="preserve">Et arguitur primo /  velocitas motꝰ <lb/>difformis quo ad tempus et ſubiectum ſimul nõ at­<lb/>tendi habeat penes lineam deſcriptam etc. </s>
              <s xml:id="N20685" xml:space="preserve">Quia ſi <lb/>ſic ſequeretur /  adequata velocitas talis motꝰ mē­<lb/>ſuranda eēt penes reductionē ad vniformitatē: ſed <lb/>ↄ̨ñs eſt falſum / igitur illud ex quo ſequitur /. </s>
              <s xml:id="N2068E" xml:space="preserve">Seque-<lb/>la patet et arguitur falſitas conſequentis. </s>
              <s xml:id="N20693" xml:space="preserve">quia tūc <lb/>ſequeretur /  ſi vna rota inciperet moueri circulari­<lb/>ter cõtinuo vniformiter intendo motū ſuū a gradu <lb/>quarto vſ ad octauū in hora adequate: tunc talis <lb/>rota in tota illa hora moueretur adequate veloci-<lb/>tate vt ſex tranſeundo ſpaciū natū abſolui a veloci­<lb/>tate vt .6. in hora adeq̈te: ſed ↄ̨ñs eſt falſū / igitur il-<lb/>lud ex quo ſequitur /. </s>
              <s xml:id="N206A4" xml:space="preserve">Sequela ptꝫ / q2 tota illa veloci­<lb/>tas q̄ (vt conſtat) eſt vniformiter difformis a quar-<lb/>to vſ ad octauum correſpondet motui vniformi vt <lb/>6. ex ſupradictis </s>
              <s xml:id="N206AD" xml:space="preserve">Falſitas conſequentis probatur: <lb/>q2 tunc ſequeretur /  ſi illa rota ſic incipiens moue­<lb/>ri vniformiter difformiter cõtinuo vniformiter in-<lb/>tendendo motum ſuum a quarto vſ ad octauū cõ­<lb/>tinuo etiã rarefieret per illam horam: ipſa adeq̈te <lb/>moueretur etiã velocitate vt .6. / ſed conſequens ē fal­<lb/>ſum / igitur illud ex quo ſequitur /. </s>
              <s xml:id="N206BC" xml:space="preserve">Sequela patet / q2 <lb/>ille motus vt ponitur eſt vniformiter difformis a q̈r­<lb/>to vſ ad octauū: et velocitas vniformis cui correſ­<lb/>pondet eſt vt .6. / ergo ſi illa rota mouetur vniformi­<lb/>ter difformiter continuo ī illa hora: a quarto vſ <lb/>ad octauum: ipſa adequate in illa hora mouetur ve­<lb/>locitate vt .6. </s>
              <s xml:id="N206CB" xml:space="preserve">Sed iam ꝓbo falſitatem conſequētis / <lb/>q2 ſi illa rota nõ rarefieret ſed ſoluꝫ moueretur mo­<lb/>tu circulari vniformiter difformi in illa hora a q̈r-<lb/>to vſ ad octauū ſine rarefactione: tūc ipſa moue-<lb/>ret̄̄ ī illa hora adeq̈te velocitate vt .6.: ſed addita il-<lb/>la rarefactiõe ipſa mouet̄̄ velociꝰ ꝙ̄ tūc: igr̄ ī illo ca­<lb/>ſu quo rarefit ipſa mouet̄̄ maiori velocitate ꝙ̄ ſit ve­<lb/>locitas vt .6. </s>
              <s xml:id="N206DC" xml:space="preserve">Cõſequentia patet ex ſe et arguitur mi­<lb/>nor / q2 ex ſuperius dictis velocitas totiꝰ illius rote <lb/>attendi hꝫ cõtinuo penes pūctū mediū vel ſūmū. </s>
              <s xml:id="N206E3" xml:space="preserve">ſꝫ <lb/>pūtus medius et ſūmꝰ in tota hora adequate ꝑ mo-<lb/>tū circularē quo mouet̄̄ a q̈rto vſ ad octauum per­<lb/>tranſit tm̄ ſpaciū ac ſi nõ rarefieret: et in ſuꝑ ꝑ motū <lb/>rarefactionis pertranſiuit illud ſpaciū ꝑ qḋ plꝰ di­<lb/>ſtat a centro illiꝰ rote ꝙ̄ diſtabat a prīcipio illiꝰ mo­<lb/>tus: igr̄ maius ſpaciū ꝑtrãſit qñ rarefit ꝙ̄ qñ nõ ra­<lb/>refit / quod fuit probandum.               <anchor type="note" xlink:href="note-0169-01" xlink:label="note-0169-01a"/>               </s>
              <s xml:id="N206F9" xml:space="preserve">¶ Dices et bene ad ar-<lb/>gumentum concedendo ſequelam et negando falſi-<lb/>tatem conſequentis. </s>
              <s xml:id="N20700" xml:space="preserve">et ad ꝓbationem concedo ſeq̄-<lb/>lam et nego iterum falſitatem conſequentis: et cū ꝓ-<lb/>batur nego ſequelam:  vlꝫ ſi illa rota ſic incipiēs <lb/>moueri vniformiter difformiter continuo vniformi­<lb/>ter intendendo motum ſuum et ipſa adequate mo-<lb/>ueretur etiam velocitate vt ſex. </s>
              <s xml:id="N2070D" xml:space="preserve">Et ratio eſt / quia il-<lb/>la rota mouetur duplici motu per vtrū deſcriben­<lb/>do ſpacium: puta motu circulari vel quodammodo               <cb chead="Capitulum quartum"/>               habente naturam motus circularis (quia continuo <lb/>mouetur ſuper eodem axe quamuis non proprie li­<lb/>neam circularem deſcribat / vt ſuperius dictum eſt) <lb/>et inſuper mouetur punctus a cuius velocitate deb3 <lb/>ſumi totalis velocitas ipſius rote motu rarefactio­<lb/>nis continuo recedendo a centro </s>
              <s xml:id="N20721" xml:space="preserve">Quare velocitas <lb/>illius puncti et ex conſequenti ipſius rote debet cõ-<lb/>menſurari penes lineam aggregatam ex linea quã <lb/>deſcriberet ille punctus ſecluſa rarefactione: et pe-<lb/>nes lineam breuiſſimam per quam plus diſtat a cē­<lb/>tro ꝙ̄ ante rarefactionem diſtabat.</s>
            </p>
            <div xml:id="N2072E" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0169-01a" xlink:label="note-0169-01" xml:id="N20732" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N20738">
              <s xml:id="N20739" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>ſi rota b. inciperet moueri circulariter puncto eius <lb/>medio a cuius velocitate (vt ſuppono) debet com-<lb/>menſurari totalis rote velocitas mouēte in prima <lb/>parte proportionali hore proportiune quadrupla <lb/>diuiſe velocitate vt quatuor et in ſecunda in duplo <lb/>velocius: et in tertia in duplo velocius ꝙ̄ in ſecun-<lb/>da: et ſic conſequenter: et cum hoc in qualibet parte <lb/>proportionali illa rota vniformiter rarefieret tali­<lb/>ter  ille punctus medius in qualibet parte ꝓpor-<lb/>tionali acquireret pedalem diſtanttam a centro ſu­<lb/>pra diſtantiam habitam: tunc ipſa rota in illa ho-<lb/>ra adequate finite deſcriberet ad lineam deſcriptam <lb/>in prima parte proportionali: ſecundum conſequens eſt <lb/>falſum / igitur illud ex quo ſequitur: </s>
              <s xml:id="N20758" xml:space="preserve">Sequela patet <lb/>ex primo correlario ſeptime concluſionis preceden­<lb/>tis capitis: et falſitas conſeqnentis probatur quia <lb/>punctus ille a cuius velocitate debet ſumi veloci-<lb/>tas totius rote infinitam lineam deſcribit in illa <lb/>hora. </s>
              <s xml:id="N20765" xml:space="preserve">ergo ſequitur /  non pertranſit in totali ho-<lb/>ra duplum ſpacium adequate ad ſpacium ꝑirã-<lb/>ſitum in prima parte proportionali: </s>
              <s xml:id="N2076C" xml:space="preserve">Antecedens <lb/>probatur / quia ille punctus deſcribit lineam in illa <lb/>hora qua magis diſtat a centro per pedale ꝙ̄ an-<lb/>tea: et per bipedale ꝙ̄ antea: et per quadrupedale: <lb/>et ſic in infinitum: cum ex caſu in qualibet parte pro­<lb/>portionali deſcribit pedalem diſtantiam per rare­<lb/>factionem recedendo a centro. </s>
              <s xml:id="N2077B" xml:space="preserve">igitur ille punctus ī-<lb/>finitam lineam deſcribit in illa hora / quod fuit pro­<lb/>bandum.</s>
            </p>
            <p xml:id="N20782">
              <s xml:id="N20783" xml:space="preserve">Secundo principaliter contra ſecun­<lb/>dam partem queſtionis arguitur ſic. </s>
              <s xml:id="N20788" xml:space="preserve">quia ſi illa <lb/>pars eſſet vera ſequeretur /  aliquod mobile in ali­<lb/>quo tempore continuo remitteret motum ſuum pro­<lb/>prium vſ ad non gradum: et tamen continuo in eo­<lb/>dem tempore velocius et velocius ſpacium pertran­<lb/>ſiret: ſed hoc videtur implicare / igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N20797" xml:space="preserve">Sequela probatur. </s>
              <s xml:id="N2079A" xml:space="preserve">et pono /  ſortes mo-<lb/>ueatur in aliqua naui verſus eandem differentiam <lb/>verſus quam mouetur nauis ab aliquo gradu: con­<lb/>tiuuo remittendo motum ſuum vſ ad non gradū <lb/>ipſa naue continuo intendente motum ſuum ab eo­<lb/>deꝫ gradu velocius ꝙ̄ ſortes remittat. </s>
              <s xml:id="N207A7" xml:space="preserve">Quo poſito <lb/>ſortes continuo remittit motuꝫ ſuum et hoc vſ ad <lb/>non gradum: et tamen continuo in eodem tempore <lb/>velocius et velocius ſpacium pertranſit: quod fuit <lb/>probandum: igitur propoſitum. </s>
              <s xml:id="N207B2" xml:space="preserve">Maior patet ex ca­<lb/>ſu et minor probatur. </s>
              <s xml:id="N207B7" xml:space="preserve">quia continuo velocitas mix-<lb/>ta ſiue compoſita ex velocitate propria qua moue-<lb/>tur ſortes et ex velocitate ipſins nauis eſt maior et <lb/>maior cum continuo maiorem velocitatem acqui-<lb/>rit ꝙ̄ deperdit ex caſu: igitur continuo ſortes velo-<lb/>cius et velocius ſpacium pertranſit / quod fuit pro-<lb/>bandum.               <anchor type="note" xlink:href="note-0169-02" xlink:label="note-0169-02a"/>               </s>
              <s xml:id="N207CB" xml:space="preserve">¶ Dices et bene concedendo ſequelam.</s>
            </p>
            <div xml:id="N207CE" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0169-02a" xlink:label="note-0169-02" xml:id="N207D2" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N207D8">
              <s xml:id="N207D9" xml:space="preserve">Nec hoc eſt inconueniens quando mobile mouetur <lb/>motu mixto ex motu proprio et motu lationis.</s>
            </p>
            <pb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū" file="0170" n="170"/>
            <p xml:id="N207E2">
              <s xml:id="N207E3" xml:space="preserve">Sed cõtra / q2 tūc ſequeretur /  ſtaret <lb/>ī caſu ſortē valde fatigari nitendo moueri nullo im­<lb/>pedimēto poſito imo ipſo ſorte habēte optimã diſ­<lb/>poſitionē. </s>
              <s xml:id="N207EC" xml:space="preserve">ad currenduꝫ et ad mouēdū: et tñ nullo pa­<lb/>cto moueri: ſed hoc ē falſuꝫ igitur. </s>
              <s xml:id="N207F1" xml:space="preserve">Falſitas ↄ̨ñtꝪ pꝫ / <lb/>q2 ſi nullū ē īpedimentū: et ſortes nitit̄̄ moueri: ſeq̇t̄̄ / <lb/> ipſe ſortes mouetur. </s>
              <s xml:id="N207F8" xml:space="preserve">Itē ſortes fatigat̄̄: et nõ niſi <lb/>q2 mouetur: igr̄ ſortes mouetur </s>
              <s xml:id="N207FD" xml:space="preserve">Seq̄la tñ ꝓbatur et <lb/>pono caſu /  ſortes ſit in naui q̄ moueat̄̄ ſus oriē-<lb/>tē: et ſortes nitatur moueri ſus occidentē. </s>
              <s xml:id="N20804" xml:space="preserve">ita  ſor­<lb/>tes deſcribat aliquod ſpaciū in ipſa naui ita velo­<lb/>citer ſicut nauis mouetur adequate: et moueat̄̄ na-<lb/>uis ita velociter  ſortes fatigetur plurimū. </s>
              <s xml:id="N2080D" xml:space="preserve">Quo <lb/>poſito arguitur ſic / ſortes fatigatur nitendo moue­<lb/>ri nullo īpedimēto poſito et tñ nõ mouetur igr̄. </s>
              <s xml:id="N20814" xml:space="preserve">Mi-<lb/>nor ꝓbatur / q2 ſortes ſemꝑ eſt in eodē loco reſpectu <lb/>ſpacii fixi ex quo debet ſumi idētitas loci et īmobili­<lb/>tas. </s>
              <s xml:id="N2081D" xml:space="preserve">vt patet ꝑ phm̄ quarto phiſicoꝝ dicentē locū eē <lb/>terminū cõtinētis īmobilē ṗmū: igitur ſortes ī tali <lb/>caſu nõ mouet̄̄ (nullū eī ſpaciū fixū deſcribit) / igitur</s>
            </p>
            <p xml:id="N20824">
              <s xml:id="N20825" xml:space="preserve">Tertio prīcipalit̄̄ ↄ̨̨tra eadē ꝑtē q̄ſtio­<lb/>nis arguitur ſic: q2 nullꝰ eſt motꝰ mixtus. </s>
              <s xml:id="N2082A" xml:space="preserve">g̊ illa pars <lb/>p̄ſupponit falſum et ꝑ ↄ̨ñs falſa. </s>
              <s xml:id="N2082F" xml:space="preserve">Añs ꝓbatur / q2 ſi <lb/>eſſet aliq̇s motus mixtus maxime eſſet motus cõpo­<lb/>ſitus ex aſcenſu et deſcēſu: ſꝫ nullus eſt dabilis ta-<lb/>lis: igitur. </s>
              <s xml:id="N20838" xml:space="preserve">Probat̄̄ minor / q2 ſi aliq̇s talis eēt dabi­<lb/>lis: ſeq̄retur /  dabile eēt vnū corpꝰ finitū cuius vna <lb/>pars aſcenderet et alia deſcenderet: et relictum ſue <lb/>naturali diſpoſitione ſic ꝑpetuo moueretur ↄ̨tinuo <lb/>vna ꝑte eiꝰ aſcendente et alia deſcendēte: ſꝫ ↄ̨ñs ē fal­<lb/>ſum: igr̄ illḋ ex quo ſeq̇t̄̄. </s>
              <s xml:id="N20845" xml:space="preserve">Seq̄la ꝓbatur et pono caſū / <lb/> terra ſit ꝑforata ꝑ cētrū mūdi ab oriēte in occidē­<lb/>tē: et capiat̄̄ globꝰ terre vniformis grauitatis vĺ ali­<lb/>cuiꝰ alteriꝰ figure (ī idē reddit) descēdat illa terra <lb/>ꝑ illḋ foramē vſ. ad cētrū mūdi illo foramīe vacuo <lb/>exñte ꝑmittat deꝰ illã terrã moueri tãdiu ̄diu ha­<lb/>buerit ꝓportionē maioris ineq̈litatis ad mouēdū. <lb/></s>
              <s xml:id="N20855" xml:space="preserve">Quo poſito ſic argumētor. </s>
              <s xml:id="N20858" xml:space="preserve">illa terra ꝑpetuo moue­<lb/>bit̄̄ ↄ̨tinuo vna ꝑte eiꝰ aſcēdēte et alṫa deſcēdēte: igr̄ <lb/>ꝓpoſitū </s>
              <s xml:id="N2085F" xml:space="preserve">Probat̄̄ añs / q2 īclinatio illiꝰ ṫre ē  cētrū <lb/>eiꝰ ſit cētrū mūdi: cū idē ſit locꝰ totiꝰ et ꝑtꝪ prīo celi. <lb/></s>
              <s xml:id="N20865" xml:space="preserve">igr̄ illa terra ſue naturali diſpoſitioni relicta cõti­<lb/>nuo mouebit̄̄ quovſ (ſi fieri p̄t) cētrū eiꝰ ſit cētrum <lb/>mundi: ſꝫ ſic mouēdo ꝑ infinitū tp̄s mouebit̄̄ ãtea̄ <lb/>(ſi fieri p̄t) cētrū eiꝰ fiat cētrū mūdi: igr̄ illa terra ꝑ-<lb/>petuo mouebit̄̄ cõtinuo vna ꝑte eiꝰ aſcendēte et alia <lb/>deſcēdēte: qḋ fuit ꝓbandū </s>
              <s xml:id="N20872" xml:space="preserve">Sꝫ iam ꝓbo /  talis terra ſic <lb/>mouēdo ꝑ infinitū tp̄s mouebit̄̄ antea ꝙ̄ etc. cētrū eiꝰ <lb/>fiat cētrū mūdi. </s>
              <s xml:id="N20879" xml:space="preserve">Qḋ ſic ꝓbat̄̄ et volo /  diuidat̄̄ illa <lb/>terra in q̈tuor ꝑtes eq̈les: et  vna illaꝝ ſit vltra cen­<lb/>trū reliq̄ vero tres ſint citra centrū: et manifeſtū eſt <lb/> q̈rta vltra cētrū reſiſtit tribꝰ q̈rtis citra cētruꝫ ne <lb/>deſcēdãt vt ↄ̨ſtat: et deſcēdūt ſiue īcipiūt deſcendere <lb/>illi tres q̈rte a ꝓportione tripla mouēdo vel mīori: <lb/>vt patet ex caſu: diuido igr̄ medietatē exceſſus quo <lb/>pars citra cētrū excedit ꝑtē vltra cētrū q̄ q̇dē medie-<lb/>tas exceſſus eſt vna q̈rta īter cētrū illius globi et cē­<lb/>trū mundi: et hoc ꝑ ꝑtes ꝓportionales ꝓportiõe du­<lb/>pla maioribꝰ ſus cētrū mūdi terminatis quo poſi­<lb/>to arguit̄̄ ſic q̄libet pars ꝓportionalis illius exceſ­<lb/>ſus descēdet: et ꝑ tãtū tꝑis vel maiꝰ mouebit̄̄ ſiue de­<lb/>ſcēdet q̄libet ſicut īmediate p̄cedens eã: et ſūt infini-<lb/>te: igr̄ ꝑ infinitꝫ tp̄s mouebitur talis terra / qḋ fuit ꝓ­<lb/>bãdū </s>
              <s xml:id="N2089A" xml:space="preserve">Probat̄̄ minor / q2 ṗma illaꝝ ꝑtiū deſcendet <lb/>a ꝓportione tripla vel minori. </s>
              <s xml:id="N2089F" xml:space="preserve">et ſcḋa deſcendet a ꝓ­<lb/>portione ſuprabiꝑtiēs tertias vel minori q̄ ē minor <lb/>̄ ſubdupla ad triplã vt ↄ̨ſtat intuenti: et tertia a ꝓ­<lb/>portione ſuprabipartiente ſeptimas vel minori q̄ <lb/>eſt minor ꝙ̄ ſubdupla ad ꝓportionē ſuprabipartiē­               <cb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū"/>               tē tertias / vt patet aſpiciēti: et quarta deſcendet a ꝓ­<lb/>portione ſuprabipartiente quīdecimas vel minori <lb/>q̄ eſt minor ꝙ̄ ſubdupla ad ꝓportioneꝫ ſuprabipar­<lb/>tientē ſeptimas / et ſic ↄ̨̨ñter repperies  q̄libet pars <lb/>ꝓportionalis medietatis illius exceſſus ſequēs de­<lb/>ſcendit a ꝓportione ſubdupla vel minor ad ꝓpor-<lb/>tionē a qua īcipit deſcendere pars īmediate prece-<lb/>dens: et ille ꝑtes ꝓportionales cõtinuo ſe hñt in pro­<lb/>portione dupla: igr̄ ꝑ tãtū tꝑis vel maius mouebit̄̄ <lb/>ſiue descēdet q̄libet pars ꝓportionalis ſicut īmedi­<lb/>ate p̄cedēs eã: vel ſaltē ſequitur ꝑ infinitum tp̄s mo­<lb/>uebitur talis terra / qḋ ꝓbare intendimus.</s>
            </p>
            <p xml:id="N208C3">
              <s xml:id="N208C4" xml:space="preserve">In oppoſitū tñ arguit̄̄ ſic / q2 penes ali­<lb/>quid menſnrãda ē tã̄ penes effectū velocitas motꝰ <lb/>difformis ſcḋm tp̄s et ſubiectum ſimul et ēt motꝰ mix­<lb/>ti: et nõ niſi penes id qḋ dr̄ ī titulo q̄ſtiõis: igr̄ qõ a</s>
            </p>
            <p xml:id="N208CD">
              <s xml:id="N208CE" xml:space="preserve">Pro enucleatione huius parue q̄ſtio-<lb/>nis notãdū eſt primo:  ī oī motu difformi quo ad <lb/>tp̄s et ſubiectū ſimul velocitas mēſurãda ē penes re­<lb/>ductionē ad vniformitatē ſaltē denoīationis vt ſu­<lb/>perius dicebat̄̄ ī ſecūdo capite huiꝰ tractatꝰ </s>
              <s xml:id="N208D9" xml:space="preserve">¶ Hoc <lb/>tñ vnū aduertendū eſt  motus difformis quo ad tē­<lb/>pus et ſubiectū ſimul aliqñ fit ſecluſo alio motu ſub­<lb/>iecti puta rarefactionis aut ↄ̨dēſatiõis etc / vt cuꝫ ro­<lb/>ta nõ rarefacta aut cõdēſata cõtinuo circulariṫ ve-<lb/>locius et velocius mouet̄̄ aut tardius et tardius. </s>
              <s xml:id="N208E6" xml:space="preserve">Ali­<lb/>quando vero fit talis motus cõcomitante rarefacti­<lb/>one aut condēſatione ſiue augmentatione etc. </s>
              <s xml:id="N208ED" xml:space="preserve">Pri-<lb/>mo mõ debet mēſurari talis motꝰ velocitas penes <lb/>velocitatem qua mouet̄̄ pūctꝰ medius aut velociſ-<lb/>ſime motꝰ ſcḋm diuerſitatē opinionuū eo mõ quo ſu­<lb/>perius dicebatur de motu difformi quo ad ſubiectū <lb/>tm̄ </s>
              <s xml:id="N208FA" xml:space="preserve">Et ēt mēſurãda ē velocitas illiꝰ motus penes li-<lb/>neã deſcriptã a pūcto medio talis corꝑis vel velo-<lb/>ciſſime moto: ſed tale pūctū duplici motu mouetur <lb/>motu vcꝫ locali et rarefactionis ſiue cõdēſatiõis etc. <lb/></s>
              <s xml:id="N20904" xml:space="preserve">Et ideo tale pūctū tantã lineã deſcribit ac ſi moue-<lb/>retur ṗmo mõ: et in ſuꝑ deſcribit illã lineã ꝑ quã plꝰ <lb/>diſtat ſi rarefiat: aut minus ſi condenſetur: a cētro <lb/>talis motꝰ ꝙ̄ antea diſtabat a principio motꝰ. </s>
              <s xml:id="N2090D" xml:space="preserve">vt ſi <lb/>rota moueat̄̄ ī hora cõtinuo rarefiēdo: ita  ꝑ rare­<lb/>factionē acq̇rat pūctus penes cuiꝰ motū debet attē­<lb/>di velocitas rote pedalē diſtãtiã a cētro ſupra diſtã­<lb/>tiã iã habitã: et moueat̄̄ talis pūctus motu circula-<lb/>ri cõtinuo velociꝰ et velociꝰ: tūc dico /  velocitas ta-<lb/>lis motus mēſurãda eſt penes lineã quã deſcriberet <lb/>motu illo circulari ſi non rarefieret: et penes illã li-<lb/>neã pedalē quã motu rarefactionis deſcribit</s>
            </p>
            <p xml:id="N20920">
              <s xml:id="N20921" xml:space="preserve">Hic tñ tu aduerte /  nõnū̄ mouet̄̄ aliqḋ mobile et <lb/>motu recto er circulari et rarefactionis ſimul: ita <lb/> cõtinuo cētrū illiꝰ corꝑis moueatur: quēadmodū <lb/>contingit ſi pila vel aliqḋ aliud corpꝰ ſpericū vel al­<lb/>teriꝰ figure moueat̄̄ motu recto et circulari continuo <lb/>rotando continuo rarefiendo et ī hoc et ſimili caſu <lb/>velocitas talis mobilis iudicãda eſt penes velocita­<lb/>tē cētri mobilis. </s>
              <s xml:id="N20932" xml:space="preserve">Nõ eī video quo° certiꝰ et cõmodius <lb/>talis motꝰ velocitas ↄ̨mēſurari dēat. </s>
              <s xml:id="N20937" xml:space="preserve">¶ Ex his faci­<lb/>le pꝫ ↄ̨ſiderãti  tot modꝪ tīgit corpꝰ moueri motu <lb/>difformi quo ad tp̄s et ſubiectū ſimul quot ↄ̨tīgit ip­<lb/>ſū moueri motu difformi quo ad tp̄s dūtaxat. </s>
              <s xml:id="N20940" xml:space="preserve">Põt <lb/>eī pūctꝰ penes cuiꝰ velocitatē attendi d3 talis motꝰ <lb/>velocitas in q̊libet illoꝝ triū modoꝝ moueri ī prīa <lb/>ꝑte ꝓportionali hore ̄uis ꝓportione ꝑtite aliquã­<lb/>tula velocitate. </s>
              <s xml:id="N2094B" xml:space="preserve">et in ſcḋa in duplo velociꝰ: et ī tertia <lb/>ī triplo velociꝰ ꝙ̄ ī ṗma: et ſic ↄ̨ñter. </s>
              <s xml:id="N20950" xml:space="preserve">vel quouis alio° <lb/>et tūc ī iſto et ſiĺibꝰ caſibus velocitas et ſpaciū ꝑtran­<lb/>ſitū mediãte tali velocitate ex his q̄ dcã ſūt p̄ceden-<lb/>tibus captis cõmode menſuratur inſpectis theore-<lb/>matibus ibidem demonſtratis</s>
            </p>
            <pb chead="Secundi tractatus" file="0171" n="171"/>
            <note position="left" xml:id="N2095F" xml:space="preserve">dupliciṫ <lb/>dr̄ aliq̇d <lb/>moueri <lb/>motu <lb/>mixto ex <lb/>pĺibꝰ mo­<lb/>tibus.</note>
            <p xml:id="N2096F">
              <s xml:id="N20970" xml:space="preserve">Notandem eſt ſecundo /  dupliciṫ p̄t <lb/>intelligi aliq̇d moueri motu mixto ex pĺibꝰ motibꝰ <lb/></s>
              <s xml:id="N20976" xml:space="preserve">Primo modo eque primo ita  ſecūdum ſe et quod­<lb/>libet ſui moueatur de per ſe quolibet illorum motu­<lb/>um: et non aliquo illorum ad motum alterius: vt qñ <lb/>idem mouetur ſimul motu locali et motu alteratio­<lb/>nis. </s>
              <s xml:id="N20981" xml:space="preserve">Secundo modo dicitur aliquid moueri motu <lb/>mixto ex pluribus motibus non eque primo: ſꝫ vno <lb/>motu ex ſe: et alio ad motum alterius: ſic  vnus il-<lb/>lorum motuuꝫ ſit illi mobili ꝓprius: et alter nõ. </s>
              <s xml:id="N2098A" xml:space="preserve">quē­<lb/>admodum fit quãdo homo mouetur in naui mota. <lb/></s>
              <s xml:id="N20990" xml:space="preserve">Et de tali motu mixti principaliter in preſenti no-<lb/>tabili loqui intendimus </s>
              <s xml:id="N20995" xml:space="preserve">Poteſt addi tertius modꝰ <lb/>qui eſt cum vna pars aſcendit et alia deſcendit               <anchor type="note" xlink:href="note-0171-01" xlink:label="note-0171-01a"/>               </s>
              <s xml:id="N2099F" xml:space="preserve">¶ Un­<lb/>de velocitas talis motus debet attendi penes ſpa-<lb/>cium interceptum inter punctum fixū et quieſcens et <lb/>punctum ſiue terminum in quo eſt tale mobile in fi-<lb/>ne motus: hoc eſt penes lineam deſcriptã a tali mo­<lb/>bili inter illos duos terminos. </s>
              <s xml:id="N209AC" xml:space="preserve">vt ſi ſortes incipiat <lb/>moueri ſimul cum naue mota verſus orientē veloci­<lb/>tas motus ſortis debet cõmenſurari penes lineam <lb/>deſcriptam ab ipſo ſorte a puncto fixo a quo ince-<lb/>pit ſortes moueri vſ ad punctum fixum in quo eſt <lb/>ſortes in termino motus. </s>
              <s xml:id="N209B9" xml:space="preserve">Et hoc vniuerſaliter ē ve-<lb/>rum ſiue ſortes moueatur ad oppoſitum nauis: ſi-<lb/>ue verſus eandē differētiã verſus quã mouetur na­<lb/>uis ſiue nec ad oppoſitam differentiam necud ean-<lb/>dem ſicut eſſet ſi ſortes moueretur a ſeptentrione ī <lb/>meridieꝫ in naui mota ab oriente in occidentem.</s>
            </p>
            <div xml:id="N209C6" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0171-01a" xlink:label="note-0171-01" xml:id="N209CA" xml:space="preserve">penes q̇d <lb/>velocitaſ <lb/>motꝰ mix­<lb/>to hēat <lb/>attendi</note>
            </div>
            <note position="left" xml:id="N209D8" xml:space="preserve">correlari­<lb/>um petri <lb/>ḋ aliaco.</note>
            <p xml:id="N209E0">
              <s xml:id="N209E1" xml:space="preserve">Ex quibus pulchre et ingenioſe infert dominꝰ car­<lb/>dinalis de aliaco quatuor correlaria que ſub eadē <lb/>forma ſequuntur ſub qua ea ſcriptis mandauit</s>
            </p>
            <note position="left" xml:id="N209E8" xml:space="preserve">.1. correl.</note>
            <p xml:id="N209EC">
              <s xml:id="N209ED" xml:space="preserve">Primum eſt /  poſſibile eſt ex duobus rectis mo-<lb/>tum circularē deſcribere id eſt  poſſibile eſt aliq̇d <lb/>moueri duplici motu recto deſcribendo circulū vel <lb/>partes circuli: </s>
              <s xml:id="N209F6" xml:space="preserve">Uerbi gratia. </s>
              <s xml:id="N209F9" xml:space="preserve">deſcribatur vnus cir-<lb/>culum deinde deſcribatur linea contingens circulū <lb/>in puncto: equalis diametro illius circuli: et eque di­<lb/>ſtans ab illo diametro. </s>
              <s xml:id="N20A02" xml:space="preserve">et in iſta linea in puncto con­<lb/>tactus ſit muſca a. et vltra ponatur /  iſta linea iuci­<lb/>piat moueri vniformiter infra circulum quovſ co­<lb/>operiat diametrū illius circuli: et muſca īcipiat mo­<lb/>ueri vniformiṫ ſupra illã ſic  dū linea illa cooꝑiet <lb/>diametrū circuli  tūc muſca ſit in extrēo pūcto li­<lb/>nee </s>
              <s xml:id="N20A11" xml:space="preserve">Tūc in iſto caſu muſca deſcribit q̈rtã ꝑtē circuli <lb/>et tamen mouetur ſoluꝫ duobus motibus rectis ſcꝫ <lb/>vno ex ſe et alio ad motū linee. </s>
              <s xml:id="N20A18" xml:space="preserve">Et ſi ponatur /  illa <lb/>linea moueat̄̄ vltra diametrū quovſ contingat <lb/>circulū ī pūcto in alia parte circuli: et muſca reuer-<lb/>tat̄̄ ad locū ſuū. </s>
              <s xml:id="N20A21" xml:space="preserve">Tūc cū muſca ꝑuenerit ad cõtactū: <lb/>muſca <gap/>ſcripſerit medietatē circuli. </s>
              <s xml:id="N20A28" xml:space="preserve">et ſi vltra adhuc <lb/>ponat̄̄ illã lineã aſcendere: in fine habebit̄̄  muſca <lb/>deſcripſerit circulū.               <anchor type="note" xlink:href="note-0171-02" xlink:label="note-0171-02a"/>               </s>
              <s xml:id="N20A34" xml:space="preserve">¶ Scḋm correlariū /  ex duo-<lb/>bus motibꝰ rectis põt fieri vnꝰ motus mixtus ī eodē <lb/>tꝑe deſcribēs coſtã alicuiꝰ q̈drati et diametrū eiuſdē <lb/></s>
              <s xml:id="N20A3C" xml:space="preserve">Uerbi gr̄a deſcribat̄̄ q̈dratū: et īcipiat eiꝰ coſta ſuꝑi­<lb/>or deſcendere quovſ cooꝑiat coſtã inferiorē: et vl-<lb/>tra ponat̄̄ /  muſca a. ſit in vno termino illius coſte <lb/>et īcipiat moueri vniformiter ꝑ illã coſtã ſic  dū co­<lb/>ſta cooꝑiet aliã coſtã  tunc muſca ſit in alio termīo <lb/>coſte. </s>
              <s xml:id="N20A49" xml:space="preserve">Tūc in iſto caſu muſca a. deſcribit diametrū <lb/>q̈drati: et etiã coſtã eiꝰ in eodē tꝑe: q2 mouet̄̄ ſuꝑ illã <lb/>coſtã motu ꝓprio.               <anchor type="note" xlink:href="note-0171-03" xlink:label="note-0171-03a"/>               </s>
              <s xml:id="N20A55" xml:space="preserve">¶ Tertiū correlariū </s>
              <s xml:id="N20A58" xml:space="preserve">Poſſibile ē <lb/>idē mobile moueri motu ſimplici cuius quelibet ꝑs <lb/>mouet̄̄ motu mixto </s>
              <s xml:id="N20A5F" xml:space="preserve">Uerbi gr̄a ſi aliquod ſpericū de­<lb/>ſcendat rotãdo ꝑ diametrū mundi ad cētrū: tūc illḋ <lb/>totū rotūdū mouet̄̄ motu ſimplici: tñ q̄libet pars ꝑ-<lb/>ticipat de circuitiõe ī ſuo motu et ſic q̄libet pars mo­<lb/>uetur motu mixto.               <anchor type="note" xlink:href="note-0171-04" xlink:label="note-0171-04a"/>               </s>
              <s xml:id="N20A6F" xml:space="preserve">¶ Quartū correlarium </s>
              <s xml:id="N20A72" xml:space="preserve">Poſſi-               <cb chead="Capitulum quartum"/>               bile eſt ex duobus motibꝰ regulibus fieri vnū ir-<lb/>regularē: </s>
              <s xml:id="N20A7A" xml:space="preserve">Uerbi gr̄a moueat̄̄ nauis vniformiter ab <lb/>oriēte in occidentē: moueat̄̄ etiã ſortes vniformiter <lb/>circulariter intra nauē: et certū eſt  ex illis duobꝰ <lb/>motibus reſultat vnus irregularis: quia cū ſortes <lb/>eſt in medietate nauis in qua mouetur ad motū ſiue <lb/>cū motu ipſius nauis tunc motus eius velocitatur. <lb/></s>
              <s xml:id="N20A88" xml:space="preserve">et dū eſt in alia medietate tunc motus eius retarda­<lb/>tur. </s>
              <s xml:id="N20A8D" xml:space="preserve">Per motū aūt regularē motum vniformē intel­<lb/>ligas: per irregularē vero motū difformē et hoc quo <lb/>ad tp̄s: </s>
              <s xml:id="N20A94" xml:space="preserve">¶ Multa his ſimilia correlaria ex dictis fa­<lb/>cile poteris inferre.</s>
            </p>
            <div xml:id="N20A99" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0171-02a" xlink:label="note-0171-02" xml:id="N20A9D" xml:space="preserve">2. correl.</note>
              <note position="left" xlink:href="note-0171-03a" xlink:label="note-0171-03" xml:id="N20AA3" xml:space="preserve">.3. correl.</note>
              <note position="left" xlink:href="note-0171-04a" xlink:label="note-0171-04" xml:id="N20AA9" xml:space="preserve">4. correl.</note>
            </div>
            <p xml:id="N20AAF">
              <s xml:id="N20AB0" xml:space="preserve">Notandum eſt tertio. </s>
              <s xml:id="N20AB3" xml:space="preserve">Tangendo ma­<lb/>teriã tertii argumēti (cuius principalis inquiſitio ē <lb/>an terra de qua fit mentio in caſu eius perpetuo ſic <lb/>moueretur: ita  non poſſet relicta ſue naturali diſ­<lb/>poſitioni taliter moueri  centrū eius fiat centrum <lb/>mundi)               <anchor type="note" xlink:href="note-0171-05" xlink:label="note-0171-05a"/>                teſte phõ primo de celo et mundo idē ē na-<lb/>turalis locus totiꝰ et partis. </s>
              <s xml:id="N20AC7" xml:space="preserve">Inquit em̄ ad quēcū <lb/>locum natum eſt aliquid natura moueri ad eundeꝫ <lb/>natū eſt moueri quodlibet congenee cõſimiliſ na-<lb/>ture. </s>
              <s xml:id="N20AD0" xml:space="preserve">Quare ſi aliqua terra: eſſet in aere: remoto ī­<lb/>pedimento ipſa deſcenderet quo ad vſ cētrū eius <lb/>ēfficeretur cētrū mūdi. </s>
              <s xml:id="N20AD7" xml:space="preserve">Nec pars illius terre reſiſtit <lb/>ipſi terre ne cētrū eius fiat cētrū mundi:               <anchor type="note" xlink:href="note-0171-06" xlink:label="note-0171-06a"/>               qm̄ idem eſt <lb/>appetitus partis et totius cuius ē pars vt ſatis na­<lb/>turaliter inducit calculator in capitulo de loco ele-<lb/>mēti </s>
              <s xml:id="N20AE7" xml:space="preserve">Unū tñ eſt qḋ ex ſubtili minerua et officina eiuſ­<lb/>dem calculatoris in hoc notabili inferre intendo: <lb/>vcꝫ  ꝑforata ipſa terra vt ponit̄̄ ī caſu tertii argu­<lb/>menti et deſcendente q̈drato terreo vt ibidē ponit̄̄ ſi <lb/>cū talis globus deuenit ad cētrū terre pars vltra cē­<lb/>trū reſiſteret parti citra cētrū ne deſcēderet: ꝑpetuo <lb/>tale q̈dratū ibi moueretur ceteris īpedimētis et ad­<lb/>iumētis deductis. </s>
              <s xml:id="N20AF8" xml:space="preserve">¶ Ad qḋ demonſtrãdū: īducã du-<lb/>as ſupoſitiones quarum prior eſt.</s>
            </p>
            <div xml:id="N20AFD" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0171-05a" xlink:label="note-0171-05" xml:id="N20B01" xml:space="preserve">phūs .i. <lb/>ce. et mū.</note>
              <note position="right" xlink:href="note-0171-06a" xlink:label="note-0171-06" xml:id="N20B09" xml:space="preserve">cal. <gap/> lo. <lb/>ele.</note>
            </div>
            <p xml:id="N20B13">
              <s xml:id="N20B14" xml:space="preserve">Tali quadrato ſic deſcendente: vna-<lb/> parte eius minore medietate illius quadrati exi-<lb/>ſtente vltra centrum mundi reſidua vero parte to-<lb/>tiꝰ q̈drati exiſtēte citra cētrū mūdi: pars intercepta <lb/>inter cētrū mūdi et cētrū talis q̈drati ē medietas ex­<lb/>ceſſus quo pars citra cētrū mūdi excedit ꝑtem exi-<lb/>ſtentē vltra cētrū mundi: </s>
              <s xml:id="N20B23" xml:space="preserve">Exēplū vt ſi vua quarta ta­<lb/>lis q̈drati fuerit vltra centrū mundi adequate tres <lb/>erūt citra cetrū. </s>
              <s xml:id="N20B2A" xml:space="preserve">et ſic pars citra centrū mundi exce-<lb/>dit ꝑtē vltra centrū mūdi ꝑ duas quartas / vt cõſtat: <lb/>et medietas talis exceſſus ē vna q̈rta ex quo totꝰ ex-<lb/>ceſſus eſt duarū q̈rtarū: et vna quarta p̄ciſe interci-<lb/>pit̄̄ inter cētrū illiꝰ quadrati et centrū mundi q2 vna <lb/>medietas medietatis cuiꝰ vna pars eſt vltra cētrum <lb/>mūdi et reliq̈ ē citra centrum mūdi / igit̄̄ pars interce­<lb/>pta inter centrū mūdi et centrū talis q̈drati ē medi­<lb/>etas talis exceſſus </s>
              <s xml:id="N20B3D" xml:space="preserve">Hac exēplari ꝓbatione p̄miſſa ꝓ-<lb/>batur gñaliter ſuppoſitio. </s>
              <s xml:id="N20B42" xml:space="preserve">Sit pars ītercepta īter <lb/>cētrū q̈drati et centrū mūdi d. ſit c. pars eq̈lis ipſi <lb/>d. ī medietate ſuꝑiori talis q̈drati hoc eſt magis re­<lb/>mota a cētro: et ſit reſidua pars talis medietatis ſu­<lb/>ꝑioris b. q̄ pars b. (vt opꝫ) ē eq̈lis ꝑti vltra cētrū (ſi <lb/>eī ab eq̈libꝰ eq̈lia demas remanētiã ſūt eq̈lia: eq̈les <lb/>eī ſūt medietates illius globi et ēt d. et c.) </s>
              <s xml:id="N20B51" xml:space="preserve">Tūc dico / <lb/> d. eſt medietas totius exceſſus quo pars citra cē­<lb/>trum mundi excedit partem vltra centrum mundi. <lb/></s>
              <s xml:id="N20B59" xml:space="preserve">Quod ſic oſtenditur. </s>
              <s xml:id="N20B5C" xml:space="preserve">quia tota pars citra centrum <lb/>mūdi excedit partem vltra centrum mūdi per d. et c. <lb/>adequate et d. eſt equale ipſi c. ex hypotheſi / ergo d. <lb/>eſt vna medietas illius totalis exceſſus compoſiti ex <lb/>c. et d. quo totali exceſſu pars citra centrum mūdi ex­<lb/>cedit partem vltra cētrū mundi / quod fuit ꝓbandū <lb/></s>
              <s xml:id="N20B6A" xml:space="preserve"><pb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū" file="0172" n="172"/>               Patet ↄ̨ña cū minore et ꝓbatur maior: q2 tota ꝑs <lb/>citra centrum mundi continet b. partem equalem <lb/>parti citra centrū mūdi ex hypotheſi: et inſuꝑ cõti-<lb/>net d. et c. / igr̄ ꝑ d. et c. pars citra centrū mūdi exce-<lb/>dit partē vltra centrū mundi / qḋ fuit ꝓbandū. </s>
              <s xml:id="N20B79" xml:space="preserve">Ptꝫ <lb/>ↄ̨ña intelligenti / quid ſit vnū excedere alterum per <lb/>aliquid: et ſic patet ſuppoſitio .</s>
            </p>
            <p xml:id="N20B80">
              <s xml:id="N20B81" xml:space="preserve">Scḋa ſuppoſitio. </s>
              <s xml:id="N20B84" xml:space="preserve">Qñ inter aliquos <lb/>terminos eſt ꝓportio maioris īequalitatis et ma-<lb/>iore quartã exceſſus quo minorē excedit deꝑdente <lb/>adequate: minore eandē dūtaxat quartã acq̇ren-<lb/>te que a minori deperdit̄̄: ꝓportio inter datos ter-<lb/>minos pluſ̄ ad ſubduplum ſui diminuit̄̄ et ex ↄ̨ñti <lb/>data ꝓportio vltra ſuã medietatē deꝑdit. </s>
              <s xml:id="N20B93" xml:space="preserve">Probat̄̄ <lb/>ſit ꝓportio f. īter a. terminū maiorem et e. terminū <lb/>minorē: diuidat̄̄ exceſſus quo a. excedit e: in q̈tuor <lb/>partes equales adequate hoc eſt in quatuor q̈rtas <lb/>et ſignētur ibi īter a. et e. ãnumeratis extremis q̇n <lb/>termini cõtinuo arithmetice ꝓportionabiles quoꝝ <lb/>primꝰ ſit a. ſecūdus b. qui excedit̄̄ ab a. ꝑ vnã quar-<lb/>tã illiꝰ exceſſus quo a. excedit e. adequate, et tertius <lb/>ſit c. qui excedat̄̄ a b. ꝑ aliã quartã illius exceſſus, et <lb/>quartꝰ ſit d. que excedat̄̄ a c. ꝑ vnã aliã quartã ex-<lb/>ceſſus, et quītus ſit e. terminꝰ minor ꝓportiõis date <lb/>qui excedit̄̄ ab ipſo d. ꝑ vltimam quartã exceſſus: et <lb/>manifeſtū eſt illos quī termīos cõtinuo eſſe arith­<lb/>metice ꝓportionabiles cū equali exceſſu exupe­<lb/>rent. </s>
              <s xml:id="N20BB2" xml:space="preserve">deꝑdat igr̄ a. terminꝰ maior vnã quartã exceſ-<lb/>ſus illã vcꝫ ꝑ quã b. terminū excedit: et illã adequate <lb/>acq̇rat e. terminꝰ minor. </s>
              <s xml:id="N20BB9" xml:space="preserve">Tūc dico /  data ꝓportio <lb/>diminuit̄̄ et plus quã ſuã medietatē deꝑdit et ex hoc <lb/>plus quã ad ſubduplū diminuit̄̄. </s>
              <s xml:id="N20BC0" xml:space="preserve">Quod ſic oſtendi­<lb/>tur / q2 ꝓportio f. diminuit̄̄ et plus quã ſui medieta-<lb/>tem deꝑdit ꝓpoſitū. </s>
              <s xml:id="N20BC7" xml:space="preserve">Maior ptꝫ manifeſte ex ſe­<lb/>cūdo correlario tertie concluſionis octaui capitis <lb/>ſecūde partis auxiliãte hypotheſi: et minor ꝓbatur / <lb/>q2 illa ꝓportio f. q̄ eſt inter a. et e. cõponit̄̄ adequate <lb/>ex quatuor proportionibꝰ puta ex ꝓportiõe d. ad e. <lb/>et ex ꝓportiõe c. ad d. et ex ꝓportiõe b. ad c. et ex q̈rta <lb/>ꝓportione ipſiꝰ a. ad b. / vt cõſtat cõſideranti hypo-<lb/>theſim: et ille ꝓportiones ſunt cõtinuo minores et <lb/>minores et minori exceſſu continuo ſeſe excedunt: <lb/>igitur aggregatum ex duabus extremis proporti-<lb/>onibus puta ex ꝓportione d. ad e. et ex ꝓportione a. <lb/>ad b. eſt maiꝰ quã medietas aggregati ex illis qua­<lb/>tuor ꝓportionibꝰ: et ꝑ ↄ̨ñs eſt maius quã medietas <lb/>ipſiꝰ f. ꝓportionis adequate ex illis quatuor ꝓpor­<lb/>tionibꝰ cõpoſite. </s>
              <s xml:id="N20BE6" xml:space="preserve">Ptꝫ hec ↄ̨ña ex quarto correlario <lb/>ſecūde cõcluſionis ſecūdi capitis ſecunde partis: et <lb/>aggregatū ex illis extremis ꝓportiõibꝰ ꝑdit ꝓpor­<lb/>tio f. / vt ptꝫ ex hypotheſi auxiliãte primo correlario <lb/>ſexte concluſiõis octaui capitis ſecūde partis. </s>
              <s xml:id="N20BF1" xml:space="preserve">(Ter-<lb/>minꝰ em̄ maior puta a. cū deꝑdit exceſſum quo exce­<lb/>dit b. deꝑdit ꝓportionē q̄ eſt ipſiꝰ a. ad b. et terminꝰ <lb/>minor puta e. cū acq̇rit illū exceſſum quo excedit̄̄ a <lb/>d. acq̇rit illã ꝓportionē adequate q̄ eſt ipſiꝰ d. ad e.) / <lb/>igr̄ ꝓportio f. plus quã ſui medietatē deꝑdit / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N20C00" xml:space="preserve">Prima pars mīoris vcꝫ  ille ꝓportiões <lb/>ſunt cõtinuo minores et mīoris ꝓbat̄̄ / q2 qñ īter ali-<lb/>quos termīos eſt aliqua ꝓportio maioris inequa-<lb/>litatis: et maiores equali exceſſu excedūt ſuos mīo-<lb/>res ſemꝑ inter maiores eſt minor ꝓportio quã inter <lb/>mīores / vt ptꝫ ex octaua ſuppoſitiõe quarti capitis <lb/>ſecūde partis: ſed oēs illi termini .a. b.c.d. excedūt <lb/>ſuos minores eq̈li exceſſu et d. et e. ſunt minores quã <lb/>d. et c. et d. et c. mīores quã c. et b. et c. et b. minores quã <lb/>b. et a. / igr̄ ꝓportio ipſiꝰ d. ad e. eſt maior ꝓportiõe <lb/>c. ad d. et ꝓportio c. ad d. maior eſt ꝓportionē b. ad <lb/>c. et ꝓportio b. ad c. maior ꝓportiõe a. ad b. et ſic ille               <cb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū"/>               ꝓportiones ſunt ↄ̨tinuo minores et mīores / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N20C1E" xml:space="preserve">Sed iã ꝓbo aliã partē minoris vcꝫ  cõti­<lb/>nuo minori exceſſu ſe excedant: q2 ꝓportio ipſiꝰ d. <lb/>ad e. ꝑ maiorē ꝓportionē excedit ꝓportionē ipſiꝰ c. <lb/>ad d. quã ꝓportio ipſius c. ad d. excedit ꝓportionē <lb/>ipſiꝰ b. ad c. et ꝓportio ipſiꝰ c. ad d. ꝑ maiorē ꝓpor-<lb/>tionē excedit ꝓportionē b. ad. c. quã ꝓportio b. ad c. <lb/>excedat ꝓportionē a. ad b. / igr̄ ille ꝓportiões conti-<lb/>nuo minori exceſſu ſe excedūt. </s>
              <s xml:id="N20C2F" xml:space="preserve">Maior ptꝫ ex quinto <lb/>correlario quīte cõcluſionis octaui capitis ſecūde <lb/>partis qm̄ .b.c.d.e. ſunt quatuor termini continuo <lb/>arithmetice ꝓportionabiles ex hypotheſi: igr̄ pro­<lb/>portio q̄ eſt inter duos termīos mīores puta inter <lb/>d. et e. ꝑ plus excedit ſecūdã ꝓportionē q̄ eſt inter c. <lb/>et d. quã illa ſcḋa excedat tertia q̄ eſt ipſiꝰ b. ad c. / vt <lb/>ptꝫ ex correlario allegato. </s>
              <s xml:id="N20C40" xml:space="preserve">Et ſic ꝓbabis minorem <lb/>capiendo iſtos quatuor terminos cõtinuo arithme­<lb/>tice ꝓportionabiles puta .a. b.c.d. </s>
              <s xml:id="N20C47" xml:space="preserve">Et ſic ptꝫ corre-<lb/>larium. </s>
              <s xml:id="N20C4C" xml:space="preserve">¶ Cõſimiliter ꝓbares /  diuiſo exceſſu quo <lb/>maior terminꝰ excedit minorē in qñ partes eq̈les <lb/>maiore termino deꝑdente vnã illaꝝ quītaꝝ minore <lb/>acq̇rente eandē  tūc ꝓportio inter datos termīos <lb/>perdit plus quã duas quītas ſui et ſi exceſſus diui-<lb/>datur in ſex partes equales maiore deꝑdente vnã <lb/>illaꝝ et minore acq̇rente eandē: ꝓportio īter datos <lb/>terminos perdit plus quam vnã tertiã: et ſi diuidat̄̄ <lb/>exceſſus in ſeptē maiore deꝑdente vnã illaꝝ et mīore <lb/>acq̇rente eandē: ꝓportio inter datos termīos ꝑdit <lb/>plus quã duas ſeptimas / et ſic ↄ̨ñter. </s>
              <s xml:id="N20C63" xml:space="preserve">Oīa iſta patēt <lb/>ex deductionibꝰ quīti correlarii prime cõcluſionis <lb/>et quīti correlarii ſecūde cõcluſionis ſecūdi capitis <lb/>ſecūde partis. </s>
              <s xml:id="N20C6C" xml:space="preserve">¶ Ex his inducit̄̄ et demõſtratur ꝓpo­<lb/>ſitū vcꝫ  illud quadratū terreū ꝑpetuo moueret̄̄ <lb/>in tali caſu. </s>
              <s xml:id="N20C73" xml:space="preserve">Sit vna pars illiꝰ q̈drati vltra centruꝫ <lb/>mūdi minor medietate: et diuidat̄̄ pars intercepta <lb/>inter centrū illiꝰ quadrati et centrū mūdi q̄ eſt me-<lb/>dietas totiꝰ exceſſus partis citra centrū mundi ad <lb/>partē vltra centrū mūdi ex prima ſuppoſitione et <lb/>hoc ꝑ partes ꝓportionales ꝓportione dupla ma-<lb/>ioribꝰ ſus centrū mundi terminatis: q̄ pars ſit d. <lb/>ſit totū illud quadratū vniforme in grauitate: ſit <lb/>etiã ꝓportio totiꝰ partis citra centrū mūdi ad par­<lb/>tē vltra centrū mūdi f. </s>
              <s xml:id="N20C88" xml:space="preserve">Quo poſito ſic argr̄ q̈dratū <lb/>illud tamdiu mouebit̄̄ quãdiu aliqua pars ipſius <lb/>d. partis intercepte inter centrū q̈drati et centrum <lb/>mundi fuerit citra centrū mūdi qm̄ tamdiu excedet <lb/>pars citra centrū partē vltra centrū q2 tūc cõtinuo <lb/>erit maior: ſed ꝑpetuo aliqua pars ipſiꝰ d. partis <lb/>erit citra centrū mūdi: g̊ ꝑpetuo tale q̈dratū moue­<lb/>bitur / qḋ fuit ꝓbandū. </s>
              <s xml:id="N20C99" xml:space="preserve">Cõſequētia ptꝫ cū maiore et <lb/>ꝓbat̄̄ minor / q2 ꝑpetuo aliqua pars aggregati ex <lb/>oībus partibꝰ ꝓportionalibꝰ ipſiꝰ d. partis deſcē­<lb/>det: g̊ ꝑpetuo aliqua pars ipſiꝰ d. partis erit citra <lb/>centrū mūdi / qḋ fuit ꝓbandū, </s>
              <s xml:id="N20CA4" xml:space="preserve">Cõſequētia ptꝫ et pro­<lb/>batur añs / q2 prima pars ꝓportionalis ipſius d. <lb/>partis incipit deſcēdere a ꝓportiõe f. vt habet̄̄ hy-<lb/>potheſi: et ſecūda pars ꝓportiõalis ipſiꝰ d. partis <lb/>incipit deſcēdere a ꝓportiõe ſubdupla ad ꝓportio­<lb/>nē f. vel a minori: et tertia īcipit deſcēdere a ſubdu-<lb/>pla vel minori ſubdupla ad ꝓportionē a q̈ incipit <lb/>deſcēdere ſcḋa / et ſic ↄ̨ñter q̄libet pars ꝓportiõalis <lb/>ipſiꝰ d. ſequēs īcipiet deſcēdere a ꝓportione ſubdu­<lb/>pla vel minori ad ꝓportionē a qua īcipit deſcēde-<lb/>re pars īmediate p̄cedēſupra: et q̄libet pars quãdiu ali-<lb/>q̇d eiꝰ deſcēdit cõtinuo deſcēdit ſiue mouet̄̄ a mīori <lb/>ꝓportione ꝙ̄ ſit illa a qua incipit illa eadem pars <lb/>deſcēdere (cū cõtinuo partis citra centrū mūdi ad <lb/>partē vltra centrū mūdi ꝓportio a qua partes ille <lb/>deſcendūt cõtinuo diminuatur: continuo em̄ pars               <pb chead="Secundi tractatus" file="0173" n="173"/>               citra centrū mūdi efficit̄̄ minor et pars vltra centrū <lb/>mūdi maior) / igr̄ perpetuo aliqua pars aggregati <lb/>ex oībus partibꝰ ꝓpotiõalibꝰ ipſiꝰ d. partis deſcē-<lb/>det / qḋ fuit ꝓbandū. </s>
              <s xml:id="N20CD0" xml:space="preserve">Conſequētia ꝓbat̄̄ / q2 ſi q̄libet <lb/>pars ꝓportionalis cõtinuo ipſius d. partis diuiſe <lb/>ꝓportione dupla deſcēderet ſiue moueret̄̄ a ꝓpor-<lb/>tione a qua ipſa īcipit deſcendere: ꝑpertuo aliqua <lb/>pars aggregati ex oībus partibꝰ ꝓportionalibus <lb/>ipſiꝰ d. partis deſcēderet / g̊ ſi q̄libet pars ꝓportio-<lb/>nalis ipſiꝰ d. partis cõtinuo deſcēderet et mouetur <lb/>a ꝓportione minori ꝙ̄ ſit illa a qua īcipit deſcēde-<lb/>re: ꝑpetuo aliqua pars aggregati ex oībus parti-<lb/>bus ꝓportionalibꝰ ipſiꝰ d. partis deſcendit / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N20CE7" xml:space="preserve">Cõſequētia ptꝫ cū ãtecedēte ex deductione <lb/>ſecūdi argumēti ſexti capitis primi tractatꝰ huius <lb/>partis: hoc addito /  ille partes cõtinuo ſe habent <lb/>in ꝓportione dupla: et in tꝑe in quo adequate deſcē­<lb/>dit aliqua pars ſcḋm ſe vel aliquid eiꝰ p̄tereundo <lb/>centrū mūdi ipſa pars deſcribit tm̄ ſpaciū quanta <lb/>ipſamet pars eſt / vt ptꝫ intuenti caſum. </s>
              <s xml:id="N20CF6" xml:space="preserve">Sed iã ꝓbo <lb/>ſcḋam partē maioris vcꝫ  ſecūda pars ꝓportona­<lb/>lis ipſiꝰ d. partis īcipit deſcēdere a ꝓportione ſub­<lb/>dupla ad ꝓportionē f. vĺ minori: q2 cū primū ṗma <lb/>pars proportionalis ipſius d. partis eſt totaliter <lb/>vltra centrū mūdi, pars citra centrū mundi perdit <lb/>quartã partē exceſſus quo excedit partē vltra cen-<lb/>trū mūdi: et illã acquirit pars vltra centrū mūdi / vt <lb/>cõſtat: g̊ tūc ꝓportio f. partis citra centrū ad partē <lb/>vltra centrū ꝑdit pluſ̄ medietatē ſui: et pluſ̄ ad <lb/>ſubduplū ſui diminuit̄̄: ptꝫ ↄ̨ña ex ſecūda ſuppoſi-<lb/>tione huiꝰ notabilis hoc addito  pars citra cen-<lb/>trū eſt terminꝰ maior proportionis f. et pars vltra <lb/>centrū eſt terminꝰ minor. </s>
              <s xml:id="N20D13" xml:space="preserve">Et ab illa proportione q̄ <lb/>eſt minor quã ſubdupla ad f. īcipit ſecūda pars ꝓ-<lb/>portionalis ipſiꝰ d. partis deſcēdere / vt cõſtat: g̊ ꝓ-<lb/>poſitū. </s>
              <s xml:id="N20D1C" xml:space="preserve">Et iſto modo ꝓbabis  tertra īcipit deſcen­<lb/>dere a ꝓportione ſubdupla vel mīori ſubdupla ad <lb/>proportionē a qua incipit deſcendere ſecūda: et ſic <lb/>ↄ̨ñter de aliis partibꝰ. </s>
              <s xml:id="N20D25" xml:space="preserve">Sed iã ꝓbo maiorē vcꝫ  cū <lb/>primū prima pars proportionalis ipſiꝰ d. partis <lb/>eſt totaliter vltra centrū pars citra centrū mundi <lb/>perdit quartã partē exceſſus quo ipſa excedit par-<lb/>tem vltra centrū mūdi: q2 ipſa d. pars eſt medietas <lb/>exceſſus quo pars citra centrū excedit partē vltra <lb/>centrū / vt ptꝫ ex prima ſuppoſitione huiꝰ notabilis / <lb/>g̊ prima pars proportionalis proportione dupla <lb/>ipſiꝰ d. partis eſt quarta pars totiꝰ exceſſus: et illã <lb/>ꝑdit pars citra centrū mūdi primū ipſa eſt tota­<lb/>liter vltra centrū: g̈ propoſitū. </s>
              <s xml:id="N20D3C" xml:space="preserve">Ptꝫ g̊ maior: et totū <lb/>añs / et ꝑ ↄ̨ñs cõcluſio q̄ fuerat probanda.               <anchor type="note" xlink:href="note-0173-01" xlink:label="note-0173-01a"/>               </s>
              <s xml:id="N20D46" xml:space="preserve">¶ Ex his <lb/>infero aliqua correlaria. </s>
              <s xml:id="N20D4B" xml:space="preserve">Primū in caſu huiꝰ de-<lb/>monſtrationis īmediate poſt inſtãs / qḋ eſt preſens <lb/>aſcendet aliq̇d īmediate poſt illud deſcēdet : et tñ <lb/>nichil īmediate poſt hoc aſcendet qḋ īmediate poſt <lb/>hoc deſcendet. </s>
              <s xml:id="N20D56" xml:space="preserve">Probat̄̄ prima pars / q2 quocun <lb/>inſtanti dato illiꝰ tꝑis in quo deſcēdet tale quadra­<lb/>tū q̄libet pars illiꝰ quadrati q̄ eſt citra centrū īme-<lb/>diate poſt tale inſtans deſcendet / vt ſatis conſtat et <lb/>īmediate poſt idē inſtans aliqua talis pars aſcen-<lb/>det: igr̄ in caſu demonſtrationis, īmediate poſt in-<lb/>ſtans / qḋ eſt preſens aliq̇d aſcēdet qḋ īmediate poſt <lb/>idē inſtans deſcendet ſcḋa pars ptꝫ ex falſitate ſue <lb/>cõtradictorie. </s>
              <s xml:id="N20D69" xml:space="preserve">Ad hoc em̄  aliquid aſcendat non <lb/>ſufficit aliquã partē eiꝰ aſcendere: ſed requiritur /  <lb/>maior pars ꝙ̄ eiꝰ medietas aſcendat. </s>
              <s xml:id="N20D70" xml:space="preserve">Conſimiliter <lb/>dicat̄̄ de deſcensu.               <anchor type="note" xlink:href="note-0173-02" xlink:label="note-0173-02a"/>               </s>
              <s xml:id="N20D7A" xml:space="preserve">¶ Scḋm correlariū. </s>
              <s xml:id="N20D7D" xml:space="preserve">Immediate <lb/>poſt inſtans qḋ eſt preſens aſcendet aliq̇d qḋ p̄ſens <lb/>aſcendet aliq̇d qḋ īmediate poſt idē inſtans deſcen­<lb/>det: et tñ nõ īmediate poſt inſtãs qḋ eſt p̄ſens deſcen­               <cb chead="Capitulū quartū."/>               det aliq̇d qḋ īmediate poſt idem inſtans aſcendet. <lb/></s>
              <s xml:id="N20D8A" xml:space="preserve">Ptꝫ prima pars huiꝰ ex priori correlario. </s>
              <s xml:id="N20D8D" xml:space="preserve">Et ſcḋa <lb/>ꝓbat̄̄ / q2 ↄ̨tradictoria illiꝰ eſt falſa / vt ptꝫ ꝑ falſitatē <lb/>prime exponētis q̄ eſt iſta poſt inſtans quod eſt pre­<lb/>ſens deſcendet aliquid quod īmediate poſt idem in­<lb/>ſtans aſcendet q2 nulla pars illiꝰ corporis quadra­<lb/>ti que poſt inſtans quod eſt preſens deſcendit īme-<lb/>diate poſt idem inſtans aſcendet.               <anchor type="note" xlink:href="note-0173-03" xlink:label="note-0173-03a"/>               </s>
              <s xml:id="N20DA1" xml:space="preserve">¶ Tertiū correla­<lb/>riū. </s>
              <s xml:id="N20DA6" xml:space="preserve">Immediate poſt inſtans quod eſt p̄ſens aſcen-<lb/>det aliq̇d qḋ īmediate poſt idē inſtans quod eſt pre­<lb/>ſens deſcendet: et tñ nichil ſimul aſcendet, et deſcen-<lb/>det adequate diuiſiue capiendo ly. </s>
              <s xml:id="N20DAF" xml:space="preserve">et ſicut ſtat  ſor­<lb/>tes īmediate poſt hoc erit albus, et immediate poſt <lb/>hoc erit niger: et tamen nõ ſimul erit albus et niger <lb/></s>
              <s xml:id="N20DB7" xml:space="preserve">Patet correlarium. </s>
              <s xml:id="N20DBA" xml:space="preserve">¶ Ex his tribus notabilibus <lb/>patet facile reſponſio ad queſtionem.</s>
            </p>
            <div xml:id="N20DBF" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0173-01a" xlink:label="note-0173-01" xml:id="N20DC3" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0173-02a" xlink:label="note-0173-02" xml:id="N20DC9" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0173-03a" xlink:label="note-0173-03" xml:id="N20DCF" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N20DD5">
              <s xml:id="N20DD6" xml:space="preserve">Ad rationes ante oppoſitū. </s>
              <s xml:id="N20DD9" xml:space="preserve">Ad primã <lb/>reſponſum eſt ibi vſ ad replicam ad quam reſpo-<lb/>deo negando ſequelam, et ad probationem dico /  <lb/>illud correlarium ibi adductum ad probationem <lb/>illiꝰ ſequele nõ eſt ad propoſitū, q2 ſupponit ꝓpor­<lb/>tionē tēpoꝝ excedere proportionē velocitatū. </s>
              <s xml:id="N20DE6" xml:space="preserve">Cuiꝰ <lb/>oppoſitū ī caſu argumēti eſt verū. </s>
              <s xml:id="N20DEB" xml:space="preserve">Cõmēſurãda em̄ <lb/>eſt vtra velocitas, et qua illud corpus mouet̄̄ cir-<lb/>culariter, et qua mouetur motu rarefactiõis pūcto <lb/>eiꝰ a quo debet ſumi velocitas totiꝰ motus cõtinuo <lb/>acquirente maiorē et maiorē diſtantiam a centro / vt <lb/>ptꝫ ex deductione eiuſdē replice.               <anchor type="note" xlink:href="note-0173-04" xlink:label="note-0173-04a"/>               </s>
              <s xml:id="N20DFD" xml:space="preserve">¶ Ex quo ſequitur / <lb/> poſſibile eſt aliquod corpꝰ circulare cõtinuo vni-<lb/>formiter et eque velociter moueri: et tñ ipſū ↄ̨tinuo <lb/>rarefieri et effici maiꝰ. </s>
              <s xml:id="N20E06" xml:space="preserve">Probat̄̄ ponēdo /  vna rota <lb/>incipiat moueri circulariter pūcto medio ſemidia-<lb/>metri incipiēte moueri velocitate vt .4. et volo /  ſiĺ <lb/>incipiat rarefieri illud corpus acquirendo in hora <lb/>pedalē diſtantiã adequate a centro ſupra diſtan-<lb/>tiã p̄habitã, eo tñ modo moueat̄̄ ille punctꝰ medius <lb/>ſemidiametri  nun̄ ꝑtranſeat ſiue deſcribat ma­<lb/>iorē lineã in aliquo tꝑe ꝙ̄ nata ſit deſcribi a veloci-<lb/>tate vt .4. in eodē tꝑe quo poſito ſequit̄̄ correlariū. <lb/>               <anchor type="note" xlink:href="note-0173-05" xlink:label="note-0173-05a"/>               </s>
              <s xml:id="N20E20" xml:space="preserve">¶ Sequit̄̄ ſecūdo /  ſi aliqua rota in hora moueat̄̄ <lb/>circulariter puncto medio ſemidiametri continuo <lb/>motu circulari mouēte vniformiter, motu vero ra-<lb/>refactionis cõtinuo intendente motū ſuū in q̈libet <lb/>parte proportionali hore ꝓportione dupla ſequē-<lb/>te in duplo velociꝰ rarefiente ꝙ̄ in īmediate p̄cedēti <lb/>tūc ſpaciū deſcriptū a tali puncto eſt infinitū. </s>
              <s xml:id="N20E2F" xml:space="preserve">Ptꝫ <lb/>hoc correlariū ex ſexta concluſione ꝑcedētꝪ capitis</s>
            </p>
            <div xml:id="N20E34" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0173-04a" xlink:label="note-0173-04" xml:id="N20E38" xml:space="preserve">1. correĺ</note>
              <note position="right" xlink:href="note-0173-05a" xlink:label="note-0173-05" xml:id="N20E3E" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N20E44">
              <s xml:id="N20E45" xml:space="preserve">Ad ſecundã rationē reſponſum eſt ibi <lb/>vſ ad replicã: ad quã reſpõdeo negando ſequelã <lb/>et ad probationē nego  nullū ſit īpedimentū. </s>
              <s xml:id="N20E4C" xml:space="preserve">īmo <lb/>cõtra motio nauis eſt ſorti īpedimento. </s>
              <s xml:id="N20E51" xml:space="preserve">Fatigat̄̄ tñ <lb/>ſortes nõ ꝑ motū quo deſcribat aliquod ſpacium <lb/>fixū: ſed q2 deſcribit aliquod ſpaciū nõ fixū ad cuiꝰ <lb/>deſcriptionē nõ ſequit̄̄ ſortē proprie moueri. </s>
              <s xml:id="N20E5A" xml:space="preserve">Ma-<lb/>net enim ſortes in eodem loco fixo.</s>
            </p>
            <p xml:id="N20E5F">
              <s xml:id="N20E60" xml:space="preserve">Ad ṫciã rationē rñdeo negãdo añs: et <lb/>ad ꝓbationē ↄ̨cedo maiorē, et nego mīorē et ad ꝓba­<lb/>nē diſtinguo ſeq̄lã aut ſi tale corpꝰ ſit taliter diſpo­<lb/>ſitū  partes eiꝰ proportionales ꝓportiõe dupla <lb/>ita ſe habeant  ſcḋm eã dimenſionē ſcḋm quã de-<lb/>ſcendūt cõtinuo ſe habet in ꝓportione dupla oībꝰ <lb/>aliis iuuamentis et īpedimētis deductis: et ſic cõce-<lb/>do ſequelã. </s>
              <s xml:id="N20E71" xml:space="preserve">Si vero partes eiꝰ proportionales pro­<lb/>portione dupla ſe habuerīt in maiori proportione <lb/>quã ſit ꝓportio dupla et hoc quantū ad dimēſionē <lb/>ſcḋm quã deſcendūt, et ſic nõ oportet. </s>
              <s xml:id="N20E7A" xml:space="preserve">Nego igitur <lb/>illo modo ſeq̄lã. </s>
              <s xml:id="N20E7F" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  ita põt aliqḋ cor-               <pb chead="Dc motu rarefactionis  condenſationis." file="0174" n="174"/>               pius diſponi difformiṫ in partibꝰ ſuis  ipſū ī tꝑe <lb/>finito mouebit̄̄ q̊vſ cētrū eiꝰ ſit cētrū mūdi. </s>
              <s xml:id="N20E89" xml:space="preserve">Pro-<lb/>bat̄̄ et pono /  ꝑs ītercepta īter centrū mūdi et cētrū <lb/>corporis diuidat̄̄ ꝑ partes proportionales ꝓpor-<lb/>tione dupla maioribꝰ ſus centrū mūdi termina-<lb/>tis / vt ponit̄̄ in tertio notabili q̄ pars ſit d. et poſt̄ <lb/>prima pars proportionalis ipſiꝰ d. partis ꝑtrãſit <lb/>centrū q̄ (vt ſuppono) ꝑtranſit centrū ſcḋm ſe et qḋ-<lb/>libet ſui in hora, ſigno ꝓportionē a qua d3 tcrtia <lb/>pars proportionalis d. partis incipere ꝑtranſire <lb/>centrū mūdi q̄ ſit f. </s>
              <s xml:id="N20E9E" xml:space="preserve">Et manifeſtū eſt /  aliqḋ ſpaciū <lb/>ſufficit ꝑtrãſiri ī medietate hore mediante velocita­<lb/>te nata prouenire a proportiõe f. pono igr̄ /  ſcḋa <lb/>pars proportionalis ipſiꝰ d. partis diminuat̄̄ m <lb/>dimenſionē ſcḋm quã ꝑtrãſit centrū mūdi, quouſ <lb/>ſit ſcḋm illã dimenſionē equalis ſpacio nato ꝑtrã-<lb/>ſiri ab .f. proportiõe in medietate hore. </s>
              <s xml:id="N20EAD" xml:space="preserve">ipſa tñ ſemꝑ <lb/>manēte tanta quãta erat antea: ita  augeat̄̄ ſcḋm <lb/>aliã dimenſionē. </s>
              <s xml:id="N20EB4" xml:space="preserve">Et poſt̄ ſcḋa pars proportiona­<lb/>lis d. ꝑtis ꝑtranſit cētrū mūdi ſcḋm ſe et qḋlꝫ ſui ſi-<lb/>gno ꝓportionē q̄ ſit g. a qua d3 quarta pars ꝓpor­<lb/>tiõalis deſcēdere q̄ eſt minor f. / vt cõſtat. </s>
              <s xml:id="N20EBD" xml:space="preserve">Et manife-<lb/>ſtū eſt /  aliquod ſpaciū ſufficit ꝑtranſiri in quarta <lb/>parte hore mediante ꝓportiõe g̊ pono igr̄ /  tertia <lb/>pars ꝓportionalis d. partis dimīnuat̄̄ ſcḋm dimē­<lb/>ſionē ſcḋm quã ꝑtranſit centrū mūdi quovſ ſcḋ3 <lb/>illã dimenſionē ſit eq̈lis ſpacio nato ꝑtranſiri a g. <lb/>ꝓportione in quarta parte hore. </s>
              <s xml:id="N20ECC" xml:space="preserve">Et ſic fiat de qua-<lb/>libet ſequēte  ipſa vcꝫ diminuat̄̄ ſcḋm dimenſionē <lb/>ſcḋm quã ꝑtranſit centrū mūdi quovſ ſit equalis <lb/>ſpacio nato ꝑtranſiri a ꝓportione a qua d3 īcipere <lb/>ꝑtranſire centrū mūdi pars īmediate ſequēs et hoc <lb/>in tꝑe ſubduplo vel minori ꝙ̄ ſit tēpus in quo ade-<lb/>quate pars īmediate p̄cedens ꝑtranſit centrū mūdi <lb/>qualibet tñ cõtinuo manēte tanta quãta erat antea <lb/>ita  augeat̄̄ ſcḋm aliã dimenſionē. </s>
              <s xml:id="N20EDF" xml:space="preserve">Tūc manifeſtū <lb/>eſt /  totū illud corpus poſt̄ prima pars d. partis <lb/>p̄teriuit centrū mūdi mouebit̄̄ p̄ciſe ꝑ vnã horã vĺ ꝑ <lb/>minꝰ tēpꝰ ante quã centrū illiꝰ corporis fiat centrū <lb/>mūdi. </s>
              <s xml:id="N20EEA" xml:space="preserve">Quod ſic oſtendit̄̄ / q2 quelibet pars ꝓporti-<lb/>onalis ipſiꝰ d. partis ſequēs ꝑtranſibit in caſu po­<lb/>ſito cētrū in tꝑe ſubduplo vĺ mīori ad tēpus in quo <lb/>ꝑtranſibit pars īmediate p̄cedens / vt facile ptꝫ ex ca­<lb/>ſu: et prima ꝑtranſit centrū in vna hora vt ſupponi­<lb/>tur: ergo oēs alie pertranſibunt in vna hora vel in <lb/>minori tempore et ſic in tempore finito centrū illiꝰ <lb/>corporis fit centrū mūdi: põt igitur taliter diſponi <lb/>corpus  ipſum in tēpore finito preciſe mouebitur <lb/>quovſ centrum eiꝰ fiat centrum muudi / quod fuit <lb/>probandū.               <anchor type="note" xlink:href="note-0174-01" xlink:label="note-0174-01a"/>               </s>
              <s xml:id="N20F06" xml:space="preserve">Et hoc ex ſequitur /  demonſtratio cal-<lb/>culatoris in capitulo de loco elementi non eſt effi-<lb/>cax non enim limitat ſiue determinat diſpoſiteonē <lb/>illius corporis quod tamen oportet / vt ptꝫ ex dictis</s>
            </p>
            <div xml:id="N20F0F" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0174-01a" xlink:label="note-0174-01" xml:id="N20F13" xml:space="preserve">Oñditur <lb/>Cal. de-<lb/>monſtra­<lb/>tio in effi­<lb/>cax.</note>
            </div>
          </div>
        </div>
        <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
          <p xml:id="N20F26">
            <s xml:id="N20F27" xml:space="preserve">Sequitur tractatus tertius huius <lb/>tertie partis de motu rarefactionis <lb/> condenſationis.</s>
          </p>
          <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
            <head xml:id="N20F33" xml:space="preserve">Capitulū primū in quo diſputatiue inquiritur. <lb/>Quid ſi raritas et dēſitas et penes q̇d raritatis et <lb/>dēſitatis intēſio et rarefactiõis et condenſationis <lb/>ſit velocitas attendenda.</head>
            <p xml:id="N20F3C">
              <s xml:id="N20F3D" xml:space="preserve">Exacto tractatu de motu locali <lb/>inſequendo veſtigia patrū, et maioꝝ ſub-<lb/>iungã tractatū de motu augmeutationis <lb/>et rarefactionis et inquirendo ſubſtantiã raritatis <lb/>et denſitatis velocitatem et tarditatem rarefacti-<lb/>onis et condenſationis.</s>
            </p>
            <cb chead="Dc motu rarefactionis  condenſationis."/>
            <p xml:id="N20F4C">
              <s xml:id="N20F4D" xml:space="preserve">Quero vtrum raritas  denſitas ſit <lb/>poſſibilis, et argr̄ primo /  nõ q2 ſi raritas et denſi­<lb/>tas ſit poſſibilis, vel tã raritas ꝙ̄ denſitas dicunt̄̄ <lb/>poſitiue, et ſunt qualitates aut nõ: nullum iſtoꝝ eſt <lb/>dicendū: igr̄ nec raritas nec denſitas eſt poſſibilis <lb/>nõ primū q2 raritas ita ſe habet  equevelociter et <lb/>eque proportionabiliter ſicut raritas acquirit̄̄ ita <lb/>velociter et proportionabiliter denſitas deꝑditur: <lb/>ſed hoc non põt eſſe de duobꝰ poſitiuis: igr̄ raritas <lb/>et dēſitas nõ ſūt qualitates poſitiue. </s>
              <s xml:id="N20F62" xml:space="preserve">Maior ꝓbat̄̄. <lb/></s>
              <s xml:id="N20F66" xml:space="preserve">Quia quantū aliquid de raritate acq̇rit tm̄ deper­<lb/>dit de denſitate cū acq̇ſitio raritatis nõ ſit niſi dē, <lb/>perditio denſitatis et eque ꝓportionabiliter ſicut <lb/>aliq̇d rarefit ſiue efficit̄̄ magis rarum ita ꝓportiõa­<lb/>biliter efficit̄̄ minꝰ diuiſum q2 ſi in duplo magis ra­<lb/>riū efficit̄̄ aliq̇d illud in duplo minꝰ denſum efficit̄̄ <lb/>et ecõtra: igr̄ equevelociter et eque ꝓportionabiliter <lb/>ſicut raritas acq̇rit̄̄: ita denſitas deꝑdit̄̄, et ſic patet <lb/>maior. </s>
              <s xml:id="N20F79" xml:space="preserve">Probatur minor / q2 ſi aliqua duo poſitiua <lb/>poſſunt ita ſe habere  equevelociter et eque ꝓpor­<lb/>tionabiliter ſicut vnū deꝑdit̄̄ ita aliud augeat̄̄ ſeu <lb/>intēdat̄̄ ſint illa a. et b. et augeat̄̄ a. et deꝑdatur b. </s>
              <s xml:id="N20F82" xml:space="preserve">Et <lb/>argr̄ ſic / vĺ a. et b. ſūt eq̈lia vt īeq̈lia ſi eq̈lia et argr̄ ſic <lb/></s>
              <s xml:id="N20F88" xml:space="preserve">Eq̄velociṫ auget̄̄ a. ſicut diminuit̄̄ b. / g̊ ↄ̨tinuo a . erit <lb/>maiꝰ b. et cõtinuo tm̄ a aēq̇;ret quãtū b. deꝑdet. </s>
              <s xml:id="N20F8D" xml:space="preserve">Cõ-<lb/>ſequentia ptꝫ de ſe / q2 equevelociter auget̄̄ vnū ſi-<lb/>cut aliud diminuit̄̄. </s>
              <s xml:id="N20F94" xml:space="preserve">Et vltra cõtinuo a. erit maiꝰ b. <lb/>et ↄ̨tinuo tm̄ acq̇rit a. ̄tū deꝑdit b. / igr̄ ↄ̨tinuo b. ma­<lb/>iorē ꝓportionē deꝑdit ꝙ̄ a. acq̇rit et ꝑ ↄ̨ñs non eque­<lb/>velociter et eque ꝓportionabiliter auget̄̄ a. ſicut di­<lb/>minuit̄̄ b. / ptꝫ hec ↄ̨ña ꝑ hanc maximã geometricam <lb/></s>
              <s xml:id="N20FA0" xml:space="preserve">Qñcun certa latitudo ſiue quantitas demitur a. <lb/>minori: et addat̄̄ maiori maiorē ꝓportionē deꝑdit <lb/>minꝰ ꝙ̄ acq̇rat maiꝰ (qm̄ ꝑ additionē equalis quãti­<lb/>tatis maiori et minori: maiorē ꝓportionē acq̇rit mi­<lb/>nus ꝙ̄ maiꝰ / vt dictū eſt in ſcḋa parte) / igr̄ ꝑ ſubſtra­<lb/>ctionē cuiuſdē a minori et appoſitionē maiori ma-<lb/>iorē ꝓportionē deꝑdit minꝰ ꝙ̄ acq̇rat maius: et ſic <lb/>ptꝫ /  ſi ſint equalia nõ põt vnū illoꝝ equevelociter <lb/>et eque ꝓportiõabiliter augeri ſiue aliud diminui. <lb/></s>
              <s xml:id="N20FB4" xml:space="preserve">Si vero ſint inequalia et minꝰ illoꝝ diminuatur et <lb/>maiꝰ illoꝝ auget̄̄ equevelociter iã ſequeret̄̄ /  minꝰ <lb/>illoꝝ maiorē ꝓportionē deꝑdit ꝙ̄ maius acq̇rat / vt <lb/>ptꝫ ex ſuperiori deductione. </s>
              <s xml:id="N20FBD" xml:space="preserve">Si vero maiꝰ diminuit̄̄ <lb/>ita velociter ſicut minꝰ auget̄̄: ſequit̄̄ /  cõtinuo ma­<lb/>iorē ꝓportionē acq̇rit minꝰ ꝙ̄ deꝑdat maius: q2 qñ <lb/>aliqua latitudo demitur a maiori et addit̄̄ minori: <lb/>maiorē ꝓportionē acq̇rit minꝰ ꝙ̄ deꝑdat maiꝰ: igr̄ <lb/>et ſic ptꝫ /  nõ eſt dicendū raritatem et denſitatē eſſe <lb/>qualitates poſitiuas. </s>
              <s xml:id="N20FCC" xml:space="preserve">Sed nec diceuumū eſt ipſas <lb/>nõ eſſe qualitates q2 hoc eſt contra cõmentatorem <lb/>in ſeptīo phiſicoꝝ quē inſequit̄̄ ibi Burleꝰ et in tra­<lb/>ctatu ſuo de intenſione formarū.               <anchor type="note" xlink:href="note-0174-02" xlink:label="note-0174-02a"/>               </s>
              <s xml:id="N20FDA" xml:space="preserve">¶ Dices forte ad <lb/>punctū argumēti negando  ſit īpoſſibile vnū po-<lb/>ſituū equevelociter et eque ꝓportiõabiliter augeri <lb/>ſicut diminuit̄̄. </s>
              <s xml:id="N20FE3" xml:space="preserve">Et ad ꝓbationē dices /  argumen-<lb/>tū illud nõ ꝓbat qñ maiꝰ diminuit̄̄ et minꝰ auget̄̄: vt <lb/>in diminutione ſextipedalis et augmentatione qua­<lb/>drupedalis. </s>
              <s xml:id="N20FEC" xml:space="preserve">Cū em̄ ſextipedale deperdit duo peda­<lb/>lia, et illa acq̇rat q̈drupedale in eodē tꝑe, manifeſtū <lb/>eſt /  ita velociter diminuitur ſextipedale ſicut au-<lb/>getur quadrupedale et eque ꝓportiõabiliter: quia <lb/>ſextipedale deꝑdit ꝓportionē ſexquialterã et qua­<lb/>drupedale acquirit tantam vt notum eſt.</s>
            </p>
            <div xml:id="N20FF9" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0174-02a" xlink:label="note-0174-02" xml:id="N20FFD" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N21003">
              <s xml:id="N21004" xml:space="preserve">Sed cõtra / q2 ſaltē habeo /  duo poſi-<lb/>tiua nõ poſſunt ita ſe hēre. </s>
              <s xml:id="N21009" xml:space="preserve"> cõtinuo equevelociter <lb/>et eque ꝓportionabiliter ſicut vnū auget̄̄ ita alteꝝ <lb/>diminuatur. </s>
              <s xml:id="N21010" xml:space="preserve">Sed cõtinuo equevelociter et eq̄ ꝓpor­               <pb chead="Tertii tractatus" file="0175" n="175"/>               tionabiliter ſicut raritas augetur ita et dēſitas di­<lb/>minuit̄̄ / g̊ raritas et denſitas nõ ſunt poſitiua. </s>
              <s xml:id="N2101A" xml:space="preserve">Con­<lb/>ſequētia eſt nota cū minori, et argr̄ maior / q2 ſi illḋ <lb/>eſſet poſſibile de aliquibꝰ poſitiuis: hoc maxīe eſſet <lb/>qñ maiꝰ diminuit̄̄ et minꝰ auget̄̄ ſicut dictū eſt in ſo-<lb/>lutione: ſed hoc nõ: igr̄. </s>
              <s xml:id="N21025" xml:space="preserve">Probat̄̄ minor / q2 vel illud <lb/>minꝰ qḋ augetur ſemꝑ in augmentatione manebit <lb/>minꝰ altero, vel aliqñ deueniet ad equalitatē: ſi cõ-<lb/>tinuo illud qḋ augetur erit minꝰ illo qḋ diminuitur <lb/>et ita velociter diminuit̄̄ maiꝰ ſicut augetur minus <lb/>ſequit̄̄ /  cõtinuo in toto illo tꝑe in quo erit minus <lb/>ipſum velociꝰ ꝓportiõabiliter augebit̄̄ ꝙ̄ aliud di-<lb/>minuitur volo dicere in quolibet inſtãti intrinſeco <lb/>illiꝰ tēporis: ptꝫ hec ↄ̨ña regulã geometricã. </s>
              <s xml:id="N21038" xml:space="preserve">Qñcū­<lb/> aliqua latitudo demit̄̄ a maiori et addit̄̄ minori <lb/>ipſo manēte minori ꝙ̄ illud ad quo demit̄̄ illa latitu­<lb/>do cõtinuo maiorē ꝓportionē acquirit illud minꝰ <lb/>̄ deꝑdat illud maiꝰ. </s>
              <s xml:id="N21043" xml:space="preserve">Quod ptꝫ / q2 ſi poſt̄ illa la­<lb/>titudo eſt addita minori addat̄̄ tanta latitudo illi <lb/>maiori a quo fuit dēpta, minorē ꝓportionē acq̇ret <lb/>illud maiꝰ ꝙ̄ deꝑdet illud minꝰ: g̊ qñ maius deꝑdat <lb/>illã latitudinē et minꝰ acq̇rit eandē maiorē ꝓporti-<lb/>onē acq̇rit minꝰ ꝙ̄ deꝑdat maiꝰ, cū nõ deꝑdat niſi <lb/>illã quã acq̇ſiuit: igr̄ illa regula eſt vera. </s>
              <s xml:id="N21052" xml:space="preserve">Si aūt illa <lb/>ꝑueniant ad equalitatē, iã nõ eque velociter et eque <lb/>ꝓbationabiliter vnū illoꝝ augebitur ſicut aliud di­<lb/>minuitur / vt ꝓbatū eſt in argumento               <anchor type="note" xlink:href="note-0175-01" xlink:label="note-0175-01a"/>               </s>
              <s xml:id="N21060" xml:space="preserve">¶ Cõfirmatur <lb/></s>
              <s xml:id="N21064" xml:space="preserve">Quia raritas et denſitas inter ſe nõ differūt cū idē <lb/>ſit ꝓpinquitas punctoꝝ et diſtantia eorūdē: igr̄ ille <lb/>nõ ſunt qualitates poſitiue.               <anchor type="note" xlink:href="note-0175-02" xlink:label="note-0175-02a"/>               </s>
              <s xml:id="N21070" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo. </s>
              <s xml:id="N21073" xml:space="preserve">Q2 <lb/>ſi eſſent qualitates eſſent cõtrarie: ſed hoc eſt falſū / <lb/>q2 tūc nullū rarū eſſet denſum et eocõtra et aliquid <lb/>eſſet qḋ nõ eſſet rarū ne dēſum : q2 rarū et denſum <lb/>eſſent termini cõtrarii.               <anchor type="note" xlink:href="note-0175-03" xlink:label="note-0175-03a"/>               </s>
              <s xml:id="N21083" xml:space="preserve">¶ Cõfirmatur tertio. </s>
              <s xml:id="N21086" xml:space="preserve">Quia <lb/>tūc ſeq̇tur /  poſſibile eſt dare rarū vniformiter dif­<lb/>forme a certo gradu vſ ad nõ gradū, vt ab octa-<lb/>uo vſ ad nõ gradū: ſed ↄ̨ñs eſt falſū: g̊ et illud ex q̊ <lb/>ſeq̇tur. </s>
              <s xml:id="N21091" xml:space="preserve">Cõſequētia ꝓbatur: q2 oīs qualitas corpo-<lb/>rea poteſt eſſe vniformiter difformis a certo gradu <lb/>vſ ad nõ gradū: ſed raritas eſt huiuſmodi per te <lb/>igr̄. </s>
              <s xml:id="N2109A" xml:space="preserve">Maior ptꝫ / q2 vbicū eſt qualitas vniformis: <lb/>ibi eſt vna medietas intenſiua vniformiter diffor-<lb/>mis a maximo gradu quē hꝫ illa qualitas vſ ad <lb/>nõ gradū: vt ptꝫ iutuenti. </s>
              <s xml:id="N210A3" xml:space="preserve">Sed iam argr̄ falſitas cõ­<lb/>ſequentis / q2 ſit illud a. / et arguo ſic / illud eſt vniformi­<lb/>ter difformiter rarū ab octauo vſ ad nõ gradū: g̊ <lb/>prima pars ꝓportionalis eiꝰ eſt aliqualiter rara et <lb/>ſcḋa in duplo minꝰ rara, et tertia in duplo minꝰ ra-<lb/>ra ꝙ̄ ſcḋa, et ſic ↄ̨ñter / vt ptꝫ de albedine vniformiter <lb/>difformi ab octauo vſ ad nõ g̈dū, et ꝑ ↄ̨ñs ṗma ꝑs <lb/>ꝓportiõalis eſt aliq̈liṫ denſa, et ſcḋa in duplo den­<lb/>ſior, et tertia in duplo denſior ꝙ̄ ſcḋa. etc̈. / igr̄ a. eſt <lb/>infinite denſū q2 infinitã materiã cõtinet ſub finita <lb/>quãtitate, nã q̄libet pars ꝓportionalis cõtinet tan­<lb/>tam materiã ſicut prima: q2 in quacū ꝓportione <lb/>aliqua pars ꝓportiõalis eſt minor prima in eadē <lb/>eſt denſior prima, et vltra a. eſt īfinite denſum: g̊ nõ <lb/>eſt rarū, et ſic nõ eſt vniformiter difformiter rarum / <lb/>quod eſt oppoſitū cõceſſi.               <anchor type="note" xlink:href="note-0175-04" xlink:label="note-0175-04a"/>               </s>
              <s xml:id="N210C9" xml:space="preserve">¶ Cõfirmatur quarto / q2 <lb/>rarū eſt qḋ ſub magna quãtitate cõtinet parum de <lb/>materia, denſum vero eſt /  ſub parua quãtitate cõ­<lb/>tinet multū de materia: et hoc deſcribendo rarū et <lb/>denſum: g̊ dato  a. nullã qualititatē haberet et ſub <lb/>finita quantitate finitam materiam contineret ad <lb/>huc illud eſſet rarum et denſum, vt facile deducitur <lb/>ex deſcriptione rari et denſi: igitur raritas et den-<lb/>ſitas nõ ſunt qualitates nec poſitiue ſe habent.</s>
            </p>
            <div xml:id="N210DC" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0175-01a" xlink:label="note-0175-01" xml:id="N210E0" xml:space="preserve">1. confir-<lb/>matio</note>
              <note position="left" xlink:href="note-0175-02a" xlink:label="note-0175-02" xml:id="N210E8" xml:space="preserve">2. confir-<lb/>matio</note>
              <note position="left" xlink:href="note-0175-03a" xlink:label="note-0175-03" xml:id="N210F0" xml:space="preserve">3. confir-<lb/>matio</note>
              <note position="left" xlink:href="note-0175-04a" xlink:label="note-0175-04" xml:id="N210F8" xml:space="preserve">4. confir­<lb/>matio.</note>
            </div>
            <p xml:id="N21100">
              <s xml:id="N21101" xml:space="preserve">Scḋo prīcipaliter. </s>
              <s xml:id="N21104" xml:space="preserve">Tangēdo penes <lb/>quid maioritas raritatis et dēſitatis attēdat̄̄ argr̄               <cb chead="Capitulū primū."/>               ſic. </s>
              <s xml:id="N2110C" xml:space="preserve">Si raritas et denſitas eſſent poſſibiles vel ī qua­<lb/>cun ꝓportione raritas efficitur maior: ꝓportio <lb/>quãtitatis ad materiã efficiret̄̄ maior, et nõ quãti-<lb/>tas in illa ꝓportione, vel in quacū ꝓportione ra­<lb/>ritas efficit̄̄ maior: quãtitas efficit̄̄ maior. </s>
              <s xml:id="N21117" xml:space="preserve">Sed neu­<lb/>trū iſtoꝝ eſt dicendū: igr̄ raritas et denſitas nõ ſūt <lb/>poſſibiles. </s>
              <s xml:id="N2111E" xml:space="preserve">Minor ptꝫ / q2 iſte due ſunt famate opi-<lb/>niones quas maior tangit de maioritate et minori­<lb/>tate raritatis et nõ plures ꝓ nūc practicantur. </s>
              <s xml:id="N21125" xml:space="preserve">Sed <lb/>iam ꝓbatur minor: et primo  nõ in quacū ꝓpor­<lb/>tione raritas efficitur maior proportio quãtitatis <lb/>ad materiã efficitur maior: q2 tūc ſeq̄retur /  ad du­<lb/>plationē raritatis nõ ſeq̄retur duplatio quãtita-<lb/>tis q2 aliqñ ſequitur magis ꝙ̄ duplatio quantita-<lb/>tes, et aliqñ minꝰ, et aliqñ adequata duplatio: igr̄. <lb/></s>
              <s xml:id="N21135" xml:space="preserve">ſed ↄ̨ñs eſt falſū: igr̄. </s>
              <s xml:id="N21138" xml:space="preserve">Falſitas ↄ̨ñtis argr̄ / q2 rarum <lb/>eſt qḋ ſub magna quãtitate cõtinet modicū de ma-<lb/>teria, ergo illud erit in duplo magis rarum quod <lb/>ſubdupla maiori quantitate ↄ̨tinet equale de ma-<lb/>teria, et ſic ſemꝑ ad duplationē raritatis ſequitur <lb/>duplatio quãtitatꝪ. </s>
              <s xml:id="N21145" xml:space="preserve">Sed iam ꝓbo ſequelã: et capio <lb/>vnū pedale cuiꝰ quãtitatis ad materiã ſit ꝓportio <lb/>ſexq̇altera et volo /  dupletur eiꝰ raritas quo po-<lb/>ſito argr̄ ſic / quãtitas illiꝰ pedalis nõ efficitur in du­<lb/>plo maior: ſed p̄ciſe in ſexq̇altero maior: igr̄ ꝓpoſi­<lb/>tum. </s>
              <s xml:id="N21152" xml:space="preserve">Probat̄̄ añs, q2 in fine ꝓportio quantitatis <lb/>ad materiã erit dupla ad ſexquialterã puta dupla <lb/>ſexquiq̈rta: g̊ ſeq̇tur,  p̄ciſe quãtitas acq̇ſiuit pro­<lb/>portionē ſexq̇alterã et nõ duplã. </s>
              <s xml:id="N2115B" xml:space="preserve">Ptꝫ ↄ̨ña / q2 ꝓpor-<lb/>tio quãtitatis ad materiã in fine cõponitur ex dua­<lb/>bus ſexq̇alteris: et iã quãtitas ad materiã habebat <lb/>ꝓportionē ſexquialterã: g̊ modo p̄ciſe acq̇ſiuit ſexq̇al­<lb/>terã ſupra ſe. </s>
              <s xml:id="N21166" xml:space="preserve">Probat̄̄ ſcḋa / q2 ſi acq̇ſiuiſſet duplaꝫ <lb/>ꝓportionē ſupra ſe in fine ꝓportio quantitatis ad <lb/>materiã fuiſſet tripla q̄ ex dupla et ſexq̇altera cõpo­<lb/>nitur et ſic nõ ad duplationē raritatis fuiſſet ſequu­<lb/>ta duplatio ꝓportionis cū tripla ſit maior ꝙ̄ du-<lb/>pla ad ſexq̇alterã / vt pꝫ ex ſecūda parte huiꝰ operꝪ <lb/>et ſic ſeq̇tur /  ad duplationē raritatis aliqñ ſeq̇tur <lb/>minꝰ ꝙ̄ duplatio quãtitatis. </s>
              <s xml:id="N21177" xml:space="preserve">Q, vero aliqñ <lb/>ſeq̈tur p̄ciſe duplatio quãtitatis ꝓbatur ponendo <lb/> ꝓportio quãtitatis ad materiã ſit dupla, et  du­<lb/>pletur raritas, et ſic habebitur intentū. </s>
              <s xml:id="N21180" xml:space="preserve">Nã tūc ꝓ-<lb/>portio quãtitatis ad materiã efficeretur quadru-<lb/>pla q̄ eſt dupla ad duplã, et iã antea ꝓportio ̄tita­<lb/>tis ad materiã fuit dupla adequate: g̊ modo acq̇ſi-<lb/>uit aliquã ꝓportionē duplã, et ſic ſeq̇tur /  quãtitas <lb/>acq̇ſiuit duplã ꝓportionē ſupra ſe: qm̄ tantã acq̇ſi-<lb/>uit ſupra ſe quantam ſupra ſuam materiam. </s>
              <s xml:id="N2118F" xml:space="preserve">Sed <lb/>iam ꝓbo /  nõ in quacū ꝓportione raritas effici­<lb/>tur maior quãtitas efficitur maior: q2 alias ſeq̄ret̄̄ / <lb/> poſſet dari infinite rarū: ſed ↄ̨ñs eſt falſum: igr̄ et <lb/>illud ex quo ſeq̇tur. </s>
              <s xml:id="N2119A" xml:space="preserve">Seq̄la ꝓbatur et capio vnū pe-<lb/>dale vniforme ꝑ totū et volo /  rarefiat in īfinitum <lb/>quo poſito illud erit īfinite raꝝ qm̄ ad duplationē <lb/>eiꝰ ſeq̇tur duplatio raritatis et ad triplationē quã­<lb/>tatis ſeq̇tur triplatio raritatis / et ſic cõſequenter: <lb/>et acquiret̄̄ quãtitas īfinita: g̊ raritas īfinita. </s>
              <s xml:id="N211A7" xml:space="preserve">Sed <lb/>falſitas ↄ̨ñtis argr̄ et ſi illud eſt infinite rarū: ſequit̄̄ / <lb/> nullã materiã cõtinet, et vltra nullã materiã cõti­<lb/>net. </s>
              <s xml:id="N211B0" xml:space="preserve">g̊ nec eſt rarū nec eſt dēſum. </s>
              <s xml:id="N211B3" xml:space="preserve">Conſequētia ptꝫ et <lb/>argr̄ ſeq̄la qm̄ vt ſuppono ipſum eſt vniforme, et <lb/>vniformiter rarefactū: ſi igr̄ hꝫ aliquã materiaꝫ in <lb/>aliqua parte ſui cū ipſum ſit vniforme: ſeq̇tur /  in <lb/>qualibet tanta ſui parte hꝫ tantaꝫ ſicut ipſa eſt: et <lb/>ſunt infinite partes illi parti equales: g̊ ſeq̇tur /  <lb/>hꝫ īfinitã materiã, et ſic eſt īfinite raꝝ / qḋ fuit ꝓbandū</s>
            </p>
            <pb chead="De motu rarefactionis et condenſationis." file="0176" n="176"/>
            <p xml:id="N211C6">
              <s xml:id="N211C7" xml:space="preserve">Tertio prīcipaliṫ arguit̄̄ ſic. </s>
              <s xml:id="N211CA" xml:space="preserve">Si rari-<lb/>tas et denſitas eſt poſſibilis: vel per ipſam rarefa-<lb/>ctionem acquireretur ſubſtantia: vel quantitas ſed <lb/>neutrum iſtorū eſt dicendum: igitur non primum / q2 <lb/>rarefactio non ponitur motus ad ſubſtantiã: quia <lb/>tunc eſſet generatio: nec ſecundem quia tunc ſequi-<lb/>tur penetratio dimenſionum naturaliter quod eſt ī­<lb/>poſſibile. </s>
              <s xml:id="N211DB" xml:space="preserve">Sequela ꝓbatur: et poſito  aliquid pu-<lb/>ta pedale rarefiat per totum vniformiter per vnam <lb/>horam quouſ ſit bipedale et arguitur ſic in quo-<lb/>libet inſtanti intrinſeco talis rarefactionis illḋ pe­<lb/>dale habet per totum aliam et aliam quantitatem <lb/>per te et quelibet pars eius rarefit: et non corrumpi-<lb/>tur quantitas prehabita. </s>
              <s xml:id="N211EA" xml:space="preserve">igitur manet cum illa eã <lb/>penetrando. </s>
              <s xml:id="N211EF" xml:space="preserve">Conſequentia non eſt dubia: et maior <lb/>arguitur. </s>
              <s xml:id="N211F4" xml:space="preserve">quia in quolibet inſtanti intrinſeco illud <lb/>eſt magis rarum ꝙ̄ in inſtanti precedenti: igitur in <lb/>quolibet tali eſt maior quantitas acquiſita ꝙ̄ in p̄-<lb/>cendenti. </s>
              <s xml:id="N211FD" xml:space="preserve">et ſic in quolibet habet aliam et aliam quan­<lb/>titatem /  fuit probandum. </s>
              <s xml:id="N21202" xml:space="preserve">Sed iam probatur mi-<lb/>nor: quia quantitatis precedens non habet contra-<lb/>rium. </s>
              <s xml:id="N21209" xml:space="preserve">igitur non corrumpitur: nam ſi corrumpere-<lb/>tur maxime eſſet a contratio: aut a deſitione ſubie-<lb/>cti aut ab abſentia conſeruantis ſed nullo iſtorum <lb/>modorum poteſt corrumpi: cum non poſſit a contra­<lb/>rio: nec a deſitione ſubiecti nec ab abſentia conſer-<lb/>uantis. </s>
              <s xml:id="N21216" xml:space="preserve">cum nec habet contrarium nec ſubiectuꝫ de­<lb/>ſinat nec ab aliquo dependet in ↄ̨ſeruando ꝙ̄ a ſub­<lb/>iecto               <anchor type="note" xlink:href="note-0176-01" xlink:label="note-0176-01a"/>               </s>
              <s xml:id="N21222" xml:space="preserve">Nec valet dicere vt innuit Marſilus  quan­<lb/>titas ſequens non manet cuꝫ precedente ymmo cor­<lb/>rumpitur maiori adueniente quantitate: quia (vt ī­<lb/>quit) quantitas maior minori contrariatur: tū pri­<lb/>mo quia quantitates contrariari eſt ↄ̨tra oēm mo­<lb/>dum opinãdi phõphoꝝ: et ſignanter phī oppoſituꝫ <lb/>aſſerentis: </s>
              <s xml:id="N21231" xml:space="preserve">Tum ſecundo quia tunc pars contraria­<lb/>tur toti. </s>
              <s xml:id="N21236" xml:space="preserve">Nam per eum omnis quantitatis pedalis cõ­<lb/>trariatur ſemipedali: mõ ſemipedalis quantitas ē <lb/>pars pedalis quãtitatis: </s>
              <s xml:id="N2123D" xml:space="preserve">Tum tertio / quia ſequere­<lb/>tur in quacun rarefactione infinitas quantitates to­<lb/>tales corrūpi: et infinitas tales generari: ſꝫ hoc eſt <lb/>falſum / igr̄ et illud ex quo ſequit̄̄. </s>
              <s xml:id="N21246" xml:space="preserve">falſitas ↄ̨ñtis ꝓba­<lb/>tur / quia nulla virtus finita poteſt infinita totalia <lb/>gignere aut corrumpre: </s>
              <s xml:id="N2124D" xml:space="preserve">Sequela tamen ꝓbatur / <lb/>q2 in quolibet inſtanti per eum eſt noua qualitas ī <lb/>toto: et ſunt infinita inſtantia in quãtulocū tꝑe ra­<lb/>refactonis: ergo ſunt īfinite quantitates noue to-<lb/>tales / et ꝑ ↄ̨ñs īfinite corrupte: cū in quolibet inſtan­<lb/>ti ītrīſeco incipiat eſſe aliqua quantitas per primū <lb/>eſſe et eãdē quãtitas in eodē deſinat eſſe per vltimū <lb/>eē et hec eſt eadem ymaginatio oīno ſic ymaginatio <lb/>burlei de intenſione formarū.               <anchor type="note" xlink:href="note-0176-02" xlink:label="note-0176-02a"/>               </s>
              <s xml:id="N21265" xml:space="preserve">Et ideo dices aliter <lb/>et bene cum doctore ſubtili  ꝑ rarefactionē nec ac­<lb/>q̇rit̄̄ ſubſtantia: nec quantitas: ſed rarefactio ē mu­<lb/>tatio localis adhūc ſenſū  ꝑ rarefactionē acq̇rit̄̄ <lb/>locꝰ maior̄ antea et ꝑ ↄ̨dēſationē deꝑdit̄̄ locꝰ: </s>
              <s xml:id="N21270" xml:space="preserve">Ita <lb/> cū aliq̇d rarefit ꝑtes eiꝰ magis diſtant ꝙ̄ antea ꝑ­<lb/>tes in̄ mediate: qm̄ īmediate ſꝑ īmediate manēt</s>
            </p>
            <div xml:id="N21277" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0176-01a" xlink:label="note-0176-01" xml:id="N2127B" xml:space="preserve">marſiliꝰ</note>
              <note position="left" xlink:href="note-0176-02a" xlink:label="note-0176-02" xml:id="N21281" xml:space="preserve">Dicitur.</note>
            </div>
            <note position="left" xml:id="N21287" xml:space="preserve">Scotus.</note>
            <p xml:id="N2128B">
              <s xml:id="N2128C" xml:space="preserve">Cõtra </s>
              <s xml:id="N2128F" xml:space="preserve">Q2 ſi ī rarcfactiõe dūtaxat acq̇­<lb/>reret̄̄ maior locꝰ ſeq̇ret̄̄ in oī rarefactione oīa natu-<lb/>ralia rarefieri vel penetrationē dimenſionū eē: ſed <lb/>vtrū iſtoꝝ naturaliter eſt impoſſibile. </s>
              <s xml:id="N21298" xml:space="preserve">igr̄ rarefa-<lb/>ctio ēt iſto mõ eſt naturaliter īpoſſibilis. </s>
              <s xml:id="N2129D" xml:space="preserve">Seq̄la ꝓ-<lb/>bat̄̄ et ponat̄̄ vnū pedale rarefieri q̊uſ ſit bipedale: <lb/>et acq̇rat locū pedalē loco p̄habito: in q̊ locu pedali <lb/>erat pedale aeris qḋ pedale aeris vocet̄̄ a. et arguit̄̄ <lb/>vel a. manet adhuc cū corpore rarefacto in eodē lo-<lb/>cõ vel non: ſi ſic habeo intentū vcꝫ  cū aliq̇d rare-               <cb chead="De motu rarefactionis et condenſationis."/>               fit ē penetratio dimenſionū. </s>
              <s xml:id="N212AD" xml:space="preserve">Si nõ manet ſed expel­<lb/>lebat̄̄ ad aliū locū pedalē / tunc ſeq̇tur /  corpus exi-<lb/>ſtens in iſto alio loco pedali pellebat̄̄ ad aliū locū: <lb/>et exiſtens in illo ad aliū locū et cū nõ ſit ꝓceſſus ī in­<lb/>finitū in illis pedalibꝰ antea ꝙ̄ deueniat̄̄ ad celū ſe-<lb/>quitur /  etiã celū pellebat̄̄. </s>
              <s xml:id="N212BA" xml:space="preserve">et in tali mutatione lo-<lb/>cali ſꝑ fiebat rarefactio: cum motus ſit cauſa rare-<lb/>factiõis: igr̄ data vna rarefactione oīa alia rarefi-<lb/>unt. </s>
              <s xml:id="N212C3" xml:space="preserve">vel ſaltē mutant̄̄ localiter / quod fuit ꝓbandum <lb/>nõ em̄ maius incõueniens eſt  oīa rarefiãt ꝙ̄  om­<lb/>nia mutant locū: cū vnū rarefit               <anchor type="note" xlink:href="note-0176-03" xlink:label="note-0176-03a"/>               </s>
              <s xml:id="N212CF" xml:space="preserve">Nec oportet dicere / <lb/> cū aliq̇d rarefit aliq̇d denſat̄̄ et eo cõtra vt inquit <lb/>hentiſber in illo ſophiſmate neceſſe eſt aliq̇d ↄ̨dēſa­<lb/>ri cū aliq̇d rarefit q2 cū rarefactio et condenſatio ſi <lb/>fiant a diuerſis cauſis et cõtrariis puta condenſa-<lb/>tio a frigiditate et rarefactio a caliditate / vt patet <lb/>ex quarto metheororū vel ab aliis cauſis ↄ̨trariis: <lb/>volo /  in loco vbi fit rarefactio nulla penitꝰ ſit fri-<lb/>giditas aut aliqua cauſa condenſans quo poſito <lb/>nulla fiet condenſatio propter deffectum cauſe con­<lb/>denſantis et tunc fiet rarefactio: igitur rarefactio <lb/>poſſiblis eſt ſint condenſatione. </s>
              <s xml:id="N212E8" xml:space="preserve">Nec valet dice-<lb/>re  ̄uis non ſit cauſa ſufficiens condenſationis <lb/>in loco vbi fit rarefactio nichilominus alibi eſt ta-<lb/>lis cauſa et ibi ordine nature fiet cõdenſatio: q2 tunc <lb/>ſequeretur /  oportet omnia corpora intermedia ī­<lb/>ter locum rarefactionis et condenſationis mutari / <lb/>quod tamen eſt falſum: </s>
              <s xml:id="N212F7" xml:space="preserve">Sequela patet / q2 alias ī lo­<lb/>co rarefactionis daretur penetratio dimenſionum <lb/>et in loco condenſationis daretur vacuum / vt patet <lb/>inſpicienti.</s>
            </p>
            <div xml:id="N21300" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0176-03a" xlink:label="note-0176-03" xml:id="N21304" xml:space="preserve">hētiſber. <lb/>phūs .4, <lb/>metheo.</note>
            </div>
            <p xml:id="N2130E">
              <s xml:id="N2130F" xml:space="preserve">Quarto arguitur ſic </s>
              <s xml:id="N21312" xml:space="preserve">Si rarefactio et <lb/>condenſatio eſſent poſſibiles ſequeretur /  rarū vni­<lb/>formiter difforme vĺ difformiter difforme cuiꝰ vtra­<lb/> medietas eſt vniformis correſponderet gradui <lb/>medio: ſed couſequens eſt falſum / ergo et añs. </s>
              <s xml:id="N2131D" xml:space="preserve">Seq̄-<lb/>la patet et falſitas conſequentis arguitur: et capio <lb/>vnum pedale cuius vna medietas ſit rara vt octo et <lb/>alia vt quatuor. </s>
              <s xml:id="N21326" xml:space="preserve">et arguitur ſic. </s>
              <s xml:id="N21329" xml:space="preserve">Si raritas illius pe­<lb/>dalis correſponderet ſuo gradui medio ſequeretur / <lb/> illud pedale poſſet ad vniformitatem reduci: ita <lb/> continuo correſpoudret tali gradui medio me-<lb/>dietate intenſiore continuo tantum perdente ̄tum <lb/>alia acquirit. </s>
              <s xml:id="N21336" xml:space="preserve">ſed conſequens eſt falſum. </s>
              <s xml:id="N21339" xml:space="preserve">igitur et an­<lb/>tecedens: falſitas conſequentis probatur et volo /  <lb/>medietas rara vt octo perdat vnum gradum rari-<lb/>tatis: et tãtum acquirat medietas minus rara quo <lb/>poſito ſic argumentor tale pedale rarefit et tamen <lb/>tantū acquirit raritatis medietas minus rara quã­<lb/>tū deperdit medietas magis rara. </s>
              <s xml:id="N21348" xml:space="preserve">igitur nõ poteſt <lb/>reduci ad vniformitatē ipſo cõtinuo manente eque <lb/>raro. </s>
              <s xml:id="N2134F" xml:space="preserve">Conſequentia patet cum maiore et arguitur <lb/>minor: q2 quando medietas rarior que eſt vt octo <lb/>perdit vnum gradum raritatis: ipſa efficitur in ſex­<lb/>quiſeptimo minus rara et ſic perdit vnam octauaꝫ <lb/>ſui que eſt vna ſexdecima pedalis: et medietas mi-<lb/>nus rara acquirit vnum gradum raritatis et habe­<lb/>bat quatuor: ergo efficitur in ſexquiquarto rarior. <lb/></s>
              <s xml:id="N2135F" xml:space="preserve">et ſic efficitur in ſexquiquarto maior: et per conſe-<lb/>quens acquiſiuit vnam quartam ſui: et illa quarta <lb/>eſt vna octaua pedalis: igitur maiorem quantita-<lb/>tem acquiſiuit totale pedale ꝙ̄ deperdit, cnm acqui­<lb/>ſiuit octauam et deperdit ſexdecimam dumtaxat) <lb/>nec acquiſiuit materiam aliquam, nec deperdit. <lb/></s>
              <s xml:id="N2136D" xml:space="preserve">igitur ipſum pedale efficitur rarius ꝙ̄ antea: et per <lb/>conſequens non poteſt illo modo ad vniformita-<lb/>tē reduci ipſo ↄ̨tinuo manente eq̄ raro: et eq̄ denſo. <lb/></s>
              <s xml:id="N21375" xml:space="preserve">¶ Dices forte ↄ̨cedēdo /  nõ eſt poſſibile tale rarum               <pb chead="Tertii tractatus" file="0177" n="177"/>               ad vniformitatē reduci medietate rariori tãtum de­<lb/>perdente quantū minus rara medietas acquirit ip­<lb/>ſo difformi manēte cõtinuo ſub eodē gradu rarita­<lb/>tis: ſed bene p̄t fieri  reducat̄̄ ad vniformitatē ſub <lb/>eodē gradu ſub quo eſt puta ſub gradu medio in to­<lb/>to tꝑe: ̄uis in tp̄e medio ſit magis raruꝫ. </s>
              <s xml:id="N21387" xml:space="preserve">hoc eſt in <lb/>quolibet inſtanti intrīſeco. </s>
              <s xml:id="N2138C" xml:space="preserve">Uolo dicere /  poſt̄ <lb/>pars minꝰ rara acq̇ſiuerit medietatē exeſſꝰ ꝑ queꝫ <lb/>medietas magis rara excedit eã tunc totum mane-<lb/>bit eq̄ rarum ſicut erat in principio qñ erat difformi-<lb/>ter difforme cuiꝰ vtra medietas erat vniformis.</s>
            </p>
            <p xml:id="N21397">
              <s xml:id="N21398" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
              <s xml:id="N2139B" xml:space="preserve">Q2 volo /  in hora illa medie­<lb/>tas q̄ eſt vt octo deꝑdat duos gradꝰ et tm̄ acq̇rat me­<lb/>dietas minus rara puta vt quatuor quo poſito in fi­<lb/>ne pars minꝰ rara acq̇ſiuit medietatē exeeſſus per <lb/>quē exceſſū pars magis rara excedebat eã: et totum <lb/>manet vniforme ſub gradu medio inter octauum et <lb/>quartū q̇ ē vt ſex et tūc totale corpꝰ eſt rarius ꝙ̄ erat <lb/>in principio qñ erat difformiter difforme cuiꝰ vtra­<lb/> medietas eſt vniformis. </s>
              <s xml:id="N213AE" xml:space="preserve">igr̄ antea erat minus ra­<lb/>rū ꝙ̄ vt ſex. / et ꝑ ↄ̨ñs ſolutio nulla: </s>
              <s xml:id="N213B3" xml:space="preserve">Coña pꝫ cū maio-<lb/>re: et argr̄ minor v3  tale corpꝰ rarefit. </s>
              <s xml:id="N213B8" xml:space="preserve">q2 in fine ē <lb/>maius ꝙ̄ erat antea et nullã materiã acq̇ſiuit: igr̄ ra­<lb/>refit: </s>
              <s xml:id="N213BF" xml:space="preserve">Argr̄ maior / q2 medietas eiꝰ puta rarior effe-<lb/>cta eſt in ꝓportione ſexq̇tertia minus rara: et ꝑ ↄ̨ñs <lb/>in eadē ꝓportione minor: et ſic ip̄a deꝑdit vnã quar­<lb/>tã ſui q̄ ē vna octaua pedalis: medietas vero minꝰ <lb/>rara effecta eſt in ſexq̇altero rarior / vt pꝫ ex caſu igr̄ <lb/>effecta ē ī ſexquialtero maior: et ſic ipſa acq̇ſiuit medie­<lb/>tatē ſui ſupra ſe q̄ medietas eiꝰ eſt vna quarta peda­<lb/>lis: igr̄ totū illud corpꝰ in duplo maiorē quãtitatē <lb/>acq̇ſiuit ꝙ̄ deꝑdit: igr̄ eſt maiꝰ: qḋ fuit probandum. <lb/>               <anchor type="note" xlink:href="note-0177-01" xlink:label="note-0177-01a"/>               </s>
              <s xml:id="N213D9" xml:space="preserve">¶ Dices forte et bene /  nõ p̄t ſic / rarū vniformiṫ dif­<lb/>forme cuiꝰ vtra medietas eſt vniformis ad vnifor­<lb/>mitatē reduci:               <anchor type="note" xlink:href="note-0177-02" xlink:label="note-0177-02a"/>               ſed ſubtiliter dicit ſuiſeth calcula­<lb/>tor ad reducendū raritatē ad vniformitatē oportet <lb/>reducere denſitatem: ſicut ad reducendã remiſſiõeꝫ <lb/>oportet reducere intenſionē: q2 oē vniformiter den­<lb/>ſū ē vniformiter rarū: et ſic ſi dēſitas eſt vniformita­<lb/>ti reſtituta etiam raritas.</s>
            </p>
            <div xml:id="N213EF" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0177-01a" xlink:label="note-0177-01" xml:id="N213F3" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0177-02a" xlink:label="note-0177-02" xml:id="N213F9" xml:space="preserve">calcula. <lb/>ſuiſeth.</note>
            </div>
            <p xml:id="N21401">
              <s xml:id="N21402" xml:space="preserve">Sꝫ ↄ̨̨tra / q2 tūc ſeq̇ret̄̄ /  denſum vni-<lb/>formiter difforme cuius vna medietas eſt dēſa vni-<lb/>formiter vt octo et alia medietas vt quatuor poſſet <lb/>reduci ad vniformitatem medietate denſiori tãtum <lb/>perdente adequate quantum medietas minus dē-<lb/>ſa acquirit: ipſo corpore contino manente eque <lb/>denſo: ſed conſequens ē falſum / igitur illud ex quo <lb/>ſequitur </s>
              <s xml:id="N21413" xml:space="preserve">Falſitas cõſequenis probatur et pono /  <lb/>medietas vnius pedalis ſit denſa vt octo: et alia vt <lb/>quatuor; et ī vna medietate hore deꝑdat medietas <lb/>denſior vnum gradum denſitatis et tantum acqui-<lb/>rat medietas minus denſa. </s>
              <s xml:id="N2141E" xml:space="preserve">Quo poſito ſic arguo <lb/>totale corpus in illa media hora cõdenſatur: ergo <lb/>ſequitur /  non valet ſic ad vniformitatem reduci ꝑ <lb/>te minus denſa tantum acquirente quantuꝫ magis <lb/>denſa deperdit: continuo ipſo manente eque den-<lb/>ſo. </s>
              <s xml:id="N2142B" xml:space="preserve">Conſequentia patet: et arguitur antecedens / q2 <lb/>ipſum efficitur minus quã antea et nullã materiam <lb/>deperdit: ergo ſequitur /  cõdenſatur: </s>
              <s xml:id="N21432" xml:space="preserve">Patet cõſe-<lb/>quentia cum minore et arguitur maior videlicet  <lb/>efficitur minus: q2 medietas denſior perdit vnum <lb/>gradum denſitatis: et ſic efficitur in ſexquiſeptimo <lb/>minus denſa: igitur in ſexquiſeptimo magis rara. <lb/></s>
              <s xml:id="N2143E" xml:space="preserve">et maior et per ↄ̨ñs acq̇rit vnã ſeptimam ſui que eſt <lb/>quatuor decīa vnius pedalis: alia vero pars vel me­<lb/>dietas que eſt denſa vt quatuor acquirit vnuꝫ gra-<lb/>dum denſitatis. </s>
              <s xml:id="N21447" xml:space="preserve">et ſic efficitur in ſexquiquarto den-<lb/>ſior et per ↄ̨ñs in ſexq̇quarto minor et ſic ꝑdit vnam               <cb chead="Capitulum primum"/>               quintã ſui q̄ eſt decima vniꝰ pedalis: igr̄ illud tota-<lb/>le corpus perdidit vnã decimã: et acq̇rit vnã quatuor <lb/>decimã ſui. </s>
              <s xml:id="N21453" xml:space="preserve">magis igr̄ deꝑdit ꝙ̄ acq̇rit et ex ↄ̨ñti effi­<lb/>citur minus ꝙ̄ erat antea  fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0177-03" xlink:label="note-0177-03a"/>               </s>
              <s xml:id="N2145D" xml:space="preserve">¶ Dices et <lb/>bñ /  argumentū bñ ꝓbat talia difformia in dēſitate <lb/>poſſe ſic ad vniformitatē reduci ip̄is manētibꝰ con-<lb/>tinuo ſub eodē gradu dēſitatꝪ: q2 neceſſe ē qñ ſic vna <lb/>medietas tm̄ acquirit quãtum: alia deperdit de dē­<lb/>ſitate: ipſa difformia per aliquod tempus condēſa­<lb/>ri: et ꝑdere quantitatē: ſed tunc per tempus ſequens <lb/>tantum rarefient ̄tum antea fuerunt condenſata, <lb/>et ſic in totali tempore ipſa nec rarefiunt nec condē­<lb/>ſantur vt ſi medietas vt octo in hora perdat duos <lb/>gradus adequate: et tantum medietas vt quatuor <lb/>adequate acquirat: tunc in fine quantū vna medie-<lb/>tas acquiſiuit tantum alia deperdit et manebit ade­<lb/>quate illud pedale in fine tante quantitatis quante <lb/>erat antea. </s>
              <s xml:id="N2147C" xml:space="preserve">Quod patet ſic /q2 illa medietas vt octo <lb/>perdit proportionem ſexquitertiam denſitatis: et <lb/>per conſequens ipſa efficitur in ſexquitertio maior / <lb/>igitur ipſa acquiſiuit vnam tertiam ſui que eſt vna <lb/>ſexta pedalis: altera vero medietas effecta eſt in ſex­<lb/>quialtero denſior: igitur in ſexquialtero minor: et ꝑ <lb/>conſequens ipſa deperdit vnam tertiam ſui que eſt <lb/>ſexta vnius pedalis: igitur quantū illud corpus ac­<lb/>quiſiuit de quantitate tãtum deperdit: et in fine ma­<lb/>nebit vniforme ſub gradu medio qui eſt ſextus: igr̄ <lb/>nunc illi gradui ſua denſitas correſpondet. </s>
              <s xml:id="N21493" xml:space="preserve">quod <lb/>fuit inducendum.</s>
            </p>
            <div xml:id="N21498" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0177-03a" xlink:label="note-0177-03" xml:id="N2149C" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N214A2">
              <s xml:id="N214A3" xml:space="preserve">Sed contra hanc ſolutionē arguitur <lb/>ſic / q2 tale pedale per totam illam horam rarefit: <lb/>igitur per nullam partem illius hore condenſatur <lb/>et etiam in fine manebit rarius ꝙ̄ antea: et ſic nõ ma­<lb/>nebit ita denſum ſicut antea: nec eidē gradui correſ­<lb/>pondebit et per conſequens ſolutio nulla. </s>
              <s xml:id="N214B0" xml:space="preserve">Arguitur <lb/>ãtecedēs / quia continuo in illa hora per maioreꝫ ꝑ­<lb/>tem erit deperditio denſitatis ꝙ̄ acquiſitio eiuſdē <lb/>eodē gradus / vt patet ex caſu: ergo illḋ pedale remit­<lb/>titur in denſitate et per conſequens ipſum rarefit ꝑ <lb/>totum illud tempus / quod fuit probandum. </s>
              <s xml:id="N214BD" xml:space="preserve">Antece­<lb/>dens patet / quia continuo pars que remittitur ī dē­<lb/>ſitate erit maior ꝙ̄ pars que intenditur in denſita-<lb/>te / vt patet intuenti. </s>
              <s xml:id="N214C6" xml:space="preserve">Conſequentia patet a ſimili / q2 <lb/>ſi continuo aliquod corpus per maiorem parteꝫ ac­<lb/>quirit albedinem ꝙ̄ nigredine eodem gradu ma-<lb/>nifeſtum eſt /  tale corpus remittitur in nigridine: <lb/>dato  ipſum antea fuerit nigrū vt facile eſt inſpi-<lb/>cere: igr̄ a ſimili ſi per maiorē partē ē remiſſio den­<lb/>ſitatis ꝙ̄ intenſio eiuſdem eodeꝫ gradu ſequitur to­<lb/>tum remitti in denſitate.               <anchor type="note" xlink:href="note-0177-04" xlink:label="note-0177-04a"/>               </s>
              <s xml:id="N214DC" xml:space="preserve">¶ Et confirmatur </s>
              <s xml:id="N214DF" xml:space="preserve">Q2 non <lb/>eſt dabile inſtans in toto illo tempore in quo tale <lb/>corpus incipit rarefieri poſt̄ condenſabatur: igi-<lb/>tur falſum eſt dicere  ſemper quando aliquod cor­<lb/>pus ſic ad vniformitatem denſitatis reducit̄̄  tp̄m <lb/>per aliquod tempus primo condenſatur et deiñ ꝑ <lb/>tempus ſequens rarefit acquirendo quantitatem <lb/>quam perdiderat </s>
              <s xml:id="N214F0" xml:space="preserve">Probatur antecedens / q2 maxīe <lb/>tale inſtans eſſet inſtans medium illius temporis <lb/>in quo videlicet medietas denſitatis deperdende a <lb/>medietate denſiori eſt deperdita et reliqua medie-<lb/>tas incipit deperdi: ſed hoc eſt falſum / igitur illḋ ex <lb/>quo ſequitur </s>
              <s xml:id="N214FD" xml:space="preserve">Sequela patet / q2 non videtur qḋ in-<lb/>ſtans ſit illud niſi fuerit medium inſtans. </s>
              <s xml:id="N21502" xml:space="preserve">Falſitas <lb/>tamen conſequentis arguitur: et capio vnum bipe-<lb/>dale cuius vna medietas ſit denſa vt duodecim et <lb/>alia vt dimidium: et volo /  per horam vniformiter <lb/>medietas denſior deperdat quin gradus cum tri­<lb/>bus quartis et tm̄ acq̇rat medietas minus dēſa ita <lb/> totum in fiue maneat vniforme. </s>
              <s xml:id="N21511" xml:space="preserve">et arguitur ſic               <pb chead="De motu rarefactionis et condenſationis." file="0178" n="178"/>               ante inſtans medium totius temporis. </s>
              <s xml:id="N21519" xml:space="preserve">incipiet tale <lb/>corpus rarefieri poſt̄ condēſabit̄̄: igitur inſtans <lb/>mediū illius temporis non eſt inſtans in quo tale <lb/>corpus incipit rarefieri poſt̄ antea condenſabat̄̄. <lb/></s>
              <s xml:id="N21523" xml:space="preserve">Conſequētia pꝫ et arguit̄̄ añs et volo /  illa medie-<lb/>tas denſior deperdat vniformiter duos gradꝰ den­<lb/>ſitatis et illos acq̇rat medietas minus denſa / et ma­<lb/>nifeſtum eſt /  medietas denſior efficitur in ſexqui­<lb/>quinto minus denſa et ſic acquirit ſupra ſe vnam <lb/>quintam pedalis: et alia medietas efficitur in quī-<lb/>tuplo denſior ꝙ̄ erat antea et ſic deꝑdit q̈tuor quin­<lb/>tas ſui et manet p̄ciſe vna quīta pedalis: volo dein­<lb/>de  medietas dēſior ꝑdat medietatem vnius gra-<lb/>dus et tm̄ acq̇rat medietas minꝰ denſa eq̄ velociter: <lb/></s>
              <s xml:id="N21539" xml:space="preserve">Et argr̄ ſic / in tꝑe illo in q̊ pars denſior deperdit me­<lb/>dietate vnius gradus et pars minꝰ denſa tm̄ acq̇rit <lb/>iã totū rarefit. </s>
              <s xml:id="N21540" xml:space="preserve">et illud tp̄s eſt añ inſtans medium vt <lb/>pꝫ ex ſe: igr̄ añ inſtãs mediū totiꝰ tꝑis īcipit tale cor­<lb/>pus rarefieri poſt̄ cõdēſabat̄̄. </s>
              <s xml:id="N21547" xml:space="preserve">pꝫ ↄ̨ña et argr̄ ma­<lb/>ior / q2 in tp̄e illo pars dēſior q̄ ē maior pedali deꝑ-<lb/>dit ꝓportionē ſexquidecimã nonnã in dēſitate et ſic <lb/>acq̇rit vnã decimã nonã vniꝰ pedalis et plus. </s>
              <s xml:id="N21550" xml:space="preserve">Pars <lb/>vero minus denſa efficit̄̄ in ſexquiquīto denſior, et <lb/>ꝑ ↄ̨ñs in ſexq̇quinto minor et ſic perdit vnã ſextã ſui <lb/>et ipſa eſt vna quinta pedalis. </s>
              <s xml:id="N21559" xml:space="preserve">g̊ perdit vnã ſextam <lb/>quinte pedalis: et ſexta vnius quīte pedalis eſt vna <lb/>trigeſima pedalis / vt pꝫ intuenti: igr̄ illḋ totale cor­<lb/>pus ꝑdit vnã trigeſimã vniꝰ pedalis et acq̇rit pluſ̄ <lb/>vnã decimã nona in tp̄e illo añ inſtãs mediū: igitur <lb/>plus acq̇rit de quãtitate ꝙ̄ deperdit et per cõſeq̄ns <lb/>rarefit / quod fuit probandum.</s>
            </p>
            <div xml:id="N21568" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0177-04a" xlink:label="note-0177-04" xml:id="N2156C" xml:space="preserve">cõfirma.</note>
            </div>
            <p xml:id="N21572">
              <s xml:id="N21573" xml:space="preserve">Quīto prīcipaliṫ argr̄ ſic </s>
              <s xml:id="N21576" xml:space="preserve">Si raritas <lb/>et denſitas eēnt poſſibiles. </s>
              <s xml:id="N2157B" xml:space="preserve">Seq̄ret̄̄ /  datis duobꝰ <lb/>corporibꝰ inequalibus maiore plus continente de <lb/>materia ꝙ̄ minus ſemꝑ maius eſſet dēſius minore. <lb/></s>
              <s xml:id="N21583" xml:space="preserve">ↄ̨ñs eſt falſū. </s>
              <s xml:id="N21586" xml:space="preserve">igr̄ et añs </s>
              <s xml:id="N21589" xml:space="preserve">Seq̄la ſuadet̄̄ q2 capto cor-<lb/>pore bipedali vniformiter qḋ habeat tres gradus <lb/>materie. </s>
              <s xml:id="N21590" xml:space="preserve">et pedali  habeat vnum gradū materie <lb/>dūtaxat manifeſtū eſt  maius eſt dēſius mīore q2 <lb/>ſi manente eadem quãtitate maius ꝑderet vnū gra­<lb/>dū materie. </s>
              <s xml:id="N21599" xml:space="preserve">ipſū rarefieret: et in fine maneret vnifor­<lb/>miter eq̄ denſū cū pedali. </s>
              <s xml:id="N2159E" xml:space="preserve">igr̄ mõ eſt denſius illo pe­<lb/>dali / qḋ fuit ꝓbãdū </s>
              <s xml:id="N215A3" xml:space="preserve">Falſitas tñ ↄ̨ñtis ꝓbat̄̄ et capio <lb/>vnū pedale qḋ habeat duos gradus materie: et vnū <lb/>bipedale vniforme qḋ habeat tres / et argr̄ ſic / illud <lb/>pedale ē dēſius illo bipedali maiori continēte plus <lb/>de materia: igr̄ nõ ſi aliq̇d eſt maiꝰ plꝰ ↄ̨tinēs de ma­<lb/>teria ꝙ̄ aliud minꝰ eo ipſū ē eo: dēſiꝰ. </s>
              <s xml:id="N215B0" xml:space="preserve">Probat̄̄ añs <lb/>et volo /  ſtãte quãtitate ipſius pedalis perdat me-<lb/>dietatē vniꝰ gradꝰ materie. </s>
              <s xml:id="N215B7" xml:space="preserve">q̊ poſito illḋ pedale ra­<lb/>refit vt notū eſt et in fine manebit eq̄ dēſū cū bipeda­<lb/>li: igr̄ antea erat dēſius. </s>
              <s xml:id="N215BE" xml:space="preserve">Coña pꝫ cū maiore et argr̄ <lb/>minor / q2 illud pedale in fine manebit eq̄ dēſū ſicut <lb/>medietas illius bipedalis q2 cõtinebit tm̄ de mate­<lb/>ria adeq̈te ſicut medietas illius bipedalis: et bipe-<lb/>dale eſt vniforme vt ponit̄̄: g̊ illud pedale eſt ita dē­<lb/>ſū ſicut bipedale / qḋ fnit ꝓbãdū.               <anchor type="note" xlink:href="note-0178-01" xlink:label="note-0178-01a"/>               </s>
              <s xml:id="N215D0" xml:space="preserve">¶ Dices et bñ negã­<lb/>do ſeq̄lã īmo aliqñ minꝰ ē dēſius maiore: et eↄ̈: et ali­<lb/>qñ eq̄ denſum vt apparere poteſt ex argumento.</s>
            </p>
            <div xml:id="N215D7" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0178-01a" xlink:label="note-0178-01" xml:id="N215DB" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N215E1">
              <s xml:id="N215E2" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
              <s xml:id="N215E5" xml:space="preserve">Q2 tūc ſeq̄ret̄̄ /  nõ poſſet da­<lb/>ri certa regula ad ſciēdū qñ vnū e denſius altero: et <lb/>qñ maius eſt dēſius minore vel econtra: quod ſi ne-<lb/>ges des illam. </s>
              <s xml:id="N215EE" xml:space="preserve">ſed cõſequēs eſt falſum: igitur illud <lb/>ex quo ſequitur.</s>
            </p>
            <p xml:id="N215F3">
              <s xml:id="N215F4" xml:space="preserve">Sexto prīcipaliṫ argr̄ ſic  hoc tãgen­<lb/>do rara difformia. </s>
              <s xml:id="N215F9" xml:space="preserve">Q2 ſi raritas et denſitas eſſent <lb/>poſſibiles ſeq̄ret̄̄ /  dabile eēt raꝝ vniformiter dif­<lb/>forme ab aliquo gradu vſ ad non gradū: et eiꝰ ra­               <cb chead="De motu rarefactionis et condenſationis."/>               ritas correſponderat gradui medio: ſed ↄ̨ñs eſt fal­<lb/>ſum: igitur et antecedēs. </s>
              <s xml:id="N21605" xml:space="preserve">Sequela ꝓbatur / quia da­<lb/>bile eſt rarum vniformiter difforme a certo gradu <lb/>vſ ad nõ gradū: g̊ etiã pari forma dabile eſt rarū <lb/>vniformiter difforme a certo gradu vſ ad nõ gra­<lb/>dū. </s>
              <s xml:id="N21610" xml:space="preserve">Sed falſitas conſequentis ꝓbatur / q2 ex illo ſe-<lb/>quitur aliquid eē rarū et idē non eē rarum / quod eſt <lb/>impoſſibile: </s>
              <s xml:id="N21617" xml:space="preserve">Sequela ꝓbatur / q2 capto tali corpo-<lb/>re vniformiter difformiter raro a gradu quarto vſ­<lb/> ad non gradū: tale corpus eſt raꝝ vt duo ꝑ te cū <lb/>eius raritas correſpondeat ſuo gradui medio: et eſt <lb/>nõ rarū cū ſit infinite dēſum: igr̄ intentū: minor pro­<lb/>batur / q2 prīa ꝑs ꝓportionalis illiꝰ corporis ꝓpor­<lb/>tione dupla eſt aliq̈liter denſa. </s>
              <s xml:id="N21626" xml:space="preserve">et ſecunda in duplo <lb/>denſior et tertia in quadruplo et ſic in infinitū: igit̄̄ <lb/>illud corpus eſt infinite dēſum: et per ↄ̨ñs non rarum. <lb/></s>
              <s xml:id="N2162E" xml:space="preserve">Q, ſecunda pars ꝓportiõalis ſit in duplo den-<lb/>ſior prīa patet / q2 eſt in ſubduplo rarior;: g̊ in duplo <lb/>denſior: pꝫ ↄ̨ña qm̄ ī quacū ꝓportione raritas ē <lb/>minor: in eadem denſitas ē maior. </s>
              <s xml:id="N21637" xml:space="preserve">vt ſatis facile ꝓ­<lb/>bari p̄t ex diffinitionibꝰ magis rari et magis denſi <lb/>et añs pꝫ / q2 prīa ꝑs ꝓportionalis eſt rara vt tria, <lb/>cū eius raritas ſit vniformiter difformis a quatuor <lb/>vſ ad duo: et ſcḋa pars proportionalis eſt rara vt <lb/>vnū cū dimidio: ſꝫ vnū cū dimidio eſt ſubdupluꝫ ad <lb/>tria. </s>
              <s xml:id="N21646" xml:space="preserve">igr̄ ſcḋa pars ꝓportionalis eſt in ſubduplo ra­<lb/>rior ꝙ̄ prima / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N2164B" xml:space="preserve">Et ſic ꝓbabis /  tertia <lb/>eſt in duplo denſior ꝙ̄ ſcḋa et quarta in duplo den-<lb/>ſior ꝙ̄ tertia: et ſic in infinitū. </s>
              <s xml:id="N21652" xml:space="preserve">igit̄̄ totū cõtinet infini­<lb/>tã materiã ſub finita quantitate: et ꝑ ↄ̨ñs non eſt ra-<lb/>rū. </s>
              <s xml:id="N21659" xml:space="preserve">Oīs em̄ pars illius ꝓportionalis tantū cõtinet <lb/>de materia ſicut prīa / vt pꝫ calculatanti igit̄̄.               <anchor type="note" xlink:href="note-0178-02" xlink:label="note-0178-02a"/>               </s>
              <s xml:id="N21663" xml:space="preserve">¶ Dices <lb/>et bñ negando ſequelã et ad ꝓbationē conceſſo añte <lb/>negãdo ↄ̨ñam / q2 ad raꝝ vniformiter difformi a cer­<lb/>to gradu vſ ad non gradū ſeq̇tur ipſum eſſe rarū <lb/>et non rarum vt bene ꝓbat argumentum. </s>
              <s xml:id="N2166E" xml:space="preserve">Ad rarū <lb/>vero vniformiṫ difforme a gradu vſ certū gradū <lb/>illḋ nõ ſeq̇tur: nec aliud etiam incõueniens iõ negã-<lb/>da eſt ſimilitudo.</s>
            </p>
            <div xml:id="N21677" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0178-02a" xlink:label="note-0178-02" xml:id="N2167B" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N21681">
              <s xml:id="N21682" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
              <s xml:id="N21685" xml:space="preserve">Q2 eadē rõe ſeq̄ret̄̄ /  nõ poſ­<lb/>ſet dari denſū vniformiter difforme a certo gradu <lb/>vſ ad non gradū: ſed ↄ̨ñs ē falſū: igr̄ et añs. </s>
              <s xml:id="N2168C" xml:space="preserve">Seq̄­<lb/>la pꝫ / q2 non eſt maior ratio de raritate vniformiṫ <lb/>difformi a gradu vſ ad nõ gradū quã de dēſitate <lb/>vniformiter difformi a gradu vſ ad nõ graduꝫ: g̊ <lb/>ſi vnū nõ eſt dabile: nec aliud cõcedēdū erit. </s>
              <s xml:id="N21697" xml:space="preserve">Sꝫ iã ꝓ­<lb/>bat̄̄ falſitas conſequentis / q2 ad denſum vniformi-<lb/>ter difforme a certo gradu vſ ad nõ gradū nulluꝫ <lb/>ſeq̇tur incõueniens: igr̄ denſū vniformiter difforme <lb/>a certo gradu vſ ad nõ gradū ē poſſiblle. </s>
              <s xml:id="N216A2" xml:space="preserve">Et ſi ne­<lb/>gas  ad illud nullū ſequat̄̄ īcõueuiēs des illud / igr̄ <lb/>inconueniēs / qḋ ſeq̇tur. </s>
              <s xml:id="N216A9" xml:space="preserve">et nõ poteris. </s>
              <s xml:id="N216AC" xml:space="preserve">q2 nõ ſequitur <lb/>illud quod ſequitur ad rarum vniformiter diffor-<lb/>me a certo gradu vſ ad non gradum: nec aliquod <lb/>aliud: igitur. </s>
              <s xml:id="N216B5" xml:space="preserve">Antecedens probatur / quia licet talis <lb/>vniformiter difformiter denſi etc. ſecunda pars pro­<lb/>portionalis ꝓportione dupla ſit in ſubduplo den­<lb/>ſior et per conſequens duplo rarior ꝙ̄ prima et ter-<lb/>tia in duplo rarior ꝙ̄ ſecunda: et quarta ꝙ̄ tertia et <lb/>ſic in infinitum: non tamen eo illud denſum vnifor-<lb/>miter difformiter etc. eſt infinite rarum. </s>
              <s xml:id="N216C4" xml:space="preserve">Continet <lb/>enim ſub finita quantitate aliquam materiam: vt <lb/>patet. </s>
              <s xml:id="N216CB" xml:space="preserve">igitur non ſequitur tale inconueniens / quod <lb/>fuit probandum.               <anchor type="note" xlink:href="note-0178-03" xlink:label="note-0178-03a"/>               </s>
              <s xml:id="N216D5" xml:space="preserve">¶ Et confirmatur </s>
              <s xml:id="N216D8" xml:space="preserve">Quia <lb/>ſi raritas et denſitas eſſent poſſibiles ſequeretur /  <lb/>poſſet dari infinite denſum / ſed conſequens eſt fal-<lb/>ſum. </s>
              <s xml:id="N216E1" xml:space="preserve">igitur illud ex quo ſequitur falſitas conſequē­<lb/>tio oſtenditur / q2 illud denſum īfinite eēt aliq̈liṫ ma­<lb/>gnū. </s>
              <s xml:id="N216E8" xml:space="preserve">et poſſet eiꝰ pūcta adhuc mag approxīari et ad               <pb chead="Tertii tractatus" file="0179" n="179"/>               inuicem approximari: et tūc tale condenſaret̄̄: igi-<lb/>tur non eſſet ante illam approximationem puncto­<lb/>rum infinite denſum. </s>
              <s xml:id="N216F4" xml:space="preserve">Conſequentia patet et mi-<lb/>nor ꝓbatur. </s>
              <s xml:id="N216F9" xml:space="preserve">q2 condenſari nihil aliud eſt ꝙ̄ puncta <lb/>approximari / vt patet ex deſcriptione cõdēſatiõis <lb/></s>
              <s xml:id="N216FF" xml:space="preserve">¶ Dices et bñ cõcedēdo ſeq̄lã et negãdo falſitatē cõ­<lb/>ſequētis: et ad ꝓbatiouē concedo /  pūcta illiꝰ cor-<lb/>poris poſſūt ad inuicē aproximari: et nego  tunc <lb/>condenſaretur tale corpus: et cū ꝓbat̄̄ /  ſic per dif­<lb/>finitionem condenſationis: dico /  non ſic deſcribi­<lb/>tur condēſatio. </s>
              <s xml:id="N2170C" xml:space="preserve">Sed de hoc videbit̄̄ poſtea. </s>
              <s xml:id="N2170F" xml:space="preserve">Si enim <lb/>alicuius pedalis prīa pars ꝓportionalis propor-<lb/>tione dupla aliq̇d cõtineat de materia: et ſecūda tm̄ <lb/>de materia: et tertia tm̄: et ſic ↄ̨ñter. </s>
              <s xml:id="N21718" xml:space="preserve">Ita  prima ſit <lb/>aliquãtulū denſa: ſecūda ī duplo dēſior: et tertia ī q̈­<lb/>druplo: et ſic cõſequēter: tūc cõſtat  tale corpꝰ ē īfi-<lb/>nite dēſū: et ſub pedali quantitate infinitam mate-<lb/>riam continet.</s>
            </p>
            <div xml:id="N21723" level="5" n="10" type="float">
              <note position="right" xlink:href="note-0178-03a" xlink:label="note-0178-03" xml:id="N21727" xml:space="preserve">.1. confir.</note>
            </div>
            <p xml:id="N2172D">
              <s xml:id="N2172E" xml:space="preserve">Sꝫ ↄ̨̨tra / q2 ſi ſolutio eſſet a ſeq̄ret̄̄ /  <lb/>poſſet dari finitū īfinite dēſū vniformiter: ſꝫ ↄ̨ñs eſt <lb/>falſū: igr̄ ſolutio nulla. </s>
              <s xml:id="N21735" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 tale corpus <lb/>de quo fit mētio in ſolntiõe eſt finitū īfinite dēſū dif­<lb/>formiter / vt dictis: igr̄ illud corpꝰ finitū p̄t reduci ad <lb/>vniformitatē: q̊ facto tale corpꝰ finitū eſſet īfinite dē­<lb/>ſū vniformiter: igit̄̄. </s>
              <s xml:id="N21740" xml:space="preserve">Sꝫ iã ꝓbat̄̄ falſitas ↄ̨ñtis: q2 ſi <lb/>aliq̇d eſt finitum infinite dēſū vniformiter ſeq̇tur /  <lb/>prīa pars ꝓportionalis eſt ita denſa ſicut ſcḋa ade­<lb/>quate: et ſecunda ſicut tertia et tertia ſicut quarta / et <lb/>ſic ↄ̨ñter: et vltra prīa pars ꝓportiõalis eius eſt ita <lb/>dēſa ſicut ſcḋa adequate etc. / igit̄̄ ſecūda ī duplo mi­<lb/>nus continet de materia ꝙ̄ tertia: et ſic ↄ̨ñter: g̊ reſi­<lb/>duū ex oībus dēpta prīa habet tm̄ de materia ſicut <lb/>prima: ſꝫ materia prime eſt finita: igit̄̄ materia to-<lb/>tius corporis ē finita: et quãtitas ſimiliter finita: igr̄ <lb/>totū corpꝰ ē finite denſū. </s>
              <s xml:id="N21757" xml:space="preserve">et ſic nõ eſt vniformiter īfini­<lb/>te dēſū / qḋ fuit ꝓbandū. </s>
              <s xml:id="N2175C" xml:space="preserve">Et ſi dicas /  ſecūda ꝑs pro­<lb/>portionalis continet tãtã materiã ſicut prīa et q̄lib3 <lb/>ſequens ſimiliter quia īfinitã: iã ſeq̇t̄̄ /  ad quodlib3 <lb/>pūctū talis corporis ē materia īfinita: et  ē penetra­<lb/>tio dimenſionū vel  materia ṗme ꝑtis ꝓportiona­<lb/>lis ē reducta ad nõ quãtū: et ſiĺr materia ſcḋe. </s>
              <s xml:id="N21769" xml:space="preserve">et ter-<lb/>tie / et ſic ↄ̨ñter: et ꝑ ↄ̨ñs totū illud corpꝰ erit reductum <lb/>ad nõ quãtū et ſic nõ erit finitū īfinite dēſū vniformi­<lb/>ter / qḋ fuerat demonſtrãdū. </s>
              <s xml:id="N21772" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo </s>
              <s xml:id="N21775" xml:space="preserve">Q2 ſi ra­<lb/>ritas eēt poſſibilis: ēt poſſibilis eēt raritas īfinita <lb/>ī ſubiecto finito: ſꝫ ↄ̨ñs eſt falſū. </s>
              <s xml:id="N2177C" xml:space="preserve">igr̄ illud ex quo ſeq̇­<lb/>tur. </s>
              <s xml:id="N21781" xml:space="preserve">Seq̄la apparet et falſitas ↄ̨ñtis deducir̄: q2 vel <lb/>tale ſubiectū finitū cõtinet infinitã materiã vel fini-<lb/>tã ſi infinitã iã illud nõ ē rarū: et ꝑ ↄ̨ñs nõ ē īfinite ra­<lb/>rū. </s>
              <s xml:id="N2178A" xml:space="preserve">Si finitã vel igr̄ cõtinet tãtã quantã vnū aliḋ ſub­<lb/>ieetū eq̈le illi finite rarū vel maiorē vel minorē. </s>
              <s xml:id="N2178F" xml:space="preserve">Si <lb/>tantã ſeq̇t̄̄ /  illa ſubiecta ſūt eq̄ rara: et vnū ē finite <lb/>raꝝ. </s>
              <s xml:id="N21796" xml:space="preserve">ir̄ et aliud. </s>
              <s xml:id="N21799" xml:space="preserve">Si maiorē iã ſeq̇t̄̄ /  hoc nõ eſt ita ra­<lb/>rū. </s>
              <s xml:id="N2179E" xml:space="preserve">Si minorē cū nõ ſit poſſibile  aliq̈ materia ſit ī­<lb/>finite modica ſeq̇t̄̄ /  ī aliq̈ ꝓportiõe materiã mino-<lb/>rē cõtinebit et ſic in eadē ꝓportiõe erit magꝪ rarū et <lb/>ꝑ ↄ̨ñs nõ erit īfinite rarū / quod fuit ꝓbandum.</s>
            </p>
            <p xml:id="N217A7">
              <s xml:id="N217A8" xml:space="preserve">Septīo prīcipaliṫ argr̄ ſic īq̇rēdo ma­<lb/>teriam de raritate et dēſitate difformi. </s>
              <s xml:id="N217AD" xml:space="preserve">q2 ſi raritas <lb/>et dēſitas eſſent poſſibiles ſeq̄ret̄̄ /  pedale cuius pri­<lb/>ma ꝑs ꝓportionalis ꝓportione dupla eſſet aliquã­<lb/>tulū rara et ſecunda in duplo rarior ꝙ̄ prīa: et tertia <lb/>ī duplo rarior ꝙ̄ ſcḋa et q̈rta in duplo rarior ꝙ̄ ter­<lb/>tia: et ſic ↄ̨ñter eſſet infinite rarū: ſed ↄ̨ñs eſt flm̄: igit̄̄ <lb/>illud ex q̊ ſeq̇tur </s>
              <s xml:id="N217BC" xml:space="preserve">Seq̄lã ꝓbat̄̄ / q2 raritas prīe ꝑtis ꝓ­<lb/>portiõalis illiꝰ corꝑis denoīat totale corpꝰ aliquã­<lb/>tū rarū et raritas ſcḋe ꝑtis ꝓportionalis tm̄ deno-<lb/>minat et raritas tertie ꝑtis: ſiĺr / et ſic ↄ̨ñter: igit̄̄ ibi               <cb chead="Capitulum tertium"/>               ſūt īfinite denoīatiões eq̈les nõ cõicãtes illud corpꝰ <lb/>denoīantes: igit̄̄ illud corpꝰ ē īfinite raꝝ. </s>
              <s xml:id="N217CA" xml:space="preserve">Añs pꝫ / q2 <lb/>raritas ſcḋe ꝑtis eſt in ſubduplo ſubiecto: et ī duplo <lb/>maior ꝙ̄ prime ꝑtis raritas: igr̄ tm̄ denoīat totale <lb/>corpꝰ ſicut raritas prīe partis et eadē rõne raritas <lb/>tertie tm̄ ſicut raritas ſcḋe / et ſic ↄ̨ñter: igt̄̄ intētū </s>
              <s xml:id="N217D5" xml:space="preserve">Sꝫ <lb/>falſitas ↄ̨ñtis ꝓbat̄̄: q2 illud corpꝰ pedale ſub finita <lb/>quãtitate cõtinet aliquãtã materiã: igr̄ nõ ē īfinite <lb/>rarū. </s>
              <s xml:id="N217DE" xml:space="preserve">itē illud pedale ē aliq̈liṫ denſū: igr̄ nõ ē īfinite <lb/>raꝝ. </s>
              <s xml:id="N217E3" xml:space="preserve">Coña pꝫ et arguit̄̄ añs / q2 prīa ꝑs ꝓportiõalis <lb/>illiꝰ pedalis eſt aliq̈liṫ denſa: et ſcḋa in duplo minꝰ <lb/>et tertia ī duplo minꝰ ꝙ̄ ſcḋa: et ſic ↄ̨ñter: igr̄ prima <lb/>ꝑs ꝓportionalis cõtinet aliquãtã materiã et ſcḋa in <lb/>q̈druplo minorē: et tertia in q̈druplo minorē ꝙ̄ ſcḋa / <lb/>et ſic ↄ̨ñter: igit̄̄ aggregatū ex illis oībꝰ materiebꝰ <lb/>dēpta mã prīe ꝑtis eſt ſubtriplū ad materiaꝫ prīe <lb/>ꝑtis ſed materia prime ꝑtis eſt vt tria (vt ſuppono) / <lb/>igit̄̄ tota materia illiꝰ corꝑis pedalis eſt vt q̈tuor: et <lb/>ꝑ ↄ̨ñs illud corpus eſt ita dēſū adeq̈te ſicut vnū aliḋ <lb/>pedale vniformite qḋ hꝫ q̈tuor gradꝰ materie / qḋ fuit <lb/>ꝓbãdū.               <anchor type="note" xlink:href="note-0179-01" xlink:label="note-0179-01a"/>               </s>
              <s xml:id="N21801" xml:space="preserve">Et ↄ̨firmat̄̄ </s>
              <s xml:id="N21804" xml:space="preserve">Et capio vnū corpꝰ cuiꝰ prīa ꝑs <lb/>ꝓportiõalis ꝓportiõe dupla ſit aliquãtulum rara <lb/>vniformitet puta vt duo: et ſecūda in duplo minus <lb/>et tertia in duplo minus ꝙ̄ ſcḋa / et ſic ↄ̨ñter ſequitur / <lb/> illud corpus eſſet rarum et nõ eſſet rarum: ſed cõ-<lb/>ſequens implicat: igit̄̄ et q̄ſtio </s>
              <s xml:id="N21811" xml:space="preserve">Sequela ꝓbatur / q2 <lb/>illud eſt rarū vt vnū cuꝫ vna tertia: igr̄ illud eſt raꝝ <lb/></s>
              <s xml:id="N21817" xml:space="preserve">Añs ꝓbatur / q2 ſi eſſet vnum corpus cuius prīa pro­<lb/>portionalis ꝓportione dupla eēt intenſa vt duo: et <lb/>ſecunda in duplo minus. </s>
              <s xml:id="N2181E" xml:space="preserve">et tertia in duplo minus ̄ <lb/>ſecunda / et ſic couſequenter. </s>
              <s xml:id="N21823" xml:space="preserve">totū eēt intenſū vt vnuꝫ <lb/>cū vna tertia / vt ꝓbabitur infra. de intenſione: igit̄̄ <lb/>pari ratione illud corpꝰ cuiꝰ vna ꝑs ꝓportionalis <lb/>ꝓportione dupla eſt rara vt duo: et ſcḋa in duplo <lb/>minus et tertia in duplo minus ꝙ̄ ſcḋa / et ſic cõſequē­<lb/>ter eſt rarū vt vnū cū vna tertia / quod fuit ꝓbanduꝫ <lb/></s>
              <s xml:id="N21831" xml:space="preserve">Sed  nõ ſit rarū ꝓbat̄̄ / q2 eſt infinite denſū: g̊ nõ eſt <lb/>rarum antecedens ꝓbatur / q2 ſub finita quantitate <lb/>infinitam materiam continet / quod probatur / q2 q̄-<lb/>libet pars proportionalis continet tantum de ma­<lb/>teria ſicut prima: ergo tota materia illius totiꝰ eſt <lb/>infinita añs ꝓbatur / q2 cū ſecunda pars ꝓportiõa-<lb/>lis eſt in duplo minus rara ꝙ̄ prīa ipſa eſt in duplo <lb/>denſior ꝙ̄ prīa et eſt in duplo minor: g̊ tm̄ cõtinet de <lb/>materia adeq̈te quãtã cõtinet prīa. </s>
              <s xml:id="N21844" xml:space="preserve">Coña ptꝫ / q2 ſi ſe­<lb/>cūda eēt eq̄ dēſa cū prīa in duplo minorē materiaꝫ <lb/>cõtiueret ꝙ̄ prīa / vt patet: ergo cū modo ſit ī duplo <lb/>denſior ꝙ̄ tunc eſſet mõ ſub eadē quãtitate in duplo <lb/>maiorē materiã cõtinet ꝙ̄ tunc contineret. </s>
              <s xml:id="N2184F" xml:space="preserve">Et eodē° <lb/>ꝓbabis /  tertia tãtã materiã cõtinet ſicut ſecūda et <lb/>q̈rta ſicut tertia et ſic ī iufinitū: et ſic pꝫ /  iliud conti­<lb/>net infinitã materiã ſub finita quãtitate / qḋ fuit pro­<lb/>bãdū.               <anchor type="note" xlink:href="note-0179-02" xlink:label="note-0179-02a"/>               </s>
              <s xml:id="N2185F" xml:space="preserve">¶ Cõfirmaṫ ſcḋo </s>
              <s xml:id="N21862" xml:space="preserve">Et capio vnū pedale cuiꝰ pri­<lb/>ma ꝑs ꝓportiõalis ꝓportione decupla ſit dēſa ali­<lb/>qualiter et ſcḋa ī duplo magis: et tertia ī duplo ma­<lb/>gis ꝙ̄ ſcḋa et quarta in duplo magis ꝙ̄ tertia: et ſic <lb/>couſequenter: et ſic arguo ſequeretur ex queſtiõe  <lb/>illud corpus eſſet infinite denſum: ſed conſequēs eſt <lb/>falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N21871" xml:space="preserve">Sequela pro-<lb/>batur / quia ſi alicuius corporis diuiſi per partes ꝓ-<lb/>portionales propoſitione dupla prima pars ꝓpor­<lb/>tionalis ſit aliquantulum denſa: et ſecunda in du-<lb/>plo denſior: et tertia in duplo denſior ꝙ̄ ſecun-<lb/>da: et quarta in duplo denſior ꝙ̄ tertia: et ſic conſe-<lb/>quenter: totum illud corpus eſt infinite denſum cuꝫ <lb/>contineat ſub finita quantitate infinitam materi-<lb/>am / vt probatum eſt in confirmatione ſuperiori: <lb/>igitur pari ratione etiam corpus diuiſum per par­<lb/>tes ꝓportionales ꝓportione decupla cuius prima               <pb chead="De motu rarefactionis et condenſationis." file="0180" n="180"/>               ꝑs ꝓportionalis ſit aliquãtulū denſa et ſcḋa in du-<lb/>plo magis et tertia in duplo magis ꝙ̄ ſecūda: et ſic <lb/>conſequēter erit etiã denſū infinite / qḋ fuit ꝓbãdum <lb/></s>
              <s xml:id="N21892" xml:space="preserve">Sed modo ꝓbatur falſitas conſequētis / quia illud <lb/>corpus diuiſū ꝓportione dedupla etc. ſub finita quã­<lb/>titate cõtinet finitã materiã p̄ciſe: igr̄ eſt finite den-<lb/>ſum. </s>
              <s xml:id="N2189B" xml:space="preserve">Añs ꝓbatur et ſuppono /  prīa eius pars ſit <lb/>dēſa vt vnū: ſecūda pars ꝓportionalis eius ſi tãtã <lb/>materiã contineret quantã continet prima eēt ī de-<lb/>cuplo denſior / et ꝑ ↄ̨ñs vt decē cū ſit in decuplo mīor <lb/>ſed modo eſt in quintuplo minus denſa ꝙ̄ tunc eēt: <lb/>et hoc ſub eadē quãtitate (quia duplum ad ſubdecu­<lb/>plū eſt ſubquītuplū ad decuplū / vt patet) et mõ eſt p̄­<lb/>ciſe denſa vt duo / vt ptꝫ ex caſu: igr̄ mõ in quītuplo <lb/>minus continet de materia ꝙ̄ tūc ↄ̨tineret ſꝫ tūc cõ-<lb/>tinet tantã materiã quãtã cõtinet prīa: igr̄ mõ ī quī­<lb/>tuplo minorē materiã ↄ̨tinet ꝙ̄ prīa: et pari rõe ter­<lb/>tia pars ꝓportionalis in quintuplo minus de ma­<lb/>teria ↄ̨tinet ꝙ̄ ſecūda et q̈rta in quītuplo minꝰ ꝙ̄ ter­<lb/>tia etc. / igr̄ aggregatum ex omnibus illis materie-<lb/>bus eſt ſexquiq̈rtum ad materiã prīe ꝑtis ꝓportio­<lb/>nalis: ſed materia prīe ꝑtis ꝓportionalis eſt finita <lb/>vt quatour vt ſuppono: igr̄ tota materia totiꝰ cor-<lb/>corporis eſt vt quī: et ꝑ ↄ̨ñs finita / qḋ fuit ꝓbandū</s>
            </p>
            <div xml:id="N218C0" level="5" n="11" type="float">
              <note position="right" xlink:href="note-0179-01a" xlink:label="note-0179-01" xml:id="N218C4" xml:space="preserve">.1. confir.</note>
              <note position="right" xlink:href="note-0179-02a" xlink:label="note-0179-02" xml:id="N218CA" xml:space="preserve">2. confir.</note>
            </div>
            <p xml:id="N218D0">
              <s xml:id="N218D1" xml:space="preserve">Octauo arguit̄̄ ſic. </s>
              <s xml:id="N218D4" xml:space="preserve">Quia ſi raritas et <lb/>denſitas eēt poſſibilis ſequeretur /  aliquid eſſet ī-<lb/>finite denſum. </s>
              <s xml:id="N218DB" xml:space="preserve">et idem eſſet denſum ſolum finite: ſed <lb/>ↄ̨ñs īplicat: igr̄ et illḋ ex q̊ ſeq̇t̄̄. </s>
              <s xml:id="N218E0" xml:space="preserve">Seq̄la ꝓbat̄̄ et capio <lb/>vnū dēſū vniformiṫ diuiſū ꝑ ꝑtes ꝓportõales ꝓpor­<lb/>tione dupla et volo /  ī prīa ꝑte huiꝰ hore pars pro­<lb/>portiõalis ṗma ↄ̨denſet̄̄ aliquantū: et in ſcḋa ꝑte iſti­<lb/>us hore ſecūda ꝑs corꝑis illiꝰ cõdenſet̄̄ in duplo plꝰ <lb/>et in tertia ꝑte tertia in triplo plus. </s>
              <s xml:id="N218ED" xml:space="preserve">et ſic ↄ̨ñter </s>
              <s xml:id="N218F0" xml:space="preserve">Quo <lb/>poſito in fine hore tale corpꝰ eſt finite denſū et īfinite <lb/>q2 infinite denſa ē aliq̈ pars eiꝰ. </s>
              <s xml:id="N218F7" xml:space="preserve">igr̄ ꝓpoſitū. </s>
              <s xml:id="N218FA" xml:space="preserve">Q, ſit <lb/>finite denſū argr̄ ſic / q2 apparet  ſit denſū p̄ciſe ſi-<lb/>cut ſcḋa ꝑs ꝓportionalis eius vt deducebat̄̄ ſuꝑius <lb/>de motu: et īfra videbit̄̄ de q̈litate difformiter ſic exi­<lb/>ſtente in corꝑe pedali.               <anchor type="note" xlink:href="note-0180-01" xlink:label="note-0180-01a"/>               </s>
              <s xml:id="N2190A" xml:space="preserve">¶ Dices forte negãdo ſeq̄lam <lb/>et ad probationem admiſſo caſu negando  illud <lb/>ſit in fine īfinite dēſū: et ad ꝓbationē cū dr̄ īfinite dē­<lb/>ſa ē aliq̈ pars eiꝰ: igr̄ ē infinite dēſū ↄ̨ceſſo añte: ne-<lb/>gat̄̄ ↄ̨ña: q2 nec de motu nec de intenſione tenet illa <lb/>ↄ̨ña: et ſic pꝫ /  ſolū eſt finite denſum in fine.</s>
            </p>
            <div xml:id="N21917" level="5" n="12" type="float">
              <note position="left" xlink:href="note-0180-01a" xlink:label="note-0180-01" xml:id="N2191B" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N21921">
              <s xml:id="N21922" xml:space="preserve">Sꝫ ↄ̨̨tra / q2 ſi illḋ corpꝰ in fine eēt ſolū <lb/>finite denſū poſſet dari eius adeq̈ta denſitas / ſꝫ ↄ̨ñs <lb/>eſt falſū: igr̄ et añs. </s>
              <s xml:id="N21929" xml:space="preserve">Coña pꝫ: et argr̄ falſitas ↄ̨ñtꝪ: q2 <lb/>ſi poſſet dari eiꝰ adeq̈ta denſitas maxīe eēt dando <lb/>denſitatē ſcḋe ꝑtis ꝓportionalis: ſꝫ illḋ corpꝰ nõ eſt <lb/>in fine ita denſū ſicut ſcḋa pars ꝓportiõalis eiꝰ: igr̄ <lb/>ꝓpoſitū. </s>
              <s xml:id="N21934" xml:space="preserve">Minor ꝓbat̄̄ et volo /  ṗma ꝑs ꝓportiona­<lb/>lis illius corꝑis ↄ̨denſet̄̄ ad ſubduplū: et tūc pꝫ ex ca­<lb/>ſu /  ſcḋa pars cõdenſabit̄̄ ad ſubq̈druplū: q2 ī du-<lb/>plo magꝪ. </s>
              <s xml:id="N2193D" xml:space="preserve">et arguo ſic / ī fine tale corpꝰ nõ erit ī qua­<lb/>druplo dēſiꝰ ꝙ̄ ſit nūc / igr̄ in fine nõ erit ita dēſū ſi-<lb/>cut ſcḋa pars ꝓportionalis eiꝰ q̄ erit in fine in q̈dru­<lb/>plo denſior ꝙ̄ nūc. </s>
              <s xml:id="N21946" xml:space="preserve">Añs ꝓbat̄̄ / q2 in fine illḋ corpus <lb/>nõ erit in q̈druplo minus ꝙ̄ ſit nūc ſꝫ maiꝰ: et eq̈liter <lb/>ↄ̨tinebit de materia ī fine ſicut nūc: igr̄ ī fine nõ erit ī <lb/>q̈druplo dēſiꝰ ꝙ̄ ſit nūc </s>
              <s xml:id="N2194F" xml:space="preserve">Maior ꝓbat̄̄ / q2 prīa ꝑs ꝓ-<lb/>portiõalis eiꝰ q̄ mõ ē medietas ↄ̨dēſabit̄̄ ab ſubdu-<lb/>plū. </s>
              <s xml:id="N21956" xml:space="preserve">igr̄ ī fine manebit q̈rta illiꝰ (illiꝰ in̄ in ṗncipio) <lb/>et alie ꝑtes ꝓportiõales nõ ↄ̨dēſant̄̄ ad nõ q̈ntū: igr̄ <lb/>aggregatū ex illa ṗma ꝑte et aliis erit magꝪ ꝙ̄ q̈rta <lb/>illiꝰ ī prīcipio. </s>
              <s xml:id="N2195F" xml:space="preserve">igr̄ ī fine illḋ corpꝰ nõ erit ī q̈druplo <lb/>minꝰ ꝙ̄ ſit nūc / qḋ fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0180-02" xlink:label="note-0180-02a"/>               </s>
              <s xml:id="N21969" xml:space="preserve">¶ Et ↄ̨firmat̄̄ </s>
              <s xml:id="N2196C" xml:space="preserve">Et capio <lb/>vnū pedale diuiſū ꝑ ꝑtes ꝓportionales ꝓportione <lb/>dupla: et prīa ſit aliq̈liṫ dēſa: et ſcḋa in ſexquialtero               <cb chead="De motu rarefactionis et condenſationis."/>               dēſior et tertia ī ſexq̇tertia dēſior ꝙ̄ prīa et q̈rta ī ſex­<lb/>q̇q̈to dēſior ꝙ̄ prīa / et ſic ↄ̨ñṫ ꝓcedēdo ꝑ oēs ſpēs ꝓ-<lb/>portiõis ſuꝑparticularis / et arguo ſic / ſi raritas et dē­<lb/>ſitas eſſet poſſibilis tale corpꝰ eēt alicuiꝰ denſitatis / <lb/>ſꝫ hoc ē falſū: igr̄. </s>
              <s xml:id="N2197E" xml:space="preserve">Minor ꝓbat̄̄ / q2 nõ p̄t dari eiꝰ ade­<lb/>quata denſitas: igr̄ nõ eſt alicuiꝰ adeq̈te denſitatꝪ: g̊ <lb/>ꝓpoſitū.               <anchor type="note" xlink:href="note-0180-03" xlink:label="note-0180-03a"/>               </s>
              <s xml:id="N2198A" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo </s>
              <s xml:id="N2198D" xml:space="preserve">Et capio vnū pedale diui­<lb/>ſū ꝑ ꝑtes ꝓportionales ꝓportiõe tripla: et prīa ali­<lb/>quantulū dēſa: et ſecūda in duplo magis dēſa et ter­<lb/>tia in ſexq̇altero denſior ꝙ̄ prīa et q̈rta in ſuꝑbiꝑti­<lb/>ente tertia denſior ꝙ̄ prīa et quīta in duplo ſexq̇al-<lb/>tero dēſior ꝙ̄ prīa: et ſexta in duplo ſuꝑbipartiente <lb/>tertias denſior ꝙ̄ prīa: et ſeptima ī triplo denſior ̄ <lb/>prīa / et ſic ↄ̨ñter capiēdo prīo prīas ſpēs qnin ge-<lb/>nerū ꝓportionū et deinde alias quin / et ſic cõſequē­<lb/>ter. </s>
              <s xml:id="N219A2" xml:space="preserve">Quo poſito ſic arguo / ſi denſitas eſſet. poſſibi-<lb/>lis daret̄̄ adequata denſitas illius corꝑis: ſed ↄ̨ñs <lb/>eſt falſū: igr̄ / et illud ex quo ſeq̇tur. </s>
              <s xml:id="N219A9" xml:space="preserve">Et ſi aduerſarius <lb/>minorem neget det illam: et in dubie facile eum cal-<lb/>culator philoſophus impugnabit.</s>
            </p>
            <div xml:id="N219B0" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0180-02a" xlink:label="note-0180-02" xml:id="N219B4" xml:space="preserve">.1. confir.</note>
              <note position="right" xlink:href="note-0180-03a" xlink:label="note-0180-03" xml:id="N219BA" xml:space="preserve">2. confir.</note>
            </div>
            <p xml:id="N219C0">
              <s xml:id="N219C1" xml:space="preserve">Nono argr̄ ſic. </s>
              <s xml:id="N219C4" xml:space="preserve">Si q̄ſtio eſſet a ſeq̄-<lb/>ret̄̄ aliq̇d ſiĺ rarefieri et ↄ̨dēſari: ſꝫ ↄ̨ñs eſt īpoſſibile / <lb/>g̊ et añs. </s>
              <s xml:id="N219CB" xml:space="preserve">Seq̄la ꝓbat̄̄: et pouo /  pedale vniforme di­<lb/>uidat̄̄ ꝑ partes ꝓportiõales ꝓportiõe dupla: et in <lb/>ṗma pate ꝓportiõali huiꝰ hore ṗma pars ꝓportio­<lb/>nalis talis corꝑis rarefiat ad duplū ſui, et in ſcḋa <lb/>parte ꝓportiõali ſcḋa ↄ̨dēſet̄̄ ad ſubduplū: et in ter­<lb/>tia ſiĺr ad ſubduplum: et ſic ↄ̨ñter </s>
              <s xml:id="N219D8" xml:space="preserve">Quo poſito argr̄ <lb/>ſic in fine tale corpꝰ eſt rariꝰ: et ſiĺr dēſiꝰ ꝙ̄ ſit modo: <lb/>igr̄. </s>
              <s xml:id="N219DF" xml:space="preserve">Qḋ ſit dēſiꝰ ꝓbat̄̄ / q2 īfinite partes eiꝰ ſunt den­<lb/>ſiores in duplo ꝙ̄ erãt ãtea: igr̄ totū eſt dēſiꝰ ꝙ̄ erat <lb/>ãtea. </s>
              <s xml:id="N219E6" xml:space="preserve">Sꝫ  ſit rariꝰ ꝓbat̄̄ / q2 eſt maiꝰ ꝙ̄ erat antea: et <lb/>non niſi ꝑ rarefactionē vt facile habet̄̄ ex caſu: igit̄̄ <lb/>ipſū eſt rariꝰ: añs ꝓbat̄̄ / q2 plus quãtitatis acq̇ſiuit <lb/>ṗma pars ꝓportiõalis ꝙ̄ ꝑdidit aggregatū ex oī-<lb/>bus ſequētibꝰ eã: igr̄ totale corpꝰ effectū eſt maius. <lb/></s>
              <s xml:id="N219F2" xml:space="preserve">Añs ptꝫ: q2 ṗma pars ꝓportiõalis cū eſſet ſemipe-<lb/>dalis acq̇ſiuit ſemipedalē quãtitatē: et oēs alie ſe-<lb/>quētes perdiderūt quartã ꝑtē pedalis: igr̄ ṗma ꝑs <lb/>magꝪ acq̇ſiuit ꝙ̄ oēs alie ſeq̇ntes ꝑdiderūt </s>
              <s xml:id="N219FB" xml:space="preserve">Minor ꝓ-<lb/>bat̄̄ / q2 ſcḋa ꝑs ꝓportõaĺ q̄ ē vna q̈rta pedaĺ ꝑdidit <lb/>medietatē ſui: et ſic ꝑdidit octauaꝫ pedalis: et tertia <lb/>ꝑdidit medietatē illiꝰ octaue, et q̈rta iteꝝ ſubduplã <lb/>quãtitatē ad tertiã: et ſic ↄ̨ñter ꝓcedēdo ꝑ ꝓportiõeꝫ <lb/>ſubduplã: igr̄ aggregatū ex oībꝰ partibꝰ ꝓportiõa­<lb/>libꝰ ſeq̄ntibꝰ ſcḋam ꝑdidit tm̄ ̄titatis ̄tū ꝑdidit <lb/>ſcḋa: et ſcḋa ꝑdidit vnã octauã pedalis: igr̄ aggre-<lb/>gatū ex ipſa et oībꝰ ſeq̄ntibꝰ eã ꝑdidit q̈rtã partē pe­<lb/>dalis / qḋ fuit ꝓbãdū: et ꝑ ↄ̨ñs totū corpus acq̇ſiuit <lb/>q̈rtã partē pedalis: et ſic eſt maiꝰ in ſexquiq̈rto: et ꝑ <lb/>ↄ̨ñs eſt rarefactū / qḋ fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0180-04" xlink:label="note-0180-04a"/>               </s>
              <s xml:id="N21A19" xml:space="preserve">¶ Et cõfirmat̄̄ et <lb/>pono caſū /  ſit aliqḋ corpꝰ diuiſū ꝑ partes ꝓpor-<lb/>tiõales ꝓportiõe dupla: et volo /  in ṗma ꝑte ꝓpor­<lb/>tionali huiꝰ hore rarefiat ṗma pars talis corporis <lb/>ſus ſcḋam ↄ̨dēſando ſcḋam ad ſubduplū eq̄ velo­<lb/>ciṫ ita  tm̄ rarefiat ̄tū alia ↄ̨denſabit̄̄ oībꝰ aliis <lb/>q̇eſcētibꝰ: et ī ſcḋa ꝑte ꝓportiõali rarefiat ſcḋa ſus <lb/>tertiã cõdēſando tertiã ad ſubduplū et in tertia ra­<lb/>refiat tertia verſus quartã condenſando eã ad ſub­<lb/>duplū ceteris q̇eſcētibꝰ. </s>
              <s xml:id="N21A2E" xml:space="preserve">et ſic in īfinitū </s>
              <s xml:id="N21A31" xml:space="preserve">Quo poſito <lb/>in fine hore illud corpus ē dēſiꝰ ꝙ̄ erat et etiã rarius / <lb/>igitur aliquid ſimul rarefit et cõdenſat̄̄ ſi raritas et <lb/>denſitas ſit poſſibilis. </s>
              <s xml:id="N21A3A" xml:space="preserve">Añs ꝓbat̄̄ / q2 prīa ꝑs ꝓpor­<lb/>tionalis eſt maior ꝙ̄ erat antea: et aggregatū ex ip­<lb/>ſa et ſecunda maius ꝙ̄ erat antea: et aggregatū ex <lb/>ipſa ſecunda et tertia maius ꝙ̄ erat antea, et aggre­<lb/>gatū ex mille primis, et ex quotcun finitis compu­<lb/>tata prima eſt maius ꝙ̄ erat antea: igr̄ illud corpꝰ <lb/>totale eſt maius ꝙ̄ erat antea: et ꝑ cõſequēs rarius. <lb/></s>
              <s xml:id="N21A4A" xml:space="preserve"><pb chead="Tertii tractatus" file="0181" n="181"/>               Antecedens probatur / quia aggregatū ex ṗma et ſe­<lb/>cūda eſt maiꝰ ꝙ̄ erat antea q2 prīa acq̇ſiuit aliquan­<lb/>tam quantitatē: et ſecunda ſubduplam perdidit: igi­<lb/>tur aggregatū ex illis magis acquiſiuit ꝙ̄ ꝑdiderit / <lb/>et ſic ꝓbatur de quocū aggregato. </s>
              <s xml:id="N21A59" xml:space="preserve">Sed  tale cor­<lb/>pus nõ ſit rarius ꝓbat̄̄ / q2 in fine adequate ē tm̄ quã­<lb/>tum erat antea: igitur non eſt rarius. </s>
              <s xml:id="N21A60" xml:space="preserve">Probat̄̄ / an-<lb/>tecedens / q2 prima pars ꝓportionalis eius aliquã <lb/>quantitatem acquiſiuit (acquiſiuit inquã ad bonum <lb/>ſenſum vt in propoſito debet ſumi) et aggregatum <lb/>ex omnibus ſequentibus tantū adequate deꝑdidit: <lb/>g̊ illud corpus manet equale tm̄ vi3 quãtū erat an-<lb/>tea </s>
              <s xml:id="N21A6F" xml:space="preserve">Minor probatur / q2 prima pars ꝓportionalis <lb/>acquiſiuit aliquã quãtitatē: et ſecūda perdidit in du­<lb/>plo minorem: et tertia in duplo minoreꝫ perdidit ̄ <lb/>ſecunda: et ſic conſequenter / ergo aggregatum ex oī­<lb/>bus ſequentibus primam quantitatē eſt equale pri­<lb/>me: et illa eſt quãtitas deꝑdita: igitur quantitas de­<lb/>perdita eſt equalis oīno quãtitati aquiſite</s>
            </p>
            <div xml:id="N21A7E" level="5" n="14" type="float">
              <note position="right" xlink:href="note-0180-04a" xlink:label="note-0180-04" xml:id="N21A82" xml:space="preserve">cõfirma.</note>
            </div>
            <p xml:id="N21A88">
              <s xml:id="N21A89" xml:space="preserve">Decimo prīcipaliter arguitur ſic. </s>
              <s xml:id="N21A8C" xml:space="preserve">Si <lb/>raritas et denſitas eſſet poſſibilis ſequeretur /  ali­<lb/>quod corpus pedale per totã horã iſtam ſequentem <lb/>eſſet maius ꝙ̄ nunc eſt: et in fine eſſet adequate eque <lb/>magnum ſicut nunc eſt: et tamen tunc nihil perderet <lb/>ſꝫ hoc apparet impoſſibile: igitur impoſſibilitas cõ­<lb/>ſequētis coloratur q2 ſi ꝑ totã horaꝫ eſſet maius ̄ <lb/>nūc eſt capio / igr̄ quãtitatē et exceſſum ꝑ quã erit ma­<lb/>ius per totã horã: , arguitur ſic talis exceſſus erit <lb/>deꝑditꝰ in fine hore: et erit ꝑ totã iſtam horam. </s>
              <s xml:id="N21AA1" xml:space="preserve">igit̄̄ <lb/>aliq̇d ꝑdit in fine hore / quod fuit negatum: et ſic par­<lb/>tes illiꝰ illati nõ ſe cõpatiuntur. </s>
              <s xml:id="N21AA8" xml:space="preserve">Sed ſequela proba­<lb/>turi et pono pono caſum / ꝙ̄ in prima medietate huius ho-<lb/>re future prima medietas pedalis corporis date ra­<lb/>refiat ad duplū et in ſecunda medietate iterū condē­<lb/>ſetur vniformiter et eque velociter ſicut rarefiebat: <lb/>quo poſito in fine hore tale corpꝰ erit adequate pe-<lb/>dale: et tm̄ adequate erat in principio et per totã ho­<lb/>rã erit maiꝰ pedali: igitur ꝓpoſituꝫ. </s>
              <s xml:id="N21AB9" xml:space="preserve">¶ Dices et bene <lb/>concedendo illatum nec illud inconuenit.</s>
            </p>
            <p xml:id="N21ABE">
              <s xml:id="N21ABF" xml:space="preserve">Sed cõtra ſi illud eſſet verū ſequeret̄̄ <lb/>pariformiter /  aliq̇d eſt nūc pedale et ꝑ totã iſtã ho­<lb/>rã ſequentē cõtinuo erit maiꝰ et tñ in fine erit minꝰ ̄ <lb/>nūc eſt: nihil in fine deꝑdēdo: ſed conſequēs videtur <lb/>impoſſibile: igit̄̄ illud ex quo ſeq̇tur. </s>
              <s xml:id="N21ACA" xml:space="preserve">Sequela tñ de­<lb/>ducit̄̄: et capio vnū corpus pedale diuiſū ad ymagi-<lb/>nationē ꝑ partes ꝓportionales: et hora ſimiliter fu­<lb/>tura diuidat̄̄ (maiorbus terminatis ſus inſtãs / qḋ <lb/>eſt pñs) et in prīa ꝑte ꝓportionali hore acq̇rat prīa <lb/>pars corporis vnū pedale ceteris quieſcētibꝰ: et ī ſe­<lb/>cunda ꝑte ſecunda pars corporis acq̇rat duo peda­<lb/>lia cõdenſando primã vſ ad ſubduplã quãtitatem <lb/>reſpectu illiꝰ quã hꝫ in īſtãti pñti: et in tertia acq̇rat <lb/>tertia ꝑs corporis q̈tuor pedalia ↄ̨dēſando ſcḋam <lb/>ad ſubduplã quãtitatē reſpectu illiꝰ quã hꝫ in īſtãti <lb/>pñti: et ſic in īfinitū. </s>
              <s xml:id="N21AE3" xml:space="preserve">quo poſito in fine hore illud cor­<lb/>pus manebit ſubduplū reſpectu magnitudinis quã <lb/>nūc hꝫ q2 q̄libet pars ꝓportionalis eius cõdēſabit̄̄ <lb/>ad ſubduplū: et tñ in illo īſtanti in fine nihil deꝑdet <lb/>qm̄ q̇cq̇d ꝑdet: ꝑdet in aliqua parte ꝓportionali: et <lb/>ꝑ totã horã cõtinuo erit maius: et maius vt facile ex <lb/>caſu iudicat̄̄ ymo ex caſu in īfinitū creſcit: igr̄ ꝓpoſi­<lb/>tū. </s>
              <s xml:id="N21AF4" xml:space="preserve">Eodē modo poſſet deduci concluſio illata eſto  <lb/>illud pedale nõ augeretur in infinitū imo ſemꝑ eſſet <lb/>citra bipedale: ponēdo  in prīa ꝑte ꝓportiõali ho­<lb/>re ṗma pars ꝓportionalis illiꝰ pedalis acq̇rat vnã <lb/>partē ꝓportionē vnius pedalis et in ſecunda ꝑte ꝓ-<lb/>portionali acquirat ſcḋa pars duas ṗmas ꝑtes ꝓ-<lb/>portionales et prīa cõdenſarett̄̄ ab ſubſexq̇alterū vel               <cb chead="Capitulum tertium"/>               ad ſubſexq̇tertium ī idē īcidit reſpectu quãtitatꝪ quã <lb/>habet in inſtanti / qḋ eſt pñs et ſic in īfinitum. </s>
              <s xml:id="N21B08" xml:space="preserve">quo po­<lb/>ſito manifeſtū eſt  illud corpꝰ ſꝑ erit maius et ma-<lb/>ius ꝑ totã illã horã: et nū̄ erit bipedale: et tñ in fine <lb/>erit minus (minus in̄ in ſubſexq̇tertio) qm̄ perdet <lb/>vnã quartã vt patuit ex regulis ꝓportionum: ſꝫ hoc <lb/>videtur inconueniens: igitur.</s>
            </p>
            <p xml:id="N21B15">
              <s xml:id="N21B16" xml:space="preserve">In oppoſitū arguit̄̄ experimēto  au­<lb/>ctoriate: </s>
              <s xml:id="N21B1B" xml:space="preserve">Experimēto ſic nã videmus aquã igni op­<lb/>poſitã maiorari et puncta in ea magis diſtare ꝙ̄ au­<lb/>tea: et talis maioratio a phīs rarefactio vocat̄̄: igr̄ <lb/>rarefactio ē poſſibilis ꝑ ↄ̨ñs raritas. </s>
              <s xml:id="N21B24" xml:space="preserve">Itē videmꝰ <lb/>aquam bulientem cum ab igne ſeperatur minora-<lb/>ri et eius puncta ꝓximiora effici: et talis minoratio <lb/>vocatur a phīs coudenſatio: igitur condenſatio eſt <lb/>poſſibilis et per conſequens denſitas. </s>
              <s xml:id="N21B2F" xml:space="preserve">Auctoritate <lb/>autem probatur:               <anchor type="note" xlink:href="note-0181-01" xlink:label="note-0181-01a"/>               </s>
              <s xml:id="N21B39" xml:space="preserve">Nam philoſopbus quarto phiſi­<lb/>corum in capitulo primo videlicet </s>
              <s xml:id="N21B3E" xml:space="preserve">Sunt autem qui­<lb/>dam qui per rarum et denſuꝫ opinantur manifeſtū <lb/>eſſe vacuū: aſſerit rarū et denſum eſſe / igitur.               <anchor type="note" xlink:href="note-0181-02" xlink:label="note-0181-02a"/>               </s>
              <s xml:id="N21B4A" xml:space="preserve">Itē phi­<lb/>loſophus et commētator eius ſeptimo phiſicorum <lb/>cõmento quindecimo ponunt motum rarefactiõis <lb/>et condenſationis vbi cõmentator īquit denſitas ni­<lb/>hil aliud eſt ꝙ̄ trãſmutatio alicuius ad minorē ma­<lb/>gntiudinem:               <anchor type="note" xlink:href="note-0181-03" xlink:label="note-0181-03a"/>               </s>
              <s xml:id="N21B5C" xml:space="preserve">Raritas vero econtra: hoc idem habe­<lb/>tur ex philoſopho quarto metheororum cõmento <lb/>decimo ſeptimo / igitur raritas et denſitas ſunt poſ­<lb/>ſibiles.</s>
            </p>
            <div xml:id="N21B65" level="5" n="15" type="float">
              <note position="right" xlink:href="note-0181-01a" xlink:label="note-0181-01" xml:id="N21B69" xml:space="preserve">phūs. .4. <lb/>phiſi.</note>
              <note position="right" xlink:href="note-0181-02a" xlink:label="note-0181-02" xml:id="N21B71" xml:space="preserve">phūs et <lb/>cõmē. 7. <lb/>phi. cõ. 15</note>
              <note position="right" xlink:href="note-0181-03a" xlink:label="note-0181-03" xml:id="N21B7B" xml:space="preserve">phūs .4: <lb/>me. cõ. 17</note>
            </div>
            <p xml:id="N21B83">
              <s xml:id="N21B84" xml:space="preserve">Pro deciſione huius q̄ſtionis tria or-<lb/>dine faciemus primo notabilis diuerſarum opini-<lb/>onum et complurium terminorum declaratiua po-<lb/>nemus. </s>
              <s xml:id="N21B8D" xml:space="preserve">Secundo aliquas concluſiones de intenſio­<lb/>ne denſitatis difformis inducemus: et tertio quedã <lb/>dubia cum ſolutionibus argumentorum ante op-<lb/>poſitum adiiciemus.</s>
            </p>
            <p xml:id="N21B96">
              <s xml:id="N21B97" xml:space="preserve">Notãdū eſt prīo /  de entitate ſiue ſub­<lb/>ſtantia ipſius raritatis et denſitatis quadruplex ē <lb/>opinio / vt ex dictis calculatoris in capitulo de rari­<lb/>tate et denſitate circa principiū clare haberi poteſt</s>
            </p>
            <p xml:id="N21BA0">
              <s xml:id="N21BA1" xml:space="preserve">Prima opinio eſt /  raritas et dēſitas <lb/>ſunt qualitates contrarie velut albedo et nigredo: <lb/>ita  ipſa raritas nõ eſt ipſa res rara. </s>
              <s xml:id="N21BA8" xml:space="preserve">nec eſt pun-<lb/>ctorum diſtantia in materia ꝓportionata ſecundū <lb/>hanc opinioneꝫ: ſed eſt vna qualitas ſicut eſt nigre­<lb/>do que ſi fuerit in ſubiecto denominabit ipſum ra-<lb/>rum dūmodo contrariū non impediat puta denſi-<lb/>tas. </s>
              <s xml:id="N21BB5" xml:space="preserve">Si vero non fuerit talis qualitas ī aliquo ſub­<lb/>iecto puta in igne aut in aere / tunc nec aer nec ignis <lb/>diceretur rarus. </s>
              <s xml:id="N21BBC" xml:space="preserve">Et huius opinionis vt ſuperiꝰ ta-<lb/>ctum eū in quodam argumento fuerunt aliqui doc­<lb/>tores vt Galterus Burleus in ſeptimo phiſicorum <lb/>et in ſuo tractatu de intenſione formarum.               <anchor type="note" xlink:href="note-0181-04" xlink:label="note-0181-04a"/>               </s>
              <s xml:id="N21BCA" xml:space="preserve">Et com­<lb/>mentator ſeptimo phiſicorum commento quindeci­<lb/>mo vt ſibi imponit burleus.               <anchor type="note" xlink:href="note-0181-05" xlink:label="note-0181-05a"/>               </s>
              <s xml:id="N21BD6" xml:space="preserve">Eiuſdem etiam ſenten­<lb/>tie fuit Paulus venetus in quarto phiſicorum.               <anchor type="note" xlink:href="note-0181-06" xlink:label="note-0181-06a"/>               </s>
              <s xml:id="N21BE0" xml:space="preserve">et ēt <lb/>hec queſtio temporibus archite philoſophi qui pre­<lb/>dicamnta edidit vĺ quē imitatus eſt philoſophus <lb/>in libro predicamentorum agitabatur inter philo­<lb/>ſophos: vt facile eſt intueri ex verbis phī in capitu­<lb/>lo de qualitate in libro predicamentorum vbi dubi­<lb/>tat an rarum et denſum ſint qualia hoc eſt denomi-<lb/>nata a q̈litatibus an ſint poſitiones nec opineris <lb/>ſolum de terminis ibi eſt contentionem.</s>
            </p>
            <div xml:id="N21BF3" level="5" n="16" type="float">
              <note position="right" xlink:href="note-0181-04a" xlink:label="note-0181-04" xml:id="N21BF7" xml:space="preserve">burle. 7. <lb/>phi. <lb/>cõ. 7. phi</note>
              <note position="right" xlink:href="note-0181-05a" xlink:label="note-0181-05" xml:id="N21C01" xml:space="preserve">paulꝰ ve­<lb/>netus .4.</note>
              <note position="right" xlink:href="note-0181-06a" xlink:label="note-0181-06" xml:id="N21C09" xml:space="preserve">architas <lb/>phūs ī p̄­<lb/>di: quali.</note>
            </div>
            <p xml:id="N21C13">
              <s xml:id="N21C14" xml:space="preserve">Secunda opionio eſt /  raritas dicitur <lb/>poſitiue denſitas vero eſt priuatuū eius: et mea ſen­<lb/>tentia hec opinio voluit aſſere raritatem eē quã-<lb/>dã qualitatē et denſitatem eſſe priuationem eius: ſi­               <pb chead="De motu rarefactionis  condenſationis." file="0182" n="182"/>               cut lux eſt quedam qualitas: et tenebre ſunt eiꝰ pri-<lb/>uatio. </s>
              <s xml:id="N21C24" xml:space="preserve">et intenſio eſt quedaꝫ qualitas: et remiſſio eiꝰ <lb/>priuatio: ita  quando aliquid rarefit aliqua qua­<lb/>litas que dicitur raritas ei acquiritur cum vero cõ­<lb/>denſatur non acquiritur ei aliqua qualitas que di­<lb/>catur denſitas: ſed tale corpus deperdit raritatem <lb/></s>
              <s xml:id="N21C30" xml:space="preserve">Alii aūt aliter intelligunt hanc opinionem dicen-<lb/>tes  ſecundum eaꝫ, ne raritas, ne denſitas ſūt <lb/>qualitates: ſed ipſa raritas eſt ipſamet res rara: et <lb/>ipſa denſitas ipſammet res denſa. </s>
              <s xml:id="N21C39" xml:space="preserve">Dicitur tamen <lb/>raritas poſitiuum ſecundum hanc opinionem: q2 <lb/>quando aliquid rarefit ei acquiritur quantitas ip­<lb/>ſum efficitur maius: quando viro condenſatur ip­<lb/>ſum efficitur minus. </s>
              <s xml:id="N21C44" xml:space="preserve">Et ideo raritas dicitur poſiti­<lb/>ue: denſitas vero priuatiue: quia per denſitatē ſub-<lb/>iectum aliqua quãtitate priuatur per raritatē ve-<lb/>ro aliquam quantitatem acquirit.</s>
            </p>
            <p xml:id="N21C4D">
              <s xml:id="N21C4E" xml:space="preserve">Tertia opinio eſt /  denſitas dicitur <lb/>poſitiue et raritas priuatiue non tamen dicit den­<lb/>ſitatem eſſe qualitatem: et addit  ex vniformi rare­<lb/>factione alicuius per tempus ſecundum ſe totuꝫ ac­<lb/>quiritur vniformiter quãtitas: addit ſecundo  ſi <lb/>rarius et denſius equalis quantitatis eque veloci-<lb/>ter rarefiunt: denſius maiorem quantitatem acqui­<lb/>rit ꝙ̄ rarius.</s>
            </p>
            <p xml:id="N21C5F">
              <s xml:id="N21C60" xml:space="preserve">Quarta vero poſitio eſt /  denſitas di­<lb/>ditur poſitiue. </s>
              <s xml:id="N21C65" xml:space="preserve">et raritas priuatiue: et  raritas eſt <lb/>ipſamet res rara: et denſitas ſimiliter: et differt hec <lb/>opinio a tertia. quia addit contradictorias ꝓpoſi­<lb/>tiones duabus propoſitionibus quas addit tertia / <lb/>vt poſtea plus declarabitur. </s>
              <s xml:id="N21C70" xml:space="preserve">Hãc autem opinionē <lb/>principaliter intendo ſuſtentare et declarare. </s>
              <s xml:id="N21C75" xml:space="preserve">q2 ea <lb/>eſt quã deffenſat calculator in hac materia ceteros <lb/>excellens. </s>
              <s xml:id="N21C7C" xml:space="preserve">et quia ipſa et dictis philoſophorum et <lb/>naturalibus experimentis conformior ceteris opi­<lb/>nionibus apparet. </s>
              <s xml:id="N21C83" xml:space="preserve">Hic oponionibus ſic recitatis.</s>
            </p>
            <p xml:id="N21C86">
              <s xml:id="N21C87" xml:space="preserve">Querit̄̄ vtrum ipſe ſint ſuſtentabiles <lb/>et ſignãter de tribꝰ primis. </s>
              <s xml:id="N21C8C" xml:space="preserve">¶ Et argr̄ primo /  ṗma <lb/>nõ ſit poſſiblis per argumentū primū ante oppo-<lb/>ſitū in quo ꝓbatur /  raritas et denſitas nõ poſſūt <lb/>poſitiue accipi ſicut albedo et nigredo.</s>
            </p>
            <p xml:id="N21C95">
              <s xml:id="N21C96" xml:space="preserve">Secundo arguit̄̄. </s>
              <s xml:id="N21C99" xml:space="preserve">Si raritas  den-<lb/>ſitas eſſent qualitates et ſignanter contrarie / vt di­<lb/>cit opinio. </s>
              <s xml:id="N21CA0" xml:space="preserve">Sequeretur /  aliquid nec eſſet rarum <lb/>nec denſum: et contineret finitam materiam ſub fi-<lb/>nita quãtitate / ↄ̨ñs eſt falſum: ergo et ãtecedēs. </s>
              <s xml:id="N21CA7" xml:space="preserve">Se­<lb/>quela ꝓbatur: et pono /  ſit a. corpꝰ pedale habens <lb/>duos g̈dus materie: et habeat q̈tuor gradus rarita­<lb/>tis et quatuor denſitatis quo poſito illud nec eſt ra­<lb/>rum: nec eſt denſum: q2 raritas et dēſitas ſunt qua-<lb/>litates cõtrarie equales in ipſo: et ſic ſe īpediunt: et <lb/>tñ ipſum certã materiã cõtinet ſub finita quãtitate / <lb/>vt ponit caſus igr̄. </s>
              <s xml:id="N21CB8" xml:space="preserve">Sed iam probo falſitatē ↄ̨ñtis: q2 <lb/>ſeq̇tur bene cõtinet finitã materiã ſub finita quãti-<lb/>tate: g̊ ſequit̄̄ /  eſt rarū / vt ptꝫ ex diffinitione rari: et <lb/>nõ eſt rarum ꝑ te: igr̄ ↄ̨tradictio.</s>
            </p>
            <p xml:id="N21CC1">
              <s xml:id="N21CC2" xml:space="preserve">Tertio contra eandem opinionem ar­<lb/>guitur: quia ſi illa eſſet vera ſequeretur /  aliquid <lb/>eſſet infinite rarū quod eſſet etiam denſum: ↄ̨ñs im­<lb/>plicat: igr̄. </s>
              <s xml:id="N21CCB" xml:space="preserve">Argr̄ añs, et pono /  a. ſit vnū corpꝰ di-<lb/>uiſum ꝑ partes ꝓportionales ꝓportione dupla: et <lb/>prima pars ꝓportionalis ſit aliqualiter rara: et ſe­<lb/>cunda in duplo magis et tertia in duplo magis ̄ <lb/>ſecūda: et quarta in duplo magis ꝙ̄ tertia: et ſic in <lb/>infinitū: quo poſito argr̄ ſic / a. eſt infinite rarum: et <lb/>eſt dēſuꝫ: igr̄ ꝓpoſitū </s>
              <s xml:id="N21CDA" xml:space="preserve">Probatur maior / q2 raritas               <cb chead="De motu rarefactionis  condenſationis."/>               prime partis ꝓportionalis denoīat ipſum aliqua­<lb/>liter raꝝ: et raritas ſecūde partis tm̄ (cū ſit dupla <lb/>in ſubdupla parte) et raritas tertie tm̄ ſicut rari-<lb/>tas ſecūde (cū ſit dupla in ſubduplo ſubiecto) et ſic <lb/>in infinitū: igr̄ q̄libet pars ꝓportiõalis alia a pri-<lb/>ma denoīat tm̄ illud corpꝰ rarum ſicut prima: et ſūt <lb/>infinite: igr̄ infinite rarum denominãt illud corpꝰ: <lb/>et ſic eſt infinite rarum </s>
              <s xml:id="N21CEE" xml:space="preserve">Sed  ſit denſum probatur / <lb/>quia habet finitam materiam vt notum eſt ſub fini­<lb/>ta quantitate vt ponitur: igitur eſt denſum.</s>
            </p>
            <p xml:id="N21CF5">
              <s xml:id="N21CF6" xml:space="preserve">Contra ſcḋam opinionē quarto argr̄ ſic / q2 ſi <lb/>illa eſſet a ſeq̄ret̄̄ / q2 oē raꝝ eſſet īfinite deſū <lb/>et ſic eſſet raꝝ et nõ eēt raꝝ: qḋ īplicat: ꝓbatur ſeq̄la / <lb/>q2 in oī raro m illã opinionē eſt infinita denſitas: <lb/>igr̄ oē rarum eſt īfinite denſum. </s>
              <s xml:id="N21D01" xml:space="preserve">Argr̄ añs: et capio <lb/>aliquod raꝝ in quo ſit ꝑ totū raritas vt quatuor q̄ <lb/>ꝑ te eſt quedã qualitas aut poſitiue dr̄. </s>
              <s xml:id="N21D08" xml:space="preserve">Diuido igr̄ <lb/>illã raritatē ꝑ partes ꝓportionales m intenſionē <lb/>et hoc ꝓportione dupla: et arguo ſic / prima pars ꝓ-<lb/>portionalis illius raritatis eſt aliqualiter denſa, <lb/>ſiue hꝫ aliquã denſitatē: ſicut pars intēſa qualita-<lb/>tis hꝫ aliquã remiſſionē: et ſecūda pars ꝓportiona­<lb/>lis eſt in duplo minor raritas: igr̄ in duplo maior <lb/>denſitas et tertia in quadruplo minor raritas quã <lb/>prima: igr̄ in quadruplo maior dēſitas: et quarta <lb/>in octuplo minor raritas / g̊ in octuplo maior dēſi-<lb/>tas: et ſic in īfinitū: g̊ īfinita dēſitas eſt in tali corꝑe. <lb/>               <anchor type="note" xlink:href="note-0182-01" xlink:label="note-0182-01a"/>               </s>
              <s xml:id="N21D26" xml:space="preserve">¶ Et cõfirmat̄̄. </s>
              <s xml:id="N21D29" xml:space="preserve">Quia vbicū eſt aliquod poſituū <lb/>ibi eſt in īfinitū de ſuo priuatiuo (dūmodo priua-<lb/>tiuū et poſitiuū ſe cõpatiant̄̄) ſed raritas ſe hꝫ po-<lb/>ſitiue: et denſitas priuatiue: et ſe cõpatiunter: ergo <lb/>vbicū eſt aliqua raritas ibi eſt infinita denſitas <lb/>ſeu in īfinitū magna denſitas. </s>
              <s xml:id="N21D36" xml:space="preserve">Probat̄̄ maior īdu­<lb/>ctiue / q2 vbi eſt aliq̈ magnitudo ibi eſt in īfinitū par­<lb/>ua quantitas: et vbi eſt aliqua diſtãtia ibi eſt in īfi-<lb/>nitū magna ꝓpinq̇tas: q2 ꝓpinq̇tas dr̄ priuatiue <lb/>ad diſtantiã. </s>
              <s xml:id="N21D41" xml:space="preserve">et vbicū eſt aliqua intenſio ibi īfinita <lb/>remiſſio eſt vt facile eſt intueri: q2 ibi eſt aliqualis <lb/>intenſio: et ſubdupla, et ſubquadrupla, et ſic in īfini­<lb/>tum: et ſic de aliis priuatiue ſi que ſint talia.</s>
            </p>
            <div xml:id="N21D4A" level="5" n="17" type="float">
              <note position="right" xlink:href="note-0182-01a" xlink:label="note-0182-01" xml:id="N21D4E" xml:space="preserve">Confir-<lb/>matio</note>
            </div>
            <p xml:id="N21D56">
              <s xml:id="N21D57" xml:space="preserve">Quninto contra eandē arguo ſic. </s>
              <s xml:id="N21D5A" xml:space="preserve">Si <lb/>raritas diceret̄̄ poſitiue ſeq̄ret̄̄ /  aliquod corpus <lb/>aliqualiter rarū ꝑ ſolã rarefactionē ſiue inductio-<lb/>nē raritatis: et motū ↄ̨ñtem raritatē q̇ motꝰ eſt aug­<lb/>mentatio: ipſum efficiret̄̄ denſius: ſed ↄ̨ñs eſt mani­<lb/>feſte falſum: q2 tunc ipſum efficiret̄̄ maiꝰ equaliter <lb/>cõtinens de materia: ergo nõ efficeretur denſiꝰ: īmo <lb/>rariꝰ / et ſic illud ↄ̨ñs eſt falſum. </s>
              <s xml:id="N21D6B" xml:space="preserve">Sed iã ꝓbo ſequelã <lb/>et capio vnū corpꝰ tripedale cuius vna medietas ſit <lb/>rara vt duodecim: et alia rara vt duo: et volo /  illa <lb/>rara vt duo acq̇rat duos g̈dus raritatis quieſcēte <lb/>altera rara vt duodecim. </s>
              <s xml:id="N21D76" xml:space="preserve">Quo poſito argr̄ ſic in fi­<lb/>ne illiꝰ rarefactionis illud corpꝰ eſt minꝰ rarū ꝙ̄ an­<lb/>tea: igr̄ ꝓpoſitū </s>
              <s xml:id="N21D7D" xml:space="preserve">Añs argr̄: q2 antea illud corpꝰ erat <lb/>rarum vt ſeptē: q2 medietas rara vt .12. denoīabat <lb/>vt ſex: et medietas rara vt duo denoīabat vt vnum / <lb/>igr̄ tota illa raritas erat vt ſeptē: et modo eſt vt ſex <lb/>cū duabꝰ tertiis p̄ciſe: igr̄ eſt minꝰ rarum ꝙ̄ antea. <lb/></s>
              <s xml:id="N21D89" xml:space="preserve">Sed iam ꝓbo /  modo eſt rarū vt ſex cū duabꝰ ter-<lb/>tiis p̄ciſe: q2 illud corpꝰ eſt modo tripedale, q2 ãtea <lb/>erat bipedale et eius vna medietas pedalis effecta <lb/>eſt in duplo maior: et ſic effecta eſt bipedalis et per <lb/>conſequens effecta eſt due tertie totiꝰ et ille due ter-<lb/>tie habent raritatem vt quatuor per totum: et ſic il-<lb/>la raritas denominat totum rarum vt duo cū dua­<lb/>bus tertiis. </s>
              <s xml:id="N21D9A" xml:space="preserve">Reliquuꝫ vero pedale que eſt vna tertia <lb/>eſt rarum vt duodecim: et ſic denominat totum vt q̈­<lb/>tuor: modo quatuor et duo cum duabus tertiis ſūt               <pb chead="Tertii tractatus" file="0183" n="183"/>               ſex. cū duabꝰ tertiis: ergo totū eſt rarum vt ſex cum <lb/>duabꝰ tertiis / quod fuit ꝓbandū. </s>
              <s xml:id="N21DA8" xml:space="preserve">Et hoc eſt optimū <lb/>argumētū cõtra iſtã opinionē quod apparētiſſime <lb/>impugnat eã ſiue teneatur ſecundum iſtam opnionē <lb/>raritatem eſſe qualitatem ſiue non: dummodo di-<lb/>catur raritas poſitiue.</s>
            </p>
            <p xml:id="N21DB3">
              <s xml:id="N21DB4" xml:space="preserve">Sexto ↄ̨̨tra eandē ſcḋam opinionem <lb/>argr̄. </s>
              <s xml:id="N21DB9" xml:space="preserve">Si raritas eſſet qualitas aut poſitiue dicere­<lb/>tur: ſeq̄retur /  difformiter difforme cuius vtra <lb/>medietas eſſet vniformis nõ correſpõderet ſuo gra­<lb/>dui medio: ſed ↄ̨ñs eſt falſum:. igr̄ / et illud ex quo ſe-<lb/>quit̄̄. </s>
              <s xml:id="N21DC4" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono /  ſit vnū bipedale cuiꝰ <lb/>vna medietas ſit rara vt octo, et alia vt q̈tuor, et ar­<lb/>guit̄̄ ſic / raritas iſtiꝰ corꝑis nõ correſpõdet ſuo g̈dui <lb/>medio que eſt vt ſex: igr̄. </s>
              <s xml:id="N21DCD" xml:space="preserve">Argr̄ añs: et volo /  medie­<lb/>tas rara vt octo deꝑdat duos g̈dus raritatis: et tm̄ <lb/>acq̇rat medietas minꝰ rara vniiformiter in eodem <lb/>tēpore quo poſito in fine totū illud manebit vnifor­<lb/>me vt ſex, et manebit rariꝰ ꝙ̄ eſt modo: g̊ raritas eiꝰ <lb/>nõ correſpondet g̈dui medio q̄ eſt raritas vt ſex. </s>
              <s xml:id="N21DDA" xml:space="preserve">Sꝫ <lb/>iam ꝓbo minorē vcꝫ  illud corpus in fine manebit <lb/>rariꝰ ꝙ̄ ſit modo: q2 illa medietas q̄ eſt rara vt qua­<lb/>tuor acq̇ret proportionē ſexq̇altera raritatis ſupra <lb/>ſe, et eſt vnū pedale: igr̄ acq̇ret ſemipedale: medie-<lb/>tas vero rarior deꝑdet ꝓportionē ſexq̇tertiã rari-<lb/>tatis et eſt pedalis: igr̄ deꝑdet vnã quartã pedalis: <lb/>ergo ſequit̄̄ / ꝙ̄ maiorē quantitatē acq̇rit totū illud <lb/>corpꝰ ꝙ̄ deꝑdit: et ꝑ ↄ̨ñs eſt rariꝰ ꝙ̄ antea: et eſt rarū <lb/>vniformiter vt ſex puta g̈du medio inter .4. et .8. igr̄ <lb/>antea qñ erat difforme erat minus rarū ꝙ̄ ſit gra-<lb/>dus mediꝰ : et ſic ſua raritas non correſpõdebit ſuo <lb/>gradui medio, quod fuit probandum.</s>
            </p>
            <p xml:id="N21DF5">
              <s xml:id="N21DF6" xml:space="preserve">Septimo. </s>
              <s xml:id="N21DF9" xml:space="preserve">Contra tertiã opinionē ar­<lb/>guitur ſic: et ſignãter contra primã ꝓpoſitionē quã <lb/>addit opinio vcꝫ  ex vniformi rarefactiõe ſiue ac-<lb/>quiſitione raritatis per tēpus ſequit̄̄ vniformis ac­<lb/>quiſitio quantitatis q2 ſi ita eſt: capio vnū pedale <lb/>rarū vt quatuor / et volo /  acquirat vniformiter per <lb/>horam quatuor gradus raritatis: et argr̄ ſic / in illa <lb/>hora totale illud pedale difformiter acquirit quanti­<lb/>tatē: et vniformiter raritatē: igr̄ illa ꝓpoſitio falſa <lb/></s>
              <s xml:id="N21E0D" xml:space="preserve">Maior ꝓbatur vcꝫ /  difformiter acq̇rit ̄titatē q2 <lb/>bene ſequitur vniformiter acq̇rit raritatē: ergo vni­<lb/>formiter deꝑdit denſitatē. </s>
              <s xml:id="N21E14" xml:space="preserve">Patet ↄ̨ña / quia nichil <lb/>aliud eſt vniformiter acq̇rere raritatē ꝙ̄ vniformi-<lb/>ter deꝑdere denſitatē (raritas em̄ ſecundū hanc o-<lb/>pinionē priuatiue dr̄) et vltra vniformiter deperdit <lb/>denſitatē: g̊ difformiter acq̇rit quantitatem: añs eſt <lb/>verū : g̊ et ↄ̨ñs. </s>
              <s xml:id="N21E21" xml:space="preserve">Probo tñ hanc vltimã cõſequentiam / <lb/>q2 cõtinuo in equali tēpore tale corpus maiorē ꝓ-<lb/>portionē denſitatis deꝑdit: igr̄ continuo in equali <lb/>tēpore maiorē quantitatē acq̇rit. </s>
              <s xml:id="N21E2A" xml:space="preserve">Conſequētia ptꝫ / <lb/>q2 eque ꝓportionabiliter ſicut deꝑditur denſitas <lb/>maioratur quantitas: et añs ꝓbatur / q2 ↄ̨tinuo illa <lb/>denſitas qñ deꝑditur eſt minor: et cõtinuo eque velo­<lb/>citer deꝑditur: g̊ cõtinuo maiorē ꝓportionē deꝑdit <lb/></s>
              <s xml:id="N21E36" xml:space="preserve">pꝫ ↄ̨ña ex ſcḋa ꝑte q̈rto capite octaua ſuppoſitiõe <lb/>               <anchor type="note" xlink:href="note-0183-01" xlink:label="note-0183-01a"/>               </s>
              <s xml:id="N21E40" xml:space="preserve">¶ Confirmatur / q2 ſecūda ꝓpoſitio quã addit hec ſe-<lb/>tunda opinio: videlicet  ſi rarius et denſius equa­<lb/>lia eque velociter rarefiant: cõtinuo denſiꝰ maioreꝫ <lb/>quantitatē acquirit ꝙ̄ rarius repugnat alteri pro­<lb/>poſitioni quã addit quã immediate ꝓcedens argu-<lb/>mentum impugnat: igitur illa opinio non coheret <lb/>ſibi ipſi: arguitur antecedens et capio duo pedalia <lb/>vnū denſum vt quatuor et aliud denſum vt duo et ma­<lb/>nifeſtum eſt ſecundam iſtam opinionem  denſum <lb/>vt duo ē magꝪ raꝝ / volo igit̄̄ /  vtrū illoꝝ rarefiat <lb/>eque velociter acquirendo infinitam raritatem in               <cb chead="Capitulū primū."/>               hora. </s>
              <s xml:id="N21E5A" xml:space="preserve">quo poſito arguo ſic / vtrum illorum in hora <lb/>acquiſiuit equalē quantitatem quia infinitam cum <lb/>vtrum ſit infinite rarum in fine et vniformiter acq̇­<lb/>rebat raritatem ſicut quantitatem / vt dicit prima <lb/>ꝓpoſitio: et tamen vnum illorum erat denſius et ali­<lb/>ud rariꝰ et eque velociter rare fiebant per illud tem­<lb/>pus / ergo non ſi rariꝰ et denſius equalis quantita­<lb/>tis eque velociter rarefiant denſius maiorem quan­<lb/>titatem acquirit ꝙ̄ rarius q2 in caſu illo acquirit <lb/>equalem. </s>
              <s xml:id="N21E6F" xml:space="preserve">vel ſi ſic iam non vniformiter ſicut acq̇rit̄̄ <lb/>raritas acquiritur quantitas: et ꝑ ↄ̨ñs vna ꝑs repu­<lb/>gnat alteri               <anchor type="note" xlink:href="note-0183-02" xlink:label="note-0183-02a"/>               </s>
              <s xml:id="N21E7B" xml:space="preserve">¶ Dices forte /  hec opinio intelligit dū­<lb/>modo vtrum acquirit finitam raritatem modo <lb/>in propoſitio vtrum acquirit īfinitam.</s>
            </p>
            <div xml:id="N21E82" level="5" n="18" type="float">
              <note position="left" xlink:href="note-0183-01a" xlink:label="note-0183-01" xml:id="N21E86" xml:space="preserve">ↄ̨firma.</note>
              <note position="right" xlink:href="note-0183-02a" xlink:label="note-0183-02" xml:id="N21E8C" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N21E92">
              <s xml:id="N21E93" xml:space="preserve">Sed contra. </s>
              <s xml:id="N21E96" xml:space="preserve">Quia eſto  vtrū ac-<lb/>quirit finitam raritatem rarius videlicet et denſiꝰ <lb/>adhuc tamen rarius maiorem quantitatem acqui­<lb/>rit / igitur ſolutio nulla. </s>
              <s xml:id="N21E9F" xml:space="preserve">Arguitur antecedēs et volo / <lb/> ſint duo pedalia a. et b.a. denſum vt quattuor <lb/>b. denſum vt octo et tam a. ꝙ̄ b. acquirat duos gra­<lb/>dus raritatꝪ / quo poſito arguitur ſic / a. maiorē quã­<lb/>titatem acquirit quã b. et eſt rarius b. et eque velo-<lb/>citer rarefit cum b. / igitur quãdo rarius et denſius <lb/>eque velociter rare fiunt rarius maiorem quantita­<lb/>tem acquirit ꝙ̄ denſius. </s>
              <s xml:id="N21EB0" xml:space="preserve">Probat̄̄ maiori / q2 ſi a. ac-<lb/>quirit duos g̈dus raritatis: et b. ſimiliter: ſequit̄̄ /  <lb/>vtrū illoꝝ deꝑdit duos g̈dus denſitatis: et ſic a. <lb/>efficitur in duplo minꝰ dēſum, et per ↄ̨ñs efficitur in <lb/>duplo maiꝰ, et acq̇rit vnū pedale, b. vero cū deꝑdat <lb/>duos g̈dus denſitatis et ſit vt octo, deꝑdit ꝓporti-<lb/>onē ſexq̇tertia denſitatis, et ſic efficit̄̄ in ſexq̇tertio <lb/>maiꝰ, et per ↄ̨ñs acq̇rit vnã tertiã pedalis: et aliud <lb/>rariꝰ acq̇rit vnū pedale / vt dictū eſt: igr̄ maiorē quã­<lb/>titatē acq̇rit rarius ꝙ̄ denſius eq̈le qñ et eque velo-<lb/>citer rarefiūt: quod fuit ꝓbandū. </s>
              <s xml:id="N21EC7" xml:space="preserve">Et hec ferme ſunt <lb/>ex ſubtili minerua               <anchor type="note" xlink:href="note-0183-03" xlink:label="note-0183-03a"/>               </s>
              <s xml:id="N21ED1" xml:space="preserve">Calculatoris excerpta qui mul-<lb/>ta alia in has tres opiniones argumenta coniecit <lb/>que apud eum poteris conſpicere.</s>
            </p>
            <div xml:id="N21ED8" level="5" n="19" type="float">
              <note position="right" xlink:href="note-0183-03a" xlink:label="note-0183-03" xml:id="N21EDC" xml:space="preserve">calcula.</note>
            </div>
            <note position="right" xml:id="N21EE2" xml:space="preserve">cõmē. 7. <lb/>phi. c. 15.</note>
            <p xml:id="N21EE8">
              <s xml:id="N21EE9" xml:space="preserve">In oppoſitum arguit̄̄ / pro prima opi-<lb/>nione auctorttate cõmentatoris ſeptimo phiſicorū <lb/>cõmenento quindecimo vt ſuperius allegatum ē. </s>
              <s xml:id="N21EF0" xml:space="preserve">Itē <lb/>raritas et denſitas videntur effectus qualitatū pri­<lb/>marum: igitur ſunt qualitates ſecunde.</s>
            </p>
            <p xml:id="N21EF7">
              <s xml:id="N21EF8" xml:space="preserve">Pro ſecunda opinione arguit̄̄ ſic / ſem­<lb/>per ad inductionē raritatis ſequitur acquiſitio ali­<lb/>cuius poſitiui puta quantitatis: igitur raritas eſt <lb/>quoddã poſitiuuꝫ. </s>
              <s xml:id="N21F01" xml:space="preserve">Colorat̄̄ ↄ̨ña / q2 nullū priuatiuū <lb/>neceſſario eſt cauſa alicuiꝰ poſitiui: hoc eſt nõ eſt ne­<lb/>ceſſe  ad priuationē alicuiꝰ poſitiui ſequat̄̄ neceſ-<lb/>ſario neceſſitate ſimpliciter acq̇ſitio alteriꝰ poſitiui / <lb/>g̊ ſi raritas eſſet ſiue diceret̄̄ priuatiue: nun̄ ad ac­<lb/>q̇ſitionē eiꝰ neceſſario ſimpliciter ſeq̄retur acq̇ſitio <lb/>quãtitatis aut alicuiꝰ alteriꝰ poſitiui.               <anchor type="note" xlink:href="note-0183-04" xlink:label="note-0183-04a"/>               </s>
              <s xml:id="N21F15" xml:space="preserve">¶ Et ↄ̨firmat̄̄ <lb/>hoc inductiue nun̄ enim ad acquiſitionem ſilentii / <lb/>ſequitur neceſſario acquiſitio alicuius poſitiui: nec <lb/>ad acquiſitionem tenebrarum, nec ad acquiſitionē <lb/>paruitatis: et ſimiliter remiſſionis: et ſic de ſingu-<lb/>lis priuatiuis: igitur ſi raritas eſſꝫ priuatiuū nõ ne­<lb/>ceſſario ad acquiſitionem raritatis ſequeretur ac-<lb/>quiſitio alicuiꝰ poſitiui </s>
              <s xml:id="N21F26" xml:space="preserve">Patet hec cõſequentia a ſi­<lb/>mili. </s>
              <s xml:id="N21F2B" xml:space="preserve">¶ Pro tertia opinione non arguo / quia nõ in-<lb/>tendo ea deffenſare quamuis forte ſit deffēſabilis.</s>
            </p>
            <div xml:id="N21F30" level="5" n="20" type="float">
              <note position="right" xlink:href="note-0183-04a" xlink:label="note-0183-04" xml:id="N21F34" xml:space="preserve">cõfirma.</note>
            </div>
            <p xml:id="N21F3A">
              <s xml:id="N21F3B" xml:space="preserve">Pro ſolutione huius dubitationis ad­<lb/>uertendum eſt  cum occurrit contrapugnantia et <lb/>opinionum diuerſitas de entitate alicuius rei tunc <lb/>diuerſimode opinantes diuerſas talis rei couſtitu­<lb/>unt diffinitiões. </s>
              <s xml:id="N21F46" xml:space="preserve">et proprietates vt cū occurrit diffi-               <pb chead="De motu rarefactionis  condenſationis." file="0184" n="184"/>               <anchor type="note" xlink:href="note-0184-01" xlink:label="note-0184-01a"/>               cultas de cõplexe ſignificabilibꝰ an ſint ētia in reꝝ <lb/>natura exiſtentia, an ſint entia largo modo capi-<lb/>endo eo modo quo latius Gregoriꝰ de arimino hãc <lb/>materiã in primo ſententiaꝝ diſquirit: oportet  <lb/>hi qui opinant̄̄ cõplexe ſignificabilia eſſe vere entia <lb/>realia q̄ ſignificantur ꝑ extrema ꝓpoſitionis alio <lb/>modo diffiniant cõplexe ſignificabilia ꝙ̄ hi qui opi­<lb/>nantur ea nõ eſſe vere et realiter entia. </s>
              <s xml:id="N21F61" xml:space="preserve">Et ſiĺr dicen­<lb/>dum eſt de diuerſitate opinionū inquirentiū enti-<lb/>tatē ſecundaꝝ intentionū.               <anchor type="note" xlink:href="note-0184-02" xlink:label="note-0184-02a"/>               </s>
              <s xml:id="N21F6D" xml:space="preserve">Scotꝰ em̄ diceret / ſcḋam <lb/>intentionē eſſe obiectiue in intellectu, nec eſſe crea-<lb/>turã aut creatorē. </s>
              <s xml:id="N21F74" xml:space="preserve">Noīalis vero diceret ſcḋam intē­<lb/>tionē eſſe terminū, et eſſe vere ens creatorē, aut cre-<lb/>turã. </s>
              <s xml:id="N21F7B" xml:space="preserve">Nec noīalis admitteret diffinitionē realis <lb/>aut eo cõtra, ſi debeat ſerio reſpondere. </s>
              <s xml:id="N21F80" xml:space="preserve">Et idē di-<lb/>cendū eſt de quãtitate quã realis dffinit eſſe acci-<lb/>dens inherens ſubſtantie nullo pacto eſſe ſubſtan-<lb/>tiã. </s>
              <s xml:id="N21F89" xml:space="preserve">Noīalis vero eocõtra oppoſitã diffinitionem <lb/>quãtitati aſſcribit. </s>
              <s xml:id="N21F8E" xml:space="preserve">Idē dicendū eſt de paternitate / <lb/>quã realis diffinit eſſe accidens reſpectiuū intrin-<lb/>ſecus diſtinctū a patre. </s>
              <s xml:id="N21F95" xml:space="preserve">Noīalis vero dicit paterni­<lb/>tatē eſſe patrē / qui de ſubſtantia ſua genuit filiū: et <lb/>ꝓfecto ſi realis admitteret diffinitionē noīalis ne­<lb/>qua̄ poſſet contradictionē euadere. </s>
              <s xml:id="N21F9E" xml:space="preserve">Eocõtra vero <lb/>de noīalibꝰ cenſendū eſt. </s>
              <s xml:id="N21FA3" xml:space="preserve">Ex quibꝰ ꝑſpicuū euadet <lb/>opere preciū eſſe cū controuerſia et opinionuū repu-<lb/>gnantia de rerū entitate interuenerit ſiue occurre­<lb/>rit ꝑ opinionū varietate varias diffinitiões cude-<lb/>re. </s>
              <s xml:id="N21FAE" xml:space="preserve">Ex quo clare deducitur in hac opinionū varie-<lb/>tate circa entitatē raritatis et denſitatis neceſſe eē <lb/>ꝑ opinionū varietate varias raritatis et denſita-<lb/>tis deſcriptiones aſſignare. </s>
              <s xml:id="N21FB7" xml:space="preserve">Primã em̄ opinionē <lb/>aut ſcḋam diffinitionibus quarte vti, eſſet perinde <lb/>at nominalē in cõtrouerſia de relatione an a fū-<lb/>damento diſtinguat̄̄ realiū diffinitionē aſſumere. <lb/>               <anchor type="note" xlink:href="note-0184-03" xlink:label="note-0184-03a"/>               </s>
              <s xml:id="N21FC7" xml:space="preserve">His em̄ diffinitionibꝰ aſſumptis facile ad cõtradi-<lb/>ctionē duceret̄̄. </s>
              <s xml:id="N21FCC" xml:space="preserve">Dico igr̄ ad ꝓpoſitū accedendo /  <lb/>ſcḋm primã opinionē q̄ ponit raritatē et denſitatē <lb/>eſſe qualitates oportet ſic diffinire: raritas eſt que­<lb/>dam qualitas qua aliquid denoīatur rarū ſiue na­<lb/>tum eſt denoīari. </s>
              <s xml:id="N21FD7" xml:space="preserve">rarū o eſt res habens raritatē <lb/>denominantē ipſam rarã. </s>
              <s xml:id="N21FDC" xml:space="preserve">denſitas vero eſt aliqua <lb/>qualitas qua aliquid denoīatur denſum ſiue natū <lb/>eſt denoīari: denſum quidē eſt res habens denſita­<lb/>tem denoīanteꝫ ipſam denſã.               <anchor type="note" xlink:href="note-0184-04" xlink:label="note-0184-04a"/>               </s>
              <s xml:id="N21FEA" xml:space="preserve">¶ Ex quo ſequit̄̄ pri-<lb/>mo /  ſi ſit vnū pedale habens quatuor gradus ra­<lb/>ritatis hoc eſt illius qualitatis: et habeat in tri-<lb/>plo plus de materia quã aliud pedale quod habet <lb/>duos gradus eiuſdē qualitatis illud quod habet <lb/>in triplo plus de materia eſt magis rarū in duplo <lb/>               <anchor type="note" xlink:href="note-0184-05" xlink:label="note-0184-05a"/>               </s>
              <s xml:id="N21FFE" xml:space="preserve">¶ Ex quo ſequit̄̄ ſecūdo hanc ↄ̨ñam nõ valere ſcḋm <lb/>hanc opinionē: iſta duo ſunt equalia et vnū illoruꝫ <lb/>habet in quadruplo plus de materia ꝙ̄ aliud: ergo <lb/>illud eſt in duplo denſius ꝙ̄ aliud, qm̄ hec opinio <lb/>nullo modo aſpicit materiã: ſed preciſe gradus il-<lb/>lius qualitatis q̄ eſt denſitas ſiue raritas.               <anchor type="note" xlink:href="note-0184-06" xlink:label="note-0184-06a"/>               </s>
              <s xml:id="N22010" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio /  hec ↄ̨ña nichil valet ſecundū hãc opinionē <lb/>hoc pedale hꝫ multū de materia ſub modica quã-<lb/>titatē: g̊ eſt denſuꝫ qm̄ poſſibile eſt  habeat multã <lb/>materiã: et nullã denſitatē habeat: quare nõ erit dē­<lb/>ſum / vt ptꝫ ex diffinitiõe data. </s>
              <s xml:id="N2201D" xml:space="preserve">Et dicas /  ibi argr̄ <lb/>a diffinitione ad diffinitū negat illud hec opinio: <lb/>qm̄ oīno eodē mõ ↄ̨ſiderat de raritate et dēſitate et <lb/>a caliditate et frigiditate.               <anchor type="note" xlink:href="note-0184-07" xlink:label="note-0184-07a"/>               </s>
              <s xml:id="N2202B" xml:space="preserve">¶ Seq̇t̄̄ q̈rto aliqḋ peda­<lb/>le eſſe  nec eſt rarū ne denſum ptꝫ de illo pedali <lb/>in quo ſunt quatuor gradus raritatis et quatuor <lb/>gradus denſitatis. </s>
              <s xml:id="N22034" xml:space="preserve">ſūt em̄ raritas et denſitas cõ-<lb/>trarie qualitates ſuas denoīationes in gradibus <lb/>equalibꝰ equaliter extenſis īpedientes more aliaꝝ               <cb chead="De motu rarefactionis  condenſationis."/>               repugnãtiū qualitatū               <anchor type="note" xlink:href="note-0184-08" xlink:label="note-0184-08a"/>               </s>
              <s xml:id="N22043" xml:space="preserve">¶ Seq̇t̄̄ quīto /  ̄uis cõiter <lb/>ad acquiſitionē denſitatis ſequat̄̄ diminutio quã­<lb/>titatis et ad introductionē raritatis ſequatur aug­<lb/>mentatio quãtitatis vt in pluribꝰ: tñ nõ neceſſario <lb/>id quod condenſatur diminuit̄̄ aut id quod rarefit <lb/>augetur. </s>
              <s xml:id="N22050" xml:space="preserve">Rarefactio em̄ et cõdenſatio ſunt altera-<lb/>tiones, nec ſecundum illã opinionē eas neceſſario <lb/>inſequūtur augmentio et diminutio. </s>
              <s xml:id="N22057" xml:space="preserve">Quēadmodū <lb/>vt in pluribꝰ caliditas rarefacit et inducit extenſi-<lb/>onē quantitatis: et frigiditas diminuit in pluri­<lb/>bus quantitatē: nõ tñ neceſſario hoc fit, nec natura­<lb/>liter, nec ſimpliciter. </s>
              <s xml:id="N22062" xml:space="preserve">Stat em̄ aliqua calefieri et ↄ̨ti­<lb/>nuo magis et cõtinuo minorari: vt poſtea in dubio <lb/>quodã patebit.               <anchor type="note" xlink:href="note-0184-09" xlink:label="note-0184-09a"/>               </s>
              <s xml:id="N2206E" xml:space="preserve">¶ Sed inſequendo ſcḋam opinionē <lb/>diffinienda eſt ſic raritas: raritas eſt quedã quali-<lb/>tas qua aliquid dr̄ rarū vel que nata eſt rarū de-<lb/>noīare: rarū o eſt habēs raritatē ipſū denoīanē <lb/></s>
              <s xml:id="N22078" xml:space="preserve">Denſitas vero eſt raritas remiſſia eo modo quo di­<lb/>cimus remiſſionē eſſe qualitatē remiſſam: puta nõ <lb/>infinite intenſam. </s>
              <s xml:id="N2207F" xml:space="preserve">Denſum vero eſt habens rarita­<lb/>tem finitã denoīantē ipſum rarū.               <anchor type="note" xlink:href="note-0184-10" xlink:label="note-0184-10a"/>               </s>
              <s xml:id="N22089" xml:space="preserve">¶ Ex quo ſequit̄̄ / <lb/> eodē mods loquendū eſt ſecundū hanc opinionē <lb/>de raritate ſicut de intenſione, et de denſitate ſicut <lb/>de remiſſione.               <anchor type="note" xlink:href="note-0184-11" xlink:label="note-0184-11a"/>               </s>
              <s xml:id="N22097" xml:space="preserve">¶ Sequit̄̄ ſecūdo /  eodē modo ſecū­<lb/>dum hãc opinionē et precedentē raritas difformis <lb/>ad vniformitatē reducitur ſicut albedo difformis. <lb/>               <anchor type="note" xlink:href="note-0184-12" xlink:label="note-0184-12a"/>               </s>
              <s xml:id="N220A5" xml:space="preserve">¶ Sequit̄̄ tertio /  nõ repugnat ſecundū hanc opi-<lb/>nionē pedale habere infinitã materiã: et eſſe rarum <lb/>vt puta ſi habeat infinite intenſam raritatem. </s>
              <s xml:id="N220AC" xml:space="preserve">His <lb/>poſitis pono duas concluſiones.</s>
            </p>
            <div xml:id="N220B1" level="5" n="21" type="float">
              <note position="left" xlink:href="note-0184-01a" xlink:label="note-0184-01" xml:id="N220B5" xml:space="preserve">gregoriꝰ <lb/>de ari. 2. <lb/>ſentētia.</note>
              <note position="left" xlink:href="note-0184-02a" xlink:label="note-0184-02" xml:id="N220BF" xml:space="preserve">Scotus.</note>
              <note position="left" xlink:href="note-0184-03a" xlink:label="note-0184-03" xml:id="N220C5" xml:space="preserve">diffītiõeſ <lb/>m ṗmaꝫ <lb/>opiniõeꝫ</note>
              <note position="left" xlink:href="note-0184-04a" xlink:label="note-0184-04" xml:id="N220CF" xml:space="preserve">.1. correl.</note>
              <note position="left" xlink:href="note-0184-05a" xlink:label="note-0184-05" xml:id="N220D5" xml:space="preserve">2. correl.</note>
              <note position="left" xlink:href="note-0184-06a" xlink:label="note-0184-06" xml:id="N220DB" xml:space="preserve">.3. correl:</note>
              <note position="left" xlink:href="note-0184-07a" xlink:label="note-0184-07" xml:id="N220E1" xml:space="preserve">4. correĺ</note>
              <note position="right" xlink:href="note-0184-08a" xlink:label="note-0184-08" xml:id="N220E7" xml:space="preserve">.5. correl.</note>
              <note position="right" xlink:href="note-0184-09a" xlink:label="note-0184-09" xml:id="N220ED" xml:space="preserve">dtffīnitiõeſ <lb/>iuxta ſe-<lb/>cūdã opi­<lb/>nionem.</note>
              <note position="right" xlink:href="note-0184-10a" xlink:label="note-0184-10" xml:id="N220F9" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0184-11a" xlink:label="note-0184-11" xml:id="N220FF" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0184-12a" xlink:label="note-0184-12" xml:id="N22105" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N2210B">
              <s xml:id="N2210C" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N2210F" xml:space="preserve">Et ſi prima opinio <lb/>multa concedat que cõiter et paſſim negantur ipſa <lb/>tñ ꝓbabilis eſt. </s>
              <s xml:id="N22116" xml:space="preserve">Prima pars ptꝫ ex correlariis ſu-<lb/>pra ex ea inductis. </s>
              <s xml:id="N2211B" xml:space="preserve">ſecunda patꝫ per rationē in op-<lb/>poſitū adduciã: et tertia vcꝫ  ſit facile ſuſtentabi-<lb/>lis patebit ſoluendo rationes qui ei aduerſantur.</s>
            </p>
            <p xml:id="N22122">
              <s xml:id="N22123" xml:space="preserve">Secūda concluſio. </s>
              <s xml:id="N22126" xml:space="preserve">Secunda opinio <lb/>licꝫ videatur extranea ex eo q2 in diſſuetudinē abiit <lb/>tñ ipſa ꝓbalitate fulcitur et deffenſatur. </s>
              <s xml:id="N2212D" xml:space="preserve">Prima <lb/>pars ex ſe ptꝫ ſaltē diebꝰ noſtris. </s>
              <s xml:id="N22132" xml:space="preserve">Secūda autē in <lb/>argumento in oppoſitū coloratur. </s>
              <s xml:id="N22137" xml:space="preserve">Et ſic ptꝫ / quid <lb/>dicendū ſit ad dubiū /  vcꝫ due prime opiniones ꝓ­<lb/>babiles et ſuſtētabiles ſunt. </s>
              <s xml:id="N2213E" xml:space="preserve">De tertia o nichil ad <lb/>preſens dico ꝓpter eas ꝓpoſitiones quas addit <lb/>q̄ nõ multū coherent vt argumenta in eã oſtendunt</s>
            </p>
            <p xml:id="N22145">
              <s xml:id="N22146" xml:space="preserve">Ad argumenta ante oppoſitū contra <lb/>primã opinionē. </s>
              <s xml:id="N2214B" xml:space="preserve">Ad primū reſpondebitur in calce <lb/>queſtiõis: vbi dicetur ad argumenta in oppoſitum <lb/>q̄ſtionis principalis. </s>
              <s xml:id="N22152" xml:space="preserve">¶ Ad ſecundū reſpondeo cõ-<lb/>cedendo ſequelã: et negando falſitate cõſequētis <lb/>et ad ꝓbationē nego conſequentiã: et cū ꝓbatur ꝑ <lb/>locū a diffinitione nego illã eſſe diffinitionē vt di-<lb/>ctum eſt. </s>
              <s xml:id="N2215D" xml:space="preserve">et ꝓfecto videtur michi illam diffinitionē <lb/>etiam ſecundū quartã opinionē nõ esse ſufficientē: <lb/>qm̄ ſequeretur nullū accidens aut formã ſubſtan-<lb/>tialē poſſe rarefieri nec etiam quãtitatē: licet diſtī­<lb/>guatur a re quanta qm̄ talia nullã materiã conti-<lb/>nent: niſi velis ꝓterue dicere aliqua rarefieri poſſe <lb/>que rara eſſe nõ poſſunt: ſed dubio ꝓcul cõueniens <lb/>eſt vt ea que rarefiãt etiã rara dicãtur. </s>
              <s xml:id="N2216E" xml:space="preserve">¶ Ad tertiū <lb/>negatur ſequela, et ad ꝓbationē admitto caſum, et <lb/>concedo illud corpus eſſe infinite raꝝ perinde at <lb/>concederetur illud eſſe infinite album ſi ſic haberet <lb/>infinitam albedinē ſuo ī permixtã contrario: et ne-<lb/>go illud eſſe denſum: et ad ꝓbationē nego cõſequē-<lb/>tiam nec ibi argr̄ a diffinitiõe ad diffinitū / vt dictū <lb/>eſt </s>
              <s xml:id="N2217F" xml:space="preserve">¶ Ad quartū quod eſt coutra ſecuudã opinionē               <pb chead="Tertii tractatus" file="0185" n="185"/>               reſondeo negando ſequelã, et ad ꝓbationē ↄ̨cedo <lb/>añs: et nego conſequentiã: non em̄ maioris coloris <lb/>aut apparentie eſt illa ↄ̨ña  iſta in quolibet ma-<lb/>gno eſt īfinita paruitas / g̊ quodlibet magnū eſt īfi-<lb/>nite paruū, vel ꝙ̄ iſta in quolibet intenſo eſt īfini-<lb/>ta remiſſio capiendo ly īfinitū ſyncathegoreuma-<lb/>tice: g̊ quodlibet īfinitū eſt īfinite remiſſum: ſed ille <lb/>cõſequētie nichil valent / vt ſatis cõſtat: g̊ nec alte-<lb/>ra. </s>
              <s xml:id="N22197" xml:space="preserve">Ad quintū / quod eſt cõtra ſecundã opinionē re-<lb/>ſpõdeo cõcedendo ſequelã vt bene ꝓbat argumen-<lb/>tum, et negando falſitatē conſequentis. </s>
              <s xml:id="N2219E" xml:space="preserve">Cēſere em̄ <lb/>aut iudicare aliquid eſſe minus aut magis rarum <lb/>ſecundū hanc opinionē ex maioritate aut minorita­<lb/>te quantitatis ſtante eadē materia: eſt a principio <lb/>huiꝰ opinionis plurimū deuiare. </s>
              <s xml:id="N221A9" xml:space="preserve">Si tñ tu velis in-<lb/>telligere per rarefactionē, rarefactionē totius ſiue <lb/>īductionē raritatis qua totū rarefit, et ſic eo modo <lb/>nego iſtã ſequelã: qm̄ in caſu argumenti totū iſtud <lb/>corpus nõ rarefit: ſed efficitur minꝰ rarū vt bene ꝓ­<lb/>bat argumentū. </s>
              <s xml:id="N221B6" xml:space="preserve">Si vero ꝑ rarefactionē intelligas <lb/>rarefactionē partialē qua aliqua pars illiꝰ corpo­<lb/>ris acq̇rit aliquos gradus illius qualitatis que eſt <lb/>raritas, et ſic eo modo concedo tibi ſequelã vt con-<lb/>ceſſi: nec iſtud cõſequens videtur afferre maiꝰ incon­<lb/>ueniens ꝙ̄ iſtud (ſuppoſito  caliditas vt in pluri-<lb/>bus augmentat ſiue maior at quantitatē) aliquod <lb/>calidū ꝑ ſolã calefactionē ſiue inductionē calidita-<lb/>tis et motū cõſequētem vt in pluribꝰ inductionē ca-<lb/>liditatis qui motus eſt augmentio efficitur minus <lb/>calidū: ſed iſtud cõſequēs nõ eſt incõueniens / vt pro­<lb/>babitur: igr̄ nec aliud ꝓbatur mīor: et poſito  vna <lb/>medietas corporis bipedalis ſit calida vt .12. et alia <lb/>vt duo, et acq̇rat medietas calida vt duo duos gra­<lb/>dus caliditatis: ita vt efficiatur calida vt quatuor <lb/>alia medietate quieſcente: et efficiat̄̄ alia medietas <lb/>minꝰ calida qñ acq̇rit illos duos gradus in duplo <lb/>maior. </s>
              <s xml:id="N221DB" xml:space="preserve">quo poſito iſtud corpꝰ efficitur minꝰ calidū <lb/>̄ antea, et hoc ſolū ꝑ īductionē caliditatis et motū <lb/>vt in pluribꝰ cõſequentē inductionē caliditatis: igr̄ <lb/>ꝓpoſitū. </s>
              <s xml:id="N221E4" xml:space="preserve">Cõſequētia ptꝫ cū minore, et argr̄ maior: <lb/>q2 iſtud corpus in principio inductionis illiꝰ calidi­<lb/>tatis eſt calidū vt ſeptē, et in fine eſt calidū vt ſex cū <lb/>duabꝰ tertiis: vt ptꝫ ex mõ ꝓbãdi quarti argumēti <lb/>quod modo ſoliumꝰ: igr̄. </s>
              <s xml:id="N221EF" xml:space="preserve">Alio modo etiã põt nega­<lb/>ri ſequela ſimpliciter, et hoc ſi teneamꝰ intenſionē <lb/>qualitatis correſpondere ſuo gradui ſummo: qm̄ <lb/>id oportebit dicere ſecundū hanc opinionē de rari­<lb/>tate difformi: qm̄ ſecundū eã raritas qualitas eſt. <lb/></s>
              <s xml:id="N221FB" xml:space="preserve">¶ Ad ſextū / quod eſt etiã cõtra ſcḋam opinionē re-<lb/>ſpondeo negando ſequelã, et ad ꝓbationē admiſſo <lb/>caſu, concedo  in fine illud corpus manebit rarū <lb/>vt ſex: et nego  manebit rariꝰ ꝙ̄ ſit modo, et ad ꝓ-<lb/>bationē nego hanc cõſequentiã: maiorē quantita-<lb/>tem acq̇rit ꝙ̄ deꝑdit manente eadem materia: g̊ eſt <lb/>rariꝰ. </s>
              <s xml:id="N2220A" xml:space="preserve">Et ratio eſt: q2 intenſio raritatis nõ ſequitur <lb/>maiorationē ꝓportionis quantitatis ad materiã: <lb/>ſed ſequitur additionē gradus raritatis ſequētis <lb/>gradibꝰ p̄cedentibꝰ: ſicut fit de albedine et nigredīe <lb/></s>
              <s xml:id="N22214" xml:space="preserve">Rariꝰ autē m modū huiꝰ opinionis eſt illud  hꝫ <lb/>raritatē magis denominantē ipſum: ſiue habeat <lb/>plus de quantitate ſiue minꝰ nõ eſt cura. </s>
              <s xml:id="N2221B" xml:space="preserve">¶ Ad ſepti­<lb/>mū argumentū quod eſt cõtra tertiã opinionē cuiꝰ <lb/>fundamēta et prīcipia nõ exacte capio nõ reſpõdeo <lb/>nec decreui ad argumeuta eã expugnantia reſpon­<lb/>dere: nec illi opinioni ſuppetias dare.</s>
            </p>
            <p xml:id="N22226">
              <s xml:id="N22227" xml:space="preserve">Notandū eſt ſcḋo circa materiã ſecñ-<lb/>di argumenti principalis ante oppoſitū:  vt ex-<lb/>ſcrinio calculatorio in capite de raritate et denſita­               <cb chead="Capitulū primū."/>               te colligi põt (et quidē aperte) duplex eſt opinio ra-<lb/>tione fulcita: penes quid habeat attendi: et cõmen­<lb/>ſurari raritatis aut denſitatis maioritas. </s>
              <s xml:id="N22235" xml:space="preserve">quaruꝫ <lb/>prior eſt /  ipſa raritas attenditur penes ꝓporti-<lb/>onē quantitatis ſubiecti ad eiꝰ materiã et maiori-<lb/>tas raritatis penes maiorē ꝓportionē quantitatꝪ <lb/>ad materiã. </s>
              <s xml:id="N22240" xml:space="preserve">Denſitas autē penes ꝓportionē mate-<lb/>rie ad quantitatē, et eiuſdē raritas penes maiorem <lb/>ꝓportionē materie ad quantitatē (et loquor de pro­<lb/>portione maioris inequalitatis) </s>
              <s xml:id="N22249" xml:space="preserve">Exemplū vt ſi īter <lb/>quantitatē vniꝰ pedalis et ſuã materiã ſit ꝓportio <lb/>dupla illud eſt rarū: et ſi alteriꝰ pedalis quãtitatis <lb/>ad materiã eſſet ꝓportio maior dupla illud eſt ma­<lb/>gis rarū: q2 ꝓportio eſt maior: et ſi vniꝰ alteriꝰ pe-<lb/>dalis materie ad quantitatē eſt ꝓpoportio dupla <lb/>illud eſt denſum: et ſi ꝓportio materie ad quantita­<lb/>tem maioretur illud efficeretur denſius. </s>
              <s xml:id="N2225A" xml:space="preserve">Poſterior <lb/>autē opinio diiudicat raritatē penes quantitatem <lb/>in cõparationē ad materiã vel (vt verbis calculato­<lb/>riis loquar) in materia ꝓportionata. </s>
              <s xml:id="N22263" xml:space="preserve">differentiam <lb/>autē inter has duas opinationes talis ferme a cal­<lb/>culatore ſignatur loco preallegato: nã prima opi-<lb/>natio aſſeuerat ad duplationē raritatis non ſequi <lb/>duplationē quantitatis: nec ad ſexq̇alterationem <lb/>raritatis etiã ſequi quantitatē effici in ſexquialte­<lb/>ro maiorē: ſed dicit ad duplationem raritatis ſiue <lb/>ſexquialterioneꝫ ſequi duplationem proportio­<lb/>nis quãtitatis ad materiam ſiue ſexquialteratio-<lb/>nem et ſic de aliis proportionibus. </s>
              <s xml:id="N22278" xml:space="preserve">¶ Secunda vc-<lb/>ro aſſerit ſemper ad duplationem ſequi duplatio-<lb/>nem quantitatis: et ad triplationem raritatis ſe-<lb/>qui idemtidam triplationem quantitatis. </s>
              <s xml:id="N22281" xml:space="preserve">Exem-<lb/>plum vt eſto  vniꝰ pedalis ꝓportio quãtitatis ad <lb/>materiam ſit ſexq̇altera et dupletur eius raritas: <lb/>tunc ſecundū hanc opinionem eius quantitas non <lb/>efficitur in duplo maior (et ſi raritas ad duplum <lb/>maioretur) ſed duplatur ꝓportio quantitatis ad <lb/>materiã: ita  efficitur ꝓportio quantitatis ad ma­<lb/>teriam dupla ad ſexquialterã cuiuſmodi eſt ꝓpor-<lb/>tio dupla ſexq̇quarta qualis eſt nomē ad quatuor <lb/>et ſic illa quantitas effecta eſt in ſexquialtero ma-<lb/>ior vt pote pedalis cū dimidia. </s>
              <s xml:id="N22298" xml:space="preserve">Sed ſi tale pedale <lb/>ſecundū alteram opinionē efficitur in duplo rariꝰ <lb/>eius quantitas duplabitur et efficietur bipedalis: <lb/>et ſic ptꝫ /  ſecundã priorem opinionem  ad dupla­<lb/>tionē raritatis nõ ſequitur duplatio quantitatis. <lb/></s>
              <s xml:id="N222A4" xml:space="preserve">Secundū alterã vero ſemꝑ ſequitur duplatio quã­<lb/>titatis raritatis duplicationem. </s>
              <s xml:id="N222A9" xml:space="preserve">Et vt hec opinio <lb/>clarius intelligatur et eius fundamenta et baſes co­<lb/>gnoſcant̄̄. </s>
              <s xml:id="N222B0" xml:space="preserve">¶ Quero vtrū ipſa poſſit vera ſuſtētari.</s>
            </p>
            <p xml:id="N222B3">
              <s xml:id="N222B4" xml:space="preserve">Et argr̄ primo  nõ. </s>
              <s xml:id="N222B7" xml:space="preserve">Qm̄ ſi ipſa eſſet <lb/>a ſequeretur /  quelibet ꝓportio quantitatis ad <lb/>materiam certos gradus raritatis ꝓduceret ita  <lb/>vbicun eſſet proportio dupla quantitatis ad ma­<lb/>teriam: ibi eſſent certi gradus raritatis q̇ ſint duo <lb/>gratia exēpli et vbi eſſet ꝓportio quadrupla quã-<lb/>titatis ad materiã ibi eſſent in duplo plures gra-<lb/>dus raritatis. </s>
              <s xml:id="N222C8" xml:space="preserve">Et vbi eſſet ſexq̇altera ꝓportio quã-<lb/>titatis ad materiã: ibi eſſet raritas nata ꝓuenite a <lb/>ꝓportiõe ſexq̇altera que ſe habet ad raritatē natã <lb/>ꝓuenire a ꝓportione dupla ſicut ſe hꝫ ſexquialtera <lb/>ꝓportio ad ꝓportionē duplã: ſed hoc couſequens <lb/>eſt falſum: igr̄ et illud ex quo ſequitur. </s>
              <s xml:id="N222D5" xml:space="preserve">Sequela pro­<lb/>batur / qm̄ m hanc opinionē certa ꝓportio quãti-<lb/>tatis ad materiã certã raritatē ꝓducit: et in duplo <lb/>maior ꝓportio in duplo maiorē raritatē, et in ſexq̇­<lb/>altero maior ꝓportio ī ſexq̇altero maiorē rarita-<lb/>tem: igr̄ in quacū ꝓportione ſe hñt ꝓportiones               <pb chead="De motu rarefacttonis  condenſationis." file="0186" n="186"/>               quantitatis ad materiã in eadē ꝓportione ſe hñt <lb/>raritates ab eis producte, et ꝑ ↄ̨ñs a qualibet pro-<lb/>portione certa raritas nata eſt ꝓuenire  fuit pro-<lb/>bandū. </s>
              <s xml:id="N222ED" xml:space="preserve">Sed falſitas cõſequentis oſtenditur / q2 ſe-<lb/>queret̄̄ /  cū pedale in quo eſt ꝓportio quadrupla <lb/>quantitatis ad materiã, et tripedale in quo eſt du-<lb/>pla ꝓportio quãtitatis ad materiã augmētaret̄̄ <lb/>ad duplã quantitatē, eque velociter acq̇rerēt de ra­<lb/>ritate: ſed hoc videtur falſum. </s>
              <s xml:id="N222FA" xml:space="preserve">igr̄ et illud ex quo ſe­<lb/>quit̄̄. </s>
              <s xml:id="N222FF" xml:space="preserve">Falſitas cõſequentis oſtenditur: q2 cū illa pu­<lb/>ta tripedale et pedale augmentãtur ad duplã quã-<lb/>titatē: etiã augmentantur ad duplã raritatē q2 ſi-<lb/>cut quantitas efficitur maior ita etiã raritas ma-<lb/>nente eadē materia: ſed tripedale minorē raritatē <lb/>habebat ꝙ̄ pedale. </s>
              <s xml:id="N2230C" xml:space="preserve">et quodlibet illoꝝ acq̇ſiuit tantã <lb/>raritatē quantã habebat cū vtrū fuerit augmen-<lb/>tatū ad duplum: g̊ ſequitur /  maiorē raritatē acq̇-<lb/>ſiuit pedale quã tripedale: patꝫ hec ↄ̨ña: q2 qñ duo <lb/>inequalia efficiūtur in duplo maior a maiorē lati-<lb/>tudinē acquirit maiꝰ quã minꝰ: vt cõſtat. </s>
              <s xml:id="N22319" xml:space="preserve">Sed ſeque­<lb/>la probatur: q2 vtrū illoꝝ acq̇rit ꝓportionem du­<lb/>plam: g̊ ſequitur /  vtrū illoꝝ acq̇rit raritatē na­<lb/>tam prouenire a proportione dupla: ſed m iſtam <lb/>opinionē oīs raritas nata prouenire a proportiõe <lb/>dupla eſt equalis cuilibet nate ꝓuenire a quacū <lb/>proportione dupla: igr̄ propoſitū. </s>
              <s xml:id="N22328" xml:space="preserve">¶ Dices forte et <lb/>bene concedendo ſequelã et negando falſitatē con-<lb/>ſequentis: et ad probationē concedo ſequelã: et ne-<lb/>go falſitatē conſequentis et ad probationē falſita-<lb/>tis ↄ̨ñtis: nego hanc cõſequētiã hoc efficitur in du-<lb/>plo maiꝰ: g̊ in duplo rariꝰ: īmo vt m argumentuꝫ <lb/>ante oppoſitū prīcipalis queſtiõis oſtendit aliqñ <lb/>ſtat  aliqñ ad duplationē quantitatis ſequeatur <lb/>duplatio raritatis et aliqñ minor et aliqñ maior.</s>
            </p>
            <p xml:id="N2233B">
              <s xml:id="N2233C" xml:space="preserve">Sꝫ ↄ̨̨tra. </s>
              <s xml:id="N2233F" xml:space="preserve">Quia tunc ſequeret̄̄ /  qñ-<lb/>cun duo equalia quantitatiue, ſiue equalia, ſiue <lb/>inequalia in raritate equaliter acquirerēt de quã­<lb/>titate: ipſa equaliter rarefierent: ſed conſequens <lb/>eſt falſum: igr̄ et illud ex quo ſequitur. </s>
              <s xml:id="N2234A" xml:space="preserve">Falſitas cõ-<lb/>ſequentis probatur: q2 ſint duo corpora equalia <lb/>ī eque rara q̄ equales quãtitates acq̇rant: tūc eque <lb/>ꝓportionabiliter ſicut acq̇runt de quantitate acq̇-<lb/>runt de raritate: ſed equalē ꝓportionē acq̇runt de <lb/>quantitate: g̊ equaliter acq̇runt de raritate: et rari­<lb/>tas vniꝰ eſt minor ꝙ̄ raritas alterius: g̊ raritas mi­<lb/>nor mīorē latitudinē raritatꝪ acq̇rit  raritas ma­<lb/>ior: ptꝫ hec cõſequentia ꝑ hanc maximã. </s>
              <s xml:id="N2235D" xml:space="preserve">Qñcun <lb/>aliqua duo inequalia eque velociter ꝓportionabi­<lb/>liter maiorantur velociꝰ maiorat̄̄ maiꝰ in eodē tꝑe / <lb/>vt pꝫ ſi ſex et quatuor debeant ad ſexq̇alteꝝ maio­<lb/>rari eodem tꝑe adequate: tunc em̄ in tꝑe quo ſex ac­<lb/>quirit tria quatuor atq̇rit duo. / vt conſtat: ſed in ꝓ-<lb/>poſito. </s>
              <s xml:id="N2236C" xml:space="preserve">vtra illarū raritatū eque ꝓportionaliter <lb/>maiorat̄̄: g̊ maior raritas maiorē latitudinē rari-<lb/>tatis acq̇rat ꝙ̄ minor in eodē tꝑe. </s>
              <s xml:id="N22373" xml:space="preserve">Sed ſequela ꝓba­<lb/>tur qm̄ illa ſunt equalia, et equales quãtitates acq̇­<lb/>runt: igr̄ equales ꝓportiones, et vltra equales pro­<lb/>portiones: g̊ equales raritates ptꝫ cõſequentia: q2 <lb/>ab equalibꝰ ꝓportionibus quãtitatis ad materiã <lb/>equales raritates nate ſunt prouenire: vt patet ex <lb/>opinione et reſponſione: igitur.</s>
            </p>
            <p xml:id="N22382">
              <s xml:id="N22383" xml:space="preserve">Scḋo ad idē argr̄ ſic. </s>
              <s xml:id="N22386" xml:space="preserve">Si illa poſitio <lb/>eſſet vera ſequeretur /  oporteret ſignare gradꝰ in <lb/>quantitate, et etiã in materia: ſed hoc eſt falſū: igr̄ <lb/>illud ex quo ſeq̇tur. </s>
              <s xml:id="N2238F" xml:space="preserve">Falſitas ↄ̨ñtis oſtēditur: qm̄ nec <lb/>quantitas, nec materia ſuſcipiant magis et minus / <lb/>igr̄ nõ habent gradus. </s>
              <s xml:id="N22396" xml:space="preserve">Sed ſeq̄la ꝓbatur / qm̄ rari-<lb/>tas et raritatꝪ maioritas penes ꝓportionē quãti-               <cb chead="De motu rarefactionis  condenſationis."/>               tatis ad materiã d3 ſumi: vt dicit opinio et dēſitas <lb/>eocontra penes ꝓportionē materia ad quantitatē / <lb/>g̊ oportet quãtitatē materiã exuperare cū aliquid <lb/>rarū dicit̄̄: et materiã quantitatē excedere cū aliq̇d <lb/>denſum efficitur: ſed nun̄ quantitas exuperat ma­<lb/>teriam extenſiue: q2 ſunt equalis extenſionis: igit̄̄ <lb/>oportet /  exuperet intenſiue: q2 alias nun̄ erit ꝓ-<lb/>portio maioris inequalitatis quantitatis ad ma-<lb/>teriã vel econtra.               <anchor type="note" xlink:href="note-0186-01" xlink:label="note-0186-01a"/>               </s>
              <s xml:id="N223B3" xml:space="preserve">¶ Dices et bene concedendo ſeque­<lb/>lam, ꝑ gradus quantitatis nõ intelligendo gradꝰ <lb/>intenſionis quãtitatis: ſed intelligendo certas ꝓ-<lb/>portiones quantitatis vt puta  vna quarta peda­<lb/>lis ſit vnus gradus quantitatis: et vna octaua pe-<lb/>dalis medietas vniꝰ gradus quantitatis etc̈. vnus <lb/>vero gradus materie ſit certa portio materie vtpo­<lb/>te tanta quãta eſt in vna octaua vniꝰ pedalis terre <lb/>exiſtēs in ſua naturali diſpoſitione quod (exēpli <lb/>gratia dico) capias em̄ ꝓ libito quãtū volueris de <lb/>materia ꝓ vno gradu, et etiã de quantitate ſicut di­<lb/>cimus de gradibꝰ qualitatis: et m hoc negetur fal­<lb/>ſitas conſequētis, et concedat̄̄  nec quantitas: nec <lb/>materia ſuſcipiūt magis et minꝰ: cū hoc tñ ſtat  et <lb/>ſi quantitas nõ hꝫ gradus intentionales hꝫ tñ extē­<lb/>ſionales. </s>
              <s xml:id="N223D4" xml:space="preserve">et ſimiliter ̄uis materia nõ hꝫ gradus in­<lb/>tenſionales hꝫ tñ gradus entitatiuos qui ſunt par­<lb/>tes ipſius materie vt declarant cõiter hanc mate-<lb/>riam de raritate et denſitate tractantes.</s>
            </p>
            <div xml:id="N223DD" level="5" n="22" type="float">
              <note position="right" xlink:href="note-0186-01a" xlink:label="note-0186-01" xml:id="N223E1" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N223E7">
              <s xml:id="N223E8" xml:space="preserve">Sed cõtra. </s>
              <s xml:id="N223EB" xml:space="preserve">Quia tunc ſequeretur /  <lb/>nullū rarū eſſet denſuꝫ: ſed hoc eſt falſum: igr̄ illud <lb/>ex quo ſequitur. </s>
              <s xml:id="N223F2" xml:space="preserve">Falſitas ↄ̨ñtis oſtēditur, q2 capto <lb/>vno denſo finite benſo, illud eſt rarū: igr̄. </s>
              <s xml:id="N223F7" xml:space="preserve">Probat̄̄ <lb/>añs, q2 illud ſub magna quantitate continet parū <lb/>de materia: igr̄ eſt rarum, ptꝫ ex diffinitione rari. <lb/></s>
              <s xml:id="N223FF" xml:space="preserve">Sed iam ꝓbo ſequelã, qm̄ ſi aliquid eſt rarū in eo <lb/>quantitas ſe hꝫ in ꝓportiõe maioris inequalitatis <lb/>ad materiã, et ſi ipſum eſſet denſum in eo materia <lb/>ſe hꝫ in ꝓportione maioris in inequalitatis ad quã-<lb/>titatē: ſed īpoſſibile eſt  in eodē ſaltem exiſtēte in <lb/>eodē loco etc̈. quantitas excedat materiam, et exce-<lb/>datur ab ea: igr̄ īpoſſibile eſt  aliquid ſit rarum et <lb/>denſum: quod fuit ꝓbandū.               <anchor type="note" xlink:href="note-0186-02" xlink:label="note-0186-02a"/>               </s>
              <s xml:id="N22415" xml:space="preserve">¶ Dices et bene conce-<lb/>dendo ſequelã (vt hec opinio eã concedit) et negãdo <lb/>falſitatē ↄ̨ñtis, et ad ꝓbattonē negando hanc con-<lb/>ſequentiam in hoc corpore eſt modica materia ſub <lb/>magna quantitate: g̊ hoc eſt rarum, nec ibi argr̄ a <lb/>diffinitiõe ad diffinitū: ſed oportet dicere vt poſtea <lb/>clarius et latius dicetur in hoc corpore quantitas <lb/>excedit materiam, et hꝫ ad materiam ꝓportionem <lb/>maioris inequalitatis: igitur illud corpus eſt rarū / <lb/>et ſic conſequentia eſt bona.</s>
            </p>
            <div xml:id="N2242A" level="5" n="23" type="float">
              <note position="right" xlink:href="note-0186-02a" xlink:label="note-0186-02" xml:id="N2242E" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N22434">
              <s xml:id="N22435" xml:space="preserve">Sed contra. </s>
              <s xml:id="N22438" xml:space="preserve">Quia tunc ſequeret̄̄ hec <lb/>concluſio aliquod corpus naturale, nec eſt rarum <lb/>nec denſum naturaliter. </s>
              <s xml:id="N2243F" xml:space="preserve">Seq̄la ꝓbatur / q2 capio a. <lb/>pedale in cuiꝰ qualibet quarta eſt vnꝰ gradus ma-<lb/>terie: quo poſito ibi inter materiã et quantitatē eſt <lb/>ꝓportio equalitatis: igr̄ ibi gradus quãtitatis nõ <lb/>excedūt gradus materie. </s>
              <s xml:id="N2244A" xml:space="preserve">igr̄ tale pedale nõ eſt raꝝ <lb/>nec gradus materie excedūt gradus quantitatis: <lb/>igr̄ nõ eſt denſum: igr̄ aliquod pedale eſt  nec eſt <lb/>rarū nec eſt denſum / quod fuit probandū. </s>
              <s xml:id="N22453" xml:space="preserve">Falſitas <lb/>ↄ̨ñtis oſtenditur / q2 tale pedale hꝫ certã materiam <lb/>ſub certa quantitate puta paruã materiã ſub ma-<lb/>gna quantitate: igr̄ illud eſt rarū.               <anchor type="note" xlink:href="note-0186-03" xlink:label="note-0186-03a"/>               </s>
              <s xml:id="N22461" xml:space="preserve">¶ Dices et bene <lb/>concedendo quod infertur.</s>
            </p>
            <div xml:id="N22466" level="5" n="24" type="float">
              <note position="right" xlink:href="note-0186-03a" xlink:label="note-0186-03" xml:id="N2246A" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N22470">
              <s xml:id="N22471" xml:space="preserve">Sed contra. </s>
              <s xml:id="N22474" xml:space="preserve">Quia tunc ſequeretnr / <lb/> bipedale ī cuiꝰ vna medietate eſt ꝓportio dupla <lb/>quãtitatis ad materiã et iu alia eſt ꝓportio eq̈lita-               <pb chead="Tertii tractatus" file="0187" n="187"/>               tis quantitatis ad materiã eſſet rarū: et bipedale <lb/>in cuiꝰ vna medietate eſſet ꝓportio dupla quãtita-<lb/>tis ad materiã et in alia eſſet ꝓportio dupla mate-<lb/>rie ad quantitatē eſſet denſum et nõ rarū et bipeda­<lb/>le in cuiꝰ vna medietate eſſet ꝓportio dupla quan-<lb/>titatis ad materiã: et in alia eſſe ꝓportio ſexq̇al-<lb/>ra materie ad quantitatē nec eſſet rarū nec denſuꝫ / <lb/>ſed cõſequēs videtur falſum: igr̄ illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N2248F" xml:space="preserve">Seq̄la ꝓbatur / qm̄ ſi in vna medietate bipedalis eſt <lb/>ꝓportio dupla quantitatis ad materiaꝫ: et in alia <lb/>ꝓportio equalitatis cū vtra medietas bipedalis <lb/>ex dictis habeat quatuor gradus quantitatis: ſe-<lb/>quitur /  vna medietas illiꝰ bipedalis hꝫ duos g̈dꝰ <lb/>materie, et altera .4. / et ꝑ ↄ̨ñs totum illud bipedale <lb/>hꝫ ſex gradus materie et hꝫ .8. quãtitatis: g̊ in eo eſt <lb/>ꝓportio maioris inequalitatis quãtitatis ad ma-<lb/>teriã / et ꝑ ↄ̨ñs ipſū eſt rarū / et ſic ptꝫ prima pars illa­<lb/>ti. </s>
              <s xml:id="N224A4" xml:space="preserve">Secūda pars ꝓbatur / qm̄ ſi vna medietas bipe-<lb/>dalis ita ſe hꝫ  in ea eſt ꝓportio dupla quautita-<lb/>tis ad materiã, et in reliqua materie ad quantitatē <lb/>et vtra medietas bipedalis hꝫ q̈tuor gradꝰ quãti­<lb/>tatis / ſequit̄̄ /  vna medietas illiꝰ bipedalis habet <lb/>duos gradus materie et reliqua hꝫ octo: et ꝑ conſe-<lb/>quens materia illiꝰ bipedalis eſt vt decē, et quanti-<lb/>tas eſt vt octo: igr̄ in hoc bipedali eſt ꝓportio ma-<lb/>ioris inequalitatis materie ad quantitatē hoc igr̄ <lb/>fidē facit illud bipedale denſum eſſe. </s>
              <s xml:id="N224B9" xml:space="preserve">Et ꝑ hoc etiaꝫ <lb/>ptꝫ tertia pars: qm̄ in tali bipedali (ſi bene calcula­<lb/>ueris) reperies octo gradus materie gradibꝰ quã-<lb/>titatꝪ equari. </s>
              <s xml:id="N224C2" xml:space="preserve">Quare illud bipedale nec rarum nec <lb/>denſum erit / quod fuit ꝓbãdū. </s>
              <s xml:id="N224C7" xml:space="preserve">Sed iã ꝓbo falſita­<lb/>tem cõſequentis: qm̄ illud bipedale in cuiꝰ vna me-<lb/>dietate eſt dupla ꝓportio quantitatis ad materiã <lb/>et in alia eſt dupla ꝓportio materie ad quantitatē <lb/>hꝫ vnã medietatē rarã vt duo: et aliū denſaꝫ vt duo <lb/>volo em̄ /  ꝓportio dupla nata ſit ꝓducere rarita­<lb/>tem vt duo, et etiã denſitatē vt duo </s>
              <s xml:id="N224D6" xml:space="preserve">Nec valet hoc ne­<lb/>gari: q2 aliqua ꝓportio nata eſt ꝓducere raritateꝫ <lb/>vt duo: et aliqua denſitatē vt duo: ponãtur igr̄ ille <lb/>ꝓportiones in illis medietatibꝰ et ſic ſemꝑ ꝓcedit <lb/>argumentū: igr̄ illud bipedale nec eſt rarū, nec dē-<lb/>ſum. </s>
              <s xml:id="N224E3" xml:space="preserve">Ptꝫ hec cõſequētia a ſimili: qm̄ ſi vniꝰ bipeda­<lb/>lis vna medietas eſſet calida vt duo et altera frigi-<lb/>da vt duo: illud nec eſſet calidum nec frigidum. </s>
              <s xml:id="N224EA" xml:space="preserve">Et <lb/>ſic facile eſt inferre oppoſitum aliarum partium.</s>
            </p>
            <p xml:id="N224EF">
              <s xml:id="N224F0" xml:space="preserve">Tertio ad idē argr̄. </s>
              <s xml:id="N224F3" xml:space="preserve">Si hec opinio eēt <lb/>vera ſeq̄retur /  rarum difformiter difforme cuius <lb/>vtra medietas eſſet vniformis nõ correſponderet <lb/>ſuo gradui medio: ſed cõſequēs eſt falſum: igr̄ illud <lb/>ex quo ſequitur. </s>
              <s xml:id="N224FE" xml:space="preserve">Falſitas cõſequētis oſtenditur: q2 <lb/>oē qualificatū vniformiter difforme correſpondet <lb/>ſuo gradui medio: et etiã difformiter difforme cuiꝰ <lb/>vtra medietas eſt vniformis: igr̄ a ſimili ita d3 <lb/>eſſe ꝓpoſito. </s>
              <s xml:id="N22509" xml:space="preserve">Seq̄la ꝓbatur. </s>
              <s xml:id="N2250C" xml:space="preserve">et capio vnū bipedale <lb/>in cuiꝰ vna medietate ſit ꝓportio dupla quãtitatis <lb/>ad materiã, et in alia medietate ſit ꝓportio quadru­<lb/>pla, et volo /  ꝓportioni dupla correſpondeãt duo <lb/>gradus raritatis, et ex hoc quadruple quatuor: ita <lb/> vna medietas ſit rara vt duo, et alia vt quatuor <lb/></s>
              <s xml:id="N2251A" xml:space="preserve">Quo poſito ſic argumentor: illud bipedale eſt dif-<lb/>formiter difforme cuiꝰ vtra medietas eſt vnifor-<lb/>mis, et eiꝰ raritas nõ correſpondet ſuo gradui me-<lb/>dio: igr̄ ꝓpoſitū. </s>
              <s xml:id="N22523" xml:space="preserve">Argr̄ minor / qm̄ ſi eiꝰ raritas cor-<lb/>reſponderet ſuo gradui medio: ipſa eſſet vt tria vt <lb/>ſatis ptꝫ, nã gradus vt tria eſt medius inter q̈tuor <lb/>et duo: ſed hoc eſt falſum: igr̄. </s>
              <s xml:id="N2252C" xml:space="preserve">Cuiꝰ cõſequētis falſi-<lb/>tas oſtenditur qm̄ raritas vt tria q̄ eſt ſexquialtera <lb/>ad raritatē vt duo correſpondet ꝓportioni ſexq̇al­<lb/>tere ad ꝓportionē duplã que ꝓportio ſexquialtera               <cb chead="Capitulū primū."/>               vcꝫ ad duplã eſt ꝓportio irrationalis / vt ptꝫ ex ſecū­<lb/>da parte huiꝰ operis: ſed quãtitatis illiꝰ bipedalis <lb/>ad ſuã materiã nõ eſt ꝓportio irrationalis que eſt <lb/>ſexquialtera ad duplã: g̊ ſequitur /  raritas illius <lb/>bipedalis nõ eſt vt tria. </s>
              <s xml:id="N22540" xml:space="preserve">Ptꝫ hoc cõſequentia / qm̄ ra­<lb/>ritas vt tria non eſt nata ꝓuenire niſi a ꝓportione <lb/>ſexquialtera ad duplã. </s>
              <s xml:id="N22547" xml:space="preserve">Secundū / em̄ hanc opinio-<lb/>nē in quacū ꝓportione ſe habent raritates ad in­<lb/>uicē in eadē ꝓportione ſe habent ꝓportiones a qui­<lb/>bus ꝓueniūt. </s>
              <s xml:id="N22550" xml:space="preserve">Sed iam ꝓbo /  quantitatis illiꝰ bi-<lb/>pedalis ad ſuã materiã nõ ſit ꝓportio irratiõalis <lb/>que ſit ſexquialtera ad duplã: qm̄ materia vniꝰ me­<lb/>dietatis eſt duoꝝ graduū puta illiꝰ in qua eſt ꝓpor­<lb/>tio dupla quantitatis ad materiã: et materia alte-<lb/>rius medietatis eſt vniꝰ gradus, et ſic tota materia <lb/>eſt vt tria quantitas vero vt octo, qm̄ vna quarta <lb/>pedalis eſt vnꝰ gradus quantitatis vt predictū eſt <lb/>modo .8. ad .3. eſt ꝓportio dupla ſuꝑbipartiens ter­<lb/>tias q̄ eſt minor ꝙ̄ ſexquialtera ad duplã. </s>
              <s xml:id="N22565" xml:space="preserve">Cõtinet <lb/>em̄ duplã et ſexquitertiã adequate ſupra duplam et <lb/>ſexquitertia eſt minor ꝙ̄ medietas duple vt patꝫ ex <lb/>ſecūda parte huius operis: g̊ cõtinet duplã, et minꝰ <lb/>̄ medietatē duple adequate: , ꝑ cõſequēs eſt mīor <lb/>̄ ſexquialtera ad duplã. </s>
              <s xml:id="N22572" xml:space="preserve">Itē ſexquialtera ad du-<lb/>plam eſt irrationalis / vt dictū eſt iſta vero: eſt rati-<lb/>onalis: g̊ nõ eſt ſexquialtera ad duplã / quod fuit ꝓ-<lb/>banduꝫ. </s>
              <s xml:id="N2257B" xml:space="preserve">Nec valet dicere /  non oportet ſic ſignare <lb/>gradus quantitatis aut materiae q2 quocū modo <lb/>ſignētur ſemꝑ erit ꝓportio rationalis quãtitatis <lb/>ad materiã in tali caſu et iſta raritas vt tria non eſt <lb/>nata ꝓuenire ꝓportione aliqua rationali: eſto  <lb/>raritas vt duo nata ſit produci a ꝓportiõe dupla.</s>
            </p>
            <p xml:id="N22588">
              <s xml:id="N22589" xml:space="preserve">               Quarto argr̄ ſic. </s>
              <s xml:id="N2258C" xml:space="preserve">Si iſta opinio eſſet <lb/>vera ſeq̄retur /  nõ poſſet dari cui g̈dus correſpõ-<lb/>deat raritas vniꝰ pedalis ſic ſe habentis  prima <lb/>pars ꝓportionalis eiꝰ ſit aliq̈liter rara et ſcḋa in <lb/>duplo, tertia in triplo, quarta in quadruplo ꝙ̄ pri­<lb/>ma, et ſic cõſequenter: ſed conſequēs eſt falſum: igr̄. <lb/></s>
              <s xml:id="N2259A" xml:space="preserve">Itē ſeq̄retur /  nõ poſſet dari cui correſpõderet ra-<lb/>ritas pedalis cuiꝰ prima pars ꝓportionalis ꝓpor­<lb/>tiõe dupla eſſet aliqualiter rara, ſecūda in duplo, <lb/>tertia in quadruplo ꝙ̄ prima et quarta, in octuplo <lb/>et quīta in ſexdecuplo: et ſic couſequenter : proceden­<lb/>do per numeros pariter parer: ſed hoc videtur ab-<lb/>ſurdum: igr̄. </s>
              <s xml:id="N225A9" xml:space="preserve">Seq̄la ptꝫ / qm̄ ad īueniendū in ſimili-<lb/>bus caſibꝰ raritatē adequatã taliū corpoꝝ oportet <lb/>ad īuenire materiã totalē totiꝰ corporis, et tūc vide­<lb/>re in qua ꝓportione ſe hꝫ quantitas illiꝰ corporis <lb/>ad illã materiã: et ex hoc raritatē talis corporis di­<lb/>iudicare: ſed nõ eſt modus īueniēdi in talibꝰ et ſimi-<lb/>libus caſibꝰ materiã totius corporis: etiã ad inuen­<lb/>ta et ſcita materia prime partis ꝓportionalis: igr̄ <lb/>nõ põt ſciri totalis raritas illoꝝ corpoꝝ ſic diffor-<lb/>miū in raritate. </s>
              <s xml:id="N225BE" xml:space="preserve">Sꝫ iam ꝓbo /  nõ põt materia illiꝰ <lb/>corporis īueſtigari, qm̄ cõtinue materia partis ꝓ-<lb/>portionalis ſequentis eſt minor materia partis ī-<lb/>mediate p̄cedentis. </s>
              <s xml:id="N225C7" xml:space="preserve">Et in nulla certa ꝓportione cõ-<lb/>tinuo minor: ſed cõtinuo in alia et in alia: et ſunt iſte <lb/>materie partiales infinite: igr̄ nõ apparet modus <lb/>quo totalis materia menſuretur: igitur.</s>
            </p>
            <p xml:id="N225D0">
              <s xml:id="N225D1" xml:space="preserve">Quīto argr̄. </s>
              <s xml:id="N225D4" xml:space="preserve">Si iſta optnio eſſet vera <lb/>ſeq̄retur /  raritas diceretur poſitue eodeꝫ modo <lb/>quo denſitas cū nõ ſit maior ratio de raritate ꝙ̄ de <lb/>denſitate: ſed cõſequēs eſt falſum: igr̄ illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N225DF" xml:space="preserve">Falſitas cõſequētis oſtenditur / qm̄ ſi ra-<lb/>ritas diceretur poſitiue ſequeret̄̄ /  poſſet dari vnū <lb/>finitū īfinite rarū: ſed cõſequēs eſt falſum: igr̄ illud <lb/>ex quo ſequitur. </s>
              <s xml:id="N225E8" xml:space="preserve">Falſitas huiꝰ cõſequentis oſtendit̄̄               <pb chead="Tertii tractatus" file="0188" n="188"/>               quoniã ſignetur illud et ſit vnū pedale / et arguo ſic / <lb/>illud pedale eſt infinite rarum: igitur in eo eſt infi-<lb/>nita ꝓportio quantitatis ad materiam: ſed quã-<lb/>titas eſt finita: ergo materia eſt infinite modica: <lb/>ſed non eſt dabilis materia infinite modica: igitur <lb/>eo nulla eſt materia vel ipſum nõ eſt infinite rarum <lb/>ſed non eſt dicendum  in eo nulla eſt materia: er-<lb/>go eſt dicendum  non eſt infinite rarum / quod <lb/>fuit probandum.</s>
            </p>
            <p xml:id="N22600">
              <s xml:id="N22601" xml:space="preserve">In oppoſitū tamen arguitur ſic / quia <lb/>hec apinio eſt adeo ſuſtentabilis et rationabilis ſi­<lb/>cut ſecunda: ergo eo modo poteſt deffenſari vera <lb/>ſicut ſecunda. </s>
              <s xml:id="N2260A" xml:space="preserve">Antecedens patebit ſoluendo. </s>
              <s xml:id="N2260D" xml:space="preserve">ea que <lb/>hanc poſitionem opugnant.</s>
            </p>
            <p xml:id="N22612">
              <s xml:id="N22613" xml:space="preserve">Pro ſolutione huius dubitationis: <lb/>et exacta huius opinionis inquiſitione. </s>
              <s xml:id="N22618" xml:space="preserve">Cõſideran­<lb/>dum eſt /  in hac opinioue ſicut et in aliis, peculia-<lb/>ribus definitionibus raritatis et denſitatis ſiue ra­<lb/>ri et denſi vtendum eſt. </s>
              <s xml:id="N22621" xml:space="preserve">Cum enim hec opinio dicat <lb/>ad raritatem requiri proportionem maioris ine-<lb/>qualitatis quantitatis ad materiam: et ad denſita­<lb/>tem ecõtra requiri proportionem maioris inequa-<lb/>litatis materie ad quantitatem id ſignum nobis <lb/>erit, et fidem faciet rarum hoc pacto diffiniri debe-<lb/>re.               <anchor type="note" xlink:href="note-0188-01" xlink:label="note-0188-01a"/>               </s>
              <s xml:id="N22635" xml:space="preserve">Rarum eſt illud in quo eſt proportio maioris in­<lb/>equalitatis quantitatis ad materiam.               <anchor type="note" xlink:href="note-0188-02" xlink:label="note-0188-02a"/>               </s>
              <s xml:id="N2263F" xml:space="preserve">Denſum ve-<lb/>ro ita deſcribi debet. </s>
              <s xml:id="N22644" xml:space="preserve">denſum eſt illud in quo eſt ꝓ-<lb/>portio maioris inequalitatis materie ad quanti-<lb/>tatem. </s>
              <s xml:id="N2264B" xml:space="preserve">Aliter tamen poſſunt iſti termini ſic deſcri-<lb/>bi manente eadem ſententia paululum verbis va-<lb/>riatis. </s>
              <s xml:id="N22652" xml:space="preserve">Rarum eſt cuius quãtitas eiuſdem materi-<lb/>am exuperat. </s>
              <s xml:id="N22657" xml:space="preserve">Denſum vero eſt cuius materia ſuam <lb/>excedit quantitatem. </s>
              <s xml:id="N2265C" xml:space="preserve">Quo in loco intelligendum <lb/>eſt hanc opinionem, et materie, et quantitati gra-<lb/>dus aſcribere: nõ quidem intenſionales: ita  ipſa <lb/>quantitas ſit intenſa, aut ipſa materia, velut albe­<lb/>do ſiue nigredo: ſed habet certas partes ſue ſubſtã­<lb/>tie ſiue entitatis ipſa materia: et ſimiliter ipſa quã­<lb/>titas certas portiones quas iſta opinio gradꝰ ap-<lb/>pellat: vt ſi dicamus quartã partem vnius pedalis <lb/>vnū gradum quantitatis eſſe, et medietatē quarte <lb/>mediū gradum quantitatis, et ſic cõſequenter: tunc <lb/>recte dicemus pedale quatuor gradus quãtitatis <lb/>cõtinere, et bipedale octo, et ſic cõſequēter, et pari in­<lb/>duſtria nõ abs re aſſignauerit hec opinio ipſa ma-<lb/>terie gradus: vt ſi dicamꝰ mariam exiſtentē in vna <lb/>octaua parte pedalis terre exñtis in ſua naturali <lb/>diſpoſitiõe eſſe vnū gradū materie, et medietatem <lb/>illiꝰ materie vnū mediū gradū, et ſic ↄ̨ñter diuiden-<lb/>do ex ↄ̨ñti manifeſtū nobis eſſet vnū pcdale terre in <lb/>ſua naturali, et optima diſpoſitione exiſtēs .8. gra­<lb/>dus materie ↄ̨tinere, et bipedale terre decē et ſex, et <lb/>ſic ↄ̨ñter aſcēdendo: et iſto mõ aſſignãdo g̈dus et ip̄i <lb/>materie et quãtitati facile erit inſpicere qñ gradus <lb/>quãtitatis excedunt gradꝰ materie: aut econtra, et <lb/>ſic iuidicare: vtrū tale corp° debeat dici dēſum, aut <lb/>nõ. </s>
              <s xml:id="N2268F" xml:space="preserve">Nã ſcḋm hanc opinionē nullū dēſum eſt rarum <lb/>nec rarū eſt dēſum. </s>
              <s xml:id="N22694" xml:space="preserve">Qḋ ſic patꝫ manifeſte. </s>
              <s xml:id="N22697" xml:space="preserve">Si em̄ a. <lb/>eſt dēſum gradꝰ materie ipſiꝰ a. exuperant gradus <lb/>quãtitatis eiꝰ. </s>
              <s xml:id="N2269E" xml:space="preserve">Si vero ip̄m a. ſit rarū iam gradus <lb/>quãtitatis gradꝰ materie exuperãt: ſed īpoſſibile ē <lb/> idē ſit maiꝰ altero: et ecõtra. </s>
              <s xml:id="N226A5" xml:space="preserve">Ideo nõ eſt poſſibile <lb/>huic opinioni adherēdo idē ſimul fater rarū et dē-<lb/>ſum vel ſaltē in eodē loco etc̈. </s>
              <s xml:id="N226AC" xml:space="preserve">Sequit̄̄ ſecūdo iuxta <lb/>hanc opinionē  nullū infinitarū vbi eſt infinitum de <lb/>materia eſt rarū aut denſum. </s>
              <s xml:id="N226B3" xml:space="preserve">Patet / q2 ibi, nec ma­<lb/>teria exuperat quantitatē, nec ab ea ſuperatur: vt <lb/>conſtat. </s>
              <s xml:id="N226BA" xml:space="preserve">Sequitur tertio /  aliquod finitū eſt quod               <cb chead="Capitulū primum."/>               nec eſt rarū, nec denſum: et tamen habet materiam <lb/></s>
              <s xml:id="N226C1" xml:space="preserve">Patet de pedali habēte quatuor gradus materie <lb/>eſto /  quarta pedalis ſit vnus gradus quantitatꝪ <lb/></s>
              <s xml:id="N226C7" xml:space="preserve">In tali enim pedali, nec quantitas excedit mate-<lb/>riam, nec ab ea exceditur.</s>
            </p>
            <div xml:id="N226CC" level="5" n="25" type="float">
              <note position="left" xlink:href="note-0188-01a" xlink:label="note-0188-01" xml:id="N226D0" xml:space="preserve">q̇d rarū</note>
              <note position="left" xlink:href="note-0188-02a" xlink:label="note-0188-02" xml:id="N226D6" xml:space="preserve">q̇d dēſuꝫ.</note>
            </div>
            <p xml:id="N226DC">
              <s xml:id="N226DD" xml:space="preserve">Aduertendum eſt ſecundo /  diuerſi-<lb/>mode hec opinio, et communis qui ī ſequenti no-<lb/>tabili declarabitur cenſent raritatem duplari, tri­<lb/>plari: aut in aliqua alia proportione augeri. </s>
              <s xml:id="N226E6" xml:space="preserve">Nam <lb/>opinio cõmunis aſſeuerat ad duplationem quan-<lb/>titatis ſequi duplationem raritatis: et econtra ad <lb/>duplationem raritatis ſequi duplationem quan-<lb/>titatis. </s>
              <s xml:id="N226F1" xml:space="preserve">Hec vero opinio oppoſitum dicit. </s>
              <s xml:id="N226F4" xml:space="preserve">Ali-<lb/>quando enim ad duplationem raritatis dupla-<lb/>tur quantitas, aliquando vero efficitur in ſexqui-<lb/>altero maior dumtaxat. </s>
              <s xml:id="N226FD" xml:space="preserve">vt ſecundum huius prin-<lb/>cipalis queſtionis argumentum oſtendit. </s>
              <s xml:id="N22702" xml:space="preserve">Unum ta­<lb/>men certum habet hec opinio: dicit enī ſemper ad <lb/>dupla tionem raritatis ſequi duplationē propor-<lb/>tionis quantitatis ad materiam: vt ſi ipſa propor­<lb/>tio quantitatis ad materiã fuerit dupla: duplata <lb/>raritate erit quadrupla: et ſi fuerit quadrupla: du-<lb/>plata raritate erit ſexdecupla. </s>
              <s xml:id="N22711" xml:space="preserve">Si autem tripla du­<lb/>plata raritate erit nonocupla. </s>
              <s xml:id="N22716" xml:space="preserve">ſi vero fuerit ſexqui­<lb/>altera: duplata raritate erit dupla ſexquiquarta: <lb/>et ſic in aliis exemplificandum eſt.</s>
            </p>
            <note position="right" xml:id="N2271D" xml:space="preserve">1. correĺ.</note>
            <p xml:id="N22721">
              <s xml:id="N22722" xml:space="preserve">¶ Ex quo educitur clare /  ſi quantitatis ad ma-<lb/>teriam fuerit proportio minor dupla: duplata ra-<lb/>ritate nequaquam duplabitur quantitas: ſed mi-<lb/>nus quam ad duplam augebitur: quemadmo-<lb/>dum promptum eſt in proportione ſexquitertia <lb/>intueri. </s>
              <s xml:id="N2272F" xml:space="preserve">Si veruo fuerit proportio maior dupla <lb/>neceſſum erit quantitatem pluſ̄ ad duplum au-<lb/>geri. </s>
              <s xml:id="N22736" xml:space="preserve">Si autem fuerit dupla dumtaxat quanti-<lb/>tatis ad materiam proportio: raritate dupla-<lb/>ta quantitas ipſa dupla euadet dumtaxat. </s>
              <s xml:id="N2273D" xml:space="preserve">Patet <lb/>hoc correlarium in ſingulis inducenti. </s>
              <s xml:id="N22742" xml:space="preserve">Ipſum enim <lb/>correlariū mathematico ordine et apparatu oſten­<lb/>dere ſiue demõſtrare maiori ſollicitudini eſſet quã <lb/>huic opinioni adiumento. </s>
              <s xml:id="N2274B" xml:space="preserve">Radix tamen et baſis hu­<lb/>ius opinionis eſt: ex qua baſi facile ea que ab hac <lb/>opinione aſſeuerantur claram ſortiuntur demon-<lb/>ſtrationem. </s>
              <s xml:id="N22754" xml:space="preserve">Eſt em̄ hoc fundamentum: cuilibet pro­<lb/>portioni quantitatis ad materiam determinati <lb/>gradus raritatis correſpondent: itidem et cuilibet <lb/>proportioni materie ad quantitatem determinati <lb/>gradus denſitatis correſpondent: perinde at in <lb/>motus velocitate certe proportioni potentie ad re­<lb/>ſiſtentiam certa motuum velocitas correſpondet: <lb/>et duple proportioni dupla motus velocitas: et ſex­<lb/>quialtere proportioni ſexquialtera velocitas aſcri­<lb/>bitur: volo dicere /  ſecundum hanc opinionē pro-<lb/>portioni duple quantitatis ad materiam corre-<lb/>ſpondent certi gradus raritatis qui gratia exem­<lb/>pli ſint duo, ita videlicet  vbicun ſiue in magno <lb/>corpore ſiue in paruo dupla proportio quantita-<lb/>tis ad materiam reperiatur iudicabitur tale cor-<lb/>pus rarum adequate vt duo: et vbicun reperietur <lb/>proportio quadrupla quantitatis ad materiam <lb/>raritas erit vt .4. quoniam proportio quadrupla <lb/>dupla eſt ad ipſam duplam: et ſic conſequenter tu <lb/>poteris exemplicare in aliis proportionum ſpe-<lb/>ciebus et generibus.</s>
            </p>
            <p xml:id="N2277F">
              <s xml:id="N22780" xml:space="preserve">¶ Ex quo ſequitur /  raritas proueniens a pro-<lb/>portione tripla non ſe habet in aliqua proportio-<lb/>ne rationali ad raritatem prouenientem a propor­<lb/>tione dupla. </s>
              <s xml:id="N22789" xml:space="preserve">Quod ptꝫ / q2 ꝓportio dupla et tripla <lb/>nõ ſe hñt ī in ꝓportiõe rõnali / igitur nec raritas pro-<lb/>ueniens a ꝓportione dupla ad raritatē ꝓuenieutē               <pb chead="De motu rarefactionis  condenſationis." file="0189" n="189"/>               a proportione dupla: quod patet quia proportio <lb/>dupla et tripla non ſe habent in proportione ra-<lb/>tionali / vt patet intuenti tractatum proportionum <lb/>               <anchor type="note" xlink:href="note-0189-01" xlink:label="note-0189-01a"/>               </s>
              <s xml:id="N227A0" xml:space="preserve">¶ Et exinde deducitur  ſi quãtitatis alicuius cor-<lb/>poris ad ſuam materiam fuerit proportio tripla et <lb/>alterius corporis fuerit proportio dupla: rarita-<lb/>tes illorum corporum ſunt incõmenſurabiles               <anchor type="note" xlink:href="note-0189-02" xlink:label="note-0189-02a"/>               </s>
              <s xml:id="N227AE" xml:space="preserve">¶ De­<lb/>ducitur vlterius  ſi quantitas alicuius corporis <lb/>rari ſine acquiſitione materie quadrupletur: ipſuꝫ <lb/>corpus quatuor gradus raritatis acquiret ſupra <lb/>raritatem prehabitam: quoniã talis raritas ipſi <lb/>proportioni quadruple correſpõdet: et ſi aliud cor-<lb/>pus rarum acquirat proportionē triplam ſue quã­<lb/>titatis ſine materie augmento aut decremento: ta-<lb/>le corpus acquiret maiorem raritem quam vt .2. in <lb/>nulla tamen proportione rationali maiorem ade-<lb/>quate. </s>
              <s xml:id="N227C5" xml:space="preserve">Patet hoc / quia raritas vt duo correſpon-<lb/>det proportioni duple: maior igitur raritas corre­<lb/>ſpondet triple: cum ipſa ſit maior et cū ipſa in nul-<lb/>la proportione rationali ſit maior: ſequens eſt in <lb/>nulla proportione rationali ſibi maiorem rarita-<lb/>tem correſpondere quã duple. </s>
              <s xml:id="N227D2" xml:space="preserve">Caute igitur reſpon­<lb/>dendum eſt cum queritur quante raritatis eſt cor-<lb/>pus in quo quãtitatis ad materiam eſt proportio <lb/>tripla. </s>
              <s xml:id="N227DB" xml:space="preserve">Non em̄ ſignanda eſt talis raritas per ali-<lb/>queꝫ numerū. </s>
              <s xml:id="N227E0" xml:space="preserve">Quēadmodum ſi queratur quãta eſt <lb/>velocitas correſpondens proportioni duple. </s>
              <s xml:id="N227E5" xml:space="preserve">et di-<lb/>catur exempli gratia  eſt vt .2. et deinde queratur <lb/>quantã eſt velocitas correſpondens proportioni <lb/>triple: nullo modo ſignanda eſt per aliquem nume­<lb/>rum: cum em̄ inter quoſcū numeros ſit proportio <lb/>rationalis / vt conſtat: et proportio velocitatum ſe-<lb/>quatur proportionem proportionū: naſceretur in <lb/>de proportionem triplam duple proportioni fore <lb/>cõmenſurabilem proportione ratiõali: quo nichil <lb/>in hac ſcientia falſiꝰ. </s>
              <s xml:id="N227FA" xml:space="preserve">Et ſi queras an ſecundū hanc <lb/>opinionē raritas vel denſitas diſtinguatur ab ip-<lb/>ſa materia. </s>
              <s xml:id="N22801" xml:space="preserve">¶ Reſpondeo  non. </s>
              <s xml:id="N22804" xml:space="preserve">Nã quando dici­<lb/>mus iſtud corpus eſt rarum vt .2. adequate: volumꝰ <lb/>dicere /  ibi eſt proportio dupla quãtitatis ad ma­<lb/>teriam: eſto  proportioni duple correſpondeant <lb/>duo gradus raritatis: et ſic in aliis proportionibꝰ <lb/>exēplificandū eſt. </s>
              <s xml:id="N22811" xml:space="preserve">ſēper tamen cauēdo proporti-<lb/>oni irrationali ad duplam aſſignes raritatē aliq̊ <lb/>numero ſignatam: </s>
              <s xml:id="N22818" xml:space="preserve">¶ Aduertendū eſt tertio /  ſcḋm <lb/>hanc opinionem ad diiuidicandū raritatē alicuius <lb/>corporis ſiue vniformis ſiue difformis: aſpicienda <lb/>eſt totalis eius quantitas, et totalis eius materia. <lb/></s>
              <s xml:id="N22822" xml:space="preserve">Et deinde inſpiciēda eſt ꝓportio totius quãtitatis <lb/>ad totã eius materiã: et ſecundã illam metiri opor-<lb/>tet raritatem talis corporis: vt ſi ſit vnū bipedale <lb/>cuius vna medietas ſit rara vt .2. et alia vt .4. ad vi­<lb/>dendum quanta eſt totius bipedalis raritas: capi­<lb/>enda eſt tota materia illius bipedalis que vt ↄ̨ſtat <lb/>ex predictis eſt vt .3. et deinde capienda eſt tota quã-<lb/>titas, que eſt vt .8. cum bipedale contineat .4. q̈rtas <lb/>pedalis: et aſſerendū eſt talem raritatem eſſe tantã <lb/>quãta ꝓportioni .8. ad .3. que eſt dupla ſuperbipar-<lb/>tiens tertias correſpondet. </s>
              <s xml:id="N22839" xml:space="preserve">Et ſic īuenietur totam <lb/>raritatem illius corporis non eſſe vt .3. ſed minorē: <lb/>vt patet ex deductione tertii argumenti huiꝰ dubii. <lb/>               <anchor type="note" xlink:href="note-0189-03" xlink:label="note-0189-03a"/>               </s>
              <s xml:id="N22847" xml:space="preserve">¶ Ex quo ſequitur ſecundū / hanc opinionē rarita-<lb/>tem difformiter difformē cuius vtra medietas eſt <lb/>vniformis vel vniformiter difformis nõ correſpon­<lb/>dere ſuo gradui medio vt argumentū tertiū p̄alle-<lb/>gatū bene oſtendit.               <anchor type="note" xlink:href="note-0189-04" xlink:label="note-0189-04a"/>               </s>
              <s xml:id="N22857" xml:space="preserve">¶ Ex quo ſequitur vlteriꝰ /  ra-<lb/>ritas difformis nõ eſt iudicanda penes reductioneꝫ <lb/>ad vniformitatē ſui: ſed penes reductionē ad vnifor­<lb/>mitatē ſue materie: vt ſi vna medietas cuiuſdã bi-               <cb chead="De motu rarefactionis  condenſationis."/>               pedalis habeat vnū gradū materie et alia habeat <lb/>duos capienda eſt vna medietas vniꝰ gradus illo-<lb/>rum duoꝝ et addenda eſt alteri medietati ipſiꝰ bi-<lb/>pedalis et illud manebit vniformiter rarum et eque <lb/>rarū ſicut antea: (volo em̄ /  nulla fiat deperditio <lb/>aut acquiſitio quãtitatis aut materie). </s>
              <s xml:id="N2286D" xml:space="preserve">Et eodē mö <lb/>debet fieri ſi prima pars ꝓportionalis, et ſecunda <lb/>haberet in quadruplo minꝰ quã prima, et tertia in <lb/>quadruplo minꝰ quã ſcḋa, et ſic cõſequenter: tūc re-<lb/>ducenda eſt materia ad vniformitatē et videndū eſt <lb/>quãta eſt tota materia et tota quãtitas: et penes ꝓ-<lb/>portionē totiꝰ quãtitatis ad totã materiã diiudica­<lb/>bitur raritas. </s>
              <s xml:id="N2287E" xml:space="preserve">Eſt iſto etiã modo metienda eſt denſi­<lb/>tas corporis denſi penes videlicet ꝓportionē to-<lb/>tius materie ad totã quãtitatē: et nõ penes denomi­<lb/>nationē quēadmodū fit in qualitatibꝰ difformibꝰ <lb/></s>
              <s xml:id="N22888" xml:space="preserve">Quod diligenter aīaduerte ſi hanc opinionē de-<lb/>fenſare affectas.               <anchor type="note" xlink:href="note-0189-05" xlink:label="note-0189-05a"/>               </s>
              <s xml:id="N22892" xml:space="preserve">¶ Sed nõ abs requireres quomõ <lb/>iudicanda eſt et mēſuranda materia corporis rari <lb/>aut denſi in quo eſt infinita difformitas ita  diui­<lb/>ſo tali corpore ꝓportione dupla nulla pars ꝓpor-<lb/>tionalis ſecundū talē diuiſionē ſit ita rara aut den­<lb/>ſa ſicut alia vt tangitur in quarto argumēto huiꝰ <lb/>queſtionis.               <anchor type="note" xlink:href="note-0189-06" xlink:label="note-0189-06a"/>               </s>
              <s xml:id="N228A6" xml:space="preserve">¶ Reſpõdeo breuiter /  aliquando ma­<lb/>teria talis corporis ſe habet continuo in certa <lb/>propoſitione: ita  materie prime ad materiã ſcḋe <lb/>partis ſit aliqua ꝓportio: et materie ſecūde ad ma­<lb/>teriam tertie ſit eadē ꝓportio: et ſic cõſeqnēter: ali-<lb/>quando vero nõ eadē cõtinuo ꝓportio obſeruatur <lb/>ſed in infinitum variatur puta ſi materie prime ad <lb/>materiã ſecūde ſit ꝓportio dupla: et materie partꝪ <lb/>ſecūde ad materiã tertie ſit ꝓportio tripla: et ma-<lb/>terie tertie ad materiã quarte ſit quadrupla: et ſic <lb/>cõſequēter aſcendendo per ſpecies ꝓportiõis mul-<lb/>tiplicis: et tūc nõ eſt poſſibile capacitati intellectus <lb/>finite adequate illã materiam menſurare vt iam in <lb/>ſimili dictū eſt circa materiã de motu locali penes <lb/>effectū. </s>
              <s xml:id="N228C5" xml:space="preserve">Sed ſi materie illarū partiū ꝓportionaliū <lb/>cõtinuo ſe habeant in eadē proportione: facile erit <lb/>diiudicare totalem materiam ex concluſionibus et <lb/>correlariis quīti capitis prime partis huiꝰ operis</s>
            </p>
            <div xml:id="N228CE" level="5" n="26" type="float">
              <note position="left" xlink:href="note-0189-01a" xlink:label="note-0189-01" xml:id="N228D2" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0189-02a" xlink:label="note-0189-02" xml:id="N228D8" xml:space="preserve">4. correĺ</note>
              <note position="left" xlink:href="note-0189-03a" xlink:label="note-0189-03" xml:id="N228DE" xml:space="preserve">.1. correĺ.</note>
              <note position="left" xlink:href="note-0189-04a" xlink:label="note-0189-04" xml:id="N228E4" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0189-05a" xlink:label="note-0189-05" xml:id="N228EA" xml:space="preserve">Queſtio</note>
              <note position="right" xlink:href="note-0189-06a" xlink:label="note-0189-06" xml:id="N228F0" xml:space="preserve"> Solutio <lb/>q̄ſtionis.</note>
            </div>
            <p xml:id="N228F8">
              <s xml:id="N228F9" xml:space="preserve">Ad ratiões ante oppoſitū huiꝰ dubii. <lb/></s>
              <s xml:id="N228FD" xml:space="preserve">Ad primã reſponſū eſt ibi vſ ad replicã ad quam <lb/>reſpõdeo ↄ̨cedēdo ſequelã, q2 illud ↄ̨ñs manifeſte <lb/>ſequit̄̄ ex hac poſitiõe: et negat̄̄ falſitas ↄ̨ñtis: et ad <lb/>ꝓbationē: datis illis duobus corporibꝰ equalibus <lb/>quãtitatiue et īequalibꝰ in raritate et cū ſic argr̄ eq̄ <lb/>ꝓportionabiliṫ ſicut iſta duo corpora acquirūt de <lb/>quãtitate acquirūt de raritate: negat̄̄ illud m hãc <lb/>opinionē: īmo dico /  oīa corpora ſiue eq̈lia quãti-<lb/>tatiue, ſiue īeq̈lia, ſiue eq̄ rara ſiue nõ, q̄ eque ꝓpor­<lb/>tionabiliṫ acquir̄t de quãtitate eq̈liṫ oīno acquir̄t <lb/>de raritate: qm̄ eq̈les ꝓportiones acquirūt, et ſemꝑ <lb/>ab equalibꝰ ꝓportionibꝰ eq̈les raritates nate ſunt <lb/>ꝓuenire / vt dictū eſt. </s>
              <s xml:id="N22918" xml:space="preserve">¶ Ad ſecundã rationē reſpõſū <lb/>eſt ibi vſ ad replicam: ad quam reſpondeo conce­<lb/>dendo ſequelam: et negando falſitatem conſequen­<lb/>tis. </s>
              <s xml:id="N22921" xml:space="preserve">Et ad probationem negatur hec conſequentia <lb/>in qua eſt vis rationis: vna medietas huius bipe-<lb/>dalis eſt denſa vt duo adequate, et alia rara vt duo <lb/>adequate: et raritas et denſitas non ſe compatiunt̄̄ <lb/>immo ſe cohabent ſicut cecitas et viſus; / igitur illud <lb/>corpus nec eſt rarum non eſt denſum: et ad probationē <lb/>que conſiſtit in quadam ſimilitudine concedo an-<lb/>tecedens: et nego conſequentiam: quia non eſt oīno <lb/>ſimile de illis qualitatibus et de raritate et denſi-<lb/>tate que ſunt duo oppoſita priuatiue: nam ſi               <pb chead="De motu rarefactionis et condenſationis." file="0190" n="190"/>               homo eſſet cecus ſecundum vnum oculum et vidēs <lb/>ſecundum alterum: adhuc talis homo eſſet videns <lb/></s>
              <s xml:id="N2293E" xml:space="preserve">Item ſecundum hanc opinionem intenſio raritatis <lb/>aut denſitatis non debet ſumi aut meuſurari pe-<lb/>nes denſitates partium vt oſtendit tertium notabi­<lb/>le huius dubii. </s>
              <s xml:id="N22947" xml:space="preserve">intenſio autem calidi aut frigidi po­<lb/>teſt meuſurari ex intenſionibus partium: et ideo il-<lb/>la ſimilitudo nnllo pacto quadrat huic propoſito.</s>
            </p>
            <p xml:id="N2294E">
              <s xml:id="N2294F" xml:space="preserve">Ad tertiam rationem reſpondeo con-<lb/>cedēdo ſequelam ſicut probat argumentum: et nego <lb/>falſitatem conſequentis: et ad ꝓbationem nego con­<lb/>ſequentiam: et ad ꝓbationem conſequentie: nego ſi­<lb/>militudinem ꝓpter rationem dictam in ſolutione <lb/>ſecunde rationis.</s>
            </p>
            <p xml:id="N2295C">
              <s xml:id="N2295D" xml:space="preserve">Ad quartam rationem reſpondeo ne-<lb/>gando ſequelam: immo dico /  in aliquibus talibꝰ <lb/>caſibus poteſt facile reperiri adequata materia in <lb/>aliquibus vero non ſaltem naturaliter ab intelle-<lb/>ctu finite capacitatis / vt dictum ē tertio notabili hu­<lb/>ius dubii </s>
              <s xml:id="N2296A" xml:space="preserve">In primo tamen caſu huius argumenti vi­<lb/>delicet  prima pars ꝓportionalis ſit aliqualiter <lb/>rara: et ſecunda in duplo: et tertia in triplo: et ſic con­<lb/>ſequenter diuiſione facta per partes ꝓportiõales <lb/>proportione dupla: et proportione quãtitatis prīe <lb/>partis proportionalis ad ſuam materiam exiſten-<lb/>te dupla tunc materie illarum partium proportio­<lb/>nalium continuo ſe habent in proportione quadru­<lb/>pla: et ſic ſcita materia prime partis proportiona-<lb/>lis facile ſcietur totalis materia: in infinitis tamen <lb/>caſibus vbi variatur proportio illud a finito inge-<lb/>nio et intellectu percipi non poteſt.</s>
            </p>
            <p xml:id="N22983">
              <s xml:id="N22984" xml:space="preserve">Ad quintam rationem reſpondeo ne-<lb/>gando ſequelam: et cum petitur ratio quare potiꝰ <lb/>raritas dicitur priuatiue quam poſitiue ſecnndum <lb/>hanc opiniouem reſpondeo /  ideo dicitur potius <lb/>priuatiue quam poſitiue: quia raritas intenditur <lb/>ad deperditionem ſiue remiſſionem alicuius poſiti­<lb/>ni puta materie ſine acquiſitione alicuius poſitiui <lb/>quod nū̄ eſt verum etiam de aliquo poſitiuo. </s>
              <s xml:id="N22995" xml:space="preserve">Quod ve-<lb/>ro ita fiat: aut poteſt fieri: volo /  diminuatur ſiue <lb/>dematur materia alicuius pedalis ſucceſſiue ad nõ <lb/>gradum nullo pacto maiorata quantitate: quo po­<lb/>ſito iam patet /  ibi nullum poſitum acquiritur: ſꝫ <lb/>contiuuo deperditur: nichilominus continuo pro-<lb/>portio quantitatis ad materiam maiorabitur: et <lb/>ſic continuo raritas intenditur. </s>
              <s xml:id="N229A6" xml:space="preserve">Sed quia hec ra-<lb/>tio eque bene concludit denſitatem dici priuatiue <lb/>quēadmodū et raritatem. </s>
              <s xml:id="N229AD" xml:space="preserve">quoniam per diminutio-<lb/>nem continuam quantitatis ſiue acquiſitione mate­<lb/>rie intenditur ipſa denſitas. </s>
              <s xml:id="N229B4" xml:space="preserve">ideo cum queris cau­<lb/>ſam quare raritas potius priuatiue dicitur quam <lb/>denſitas. </s>
              <s xml:id="N229BB" xml:space="preserve">Reſpondeo /  eſt illa quãtū in argumēto <lb/>aſſumis videlicet quia non poteſt reperiri infinita <lb/>raritas in ſubiecto ſiue corpore finito: ſi tamen dice­<lb/>retur poſitiue poſſet infinita raritas in ſubiecto fi-<lb/>nito reperiri / vt patet de omni poſitiuo magis et mi­<lb/>nus ſuſcipiente. </s>
              <s xml:id="N229C8" xml:space="preserve">Et per hoc patet reſponſio ad du-<lb/>bium.</s>
            </p>
            <note position="left" xml:id="N229CD" xml:space="preserve">Opinio <lb/>coīs</note>
            <p xml:id="N229D3">
              <s xml:id="N229D4" xml:space="preserve">Notandem eſt tertio tangēdo opinio­<lb/>nem commuuem quam calculator in capitulo de ra­<lb/>ritate inſequitur. </s>
              <s xml:id="N229DB" xml:space="preserve">et communiter moderni. </s>
              <s xml:id="N229DE" xml:space="preserve"> ſecun-<lb/>dum hanc opinioneꝫ aliter deſcribendi ſunt iſti ter­<lb/>mini: rarum: denſum: rarefieri: condenſari quam ſe­<lb/>cundum opiniones precedentes.               <anchor type="note" xlink:href="note-0190-01" xlink:label="note-0190-01a"/>               </s>
              <s xml:id="N229EC" xml:space="preserve">Rarum enim eſt il-<lb/>lud quod ſub magna quantitate continet modicuꝫ <lb/>de materia               <anchor type="note" xlink:href="note-0190-02" xlink:label="note-0190-02a"/>               </s>
              <s xml:id="N229F8" xml:space="preserve">Denſum vero eſt illud quod ſnb modi-               <cb chead="De motu rarefactionis et condenſationis."/>               ca quantitate multum continet de materia.               <anchor type="note" xlink:href="note-0190-03" xlink:label="note-0190-03a"/>               </s>
              <s xml:id="N22A03" xml:space="preserve">Condē-<lb/>ſari vero eſt effici magis denſum.               <anchor type="note" xlink:href="note-0190-04" xlink:label="note-0190-04a"/>               </s>
              <s xml:id="N22A0D" xml:space="preserve">Rarefieri enim ē <lb/>fieri magis rarum. </s>
              <s xml:id="N22A12" xml:space="preserve">magis autem rarum eſſe eſt ſub <lb/>maiori quantitate continere eandem materiam fi-<lb/>nitam quam antea continebat: vel ſub eadē quanti­<lb/>tate finita continere minus de materia: vel ſub mi-<lb/>nori: quantitate minus proportionale de materia <lb/>quam antea. </s>
              <s xml:id="N22A1F" xml:space="preserve">Sed magis denſum eſt illud quod ſub <lb/>eadem quãtitate continet plus de materia: vel ſub-<lb/>minori quantitate eandem materiam finitã vel ma­<lb/>iorem vel minorem in minori tamen proportione <lb/>̄ quantitas ſit minor. </s>
              <s xml:id="N22A2A" xml:space="preserve">vel ſub maiori quantitate <lb/>magis proportionale de materia. </s>
              <s xml:id="N22A2F" xml:space="preserve">Et ſi alique par­<lb/>ticule que non facile occurūt reſtant his diffini-<lb/>tionibus adiiciende eas addas cum argumenta ad <lb/>illud coegerint.               <anchor type="note" xlink:href="note-0190-05" xlink:label="note-0190-05a"/>               </s>
              <s xml:id="N22A3D" xml:space="preserve">Definitio enim breuis debet eſſe ex <lb/>ſua natura teſtimonio ciceronis in ſua nona retho­<lb/>rica.               <anchor type="note" xlink:href="note-0190-06" xlink:label="note-0190-06a"/>               </s>
              <s xml:id="N22A49" xml:space="preserve">¶ Ex his diffinitiouibus ſequitur primo /  ma­<lb/>le deſcribitur ſic condenſari </s>
              <s xml:id="N22A4E" xml:space="preserve">Condenſari eſt pun-<lb/>cta ad inuicem magis approximari quoniam ſtat <lb/> puncta magis approximentur: er in ea propor-<lb/>tione qua magis approximētur dematur de mate-<lb/>ria: et ſic tale corpus non condenſabitur. </s>
              <s xml:id="N22A59" xml:space="preserve">et tamen <lb/>puncta magis ad inuicem approximantur. </s>
              <s xml:id="N22A5E" xml:space="preserve">Item <lb/>dato pedali infinite denſo puncta illius poſſunt ma­<lb/>gis approximari: et tamen ipſum non condenſabi-<lb/>tur: quia iam eſt infinite denſum. </s>
              <s xml:id="N22A67" xml:space="preserve">Eodem modo di-<lb/>cas de rarefactione ſiue de rarefieri. </s>
              <s xml:id="N22A6C" xml:space="preserve">Non eni3 ſem­<lb/>per rarefieri ē puncta magis diſtare: pedale enim ī­<lb/>finite denſum poteſt maiorari ſtante ſua materia et <lb/>tamen non rarefiet.               <anchor type="note" xlink:href="note-0190-07" xlink:label="note-0190-07a"/>               </s>
              <s xml:id="N22A7A" xml:space="preserve">¶ Sequitur ſecundo /  ſtat ali-<lb/>quod eſſe rarum a quo aufertur medietas ſue mate­<lb/>rie manente quantitate: et tamen ipſum non effici-<lb/>tur rarius. </s>
              <s xml:id="N22A83" xml:space="preserve">Patet de corpore infinito habente ma-<lb/>teriam finitam preciſe quod eſt infinite raruꝫ a quo <lb/>ſi dematur medietas materie ipſum non efficietur <lb/>rarius cum modo ſit infinite rarum.</s>
            </p>
            <div xml:id="N22A8C" level="5" n="27" type="float">
              <note position="left" xlink:href="note-0190-01a" xlink:label="note-0190-01" xml:id="N22A90" xml:space="preserve">q̇d raruꝫ</note>
              <note position="left" xlink:href="note-0190-02a" xlink:label="note-0190-02" xml:id="N22A96" xml:space="preserve">q̇d dēſuꝫ</note>
              <note position="right" xlink:href="note-0190-03a" xlink:label="note-0190-03" xml:id="N22A9C" xml:space="preserve">q̇d ↄ̨dēſa­<lb/>ri.</note>
              <note position="right" xlink:href="note-0190-04a" xlink:label="note-0190-04" xml:id="N22AA4" xml:space="preserve">qḋ rarefi­<lb/>eri.</note>
              <note position="right" xlink:href="note-0190-05a" xlink:label="note-0190-05" xml:id="N22AAC" xml:space="preserve">cicero ī 4. <lb/>rethori.</note>
              <note position="right" xlink:href="note-0190-06a" xlink:label="note-0190-06" xml:id="N22AB4" xml:space="preserve">.1. correl.</note>
              <note position="right" xlink:href="note-0190-07a" xlink:label="note-0190-07" xml:id="N22ABA" xml:space="preserve">2. correl.</note>
            </div>
            <note position="right" xml:id="N22AC0" xml:space="preserve">3. correl.</note>
            <p xml:id="N22AC4">
              <s xml:id="N22AC5" xml:space="preserve">¶ Sequitur tertio /  aliquod corpus eſt denſum et <lb/>finitum a quo ſi remoueatur medietas quantitatis <lb/>manente materia: ipſum non efficietur denſius.</s>
            </p>
            <p xml:id="N22ACC">
              <s xml:id="N22ACD" xml:space="preserve">Patet de pedali infinite denſo poſito /  minore-<lb/>tur ad ſubduplum manente ſua materia.</s>
            </p>
            <note position="right" xml:id="N22AD2" xml:space="preserve">.4. corel.</note>
            <p xml:id="N22AD6">
              <s xml:id="N22AD7" xml:space="preserve">¶ Sequitur quarto /  ſtat quantitatem alicuius fi­<lb/>niti diminui: et ſimiliter eius materiam. </s>
              <s xml:id="N22ADC" xml:space="preserve">et ipſum cõ­<lb/>denſari. </s>
              <s xml:id="N22AE1" xml:space="preserve">ſtat ſimiliter ipſum rarefieri. </s>
              <s xml:id="N22AE4" xml:space="preserve">et ſtat ipſum <lb/>nec rafefieri nec condenſari. </s>
              <s xml:id="N22AE9" xml:space="preserve">Probatur prima <lb/>pars / quia ſtat ipſum plus proportionabiliter per­<lb/>dere de quantitate ꝙ̄ de maieria: et tunc ipſum con­<lb/>denſabitur vt poſtea ex quibuſdam concluſionibus <lb/>patebit. </s>
              <s xml:id="N22AF4" xml:space="preserve">et ſtat ipſum eque proportionabiliter de-<lb/>perdere de quantitate ſicut de materia: et ſic ipſum <lb/>nec rarefieri nec condenſari. </s>
              <s xml:id="N22AFB" xml:space="preserve">et ſtat ipſum magis <lb/>proportionabiliter deperdere de materia ꝙ̄ de quã­<lb/>titate: et ſic rarefieri. </s>
              <s xml:id="N22B02" xml:space="preserve">Et propterea poſitum eſt in de­<lb/>finitione vel minorem in minore tamen proportio-<lb/>ne ꝙ̄ quantitas ſit minor. </s>
              <s xml:id="N22B09" xml:space="preserve">Et eodem modo poteris <lb/>dicere /  aliquid per acquiſitionem quantitatis et <lb/>materie rarefit. </s>
              <s xml:id="N22B10" xml:space="preserve">et nõnun̄ condenſatur. </s>
              <s xml:id="N22B13" xml:space="preserve">Si enim <lb/>eque proportionabiliter acquirit de materia ſi-<lb/>cut de quantitate nec rarefit nec condenſatur. </s>
              <s xml:id="N22B1A" xml:space="preserve">ſi ve-<lb/>locius proportionabiliter acquirit de quantitate <lb/>̄ de materia rarefit. </s>
              <s xml:id="N22B21" xml:space="preserve">Omnia iſta patent mediante <lb/>tali fundamento. </s>
              <s xml:id="N22B26" xml:space="preserve">Si in ea proportione in qua ali-<lb/>quod corpꝰ eſt maius in ea plus cõtinet de materia <lb/>altero corꝑe mīore illa duo ſūt eq̄ rara et eq̄ denſa: <lb/>et ſi in maiori ꝓportione plus cõtineret de quanti-<lb/>tate quã de materia ꝙ̄ alterum minus: ipſum eſt ra­<lb/>rius eo. </s>
              <s xml:id="N22B33" xml:space="preserve">Si vero in maiore ꝓportione illud maiꝰ cõ­<lb/>tinet de materia quã de quantitate reſpectu alteri­               <pb chead="Tertii tractatus" file="0191" n="191"/>               us minoris ipſum eſt denſius illo minori. </s>
              <s xml:id="N22B3D" xml:space="preserve">Pro quo <lb/>intelligendo in ſuo fundamento: et radice ponã ali-<lb/>quas concluſiones: quadam diuiſione prepoſita q̄ <lb/>talis eſt. </s>
              <s xml:id="N22B46" xml:space="preserve">¶ Corporum ꝓportionabi­<lb/>liū ad inuicem in raritate et denſitate: quedam ſunt <lb/>equalia: quedam inequalia. </s>
              <s xml:id="N22B4D" xml:space="preserve">Item equalium que-<lb/>dã cõtinēt equaliter de materia: quedam inequali-<lb/>ter. </s>
              <s xml:id="N22B54" xml:space="preserve">Corporum inequalium quedam cõtinent equa-<lb/>liter de materia quedã vero nõ. </s>
              <s xml:id="N22B59" xml:space="preserve">Exēplū / vt ſi ſint duo <lb/>corpora quorum vnū eſt pedale et aliud ſemipeda-<lb/>le poſſibile eſt  vnū tm̄ contineat de materia ſicut <lb/>aliud vel vnum cõtineat plus de materia ꝙ̄ aliud. <lb/></s>
              <s xml:id="N22B63" xml:space="preserve">Item corporum inequalium inequaliter contenen-<lb/>tiū de materia: quedam ita ſe habent  minus con­<lb/>tinet minus de materia: quedã ita ſe habent  mi-<lb/>nus continet magis de materia. </s>
              <s xml:id="N22B6C" xml:space="preserve">Item minorum cõ­<lb/>tinentium minus quã maius: quoddam cõtinet mi-<lb/>nus in ea ꝓportione qua eſt minus: quoddã in ma-<lb/>iori ꝓportione: quoddã vero in minori. </s>
              <s xml:id="N22B75" xml:space="preserve">Exemplum / <lb/>vt ſi ſint duo corpora quorum vnū eſt pedale aliud <lb/>ſemipedale poſſibile eſt  ſemipedale cõtineat ma­<lb/>teriam in duplo minorem: in triplo maiorem: et in <lb/>ſexquialtero minorē quã ↄ̨tineat pedale. </s>
              <s xml:id="N22B80" xml:space="preserve">Itē corpo­<lb/>rum inequaliū quorū minus continet plus de mate­<lb/>ria ꝙ̄ maius. </s>
              <s xml:id="N22B87" xml:space="preserve">quoddã cõtinet plus de materia quaꝫ <lb/>maius in equali ꝓportione qua eſt minus. </s>
              <s xml:id="N22B8C" xml:space="preserve">quoddã <lb/>in maiori quoddã vero in minori ꝓportione quã ē <lb/>minus: </s>
              <s xml:id="N22B93" xml:space="preserve">Exēelū / vt captis pedali et ſemipedali poſſi-<lb/>bile eſt  ſemipedale continet in duplo plus de ma­<lb/>teria quam pedale: </s>
              <s xml:id="N22B9A" xml:space="preserve">Poſſibile ē  in triplo: poſſi­<lb/>bile eſt etiam  in ſexquialtero. </s>
              <s xml:id="N22B9F" xml:space="preserve">His diuiſionibꝰ po­<lb/>ſitis pono aliquas concluſiones quarum</s>
            </p>
            <p xml:id="N22BA4">
              <s xml:id="N22BA5" xml:space="preserve">Prima cõcluſio eſt hec. </s>
              <s xml:id="N22BA8" xml:space="preserve">Corpora equa­<lb/>lia equaliter continentia de materia ſunt equaliter <lb/>rara et equaliter dēſa dūmõ ſint rara et denſa. </s>
              <s xml:id="N22BAF" xml:space="preserve">Hec <lb/>concluſio patet ex diffinitionibus rari et denſi.</s>
            </p>
            <p xml:id="N22BB4">
              <s xml:id="N22BB5" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N22BB8" xml:space="preserve">Si aliqua duo in <lb/>equalia equaliter contineant de materia: minus il­<lb/>lorum in eadem ꝓportione eſt denſius in qua ē mi-<lb/>nus. </s>
              <s xml:id="N22BC1" xml:space="preserve">Probat̄̄ hec concluſio et capio duo corpora in <lb/>equalia gratia exempli pedale et ſemipedale habē-<lb/>tia equaliter de materia / et volo /  ſemipedale rare­<lb/>fiat quovſ ſit pedale ſine acquiſitione aut deper-<lb/>ditione materie. </s>
              <s xml:id="N22BCC" xml:space="preserve">quo poſito in fine illa duo corpora <lb/>ſunt eque rara et denſa / vt patet ex prima concluſio-<lb/>ne: et illud quod antea erat minus perdidit propor­<lb/>tionem duplam denſitatis cum acquiſiuerit duplã <lb/>raritatem / vt patet per duplam punctorum diſtan-<lb/>tiam ſine acquiſitione aut deperditione materie: <lb/>igitur antea erat in duplo denſius quã ſit modo: et <lb/>per conſequens in duplo denſius quolibet equali <lb/>modo in denſitate. </s>
              <s xml:id="N22BDF" xml:space="preserve">quoniam in quacun ꝓportio-<lb/>ne aliquid excedit aliud in eadeꝫ ꝓportione excedit <lb/>quolibet equale illi: igitur concluſio vera:</s>
            </p>
            <p xml:id="N22BE6">
              <s xml:id="N22BE7" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N22BEA" xml:space="preserve">Si fuerint duo cor-<lb/>pora inequalia: et minus illorum cõtinet plus ḋ ma­<lb/>teria quã maius: tunc minus eſt denſius in propor-<lb/>tione compoſita ex proportione qua maius excedit <lb/>minus: et ex proportione qua materia minoris ex-<lb/>dit materiam maioris: </s>
              <s xml:id="N22BF7" xml:space="preserve">Probatur et capio pedale <lb/>et ſemipedale quod cõtinet in duplo maigs de ma-<lb/>teria quã pedale: et volo /  illud ſemipedale rarefi-<lb/>at quouſ ſit bipedale: quo poſito arguitur ſic in fi­<lb/>ne talis rarefactionis illud corpꝰ quod antea erat <lb/>ſemipedale eſt eque denſum adequate cum alio cor­<lb/>pore pedali cū ſubdupla quãtitate duplã maṫiã cõ­<lb/>tiuet: et ipſum eſt in quadruplo minus denſum quã <lb/>erat antea cum modo puncta in quadruplo plꝰ di-               <cb chead="Capitulum primum"/>               ſtent etc. / igitur ipſum erat antea in quadruplo deu­<lb/>ſius quã ſit modo: et per conſequens in quadruplo <lb/>denſius quolibet quod eſt modo equale ei in den-<lb/>ſitate: igitur ipſum antea cum eſſet ſemipedale erat <lb/>in quadruplo denſius illo pedali: et proportio qua­<lb/>drupla eſt ꝓportio compoſita ex ꝓportione quãti-<lb/>tatis qua maius excedit minus puta dupla: et ex ꝓ-<lb/>portione qua materia minoris excedit materiam <lb/>maioris ſimiliter dupla / vt patet ex ſecunda parte <lb/>huius operis: igitur intentum. </s>
              <s xml:id="N22C1F" xml:space="preserve">ſic enim vniuerſali-<lb/>ter probabis.</s>
            </p>
            <p xml:id="N22C24">
              <s xml:id="N22C25" xml:space="preserve">Quarta concluſio </s>
              <s xml:id="N22C28" xml:space="preserve">Si ſint duo corpo-<lb/>ra inequalia inequaliter continentia de materia. <lb/></s>
              <s xml:id="N22C2E" xml:space="preserve">ita  ī q̈cū ꝓportiõe minꝰ minus eſt ī eadē ꝓpor-<lb/>tione continet minus de materia. </s>
              <s xml:id="N22C33" xml:space="preserve">talia corpora ſūt <lb/>equaliter denſa. </s>
              <s xml:id="N22C38" xml:space="preserve">Patet hec concluſio de ſe quoniã <lb/>capto corpore pedali vniformiter denſo / manifeſtū <lb/>eſt /  medietas eius eſt eque denſa ſicut totum: et ſi-<lb/>cut medietas eſt in duplo minor ita in duplo minus <lb/>continet de materia. </s>
              <s xml:id="N22C43" xml:space="preserve">Et iſto modo vniuerſaliter ꝓ-<lb/>babis de quibuſcun aliis proportionibus ſiue ra­<lb/>tionalibus ſiue non rationalibus</s>
            </p>
            <p xml:id="N22C4A">
              <s xml:id="N22C4B" xml:space="preserve">Quinta concluſio </s>
              <s xml:id="N22C4E" xml:space="preserve">Si ſint duo corpo-<lb/>ra inequalia: et minus contineat minus de materia <lb/>quam maius in maiore proportione quam ma-<lb/>ius excedat minus: tunc maiꝰ eſt deſius minore ī ea <lb/>ꝓportione qua ꝓportio materie ad materiam exce­<lb/>dit ꝓportionē quantitatū: </s>
              <s xml:id="N22C5B" xml:space="preserve">Uel ſub aliis verbis ea-<lb/>dē rententa ſententia. </s>
              <s xml:id="N22C60" xml:space="preserve">Si duorū corporum inequa-<lb/>liū ꝓportio materie maioris ad materiam mino-<lb/>ris excedit ꝓportionē quãtitatis ad quantitatem: <lb/>maius illorum eſt denſius in ꝓportione ꝑ quã pro-<lb/>portio materie maioris ad materiã minoris exce-<lb/>dit ꝓportionē quantitatū. </s>
              <s xml:id="N22C6D" xml:space="preserve">Probat̄̄ hec concluſio <lb/>et capio duo corpora ſe habentia in ꝓportione du­<lb/>pla / et volo /  materia maioris ſit tripla ad materi­<lb/>am minoris quo poſito maius eſt denſius in ꝓpor­<lb/>tione ſexquialtera ꝑ quã ꝓportio tripla excedit du­<lb/>plam: igr̄ cõcluſio vera. </s>
              <s xml:id="N22C7A" xml:space="preserve">Añs ꝓbatur: et pono /  cor­<lb/>pus maius condenſetur quovſ ſit equale minori <lb/>puta ad ſubduplū / quo poſito argr̄ ſic. </s>
              <s xml:id="N22C81" xml:space="preserve">Illud corpꝰ <lb/>quod antea erat maius eſt in triplo denſius altero <lb/>corpore quod antea erat minus eo: et ꝑ talē cõdēſa-<lb/>tionē p̄ciſe acquiſiuit duplam denſitatem: ergo ſe-<lb/>quitur /  antea habebat ſexquialteram: igitur ip-<lb/>ſum erat ãtea in ꝓportione ſexq̇altera dēſiꝰ / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N22C90" xml:space="preserve">Sequela tamē ꝓbatur / q2 qñ aliq̇d efficit̄̄ <lb/>in aliqua ꝓportiõe maiꝰ reſpectu alterius: et tūc ac­<lb/>quirit preciſe vnã partē talis ꝓportionis ſequitur / <lb/> iã antea habebat alterã ꝑtem: ſed tale corpꝰ acq̇-<lb/>ſiuit ꝓportionē triplã id eſt effectū eſt denſius ī pro­<lb/>portione tripla: et nõ acq̇ſiuit niſi duplã: ergo ſequi­<lb/>tur /  iã antea habebat adequate ſexquialterã: qm̄ <lb/>tripla ex dupla et ſexquialtera cõponit̄̄ adequate. <lb/></s>
              <s xml:id="N22CA2" xml:space="preserve">Et iſto mõ ꝓbabis de q̇buſcū aliis ꝓportiõibus.</s>
            </p>
            <p xml:id="N22CA5">
              <s xml:id="N22CA6" xml:space="preserve">Sexta concluſio </s>
              <s xml:id="N22CA9" xml:space="preserve">Si fuerint duo cor­<lb/>pora inequalia: et ꝓportio quantitatū fuerit ma-<lb/>ior proportione materie maioris ad materiã mi-<lb/>noris. </s>
              <s xml:id="N22CB2" xml:space="preserve">tunc minus eſt denſius maiori in ꝓportione <lb/>qua proportio quantitatis excedit ꝓportionē ma-<lb/>terie. </s>
              <s xml:id="N22CB9" xml:space="preserve">Probat̄̄ hec concluſio: et volo /  ſint duo cor-<lb/>pora puta pedale et bipedale: et bipedale in ſexqui-<lb/>altero plus cõtineat de materia ꝙ̄ pedale: tūc dico / <lb/> pedale eſt denſius bipedali in ꝓportione ſexqui­<lb/>tertia. </s>
              <s xml:id="N22CC4" xml:space="preserve">quoniam ꝑ talem ꝓportionē ſexquitertiam <lb/>ꝓportio quãtitatis maioris ad quãtitatē minoris <lb/>q̄ ē dupla excedit ꝓportionē maṫie maiorꝪ ad maṫi­<lb/>am minoris q̄ ē ſexq̇altera / vt ↄ̨ſtat </s>
              <s xml:id="N22CCD" xml:space="preserve">Probat̄̄ hoc ſic <lb/></s>
              <s xml:id="N22CD1" xml:space="preserve"><pb chead="De motu rarefactionis  condenſationis." file="0192" n="192"/>               Qm̄ ſi materia corporis minoris ꝑderet ꝓportio-<lb/>nē ſexquitertiã ſue materie ſtante quantitate: tunc <lb/>maius et minꝰ eſſent eque denſa / vt ptꝫ ex quarta cõ­<lb/>cluſione. </s>
              <s xml:id="N22CDE" xml:space="preserve">In ea em̄ ꝓportione qua minꝰ eſt minꝰ in <lb/>ea minꝰ ↄ̨tineret de materia. </s>
              <s xml:id="N22CE3" xml:space="preserve">Sed modo illud corpꝰ <lb/>minꝰ in ſexq̇tertio plus de materia cõtinet denſius <lb/>quã tūc: et tunc erat ita denſum ſicut modo eſt illud <lb/>bipedale: g̊ modo in ſexq̇tertio eſt denſiꝰ illo bipe-<lb/>dali: et ꝓportio ſexquitertia eſt illa ꝑ quã ꝓportio <lb/>quãtitatis maioris ad quantitatē minoris excedit <lb/>ꝓportionē materie maioris ad materiã minoris: g̊ <lb/>ꝑ ↄ̨ñs minꝰ eſt denſius maiore in ꝓportione ꝑ quantuꝫ <lb/>ꝓportio quantitatis maioris ad quantitatē mino­<lb/>ris excedit ꝓportionē materie maioris ad materiã <lb/>minoris. </s>
              <s xml:id="N22CFA" xml:space="preserve">Et ſic ꝓbabis q̇buſcū duabꝰ ꝓportiõibꝰ <lb/>̄titatū et materieꝝ īeq̈libꝰ ꝓpoſitꝪ ī caſu ↄ̨cluſiõis</s>
            </p>
            <p xml:id="N22CFF">
              <s xml:id="N22D00" xml:space="preserve">Ultima cõcluſio. </s>
              <s xml:id="N22D03" xml:space="preserve">Si duoꝝ corporum <lb/>inequaliū ꝓportio quantitatis ad quantitatē ſiue <lb/>materie ad materiã fuerit irrationalis: tūc ꝓpor-<lb/>tio raritatis vniꝰ et denſitatis ſimiliter ad denſita­<lb/>tem et raritatē alteriꝰ eſt irratiõalis. </s>
              <s xml:id="N22D0E" xml:space="preserve">Probat̄̄ / ſicut <lb/>concluſio qm̄ ꝓportio quantitatis vniꝰ ad quan-<lb/>titatē alteriꝰ nõ denoīatur ab aliquo certo numero <lb/>ita etiã diſtantia punctoꝝ nõ denoīatur ab aliquo <lb/>certo numero: et ꝑ ↄ̨ñs iam ꝓportio raritatis vnius <lb/>ad raritatē alteriꝰ eſt irratiõalis / ptꝫ ↄ̨ña ꝑ diffini-<lb/>tioneꝫ ꝓportiõis irratiõalis in ṗma ꝑte huiꝰ oꝑis.</s>
            </p>
            <p xml:id="N22D1D">
              <s xml:id="N22D1E" xml:space="preserve">Notãnda eſt quarto / q̄dã diuiſio dēſita­<lb/>tū partibꝰ alicuiꝰ ſubiecti inherentiū q̄ diuiſio huic <lb/>materie multū claritatis et vtilitatis affert: ex qua <lb/>ꝓpoſitiones nõ nulle deducūtur: ex quibꝰ ꝓpoſiti-<lb/>onibus quedã cõcluſiones huiꝰ materie ſubtilitatē <lb/>cõprehendētes naſcūtur. </s>
              <s xml:id="N22D2B" xml:space="preserve">Diuiſio vero ſub his ver-<lb/>bis deſcribetur. </s>
              <s xml:id="N22D30" xml:space="preserve">¶ Denſitates per diuerſas partes <lb/>ſubiecti diſtribute qñ ſūt equales in gradu: ſepiꝰ <lb/>o īequales. </s>
              <s xml:id="N22D37" xml:space="preserve">Exemplū primi: vt ſi vtra medietas <lb/>vniꝰ pedalis ſit denſa vt .4. </s>
              <s xml:id="N22D3C" xml:space="preserve">Exemplū ſecūdi: vt ſi al­<lb/>tera medietas ſit vt .8. et altera vt .4. </s>
              <s xml:id="N22D41" xml:space="preserve">Itē ſi ſūt equa­<lb/>les in gradu ipſe denſitates, aut extendūtur parti­<lb/>bus ſubiecti equalibꝰ, aut īequalibus. </s>
              <s xml:id="N22D48" xml:space="preserve">Exempla in <lb/>prõptu ſunt. </s>
              <s xml:id="N22D4D" xml:space="preserve">Itē ſi ſunt inequales in gradu: aut per <lb/>partes equales ſubiecti extendūtur, aut ꝑ īequales <lb/></s>
              <s xml:id="N22D53" xml:space="preserve">Preterea ſi denſitates inequales inequalibꝰ par-<lb/>tibus ſubiecti inhereãt: hoc cõtinget dupliciter: q2 <lb/>aut maior denſitas maiori parti inheret, aut mino­<lb/>ri. </s>
              <s xml:id="N22D5C" xml:space="preserve">Exemplū primi / vt ſi denſitas vt .4. inhereat ſiue <lb/>coextendatur medietati pedalis: et dēſitas vt .3. vni <lb/>q̈rte eiuſdē pedalis. </s>
              <s xml:id="N22D63" xml:space="preserve">Prepoſtero ordine denſitates <lb/>illis partibus diſtribuendo. </s>
              <s xml:id="N22D68" xml:space="preserve">exemplum ſecūdi mē-<lb/>bri patebit. </s>
              <s xml:id="N22D6D" xml:space="preserve">Itē ſi ītenſior dēſitas parti ſubiecti mi­<lb/>nori aſſcribitur et remiſſior denſitas maiori parti: <lb/>hoc tripliciter euenire ſolet: q2 aut ꝓportio illarū <lb/>partiū ſubiecti ꝓportionē illaꝝ denſitatū excedit, <lb/>aut ꝓportio denſitatū proportionē partiū ſubiecti <lb/>excedit. </s>
              <s xml:id="N22D7A" xml:space="preserve">aut ꝓportio illaꝝ partiū eſt equalis ꝓpor-<lb/>tioni denſitatū. </s>
              <s xml:id="N22D7F" xml:space="preserve">Exemplū primi / vt ſi in vna medie-<lb/>tate pedalis ponat̄̄ denſitas vt .8. et in vna quarta <lb/>denſitas vt .12. tūc ꝓportio partiū eſt maior ꝓpor-<lb/>tione denſitatū. </s>
              <s xml:id="N22D88" xml:space="preserve">Nã hec ſexquialtera eſt, illa auteꝫ <lb/>dupla. </s>
              <s xml:id="N22D8D" xml:space="preserve">Exemplum ſecūdi / vt ſi in medietate ſubiecti <lb/>ponatur denſitas vt .4. et in quarta ponat̄̄ dēſitas <lb/>vt .12. tunc ꝓportio denſitatū excedit ꝓportionem <lb/>partiū ſubiecti: </s>
              <s xml:id="N22D96" xml:space="preserve">Nã hec dupla eſt: illa vero tripla vt <lb/>conſtat. </s>
              <s xml:id="N22D9B" xml:space="preserve">Exemplū tertii / vt ſi in vna tertia ponatur <lb/>denſitas vt .6. et in vna ſexta denſitas vt .12. tūc ea-<lb/>dem eſt ꝓportio illaꝝ partiū, et etiã illaꝝ denſita-<lb/>tum. </s>
              <s xml:id="N22DA4" xml:space="preserve">Utra em̄ dupla eſt. </s>
              <s xml:id="N22DA7" xml:space="preserve">Hac partitione ſiue diui-               <cb chead="De motu rarefactionis  condenſationis."/>               ſione exacta at conſūmata: reſtat quaſdē ꝓpoſi-<lb/>tiones preambulas ſequentiū cõcluſionū probare</s>
            </p>
            <p xml:id="N22DAF">
              <s xml:id="N22DB0" xml:space="preserve">Prima ꝓpoſitio. </s>
              <s xml:id="N22DB3" xml:space="preserve">Si denſitates eque <lb/>intenſe ſiue gradu equales (quod idē eſt) partibus <lb/>eiuſdē ſubiecti extendatur equalibus: ipſe equali-<lb/>ter totū denominãt. </s>
              <s xml:id="N22DBC" xml:space="preserve">Si o partibus ſubiecti ineq̈-<lb/>libus aſſcribant̄̄: tūc illa deuſitas q̄ maiori parti <lb/>ſubiecti aſſcribit̄̄ plus totū ipſuꝫ ſubiectū denoīat <lb/>in ꝓportione in qua ſe hñt ille partes ſubiecti ad ī-<lb/>uicē: vt ſi denſitas vt .4. ſit in vna medietate alicuiꝰ <lb/>ſubiecti: et tanta denſitas intenſiue ſit in vna quar-<lb/>ta eiuſdē ſubiecti: tūc in duplo plus denomīat totū <lb/>ilud ſubiectū denſitas ī medietate quã denſitas in <lb/>quarta: q2 medietatis ad quartã eſt ꝓportio dupla <lb/></s>
              <s xml:id="N22DD0" xml:space="preserve">Probatur tñ ſecūda pars huiꝰ ꝓpoſitionis (quia <lb/>prima ex ſe ptꝫ) qm̄ ex poſitione quã iam ſuſtinemꝰ <lb/>et p̄cedenti notabili recitauimꝰ / ptꝫ /  denſitas exi-<lb/>ſtens in parte ſubiecti in ea ꝓportione minꝰ deno-<lb/>minat ſuū ſubiectū in qua eſt in minori parte ſubie­<lb/>cti: igr̄ in quacū ꝓportione aliq̈ denſitas per ma-<lb/>iorem partem alicuius ſubiecti extenditur quã alia <lb/>em̄ equalis in gradu: in eadē ꝓportione plus ſuum <lb/>ſubiectū denominat / quod fuit probandum.</s>
            </p>
            <p xml:id="N22DE3">
              <s xml:id="N22DE4" xml:space="preserve">Scḋa ꝓpoſitio. </s>
              <s xml:id="N22DE7" xml:space="preserve">Qñ inequales denſi­<lb/>tates equalibus partibus ſubtecti inherent: tūc in­<lb/>tenſior denſitas in ea ꝓportione plus denominat <lb/>totū ſubiectū in qua eſt intenſior. </s>
              <s xml:id="N22DF0" xml:space="preserve">Probat̄̄ / qm̄ ſi il-<lb/>le denſitas eſſent equales in gradu cum inhereant <lb/>partibus equalibus ipſum equaliter totū denſum <lb/>denominarēt: vt docet prior pars p̄cedentis cõclu-<lb/>ſionis: ſed modo vna illaꝝ denſitatū eſt intēſior in <lb/>f. ꝓportione exempli gratia et ſicut eſt intenſior ita <lb/>plus denoīat ceteris paribus: igr̄ in f. ꝓportione <lb/>plus denoīat ꝙ̄ reliqua, et in f. ꝓportione eſt inten-<lb/>ſior / vt ponitur: igr̄ in ea ꝓportiõe in qua intenſior <lb/>plus totū ſubiectū denoīat / quod fuit probandum.</s>
            </p>
            <p xml:id="N22E05">
              <s xml:id="N22E06" xml:space="preserve">Tertia ꝓpoſitio. </s>
              <s xml:id="N22E09" xml:space="preserve">Si inequales den-<lb/>ſitates in gradu partibus eiuſdē ſubiecti inequali­<lb/>bus accõmodant̄̄, et intenſior maiori parti depute­<lb/>tur remiſſior vero minori: tunc intenſior denſitas <lb/>plus denominant totū ꝙ̄ remiſſior in ꝓportione cõ-<lb/>poſita ex ꝓportione partis maioris ad partē mi-<lb/>norē, et denſitatis intenſioris ad denſitatē remiſſi-<lb/>orē. </s>
              <s xml:id="N22E1A" xml:space="preserve">Exemplū / vt ſi in vna medietate pedalis ponat̄̄ <lb/>denſitas vt .4. et in quarta eiuſdē ponat̄̄ denſitas <lb/>vt .2. / tūc dico intenſionē exiſtentē in medietate ſub-<lb/>iecti in quadruplo plus denominare illud ſubiectū <lb/>denſitate exiſtente in quarta eiuſdē ſubiecti: qm̄ ꝓ-<lb/>portio illaꝝ partiū et etiã denſitatū eſt dupla et ſic <lb/>cõpoſita ex illis duplis eſt quadrupla: vt ptꝫ. </s>
              <s xml:id="N22E29" xml:space="preserve">Pro­<lb/>batur tñ hec ꝓpoſitio vniuerſaliter: et ſit a. dēſitas <lb/>intenſior ꝑ maiorē partē extenſa b.o remiſſior ꝑ <lb/>minorē partē extenſa: tūc a. denſitas denoīat ſub-<lb/>iectū totale pluſ̄ b. denſitas in ꝓportione cõpoſi-<lb/>ta ex ꝓportione partis in qua eſt a. ad partē in qua <lb/>eſt b. q̄ ꝓportio ſit c. et ex ꝓportiõe denſitatis a. ad <lb/>dēſitatē b. q̄ ꝓportio ſit d. </s>
              <s xml:id="N22E3A" xml:space="preserve">Qḋ ſic oſtenditur / q2 ſi a. <lb/>denſitas eſſet equalis b. denſitati tūc a. plus deno-<lb/>minaret ſubiectū ꝙ̄ b. in ꝓportione c. q̄ eſt ꝓportio <lb/>partiū. </s>
              <s xml:id="N22E43" xml:space="preserve">vt pꝫ ex ſecūda parte prime cõcluſionis: ſꝫ <lb/>modo a. eſt intenſior denſitas quam tunc eſſet in d. <lb/>ꝓportione q̄ eſt ꝓportio illaꝝ denſitatū: igr̄ modo <lb/>in d. ꝓportione plus denoīat totū quã tūc. </s>
              <s xml:id="N22E4C" xml:space="preserve">Ptꝫ tñ <lb/>hec ↄ̨ña / q2 quãto aliqua denſitas eſt intenſior cete­<lb/>ris paribus exiſtēs in aliqua parte ſubiecti, tanto <lb/>plꝰ facit ad denoīationē ſui ſubiecti vt tenet hec po­<lb/>ſitio: igr̄ nūc a. denſitas plus facit ad denoīationē               <pb chead="Tertii tractatus" file="0193" n="193"/>               ſui ſubiecti quã b. in c. proportione partium, et in d. <lb/>ꝓportione intenſionū illaꝝ denſitatū ſimul: igitur <lb/>plus denoīat a. quã b. ſuū ſubiectū in proportione <lb/>q̄ adequate cõponitur ex proportione c. partiū et d. <lb/>intenſionū illaꝝ dēſitatum: quod fuit probandum.</s>
            </p>
            <p xml:id="N22E64">
              <s xml:id="N22E65" xml:space="preserve">Quarta ꝓpoſitio. </s>
              <s xml:id="N22E68" xml:space="preserve">Si intenſior denſi­<lb/>tas parti extendatur minori: et remiſſior maiori: ſit­<lb/> equalis ꝓportio partiū ad inuicē: et etiã denſita-<lb/>tum: tunc ille denſitates equaliter ad totius deno-<lb/>minationē faciūt. </s>
              <s xml:id="N22E73" xml:space="preserve">Exemplū / vt ſi in vna medietate <lb/>ponatur denſitas vt .4. et in vna quarta vt .8. quia <lb/>tunc inter partes et inter denſitates eſt proportio <lb/>dupla. </s>
              <s xml:id="N22E7C" xml:space="preserve">Ideo tm̄ adequate facit ad denoīationē to-<lb/>tius ſubiecti denſitas vt .8. in vna quarta quantuꝫ <lb/>denſitas vt .4. in vna medietate: q2 vtra facit vt <lb/>duo vt ptꝫ calculanti et aſpicienti attentius. </s>
              <s xml:id="N22E85" xml:space="preserve">Pro-<lb/>batur tñ generaliter / et ſit a. denſitas intenſior per <lb/>minorē partē extenſa et b. remiſſior extenſa ꝑ ma-<lb/>iorē partē, et ſit f. ꝓportio inter illas partes et etiã <lb/>ſi .f. proportio inter illas denſitates a .b. / tunc dico <lb/> b. deuſitas equaliter denoīat totū ſuū ſubiectuꝫ <lb/>cū ipſa a. denſitate. </s>
              <s xml:id="N22E94" xml:space="preserve">Quod ſic argr̄ / ſi a. dēſitas exi­<lb/>ſtens in minori parte quã b. eſſet equalis in gradu <lb/>ipſi b. tunc in f. ꝓportione minꝰ denoīaret totum ̄ <lb/>b. modo denoīat / vt ptꝫ clare ex ſecūda parte prime <lb/>ꝓpoſitionis: ſed modo in f. ꝓportiõe plus denoīat <lb/>quã tunc: q2 in f. ꝓportione eſt intenſior ceteris pa-<lb/>ribus: igitur modo tantū denominat ſicut b. / quod <lb/>fuit probandum.</s>
            </p>
            <p xml:id="N22EA5">
              <s xml:id="N22EA6" xml:space="preserve">Quinta ꝓpoſitio. </s>
              <s xml:id="N22EA9" xml:space="preserve">Si intenſior denſi­<lb/>tas parti ſubiecti extendatur minori, et remiſſior <lb/>maiori parti eiuſdē ſubiecti īhereat, et ꝓportio in-<lb/>tenſionū illaꝝ deuſitatū excedat ꝓportionē partiū <lb/>tunc denſitas exiſtēs in miuore parte ſubiecti ipſū <lb/>totū ſubiectū denſius denoīabit ꝙ̄ denſitas exiſtēs <lb/>in maiori parte in ea ꝓportione ꝑ quã ꝓportio in-<lb/>tenſionū illaꝝ denſitatū excedit ꝓportionē partiū <lb/>in quibus ſunt ille denſitates. </s>
              <s xml:id="N22EBC" xml:space="preserve">Exemplū / vt ſi in vna <lb/>medietate pedalis ponatur denſitas vt duo, et in <lb/>quarta eiuſdē denſitas vt .8. q2 ꝓportio partiū ex-<lb/>ceditur a ꝓportione quadrupla illaꝝ denſitatum <lb/>et quadrupla ex duplã per duplã. </s>
              <s xml:id="N22EC7" xml:space="preserve">Ideo in du-<lb/>plo plus denoīat denſitas vt .8. quã denſitas vt .2. <lb/>illud totale ſubiectū denoīet q2 illa vt .2. denoīat <lb/>vt vnū, alia vero vt .8. denoīat vt .2. / vt ptꝫ calculã-<lb/>ti. </s>
              <s xml:id="N22ED2" xml:space="preserve">Probat̄̄ tñ vniuerſaliter ſit a. denſitas intēſior <lb/>b. vero remiſſior exiſtens in maiore parte ſubiecti <lb/>quã a. ſit ꝓportio partiū c. ꝓportio vero intenſi-<lb/>onū illaꝝ denſitatū d. q̄ ſit maior et excedãt d. ꝓpor­<lb/>tio ipſam c. ꝓportionē ꝑ f. ꝓportionē: tunc a. denſi-<lb/>tas denoīat ſubiectū in f. ꝓportiõe denſius quã b. <lb/></s>
              <s xml:id="N22EE0" xml:space="preserve">Quod ſic argr̄ / q2 ſi ꝓportio intenſionū illaꝝ den-<lb/>ſitatū eſſet equalis ꝓportioni c. illaꝝ partiū ſubie­<lb/>cti: tūc eq̈liṫ a. faceret ad totius ſubiecti denoīatio­<lb/>nē / vt pꝫ ex preredenti ꝓportione ſed modo a. eſt iu <lb/>f. ꝓportione intenſior denſitas quam tunc / g̊ modo <lb/>in f. ꝓportione plus facit ad totius denoīationem <lb/>̄ tunc: et ꝑ ↄ̨ñs in f. ꝓportiõe modo plus facit ̄ <lb/>b. / quod fuit ꝓbandū </s>
              <s xml:id="N22EF1" xml:space="preserve">Ptꝫ ↄ̨ña / q2 tm̄ facit b. modo <lb/>ſicut tunc a. / vt ptꝫ. </s>
              <s xml:id="N22EF6" xml:space="preserve">Q, vero a. denſitas ſit nunc in f. <lb/>ꝓportione intenſior / ꝙ̄ tunc ptꝫ per hanc maximã. <lb/></s>
              <s xml:id="N22EFC" xml:space="preserve">Quãdo due ꝓportiones ſunt equales ad hoc  <lb/>vna illaꝝ excedat alterã per f. proportionē requiri­<lb/>tur  numerus maior acquirat illã f. ꝓportionē ſu­<lb/>pra ſe, ſi numerus minor debet manere inuariatus / <lb/>vt ptꝫ facile in numeris: et ſic ptꝫ propoſitio.</s>
            </p>
            <p xml:id="N22F07">
              <s xml:id="N22F08" xml:space="preserve">Sexta ꝓpoſitio. </s>
              <s xml:id="N22F0B" xml:space="preserve">Ubicū maior den­               <cb chead="Capitulū primū."/>               ſitas parti ſubiecti minori inheret, et remiſſior den­<lb/>ſitas maiori parti, eſt inter partes maior ꝓpor-<lb/>tio quã inter illaꝝ denſitatū intenſiones: tunc den­<lb/>ſitas remiſſior plus facit ad totius denoīationem <lb/>quã intenſior in ea proportione per quã proportio <lb/>partiū ꝓportionē denſitatū exuperat. </s>
              <s xml:id="N22F1B" xml:space="preserve">Exemplum <lb/>eſt facile. </s>
              <s xml:id="N22F20" xml:space="preserve">Probat̄̄ hec ꝓpoſitio generaliter / ſit a. <lb/>denſitas intenſior ī minore parte exiſtēs, b. vero re­<lb/>miſſior in maiore parte exiſtēs et ſi proportio par­<lb/>tiū c, et denſitatū d. et c. proportio partium excedat <lb/>d. ꝓportionē denſitatū per f. / tunc argr̄ ſic / ſi ꝓpor-<lb/>tio partiū puta partis maioris ad partē minoreꝫ <lb/>diminueretur per f. ꝓportionē tūc b. denſitas equa­<lb/>liter denoīaret totū ſicut a. denſitas: ſed modo eſt <lb/>in parte in f. ꝓportioue maiore quã tunc eſſet cete-<lb/>ris paribus: g̊ modo in f. ꝓportione b. plus deno-<lb/>minat quã tuuc: et per cõſequēs modo in f. ꝓportiõe <lb/>b. plus denoīat totū ſubiectū quã a. denſitas. </s>
              <s xml:id="N22F39" xml:space="preserve">Ptꝫ <lb/>cõſequētia / q2 denoīatio qua modo denoīat a. den­<lb/>ſitas, et qua tunc denoīaret b. dēſitas ſunt equales <lb/></s>
              <s xml:id="N22F41" xml:space="preserve">Q, o tunc b. equaliter denoīaret cū ipſa a. denſi-<lb/>tate ptꝫ ex quarta ꝓpoſitione. </s>
              <s xml:id="N22F46" xml:space="preserve">Et ſic ptꝫ /  in ea ꝓ-<lb/>portione denſitas remiſſior plus facit ad denoīa-<lb/>tionē totius per quam proportio partium excedit <lb/>ꝓportionē denſitatū / quod fuit ꝓbandū.               <anchor type="note" xlink:href="note-0193-01" xlink:label="note-0193-01a"/>               </s>
              <s xml:id="N22F54" xml:space="preserve">¶ Abſolu­<lb/>tis notabilibꝰ, prima parte huiꝰ q̄ſtionis expedi­<lb/>ta: reſtat ad ſecundã partē ſiue articulū huiꝰ q̄ſtio-<lb/>nis accedere qui articulus cõcluſionibus quibuſdã <lb/>ex p̄dictis ꝓpoſitonibus ſequentibꝰ accõmodatur <lb/></s>
              <s xml:id="N22F60" xml:space="preserve">His em̄ ſequētibꝰ cõcluſionibꝰ p̄ſentis q̄ſtionis dif­<lb/>ficultas notatur at abſoluitur. </s>
              <s xml:id="N22F65" xml:space="preserve">Sit igitur.</s>
            </p>
            <div xml:id="N22F68" level="5" n="28" type="float">
              <note position="right" xlink:href="note-0193-01a" xlink:label="note-0193-01" xml:id="N22F6C" xml:space="preserve">2. pars q̄­<lb/>ſtionis.</note>
            </div>
            <p xml:id="N22F74">
              <s xml:id="N22F75" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N22F78" xml:space="preserve">Diuiſo aliquo cor-<lb/>pore benſo per partes ꝓportionales quauis pro-<lb/>portione, et prima pars ꝓportionalis ſit aliquali­<lb/>ter denſa, et ſecūda in duplo plus, et tertia in triplo <lb/>plus ꝙ̄ prima, et ſic in infinitū: tunc totū corpus eſt <lb/>denſus prima parte ꝓportionali in ea ꝓportione <lb/>qua ſe hꝫ totū ſic diuiſum ad primã partē eiꝰ ꝓpor­<lb/>tionalē. </s>
              <s xml:id="N22F89" xml:space="preserve">Ptꝫ hec cõcluſio ex ꝓbatione ſecūde cõclu­<lb/>ſionis tertii capitis ſecūdi tractatus huius tertie <lb/>partis vbi et ꝓbationē et exemplū eiꝰ īueniens.               <anchor type="note" xlink:href="note-0193-02" xlink:label="note-0193-02a"/>               </s>
              <s xml:id="N22F95" xml:space="preserve">¶ Ex <lb/>hac cõcluſione ſequitur primo /  ſi aliquod corpus <lb/>diuidatur ꝓportione tripla, et prima pars ꝓpor-<lb/>tionalis eiꝰ ſit aliquantulū denſa, et ſecūda in du-<lb/>plo, et tertia in triplo quã prima, et ſic cõſequenter: <lb/>tunc totum eſt in ſexquialtero denſius prima parte <lb/></s>
              <s xml:id="N22FA3" xml:space="preserve">Et ſi diuidatur corpus ꝓportione quadrupla: totū <lb/>eſt denſius prima parte proportionali in ſexq̇ter-<lb/>tio. </s>
              <s xml:id="N22FAA" xml:space="preserve">et ſi proportiõe quītupla: totū erit denſius pri-<lb/>ma parte proportionali in ꝓportione ſexquiquar­<lb/>ta. </s>
              <s xml:id="N22FB1" xml:space="preserve">Et ſi in proportiõe ſextupla: in proportiõe ſexq̇-<lb/>quīta. </s>
              <s xml:id="N22FB6" xml:space="preserve">Et fi proportiõe ſeptupla: in proportiõe ſex-<lb/>quiſexta: et ſic cõſequēter ꝓcedendo per ſpecies pro­<lb/>portionis multiplicis ſuperparticularis. </s>
              <s xml:id="N22FBD" xml:space="preserve">Proba­<lb/>tur hoc longū correlariū / q2 corpus diuiſum ꝓpor-<lb/>tione tripla ſe hꝫ ad primã partē proportionalem <lb/>eiꝰ in proportiõe ſexq̇altera: et diuiſum proportiõe <lb/>quadrupla in proportiõe ſexq̇tertia: et diuiſum quī­<lb/>tupla ſe hꝫ ad primã partē proportiõalē in propor­<lb/>tione ſexquiquarta / et ſic cõſequēter / vt ptꝫ ex prima <lb/>parte huiꝰ operis capitulo quīto et ſexto: igr̄ in ca-<lb/>ſu correlarii ſequit̄̄ /  ſi diuidat̄̄ proportiõe tripla <lb/>ipſum erit denſius prima parte proportionali in <lb/>ſexquialtero, et ſi quadrupla in proportione ſexq̇-<lb/>tertia, et ſi quītupla in ſexquiquarta, et ſic cõſequē-<lb/>ter. </s>
              <s xml:id="N22FD8" xml:space="preserve">Ptꝫ hec cõſequentia per cõcluſionē precedentē <lb/>               <anchor type="note" xlink:href="note-0193-03" xlink:label="note-0193-03a"/>               </s>
              <s xml:id="N22FE2" xml:space="preserve">¶ Sequit̄̄ ſecundo /  ſi diuidat̄̄ corpus per partes <lb/>proportionales proportiõe dupla, diſtribuatur               <pb chead="Tertii tractatus" file="0194" n="194"/>               denſitas in partes ꝓportionales / vt ponit̄̄ in pre-<lb/>cedēti correlario: ita  prima ſit aliqualiter dēſa <lb/>ſcḋa in duplo, tertia in triplo, et ſic ↄ̨ſequēter: tunc <lb/>totum eſt in duplo denſius ſua prima parte ꝓpor-<lb/>tionali. </s>
              <s xml:id="N22FF4" xml:space="preserve">Probat̄̄ / q2 totū diuiſum per partes ꝓpor­<lb/>tionales ꝓportiõe dupla eſt duplum ad primã par­<lb/>tē ꝓportionalē eius / vt ptꝫ ex quinto capite prealle­<lb/>gato prime partis huius libri: igitur ꝑ cõcluſionē <lb/>primã immediate p̄cedentē illud eſt denſius prima <lb/>parte ꝓportionali in ꝓportione dupla.               <anchor type="note" xlink:href="note-0194-01" xlink:label="note-0194-01a"/>               </s>
              <s xml:id="N23006" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio /  diuiſo corpore ſi ꝑ partes ꝓportionales <lb/>ꝓportione dupla / vt ponit̄̄ in antecedēti correlario <lb/>totum eſt ita denſum ſicut ſcḋa pars proportiona­<lb/>lis eius. </s>
              <s xml:id="N23011" xml:space="preserve">Probat̄̄ / q2 in duplo denſius prima vt ſe-<lb/>cundū correlarium aſſerit: et ſcḋa pars ꝓportiona­<lb/>lis eſt etiã in duplo denſior prima: g̊ totū eſt ita dē­<lb/>ſum ſicut ſecūda pars ꝓportionalis / quod fuit pro­<lb/>bandū. </s>
              <s xml:id="N2301C" xml:space="preserve">Patet conſequētia ꝑ hanc maximã </s>
              <s xml:id="N2301F" xml:space="preserve">Oīa ha-<lb/>bentia equalē ꝓportionē ad vnū tertiū ſunt equa-<lb/>lia: ſꝫ totius denſitas et denſitas ſecūde partis ꝓ-<lb/>portionalis habent equalem proportionē ad den-<lb/>ſitatē prime partis ꝓportiõis puta duplã: igit̄̄ dē-<lb/>ſitas totius et ſecūde partis ꝓportionalis ſūt equa­<lb/>les / quod erat inducendū.               <anchor type="note" xlink:href="note-0194-02" xlink:label="note-0194-02a"/>               </s>
              <s xml:id="N23033" xml:space="preserve">¶ Sequit̄̄ quarto /  ſi ali­<lb/>quod corpus diuidat̄̄ ꝑ partes ꝓportiõales ꝓpor-<lb/>portione ſexquialtera: et prīa pars ꝓportionalis <lb/>ſit aliqualiter denſa: et ſecūda ī duplo: et tertia ī tri­<lb/>plo ꝙ̄ prima: et ſic cõſequēter vt ponitur in caſu pri­<lb/>me cõcluſionis et correlarii: totū eſt in triplo dēſius <lb/>prima parte ꝓportionali. </s>
              <s xml:id="N23042" xml:space="preserve">Et ſi diuidatur ꝓportio­<lb/>ne ſexquitertia: totū erit denſius prima parte pro-<lb/>portionali in quadruplo. </s>
              <s xml:id="N23049" xml:space="preserve">Et ſi in ſexquiquarta: to­<lb/>tum erit denſius prima parte ꝓportionali in ꝓpor­<lb/>tione quītupla. </s>
              <s xml:id="N23050" xml:space="preserve">et ſic ↄ̨ſequēter ꝓcedēdo ꝑ ſpecies <lb/>ꝓportionis ſuperparticularis in diuiſione corpo­<lb/>is: et per ſpecies proportionis multiplicis ex parte <lb/>denſitatis. </s>
              <s xml:id="N23059" xml:space="preserve">Probatur hoc corolariuꝫ / quia totum <lb/>diuiſum ꝑ partes porportionales proportione ſex­<lb/>quialtera eſt tripluꝫ ad primã ꝑtē eiꝰ ꝓportionalē <lb/>et ſexquitertia quadruplū: et ſexquiquarta quītu-<lb/>plum. </s>
              <s xml:id="N23064" xml:space="preserve">vt pꝫ ex prima parte huiꝰ operis: g̊ in eiſdem <lb/>ꝓportionibus ſe habēt denſitates totius ad denſi­<lb/>tatem prime partis ꝓportionalis. </s>
              <s xml:id="N2306B" xml:space="preserve">igit̄̄ correlariuꝫ <lb/>verum.               <anchor type="note" xlink:href="note-0194-03" xlink:label="note-0194-03a"/>               </s>
              <s xml:id="N23075" xml:space="preserve">¶ Sequitur quito /  ſi diuidatur corpus vt <lb/>dicitur in p̄cedenti correlario vt puta ꝓportiõe ſex­<lb/>quialtera: et prima pars ſit aliqualiter denſa: et ſe­<lb/>cunda in duplo: et tertia in triplo .etc̈. totum eſt ita <lb/>denſum ſicut tertia pars ꝓportionalis eius. </s>
              <s xml:id="N23080" xml:space="preserve">Et ſi <lb/>ſexq̇tertia ſicut quarta pars ꝓportiõalis eiꝰ. </s>
              <s xml:id="N23085" xml:space="preserve">Et ſi <lb/>ſexquiquarta ſicut quīta pars ꝓportionalis eius. <lb/></s>
              <s xml:id="N2308B" xml:space="preserve">Et ſexquiquinta: ſicut ſexta pars ꝓportionalis eiꝰ / <lb/>et ſic cõſequēter aſcendēdo ꝑ partes ꝓportionales <lb/>et per ſpecies ꝓportiõis ſuꝑparticularis in infini­<lb/>tum. </s>
              <s xml:id="N23094" xml:space="preserve">Probat̄̄ / qm̄ ſi corpus ſit diuiſum ꝓportione <lb/>ſexquialtera ipſum eſt in triplo denſius prīa par-<lb/>te ꝓportionali / vt ptꝫ ex precedenti correlario et ter­<lb/>tia pars ꝓportionalis eſt etiã in triplo denſior pri­<lb/>ma / vt ptꝫ ex caſu. </s>
              <s xml:id="N2309F" xml:space="preserve">g̊ eſt ita denſum tale corpus ſicut <lb/>tertia pars ꝓportionalis. </s>
              <s xml:id="N230A4" xml:space="preserve">Itē ſi diuidatur ꝓportio­<lb/>ne ſexquitertia ip̄m eſt in quadruplo denſius ṗma <lb/>eius parte ꝓportionali / vt pꝫ ex p̄cedenti correlario <lb/>et etiã quarta pars ꝓportionalis eiꝰ eſt in quadru­<lb/>plo denſior ṗma / vt pꝫ ex caſu. </s>
              <s xml:id="N230AF" xml:space="preserve">igit̄̄ illud corpus ita <lb/>diuiſum ꝑ partes ꝓportionales ꝓportione ſexqui­<lb/>tertia eſt ita denſum ſicut quarta pars proportio-<lb/>nalis eius. </s>
              <s xml:id="N230B8" xml:space="preserve">Et iſto mõ probabis ceteras ꝑticulas <lb/>correlarii.               <anchor type="note" xlink:href="note-0194-04" xlink:label="note-0194-04a"/>               </s>
              <s xml:id="N230C2" xml:space="preserve">¶ Sequit̄̄ ſexto /  ſi aliquod corpꝰ diui­<lb/>datur ꝑ partes ꝓportionales proportiõe ſuperbi­<lb/>patiente tertias <gap/> et partes eius ſint ita denſe / vt ſe-               <cb chead="Capitulū primum."/>               pius dictum eſt in p̄cedētibus correlariis: totū erit <lb/>denſius ṗma parte ꝓportionali in ꝓportione du-<lb/>pla ſexquialtera: ita  ſi ṗma eſt denſa vt .2. totuꝫ <lb/>erit denſum vt .5. </s>
              <s xml:id="N230D4" xml:space="preserve">Probat̄̄ correlariū / qm̄ totū erit <lb/>denſius ṗma parte proportionali in tali caſu in ꝓ­<lb/>portione qua ſe habet totū diuiſum ꝑ partes ꝓpor­<lb/>tionales ꝓportione ſuperbipartiēte tertias ad ſu­<lb/>am primã partē proportionalē / vt ptꝫ ex cõcluſione <lb/>ſed talis eſt ꝓportio dupla ſexquialtera / vt patꝫ ex <lb/>capĺo q̇nto prime partis huius operis: igit̄̄ corre-<lb/>larium verum.</s>
            </p>
            <div xml:id="N230E5" level="5" n="29" type="float">
              <note position="right" xlink:href="note-0193-02a" xlink:label="note-0193-02" xml:id="N230E9" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0193-03a" xlink:label="note-0193-03" xml:id="N230EF" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0194-01a" xlink:label="note-0194-01" xml:id="N230F5" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0194-02a" xlink:label="note-0194-02" xml:id="N230FB" xml:space="preserve">4. correĺ.</note>
              <note position="left" xlink:href="note-0194-03a" xlink:label="note-0194-03" xml:id="N23101" xml:space="preserve">5. correĺ.</note>
              <note position="left" xlink:href="note-0194-04a" xlink:label="note-0194-04" xml:id="N23107" xml:space="preserve">6. correĺ.</note>
            </div>
            <p xml:id="N2310D">
              <s xml:id="N2310E" xml:space="preserve">Secūda cõcluſio </s>
              <s xml:id="N23111" xml:space="preserve">Diuiſo corpore per <lb/>ꝑtes ꝓportiõales quauis ꝓportiõe et ī quacū pro­<lb/>portiõe ſe habuerīt ꝑtes ꝓportionales ī eadē vĺ ma­<lb/>iori ſe habuerit dēſitas mīoris ad dēſitatē maiorꝪ <lb/>totū illud corpꝰ eſt īfinite dēſum. </s>
              <s xml:id="N2311C" xml:space="preserve">patet hec cõcluſio <lb/>ex ꝓbatione ſexte cõcluſionis octaui capitis ſecūdi <lb/>tractatus huius partis.                <anchor type="note" xlink:href="note-0194-05" xlink:label="note-0194-05a"/>               </s>
              <s xml:id="N23128" xml:space="preserve">¶ Ex hac cõcluſione ſeq̇tur <lb/>primo /  partito aliquo corꝑe proportiõe ſexquial­<lb/>tera et prima pars ſit aliqualiter denſa: et ſecunda <lb/>in duplo et tertia ī duplo ꝙ̄ ſecūda: et quarta ꝙ̄ ter­<lb/>tia: totum eſt infinite denſum. </s>
              <s xml:id="N23133" xml:space="preserve">¶ Sequit̄̄ ſecundo /  <lb/>diuiſo corpore per partes proportionales ꝓpor-<lb/>tione ſexquitertia et ṗma ſit aliqualiter denſa et ſe­<lb/>cunda in ſexquialtero plus et tertia in ſexquialtero <lb/>quã ſecunda / et ſic conſequēter: totum corpus eſt in­<lb/>finite denſum </s>
              <s xml:id="N23140" xml:space="preserve">Hec correlaria ex ſecunda cõcluſione <lb/>patent: qm̄ in vtro illoꝝ proportio denſitatū cõ­<lb/>tinuo eſt maior ꝓportione partiū / ergo ſubiecta il-<lb/>la ſunt infinite denſa.</s>
            </p>
            <div xml:id="N23149" level="5" n="30" type="float">
              <note position="right" xlink:href="note-0194-05a" xlink:label="note-0194-05" xml:id="N2314D" xml:space="preserve">1. correĺ.</note>
            </div>
            <p xml:id="N23153">
              <s xml:id="N23154" xml:space="preserve">Tertia <reg norm="concluſio" type="context">cõcluſio</reg> </s>
              <s xml:id="N23157" xml:space="preserve">Diuiſo aliquo corpo­<lb/>re per partes <reg norm="proportionales" type="simple">ꝓportionales</reg> quauis proportiõe et <lb/>in certa proportiõe quelibet pars <reg norm="praecedens" type="simple context">p̄cedēs</reg> ſit <reg norm="denſior" type="context">dēſior</reg> <lb/>immediate <reg norm="ſequenti" type="context">ſequēti</reg>: totius denſitatís ad <reg norm="denſitatet" type="simple">denſitatꝫ</reg> <lb/>ſiue denoīationē qua <reg norm="totum" type="context">totū</reg> <reg norm="denominabitur" type="simple">denominabit̄̄</reg> a denſita­<lb/>te prime partis <reg norm="proportionalis" type="simple">ꝓportionalis</reg> eſt illa <reg norm="proportio" type="simple">ꝓportio</reg> qua <lb/>ſe habet totum diuiſum in proportione ↄ̨poſita ex <lb/>proportione partis <reg norm="proportionalis" type="simple">ꝓportionalis</reg> <reg norm="precedententis" type="context">precedentētis</reg> ad <reg norm="im­ mediate" type="context">ī­<lb/>mediate</reg> <reg norm="ſequentem" type="context">ſequētem</reg>: et denſitatis <reg norm="praecedentis" type="simple context">p̄cedētis</reg> ad denſi-<lb/>tatem immediate <reg norm="ſequentis" type="context">ſequētis</reg> ad <reg norm="primam" type="simple context">ṗmã</reg> eius <reg norm="partem" type="context">partē</reg> <reg norm="pro- portionalem" type="context">pro-<lb/>portionalē</reg>. </s>
              <s xml:id="N2316E" xml:space="preserve">Patet hec et cluſio <reg norm="cum" type="context">cū</reg> multis <reg norm="ſimilibus" type="simple">ſimilibꝰ</reg> ex <lb/>probatione octaue <reg norm="concluſionis" type="context">cõcluſionis</reg> tertii capitis <reg norm="ſecundi" type="context">ſecūdi</reg> <lb/>tractatus huius tertie partis videas ibi.</s>
            </p>
            <p xml:id="N23175">
              <s xml:id="N23176" xml:space="preserve">Quarta <reg norm="concluſio" type="context">cõcluſio</reg> </s>
              <s xml:id="N23179" xml:space="preserve">Diuiſo corpore per <lb/>partes <reg norm="proportionales" type="simple">ꝓportionales</reg> aliqua proportiõe multipli-<lb/>ci: et in prima parte proportionali ſit aliquantula <lb/>denſitas. </s>
              <s xml:id="N23182" xml:space="preserve">et in ſecunda in ſexquialtero maior et in <lb/>tertia in ſexquitertia maior denſitas <reg norm="quam" type="context">quã</reg> in <reg norm="prima" type="simple">ṗma</reg> / <lb/>et ſic ↄ̨ſequenter <reg norm="procedendo" type="context">procedēdo</reg> per ſpecies <reg norm="proportionis" type="simple context">ꝓportiõis</reg> <lb/>ſuperparticularis: totius corporis denſitas <reg norm="cenſen­ da" type="context">cēſen­<lb/>da</reg> eſt <reg norm="incommenſurabilis" type="context">incõmenſurabilis</reg> proportione rationali <reg norm="den­ ſitati" type="context">dē­<lb/>ſitati</reg> prime partis proportionalis et denoīationi <lb/>qua <reg norm="ipſa" type="wordlist">ip̄a</reg> denſitas exiſtens in <reg norm="prima" type="simple">ṗma</reg> parte proportio­<lb/>nali totum denominat. </s>
              <s xml:id="N23193" xml:space="preserve">vel <reg norm="ſaltem" type="context">ſaltē</reg> ſi <reg norm="commenſurabilis" type="context">cõmenſurabilis</reg> <lb/>eſt pro ſtatu iſto a nobis <reg norm="capacitatem" type="context">capacitatē</reg> <reg norm="finitam" type="context">finitã</reg> habenti-<lb/>bus nequa̄ <reg norm="commenſurari" type="context context">cõmēſurari</reg> poteſt. </s>
              <s xml:id="N2319A" xml:space="preserve">Probatur / <reg norm="quam" type="wordlist">qm̄</reg> ille <lb/>denſitates <reg norm="continuo" type="context">cõtinuo</reg> ſe habent in alia et alia <reg norm="propor- tione" type="simple">ꝓpor-<lb/>tione</reg>: et <reg norm="non" type="wordlist">nõ</reg> eſt poſſibile omnes tales proportiones <lb/><reg norm="commenſurari" type="context">cõmenſurari</reg> ab intellectu finito cum ſint infinite: et <lb/><reg norm="continuo" type="context">cõtinuo</reg> alie et alie: igitur concluſio propoſita vera <lb/></s>
              <s xml:id="N231A6" xml:space="preserve">Non <reg norm="tamem" type="context">tamē</reg> puto hanc <reg norm="concluſionem" type="context context">cõcluſionē</reg> demonſtraſſe aut <lb/>ſufficienter <reg norm="oſtendiſſe" type="context">oſtēdiſſe</reg>: <reg norm="sed" type="wordlist">ſꝫ</reg> eam <reg norm="probabiliter" type="simple">ꝓbabiliter</reg> pono.               <anchor type="note" xlink:href="note-0194-06" xlink:label="note-0194-06a"/>               </s>
              <s xml:id="N231B0" xml:space="preserve">¶ Ex <lb/>hac concluſione <reg norm="ſequitur" type="simple">ſequit̄̄</reg> primo /  ſi aliquod corpus <lb/>diuidatur <reg norm="per" type="wordlist">ꝑ</reg> partes proportionales proportione <lb/>dupla: et prima ſit aliqualiter denſa: et ſecunda in <lb/>ſexquitertio pluſ̄ prima et tertia in ſexquiquinta <lb/>pluſ̄ prima et <reg norm="quarta" type="wordlist">q̈rta</reg> in ſexquiſeptimo pluſ̄ <reg norm="prima" type="simple">ṗma</reg> /               <pb chead="De motu rarefactiouis  condenſationis." file="0195" n="195"/>               et ſic <reg norm="conſequenter" type="context context">cõſequēter</reg> <reg norm="procedendo" type="context">procedēdo</reg> <reg norm="per" type="wordlist">ꝑ</reg> ſpecies <reg norm="proportionis" type="simple">ꝓportionis</reg> ſu­<lb/>perparticularis denominatas a numeris impari­<lb/>bus: <reg norm="totius" type="simple">totiꝰ</reg> <reg norm="denſitas" type="context">dēſitas</reg> <reg norm="iudicanda" type="context">iudicãda</reg> eſt <reg norm="incommenſurabilis" type="context context">incõmēſurabilis</reg> ſal­<lb/>tem a nobis. </s>
              <s xml:id="N231C8" xml:space="preserve"><reg norm="= ſimiliter" type="wordlist">Siĺr</reg> diuiſio <reg norm="corpere" type="simple">corꝑe</reg> proportiõe tripla <lb/>et prima pars proportionalis ſit aliqualiter <reg norm="denſa" type="context">dēſa</reg> <lb/>et <reg norm="ſecunda" type="context">ſecūda</reg> in <reg norm="ſuperbipartiente" type="simple context">ſuꝑbipartiēte</reg> tertias denſior: et tertia <lb/>in <reg norm="ſuperbipartiente" type="context">ſuperbipartiēte</reg> <reg norm="quintas" type="context">quītas</reg> denſior <reg norm="quam" type="wordlist">ꝙ̄</reg> <reg norm="prima" type="simple">ṗma</reg>: et ſic ↄ̨ſe­<lb/>quenter <reg norm="continuo" type="context">cõtinuo</reg> <reg norm="procedendo" type="simple">ꝓcedendo</reg> <reg norm="per" type="wordlist">ꝑ</reg> ſpecies proportionis <lb/><reg norm="ſuperbipartientis" type="simple context">ſuꝑbipartiētis</reg> denoīatas a numeris <reg norm="imparibus" type="simple">imparibꝰ</reg> to­<lb/>tius <reg norm="denſitas" type="typo" resp="SPT">dãſitas</reg> eſt <reg norm="incommenſurabilis" type="context context">incõmēſurabilis</reg>. </s>
              <s xml:id="N231D7" xml:space="preserve">Innūera correla­<lb/>ria poſſunt iſto <reg norm="modo" type="wordlist">mõ</reg> inferri in <reg norm="quibus" type="wordlist">q̇bus</reg> <reg norm="reperietur" type="simple">reperiet̄̄</reg> denſi-<lb/>tas <reg norm="incommenſurabilis" type="context">incõmenſurabilis</reg> denſitati prime partis pro-<lb/>portionalis.</s>
            </p>
            <div xml:id="N231E0" level="5" n="31" type="float">
              <note position="right" xlink:href="note-0194-06a" xlink:label="note-0194-06" xml:id="N231E4" xml:space="preserve">1. <reg norm="corollarium" type="wordlist">correĺ.</reg></note>
            </div>
            <p xml:id="N231EA">
              <s xml:id="N231EB" xml:space="preserve">Quinta <reg norm="concluſio" type="context">cõcluſio</reg> </s>
              <s xml:id="N231EE" xml:space="preserve">Diuiſo corpore per <lb/>partes proportionales <reg norm="proportione" type="simple">ꝓportione</reg> irrationali: et <lb/>prima pars proportionalis ſit <reg norm="aliqualiter" type="wordlist">aliq̈liter</reg> denſa: et <lb/><reg norm="ſecunda" type="wordlist">ſcḋa</reg> in duplo: et tertia in triplo <reg norm="quam" type="wordlist">ꝙ̄</reg> prīa: et quarta <reg norm="in" type="wordlist">ī</reg> <lb/>quadruplo <reg norm="quam" type="wordlist">ꝙ̄</reg> prima: et ſic ↄ̨ſequēter: <reg norm="totius" type="simple">totiꝰ</reg> corporis <lb/>denſitas <reg norm="incommenſurabilis" type="context">incõmenſurabilis</reg> eſt denſitati prime par­<lb/>tis <reg norm="proportionalis" type="simple">ꝓportionalis</reg>. </s>
              <s xml:id="N231FD" xml:space="preserve"><reg norm="Probatur" type="simple">Probat̄̄</reg> hec <reg norm="concluſio" type="wordlist">ↄ̨cluſio</reg> / <reg norm="quam" type="wordlist">qm̄</reg> tota <reg norm="den­ ſitas" type="context">dē­<lb/>ſitas</reg> ſe <reg norm="habet" type="wordlist">hꝫ</reg> ad <reg norm="denſitatem" type="context">denſitatē</reg> prime partis proportiona­<lb/>lis in ea <reg norm="proportione" type="wordlist">proportiõe</reg> qua ſe <reg norm="habet" type="wordlist">hꝫ</reg> <reg norm="totum" type="context">totū</reg> diuiſum illa <reg norm="pro- portione" type="simple">ꝓ-<lb/>portione</reg> irrationali ad <reg norm="primam" type="simple context">ṗmã</reg> <reg norm="eius" type="simple">eiꝰ</reg> <reg norm="partem" type="context">partē</reg> <reg norm="proportiona- lem" type="simple context">ꝓportiona-<lb/>lē</reg>: vt <reg norm="patet" type="wordlist">pꝫ</reg> ex prima <reg norm="concluſione" type="context">cõcluſione</reg>. </s>
              <s xml:id="N23208" xml:space="preserve">Sed talis <reg norm="proportio" type="simple">ꝓportio</reg> eſt <lb/>irrationalis / vt patet: igitur <reg norm="concluſio" type="wordlist">ↄ̨cluſio</reg> vera.</s>
            </p>
            <p xml:id="N2320D">
              <s xml:id="N2320E" xml:space="preserve">Expeditis duobus prioribus articu-<lb/>lis q̄ notabilia et <reg norm="concluſiones" type="wordlist">ↄ̨cluſiones</reg> <reg norm="huius" type="simple">huiꝰ</reg> <reg norm="quaestionis" type="wordlist">q̄ſtiõis</reg> <reg norm="abſoluunt" type="context">abſoluūt</reg> <lb/>               <anchor type="note" xlink:href="note-0195-01" xlink:label="note-0195-01a"/>               </s>
              <s xml:id="N2321A" xml:space="preserve">¶ Reſtat <reg norm="tertius" type="simple">tertiꝰ</reg> articulus <reg norm="abſoluendus" type="context">abſoluēdus</reg> q̇ dubia <reg norm="huius" type="simple">huiꝰ</reg> <lb/>queſtionis enodat.</s>
            </p>
            <div xml:id="N2321F" level="5" n="32" type="float">
              <note position="left" xlink:href="note-0195-01a" xlink:label="note-0195-01" xml:id="N23223" xml:space="preserve">Tertia <lb/><reg norm="pars" type="wordlist">ꝑs</reg> <reg norm="quaestionis" type="wordlist">q̄ſtõis</reg></note>
            </div>
            <p xml:id="N2322B">
              <s xml:id="N2322C" xml:space="preserve">¶ Dubitatur <reg norm="igitur" type="simple">igit̄̄</reg> primo <reg norm="vtrum" type="context">vtrū</reg> raritas vniformiter <lb/>difformis, vel difformiter difformis cuius vtra <lb/>medietas <reg norm="eſt" type="wordlist">ē</reg> vniformis ſuo gradui medio <reg norm="correſpn­ deat" type="typo" resp="SPT">correſpn­<lb/>deat</reg> . ¶ Dubitatur ſcḋo: vtrū dabile ſit corpus fini­<lb/>tum infinite denſum et vniforme in dēſitate. </s>
              <s xml:id="N23237" xml:space="preserve">¶ Du-<lb/>bitat̄̄ tertio: vtrū dabile ſit corpus infinite rarum <lb/>vniforme in raritate. </s>
              <s xml:id="N2323E" xml:space="preserve">¶ Dubitat̄̄ quarto: vtrū illa <lb/>quin notabilia q̄ ponūtur a calculatore in capi­<lb/>tulo de raritate et denſitate ſint vera. </s>
              <s xml:id="N23245" xml:space="preserve">¶ Dubitaiur <lb/>quinto: vtrum aliq̇d ſit ita rarum ſicut denſum.</s>
            </p>
            <p xml:id="N2324A">
              <s xml:id="N2324B" xml:space="preserve">Dubitat̄̄ ſexto / nunq̇d ex vniformi acquiſitiõe ra­<lb/>ritatis ſequatur vniformis deperditio denſitatis <lb/>et econtra. </s>
              <s xml:id="N23252" xml:space="preserve">¶ Dubitat̄̄ ſeptimo / vtrū eque velociter <lb/>et eque proportionabiliter minorat̄̄ raritas ſicut <lb/>maiorat̄̄ dēſitas: et ecõtra. </s>
              <s xml:id="N23259" xml:space="preserve">¶ Dubitat̄̄ octauo / vtrū <lb/>ſi a nõ gradu raritatis acq̇rant aliqua eque velo-<lb/>citer de raritate cõtinuo manebunt eque rara.</s>
            </p>
            <p xml:id="N23260">
              <s xml:id="N23261" xml:space="preserve">¶ Dubitatur nono: vtrū quodlibet infinitū quãti-<lb/>tatiue habens infinitã materiã ſit infinite denſum <lb/></s>
              <s xml:id="N23267" xml:space="preserve">¶ Contra ṗmū dubiū arguit̄̄ prīo ſic / ſi raritas dif­<lb/>formiter difformis cuiꝰ vtra medietas eſt vnifor-<lb/>mis correſponderet gradui ſuo medio: ſeq̄ret̄̄ /  ꝑ <lb/>ſolam rarefactionē et motū ↄ̨ſequentē ipſam q̇ mo­<lb/>tus eſt augmētatio aliq̇d efficeretur denſius quam <lb/>antea erat: ſed ↄ̨ſequēs eſt falſum: igit̄̄ illud ex quo <lb/>ſequit̄̄. </s>
              <s xml:id="N23276" xml:space="preserve">Sequela ꝓbatur et pono caſum /  ſit vnum <lb/>bipedale cuius vna medietas ſit rara vt ſex: et alia <lb/>vt vnum: et volo /  rarefiat medietas vt vnū acq̇ren­<lb/>do vnū gradū raritatis: ita  efficiatur rarior in <lb/>duplo quieſcēte alia medietate vt .6. quo poſito ar­<lb/>guitur ſic / per te hec raritas huiꝰ corporis bipeda-<lb/>lis eſt vt tria cum dimidio: q2 ille eſt gradus mediꝰ <lb/>inter .6. et vnū. / et rarefacta illa medietate vt vnum <lb/>ad duplum vt ponit̄̄ in caſu: illud corpus bipeda-<lb/>le efficietur rarum. / vt .3. cum vna tertia: igitur effi-<lb/>cietur denſius quã antea erat: et hoc per ſolam ra-<lb/>refactionem et motum conſequentem rarefactionē <lb/>igitur. </s>
              <s xml:id="N23291" xml:space="preserve">Minor probatur /  vi3 illud corpus bipeda­<lb/>le efficietur rarum vt .3. cum vna tertia: quia ipſum               <cb chead="De motu rarefactiouis  condenſationis."/>               effectum eſt tripedale. </s>
              <s xml:id="N23299" xml:space="preserve">Nam medietas eius rara vt <lb/>vnum effecta eſt in duplo maior alia quieſcente et <lb/>ipſa erat pedalis. </s>
              <s xml:id="N232A0" xml:space="preserve">ergo effecta eſt bipedalis: et ꝑ cõ­<lb/>ſequens totum corpus effectū eſt tripedale cuiꝰ vna <lb/>tertia rara vt .6. denominat totū corpus rarum vt <lb/>duo: et alie due tertie denominãt ipſum rarum vt <lb/>vnum cū tertia: igitur tota raritas illius corporis <lb/>eſt vt tria cum vna tertia / quod fuit ꝓbandū. </s>
              <s xml:id="N232AD" xml:space="preserve">Iam ꝓ­<lb/>bo /  due tertie illiꝰ corporis denominãt vt vnum <lb/>cū vna tertia q2 illa medietas rara vt vnū effecta <lb/>eſt rara vt .2. et effecta eſt due tertie: ſꝫ duo gradus <lb/>raritatis exiſtentes in duabur tertiis denominãt <lb/>vt vnum cū tertia / vt cõſtat: igitur ille due tertie de­<lb/>nominant totum corpus rarum vt vnum cum vna <lb/>tertia: quod fuit probandum.</s>
            </p>
            <p xml:id="N232BE">
              <s xml:id="N232BF" xml:space="preserve">Secundo ad diem arguitur ſic. </s>
              <s xml:id="N232C2" xml:space="preserve">Si <lb/>raritas difformiter difformis cuius vtra medie-<lb/>tas eſt vniformis correſpõderet gradui medio: ſe-<lb/>queretur /  poſſet reduci ad vniformitatē ipſiꝰ gra­<lb/>dus medii: ſꝫ cõſequens eſt falſum: igit̄̄ illud ex quo <lb/>ſequitur falſitas ↄ̨ſequētis oſtēditur: et capio vnuꝫ <lb/>bipedale cuius vna medietas ſit rara vt .8. et altera <lb/>vt q̈tuor: et  medietas rara vt .8. deperdat duos <lb/>duos gradus raritatis: et illos acquirat medietas <lb/>rara. </s>
              <s xml:id="N232D7" xml:space="preserve">vt .4. / quo poſito ſic arguit̄̄ </s>
              <s xml:id="N232DA" xml:space="preserve">In fine illud corpꝰ <lb/>erit raruꝫ gradu medio puta vt .6. vt ſatis conſtat <lb/>et erit rarius ꝙ̄ antea: igitur autea nõ correſpõde-<lb/>bat gradui medio īmo remiſſiori gradui. </s>
              <s xml:id="N232E3" xml:space="preserve">Maior <lb/>eſt nota cum ↄ̨ſequētia: et minor ꝓbat̄̄ / q2 illud cor-<lb/>pus erit maius ꝙ̄ erit antea ſine acquiſitiõe mate-<lb/>rie: ergo rarius ꝙ̄ erat antea. </s>
              <s xml:id="N232EC" xml:space="preserve">Probat̄̄ añs / q2 me-<lb/>dietas rara vt .8. perdit ꝓportionē ſexquitertiam <lb/>raritatis: er ſic efficit̄̄ in ſexquitertio minor: et per <lb/>conſequēs ꝑdit vnam quartã pedalis. </s>
              <s xml:id="N232F5" xml:space="preserve">Medietas <lb/>vero rara vt .4. efficitur in ſexquialtero rarior et ſic <lb/>efficitur in ſexquialtero maior: et eſt pedalis / igitur <lb/>acquiſiuit medietatē pedalis: igitur in fine illḋ cur­<lb/>pus erit bipedale cū quarta. </s>
              <s xml:id="N23300" xml:space="preserve">Et ꝑ cõſequēs illḋ cor­<lb/>pus effectū eſt maius / quod fuit ꝓbandū.</s>
            </p>
            <p xml:id="N23305">
              <s xml:id="N23306" xml:space="preserve">Tertio ad idem arguitur ſic </s>
              <s xml:id="N23309" xml:space="preserve">Si rarū <lb/>vniformiṫ difforme correſpõderet ſuo gradui me-<lb/>dio: ſequeret̄̄ /  maior proportio eſſet medii ad ex-<lb/>tremū temiſſius quã extremi intenſioris ad punctū <lb/>mediū: ſꝫ hoc eſt fĺm. </s>
              <s xml:id="N23314" xml:space="preserve">igitur. </s>
              <s xml:id="N23317" xml:space="preserve">Sequela ꝓbatur / quia <lb/>idem eſt exceſſus quo extremū intenſius excedit pū­<lb/>ctum mediū et quo punctus medius excedit punctū <lb/>remiſſius: igitur maior eſt ꝓportio inter punctum <lb/>medium et extremū remiſſius: quã inter extremū in­<lb/>tenſius et punctum medium. </s>
              <s xml:id="N23324" xml:space="preserve">Patet hec conſequen­<lb/>tia per hanc maximam </s>
              <s xml:id="N23329" xml:space="preserve">Quãdo idē exceſſus addit̄̄ <lb/>minori et maiori quãtitati maior proportio acqui­<lb/>rit minoris quantitas ꝙ̄ maior / vt conſtat. </s>
              <s xml:id="N23330" xml:space="preserve">iam ꝓbo <lb/>falſitatem cõſequētis: et capio vnū corpus vnifor-<lb/>miter difformiter denſum ab octauo vſ ad quar-<lb/>tū: et arguo ſic / puncti medii ad extremū vt .4. eſt ꝓ-<lb/>portio ſexquialtera et extremi vt .8. ad punctum <lb/>medium eſt proportia ſexquitertia in denſitate / er­<lb/>go extremi vt .4. ad punctū medium eſt proportio <lb/>ſexquialtera in raritate: et puucti medii ad extre-<lb/>mū vt .8. eſt proportio ſexquitertia ī raritate. </s>
              <s xml:id="N23343" xml:space="preserve">Pa-<lb/>tet hec cõſequentia quoniã in quacun proportio­<lb/>ne aliquod eſt minꝰ denſum in eadem eſt rarius: igi­<lb/>tur maior eſt proportio puncti extremi intenſioris <lb/>ad punctum medium quam puncti medii ad extre-<lb/>mum remiſſius / quod fuit probanduꝫ </s>
              <s xml:id="N23350" xml:space="preserve">Patet hoc / q2 <lb/>extremum vt .4. in denſitate eſt extremū intenſius ī <lb/>raritate et extremuꝫ vt .8. in denſitate remiſſius in <lb/>raritate. </s>
              <s xml:id="N23359" xml:space="preserve">¶ In oppoſitum tamen arguitur ſic. </s>
              <s xml:id="N2335C" xml:space="preserve">quia               <pb chead="De motu rarefactionis  cõdenſationis." file="0196" n="196"/>               omnis denſitas difformiter difformis cuius vtra-<lb/> medietas eſt vniformis vel vniformiter diffor-<lb/>mis correſpondet ſuo gradui medio. </s>
              <s xml:id="N23368" xml:space="preserve">Et omnis ra­<lb/>ritas difformiter difformis: cuius vtra medie-<lb/>tas eſt vniformis et vniformiter difformis eſt den­<lb/>ſitas difformiter difformis etc̈. vel vniformiter dif­<lb/>formis: igitur omnis raritas difformiter diffor-<lb/>mis: cuius vtra medietas eſt vniformis vel vni-<lb/>formiter difformis correſpondent ſuo gradui me-<lb/>dio. </s>
              <s xml:id="N23379" xml:space="preserve">Conſequentia eſt nota, et winor probatur: q2 <lb/>eadem eſt latitudo denſitatis et raritatis. </s>
              <s xml:id="N2337E" xml:space="preserve">Nec ſe-<lb/>cundum hanc opinionem aliquo modo differunt <lb/>raritas difformis et denſitas difformis: igitur il-<lb/>la minor vera. </s>
              <s xml:id="N23387" xml:space="preserve">Sed iam probatur maior: et capio <lb/>vnum corpus difformiter difforme: cuius vra me­<lb/>dietas eſt vniformis: et manifeſtum eſt /  in medi-<lb/>etate denſiori eſt plus de materia quam in medie-<lb/>tate minus denſa: quia alias non eſſet denſior. </s>
              <s xml:id="N23392" xml:space="preserve">Ca-<lb/>pio igitur medietatem exceſſus illius materie cui <lb/>medietati exceſſus correſpondet etiam medietas <lb/>exceſſus denſitatis. </s>
              <s xml:id="N2339B" xml:space="preserve">Et volo /  ponatur in alia me-<lb/>dietate. </s>
              <s xml:id="N233A0" xml:space="preserve">Et hoc ſine deperditione aut acquiſitioue <lb/>quantitatis in aliqua illarum medietatum: quo <lb/>poſito illud corpus manebit: ita denſum ſicut an-<lb/>tea quia ſub equali quantitate continebit tantum <lb/>de materia ſicut antea: et manebit ſub gradu me-<lb/>dio: ergo modo ſua denſitas correſpondet ſuo gra­<lb/>dui medio. </s>
              <s xml:id="N233AF" xml:space="preserve">Conſequentia patet cum maiore: et ar-<lb/>guitur minor: quia vtra medietas manebit vni-<lb/>formiter denſa ſub gradu medio: igitur totum ma­<lb/>nebit denſum ſub gradu medio. </s>
              <s xml:id="N233B8" xml:space="preserve">Probatur antece­<lb/>dens per hanc maximam. </s>
              <s xml:id="N233BD" xml:space="preserve">Quandocun ſunt ali-<lb/>qua duo inequalia: et capitur medietas exceſſus <lb/>q̊ exceſſu maiꝰ excedit minꝰ: et illa medietas exceſſus <lb/>addit̄̄ minori. </s>
              <s xml:id="N233C6" xml:space="preserve">illa manebunt eq̈lia ſub gradu me-<lb/>dio inter illa: vt ſi a numero octonario demeretur <lb/>numerus binarius: et adderetur quaternario tunc <lb/>illi duo numeri manebunt equales ſub numero me­<lb/>dio puta vt .6. / vt conſtat: quia fuit medietas exceſ-<lb/>ſus quo maior numerus excedit mininorem ipſi nu-<lb/>mero minori addita: ſed ſic fit in ꝓpoſito quia me-<lb/>dietas exceſſus quo denſitas medietatis denſioris <lb/>excedit denſitateꝫ partis minus denſe additur ipſi <lb/>denſitati minori: igitur ille denſitates manent <lb/>equales.</s>
            </p>
            <note position="left" xml:id="N233DD" xml:space="preserve"> Soluit̄̄ <lb/>.1. dubiū</note>
            <p xml:id="N233E3">
              <s xml:id="N233E4" xml:space="preserve">Pro ſolutione huiꝰ dubitationis ad-<lb/>uertendum eſt /  ſecundum hanc opinionem que eſt <lb/>opinio calculatoris et ſecundum eius modum lo-<lb/>quendi. </s>
              <s xml:id="N233ED" xml:space="preserve">Raritas idem eſt omnino cum denſitate. <lb/></s>
              <s xml:id="N233F1" xml:space="preserve">Sed denſitas dicitur poſitue raritas priuatiue: <lb/>ſicut intenſio et remiſſio eadem latitudo ſunt. </s>
              <s xml:id="N233F6" xml:space="preserve">Di-<lb/>citur tamen intenſio poſitiue remiſſio vero priua-<lb/>tiue. </s>
              <s xml:id="N233FD" xml:space="preserve">Et propterea ſemper gradus denſitatis et ra­<lb/>ritatis eodem numero ſignantur: ita  denſitas <lb/>vt .8. eſt raritas vt .8. et raritas vt .4. eſt etiam den­<lb/>ſitas vt .4. et ſemper minor denſitas eſt maior ra-<lb/>ritas. </s>
              <s xml:id="N23408" xml:space="preserve">¶ Ex quo ſequitur /  denſitas vt .4. eſt maior <lb/>raritas quam denſitas vt .8. quia eſt in dupla mi-<lb/>nor denſitas: ergo in duplo maior raritas: et cum <lb/>denſitas vt .4. ſit raritas vt .4. vt nouiſſime dictum <lb/>eſt, et denſitas vt .8. ſit raritas vt .8. / ſequitur indu­<lb/>bitanter /  raritas vt .4. eſt maior raritas quam <lb/>raritas vt .8.</s>
            </p>
            <note position="left" xml:id="N23417" xml:space="preserve">Fundamē­<lb/>talis pro­<lb/>poſitio.</note>
            <p xml:id="N2341F">
              <s xml:id="N23420" xml:space="preserve">Unde ex mente calculatoris. </s>
              <s xml:id="N23423" xml:space="preserve">Pono talem funda­<lb/>mentalem propoſitionem in hac materia. </s>
              <s xml:id="N23428" xml:space="preserve">Rari-<lb/>tas intenditur per decrementum numeri: ſicut den­<lb/>ſitas per crementum (intenditur in̄ priuatiue) ita <lb/> ſi raritas vt .8. debet in eſſe raritatis intendi ad <lb/>duplum: oportet  ille numerus vt .8. decreſcat ad               <cb chead="De motu rarefactionis  cõdenſationis."/>               ſuum ſubduplum, et efficiatur vt .4. quia raritas <lb/>vt .4. eſt in duplo maior quam raritas vt .8. </s>
              <s xml:id="N23438" xml:space="preserve">Sed ſi <lb/>denſitas vt .8. debet augeri ſiue intendi ad duplū: <lb/>oportet vt efficiatur vt .16. quia raritas priuatiue <lb/>dicitur. </s>
              <s xml:id="N23441" xml:space="preserve">Denſitas vero poſitiue. </s>
              <s xml:id="N23444" xml:space="preserve">Probatur tamen <lb/>hec propoſitio quia capto corpore denſo vt octo: <lb/>manifeſtum eſt /  ſi illud debeat effici in duplo ra-<lb/>rius: ipſum debet effici in duplo minus denſum, et <lb/>per conſequens efficitur denſum vt .4. eſt ſed omne dē­<lb/>ſum vt .4. eſt rarum vt .4. / vt dictum eſt: et denſum <lb/>vt octo ſimiliter eſt rarum vt octo: igitur rarum vt <lb/>4. in duplo rarius eſt raro vt octo.</s>
            </p>
            <note position="right" xml:id="N23455" xml:space="preserve">1. rĺor.ec</note>
            <p xml:id="N23459">
              <s xml:id="N2345A" xml:space="preserve">¶ Ex quo ſequitur /  ſicut in poſitiuis maioris nu­<lb/>meri ad numerum minorem eſt ſemper proportio <lb/>maioris inequalitatis: prepoſtero ordine in priua­<lb/>tiuis minoris numeri ad numerū maiorem eſt pro-<lb/>portio maioris inequalitatis. </s>
              <s xml:id="N23465" xml:space="preserve">Exemplum: vt quia <lb/>6. gradum denſitatis ad .4. eſt proportio ſexqui-<lb/>altera, et raritas dicitur. </s>
              <s xml:id="N2346C" xml:space="preserve">priuatiue reſpectu denſi-<lb/>tatis .4. graduum raritatis ad .6. raritatis eſt pro­<lb/>portio ſexquialtera: et etiam .4. raritatis ad octo: <lb/>raritatis eſt proportio dupla: et quatuor raritatis <lb/>ad .12. eſt tripla: et quatuor ad .16. ad quadrupla: <lb/>et ſic conſequenter.</s>
            </p>
            <note position="right" xml:id="N23479" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N2347D">
              <s xml:id="N2347E" xml:space="preserve">¶ Ex quo vlterius infertur /  inter omnem gradum <lb/>raritatis et ſuum ſubduplum eſt in duplo maior la­<lb/>titudo quam inter ipſum et ſuū duplum raritatis <lb/>cuius oppoſitum ſemper contingit in poſitiuis qui­<lb/>buſcun: vt facile eſt videre. </s>
              <s xml:id="N23489" xml:space="preserve">Probatur /  rari-<lb/>tas vt octo eſt ſubdupla ad raritatem vt .4. et rari-<lb/>tas vt .2. eſt dupla raritas ad raritatem vt .4. et in <lb/>duplo maior latitudo eſt inter quartum et octauuꝫ <lb/>quam inter quartum et ſecundum : igitur maior la-<lb/>titudo eſt inter aliquem gradum et ſuum ſubduplū <lb/>quam inter ipſum et ſuum duplum.</s>
            </p>
            <note position="right" xml:id="N23498" xml:space="preserve">.3. correĺ.</note>
            <p xml:id="N2349C">
              <s xml:id="N2349D" xml:space="preserve">¶ Ex quo ſequitur / /  inter omnem gradum rarita­<lb/>tis finitum, et infinitum gradum raritatis eſt latitu­<lb/>do ſolum finita. </s>
              <s xml:id="N234A4" xml:space="preserve">Probatur / quia inter omneꝫ gra-<lb/>dum finitum denſitatis, et non gradum denſitatis <lb/>eſt latitudo ſolum finita / vt ſatis conſtat: igitur in-<lb/>ter omnem gradum finitum raritatis, et infinitum <lb/>raritatis eſt latitudo ſolū finita. </s>
              <s xml:id="N234AF" xml:space="preserve">Patet conſequen­<lb/>tia a cõuertibilibus. </s>
              <s xml:id="N234B4" xml:space="preserve">Cõuertitur enim non gradus <lb/>denſitatis et infinitus gradus raritatis: et raritas <lb/>finita: et denſitas finita. </s>
              <s xml:id="N234BB" xml:space="preserve">His ſic elucidatis ponitur.</s>
            </p>
            <p xml:id="N234BE">
              <s xml:id="N234BF" xml:space="preserve">Concluſio reſponſiua talis. </s>
              <s xml:id="N234C2" xml:space="preserve">Omnis <lb/>raritas vniformiter difformis vel difformiter dif-<lb/>formis: cuius vtra medietas eſt vniformis cor-<lb/>reſpondet ſuo gradui medio. </s>
              <s xml:id="N234CB" xml:space="preserve">Patet concluſio per <lb/>argumentum in oppoſitum factum.</s>
            </p>
            <p xml:id="N234D0">
              <s xml:id="N234D1" xml:space="preserve">Ad rationes ante oppoſitum. </s>
              <s xml:id="N234D4" xml:space="preserve">Ad pri-<lb/>mam reſpondeo negando ſequelam: et ad proba-<lb/>tionem admiſſo caſu nego minorem videlicet  il-<lb/>lud corpus in fine ſit rarum vt .3. cū duabus tertiis <lb/>et ad probationem concedo /  pars non rarefacta <lb/>denominat totum vt .2. / et nego  rarefacta <lb/>denontnat totum vt vnum cum dimidio: et ad pun­<lb/>ctum probationis concedo /  illa pars rarefacta <lb/>eſt vt due tertie: et nego /  illa effecta eſt rara vt duo / <lb/>immo dico /  effecta eſt rara vt dimidiuꝫ. </s>
              <s xml:id="N234E9" xml:space="preserve">Raritas <lb/>enim vt dimidium eſt dupla ad raritatem vt vnum <lb/>et raritas vt duo eſt ſubdupla / vt dictum eſt in no-<lb/>tabili: et ſic raritas illa duarum tertiarum deno-<lb/>minat totum vt vna tertia, et per conſequens tota <lb/>raritas eſt vt .2. cum tertia que eſt in ſexquialtero <lb/>maior raritate vt .3. cum medietate. </s>
              <s xml:id="N234F8" xml:space="preserve">Trium enī cū <lb/>dimidio ad .2. cum vna tertia eſt proportio ſexqui­<lb/>altera poſitiue, et per conſequens priuatiue duorū               <pb chead="Tertii tractatus" file="0197" n="197"/>               um tertia ad .3. cum dimidio eſt proportio ſexqui-<lb/>altera: et iſto modo ſolues ſimilia argumenta.</s>
            </p>
            <p xml:id="N23506">
              <s xml:id="N23507" xml:space="preserve">Ad ſecundam rationem. </s>
              <s xml:id="N2350A" xml:space="preserve">Reſpondeo <lb/>concedendo ſequalm, et negando falſitatem con-<lb/>ſequentis: et ad pumctum probationis dico breui-<lb/>ter /  argumentum falſo innititur quia putat ar-<lb/>guens /  rarefit debet reduci ad vniformitatem <lb/>per gradus raritatis, et hoc non eſt ita. </s>
              <s xml:id="N23517" xml:space="preserve">Sed debet <lb/>reduci vtendo gradibus denſitatis: hoc eſt dicere / <lb/> cum volumus reducere raritatem ad vniformi-<lb/>tatem debemus reducere denſitatem ſicut facimus <lb/>volentes reducere remiſſionem reducimus inten-<lb/>ſionem et reducta dēſitate reducta eſt etiam et ipſa <lb/>raritas quoniã nichil eſt aliud reducere raritatem <lb/>ad vniformitatem quam reducere denſitateꝫ: ſicut <lb/>reducere remiſſionem nichil aliud eſt quam reduce­<lb/>re intenſionem / vt conſtat. </s>
              <s xml:id="N2352C" xml:space="preserve">Qnare in propoſito ad <lb/>reducendum illud bipedale ad vniformitatē opor­<lb/>tet /  medietas denſa vt .8. que etiam eſt rara vt .8 <lb/>perdat duos gradus denſitatis, et illos acquirat <lb/>medittas denſa vt .4. que etiam eſt rara vt .4. et ſic <lb/>totum manebit vniformiter rarum gradu medio: <lb/>et etiam denſum gradu medio: et tam rarum: et tam <lb/>denſum: et tante quantitatis ſicut antea. </s>
              <s xml:id="N2353D" xml:space="preserve">Et ſic pa-<lb/>tet /  arguens falſum imaginatur quoniam opi-<lb/>natur  raritas vt .8. eſt maior raritas quam ra-<lb/>ritas vt .4. / quod eſt falſum / vt patet ex notabili: et <lb/>ideo non oportet /  medietas rara vt octo perdat <lb/>raritatem ſed acquirat, et medietas vt .4. perdat <lb/>raritatem et acquirat denſitatem.</s>
            </p>
            <p xml:id="N2354C">
              <s xml:id="N2354D" xml:space="preserve">Ad tertiam rationem. </s>
              <s xml:id="N23550" xml:space="preserve">Reſpondeo ne­<lb/>gando ſequelam, et ratio eſt quia ille modus argu­<lb/>endi non tenet in priuatiuis quãuis ſit neceſſarius <lb/>in poſitiuis.</s>
            </p>
            <note position="left" xml:id="N23559">
              <s xml:id="N2355B" xml:space="preserve">ſoluit̄̄ .2. <lb/>dubium. <lb/></s>
              <s xml:id="N23561" xml:space="preserve">Infinite <lb/>denſum.</s>
            </note>
            <p xml:id="N23566">
              <s xml:id="N23567" xml:space="preserve">Pro ſolutione ſecundi dubii. </s>
              <s xml:id="N2356A" xml:space="preserve">Danda <lb/>eſt diffinitio infinite denſi, et etiã īfinite rari. </s>
              <s xml:id="N2356F" xml:space="preserve">Unde <lb/>infinite denſum eſt illud quod ſub finita quantita-<lb/>te continet infinitum de materia: vel quod ſub infi-<lb/>nita quantitate continet vniformiter pcr totum in­<lb/>finitam materiam formaliter, vel reductiue: et re-<lb/>ductio fiat eodem modo quo reductio qualitatis <lb/>               <anchor type="note" xlink:href="note-0197-01" xlink:label="note-0197-01a"/>               </s>
              <s xml:id="N23583" xml:space="preserve">Infinite vero rarū eſt illud quod ſub infinita quã-<lb/>titate continet finitam materiam: his duabus de-<lb/>finitionibꝰ iactis vt fundamentis. </s>
              <s xml:id="N2358A" xml:space="preserve">Pono aliquas <lb/>concluſiones.</s>
            </p>
            <div xml:id="N2358F" level="5" n="33" type="float">
              <note position="left" xlink:href="note-0197-01a" xlink:label="note-0197-01" xml:id="N23593" xml:space="preserve">Infinite <lb/>rarum.</note>
            </div>
            <p xml:id="N2359B">
              <s xml:id="N2359C" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N2359F" xml:space="preserve">Poſſibile eſt dare <lb/>corpus finitum infinite denſum. </s>
              <s xml:id="N235A4" xml:space="preserve">Probatur et pono <lb/>caſum /  in prima proportionali vnius pedalis ſit <lb/>vnus gradus materie, et in ſecunda tantum: et in <lb/>tertia tantum de materia ſicut in prima. </s>
              <s xml:id="N235AD" xml:space="preserve">et ſic in in­<lb/>finitum. </s>
              <s xml:id="N235B2" xml:space="preserve">Quo poſito illud eſt finitum corpus: et in-<lb/>finite denſum, quia ſub finita quantitate continet <lb/>infinitam materiam / igitur concluſio vera.</s>
            </p>
            <p xml:id="N235B9">
              <s xml:id="N235BA" xml:space="preserve">Secunda concluſio. </s>
              <s xml:id="N235BD" xml:space="preserve">Non implicat <lb/>contradictionem dare corpus finitum infinite dē-<lb/>ſum vniformiter, ita  quelibet eius pars quanti-<lb/>tatiua ſit infinite denſa. </s>
              <s xml:id="N235C6" xml:space="preserve">Probatur hec concluſio, <lb/>quoniam nullum aliud incõueniens videtur ex hoc <lb/>ſequi, niſi  quelibet pars quantūcun parua cõ-<lb/>tinet infinitum de materia, et per cõſequens ibi eſt <lb/>penetratio materie. </s>
              <s xml:id="N235D1" xml:space="preserve">Sed hoc nullo modo implicat <lb/>igitur concluſio vera.</s>
            </p>
            <note position="left" xml:id="N235D6" xml:space="preserve">Correĺ.</note>
            <p xml:id="N235DA">
              <s xml:id="N235DB" xml:space="preserve">¶ Ex hac concluſione ſequitur /  tale corpus fini-<lb/>tum infinite denſum poteſt effici minus in duplo: et <lb/>in triplo, et ſic conſequenter: et tamen non poteſt ef­<lb/>fici denſius, nec hoc eſt inconueniens.</s>
            </p>
            <cb chead="Capitulū primum."/>
            <p xml:id="N235E6">
              <s xml:id="N235E7" xml:space="preserve">Tertia concluſio. </s>
              <s xml:id="N235EA" xml:space="preserve">Dabile eſt aliquod <lb/>corpus quod nec rarefieri nec condenſari poteſt to­<lb/>tali eius materia ſemꝑ manente vniformi omnino <lb/>nulla parte eius aliquam materiam deperdente <lb/></s>
              <s xml:id="N235F4" xml:space="preserve">Probatur / quia dato corpore infinito cuius que-<lb/>libet pars ſit infinite denſa vniformiter: illud non <lb/>poteſt rarefieri, quia ſemper in qualibet eius par-<lb/>te manebit materia infinita. </s>
              <s xml:id="N235FD" xml:space="preserve">Nec condenſari quia <lb/>iam eſt infinite denſum: ergo concluſio vera.</s>
            </p>
            <p xml:id="N23602">
              <s xml:id="N23603" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N23606" xml:space="preserve">Non eſt poſſibile <lb/>dare corpus finitum infinite rarū. </s>
              <s xml:id="N2360B" xml:space="preserve">Probatur / quia <lb/>omne tale ſub finita quantitate finitam materiam <lb/>continet: vel infinitam, ſi finitam, iam eſt denſum: <lb/>et per conſequens non infinite rarum. </s>
              <s xml:id="N23614" xml:space="preserve">Si vero in-<lb/>finitam iam eſt infinite denſum / vt patet ex defini-<lb/>tione, et per conſequens non eſt rarum: ergo tale <lb/>corpus non eſt infinite rarū. </s>
              <s xml:id="N2361D" xml:space="preserve">Et ſic patꝫ concluſio.</s>
            </p>
            <p xml:id="N23620">
              <s xml:id="N23621" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N23624" xml:space="preserve">Poſſibile eſt dare <lb/>corpus infinitum infinite rarum. </s>
              <s xml:id="N23629" xml:space="preserve">Probatur et po-<lb/>no /  deus producat vnum corpus infinitum, et pri­<lb/>mum pedale eius continet aliquantulum de mate-<lb/>ria, et ſecundum in duplo minus, et tertium in du-<lb/>plo minus ꝙ̄ ſecundum , et quartum in duplo minꝰ <lb/>̄ tertium, et ſic in infinitum. </s>
              <s xml:id="N23636" xml:space="preserve">Quo poſito ſequitur / <lb/> illud corpus eſt infinitum et infinite rarum: ergo <lb/></s>
              <s xml:id="N2363C" xml:space="preserve">Minor patet per definitionem corporis īfinite ra-<lb/>ri, illud enim finitam materiam continet: quia con­<lb/>tinet duplam ad materiam primi pedalis: habent <lb/>enim ſe ille materie cõtinuo in proportione dupla: <lb/>aggregatū ergo ex omnibus eſt duplū ad primū</s>
            </p>
            <p xml:id="N23647">
              <s xml:id="N23648" xml:space="preserve">Sexta concluſio. </s>
              <s xml:id="N2364B" xml:space="preserve">Non eſt poſſibile da­<lb/>re corpus vniformiter rarum īfinite raritatis: niſi <lb/>aliquis vellet concedere  aliquod corpus eſt infi-<lb/>nituꝫ cuiꝰ omnia puncta in infinitū diſtant: et nulla <lb/>finite. </s>
              <s xml:id="N23656" xml:space="preserve">et cuiꝰ non eſt ſignabilis aliqua pars finita. <lb/></s>
              <s xml:id="N2365A" xml:space="preserve">Probatur prima pars huius concluſionis, quia <lb/>ſignetur illud: et manifeſtum eſt /  non poteſt eſſe fi­<lb/>nitum / vt patet ex quarta concluſione: ergo eſt infi­<lb/>nitum tale corpus: capio ergo vnum pedale illius: <lb/>et arguo ſic / illud pedale eſt rarum: ergo habet ali-<lb/>quid de materia et tantum habet quodlibet pedale <lb/>illius corporis: cum ſit per te vniforme: et ſunt infi-<lb/>nita pedalia: ergo habet infinitã materiam: et per <lb/>conſequens non eſt infinite rarum. </s>
              <s xml:id="N2366D" xml:space="preserve">Patet conſe-<lb/>quentia ex definitione infinite rari. </s>
              <s xml:id="N23672" xml:space="preserve">Secunda vero <lb/>pars probatur / quia poſſet aliquis dtcere /  nõ eſt <lb/>ſignare aliquod pedale in tali corpore nec aliqua <lb/>pars finita: īmo quelibet pars illius eſt infinita: et <lb/>ſic argumentū contra eum non procedit: et per hoc <lb/>ad ſecundū et tertium dubia ſufficienter dictū puto</s>
            </p>
            <note position="right" xml:id="N2367F" xml:space="preserve">Soluit̄̄ <lb/>4. dubiū <lb/>Calcula.</note>
            <p xml:id="N23687">
              <s xml:id="N23688" xml:space="preserve">Pro quarti ſolutione dubii eſt aduer­<lb/>tendum /  calculator in capitulo de raritate et dē­<lb/>ſitate ponit quin notabilia de quorum veritate <lb/>queritur in hoc dubio: et ideo vt eorum veritas aut <lb/>falſitas appareat: oportet illa notabilia in hoc <lb/>loco recitare.</s>
            </p>
            <p xml:id="N23695">
              <s xml:id="N23696" xml:space="preserve">Primū eſt. </s>
              <s xml:id="N23699" xml:space="preserve">ſi ſint duo equaliter denſa <lb/>inequalis quantitatis que eque velociter rarefiãt <lb/>aut condenſentur: proportionaliter ſicut vnum eſt <lb/>maioris quantitatis quam reliquum ita velocius <lb/>acquiret vel deperdet de quantitate.</s>
            </p>
            <p xml:id="N236A4">
              <s xml:id="N236A5" xml:space="preserve">Secundum. </s>
              <s xml:id="N236A8" xml:space="preserve">Si ſint duo inequaliter <lb/>denſa equalia in quantitate que eque velociter ac­<lb/>quirant vel deperdant de denſitate proportiona-<lb/>li: ſicut vnum eſt alio minus denſum ita velocius               <pb chead="De motu rarefactionis  cõdenſationis." file="0198" n="198"/>               acquirit vel deperdit de quantitate.</s>
            </p>
            <p xml:id="N236B6">
              <s xml:id="N236B7" xml:space="preserve">Tertium. </s>
              <s xml:id="N236BA" xml:space="preserve">Si ſint duo inequalia in <lb/>quantitate et denſitate et ſicut vnum eſt alio maius <lb/>ita ſit eo denſius que eque velociter acquirant vel <lb/>deperdant de denſitate: eque velocitrr acquirunt <lb/>vel deperdunt de quantitate.</s>
            </p>
            <p xml:id="N236C5">
              <s xml:id="N236C6" xml:space="preserve">Quartum notabile. </s>
              <s xml:id="N236C9" xml:space="preserve">Si ſint duo ine-<lb/>qualia et inequaliter denſa ita tamen  maior ſit <lb/>proportio quantitatis vnius ad quantitatem al-<lb/>terius ꝙ̄ denſitatis vnius ad denſitatem alterius <lb/>que eque velociter acquirant vel deperdãt de den-<lb/>ſitate: velocius acquirit vel deperdit de quantita-<lb/>te maius quam minus.</s>
            </p>
            <p xml:id="N236D8">
              <s xml:id="N236D9" xml:space="preserve">Quintum. </s>
              <s xml:id="N236DC" xml:space="preserve">Si ſint duo inequalia in <lb/>quantitate et in denſitate, et minor ſi proportio <lb/>quãtitatis denſioris ad quantitatem alterius quã <lb/>denſitatis vnius ad denſitatem alterius que eque <lb/>velociter acquirant vel deperdãt de denſitate: den­<lb/>ſius tardius acquiret vel deperdet de quantitate <lb/>quam rarius. </s>
              <s xml:id="N236EB" xml:space="preserve">His notabilibus poſitis pono ali-<lb/>quas propoſitiones.</s>
            </p>
            <p xml:id="N236F0">
              <s xml:id="N236F1" xml:space="preserve">Prima propoſitio: ſecūdum notabile <lb/>eſt falſum               <anchor type="note" xlink:href="note-0198-01" xlink:label="note-0198-01a"/>               </s>
              <s xml:id="N236FB" xml:space="preserve">Probatur / quia eſt vna cõditionalis cu­<lb/>ius eſt antecedens eſt verum et conſequens falſum: er-<lb/>go illud notabile eſt falſum. </s>
              <s xml:id="N23702" xml:space="preserve">Probatur antecedēs / <lb/>et volo /  ſint duo pedalia quorum vnum ſit denſuꝫ <lb/>vt .8. et aliud vt .4. et vtrum illorum eque velociter <lb/>acquirat duos gradus denſitatis: tunc illud quod <lb/>eſt minus denſum deperdit vnam tertiam, et aliud <lb/>vnam quintam / vt patet. </s>
              <s xml:id="N2370F" xml:space="preserve">Sed vnius tertie ad vnaꝫ <lb/>quintam non eſt proportio dupla qualis eſt pro-<lb/>portio inter illorum pedalium denſitates: ergo nõ <lb/>in ea proportione qua vnuꝫ eſt minus denſum alio <lb/>in ea proportione velocius deperdit de quantita-<lb/>te: et ſic in hoc caſu anteccdens illius conditiona-<lb/>lis eſt verum, et conſequens falſum: quod fuit pro-<lb/>bandum. </s>
              <s xml:id="N23720" xml:space="preserve">Sed tu diceres /  iſta ratio nõ impugnat <lb/>notabile quoniam in notabile habetur que eque ve­<lb/>lociter acquirant vel deperdant de denſitate pro-<lb/>portionali: modo in caſu argumenti non eque pro­<lb/>portionalem denſitatem deperdunt illa duo peda­<lb/>lia. </s>
              <s xml:id="N2372D" xml:space="preserve">Sed hoc nichil eſt dicere. </s>
              <s xml:id="N23730" xml:space="preserve">Nam ſi eque propor-<lb/>tionalem denſitatem acquirerent vel deperderent <lb/>cum ſint equalia: ipſa equalem quantitatem oīno <lb/>acquirerunt aut deperderent quod eſt contra no-<lb/>tabile. </s>
              <s xml:id="N2373B" xml:space="preserve">Nec probatio qua calculator intēdit illud <lb/>notabile probare aliquid valet: quia antecedens <lb/>eius eſt falſum: videlicet hoc in qua proportione <lb/>vnum eſt minus denſum alio in ea proportione ve-<lb/>locius proportionabiliter acquirit vĺ deperdit de <lb/>denſitate. </s>
              <s xml:id="N23748" xml:space="preserve">Falſitas enim eius patet ex caſu argu-<lb/>menti contra illud notabile.</s>
            </p>
            <div xml:id="N2374D" level="5" n="34" type="float">
              <note position="left" xlink:href="note-0198-01a" xlink:label="note-0198-01" xml:id="N23751" xml:space="preserve">ↄ̈ calcuĺ.</note>
            </div>
            <p xml:id="N23757">
              <s xml:id="N23758" xml:space="preserve">Secunda propoſitio. </s>
              <s xml:id="N2375B" xml:space="preserve">Tertium nota­<lb/>bile eſt ſimiliter falſum.               <anchor type="note" xlink:href="note-0198-02" xlink:label="note-0198-02a"/>               </s>
              <s xml:id="N23765" xml:space="preserve">Probatur / quia eſt vna cõ-<lb/>ditionalis cuius antecedens eſt verū , et conſquens <lb/>falſum: ergo illud notabile eſt falſū. </s>
              <s xml:id="N2376C" xml:space="preserve">Arguitur an-<lb/>tecedens / quia capto quadrupedali denſo vt .4. et <lb/>pedali denſo vt vnum, et acquirat quadrupedale <lb/>4. gradus denſitatis, et pedale etiam eque veloci-<lb/>ter: tunc antecedens illius conditionalis eſt verum / <lb/>vt conſtat: et conſequens falſum : ergo propoſitum. <lb/></s>
              <s xml:id="N2377A" xml:space="preserve">Iam probo falſitatem conſequentis in illo caſu <lb/>quoniã illud quadrupedale efficitur in duplo den-<lb/>ſius, et per conſequens in duplo minus: et ſic perdit <lb/>bipedale: pedale vero non perdit bipedale / vt con-<lb/>ſtat cum non ſit niſi pedale: ergo tunc illa duo non <lb/>eque velociter acquirunt vel deperdunt de denſi-               <cb chead="De motu rarefactionis  cõdenſationis."/>               tate et ſic antecedens eſt verū: et conſequens falſum / <lb/>quod fuit probandū. </s>
              <s xml:id="N2378C" xml:space="preserve">Nec valet fugere ad id qḋ cal-<lb/>culator dicit in illo notabili tertio pro hoc inſtan­<lb/>ti quoniam pro inſtanti nulla fit acquiſitio quan-<lb/>titatis: et ideo illud nullo modo iuuat.</s>
            </p>
            <div xml:id="N23795" level="5" n="35" type="float">
              <note position="left" xlink:href="note-0198-02a" xlink:label="note-0198-02" xml:id="N23799" xml:space="preserve">Impuḡ-<lb/>tur terti-<lb/>um nöbi-<lb/>le calcuĺ.</note>
            </div>
            <note position="right" xml:id="N237A5" xml:space="preserve">īpugnat̄̄ <lb/>4. nõbile</note>
            <p xml:id="N237AB">
              <s xml:id="N237AC" xml:space="preserve">Tertia propoſitio. </s>
              <s xml:id="N237AF" xml:space="preserve">Quartum notabi­<lb/>le non eſt verum.               <anchor type="note" xlink:href="note-0198-03" xlink:label="note-0198-03a"/>               </s>
              <s xml:id="N237B9" xml:space="preserve">Probatur / quia eſt vna conditio-<lb/>nalis: cuius antecedens in caſu eſt verum: et conſe-<lb/>quens falſum: ergo. </s>
              <s xml:id="N237C0" xml:space="preserve">Probatur antecedens, et ca-<lb/>pio pedale et ſemipedale, et pedale ſit denſum vt .6 <lb/>ſemipedale vero vt .4. et deperdat vtrum illorum <lb/>duos gradus denſitatis in hora eque velociter. <lb/></s>
              <s xml:id="N237CA" xml:space="preserve">Quo poſito antecedens eſt verum. </s>
              <s xml:id="N237CD" xml:space="preserve">Nam illa ſunt <lb/>inequalia in quantitate et dēſitate maior et eſt pro-<lb/>portio quantitatis proportione denſitatis. </s>
              <s xml:id="N237D4" xml:space="preserve">Nam <lb/>illa eſt dupla hec vero ſexquialtera: et illa duo eque <lb/>velociter deperdunt vel acquirunt de denſitate. </s>
              <s xml:id="N237DB" xml:space="preserve">Et <lb/>tamen conſequens eſt falſum / quoniam maius illo­<lb/>rum non velocius acquirit de quantitate quã mi-<lb/>nus: immo equaliter. </s>
              <s xml:id="N237E4" xml:space="preserve">Nam vtrum illorum acqui­<lb/>rit ſemipedale / vt conſtat: ergo illud notabile falſū / <lb/>quod fuit probandum. </s>
              <s xml:id="N237EB" xml:space="preserve">Et aduerte  aliquãdo da-<lb/>ta veritate antecedentis: maius illorum equaliter <lb/>acquirit vt in caſu poſito. </s>
              <s xml:id="N237F2" xml:space="preserve">Aliquãdo maius acqui-<lb/>rit maiorem quantitatem quam minus: vt poſito <lb/>quadrupedali denſo vt .6. et pedali denſo vt .4. et <lb/>equaliter deperdat vtrum duos gradus denſita­<lb/>tis: tunc quadrupedale acquirit bipedale: pedale <lb/>vero vnū pedale preciſe. </s>
              <s xml:id="N237FF" xml:space="preserve">Aliquando maius deper-<lb/>dit minus de quantitate: vt videlicet poſito  a. ſit <lb/>9. pedum b.4.a. denſum vt .8.b. vero vt .4. et deper­<lb/>dat vtrum illorum eque velociter vnum gradum <lb/>denſitatis: tūc quadrupedale acquirit pedale cum <lb/>tertia. </s>
              <s xml:id="N2380C" xml:space="preserve">Aliud vero corpus maius acquirit pedale <lb/>cum duabus ſeptimis: modo plus eſt pedale cum <lb/>tertia quã cū duabus ſeptimis. </s>
              <s xml:id="N23813" xml:space="preserve">Ptꝫ hoc calculãti.</s>
            </p>
            <div xml:id="N23816" level="5" n="36" type="float">
              <note position="right" xlink:href="note-0198-03a" xlink:label="note-0198-03" xml:id="N2381A" xml:space="preserve">Calcuĺ.</note>
            </div>
            <note position="right" xml:id="N23820" xml:space="preserve">īpugnat̄̄ <lb/>.5. nöbile</note>
            <p xml:id="N23826">
              <s xml:id="N23827" xml:space="preserve">Quarta propoſitio. </s>
              <s xml:id="N2382A" xml:space="preserve">Quiutum nota-<lb/>bile eſt falſum.               <anchor type="note" xlink:href="note-0198-04" xlink:label="note-0198-04a"/>               </s>
              <s xml:id="N23834" xml:space="preserve">Probatur: quoniã dato  ſit vnuꝫ <lb/>ſextipedale denſum vt octo, et vnū bipedale denſū <lb/>vt .2. et vtrum illorum acquirat .4. gradus denſi-<lb/>tatis eque velociter: tunc antecedens illius conditi­<lb/>onalis eſt verum, et conſequens falſum. </s>
              <s xml:id="N2383F" xml:space="preserve">Nam tunc <lb/>denſius deperdit duo pedalia, et minus denſum nõ <lb/>perdit tantum quia tunc efficeretur non quantum / <lb/>g̊ illud notabile quintū eſt falſū / qḋ fuit ꝓbandum.</s>
            </p>
            <div xml:id="N23848" level="5" n="37" type="float">
              <note position="right" xlink:href="note-0198-04a" xlink:label="note-0198-04" xml:id="N2384C" xml:space="preserve">calcuĺ.</note>
            </div>
            <p xml:id="N23852">
              <s xml:id="N23853" xml:space="preserve">Sit ergo concluſio reſponſiua ad du­<lb/>bium quodlibet illorum notabilium dēpto primo <lb/>eſt falſum. </s>
              <s xml:id="N2385A" xml:space="preserve">Patet hec concluſio per quatuor predi-<lb/>ctas concluſiones. </s>
              <s xml:id="N2385F" xml:space="preserve">Sed quia poſſunt poni et demõ-<lb/>ſtari .4. notabilia conformia .4. his notabilibus <lb/>falſis impugnatis que plurimum ſubtilitatis ha­<lb/>bent. </s>
              <s xml:id="N23868" xml:space="preserve">Ideo huic loco ea interſerenduꝫ non ī merito <lb/>optaui illorum demonſtrationibus breuiitatis cau­<lb/>ſa et quadaꝫ alia occulta cauſa omiſſis. </s>
              <s xml:id="N2386F" xml:space="preserve">Sit igitur <lb/>               <anchor type="note" xlink:href="note-0198-05" xlink:label="note-0198-05a"/>               </s>
              <s xml:id="N23879" xml:space="preserve">Primū illorum .4. notabilium. </s>
              <s xml:id="N2387C" xml:space="preserve">¶ Si ſint duo ine-<lb/>qualiter denſa equalia tamen in quantitate que <lb/>eque velociter acquirant vel deperdant de denſita­<lb/>te: tunc in ea proportione minus denſum plus ac-<lb/>quirit vel deperdit de quantitate in qua ſe habet <lb/>denſitas denſioris ad denſitatem minus denſi in <lb/>fine depertionis vel acquiſitionis talis denſitatis. <lb/></s>
              <s xml:id="N2388C" xml:space="preserve">et nolo dicere /  per totum tempus in ea proporti-<lb/>one velocius acquirit: ſed in toto tempore cathego­<lb/>rematice. </s>
              <s xml:id="N23893" xml:space="preserve">Exēplum / vt ſi duo pedalia quoꝝ vnū eſt <lb/>denſum vt .8. et aliud vt .4. perdant duos gradus <lb/>denſitatis eque velociter dico /  pedale minꝰ den-<lb/>ſum in triplo maiorem quantitatem acquiſiuit <lb/>quam magis denſum quia proportio denſitatum               <pb chead="Tertii tractatus" file="0199" n="199"/>               in fine eſt tripla. </s>
              <s xml:id="N238A3" xml:space="preserve">Si vero duo pedalia acquirant <lb/>duos gradus denſitatis eque velociter: tūc minus <lb/>denſum maiorem quantitatem deperdit in pro-<lb/>portione ſuperbipartiente tertias: quia denſita-<lb/>tes illorum ſe habebunt in fine in proportione ſu-<lb/>perbipartiente tertias qualis eſt decem ad ſex.</s>
            </p>
            <div xml:id="N238B0" level="5" n="38" type="float">
              <note position="right" xlink:href="note-0198-05a" xlink:label="note-0198-05" xml:id="N238B4" xml:space="preserve">1. nöbile</note>
            </div>
            <note position="left" xml:id="N238BA" xml:space="preserve">2. nöbile</note>
            <p xml:id="N238BE">
              <s xml:id="N238BF" xml:space="preserve">¶ Secundū notabile: ſi ſint duo inequalia in quã-<lb/>titate et in denſitate, et ſicut eſt vnuꝫ alio maius ita <lb/>ſit eodem denſius que eque velociter acquirant de <lb/>denſitate: tunc denſius deperdit maiorem quanti-<lb/>tatem in ea proportione per quam proportio den-<lb/>ſitatum in principio excedit proportionem denſi-<lb/>tatum in fine. </s>
              <s xml:id="N238CE" xml:space="preserve">Si vero eque velociter deperdant de <lb/>denſitate: tunc denſius minorem quantitatem ac-<lb/>quirit in proportione per quam proportio denſi-<lb/>tatum in fine excedit proportionem denſitatum in <lb/>principio deperditionis denſitatum. </s>
              <s xml:id="N238D9" xml:space="preserve">Exemplum / <lb/>vt ſi ſit bipedale denſum vt .8. et pedale denſum vt <lb/>quatuor: et acquirat vtrum illoruꝫ duos gradus <lb/>dēſitatis eque velociter: tūc dico /  quantitas quã <lb/>deperdit denſius excedit quantitatem quã deper-<lb/>dit minus denſum in proportione ſexquiquinta. <lb/></s>
              <s xml:id="N238E7" xml:space="preserve">Illa em̄ eſt proportio per quã dupla excedit pro-<lb/>portionem ſuperbipartientem tertias que eſt pro-<lb/>portio denſitatum in fine. </s>
              <s xml:id="N238EE" xml:space="preserve">Exemplum ſecundi: vt ſi <lb/>illa duo corpora puta bipedale et pedale deperdãt <lb/>duos gradus denſitatis eque velociter: tunc denſiꝰ <lb/>minorem quantitatem acquirit ꝙ̄ minus denſum <lb/>in proportione ſexquialtera per quam tripla pro-<lb/>portio denſitatum in fine excedit duplam propor­<lb/>tionem denſitatum in principio.               <anchor type="note" xlink:href="note-0199-01" xlink:label="note-0199-01a"/>               </s>
              <s xml:id="N23902" xml:space="preserve">¶ Tercium nota-<lb/>bile. </s>
              <s xml:id="N23907" xml:space="preserve">Si ſint duo inequalia et inequaliter denſa. </s>
              <s xml:id="N2390A" xml:space="preserve">ita <lb/>tamen  maius ſit denſius: et  proportio quanti­<lb/>tatis vnius ad quantitatem alterius ſit maior <lb/>proportione denſitatis vnius ad denſitatem alte-<lb/>rius: que eque velociter acquirant de denſita-<lb/>te: tunc denſius maiorem quautitatem deper-<lb/>dit in ea proportione per quam proportio quanti­<lb/>tatis in principio excedit proportionem denſita-<lb/>tis in fine acquiſitionis: hoc eſt per quam propor-<lb/>tio que eſt inter quantitates in principio talis ac-<lb/>quiſitionis excedit proportionem que eſt inter dē-<lb/>ſitates in fine. </s>
              <s xml:id="N23923" xml:space="preserve">Si vero illa talia eque velociter de-<lb/>perdant de dēſitate: et proportio denſitatū in fine <lb/>ſit minor proportione quantitatum in principio: <lb/>tunc denſius maiorem quantitatē acquirit in pro-<lb/>portione per quam proportio quantitatū in prin-<lb/>cipio excedit proportionem denſitatum in fine. </s>
              <s xml:id="N23930" xml:space="preserve">Si <lb/>vero proportio denſitatū in fine fuerit equalis ꝓ-<lb/>portioni quantitatum in principio: tunc equalem <lb/>quantitatem acquirunt. </s>
              <s xml:id="N23939" xml:space="preserve">Si autem proportio den-<lb/>ſitatum in fine ſit maior proportione quantitatuꝫ <lb/>in principio: tunc minus denſum maiorem quanti­<lb/>tatem acquirit in ea proportione per quam pro-<lb/>portio denſitatū in fine excedit proportionē quan-<lb/>titatum in principio. </s>
              <s xml:id="N23946" xml:space="preserve">Exemplum primi: vt ſi bipe-<lb/>dale denſum vt .8. et pedale denſum vt .6. eque velo­<lb/>citer acquirant de denſitate acquirendo duos gra­<lb/>dus: tunc denſius deperdet maiorem quantitatem <lb/>̄ minus denſum in proportione ſupertripartien-<lb/>te quintas: quia illa eſt proportio per qnam pro-<lb/>portio dupla quantitatum in principio excedit ꝓ-<lb/>portionem denſitatum in fine que eſt ſexquiquarta <lb/></s>
              <s xml:id="N23958" xml:space="preserve">Exemplū ſecundi / vt eodem exemplo perdat vtrū <lb/>duos gradus denſitatis eque velociter: tunc denſiꝰ <lb/>maiorem quantitatem acquirit in proportione ſer­<lb/>quitertia: quia illa eſt proportio per quam propor­<lb/>tio quantitatum in principio que eſt dupla excedit               <cb chead="Capitulū primum."/>               proportionē denſitatum in fine que eſt ſexquialte-<lb/>ra / vt patet. </s>
              <s xml:id="N23968" xml:space="preserve">Exemplum tertii / vt eodem exemplo re­<lb/>tento perdat vtrum: 4. gradus denſitatis tunc e-<lb/>qualem quantitatē acquirunt quia proportio dē-<lb/>ſitatum in fine que eſt dupla eſt equalis proportiõi <lb/>quantitatū in principio cum etiam ſit dupla. </s>
              <s xml:id="N23973" xml:space="preserve">Exē-<lb/>plum .4. / vt retento eodem deperdat vtrum illoꝝ <lb/>quin gradus denſitatis: tunc minus denſum ac-<lb/>quirit maiorem quantitatem in proportione ſex-<lb/>quialtera que eſt proportio per quam tripla pro-<lb/>portio denſitatum in fine excedit proportionē du-<lb/>plam quantitatum in principio               <anchor type="note" xlink:href="note-0199-02" xlink:label="note-0199-02a"/>               </s>
              <s xml:id="N23987" xml:space="preserve">¶ Quartum nota­<lb/>bile. </s>
              <s xml:id="N2398C" xml:space="preserve">Si ſint duo inequalia in quantitate et in den-<lb/>ſitate, maiore exiſtente denſiore: et proportio denſi­<lb/>tatis vnius ad denſitatem alterius excedat ꝓpor-<lb/>tionem quantitatis eiuſdem ad quantitatem alte-<lb/>rius que eque velociter deperdant de dēſitate: tūc <lb/>minus denſum maiorem quantitatem acquirit ̄ <lb/>magis denſum in proportione per quam propor-<lb/>tio denſitatum in fine talis deperditionis excedit <lb/>proportionem quantitatum in principio. </s>
              <s xml:id="N2399F" xml:space="preserve">Si vero <lb/>illa duo equaliter acquirant de denſitate, et eque <lb/>velociter: : et proportio denſitatum in fine maneat <lb/>maior ꝙ̄ ſit proportio quantitatum in principio: <lb/>tunc minus denſum deperdit maiorem quantitatē <lb/>in proportione per quam proportio denſitatuꝫ in <lb/>fine excedit proportioneꝫ que eſt inter quantitates <lb/>in principio talis acquiſitionis ipſius denſitatis. <lb/></s>
              <s xml:id="N239B1" xml:space="preserve">Et ſi ꝓportio denſitatis in fine fuerit equalis pro-<lb/>portioni quantitatis in principio: tūc et magis dē­<lb/>ſum et minus denſum equalem quantitatem deper­<lb/>duut. </s>
              <s xml:id="N239BA" xml:space="preserve">Si autem proportio denſitatum in fine exce-<lb/>dit proportionem quantitatum in principio: tunc <lb/>magis denſum maiorem quantitatē deperdit quã <lb/>minus denſum in ea proportione per quam pro-<lb/>portio quantitatis in principio excedit proporti-<lb/>onem denſitatum in fine. </s>
              <s xml:id="N239C7" xml:space="preserve">Exemplum primi / vt ſi ſit <lb/>vnū bipedale denſum vt .8. et vnum pedale denſum <lb/>vt .2. et eque velociter deperdant vnum gradū den-<lb/>ſitatis: tunc minus denſum maiorem quantitatē <lb/>acquiret ꝙ̄ magis denſum in proportione tripla <lb/>ſexquialtera qualis eſt .7. ad .2. quia proportio dē­<lb/>ſitatum in fine que eſt ſeptupla excedit proportio-<lb/>nem duplam quantitatis que eſt in principio per <lb/>proportionem triplam ſexquialteram. </s>
              <s xml:id="N239DA" xml:space="preserve">Exemplum <lb/>ſecundi in eodem exemplo / ſi vtrum illorum ac-<lb/>quirat duos gradus denſitatis: tunc minus denſū <lb/>maiorem quantitatem deperdet in ea proportiõe <lb/>per quam proportio denſitatum in fine que eſt du­<lb/>pla ſexquialtera excedit proportionem quantita-<lb/>tum in principio que eſt dupla: et quia illa propor-<lb/>tio per quam dupla ſexquialtera excedit propor-<lb/>tionem duplã eſt ſexquiquarta. </s>
              <s xml:id="N239ED" xml:space="preserve">Ideo minus den-<lb/>ſum maiorem quantitatem acquiret in proporti-<lb/>one ſexquiquarta. </s>
              <s xml:id="N239F4" xml:space="preserve">Exemplum tertii / vt in eodem ca­<lb/>ſu. </s>
              <s xml:id="N239F9" xml:space="preserve">ſi vtrum illorum corporum acquirat .4. gra-<lb/>dus denſitatis: tunc equaliter deperdent de denſi-<lb/>tate: quia proportio denſitatum in fine erit equa-<lb/>lis proportioni quantitatum in principio. </s>
              <s xml:id="N23A02" xml:space="preserve">Exem-<lb/>plum quarti / vt in eodem exemplo. </s>
              <s xml:id="N23A07" xml:space="preserve">ſi vtrum il-<lb/>lorum corporū acquirat quī gradus denſitatis <lb/>tunc magis denſum maiorem quantitatem deper-<lb/>dit in proportione ſexquitridecimo quoniam pro-<lb/>portio quantitatum in principio que eſt dupla pro­<lb/>portionem denſitatum exuperat que eſt proportio <lb/>ſuperſextipartiens ſeptimas ꝑ proportionē ſex-<lb/>quitridecimam: vt ſatis conſtat. </s>
              <s xml:id="N23A18" xml:space="preserve">Hec notabilia que <lb/>numero quaternario abſoluūtur tanta ſubtilita-               <pb chead="De motu rarefactionis  cõdenſationis." file="0200" n="200"/>               te et induſtria et improbo labore exquiſita ſunt vt <lb/>merito quibuſcun aliis huius libelli cõcluſioni-<lb/>bus et preferri et anteponi poſſint </s>
              <s xml:id="N23A26" xml:space="preserve">Quapropter nõ <lb/>abs re eorum demonſtrationes at probationes <lb/>huic operi cenſui non interſerendas. </s>
              <s xml:id="N23A2D" xml:space="preserve">Malui enim <lb/>propter illorum notabiliū elaboratam ſubtilita-<lb/>tem et induſtriam vt eorem probationes velut ſci-<lb/>entia caballe propagentur et traducãtur.               <anchor type="note" xlink:href="note-0200-01" xlink:label="note-0200-01a"/>               </s>
              <s xml:id="N23A3B" xml:space="preserve">Et vt veꝝ <lb/>fatear: precipua cauſa non demonſtrandi hec no-<lb/>tabilia eſt: quia nondū opinior (vt cum Quītiliano <lb/>loquar) demonſtrationes illorum ſatis maturuiſſe <lb/>               <anchor type="note" xlink:href="note-0200-02" xlink:label="note-0200-02a"/>               </s>
              <s xml:id="N23A4B" xml:space="preserve">Utendū em̄ cenſeo Horatii conſilio qui in arte poe­<lb/>tica ſuadet ne p̄cipitetur editio: nõnū̄  premat̄̄ <lb/>in annū.               <anchor type="note" xlink:href="note-0200-03" xlink:label="note-0200-03a"/>               </s>
              <s xml:id="N23A57" xml:space="preserve">Uolo inſuper aliorum ſententias audire <lb/>vſus dotrina iacobi. </s>
              <s xml:id="N23A5C" xml:space="preserve">Sit oīs homo velox ad au­<lb/>diendū: tardus ad loquendum. </s>
              <s xml:id="N23A61" xml:space="preserve">Et nõ abs re quidē <lb/>qm̄ nõnū̄ credimꝰ teſte philoſopho habere demõ­<lb/>ſtationem quaꝫ non habemus: et ſcire qñ erramus <lb/></s>
              <s xml:id="N23A69" xml:space="preserve">Et hec de quarto dubio.               <anchor type="note" xlink:href="note-0200-04" xlink:label="note-0200-04a"/>               </s>
              <s xml:id="N23A71" xml:space="preserve">¶ Ad quītum dubium bre­<lb/>uiter reſpondet calculator in capitulo de raritate <lb/>et denſitate, et in capitulo de intenſione et remiſſiõe <lb/> raritas et denſitas et intenſio et remiſſio: nõ ſunt <lb/>comparabiles / et vnū dicitur poſitiue et aliud ṗua-<lb/>tiue: et ideo nichil eſt ita rarū ſicut denſum, nec ma­<lb/>gis rarum ꝙ̄ denſum: nec minus rarum ꝙ̄ denſum <lb/></s>
              <s xml:id="N23A81" xml:space="preserve">Et cum arguitur / hoc eſt aliqualiter denſum, et hoc <lb/>eſt aliqualiter rarum, et non eſt magis rarū ꝙ̄ den­<lb/>ſum: ergo hoc eſt ita rarum ſicut denſum: negat cõ­<lb/>ſequentiam: quia raritas non ſunt comparabiles <lb/>et priuatiue opponūtur. </s>
              <s xml:id="N23A8C" xml:space="preserve">Et ita reſpondet ſimiliter <lb/>ad ſeptimū dicendo  ſicut nõ ſunt comparabiles <lb/>raritas et dēſitas: ita nec deperditio deſitatis et <lb/>acquiſitio raritatis: vel econtra.               <anchor type="note" xlink:href="note-0200-05" xlink:label="note-0200-05a"/>               </s>
              <s xml:id="N23A9A" xml:space="preserve">¶ Ad ſextū dicit / <lb/> ex vniformi deperditione raritatis ſequitur vni­<lb/>formis acquiſitio denſitatis et econtra. </s>
              <s xml:id="N23AA1" xml:space="preserve">Illud tamē <lb/>ipſe videtur negare in capitulo de intenſione et re­<lb/>miſſiõe. </s>
              <s xml:id="N23AA8" xml:space="preserve">Poſſunt tamē hec dubia puta quītū, ſextū <lb/>ſeptimū cõcedi et ſine iactura defenſari prout ea de­<lb/>fenſaui iu lectura ſupra primū eapitulum. calcula-<lb/>toris. </s>
              <s xml:id="N23AB1" xml:space="preserve">Elige quod malueris.               <anchor type="note" xlink:href="note-0200-06" xlink:label="note-0200-06a"/>               </s>
              <s xml:id="N23AB9" xml:space="preserve">¶ Pro ſolutione octa­<lb/>ue dubitationis pono aliquas concluſiones.</s>
            </p>
            <div xml:id="N23ABE" level="5" n="39" type="float">
              <note position="left" xlink:href="note-0199-01a" xlink:label="note-0199-01" xml:id="N23AC2" xml:space="preserve">3. nöbile</note>
              <note position="right" xlink:href="note-0199-02a" xlink:label="note-0199-02" xml:id="N23AC8" xml:space="preserve">.4. nöbile</note>
              <note position="left" xlink:href="note-0200-01a" xlink:label="note-0200-01" xml:id="N23ACE" xml:space="preserve">Quinti-<lb/>lianus.</note>
              <note position="left" xlink:href="note-0200-02a" xlink:label="note-0200-02" xml:id="N23AD6" xml:space="preserve">Horatiꝰ <lb/>ḋ ar. po.</note>
              <note position="left" xlink:href="note-0200-03a" xlink:label="note-0200-03" xml:id="N23ADE" xml:space="preserve">Iacobi .i <lb/>pḣs .i. po­<lb/>ſterioruꝫ.</note>
              <note position="left" xlink:href="note-0200-04a" xlink:label="note-0200-04" xml:id="N23AE8" xml:space="preserve">ſoluit̄̄ .5. <lb/>dubium. <lb/>Calcuĺ.</note>
              <note position="left" xlink:href="note-0200-05a" xlink:label="note-0200-05" xml:id="N23AF2" xml:space="preserve"> Soluit̄̄ <lb/>6. dubiū</note>
              <note position="left" xlink:href="note-0200-06a" xlink:label="note-0200-06" xml:id="N23AFA" xml:space="preserve">ſoluit̄̄ .8. <lb/>dubium.</note>
            </div>
            <p xml:id="N23B02">
              <s xml:id="N23B03" xml:space="preserve">Prima ↄ̨̨cluſio </s>
              <s xml:id="N23B06" xml:space="preserve">Stat duo equaliṫ dēſa <lb/>eque cito cõdenſari vſ ad nõ gradum raritatis: <lb/>et tamen vnū in duplo velocius cõdenſabitur: ꝙ̄ re­<lb/>liquū. </s>
              <s xml:id="N23B0F" xml:space="preserve">Probatur et capio duo pedalia denſa vt .4. <lb/>et diuiſa hora per partes proportionales propor­<lb/>tione dupla vnū illorum in prima parte proporti-<lb/>onali acquirit aliquãtulum de denſitate et in ſcḋa <lb/>tantum et in tertia tantum ita  in qualibet parte <lb/>proportionali acquirat eliqualem denſitatem: et <lb/>aliud in qualibet parte proportionali acquirat in <lb/>dupla maiorem dēſitatem ꝙ̄ illud. </s>
              <s xml:id="N23B20" xml:space="preserve">Quo poſito eq̄ <lb/>cito deuenient ad nõ gradum raritatis: quia eque <lb/>cito deuenient ad gradum infinitum denſitatis, et <lb/>ſunt equaliter denſa, et vnū continuo in duplo ve-<lb/>locius cõdenſatur ꝙ̄ reliquū: igitur concluſio vera <lb/>               <anchor type="note" xlink:href="note-0200-07" xlink:label="note-0200-07a"/>               </s>
              <s xml:id="N23B32" xml:space="preserve">¶ Ex hoc ſequitur /  ſtat duo equalia eque cito de-<lb/>uenire ad nõ gradū raritatis ꝑ intēſionē dēſitatꝪ et <lb/>tñ in q̈druplo, et in quintuplo, et in quacun pro-<lb/>portione volueris vnū velocius altero condenſa-<lb/>bitur. </s>
              <s xml:id="N23B3D" xml:space="preserve">Patet eorralerium ſicut concluſio.</s>
            </p>
            <div xml:id="N23B40" level="5" n="40" type="float">
              <note position="left" xlink:href="note-0200-07a" xlink:label="note-0200-07" xml:id="N23B44" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N23B4A">
              <s xml:id="N23B4B" xml:space="preserve">Secunda concluſio. </s>
              <s xml:id="N23B4E" xml:space="preserve">Stat duo equa­<lb/>liter cõtinuo intēdi in denſitate, et eque cito deue-<lb/>nire ad nõ gradū raritatis: et tamen vnū continuo <lb/>eſſe denſius altero. </s>
              <s xml:id="N23B57" xml:space="preserve">Cõtinuo inquã vſ ad inſtans <lb/>in quo vtrum habet infinitū gradum denſitatis. <lb/></s>
              <s xml:id="N23B5D" xml:space="preserve">Probatur et capio duo pedalia quoꝝ vnū eſt deu­<lb/>ſum vt .18. et aliud vt .8. et volo /  in qualibet parte               <cb chead="De motu rarefactionis  cõdenſationis."/>               ꝓportionali hore ſequētis vtrū acquirat .4. gra­<lb/>dus quo poſito continuo vſ ad inſtans termina-<lb/>tiuum hore illa duo equaliter condenſabuntur: et <lb/>tamen vnū continuo erit denſius altero q2 ſemper <lb/>quod excedebat in principio per .8. gradus, exce-<lb/>det per .8. gradus / vt conſtat.               <anchor type="note" xlink:href="note-0200-08" xlink:label="note-0200-08a"/>               </s>
              <s xml:id="N23B74" xml:space="preserve">¶ Ex quo ſequitur /  <lb/>ſtat ſimiliter duo eque velociter acquirere de den-<lb/>ſitate, et eque cito deuenire ad infinitum gradum <lb/>denſitatis: et ſemper manere equalia in denſitate. <lb/></s>
              <s xml:id="N23B7E" xml:space="preserve">Patet hoc dato /  duo pedalia ſint eque denſa in <lb/>principio que continuo eque velociter cõdenſentur</s>
            </p>
            <div xml:id="N23B83" level="5" n="41" type="float">
              <note position="right" xlink:href="note-0200-08a" xlink:label="note-0200-08" xml:id="N23B87" xml:space="preserve">Correĺ.</note>
            </div>
            <note position="right" xml:id="N23B8D" xml:space="preserve">Calcuĺ.</note>
            <p xml:id="N23B91">
              <s xml:id="N23B92" xml:space="preserve">Tertia concluſio / a.  b. ſunt inequaliṫ <lb/>denſa et b. continuo velocius condenſabitur ꝙ̄ a. <lb/>vſ ad infinitum gradum denſitatis: et b. continuo <lb/>manebit minus denſum ꝙ̄ a. </s>
              <s xml:id="N23B9B" xml:space="preserve">Probatur et pono ca­<lb/>ſum /  a. ſit denſum vt .8.b. vero vt .4. et in qualibet <lb/>parte proportionali hore ſequentis a. acquirat .4. <lb/>gradus denſitatis b. vero in prima parte propor-<lb/>tionali acquirat .6. gradus denſitatis: et in ſecun-<lb/>da quin: et in tertia .4. cum dimidio: in quarta <lb/>.4. cum vna quarta: et in quinta .4. cum vna octaua <lb/>et ſic infinitum. </s>
              <s xml:id="N23BAC" xml:space="preserve">quo poſito ſemper b. velocius con-<lb/>denſabitur ꝙ̄ a. vſ ad inſtans terminatiuum ho-<lb/>re in quo erunt infinite denſa a. et b. et ſemper b. ma­<lb/>nebit minꝰ dēſum / vt cõſtat et apparet intuenti: igr̄.</s>
            </p>
            <p xml:id="N23BB5">
              <s xml:id="N23BB6" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N23BB9" xml:space="preserve">Stat aliqua duo <lb/>a non gradu raritatis continuo eque velociter ac-<lb/>quirere de raritate: et continuo vnum manebit ra-<lb/>rius altero in quacū proportione volueris. </s>
              <s xml:id="N23BC2" xml:space="preserve">Stat <lb/>etiam  a non gradu raritatis incipiant eque ve-<lb/>lociter acquirere de raritate: et  continuo mane-<lb/>ant eque rara. </s>
              <s xml:id="N23BCB" xml:space="preserve">Probatur prima pars huic cou-<lb/>cluſionis ex ſecunda concluſione et correlario pri-<lb/>me: hoc addito  omnino eodem modo illa remit-<lb/>tantur ab infinito gradu denſitatis deꝑdēdo den-<lb/>ſitatē et acquirēdo raritates eodē mõ oīno et eq̄ ve-<lb/>lociter ſicut deperdebant raritatem et acquirebant <lb/>denſitatem: ita  omnino eodem modo ſe habeãt <lb/>in via rarefactionis ſicut ſe habebãt in via cõden-<lb/>ſationis: et quia in via cõdenſationis ſemper vnū <lb/>erat rarius altero: et ita etiam ſe debent habere in <lb/>via rarefactionis vt ponitur in caſu: igitur in via <lb/>rarefactionis ſemper vnū erit rarius altero / quod <lb/>fuit probandum. </s>
              <s xml:id="N23BE6" xml:space="preserve">Secunda pars probatur ex corre­<lb/>lario ſecunde concluſionis: hoc addito  illa duo <lb/>poſt̄ fuerint infinite denſa incipiant omnino eo-<lb/>dem modo deperdere denſitatem et acquirere rari­<lb/>tatem ſicut antea acquirebat denſitatem et deper-<lb/>debant raritatem: ita  cõtinuo in via rarefactio-<lb/>nis oīno eodem modo ſe habeant ſicut in via con-<lb/>denſationis: et quia in via condenſationis cõtinuo <lb/>erant eque rara: ſequitur /  in via rarefactionis <lb/>continuo manebunt eque rara.</s>
            </p>
            <p xml:id="N23BFB">
              <s xml:id="N23BFC" xml:space="preserve">¶ Ex quo ſequitur /  ſtat aliqua duo incipere rare­<lb/>fieri a non gradu raritatis vnum continuo velo-<lb/>cius altero: et continuo illud quod velocius rarefit <lb/>manebit minus rarum. </s>
              <s xml:id="N23C05" xml:space="preserve">Patet hoc correlarium ex <lb/>prima concluſione auxiliãte modo probandi pre-<lb/>cedentem concluſionem.</s>
            </p>
            <p xml:id="N23C0C">
              <s xml:id="N23C0D" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N23C10" xml:space="preserve">Et eſt calculatoris <lb/></s>
              <s xml:id="N23C14" xml:space="preserve">Nichil poteſt a finito gradu quantitatis et a non <lb/>gradu raritatis incipere rarefieri ſine deperditi-<lb/>one materie: niſi ſubito efficiatur infinite quantita­<lb/>tis. </s>
              <s xml:id="N23C1D" xml:space="preserve">¶ Probatur / quia ſi illud eſt finitum quan-<lb/>titatiue, et habet non gradum raritatis / ſequitur / <lb/> ipſum eſt infinite denſum: et habet infinitam ma­<lb/>teriam: et nullam materiam deperdet. </s>
              <s xml:id="N23C26" xml:space="preserve">et iam inci-<lb/>pitur rarefieri per remotiouem de preſenti:. / igitur               <pb chead="Tertii tractatus" file="0201" n="201"/>               immediate poſt hoc erit rarum: et continet infini-<lb/>tam materiam. </s>
              <s xml:id="N23C32" xml:space="preserve">igitur immediate poſt hoc habe-<lb/>bit infinitam quantitatem. </s>
              <s xml:id="N23C37" xml:space="preserve">Patet conſequentia <lb/>qnia ſi haberet finitam quantitatem et infinitam <lb/>materiam nullo pacto eſſet rarū / et per conſequens <lb/>ſubito efficietur īfinite quãtitatis / qḋ fuit ꝓbandū <lb/>               <anchor type="note" xlink:href="note-0201-01" xlink:label="note-0201-01a"/>               </s>
              <s xml:id="N23C47" xml:space="preserve">¶ Ex hac concluſione ſequitur /  nullū finitum nec <lb/>etiam infinitū vniformiter denſum: ita  quelibet <lb/>pars eius ſit infinite denſa poteſt rarefieri ſine de-<lb/>perditione materie a ſe toto et a parte: ita  nulla <lb/>pars eiꝰ deperdat materiã. </s>
              <s xml:id="N23C52" xml:space="preserve">Patet hoc correlariū <lb/>facile / q2 tunc quelibet pars eius manebit infinite <lb/>denſa ſicut antea: quia vt ponitur nulla eius pars <lb/>debet deꝑdere aliquã materiã, nec aliquis pūctus, <lb/>et ſic ad quēlibet punctū manebit infinita denſitas <lb/>et imagineris eodē modo in iſto correlario ſicut ſi <lb/>vnum vniforme infinite calidum rarefieret nullo <lb/>puncto eius aut parte perdente caliditatem.</s>
            </p>
            <div xml:id="N23C63" level="5" n="42" type="float">
              <note position="left" xlink:href="note-0201-01a" xlink:label="note-0201-01" xml:id="N23C67" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N23C6D" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N23C71">
              <s xml:id="N23C72" xml:space="preserve">¶ Sequitur ſcḋo /  vnū vniformiter infinite denſuꝫ <lb/>per totū poteſt rarefieri: id eſt effici rarū. </s>
              <s xml:id="N23C77" xml:space="preserve">Probat̄̄ <lb/>et capio vnū infinitū infinite denſum vniformiter: <lb/>ita  ad quēlibet punctū eius ſit infinita materia. <lb/></s>
              <s xml:id="N23C7F" xml:space="preserve">et volo /  oēs gradus materie qui ſunt in ſcḋo peda­<lb/>li illius ponant̄̄ in primo pedali dempto vno et ſic <lb/>fiet de quolibet pedali ſequenti: ita  in quolibet <lb/>pedali ſequēte primū nõ maneat niſi vnus gradus <lb/>materie: quo poſito illud eſt rarū q2 nõ eſt niſi den-<lb/>ſum vt vnū: vt patebit ex dubio ſequenti / q2 infinita <lb/>denſitas in parte finita infiniti nullo modo deno-<lb/>minat infinitū. </s>
              <s xml:id="N23C90" xml:space="preserve">Et hec etiã eſt opinio calculatoris. <lb/>               <anchor type="note" xlink:href="note-0201-02" xlink:label="note-0201-02a"/>               </s>
              <s xml:id="N23C9A" xml:space="preserve">¶ Ex quo ſequitur tertio /  nõ poſſunt dari duo eq̄ <lb/>denſa quorum vnū poſſet rarefieri et nõ aliud.               <anchor type="note" xlink:href="note-0201-03" xlink:label="note-0201-03a"/>               </s>
              <s xml:id="N23CA4" xml:space="preserve">¶ Et <lb/>hoc correlariñ eſt cõtra calculatorē ponentē oppo-<lb/>ſitū in propria forma. </s>
              <s xml:id="N23CAB" xml:space="preserve">Probat̄̄ tamen / q2 nõ eſt da-<lb/>bile aliquod corpꝰ finitū infinite denſum vniformi-<lb/>ter quī ipſum poſſet effici īfinite, et deinde poſſunt <lb/>a quolꝫ pedali eiꝰ dēpto primo oēs gradus materi <lb/>vno dēpto remoueri et poni in primo pedali / vt po-<lb/>nitur in p̄cedenti correlario: quo poſito iam ptꝫ /  <lb/>ſcḋm eundē calculatorē manebit dēſum vt vnū et ra­<lb/>rum nullū eſt / igitur denſum qm̄ poſſit effici rarū et <lb/>per ↄ̨ñs correlariū veꝝ. </s>
              <s xml:id="N23CBE" xml:space="preserve">Sed tu dices /  dictū corre-<lb/>lariū nõ ſequit̄̄ niſi addicta calculatoris: et dices / <lb/> illa denſitas īfinita in primo pedali adhuc ſuffi­<lb/>cit infinite denoīare totū. </s>
              <s xml:id="N23CC7" xml:space="preserve">Quapropter alio modo <lb/>ꝓbo tale corpus poſſe effici finite denſum vniforme / <lb/>et volo /  poſt̄ primū pedale habet infinitos gra­<lb/>dus materie, et quodlibet ſequens habet preciſe <lb/>vnū:  dimiſſis duobus in primo pedali in prima <lb/>parte ꝓportionali ponat̄̄ vnꝰ gradus de reſiduis <lb/>in ſecūdo pedali, et in ſcḋa parte ꝓportionali po-<lb/>natur vnus alter in tertio, et ſic cõſequēter: quo po­<lb/>ſito in fine hore quodlibet pedale habebit preciſe <lb/>duos gradus denſitatis et materie: et ſic totū illud <lb/>corpus erit vniformiter rarū per totū vt duo: igit̄̄ <lb/>poteſt rarefieri / quod fuit probandū. </s>
              <s xml:id="N23CE0" xml:space="preserve">Si tamen ve-<lb/>lis dicere /  quodlibet infinitū quãtitatiue, habēs <lb/>infinitam materiam eſſet infinite denſum oīa iſta <lb/>locū non haberent: ſed hoc non videtur rationabi­<lb/>liter dictum / vt in ſequenti dubio declarabitur.</s>
            </p>
            <div xml:id="N23CEB" level="5" n="43" type="float">
              <note position="left" xlink:href="note-0201-02a" xlink:label="note-0201-02" xml:id="N23CEF" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0201-03a" xlink:label="note-0201-03" xml:id="N23CF5" xml:space="preserve">ↄ̈ calcuĺ.</note>
            </div>
            <note position="left" xml:id="N23CFB" xml:space="preserve">ſoluit̄̄ .9. <lb/>dubium.</note>
            <p xml:id="N23D01">
              <s xml:id="N23D02" xml:space="preserve">¶ Pro ſolutione none dubitationis pono duas <lb/>concluſiones.</s>
            </p>
            <p xml:id="N23D07">
              <s xml:id="N23D08" xml:space="preserve">Prima ↄ̨̨cluſio </s>
              <s xml:id="N23D0B" xml:space="preserve">Probabile eſt qḋlibet <lb/>habens infinitam materiam eſſe infinite denſum. <lb/></s>
              <s xml:id="N23D11" xml:space="preserve">Probatur / q2 quodlibet finitū habēs infinitã ma-<lb/>teriam eſt infinite denſum, et aliquod infinitū ha-<lb/>bens infinitã materiam eſt infinite denſum, et non <lb/>eſt maior ratio de vno habente infinitã materiam <lb/>̄ de altero: igitur qnodlibet tam finitū ꝙ̄ infinitã               <cb chead="Capitulū primum."/>               habens infinitam materiam eſt infinite denſum. <lb/>               <anchor type="note" xlink:href="note-0201-04" xlink:label="note-0201-04a"/>               </s>
              <s xml:id="N23D26" xml:space="preserve">¶ Ex quo ſequitur /  ſi ſit vnū corpus infinitū cuiꝰ <lb/>quodlibet pedale habet vnū gradum materie pre-<lb/>ciſe: illud tale eſt infinite denſum.               <anchor type="note" xlink:href="note-0201-05" xlink:label="note-0201-05a"/>               </s>
              <s xml:id="N23D32" xml:space="preserve">¶ Sequitur ſcḋo / <lb/> ſi ſit vnū infinitum cuius primum pedale habet <lb/>infinitum de materia et totum reſiduū non denſum <lb/>ſed infinite rarum: illud tale eſt infinite denſum.</s>
            </p>
            <div xml:id="N23D3B" level="5" n="44" type="float">
              <note position="right" xlink:href="note-0201-04a" xlink:label="note-0201-04" xml:id="N23D3F" xml:space="preserve">.1. correĺ</note>
              <note position="right" xlink:href="note-0201-05a" xlink:label="note-0201-05" xml:id="N23D45" xml:space="preserve">2. correĺ.</note>
            </div>
            <note position="right" xml:id="N23D4B" xml:space="preserve">.3. correĺ.</note>
            <p xml:id="N23D4F">
              <s xml:id="N23D50" xml:space="preserve">¶ Sequitur tertio /  infinite denſum debet ſic de-<lb/>finiri: infinite denſum eſt quantum habens infini-<lb/>tum de materia. </s>
              <s xml:id="N23D57" xml:space="preserve">Non enim proprie non quantum <lb/>eſt denſum: vt patet ex definitionibus rari et denſi.</s>
            </p>
            <p xml:id="N23D5C">
              <s xml:id="N23D5D" xml:space="preserve">Secūda ↄ̨̨cluſio. </s>
              <s xml:id="N23D60" xml:space="preserve">Probabilius eſt nõ <lb/>quodlibet habens infinitum de materia eſſe infi-<lb/>nite denſum. </s>
              <s xml:id="N23D67" xml:space="preserve">Probatur / quia tunc ſequeretur /  a-<lb/>liquod infinitum eſſet infinite denſum, et a moto <lb/>vno pedali eius preciſe manebit infinite rarum. <lb/></s>
              <s xml:id="N23D6F" xml:space="preserve">Patet dato /  ſit vnum infinitum in cuius primo <lb/>pedali ſit infinitum de materia et in toto reſiduo <lb/>finite tantuꝫ: quo poſito a moto primo pedali iam <lb/>illud manebit infinite rarum, et modo eſt infinite <lb/>denſum per te: igitur propoſitum.</s>
            </p>
            <p xml:id="N23D7A">
              <s xml:id="N23D7B" xml:space="preserve">Et confirmat̄̄. </s>
              <s xml:id="N23D7E" xml:space="preserve">Q2 nõ qḋlibet habens <lb/>infinitam albedinem intenſiue eſt infinite album: <lb/>ergo non quodlibet habens infinitam materiam <lb/>eſt infinite denſum. </s>
              <s xml:id="N23D87" xml:space="preserve">Conſequentia tenet a ſimili: et <lb/>antecedens patet / quia dato vno infinito cuiꝰ pri-<lb/>mum pedale ſit infinite album, et totum reſiduum <lb/>non ſit album vel finite album: illud tale nõ eſt in-<lb/>finite album: igitur aſſumptum verum.</s>
            </p>
            <note position="right" xml:id="N23D92" xml:space="preserve">.1. correĺ. <lb/>q̇d īfinite <lb/>denſum.</note>
            <p xml:id="N23D9A">
              <s xml:id="N23D9B" xml:space="preserve">¶ Ex hac concluſione ſequit̄̄ primo /  infinite den-<lb/>ſum debet ſic definiri: vt prius dictum eſt. </s>
              <s xml:id="N23DA0" xml:space="preserve">Infinite <lb/>denſum eſt illud / quod ſub finita quantitate habet <lb/>infinitã materiam, vel ſub infinita quantitate ha-<lb/>bet infinitam materiam per totum formaliter vel <lb/>reductiue. </s>
              <s xml:id="N23DAB" xml:space="preserve">Et in tali reductiõe quelibet materia po­<lb/>natur in tanto ſubiecto in quanto erat antea ade-<lb/>quate ſicut ſit in reductione qualitatis.               <anchor type="note" xlink:href="note-0201-06" xlink:label="note-0201-06a"/>               </s>
              <s xml:id="N23DB7" xml:space="preserve">¶ Ex quo <lb/>ſequitur ſecūdo /  ſi alicuius corporis infiniti pri­<lb/>mum pedale habuerit vnum gradum materie et ſe-<lb/>cundum duplam ad illam et tertium quadruplam <lb/>et quartum octuplam, et quintum ſexdecuplam, et <lb/>ſic in īfinitum: tale corpus eſt infinite denſum quia <lb/>habet per totum infinitam materiam reductiue. <lb/></s>
              <s xml:id="N23DC7" xml:space="preserve">Utendo em̄ debita reductione illa materia mane-<lb/>bit per totuꝫ infinita.               <anchor type="note" xlink:href="note-0201-07" xlink:label="note-0201-07a"/>               </s>
              <s xml:id="N23DD1" xml:space="preserve">¶ Sequitur tertio /  quãuis <lb/>vnum infinitum cuius primum pedale habet infi-<lb/>nitos gradus materie et quodlibet aliorum vnum <lb/>preciſe poſſet mediante eadem materia effici infi-<lb/>nite denſum per totum: nichilominus tamen quã-<lb/>do ſic primum pedale habet infinitos gradus ma­<lb/>terie et quodlibet aliorum vnum dumtaxat: illud <lb/>corpus eſt ſolum denſum vt vnum. </s>
              <s xml:id="N23DE2" xml:space="preserve">Probatur pri-<lb/>ma pars / quia vbi ſunt infiniti gradus materie ibi <lb/>ſunt infinities infiniti / vt patet intelligenti mate-<lb/>riam de infinito. </s>
              <s xml:id="N23DEB" xml:space="preserve">Ponantur igitur in ſecundo pe-<lb/>dali infiniti, et in tertio infiniti, et in quarto infi-<lb/>niti, et ſic conſequenter: et maneant in primo etiaꝫ <lb/>infiniti vt eſt ſatis poſſibile. </s>
              <s xml:id="N23DF4" xml:space="preserve">et patet /  in fine illud <lb/>corpus erit infinite denſum per totum per illam <lb/>materiam quam habebat antea preciſe: et ſic pa-<lb/>tet prima pars correlarii. </s>
              <s xml:id="N23DFD" xml:space="preserve">Secunda pars proba-<lb/>tur / quia ſecundum hanc opinionem denſitas infi-<lb/>nita exiſtens in parte finita corporis infiniti nihil <lb/>conducit nec aliquid confert ad denſitatem corpo­<lb/>ris infiniti: igitur non plus denominat denſitas <lb/>exiſtens in illo primo pedali quam ſi eſſet ſemota <lb/>ſed ſi illa eſſet ſemota manentibus aliis vt modo <lb/>ſunt: totum eſſet denſum preciſe vt vnum.</s>
            </p>
            <div xml:id="N23E0E" level="5" n="45" type="float">
              <note position="right" xlink:href="note-0201-06a" xlink:label="note-0201-06" xml:id="N23E12" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0201-07a" xlink:label="note-0201-07" xml:id="N23E18" xml:space="preserve">.3. correĺ.</note>
            </div>
            <pb chead="De motu rarefactionis  cõdēnaitonis." file="0202" n="202"/>
            <p xml:id="N23E22">
              <s xml:id="N23E23" xml:space="preserve">¶ Ex hiis duabus opinionibꝰ elige quã malueris <lb/></s>
              <s xml:id="N23E27" xml:space="preserve">Et per hoc pꝫ reſponſio ad dubiū               <anchor type="note" xlink:href="note-0202-01" xlink:label="note-0202-01a"/>               </s>
              <s xml:id="N23E2F" xml:space="preserve">Uide illud latius <lb/>in calculatore in capitulo de raritate et denſitate.</s>
            </p>
            <div xml:id="N23E34" level="5" n="46" type="float">
              <note position="left" xlink:href="note-0202-01a" xlink:label="note-0202-01" xml:id="N23E38" xml:space="preserve">Calcula.</note>
            </div>
            <p xml:id="N23E3E">
              <s xml:id="N23E3F" xml:space="preserve">¶ His poſitis ſit cõcluſio vniuerſalis reſponſiua <lb/>queſtionis raritas et denſitas ſunt poſſibiles / pꝫ cõ­<lb/>cluſio ex his que ſuperius dicta ſunt.</s>
            </p>
            <p xml:id="N23E46">
              <s xml:id="N23E47" xml:space="preserve">¶ Ad rationes ante oppoſitū. </s>
              <s xml:id="N23E4A" xml:space="preserve">Ad primã duplicit̄̄ <lb/>reſpõdeo prīo ſecūdū opiniõeꝫ recitatã in prīo no-<lb/>tabili q̄ tenet /  dicunt̄̄ poſitiue et ſunt qualitates et <lb/>cum ꝓbatur  nõ: quia eque velociter et eque ꝓpor-<lb/>tionabiliter ſicut denſitas auget̄̄ ita raritas dimi-<lb/>nuitur:               <anchor type="note" xlink:href="note-0202-02" xlink:label="note-0202-02a"/>               igit̄̄ raritas et denſitas nõ dicunt̄̄ poſitiue <lb/>negatur añs ſcḋm hanc opinionē et etiã aliq̇ negãt <lb/>idem añs ſcḋm alteram quorū prīceps eſt calcula-<lb/>tor in quodã dubio / et ſic patet ſecūda reſponſio ſi-<lb/>militer qm̄ ſcḋm aliã opinionem hoc etiã negatur <lb/></s>
              <s xml:id="N23E65" xml:space="preserve">¶ Ad quatuor cõfirmatiões ſimul reſpondeo bre-<lb/>uiter /  procedūt cõtra opinionē que recitata eſt in <lb/>primo notabili et ibi reſpõſum eſt ad illas .8. confir­<lb/>mationes. </s>
              <s xml:id="N23E6E" xml:space="preserve">¶ Ad ſcḋam rationem reſponſum eſt in <lb/>ſecundo notabili. </s>
              <s xml:id="N23E73" xml:space="preserve">¶ Ad tertiam rationē dictum eſt <lb/>ibi vſ ad vltimã replicã. </s>
              <s xml:id="N23E78" xml:space="preserve">ad quã reſpondeo conce­<lb/>dendo quod infert̄̄ videlicet /  oīa intermedia mu­<lb/>tantur localiter dato /  nullū intermediorū cõden­<lb/>ſetur. </s>
              <s xml:id="N23E81" xml:space="preserve">Nec hoc eſt incõueniēs: ſꝫ prout michi nūc ap­<lb/>paret videt̄̄ neceſſariū naturaliter. </s>
              <s xml:id="N23E86" xml:space="preserve">Si autē malue­<lb/>ris /  ſemꝑ vbicun eſt cauſa condēſationis ibi eſt <lb/>cauſa rarefactiõis et ecõtra et hoc ex ordine natu-<lb/>rali nõ video rationē fortē in oppoſitū. </s>
              <s xml:id="N23E8F" xml:space="preserve">Poſſet em̄ <lb/>non abſ ratiõe dici /  vbi ſit cõdenſatio a cauſis <lb/>particularibꝰ fiat a cãis vĺibꝰ rarefactio et eↄ̈ ne va­<lb/>cuū aut dimēſionū penetratio naturaĺr ſeq̈t̄̄. </s>
              <s xml:id="N23E98" xml:space="preserve">¶ Ad <lb/>quartã rationē reſpõſum eſt ibi vſ ad penultimã <lb/>replicã. </s>
              <s xml:id="N23E9F" xml:space="preserve">ad quã dico dupliciter prīo. </s>
              <s xml:id="N23EA2" xml:space="preserve">vt dictū eſt ibi <lb/>hoc addito /  nõ fiat mutatio materie de vna par-<lb/>te corꝑis in reliquã manēte eadē ̄titate: q2 iſto mõ <lb/>nec cõdenſabit̄̄ nec rarefiet: vt pꝫ ex ṗmo dubio. </s>
              <s xml:id="N23EAB" xml:space="preserve">Di­<lb/>co ſcḋo /  tale denſum difforme põt reduci ad vni-<lb/>formitatē gradus medii ſine rarefactione et condē­<lb/>ſatione. </s>
              <s xml:id="N23EB4" xml:space="preserve">Et hoc remouēdo medietatē exceſſus mate­<lb/>rie abuna medietate et addendo alteri ſiue acq̇ſitio­<lb/>ne aut deperditione ̄titatis in aliqua illarū me-<lb/>dietatū: vt ptꝫ ex argumēto ī oppoſitū primi dubii <lb/></s>
              <s xml:id="N23EBE" xml:space="preserve">¶ Ad vltimã vero replicam reſpõdeo breuiter negã­<lb/>do / hanc ↄ̨ſequentiã ꝑ maiorē partē cõtinuo erit ra­<lb/>rarefactio ꝙ̄ condenſatio: igit̄̄ hoc cõtinuo rarefit <lb/></s>
              <s xml:id="N23EC6" xml:space="preserve">Et ad probationē nego ſimilitudinē ſicut eam eſſe <lb/>negandã docet penultima replica. </s>
              <s xml:id="N23ECB" xml:space="preserve">¶ Ad ↄ̨firmatio­<lb/>nē negatur añs: immo dico /  tale inſtans eſt dabi­<lb/>le: et nego /  ſit inſtans mediū. </s>
              <s xml:id="N23ED2" xml:space="preserve">Ad minꝰ dico /  non <lb/>oportet /  ſit inſtans medi<gap/>̀ / vt ꝓbat argumētū: q2 <lb/>aliquãdo rarefit tale corpus ante inſtans medium. <lb/></s>
              <s xml:id="N23EDC" xml:space="preserve">Et dicit calculator /  vbicū calculauerit illud in-<lb/>ſtans erat ante inſtans mediū totius tꝑis. </s>
              <s xml:id="N23EE1" xml:space="preserve">Et ſi tu <lb/>queras / quod eſt illud inſtans añ inſtans medium. <lb/>               <anchor type="note" xlink:href="note-0202-03" xlink:label="note-0202-03a"/>               </s>
              <s xml:id="N23EED" xml:space="preserve">Reſpondeo tibi cum eodē calculatore  huiuſcemo­<lb/>di inquiſitio talis inſtantis maioris laboris et an­<lb/>xietatis eſſet ꝙ̄ vtilis: ſufficit em̄ pro ſolutiõe argu-<lb/>menti oſtēdere /  nec per totū tp̄s condēſat̄̄: ſꝫ ꝑ ali­<lb/>quã partē tēporis cõdenſatur: et ꝑ aliquam rarefit <lb/>               <anchor type="note" xlink:href="note-0202-04" xlink:label="note-0202-04a"/>               </s>
              <s xml:id="N23EFF" xml:space="preserve">Ip̄m eī exactū nõ in oībus eſt expetendū quēadmo­<lb/>dū nec in cõpotis auctoritate philoſophi prīo ethi­<lb/>corum: et ſecundo methaphiſices in calce.</s>
            </p>
            <div xml:id="N23F06" level="5" n="47" type="float">
              <note position="left" xlink:href="note-0202-02a" xlink:label="note-0202-02" xml:id="N23F0A" xml:space="preserve">Calcula.</note>
              <note position="left" xlink:href="note-0202-03a" xlink:label="note-0202-03" xml:id="N23F10" xml:space="preserve">Calcula.</note>
              <note position="left" xlink:href="note-0202-04a" xlink:label="note-0202-04" xml:id="N23F16" xml:space="preserve">phūs .2°. <lb/>metha. et <lb/>1. ethicoꝝ</note>
            </div>
            <p xml:id="N23F20">
              <s xml:id="N23F21" xml:space="preserve">¶ Ad quintam rationem ſufficienter reſpondet ter­<lb/>tium notabile / quod ꝓpter hãc rõnē fuit adductum. <lb/></s>
              <s xml:id="N23F27" xml:space="preserve">¶ Ad ſextã rationē reſpõſum eſt ibi nec replica ꝓce­<lb/>dit / vt patet ibi. </s>
              <s xml:id="N23F2C" xml:space="preserve">¶ Ad cõfirmationē reſpõſum eſt ibi <lb/>vſ ad replicam ad quam reſpondeo concedendo <lb/>ſequelam / vt ptꝫ ex ſecundo dubio vbi hec materia               <cb chead="De motu rarefactionis  cõdēnaitonis."/>               reſoluitur. </s>
              <s xml:id="N23F36" xml:space="preserve">Sed q2 hoc argumentū querit quomo-<lb/>do vnū pedale infinite denſum difformiter poteſt <lb/>reduci ad vniformitatē: et videt̄̄ /  oporteat ṗmã ꝑ­<lb/>tē ꝓportionalē in infinitū condenſari: et ſic videtur / <lb/> ipſa rediget̄̄ ad nõ ̄tum et pari ratione q̄libet <lb/>alia. </s>
              <s xml:id="N23F43" xml:space="preserve">Et ideo dico /  illud corpus non debet reduci <lb/>ad vniformitatē nec aliqua pars ꝓportionalis eiꝰ <lb/>debet effici in infinite denſa ꝑ ſui cõdēſatione ſine <lb/>mīo rationem: ſed per acquiſitionē materie ſtante <lb/>̄titate / vt dictum eſt in primo dubio in argumēto <lb/>ad oppoſitū facto.               <anchor type="note" xlink:href="note-0202-05" xlink:label="note-0202-05a"/>               </s>
              <s xml:id="N23F55" xml:space="preserve">¶ Ex quo ſequit̄̄ /  motꝰ augmē­<lb/>tationis non ſequitur motū rarefactionis: nec mo­<lb/>tus diminutionis ſeq̇tur motū condēſatiõis neceſ-<lb/>ſario. </s>
              <s xml:id="N23F5E" xml:space="preserve">Ad ſecūdã cõfirmationē rñdet tertiū dubium <lb/></s>
              <s xml:id="N23F62" xml:space="preserve">¶ Ad ſeptimã rationē reſpondeo negando ſeque-<lb/>lam ſicut nec in ſimili ſequitur de remiſſione. </s>
              <s xml:id="N23F67" xml:space="preserve">Et ſi <lb/>queras ꝙ̄ rarū eſt illud: dico /  eiꝰ raritas diiudi-<lb/>cari debet ex eius denſitate. </s>
              <s xml:id="N23F6E" xml:space="preserve">Eiꝰ autem denſitas pꝫ <lb/>ex argumento. </s>
              <s xml:id="N23F73" xml:space="preserve">Et ad cõfirmationē priorē reſpõdeo <lb/>negando ſequelã: et ad ꝓbationē concedo /  illud <lb/>corpus eſt infinite denſum / vt patet ex ſecunda con­<lb/>cluſione q̄ſtionis: et nego /  ſit rarū: et ad ꝓbatio-<lb/>nē nego illam ſimilitudinē qm̄ ille modus arguen-<lb/>do valet in poſitiuis: et non in priuatiuis / vt patet <lb/>de remiſſione. </s>
              <s xml:id="N23F82" xml:space="preserve">Ad poſteriorem cõfirmationē reſpõ­<lb/>deo negando ſequelã videlicet / quod ſequeretur il-<lb/>lud eſſe infinite denſum: et ad ꝓbationē nego cõſe-<lb/>quentiam: nec eſt ſimile quãdo illnd corpus diuidi­<lb/>tur ꝓportione dupla: et denſitates continuo ſe ha-<lb/>bent in proportione dupla aſcendendo: ſed ad hoc <lb/> eſſet ſimile oportet /  partes continuo ſe habe-<lb/>rent in ꝓportiõe decupla in dēſitate ita  ſicut ꝑs <lb/>ſequens eſt in decuplo mīor īmediate p̄cedēte: ita <lb/>etiam ſit decuplo denſior. </s>
              <s xml:id="N23F97" xml:space="preserve">¶ Ad octauã rationē di-<lb/>ctum eſt ibi vſ ad replicã. </s>
              <s xml:id="N23F9C" xml:space="preserve">ad quã reſpõdeo /  den­<lb/>ſitas illius corporis adequata eſt incõmēſurabilis <lb/>denſitati prime partis ꝓportiõalis / vt michi ꝓ nūc <lb/>apparet nec aliq̇s intellectꝰ finile capacitatis da-<lb/>to /  illa eēt mēſurabilis p̄t illã cõmenſurare ꝓpter <lb/>infinitã variationē ꝓportiõis. </s>
              <s xml:id="N23FA9" xml:space="preserve">Ad primã et ſecūdaꝫ <lb/>confirmationē ſimul reſpõdeo concedendo /  in ca­<lb/>ſibus ibi poſitis dabilis eſt certa dēſitas talis cor­<lb/>poris: ſed credo illam eſſe incõmēſurabilē denſita-<lb/>ti prime partis ꝓportionalis: et ſi ipſa ſit cõmēſu-<lb/>rabilis eius adequata ꝓportio ab intellectu finite <lb/>capacitatis minime īueniri poteſt eo /  īfinita va-<lb/>rietas ꝓportionū eſt inter denſitates illarū partiū <lb/>proportionalium. </s>
              <s xml:id="N23FBC" xml:space="preserve">¶ Ad nonã rationē reſpondeo <lb/>negando ſequelã: et ad ꝓbationē nego /  in fine ho-<lb/>re illud ſit denſius immo eſt rarius. </s>
              <s xml:id="N23FC3" xml:space="preserve">et ad ꝓbationē <lb/>nego hanc conſequētiã infinite partes illius ſunt dē­<lb/>ſiores ꝙ̄ erant antea etc̈. / q2 ſtat  vna ſola acq̇rat <lb/>tantū de ̄titate vel plus ꝙ̄ ille infinite omnes de­<lb/>perdant. </s>
              <s xml:id="N23FCE" xml:space="preserve">Ad cõfirmationē rēſpõdeo admiſſo caſu <lb/>negando añs. </s>
              <s xml:id="N23FD3" xml:space="preserve">immo dico /  in illo cãu in fine hore <lb/>illud corpus nõ eſt rarius nec denſius ꝙ̄ eſt in prin­<lb/>cipio. </s>
              <s xml:id="N23FDA" xml:space="preserve">Et ad ꝓbationē nego hanc cõſequentiam pri­<lb/>ma pars ꝓportionalis eſt maior ꝙ̄ erat antea: et <lb/>aggregatū ex ipſa et ſecunda eſt maius ꝙ̄ erat an­<lb/>tea et aggregatū ex ip̄a ſecūda et tertia ē maiꝰ ꝙ̄ erat <lb/>antea: et aggregatū ex ip̄a ſecūda tertia et quarta <lb/>ſimiliter: et ſic cõſequenter aggregatū ex quotcū <lb/>finitis cõputata prima eſt maius ꝙ̄ erat antea: igi-<lb/>tur illud totum eſt maius ꝙ̄ erat antea. </s>
              <s xml:id="N23FEB" xml:space="preserve">¶ Ad deci-<lb/>mã reſponſum eſt ibi vſ ad replicam ad quã etiã <lb/>reſpondeo concedendo illatum. </s>
              <s xml:id="N23FF2" xml:space="preserve">Illlud em̄ in nõ cõ­<lb/>uenit. </s>
              <s xml:id="N23FF7" xml:space="preserve">ſꝫ eſt correlariū ſequēs vt ꝓbat argumentuꝫ <lb/></s>
              <s xml:id="N23FFB" xml:space="preserve">Et hec de totali queſtiõe: et per cõſequens de tota <lb/>materia de denſitate et raritate.</s>
            </p>
            <div xml:id="N24000" level="5" n="48" type="float">
              <note position="right" xlink:href="note-0202-05a" xlink:label="note-0202-05" xml:id="N24004" xml:space="preserve">bonū cor­<lb/>relarium</note>
            </div>
            <pb chead="Tertii tractatus" file="0203" n="203"/>
          </div>
          <div xml:id="N24010" level="4" n="2" type="chapter" type-free="capitulum">
            <head xml:id="N24015" xml:space="preserve">Secundū capitulū huiꝰ tractatus / in quo ſolito <lb/>pro more diſputatiue inquirimus penes quid velo­<lb/>citas augmētationis attendi habeat.</head>
            <p xml:id="N2401C">
              <s xml:id="N2401D" xml:space="preserve">NUnc cõſequēter q̄ritur vtrū <lb/>velocitas motus augmētatiõis penes ꝓ­<lb/>portionalē acquiſitionē ̄titatis attēdi <lb/>habeat: an penes abſolutã acq̇ſitione ̄titatis.</s>
            </p>
            <p xml:id="N24026">
              <s xml:id="N24027" xml:space="preserve">Arguitur primo /  non penes propor­<lb/>tionabilē acquiſitionē ̄titatis ita  non ſemꝑ illḋ <lb/>quod in eodē tꝑe maiorem ꝓportionē acquirit ̄ <lb/>aliud velocius augmētetur ꝙ̄ aliud in eodē tēpore <lb/>quia ſi ſic tūc ſequeretur /  a. et b. ſunt equalia: et a <lb/>continuo velocius augmētabit̄̄ ꝙ̄ b. et tamen ſemꝑ <lb/>a. manebit minus .b. / ſꝫ conſequēs eſt manifeſte fal-<lb/>ſum: igitur illud ex quo ſequit̄̄. </s>
              <s xml:id="N24038" xml:space="preserve">Sequela ꝓbat̄̄: et <lb/>volo /  .a. et .b. ſint duo pedalia: et acquirat vnifor-<lb/>miter .b. in hora vnū pedale: et nichil deperdat de <lb/>qnantitate prehabita .a vero acquirat vnū pedale <lb/>vniformiter ꝑ horã: et deꝑdat vnū ſemipedale ̄ti-<lb/>tatis prehabite vniformiter in illa hora. </s>
              <s xml:id="N24045" xml:space="preserve">quo poſi-<lb/>to arguitur ſic / .a. et .b. ſunt modo equalia: et ſemꝑ .a <lb/>poſt hoc manebit minꝰ .b. / vt cõſtat qm̄ ſi nichil de­<lb/>perderet maneret equale: ſꝫ modo cõtinuo perdet. <lb/></s>
              <s xml:id="N2404F" xml:space="preserve">ergo cõtinuo manet minus: et tamē .a. cõtinuo velo­<lb/>cius augmētabitur ꝙ̄ .b. / igitur intentū. </s>
              <s xml:id="N24054" xml:space="preserve">Probatur <lb/>minor / q2 .a. cõtinuo erit minus .b. et cõtinuo equa-<lb/>lem ̄titatē acquiret cū .b. / igit̄̄ .a. cõtinuo maiorem <lb/>ꝓportionē acquiret ꝙ̄ .b. et penes acq̇ſitionē maio­<lb/>ioris ꝓportiõis in eodē tēpore attēdit̄̄ maior veloci­<lb/>tas augmētatõis: igit̄̄ .a. ↄ̨tinuo velociꝰ augmētabi­<lb/>tur ꝙ̄ .b. / quod fuit ꝓbandū. </s>
              <s xml:id="N24063" xml:space="preserve">Hec ↄ̨ſequētia patꝫ de <lb/>ſe: et prior ex octaua ſuppoſitiõe quarti capitis ſe-<lb/>cunde partis: et in aliis pleriſ locis libri arguta <lb/>eſt.               <anchor type="note" xlink:href="note-0203-01" xlink:label="note-0203-01a"/>               </s>
              <s xml:id="N24071" xml:space="preserve">¶ Dices et bene negando ſequelam: et ad ꝓbatio­<lb/>nē admiſſo caſu ad bonū ſenſum poſſet em̄ negari / <lb/>vt poſtea dicemus: reſpõdeo negando minorē vi-<lb/>delicet /  .a. cõtinuo poſt hoc velocius augmentabi­<lb/>tur ꝙ̄ .b. et ad ꝓbationē concedo /  .a. cõtinuo mane­<lb/>bit minus et nego /  ↄ̨tinuo equalē quãtitatem acq̇­<lb/>ret cū .b. ſicut de facto eſt negandū qm̄ ſi nichil de-<lb/>perderet ſemꝑ acquireret equalē ̄titatē: ſꝫ modo <lb/>cõtinuo deꝑdit: ergo cõtinuo acquirit minorē: quo­<lb/>niã in tota hora nõ acquirit .a. niſi ſemipedale. </s>
              <s xml:id="N24086" xml:space="preserve">Ma­<lb/>nebit em̄ in fine pedale cū dimidio quoniã mãſiſſet <lb/>bipedale niſi perdidiſſet dimidiū. </s>
              <s xml:id="N2408D" xml:space="preserve">¶ Item in inſtã-<lb/>ti medio hore acquiſiuit .a. vnã quartã pedalis .b. <lb/>vero vnã medietatē: et ſic in illa prīa medietate ma­<lb/>iorē quãtitatē acquiſiuit .b. ꝙ̄ .a. cuius oppoſitum <lb/>aſſumit argumētum.               <anchor type="note" xlink:href="note-0203-02" xlink:label="note-0203-02a"/>               </s>
              <s xml:id="N2409D" xml:space="preserve">¶ Ex quo a ꝑte infertur cal-<lb/>latorē male induxiſſe illud cõſequēs tan̄ ſequens <lb/>ex opinione quam impugnamus: qm̄ illa cõcluſio <lb/>nullo pacto ſequit̄̄ expoſitione. </s>
              <s xml:id="N240A6" xml:space="preserve">Teneat̄̄ igit̄̄ poſi-<lb/>tio vniuerſaliter.</s>
            </p>
            <div xml:id="N240AB" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0203-01a" xlink:label="note-0203-01" xml:id="N240AF" xml:space="preserve">Dicitur</note>
              <note position="left" xlink:href="note-0203-02a" xlink:label="note-0203-02" xml:id="N240B5" xml:space="preserve">Coutra <lb/>ca'lcna.</note>
            </div>
            <p xml:id="N240BD">
              <s xml:id="N240BE" xml:space="preserve">Sed contra hanc reſponſionē argui­<lb/>tur ſic / quia ſi illa poſitio eſſet vniuerſaliter vera / ſe­<lb/>queretur hec concluſio. </s>
              <s xml:id="N240C5" xml:space="preserve"> ſi ſint duo ſiue equalia ſiue <lb/>inequalia q̄ cõtinuo eque velociter diminuãtur per­<lb/>dendo cõtinuo equales ꝓportiones eque cito veni-<lb/>ent ad non quãtum: ſed ↄ̨ſequens eſt falſum: igitur <lb/>illud ex quo ſequit̄̄: falſitas ↄ̨ſequētis ꝓbat̄̄: q2 ſtat <lb/> aliqua duo in aliquo tepore eque velociter dimi­<lb/>nuatur ꝑdendo in illo tꝑe p̄ciſe .4. duplas: igit̄̄ tūc <lb/>ↄ̨tinuo eque velociter diminuētur: et tamē nõ eque <lb/>cito deueniēt ad nõ ̄tū: et ꝑ ↄ̨ſequēs illḋ illatuꝫ eſt <lb/>vna conditionalis q̄ eſt falſa: igitur illud cõſequēs <lb/>eſt falſum. </s>
              <s xml:id="N240DC" xml:space="preserve">¶ Dices et bñ /  de rigore illud ↄ̨ſequēs <lb/>eſt falſum ̄uis ſub illa forma ponatur a calcula-<lb/>tore: ſed oportet addere in antecedende illius con-               <cb chead="Capi. ſecundum"/>               ditionalis q̄ eque velociter diminuūtur vſ ad nõ <lb/>quãtū: et tūc illa ↄ̨cluſio eſt ↄ̨cedenda ſecundū opi-<lb/>nionē. </s>
              <s xml:id="N240EA" xml:space="preserve">Quod ſic oſtēditur / quoniã ſi aliquod corpꝰ <lb/>puta .a. in hora diminuat̄̄ ad nõ quãtū: illud corpꝰ <lb/>infinitã latitudinē ꝓportionū deperdet: et .b. aliud <lb/>corpus maius in tota illa hora eque velociter di-<lb/>minuitur cū .a. / ergo ſequit̄̄ /  infinitã latitudinē ꝓ-<lb/>portionis etiã deperdit .b. in illa hora: et vltra infi­<lb/>nitã latitudinē ꝓportionis deperdit .b. in illa hora <lb/>et nõ reſtituit̄̄ in inſtanti terminatiuo priſtine quã­<lb/>titati vt volo: igit̄̄ in inſtãti termīatiuo hore .b. erit <lb/>nõ ̄tum: et tunc .a. erit nõ ̄tum: igitur eq̄ cito .a. et .b. <lb/>deuenient ad nõ ̄tū in tali caſu: qḋ fuit ꝓbandum <lb/></s>
              <s xml:id="N24102" xml:space="preserve">Sꝫ tã probo hanc cõſequētiã .b. inifinitã latitudinē <lb/>ꝓportiõis deꝑdit ī hora et ñ reſtituit̄̄ in inſtanti ter­<lb/>minatiuo priſtine ̄titati: ergo in illo inſtanti non <lb/>quãtū manet </s>
              <s xml:id="N2410B" xml:space="preserve">Quia ſi in illo inſtãti maneret alicuiꝰ <lb/>quãtitatis: ſit illa quãtitas vna milleſima exempli <lb/>gratia: et tã ſequit̄̄ /  in illa hora nõ deꝑdit niſi mil­<lb/>lecuplã ꝓportionē: et per ↄ̨ſequēs nõ infinitã / quod <lb/>eſt oppoſitū ↄ̨ſequētis. </s>
              <s xml:id="N24116" xml:space="preserve">Et iſto modo ꝓbat̄̄ hec ↄ̨ſe-<lb/>quētia prius facta deuenit .a. ad nõ ̄tum / ergo infi­<lb/>nitam ꝓportionē deperdit: quia ſi ſolū finita puta <lb/>millecuplã iam illud in fine maneret vt vna milleſi­<lb/>ma et ſic non maneret nõ quãtum.</s>
            </p>
            <p xml:id="N24121">
              <s xml:id="N24122" xml:space="preserve">Sed contra hoc arguitur ſic / quia ſi <lb/>hoc eſſet verū ſeq̇retur eodē mõ /  ſi in aliqua duo <lb/>ſiue equalia ſiue inequalia in certa ꝓportione cõti­<lb/>nuo inequaliter diminuãtur vſ ad non quãtum ta­<lb/>lia eque cito deueniunt ad nõ quãtū: ſed conſequēs <lb/>videtur falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N2412F" xml:space="preserve">Seq̄la <lb/>ꝓbatur et volo /  ſint .a. et .b. pedale: et ꝑdat .a. in <lb/>qualibet parte ꝓportionali ꝓportionē quadruplã <lb/>b. vero ſemꝑ in duplo minorē proportionē in qua­<lb/>libet parte ꝓportionali puta ꝓportionē duplam. <lb/></s>
              <s xml:id="N2413B" xml:space="preserve">Et arguitur ſic / cū primū .a. ꝑdiderit infinitas ꝓpor­<lb/>tiones quadruplas ip̄m deuenerit ad non quantū: <lb/>et tunc .b. ꝑdidit īfinitas duplas / vt patet ex caſu: er­<lb/>go tunc .b. deuenit ad nõ quãtū. </s>
              <s xml:id="N24144" xml:space="preserve">Nõ em̄ poteſt infini­<lb/>tas duplas perdere quī infinitã latitudinē ꝓportio­<lb/>nis deperdat: et ꝑ conſequens eque cito .a et .b. de-<lb/>uenient ad nõ quãtū: quod fuit probandū. </s>
              <s xml:id="N2414D" xml:space="preserve">Et iſto <lb/>modo probabis de q̇buſcū aliis corporibus ſiue <lb/>equalibus ſiue inequalibus: dūmodo vnum altero <lb/>in certa ꝓportione continuo velocius diminuatur <lb/>ad non quantum.</s>
            </p>
            <p xml:id="N24158">
              <s xml:id="N24159" xml:space="preserve">Secūdo prīcipaliter ad idem arguit̄̄ <lb/>ſic. </s>
              <s xml:id="N2415E" xml:space="preserve">Si velocitas augmētatiõis attenderet̄̄ penes ꝓ­<lb/>portionalē acquiſitionē quãtitatis: ſequeretur hec <lb/>concluſio /  ſi aliquid inciperet ſucceſſiue augeri <lb/>a non quãto: ipſum infinite velociter inciperet au-<lb/>geri: ſꝫ conſequens eſt falſum: igitur illud ex quo ſe­<lb/>quitur. </s>
              <s xml:id="N2416B" xml:space="preserve">Falſitas cõſequēs arguit̄̄ ſic: q2 tunc ſeq̇re­<lb/>tur /  quodlibet tale infinite velociter inciperet ac-<lb/>quirere de quãtitate: ſꝫ ↄ̨ſequens eſt falſum: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N24174" xml:space="preserve">Sed tã probo ſequelam / quia <lb/>ſi .a. incipit augeri a nõ quãto poſt inſtans inceptio­<lb/>nis talis augmentationis ipſum eſt aliquãtum: et <lb/>ante illud inſtans fuit in duplo minus: et in triplo <lb/>et in quadruplo et ſic infinitum: ergo inter illud in­<lb/>ſtans et īſtans initiatiuū illud acquiſiuit infinitam <lb/>proportionem: et per cõſequēs ſequit̄̄ /  ipſum infi-<lb/>nite velociter incipit augeri. </s>
              <s xml:id="N24185" xml:space="preserve">patet conſequentia ex­<lb/>poſitione.               <anchor type="note" xlink:href="note-0203-03" xlink:label="note-0203-03a"/>               </s>
              <s xml:id="N2418F" xml:space="preserve">¶ Dices et bene concedendo cõcluſioneꝫ <lb/>illatam / vt bene ꝓbat argumentū / et negando falſi­<lb/>tatem conſequentis: et ad probationē nego iſtam <lb/>conſequentiã infinite velociter incipit augeri: ergo <lb/>infinite velociter incipit a. acquirerere de quãtitate /               <pb chead="De motu augmentationis." file="0204" n="204"/>               vt poſtea oſtenditur. </s>
              <s xml:id="N2419F" xml:space="preserve">Immo ſtat  infinite tarde in­<lb/>cipit acq̇rere de quantitate.</s>
            </p>
            <div xml:id="N241A4" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0203-03a" xlink:label="note-0203-03" xml:id="N241A8" xml:space="preserve">Dictur.</note>
            </div>
            <p xml:id="N241AE">
              <s xml:id="N241AF" xml:space="preserve">Sed cõtra / q2 tūc ſequeretur hec con­<lb/>cluſio /  ſi aliqua duo inciperent augeri a non quã­<lb/>to puta .a. et .b. et .a. in certa ꝓportiõe cõtinuo velo-<lb/>cius augeatur ꝙ̄ .b. ip̄m .a. / qḋ in certa ꝓportione cõ­<lb/>tinuo velocius augebitur ꝙ̄ .b. ꝑ magnū tempꝰ ma­<lb/>nebit minus ip̄o .b. / ſed cõſequens eſt falſum: igitur <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N241BE" xml:space="preserve">Falſitas cõſequētis arguit̄̄ ſic. <lb/></s>
              <s xml:id="N241C2" xml:space="preserve">quoniã ſi .a. et .b. a nõ quãto incipiēt cõtinuo eque­<lb/>velociter augeri cõtinuo manerēt equalia: ſed mo-<lb/>do .a. cõtinuo velocius augebit̄̄ ꝙ̄ .b. et incipiunt a <lb/>nõ quãto in eodem nſtanti: ergo ſequitur /  .a. conti­<lb/>nuo erit maius ipſo .b. et ꝑ cõſequens nū̄ manebit <lb/>minus. </s>
              <s xml:id="N241CF" xml:space="preserve">Sꝫ iam ꝓbo ſequelã / quoniã ſi ip̄m .a. / quod <lb/>velocius augetur nõ ꝑ aliquod tēpus erit minꝰ ip̄o <lb/>b. ſed ſemper maius vt dictis. </s>
              <s xml:id="N241D6" xml:space="preserve">Detur igit̄̄ vnū inſtãs <lb/>illius tēporis in quo .a. eſt maius ipſo .b. in aliqua <lb/>ꝓportione: et ſemꝑ ante illud inſtans fuit maius / vt <lb/>dicis: et ſit tale inſtans .c. et ſit gratia argumenti in <lb/>tali inſtanti ꝓportio .a. ad .b. ſexquialtera adequa­<lb/>te: et volo gr̄a exempli /  .a. cõtinuo augeatur velo-<lb/>cius .b. in proportione dupla. </s>
              <s xml:id="N241E5" xml:space="preserve">Quo poſito arguit̄̄ <lb/>ſic / .b. infinitas ꝓportiões ſexquialteras acquiſiuit <lb/>ab inſtanti initiatīo augmētationis vſ ad inſtãs <lb/>c. / vt patet ex iſto argumēto: detur igitur vnū inſtãs <lb/>quod ſit .d. ante inſtans .c. inter quod et inſtans .c.b. <lb/>acquiſiuit duas ſexquialteras: et arguit̄̄ ſic īter .d. <lb/>inſtans et .c. inſtans acq̇ſiuit .b. duas ſexq̇alteras: et <lb/>a cõtinuo in duplo velocius auget̄̄ ꝙ̄ .b. / igit̄̄ .a. inter <lb/>d. inſtans et .c. inſtans acq̇ſiuit quatuor ſexq̇alteras <lb/>et in .d. inſtanti erat maius ipſo .b. ꝑ te: igitur in .c. <lb/>inſtanti eſt ip̄m .a. pluſ̄ in ſexquialtero maius ip̄o <lb/>b. / quod eſt oppoſitū cõceſſi. </s>
              <s xml:id="N241FE" xml:space="preserve">Dictū eſt em̄ /  in .c. in-<lb/>ſtanti ſe habebãt in ꝓportione ſexq̇altera adequa­<lb/>te. </s>
              <s xml:id="N24205" xml:space="preserve">ꝓbatur ↄ̨ſia qm̄ ſi .a. et .b. in inſtãti .d. fuiſſent eq̈-<lb/>lia: et acquiſiuiſſet .d. duas ſexq̇alteras: et .a.4. vſ <lb/>ad inſtans .c. in ipſo inſtanti. c.a. exceſſiſſet .b. ꝑ du­<lb/>as ſexquialteras: ſꝫ modo in tali inſtanti .a. eſt ad­<lb/>huc maius .b. ꝑ te: et acq̇rit .4. ſexq̇alteras vſ ad ī-<lb/>ſtans .c. et .b. acquirit preciſe duas vſ ad idē īſtãs <lb/>c. / ergo ſeq̇tur /  in illo inſtãti .c.a. excedit .b. per du-<lb/>as ſexq̇alteras ; vel ꝑ plus. </s>
              <s xml:id="N24216" xml:space="preserve">Ptꝫ hec ↄ̨ſequētia ꝑ lo­<lb/>cum a maiori: et ꝑ ↄ̨ſequēs nõ ꝑ ſexq̇alteram preci-<lb/>ſe / qḋ erat inferēdū. </s>
              <s xml:id="N2421D" xml:space="preserve">Tenet hec īductio virtute huiꝰ <lb/>maxime. </s>
              <s xml:id="N24222" xml:space="preserve">Quãdo aliqua duo ſunt equalia: et in eo­<lb/>dem tēpore vnū illoruꝫ maiorē ꝓportionē acquirit <lb/>̄ reliquū: in fine tēporis illud qḋ maiorē ꝓportio­<lb/>nem acq̇ſiuit eſt maius illo qḋ minorē ꝓportionem <lb/>acq̇ſiuit in proportiõe ꝑ quam ꝓportio acq̇ſita illi / <lb/>quod in fine eſt maius excedit ꝓportionem acquiſi­<lb/>tam illi / qḋ eſt minur / vt cõſtat ex ſecūda parte: iſto <lb/>modo vniuerſaliter probabis in omnibus.</s>
            </p>
            <note position="left" xml:id="N24233" xml:space="preserve">Dicitur.</note>
            <p xml:id="N24237">
              <s xml:id="N24238" xml:space="preserve">¶ Dices et bene concedendo / quod infertur vt bene <lb/>probat argumētū: et negando falſitatē ↄ̨ſequentis <lb/>et ad ꝓbationē nego hanc cõditionalem ſi .a. et .b. <lb/>incipiant augeri et nõ quãto ↄ̨tinuo eque velociter <lb/>ipſa cõtinuo manebūt equalia. </s>
              <s xml:id="N24243" xml:space="preserve">Immo ſtat  vnuꝫ <lb/>in quacun ꝓportiõe volueris maneat minꝰ alte-<lb/>ro / vt poſtea demõſtrabitur.</s>
            </p>
            <p xml:id="N2424A">
              <s xml:id="N2424B" xml:space="preserve">Sed contra hanc ſolutionē arguitur <lb/>ſic: q2 ſi illa ſolutio eſſet bona ſequeret̄̄ /  ſi .a. et .b. <lb/>inciperēt augeri nõ quãto: et .a. in certa ꝓportiõe <lb/>cõtinuo velocius augeret̄̄ ꝙ̄ .b. ipſum .a. / quod in cer­<lb/>ta proportiõe cõtinuo velocius auget̄̄ inciperet in <lb/>infinitū eſſe minus ipſo .b. / ſed cõſequēs eſt falſum: <lb/>igitur illud ex quo ſeq̇tur. </s>
              <s xml:id="N2425A" xml:space="preserve">Falſitas conſequētis ꝓ-<lb/>batur: quia tunc ſequeretur /  quando aliqua duo               <cb chead="De motu augmentationis."/>               incipiunt augeri a non quãto vnū in certa ꝓpor-<lb/>tione cõtinuo velocius altero illud quod tardius ī­<lb/>cipit augeri incipiet in infinitū velocius acquirere <lb/>de quãtitate. </s>
              <s xml:id="N24268" xml:space="preserve">ſed hoc apparet falſum: igit̄̄ illud ex <lb/>quo ſeq̇tur. </s>
              <s xml:id="N2426D" xml:space="preserve">Seq̄la tamen ꝓbatur: quia quocū in­<lb/>ſtanti dato poſt inſtans initiatiuū augmētatiõis <lb/>inter illud et inſtans initiatiuū .a. erit aliquãtulum <lb/>minus ip̄o .b. / vt patet ex priori replica: et in duplo <lb/>minus: et in triplo: et in quadruplo: et ſic in infinitū / <lb/>ergo immediate poſt illud inſtãs initiatiuū .a. erit <lb/>in infinitū minus ip̄o .b. et iam nõ eſt minus: ergo in­<lb/>cipit eſſe in infinitū minus ip̄o .b. et tam .a. ꝙ̄ b īci­<lb/>pit a nõ ̄to acquirere quãtitatē: ergo .b. / qḋ īcipit <lb/>tardius augeri incipit infinitū velocius acq̄rere de <lb/>quãtitate .a. / quod in certa ꝓportione velocius inci­<lb/>pit augmētari: qḋ fuit ꝓbandum. </s>
              <s xml:id="N24286" xml:space="preserve">Sed iam probo / <lb/> quocun inſtanti dato poſt illud inſtãs initia-<lb/>tiuū erit .a. inter illud inſtans et inſtãs initiatiuum <lb/>aliquãtulū minus ipſo .b. et in duplo: et in quadru-<lb/>plo. et ſic in infinitū: q2 ſi nõ da oppoſitū: et dic /  be­<lb/>ne .a. erit minus ipſo .b. / ſꝫ nun̄ in quadruplo gra­<lb/>tia exēpli: et arguo ſic: capiendo vnū inſtans / qḋ ſit .c <lb/>in quo .a. eſt minus .b. / vt cõcedis: et ſuperius ꝓba-<lb/>tū eſt: et nun̄ ante illud inſtans erit in quadruplo <lb/>minus: et cū .b. acquiret infinitas ꝓportiones qua-<lb/>druplas ab inſtanti initiatiuo augmētationis vſ <lb/>ad inſtans .c. capio vnū inſtans ante .c. / qḋ ſit .d. īter <lb/>quod et .c. ip̄m .b. acquirit vnam quadruplã preciſe. <lb/></s>
              <s xml:id="N242A2" xml:space="preserve">et arguo ſic / .b. inter .d. et .c. acquiret vnã quadruplã <lb/>et .a. in duplo velocius augetur ꝙ̄ .b. vt ſuppono: g̊ <lb/>ſequitur /  a. inter .d. et .c. inſtans acq̇ret duas qua-<lb/>druplas: et in .d. inſtanti .a. non erit in quadruplo <lb/>minus ipſo .d. ſed in minori proportione minꝰ: igi­<lb/>tur in .c. inſtanti .a. erit maius .b. / quod eſt oppoſitū <lb/>conceſſi. </s>
              <s xml:id="N242B1" xml:space="preserve">Poſitū em̄ eſt et conceſſuꝫ /  a. eſſet minus <lb/>b. in .c. inſtanti: ſed nõ in quadruplo minꝰ. </s>
              <s xml:id="N242B6" xml:space="preserve">Patꝫ tñ <lb/>conſequētia / quoniã ſi in .d. inſtanti foret .a. in qua-<lb/>druplo minus ipſo .b. et inter .d. inſtans et .c. inſtans <lb/>acquireret .b vnã quadruplã: et .a. duas: tunc in .c. ī­<lb/>ſtanti .a. eſſet equale .b. / quia acquiret illaꝫ ꝓportio­<lb/>nē que deficiebat ei vt ſit equale .b. et ī ſuꝑ tãtã quãtã <lb/>b. / ergo manet equale b. / ſed modo in .d. inſtanti erit <lb/>a. minus ꝙ̄ tūc: et acq̇ret vſ ad .c. inſtans tantã ꝓ-<lb/>portionem quãtã tunc: ergo ſeq̇tur /  in .c. inſtanti <lb/>manet maius ꝙ̄ tunc et per cõſequēs maius ipſo .b. / <lb/>quod fuit inferēdum. </s>
              <s xml:id="N242CD" xml:space="preserve">Ei iſto modo ꝓbabis in qui-<lb/>buſcū aliis ſpeciebus ꝓportionum. </s>
              <s xml:id="N242D2" xml:space="preserve">Si tu em̄ di-<lb/>cas /  in ſexquialtero velocius .a. cõtinuo augebit̄̄ <lb/>̄ .b. et nun̄ erit in quadruplo minus: tunc ego po­<lb/>ſito quod .b. inter inſtans .d. et .c. acq̇rat duas q̈dru­<lb/>plas et ꝑ ↄ̨ñs ī illo tꝑe .a. acq̇ret .3. q̈druplas: et ſic ac­<lb/>quiret pluſ̄ deficiebat ei vt eſſet eq̈le .b: et inſuper <lb/>tantum quantum acq̇ſiuit .b. et ꝑ conſequēs in .c. in­<lb/>ſtanti manebit .a. maius .b. / quod eſt oppoſitum cõ-<lb/>ceſſi.</s>
            </p>
            <note position="right" xml:id="N242E5" xml:space="preserve">Confir°.</note>
            <p xml:id="N242E9">
              <s xml:id="N242EA" xml:space="preserve">Cõfirmatur / quia ſi illa poſitio eēt ve­<lb/>ra ſequeretur /  .a. inciperet a nõ quãto in infinituꝫ <lb/>velociter augeri: et tamen cõtinuo acq̇reret vnifor-<lb/>miter de quãtitate: ſed cõſequens videtur repugna­<lb/>re. </s>
              <s xml:id="N242F5" xml:space="preserve">igitur illud ex quo ſeq̇tur. </s>
              <s xml:id="N242F8" xml:space="preserve">Seq̄la probatur: et di­<lb/>uido horã futuram ꝑ partes ꝓportionales ꝓpor-<lb/>tione dupla minoribus terminatis verſus finem: et <lb/>capio vnum pedale diuiſum ꝑ partes ꝓportiona-<lb/>les ꝓportione dupla: et volo /  in prīa parte ꝓpor-<lb/>tionali temporis deperdat vniformiter primã par­<lb/>tem proportionalem ſui: et in ſecunda ſecūdam: et <lb/>in tertia tertiam: et ſic cõſequēter ſemꝑ vniformiter <lb/>deperdendo quãtitatem vſ ad non ̄tum: deinde <lb/>volo /  in alia hora ſequenti augeatur a nõ quãta               <pb chead="Tertii tractatus" file="0205" n="205"/>               oīno eodē modo ſicut diminuebat̄̄ acq̇rendo vnifor­<lb/>miter quãtitatē ſicut eam deperdebat. </s>
              <s xml:id="N24314" xml:space="preserve">quo poſito <lb/>arguit̄̄ ſic .a. in inſtanti initiatiuo alterius hore ſe-<lb/>quentis incipit vniformiter acq̇rere quãtitatē quia <lb/>vniformiter deperdit in hora priori cum poſitis in <lb/>caſu: et tamen incipit in infinitū velociter augeri / vt <lb/>patet ex principio huiꝰ ſecūdi argumēti: igit̄̄ ꝓpo­<lb/>ſitum.               <anchor type="note" xlink:href="note-0205-01" xlink:label="note-0205-01a"/>               </s>
              <s xml:id="N24328" xml:space="preserve">¶ Dices et bene cõcedēdo quod infertur: et ne­<lb/>gando  illud repugnet. </s>
              <s xml:id="N2432D" xml:space="preserve">Immo in tali caſu illud <lb/>ſeq̇tur ex hac poſitiõe.</s>
            </p>
            <div xml:id="N24332" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0205-01a" xlink:label="note-0205-01" xml:id="N24336" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2433C">
              <s xml:id="N2433D" xml:space="preserve">Sꝫ contra q2 tūc ſequeretur /  quoti-<lb/>enſcun hora diuidit̄̄ ꝓportiõe dupla et aliq̇d inci­<lb/>pit augeri a non quãto in qualibet parte ꝓportio-<lb/>nali acq̇rēdo vniformiter vnam ſui partē propor-<lb/>tionalē ꝓportione dupla: ip̄m incipit vniformiter <lb/>acq̇rere quãtitatē: et cõtinuo vniformiter aquirit. <lb/></s>
              <s xml:id="N2434B" xml:space="preserve">Patet hoc / q2 in equalibꝰ partibꝰ tēporis equaleꝫ <lb/>quãtitatē oīno acquirit: ſꝫ cõſequēs eſt falſum: igit̄̄ <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N24352" xml:space="preserve">Falſitas ↄ̨ſequētꝪ arguitur: q2 <lb/>tunc ſeq̄retur /  ſi duo inciperēt augeri a nõ quãto: <lb/>et vnū illorū in qualibet parte ꝓportionli tempo­<lb/>ris ꝓportõe dupla iucipiēdo a minoribus acq̇reret <lb/>vniformiter vnã partē ꝓportionalē ſui ꝓportione <lb/>dupla ita  in qualibet ꝑte ꝓportionali acq̇reret <lb/>proportionē duplã: et aliud in certa ꝓportione cõ-<lb/>tinuo velocius augeretur puta in qualibet parte ꝓ­<lb/>portionali talis tēporis acquirēdo ꝓportionē qua­<lb/>druplam vel octuplam cõtinuo: tunc illud quod in <lb/>certa proportiõe cõtinuo velocius augetur incipit <lb/>infinitū tarde acq̇rere de quãtitate: ſed ↄ̨ſequēs eſt <lb/>falſum: quia tūc ſequeret̄̄ /  omne qḋ a nõ quãto in­<lb/>cipit augeri: et in qualibet parte tēporis ꝓportio-<lb/>nali ꝓportione dupla maiorē ꝓportionē acquirit <lb/>quã dupla: ī īfinitū tarde acq̇reret de ̄titate quod <lb/>videt̄̄ oīno extraneū. </s>
              <s xml:id="N24375" xml:space="preserve">Sequela tamē ꝓbat̄̄: et volo / <lb/> a. ſic incipiat augeri a nõ quãto: et ī qualibet ꝑte <lb/>ꝓportiõali tēporis ꝓportiõe dupla acq̇rat pro­<lb/>portionē duplã acq̇rendo vniformiter de quãtitate <lb/>et .b. in omni ↄ̨ſimili parte tēporis acquirat maio­<lb/>rem proportionē dupla puta triplã vel quadruplã <lb/>vel octuplã, in idē redit, quo poſito arguitur ſic .a. <lb/>et .b. incipiūt augeri a nõ quãto: et .b. in certa ꝓpor-<lb/>tione cõtinuo velocius augebitur ꝙ̄ a. / ergo ſeq̇tur / <lb/> a. incipit in infinitū eē maius ip̄o .b. / et ꝑ ↄ̨ſequēs <lb/>incipit in infinitū maiorē quãtitatē acq̇rere ipſo .b. / <lb/>vt patet ex vltima replica ſecundi argumēti: et vltra <lb/>ſequitur /  in infinitū maiorē quãtitatē acquirit .a. <lb/>̄ .b. in eodē tempore: et a. cõtinuo vniformiter et eq̄ <lb/>velociter acquirit quãtitatē: ergo .b. incipit in infi-<lb/>nitū tarde acq̇rere de quãtitate / quod fuit ꝓbandū.</s>
            </p>
            <note position="left" xml:id="N24396" xml:space="preserve">Cõfir° .2.</note>
            <p xml:id="N2439A">
              <s xml:id="N2439B" xml:space="preserve">Confirmatur ſecundo / quia ſi poſitio <lb/>eſſet vera ſequeret̄̄ /  ſi a nõ quãto aliquid inciperet <lb/>augeri in qualibet parte ꝓportionali temporis ꝓ-<lb/>portiõe dupla diuiſi acquirēdo minorē ꝓportionē <lb/>̄ duplã: ip̄m inciperet in infinitū velociter acq̇rere <lb/>de quãtitate: ſꝫ cõſequēs eſt falſum: igitur illud ex <lb/>quo ſeq̇tur. </s>
              <s xml:id="N243AA" xml:space="preserve">Seq̄la ꝓbat̄̄ et capio .a. et .b. et volo /  .a. <lb/>incipiat augeri a nõ quãto in qualibet parte ꝓpor­<lb/>tionali tēporis ꝓportiõe dupla diuiſi acq̇rendo vni­<lb/>formiter ↄ̨ſimilem partē ꝓportionalē ſui ꝓportio­<lb/>ne dupla ita  in qualibet tali parte tēporis acq̇-<lb/>rat vnã ꝓportionē duplã: et .b. in qualibet conſimili <lb/>parte tēporis acquirat vnã partē ꝓportionalē ſui <lb/>ꝓportione minori dupla puta ſexquitertia vel ſex­<lb/>quialtera. </s>
              <s xml:id="N243BD" xml:space="preserve">Quo poſito arguit̄̄ ſic .a. et .b. incipiunt <lb/>augeri a nõ quãto: et b. ī certa ꝓportiõe cõtinuo tar­<lb/>dius ip̄o .a. / igit̄̄ incipit eē in infinitū maius ipſio .a. / <lb/>et per ↄ̨ſequens incipit in infinitū velociter maiorē               <cb chead="Capi. ſecundum"/>               quãtitatē acq̇rere ꝙ̄ a. in eodem tēpore. </s>
              <s xml:id="N243C9" xml:space="preserve">Patēt conſe-<lb/>quentia vt prius: et a. cõtinuo certe velociter acq̇rit <lb/>quãtitatē vt poſitū eſt: igit̄̄ .b. in infinitū velociter ac­<lb/>quirit quãtitatē / quod fuit ꝓbadū. </s>
              <s xml:id="N243D2" xml:space="preserve">Sꝫ iam probo <lb/>falſitatē cõſequētis: q2 tūc ſequeretur /  ſi a. et b. in­<lb/>ciperet a nõ quãto augeri: et a. in qualibet parte <lb/>ꝓportionali tēporis proportiõe dupla acquereret <lb/>proportionē ſexquialterã: et b. in cõſimili parte cõ-<lb/>tinuo acq̇reret ꝓportiõeꝫ ſexquitertiã: tunc vtrun <lb/>illorū inciperet infinite velociter acquirere de quã­<lb/>titate: et ꝑ cõſequēs .b. nõ īciperet velocius acq̇rere <lb/>de quãtitate ꝙ̄ a. et ſic nõ inciperet in īfinitū eē maiꝰ <lb/>ipſo a. / quod eſt ↄ̨tra cõcluſionē ꝓbatã in vltima re­<lb/>plica ſecundi argumēti. </s>
              <s xml:id="N243E9" xml:space="preserve">Falſitas cõſequētis patet / <lb/>quia nõ videt̄̄ poſſibile  vtrū illorū inciperet in­<lb/>finite velociter acquirere de quãtitate: et tamē vnuꝫ <lb/>illorum inciperet in infinitū velocius altero acqui-<lb/>rere. </s>
              <s xml:id="N243F4" xml:space="preserve">Cõſequētia tamē patet / quia vtrū illorū inci­<lb/>pit augeri a nõ quãto continuo in qualibet parte ꝓ-<lb/>portionali tēporis ꝓportiõe dupla acquirēdo mi-<lb/>norē ꝓportionem dupla: igitur.</s>
            </p>
            <note position="right" xml:id="N243FD" xml:space="preserve">Cõfir° .3.</note>
            <p xml:id="N24401">
              <s xml:id="N24402" xml:space="preserve">Confirmatur tertio / quia ſi poſitio eēt <lb/>vera ſeq̄retur /  quãtuncun magnū corpus ſit di­<lb/>uiſum per partes ꝓportionales aliquã proportio­<lb/>ne: et aliud quãtuncū parū diuiſum per partes <lb/>ꝓportionales aliqua proportione minori: in infini­<lb/>tū maior eſt aliqua pars proportionalis minoris <lb/>parte proportionali correſpõdente maioris: ſꝫ cõ-<lb/>ſequens apparet falſum: igitur illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N24414" xml:space="preserve">Sequela probatur / q2 ſi non detur vnū cētupedale <lb/>diuiſum ꝑ partes proportionales proportiõe qua­<lb/>durupla: et vnū ſemipedale vel quãtūcū paruum <lb/>volueris diuiſum ꝑ partes portionales proportio­<lb/>ne ſexquitertia ſeu quauis alia proportiõe minori <lb/>quadrupla: et diminuãtur illa duo vſ ad nõ ̄tuꝫ <lb/>ita  maius cõtinuo in qualibet parte proportio-<lb/>nali tēporis proportiõe dupla vnã ſui partiē pro-<lb/>portionalē perdat ꝑdēdo proportionē quadruplã <lb/>et ſemipedale in qualibet parte cõſimili perdat ꝓ-<lb/>portionē ſexquitertiã ꝑdendo vnam partē propor-<lb/>tionalē ſui proportiõe ſextertia quouſ veniãt ad <lb/>nõ quãtū: tūc volo /  īcipiãt oīno eodē modo acqui­<lb/>rere quãtitates deperditas et oīno eodē modo au-<lb/>geri ſicut diminuebant̄̄. </s>
              <s xml:id="N24433" xml:space="preserve">Quo poſito arguitur ſic <lb/>illud / qḋ fuit cētupedale: et illḋ quod fuit ſemipe­<lb/>dale incipit in certa portiõe tardius cõtinuo auge-<lb/>ri ꝙ̄ centupedale: igit̄̄ illud qḋ fuit ſemipedale inci­<lb/>pit in infinitū eē maius illo altero quod fuit centi-<lb/>pedale: et illud qḋ fuit centipedale incipit acquire-<lb/>re partes proportionales proportiõe quadrupla <lb/>quas antea ṗdidit: et illḋ qḋ fuit ſemipedale īcipit <lb/>acq̇rere partes proportionales proportione ſexq̇-<lb/>tertia quas antea deꝑdit: igit̄̄ incipit in infinitum <lb/>maiores partes acquirere illud quod fuit ſemipe-<lb/>dale ꝙ̄ illud qḋ fuit centipedale. </s>
              <s xml:id="N2444C" xml:space="preserve">Patet cõſequētia / <lb/>q2 immediate poſt illud qḋ fuit ſemipedale in infi-<lb/>nitū erit maius illo qḋ fuit centipedale. </s>
              <s xml:id="N24453" xml:space="preserve">igit̄̄ imme-<lb/>diate poſt hoc in infinitū maiores erunt partes pro­<lb/>portiõales illius proportiõe ſexquitertia partibꝰ <lb/>proportionalibꝰ alterius proportiõe quadrupla: <lb/>et tales partes īcipit acq̇rere: et ſemꝑ acq̇runt par-<lb/>tes correſpõdētes ſicut deperdebãt: igit̄̄ in infinitū <lb/>maior eſt aliqua pars proportionalis minoris ꝑ-<lb/>te proportionali correſpõdente maioris quod fuit <lb/>probandum.</s>
            </p>
            <p xml:id="N24466">
              <s xml:id="N24467" xml:space="preserve">Tertio prīcipaliter ad idem arguitur <lb/>ſic. </s>
              <s xml:id="N2446C" xml:space="preserve">Si illa poſitio eſſet vera ſeq̄retur hec cõcluſio                <pb chead="De motu augmentationis." file="0206" n="206"/>               ſi aliquod corpus diuidatur ꝑ partes proportio-<lb/>nales proportiõe dupla: et in aliquo tēpore puta ī <lb/>hora prīa pars proportionalis augeatur aliquã-<lb/>tulū velociter: et ſecūda in duplo velocius: et tertia <lb/>in triplo ꝙ̄ prima: et ſic ↄ̨ſequēter ſequeret̄̄ /  totuꝫ <lb/>illud corpus in fine tēporis eſſet infinite magnū: et <lb/>per cõſequēs illud corpus infinite velociter augmen-<lb/>taretur: ſꝫ cõſequēs eſt falſum: igit̄̄ et añs. </s>
              <s xml:id="N24482" xml:space="preserve">Ealſitas <lb/>cõſequētis arguit̄̄: et pono caſum /  ſit vnū corpus <lb/>diuiſum ꝑ partes proportionales proportiõe du-<lb/>pla: et in hora prima pars proportionaiis acqui-<lb/>rat proportionē ſexquialterã: et ſecūda in eodē tē-<lb/>pore acquirat duas ſexquialteras: et quarta .4. / et <lb/>ſic cõſequēter. </s>
              <s xml:id="N24491" xml:space="preserve">Quo poſito arguit̄̄ ſic: prima pars <lb/>proportionalis illiꝰ corporis aliqualiter auget̄̄: et <lb/>ſecūda in duplo magis: et tertia in triplo: et ſic cõſe­<lb/>quēter: et tamē illud corpus in fine nõ erit infinituꝫ <lb/>ſed ſolū finitū / igit̄̄ in tali caſu nõ acq̇rit īfinitã pro­<lb/>portionē: et ꝑ ↄ̨ſequēs illud illatū eſt falſum / q2 eſt <lb/>vna cõditionalis cuius añs eſt verū / et cõſequēs fal­<lb/>ſum. </s>
              <s xml:id="N244A2" xml:space="preserve">Sed iã probo /  illud in illo caſu erit finitum <lb/>in fine hore q2 ī fine hore ille partes q̄ ante augmē-<lb/>tationē ſe habebãt in proportione dupla ſe habe-<lb/>bunt ↄ̨tinuo in proportiõe ſexquitertia: igit̄̄ aggre­<lb/>gatū ex oībꝰ ſequētibiꝰ primã eſt triplū ad primaꝫ / <lb/>vt ptꝫ ītelligēti quītū caput prime partis: ſꝫ primū <lb/>eſt finitū: ergo totū eſt finitū. </s>
              <s xml:id="N244B1" xml:space="preserve">Sꝫ iã probo /  ille ꝑ-<lb/>tes cõtinuo ſe habēt in ꝓportiõe ſexquitertia: qm̄ <lb/>prima et ſcḋa ſe habēt in ꝓportiõe ſexquitertia: et ſe­<lb/>cunda et tertia: et ſic de q̇buſcū duabus immediatꝪ <lb/></s>
              <s xml:id="N244BB" xml:space="preserve">Quod ſic ꝓbat̄̄ / quoniã ſi prima et ſcḋa equalem ꝓ-<lb/>portionē acq̇ſiuiſſent puta ſexquialteram: tunc ad­<lb/>huc mãſiſſent in ꝓportiõe dupla ſicut antea vt con­<lb/>ſtat: ſed modo ſecūda que eſt minor acquirit adhuc <lb/>ſexquialterã adequate: g̊ ꝓportio dupla que eſt in-<lb/>ter primã et ſcḋam ꝑdit ſexquialterã: et ſic manet ſex­<lb/>quitertia tantū inter primã et ſecundã. </s>
              <s xml:id="N244CA" xml:space="preserve">Itē ſi tertia <lb/>pars ꝓportionalis acq̇ſiuiſſet duas ſexquialteras <lb/>adequate ſicut ſecūda: ſecunda et tertia manſiſſent <lb/>in ꝓportõe dupla: ſꝫ modo tertia acquiſiuit adhuc <lb/>vnã ſexquialterã: igit̄̄ illam ſexq̇alteram deperdit <lb/>dupla q̄ eſt inter ſecundã et tertiam: et ꝑ cõſequens <lb/>manet ſexquitertia / vt patet intelligenti quartū ca­<lb/>put ſecunde partis cū octauo: et ſit ꝓbabis de ter-<lb/>tia et quarta: et de oībus:               <anchor type="note" xlink:href="note-0206-01" xlink:label="note-0206-01a"/>               igit̄̄ ille partes cõtinuo ꝓ­<lb/>portionãtur ꝓportiõe ſexquitertia / qḋ fuit ꝓbandū <lb/>tenet hec deductio ꝑ hanc maximã biꝑtitã. </s>
              <s xml:id="N244E6" xml:space="preserve">Quãdo­<lb/>cū aliqui duo numeri vel ̄titates ſe habēt ī ali-<lb/>qua ꝓportione et equales ꝓportiões acq̇runt ſem-<lb/>per manēt in eadē proportiõe et ſi numerus mīor <lb/>ſiue ̄titas minor acq̇rat aliquã ꝓportionē vltra <lb/>numerū ſiue ̄titatē maiorē ita tamē  ſemꝑ ma-<lb/>neat minor illã ꝓportionē deperdit ꝓportio que a <lb/>principio erat inter numerū maiorē et minorē. </s>
              <s xml:id="N244F7" xml:space="preserve">Hec <lb/>maxīa claret ex quarta cõcluſiõe et ſecundo correla-<lb/>rio ſexte ↄ̨̨cluſiõis octaui capitis ſecūde partꝪ. </s>
              <s xml:id="N244FE" xml:space="preserve">Sꝫ <lb/>iam probo ſeq̄lam prīcipalē argumēti: q2 ſi prima <lb/>pars ꝓportionalis talis corporis diuiſi ꝑ partes <lb/>ꝓportionales ꝓportiõe dupla acquireret duplã <lb/>et ſecūda duas duplas: et tertia tres duplas: et q̈rta <lb/>quatuor: et ſic ↄ̨ſequēter: tūc ī fine hore illud corpꝰ <lb/>manebit īfinite magnū: igit̄̄ īfinitã ꝓportionē ac-<lb/>quiſiuit in illo tꝑe et ſic infinite velociter augmēta-<lb/>bit̄̄: igit̄̄ ſi talis corporis diuiſi ꝑ partes ꝓportio-<lb/>nales ꝓportiõe dupla prīa pars ꝓportionalis ac-<lb/>quirat aliquã proportionē: et ſecūda duas tales: et <lb/>tertia tres: et quarta .4. / et ſic ↄ̨ſequēter: tūc tale cor­<lb/>pus in illa hora infinitã proportionē acq̇rit: et ſic ī­<lb/>finite velociter augmētat̄̄: quod fuit ꝓbãdū </s>
              <s xml:id="N2451B" xml:space="preserve">Ptꝫ               <cb chead="De motu augmentationis."/>               hec cõſequētia ab inferiori ad ſuꝑius. </s>
              <s xml:id="N24521" xml:space="preserve">Sꝫ iam ꝓbo <lb/>añs / q2 in fine hore quelibet illarū partiū propor-<lb/>tionaliū erit equalis prime: et ſunt infinite / igit̄̄ illḋ <lb/>corpus erit infinitū: </s>
              <s xml:id="N2452A" xml:space="preserve">Probat̄̄ maior / q2 prīa et ſcḋa <lb/>erūt equales in fiue: et ſecunda et tertia: et tertia et <lb/>quarta: et ſic de q̇buſcū aliis immediatis: quoni-<lb/>am ſi ſcḋa acq̇reret adequate vnam duplã ſicut pri­<lb/>ma: tunc ṗma et ſcḋa adhuc manerēt in ꝓportione <lb/>dupla / vt pꝫ ex maxīa nuperrime poſita: ſꝫ modo ſe­<lb/>cunda acq̇rit adhuc vnã duplã: et illã deꝑdit ꝓpor-<lb/>portio inter ṗmã et ſcḋam: igitur totalis ꝓportio <lb/>inter primã et ſcḋaꝫ deꝑditur q2 nõ erat niſi dupla <lb/>et ſic prima et ſcḋa manēt equales. </s>
              <s xml:id="N2453F" xml:space="preserve">Itē ſi tertia p̄ciſe <lb/>acquireret duas duplas ſicut ſecūda adhuc inter <lb/>ſecūdam et tertiam maneret proportio dupla: ſed <lb/>modo illam duplã acquirit tertia: igit̄̄ ſecunda et <lb/>tertia manent equales. </s>
              <s xml:id="N2454A" xml:space="preserve">Patet / q2 quando ſubdu-<lb/>plū auget̄̄ ad duplū efficit̄̄ duplo equale. </s>
              <s xml:id="N2454F" xml:space="preserve">et iſto mõ <lb/>ꝓbabis de q̇buſcū aliis duabꝰ immediatis: igit̄̄ <lb/>oēs ille partes in fine manebūt equales: et ꝑ conſe-<lb/>quens illud corpus erit in fine infiuitū / qḋ fuit pro­<lb/>bandū.               <anchor type="note" xlink:href="note-0206-02" xlink:label="note-0206-02a"/>               </s>
              <s xml:id="N2455F" xml:space="preserve">hec inductio gñaliter pꝫ ꝑ hanc maximam. <lb/></s>
              <s xml:id="N24563" xml:space="preserve">Quãdocū alique due ̄titates ſe habēt in aliq̈ ꝓ­<lb/>portiõe maioris inequalitatis et minor acq̇rit totã <lb/>illam proportionē que eſt inter ip̄am et maiorem q̄ <lb/>maior etiã auget̄̄: et cū hoc illa minor acq̇rit etiam <lb/>illam ꝓportionē quã acq̇rit maior: tūc in fine mane­<lb/>bunt equales. </s>
              <s xml:id="N24570" xml:space="preserve">Patet / q2 minor acq̇ſiuit totū quod <lb/>deficiebat ei vt eſſet equalis alteri et cū hoc illḋ qḋ <lb/>illa maior acq̇ſiuit: ſꝫ ſic eſt in propoſito de his ꝑti­<lb/>bus īmeditatis vt cõſtat: igitur in fine ille ꝑtes ma-<lb/>nent equales.</s>
            </p>
            <div xml:id="N2457B" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0206-01a" xlink:label="note-0206-01" xml:id="N2457F" xml:space="preserve">Maxīa.</note>
              <note position="right" xlink:href="note-0206-02a" xlink:label="note-0206-02" xml:id="N24585" xml:space="preserve">Maxīa <lb/>ſiue poſi­<lb/>tio.</note>
            </div>
            <note position="right" xml:id="N2458F" xml:space="preserve">Confir°.</note>
            <p xml:id="N24593">
              <s xml:id="N24594" xml:space="preserve">Et confirmatur / quia ſi illa poſitio eēt <lb/>vera ſequeret̄̄ /  ſi aliquod corpus diuideret̄̄ ī par-<lb/>tes ꝓportionales ꝓportione dupla: et prima pars <lb/>proportionalis in hora acq̇rat aliquã proportio-<lb/>ne ita  augeat̄̄ aliquantulū velociter: et ſecūda ī <lb/>duplo velocius in eodē tꝑe: et tertia in duplo veloci­<lb/>us ꝙ̄ ſecūda: et quarta in duplo velocius ꝙ̄ tertia <lb/>in eodē tēpore / et ſic ↄ̨ſeq̄nter tunc in fine illud cor-<lb/>pus manebit infinite magnū: et ſic in illo tēpore in­<lb/>finite velociter augmētabitur: ſꝫ ↄ̨ſequēs eſt falſuꝫ / <lb/>igitur et añs. </s>
              <s xml:id="N245AB" xml:space="preserve">Falſitas cõſequētis probat̄̄: et capio <lb/>vnū pedale diuiſum in partes proportionales pro­<lb/>portione dupla: et volo /  in vna hora prima pars <lb/>proportionalis acq̇rat vnã ſexquioctauã: et in eodē <lb/>tēpore ſecunda acquirat duas ſexquioctauas: et ter­<lb/>tia. quatuor: et quarta .8. et q̇nta .16. / et ſic ↄ̨ſequen-<lb/>ter duplando. Quo poſito ſic arguo prima pars <lb/>illius corporis proportione dupla in hora aliquã­<lb/>tulū auget̄̄: et ſecūda in duplo velocius: et tertia in <lb/>duplo velocius ꝙ̄ ſecūda: et ſic ↄ̨ſequēter / et tñ in fine <lb/>illud corpus nõ erit infinite magnū nec tale corpꝰ <lb/>infinite velociter augetur: igit̄̄ illud ↄ̨ſequens fal-<lb/>ſum. </s>
              <s xml:id="N245C6" xml:space="preserve">Probat̄̄ añs / q2 ille partes proportionales q̄ <lb/>ſunt minores cõtinuo manebūt minores: nec vni̄ <lb/>aliqua ſequēs erit equalis immediate precedēti in <lb/>tali caſu: igit̄̄ illud corpus in fine nõ erit infinitum <lb/></s>
              <s xml:id="N245D0" xml:space="preserve">Probatur añs / q2 ſecunda pars non erit equalis <lb/>prime: nec tertia ſecunde: nec quarta tertia: et ſic cõ-<lb/>ſequenter vt apparet: igitur non dabunt̄̄ in tali ca­<lb/>ſu due partes quarum vna ſit equalis immediate <lb/>precedēti. </s>
              <s xml:id="N245DB" xml:space="preserve">Sed iam probo ſeq̄lam principaleꝫ: qm̄ <lb/>ſi quelibet pars proportionalis ſequens acquire­<lb/>ret adequate tot proportiões ſicut īmediate prece­<lb/>dens: tunc ille partes cõtinuo ſe haberēt in propor­<lb/>tione dupla ſicut ſe habent in ṗncipio: ſed mõ aliq̈ <lb/>pars ſequēs acquiret decē proportiones pluſ̄ im­               <pb chead="Tertii tractatus" file="0207" n="207"/>               mediate p̄cedens: et aliqua ſedecim: et aliqua trigī-<lb/>ta duas: et ſic cõſequēter: igitur aliqua acqurxt tot <lb/>proportiones ſicut immediate p̄cedēs: et cū hoc tot <lb/>proportiões vltra equales  cõſtituãt vnã duplaꝫ <lb/>vel plures: et ſic iam ille due partes manebūt equa-<lb/>les vel ſequēs erit maior īmediate p̄cedenti: et per eã­<lb/>dem rõnem quelibet ſequēs illã erit maior īmedia­<lb/>te p̄cedēti: qm̄ quelibet talis ſequēs acq̇rit tot pro-<lb/>portiões vltra proportiones acq̇ſitas a parte īme-<lb/>diate p̄cedente q̄ proportiones proportionē maio-<lb/>rem dupla cõſtituent: igit̄̄ in fine tale corpus cõpo-<lb/>netur ex īfinitis equalibꝰ nõ cõicantibꝰ etc. / et ſic erit <lb/>infinitum / quod fuit probandum.               <anchor type="note" xlink:href="note-0207-01" xlink:label="note-0207-01a"/>               </s>
              <s xml:id="N2460A" xml:space="preserve">¶ Dices et bene cõ­<lb/>cedendo ſeq̄lam vt bene probat argumentū: et negã­<lb/>do falſitatē cõſequentis: et ad probationē nego /  <lb/>in illo caſu poſito nõ dabit̄̄ aliqua pars que ſit eq̈­<lb/>lis vel maior immediate precedēte. </s>
              <s xml:id="N24615" xml:space="preserve">Immo dico /  <lb/>quinta erit maior quarta: quoniã quarta acquirit <lb/>octo ſexquioctauas: et quinta .16. ſexquioctauas: ſi <lb/>igit̄̄ quinta acquireret octo p̄ciſe ſexq̇octauas: tūc <lb/>manerent in eadē ꝓportione puta in ꝓportiõe du-<lb/>pla: ſꝫ modo quinta acq̇rit adhuc .8. ſexq̇octauas q̄ <lb/>cõponūt maiorē ꝓportionē ꝙ̄ duplã: ergo ſeq̇tur /  <lb/>quinta manet maior ip̄a quarta: et eadē rõne ſexta <lb/>manebit maior q̇nta: et ſic quelibet ſequēs. </s>
              <s xml:id="N24628" xml:space="preserve">QꝪ o <lb/>octo ſexq̇octaue cõponunt maiorē ꝓportionē quaꝫ <lb/>duplã: ptꝫ ex ſe qm̄ tres ꝓportiões quarū quelibet <lb/>eſt minor ꝓportione ſexquioctaua cū vna ſexq̇octa­<lb/>ua cõſtituūt adequate magis quã medietatē duple <lb/>quoniã cõſtituūt ſexquialteram / vt ptꝫ inter octo et <lb/>duodecim: igit̄̄ per locū a maiore octo ſexq̇octaue <lb/>cõſtituūt magis ꝙ̄ duplam: qḋ fuit ꝓbandū.</s>
            </p>
            <div xml:id="N24639" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0207-01a" xlink:label="note-0207-01" xml:id="N2463D" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N24643">
              <s xml:id="N24644" xml:space="preserve">Sed contra quia tunc ſequeretur /  <lb/>ſubito illud corpus efficiret̄̄ infinite magnū: et per <lb/>ↄ̨ſequens illud corpus nõ augmētaret̄̄ per illã ho-<lb/>ram: et ſic nõ augmētaret̄̄ cuiꝰ oppoſitū eſt conceſ-<lb/>ſum quoniã per nullū tēpus augmētaretur. </s>
              <s xml:id="N2464F" xml:space="preserve">Iã pro­<lb/>bo ſequelam. </s>
              <s xml:id="N24654" xml:space="preserve">qm̄ quocun inſtanti dato poſt īſtãs <lb/>quo ille partes ſic incipiunt augmētari / vt dictū eſt <lb/>tanta quãtitas vel maior eſt acquiſita cuilibet ſe­<lb/>quēti ſicut prime: igitur quocū inſtanti dato poſt <lb/>inſtans initiatiuū inter illud et inſtans initiatiuuꝫ <lb/>illud corpus erit infinitū. </s>
              <s xml:id="N24661" xml:space="preserve">Probo añs / q2 dato ali-<lb/>quo inſtanti in quo ṗma pars ꝓportionalis acq̇ſi-<lb/>uit aliquã ̄titatē: ſi ſecūda acq̇reret tantã ꝓportio­<lb/>nem adequate ſicut prīa ip̄a ſecūda acquireret ſub­<lb/>duplã ̄titatē ad primã vt cõſtat: ſꝫ mõ ſuꝑ illã pro­<lb/>portionē acquirit adhuc tantã ꝓportionē: ergo per <lb/>illã proportionē quã acq̇rit vltra: acq̇rit maiorem <lb/>̄titatem  ſubduplã: ergo acquirit maiorē ̄tita-<lb/>tem quã prima. </s>
              <s xml:id="N24674" xml:space="preserve">Patet cõſequētia / q2 acq̇rit pluſ̄ <lb/>duas medietates illius ̄titatis quã acq̇rit prima <lb/></s>
              <s xml:id="N2467A" xml:space="preserve">Et ſic ꝓbabis /  tertia acq̇rit pluſ̄ ſecūda: et quar­<lb/>ta ꝙ̄ tertia: ē ſic in infinitū: igitur aſſumptum verū. <lb/>               <anchor type="note" xlink:href="note-0207-02" xlink:label="note-0207-02a"/>               </s>
              <s xml:id="N24686" xml:space="preserve">¶ Confirmat̄̄ ſcḋo. / q2 ſi illa poſitio eſſet vera ſeque­<lb/>retur /  quãdo aliquod corpus diuiſum in partes <lb/>proportionales ꝓportiõe dupla </s>
              <s xml:id="N2468D" xml:space="preserve">Ita ſe haberēt  <lb/>prima pars ꝓportionalis eiꝰ acq̇reret aliquã pro-<lb/>portionē: et ſecūda in eodē tꝑe in duplo minorem: et <lb/>tertia in eodē tēpore in duplo minorē ꝙ̄ ſecūda: et <lb/>ſic cõſequēter: ſeq̄ret̄̄ /  tale corpus in nulla ꝓpor-<lb/>tione efficiret̄̄ maius ꝙ̄ antea adequate: ſed conſe-<lb/>quens eſt falſum: igitur illud ex quo ſequit̄̄. </s>
              <s xml:id="N2469C" xml:space="preserve">Falſi-<lb/>tas ↄ̨ſequentis eſt manifeſta: qm̄ illud corpus ma-<lb/>nebit finitū: et cuiuſlibet finiti ad finitū eſt ꝓportio <lb/>aliqua: igit̄̄ </s>
              <s xml:id="N246A5" xml:space="preserve">Seq̄la tamē patꝫ / qm̄ non apparet mo­<lb/>dus quo poſſet reperiri talis ꝓportio. </s>
              <s xml:id="N246AA" xml:space="preserve">¶ Idem fie-<lb/>ret ſi ṗma pars proportionalis acquireret ꝓpor-<lb/>tionem duplaꝫ: et ſecūda ſexq̇alterã: et tertia ſexqui­               <cb chead="Capi. ſecundum"/>               tertiam: et ſic ↄ̨ſequenter: tūc em̄ nõ videtur in qua ꝓ­<lb/>portione corpus fiat maius: qm̄ ille partes in nul-<lb/>la ꝓportione cõtinuo ꝓportionabiles manent.</s>
            </p>
            <div xml:id="N246B8" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0207-02a" xlink:label="note-0207-02" xml:id="N246BC" xml:space="preserve">2. confir°</note>
            </div>
            <note position="right" xml:id="N246C2" xml:space="preserve">3. confir°.</note>
            <p xml:id="N246C6">
              <s xml:id="N246C7" xml:space="preserve">¶ Cõfirmatur tertio: q2 ſi illa poſitio eſſet vera ſeq̄­<lb/>retur /  aliquid poſſet vniformiter per totū augmē­<lb/>tari et etiã diminui: cõſequēs eſt falſum: igitur illud <lb/>ex quo ſeq̇tur. </s>
              <s xml:id="N246D0" xml:space="preserve">Sequela pꝫ et volo /  vnius pedalis <lb/>quelibet pars acq̇rat ꝓportionē duplã: tūc illḋ vni­<lb/>formiter auget̄̄ per totū: q2 q̄libet pars tm̄ augmē­<lb/>tatur: ſicut totū: igitur vniformiter quo ad partes <lb/>augmētatur: ſicut illud vniformiter intendit̄̄ cuius <lb/>quelibet pars tantū intēditur ſicut totū: et ſic etiaꝫ <lb/>ꝓbabitur de diminutione. </s>
              <s xml:id="N246DF" xml:space="preserve">Sꝫ ꝓbatur falſitas ↄ̨ſe­<lb/>quentis: q2 tunc ſeq̄retur /  illud pedale infinite ve-<lb/>lociter augmētaret̄̄: q2 in eodē tēpore infinitas du-<lb/>plas acq̇rit: ſed cõſequēs eſt falſum: igitur. </s>
              <s xml:id="N246E8" xml:space="preserve">q2 non <lb/>manet niſi duplū ad illud qḋ erat ante augmenta-<lb/>tionē / vt ſatis cõſtat. </s>
              <s xml:id="N246EF" xml:space="preserve">QꝪ aūt acq̇rat īfinitas duplas <lb/>patet: q2 quelibet pars ꝓportionalis acquirit̄̄ vnã <lb/>duplã. </s>
              <s xml:id="N246F6" xml:space="preserve">¶ Quarto principaliter ad idē arguitur ſic / <lb/>quia ſi poſitio eſſet vera ſeq̄retur  nichil poſſet di­<lb/>minui vſ ad nõ quãtū ſucceſſiue ī aliq̊ tꝑe niſi illḋ <lb/>perderet vni ſignate ꝓportiõi infinitas eq̈les non <lb/>cõicantes. </s>
              <s xml:id="N24701" xml:space="preserve">ſed ↄ̨ñs eſt fĺm: igit̄̄ et illḋ ex q̊ ſequit̄̄. </s>
              <s xml:id="N24704" xml:space="preserve">Se­<lb/>q̄la pꝫ clare qm̄ ſi ꝑderet finitas tm̄: cū ille finitã ꝓ-<lb/>portionē ↄ̨ſtiuãt: ſequit̄̄ /  ꝑderet fiuitã ꝓportionē <lb/>p̄ciſe: et ſic nõ maneret ī fine nõ ̄tū / vt ↄ̨ſtat. </s>
              <s xml:id="N2470D" xml:space="preserve">Probo <lb/>tñ falſitatē ↄ̨ñtis qm̄ in aliq̊ caſu aliq̇d diminuitur <lb/>vſ ad nõ ̄tū in hora et nõ deꝑdit vni ſignate pro­<lb/>portiõi infinitas equales nõ cõicantes: igitur ↄ̨ñs <lb/>falſum. </s>
              <s xml:id="N24718" xml:space="preserve">Probatur añs et capio vnū pedale: et volo / <lb/> diuiſa vna hora per partes ꝓportionales ꝓpor­<lb/>tione dupla: in prima illarū perdat ꝓportionē ſex-<lb/>quialterã ſui: et in ſecūda ſexquitertiã ſui: et ī tertia <lb/>ſexquiquartã: et in quarta ſexq̇quintã: et ſic ↄ̨ñter ꝓ­<lb/>cedēdo ꝑ ſpecies ꝓportiõis ſuꝑparticularꝪ quo po­<lb/>ſito in fine deueniet ad non ̄tū: et tñ vni ꝓportioni <lb/>date nõ ꝑdit īfinitas equales nõ cõicãtes: igit̄̄ ꝓpo­<lb/>ſitū. </s>
              <s xml:id="N2472B" xml:space="preserve">Minor pꝫ: q2 q̄libet ſequēs in illo caſu eſt mi-<lb/>nor p̄cedēte īmo q̈libet ꝓportiõe data in īfinitū mi­<lb/>nor eſt aliq̈ ſequēs: g̊ vni ſignate nõ ꝑdit īfinitas eq̈­<lb/>les nõ cõicãtes etc̈. </s>
              <s xml:id="N24734" xml:space="preserve">Sꝫ tã ꝓbat̄̄ maior videlicet  ta-<lb/>le corpꝰ diminuet̄̄ ad nõ ̄tū. </s>
              <s xml:id="N24739" xml:space="preserve">Probat̄̄ añs: <lb/>q2 in illo caſu nõ p̄t ſignari tãta ꝓportio qñ maio-<lb/>rē ꝑdiderit: igit̄̄ infinitã ꝓportionē ꝑdidit. </s>
              <s xml:id="N24740" xml:space="preserve">Probat̄̄ <lb/>añs / q2 det̄̄ illa et ſit decupla gr̄a argumenti. </s>
              <s xml:id="N24745" xml:space="preserve">Et ar-<lb/>guit̄̄ ſic: nõ ꝑdit niſi decuplã: g̊ ſequit̄̄ /  nõ ꝑdit niſi <lb/>vſ ad ſexquidecimã nonã ꝓportiõeꝫ qḋ eſt ↄ̈ caſuꝫ <lb/>q2 in cãu ponit̄̄  ſucceſſiue ꝑdat oēs ſpēs ꝓportio­<lb/>nis ſuꝑparticularis </s>
              <s xml:id="N24750" xml:space="preserve">Seq̄la ꝓbat̄̄: qm̄ ꝓportio decu­<lb/>pla ↄ̨ponit̄̄ ex decē et octo primis ſpēbꝰ ꝓportionis <lb/>ſuꝑparticularꝪ / vt pꝫ inter .ro. et duo: illa eī ꝓportio <lb/>cõponit̄̄ ex proportõe ſexq̇altera triū ad duo: ſexq̇-<lb/>tertia quatuor ad tria ſexq̇quarta q̇n ad q̈tuor: et <lb/>ſic ↄ̨ñter vſ ad proportionē ſexq̇decimã nonã que <lb/>eſt viginti ad decē et nouē. </s>
              <s xml:id="N2475F" xml:space="preserve">Et ſic vĺr probabis data <lb/>quacū ꝓportiõe qm̄ illã ſꝑ inuenies ↄ̨poſitã ex ſu­<lb/>perparticularibꝰ ſereatim ſe hñtibꝰ.               <anchor type="note" xlink:href="note-0207-03" xlink:label="note-0207-03a"/>               </s>
              <s xml:id="N2476B" xml:space="preserve">¶ Et ↄ̨firmat̄̄ <lb/>hec ꝓbatio qm̄ latitudo oīm ſpērū ꝓportiõis ſuꝑ-<lb/>particularis ↄ̨ponit infinitã ꝓportionē: igit̄̄ ſi ali-<lb/>quid deꝑdit illã latitudinē deꝑdit infinitã ꝓportio­<lb/>nē. </s>
              <s xml:id="N24776" xml:space="preserve">Probat̄̄ añs / qm̄ ſi bipedale acq̇rat oēs ꝓpor-<lb/>tiones ſuperparticulares ſereatim: ita  in qua-<lb/>libet ꝑte ꝓportionali hore acq̇rat vnaꝫ in fine illud <lb/>rit infinite magnū: et ſic infinitã ꝓportiõeꝫ acq̇ret: <lb/>igit̄̄ ille ſpēs ꝓportiõis ſuꝑparticularis ſeriatim <lb/>ſumpte ↄ̨ſtituūt infinitã ꝓportiõeꝫ. </s>
              <s xml:id="N24783" xml:space="preserve">Probatur añs / <lb/>qm̄ ſi illud bipedale in prima parte ꝓportionali au-               <pb chead="De motu augmentationis." file="0208" n="208"/>               geat̄̄ ad ſexquialterã: ipſum efficiet̄̄ tripedale, et ſic <lb/>acq̇reret vnū pedale: et cū in ſcḋa parte ꝓportiõali <lb/>acq̇rit ꝓportionē ſexq̇tertiã, ipſum efficiet̄̄ quadru­<lb/>pedale, et ſic adhuc acq̇rit vnū pedale, et in tertia <lb/>acq̇rit ꝓportionē ſexquiquartã, et ſic efficiet̄̄ quītu-<lb/>pedale, in quarta acquirit ſexquiquintã, et ſic effi­<lb/>cietur ſextupedale, et ſic conſequēter. </s>
              <s xml:id="N24799" xml:space="preserve">igr̄ in q̈libet <lb/>parte proportionali acquirit vnū pedale et ſic effi-<lb/>citur infinitū / qḋ fuit ꝓbandum. </s>
              <s xml:id="N247A0" xml:space="preserve">Idē aſſumptū ptꝫ <lb/></s>
              <s xml:id="N247A4" xml:space="preserve">ex ſexto correla° q̈rte ↄ̨cĺonis q̈rti capitꝪ ſcḋe ꝑtꝪ</s>
            </p>
            <div xml:id="N247A7" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0207-03a" xlink:label="note-0207-03" xml:id="N247AB" xml:space="preserve">Confir°.</note>
            </div>
            <p xml:id="N247B1">
              <s xml:id="N247B2" xml:space="preserve">Quīto principaliṫ ad idē argr̄ ſic. </s>
              <s xml:id="N247B5" xml:space="preserve">Si <lb/>illa poſitio eſſet vera ſeq̄ret̄̄:  ſi aliqḋ corpꝰ in pri­<lb/>ma parte ꝓportiõali ꝓportiõe dupla vniꝰ hore ali­<lb/>quãtuluū velociter augeret̄̄, et in ſcḋa in duplo velo-<lb/>cius, et in tertia in triplo velocius ꝙ̄ in prima, et in <lb/>q̈rta in q̈druplo velocius ꝙ̄ in prima aſcendendo ꝑ <lb/>oēs ſpecies ꝓportiõis multiplicis: illud corpus in <lb/>fine eſſet īfinite magnū: ſed ↄ̨ñs eſt falſum: igr̄ illud <lb/>ex quo ſequit̄̄. </s>
              <s xml:id="N247C8" xml:space="preserve">Seq̄la ꝓbat̄̄: q2 nõ videt̄̄ cuiꝰ magni­<lb/>tudinis illud corpꝰ in fine ſit niſi īfinite: igr̄. </s>
              <s xml:id="N247CD" xml:space="preserve">Itē ac­<lb/>quirit īfinitas ꝓportiões tale corpꝰ eq̈les nõ ↄ̨mu-<lb/>nicãtes, qm̄ in prima parte ꝓportiõali acq̇rit ali-<lb/>quã, et in ſcḋa cū augmētet̄̄ in duplo velociꝰ acq̇rit <lb/>duplã<gap/> et in alia q2 augmētat̄̄ in triplo velociꝰ acq̇-<lb/>rit triplã: igr̄ īfinitas acq̇rit eq̈les etc̈. </s>
              <s xml:id="N247DC" xml:space="preserve">Sed iã ꝓbat̄̄ <lb/>falſitas ↄ̨ñtis: et volo /  vnū pedale in prima parte <lb/>ꝓportiõali tꝑis acq̇rat ꝓportionē duplã, et in ſcḋa <lb/>parte augmētet̄̄ in duplo velociꝰ, et in tertia in tri-<lb/>plo, et ſic ↄ̨ñter. </s>
              <s xml:id="N247E7" xml:space="preserve">Tunc manifeſtū eſt /  in ſcḋa parte <lb/>ꝓportiõali tantã acq̇rit ſicut in prima puta duplã <lb/>q2 auget̄̄ in duplo velociꝰ et tēpꝰ eſt ſubduplū, et in <lb/>tertia acq̇rit tres quartas vniꝰ duple, q2 auget̄̄ in <lb/>triplo velociꝰ et in q̈rta acq̇rit q̈tuor octauas vnius <lb/>duple q2 auget̄̄ in q̈druplo velociꝰ ꝙ̄ in prima: ſi eī <lb/>eq̄uelociter augmētaret̄̄ ſicut in prima cū q̈rta ꝑs <lb/>ſit in octuplo minor prima ſequit̄̄ /  in illa acq̇re-<lb/>ret vnã octauã duple: ſed mõ auget̄̄ in q̈druplo ve-<lb/>lociꝰ in eadē q̈rta parte: ergo q̈tuor octauas acq̇rit <lb/>et ſic ꝓbabis /  in quīta acq̇rit quī ſexdecīas vniꝰ <lb/>duple, et in ſexta ſex triceſimas ſecundas.</s>
            </p>
            <p xml:id="N24800">
              <s xml:id="N24801" xml:space="preserve">Quibꝰ īſpectis argr̄ ſic. </s>
              <s xml:id="N24804" xml:space="preserve">Tale corpus <lb/>acq̇rit īfinitos ordines ꝓportionū qui q̇dē ordines <lb/>ↄ̨tinuo ſe habēt in ꝓportione dupla: et primꝰ illoꝝ <lb/>ordinū eſt vna ꝓportio q̈drupla: g̊ oēs illi ordines <lb/>ↄ̨ſtiuūt duas q̈druplas: et ꝑ ↄ̨ñs vnã ſexdecuplã: et <lb/>ſic illud corpꝰ nõ acq̇rit niſi ꝓportionē ſexdecuplã <lb/>in tali caſu: et nõ īfinitã. </s>
              <s xml:id="N24813" xml:space="preserve">Probat̄̄ tñ ↄ̨ña facta. </s>
              <s xml:id="N24816" xml:space="preserve">Qm̄ <lb/>ſi illi ordines ꝓportionū ↄ̨tinuo ſe hñt in ꝓportiõe <lb/>dupla. </s>
              <s xml:id="N2481D" xml:space="preserve">manifeſtū eſt  aggregatū ex oībꝰ ſequēti-<lb/>bus primū eſt eq̈le primo: vt ptꝫ ex quīto capite pri­<lb/>me partis. </s>
              <s xml:id="N24824" xml:space="preserve">Sed cū primꝰ ordo ſit ꝓportio q̈drupla <lb/>manifeſtū eſt  oēs alii ſimĺ ſumpti ſūt etiã q̈dru-<lb/>pla: et ſic aggregatū ex oībꝰ ſimĺ eſt vna ſexdecupla / <lb/>vt ptꝫ ex ſexto capite ſcḋe partis. </s>
              <s xml:id="N2482D" xml:space="preserve">Sed iã reſtat ꝓba­<lb/>re  ibi ſunt īfiniti ordines cõtinuo ſe habētes in <lb/>ꝓportiõe dupla. </s>
              <s xml:id="N24834" xml:space="preserve">Q2 ſic ꝓbat̄̄ / q2 capiēdo ꝓportio-<lb/>nē duplã quã acq̇rit in prima parte ꝓportionali, et <lb/>medietatem illiꝰ duple ꝙ̄ acq̇rit in ſcḋa ꝑte: et vnã <lb/>quartã duple ex illis q̈rtis q̈s acquirit in tertia, et <lb/>vnã octauã duple ex illis quas acq̇rit in q̈rta, et vnã <lb/>decimãſextã duple ex illis q̈s acq̇rit in quīta parte <lb/>ꝓportionali, et ſic ↄ̨ñter: tunc manifeſtū eſt  ibi eſt <lb/>vnꝰ ordo ꝓportionū ↄ̨tinuo ſe habentiū in ꝓporti-<lb/>one ſubdupla et primū illiꝰ ordinis eſt vna ꝓportio <lb/>dupla: igr̄ totꝰ ille ordo ↄ̨ſtituit q̈druplã. </s>
              <s xml:id="N24849" xml:space="preserve">Cõſequē­<lb/>tia ptꝫ vt ſupra. </s>
              <s xml:id="N2484E" xml:space="preserve">Itē ab ↄ̨ſtituendū ſcḋm ordinē ca-<lb/>piat̄̄ alia medietas duple q̄ remanſit ex illa dupla <lb/>quã acq̇rebat corpꝰ in ſcḋa ꝑte ꝓportiõali<gap/> et deīde <lb/>capiat̄̄ vna q̈rta duple ex illis duabꝰ remanētibꝰ et               <cb chead="De motu augmentationis."/>               acq̇ſitis in tertia parte ꝓportiõali: et deīde capias <lb/>vna octaua ex octauis remanētibꝰ et acq̇ſitis ī q̈rta / <lb/>et ſic ↄ̨ñter: et manifeſtū eſt  ibi eſt alter ordo pro-<lb/>portionū ↄ̨tinuo ſe habentiū in ꝓportione dupla: <lb/>et primū illoꝝ eſt vna medietas duple: g̊ reſiduū a <lb/>prima eſt alia duple medietas: et ſic totus ſcḋus or­<lb/>do eſt vna dupla. </s>
              <s xml:id="N24868" xml:space="preserve">Itē ad īuiendū tertiū ordinem <lb/>incipias ab acq̇ſitis in tertia ꝑte ꝓportiõali et īue-<lb/>nies vnã quartã p̄ciſe duple: q2 alie dū ſunt poſite <lb/>in aliis duobꝰ ordinibꝰ: et capias illã ꝑ ṗma tertii <lb/>ordinis: deinde capias vnã ex duabꝰ octauis acq̇ſi­<lb/>tis et remanētibꝰ in q̈rta parte ꝓportiõali: et deīde <lb/>ꝑ tertia parte illiꝰ ordinis capias vnã ex tribꝰ de-<lb/>cimiſſextis derilictis et acq̇ſitis in quīta parte pro­<lb/>portiõali: et ſic ↄ̨ñter. </s>
              <s xml:id="N2487B" xml:space="preserve">Et ſic ad īuiendū quartum <lb/>ordinē incipias ab vna octaua derelicta et acq̇ſita <lb/>in quarta parte ꝓportionali. </s>
              <s xml:id="N24882" xml:space="preserve">Et ad īuiendū quī­<lb/>tum incipies ab vna ſexdecima derclicta et acq̇ſita <lb/>in quīta parte ꝓportionali: et ſic ↄ̨ñter īuenies infi­<lb/>nitos ordines et iſti ordines ↄ̨tinuo ſe habēt in pro­<lb/>portione dupla: ita  q̄libet ſequēs ordo eſt ſubdu­<lb/>plus ad īmediate p̄cedentē ordinē: igr̄ ibi ſunt īfini­<lb/>ti ordines ↄ̨tinuo ſe habētes in ꝓportione dupla: <lb/>qḋ fuit ꝓbandū. </s>
              <s xml:id="N24893" xml:space="preserve">Q, autē illi ordines ↄ̨tinuo ſe ha­<lb/>bent in ꝓportione dupla. </s>
              <s xml:id="N24898" xml:space="preserve">Ptꝫ / q2 quilibet illoꝝ or-<lb/>dinū cõponit̄̄ ex infinitis ↄ̨tinuo ſe habentibus in <lb/>ꝓportione dupla: et oīa prima oīm illoꝝ ordinum <lb/>ↄ̨tinuo ſe habent in ꝓportione dupla / vt cõſtat: igr̄ <lb/>oēs illi ordines cõtinuo ſe habent in ꝓportiõe du-<lb/>pla. </s>
              <s xml:id="N248A5" xml:space="preserve">Ptꝫ ↄ̨ña: q2 cuiuſlibet ordinis primuꝫ eſt me-<lb/>dietas illius ordinis et reſiduum alia medietas <lb/>quia in quacū proportione ſe habēt medietates <lb/>aliquoꝝ in eadē proportione ſe habent et ipſa tota <lb/>quoꝝ ſunt medietates / vt ptꝫ ex vndecima ſuppoſi-<lb/>tione ſecūdi capitis ſecūde partis: ergo oēs illi or­<lb/>dines cõtinuo ſe habent in ꝓportione dupla / quod <lb/>fuit ꝓbandū.               <anchor type="note" xlink:href="note-0208-01" xlink:label="note-0208-01a"/>               </s>
              <s xml:id="N248BB" xml:space="preserve">¶ Et confirmat̄̄ / q2 ſi illa poſitio eſſet <lb/>vera ſequeret̄̄ /  ſi aliquod corpus in prima parte <lb/>ꝓportionali alicuiꝰ hore augmētaret̄̄ aliquãtulū <lb/>velociter, et in ſecūda in duplo velocius et in tertia <lb/>in duplo velocius ꝙ̄ in ſecūda, et ſic ↄ̨ñter: tale cor-<lb/>pus in fine hore eſſet infinitū, et ſic illud corpꝰ in-<lb/>finite velociter augmētaretur. </s>
              <s xml:id="N248CA" xml:space="preserve">ſꝫ ↄ̨ſequens eſt falſū / <lb/>igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N248CF" xml:space="preserve">Sequela ꝓbatur / q2 ſi hora <lb/>ſit diuiſa per partes ꝓportionales ꝓportione du­<lb/>pla, et aliquod corpꝰ in ṗma aliquãtulū velociter <lb/>augmentet̄̄ aliquã ꝓportionē acquirendo, et in ſe-<lb/>cunda in duplo velociꝰ: et in tertia in duplo velociꝰ <lb/>̄ in ſecūda: et ſic ↄ̨ñter. </s>
              <s xml:id="N248DC" xml:space="preserve">Tūc tale corpus in fine ac-<lb/>quiſiuit tnfinitã proportionē et nõ eſt maior ratio <lb/>quãdo diuidit̄̄ hora tali diuiſione quã aliqua alia <lb/>diuiſione: igr̄ ſi hora diuidat̄̄ aliqua diuiſiõe: et in <lb/>prima aliquod corpus aliqua velocitate augmen-<lb/>tetur: et in ſecūda in duplo velociꝰ: et in tertia in du­<lb/>pio velociꝰ ꝙ̄ in ſecūda: et ſic ↄ̨ñter tale corpꝰ īfinitã <lb/>ꝓportionē acq̇ret: et augmētabit̄̄ īfinite velociṫ in <lb/>tali hora / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N248EF" xml:space="preserve">Probr̄ tñ añs vcꝫ / qḋ ſi ho­<lb/>ra diuidat̄̄ ꝓportiõe dupla etc̈. / qḋ illud corpꝰ acq̇rit <lb/>īfinitã ꝓportionē: q2 in q̈lꝫ ꝑte ꝓportiõali acquirit <lb/>tãtã ꝓportionē ſicut in ṗma. </s>
              <s xml:id="N248F8" xml:space="preserve">Nã in q̈cū ꝓportiõe <lb/>aliq̈ ꝑs eſt mīor in eadē ꝓportiõe velociꝰ augmētat̄̄ <lb/>et ſūt īfinite: g̊ īfinitas eq̈les ꝓportiões acq̇rit / et per <lb/>ↄ̨ñs īfinitã ꝓportionē acq̇rit. </s>
              <s xml:id="N24901" xml:space="preserve">Iã ꝓbo falſitatē ↄ̨ñtꝪ <lb/>et volo /  hõ diuidit̄̄ ꝑ ꝑtes ꝓportiõales ꝓportiõe q̈­<lb/>drupla, et in ṗma ꝑte augmētet̄̄ aliqḋ corpꝰ certe ve­<lb/>lociṫ puta acq̇rēdo ꝓportionē duplã: et in ſcḋa ī du­<lb/>plo velociꝰ et .3. ī duplo velociꝰ ꝙ̄ ī.2. / et ſic ↄ̨ñṫ. </s>
              <s xml:id="N2490C" xml:space="preserve">in po­<lb/>ſitū eſt, q̊ poſito ar̄ ſic. </s>
              <s xml:id="N24911" xml:space="preserve">illud corpꝰ auget̄̄ vt ponit̄̄ et <lb/>tñ nõ acquirit niſi ꝓportionē quadruplã tota illa ho­<lb/>ra: igr̄ illud conſequens eſt vna conditiõalis falſa <lb/></s>
              <s xml:id="N24919" xml:space="preserve"><pb chead="Tertii tractatus" file="0209" n="209"/>               Probat̄̄ antecedens / qm̄ ille proportiones acqui-<lb/>ſite ↄ̨tinuo ſe habent in ꝓportione dupla et prima <lb/>illaꝝ eſt dupla: ergo totū eſt vna ꝓportio q̈drupla / <lb/>vt ſepius argutū eſt. </s>
              <s xml:id="N24926" xml:space="preserve">Q, autē continuo ſe habēt in <lb/>ꝓportiõe dupla. </s>
              <s xml:id="N2492B" xml:space="preserve">Ptꝫ / q2 in prima parte ꝓportiõa-<lb/>bili acq̇rit illud corpꝰ ꝓportionē dupla: et in ſcḋa <lb/>medietatē duple: qm̄ ſi eque velociter augmētaret̄̄ <lb/>in ſcḋa ſicut in prima acq̇reret vnã quartã duple: <lb/>ſed mõ in duplo velociꝰ auget̄̄ ꝙ̄ tūc: g̊ acq̇rit vnam <lb/>medietatē duple: et ſic ꝓbabis /  in tertia parte ac­<lb/>quirit vnã quartã: et ſic ↄ̨ñter: igr̄ ↄ̨tinuo acq̇rit ꝓ-<lb/>portiões ſe habētes in ꝓportiõe ſubdupla, et ſub-<lb/>dupla / qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0209-01" xlink:label="note-0209-01a"/>               </s>
              <s xml:id="N24943" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo / q2 ſi poſi-<lb/>tio eſſet uera: ſeq̄ret̄̄ /  aliqḋ corpꝰ augmētaret̄̄, et <lb/>in nulla ꝓportiõe fierit maiꝰ: ↄ̨ñs eſt falſñ: igr̄ et il-<lb/>lud ex quo ſequit̄̄. </s>
              <s xml:id="N2494C" xml:space="preserve">Seq̄la ꝓbat̄̄: et volo /  vnū peda-<lb/>le in prima parte ꝓportiõali hore ꝓportiõe dupla <lb/>diuiſe aliq̈liter augmētet̄̄: et in ſcḋa in ſuꝑbipartiē­<lb/>te tertias velociꝰ, et in tertia in ſuꝑtripartiēte quī-<lb/>tas, et ī quarta in ſupraq̈dripartiēte ſeptīas, ī .5. et <lb/>ſupraquītipartiēte vndecimas, et ſic ↄ̨ñter ꝓcedēdo <lb/>ꝑ nūeros īpares primos et incõpoſitos. </s>
              <s xml:id="N2495B" xml:space="preserve">Quo poſi­<lb/>to ſic argr̄: tale corpꝰ augmētat̄̄ vt notū eſt: et tñ in <lb/>nulla ꝓportiõe ſit maiꝰ: igr̄. </s>
              <s xml:id="N24962" xml:space="preserve">Probat̄̄ mīor: q2 nec <lb/>in multiplici, nec ī ſuꝑparticulari, nec in ſuprapar­<lb/>tiente, nec in multiplici ſupraparticulari, nec ī mul­<lb/>tiplici ſuprabprrtiēte, et ſi hoc negas des illã. </s>
              <s xml:id="N2496B" xml:space="preserve">Itē <lb/>poſito /  in prima parte ꝓportiõali vnū pedale ac­<lb/>quirit ꝓportionē ſaꝑbipartientē tertias, et in ſcḋa <lb/>acq̇rat ꝓportionē ſuꝑbipartientē quītas, et in ter-<lb/>tia ſuꝑbipartientē ſeptīas, et in q̈rta ſuprabipar-<lb/>tiēte nonas, et ſic ↄ̨ñter ꝓcedendo ꝑ ſpecies ꝓporti-<lb/>onis ſuꝑbipartiētes: tale corpꝰ augmentabit̄̄: et in <lb/>nulla uroportione fiet maius quam erat antea igr̄</s>
            </p>
            <div xml:id="N2497C" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0208-01a" xlink:label="note-0208-01" xml:id="N24980" xml:space="preserve">Cõfir­<lb/>matio.</note>
              <note position="left" xlink:href="note-0209-01a" xlink:label="note-0209-01" xml:id="N24988" xml:space="preserve">Cõfirma­<lb/>tio .2.</note>
            </div>
            <p xml:id="N24990">
              <s xml:id="N24991" xml:space="preserve">Sexto principaliṫ ad idē argr̄ ſic. </s>
              <s xml:id="N24994" xml:space="preserve">Si <lb/>illa poſitio eſſet a ſeq̄ret̄̄ /  ſi duo corpora equa-<lb/>lia augmētarent̄̄ talr̄ /  medietas vniꝰ augmētaret̄̄ <lb/>ad duplū, et quarta alteriꝰ ad quadruplū: illa cor­<lb/>pora eq̄ velociter augmētarent̄̄: ſed ↄ̨ñs eſt falſum / <lb/>igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N249A1" xml:space="preserve">Seq̄la ptꝫ. </s>
              <s xml:id="N249A4" xml:space="preserve">qm̄ ſi eq̈lis aug-<lb/>mentatio aut acq̇ſitio ꝓportiõis in parte alicuiꝰ to­<lb/>tius aliq̇d facit ad denoīationē augmētatiõis to-<lb/>tius, ſequit̄̄ qḋ dupla ꝓportio acq̇ſita parti in du­<lb/>plo mīori tm̄ facit ſicut ſubdupla ꝓportio acq̇ſita <lb/>parti in duplo maiori: igr̄ in ꝓpoſito illa acq̇ſitio <lb/>ꝓportiõis in medietate tm̄ adequate facit ad aug-<lb/>mentū totiꝰ ſicut acq̇ſitio ꝓportiõis in duplo maio­<lb/>ris in vna quarta. </s>
              <s xml:id="N249B7" xml:space="preserve">Ptꝫ añs a ſimili de denoīatiõe <lb/>q̈litatis et denſitatis. </s>
              <s xml:id="N249BC" xml:space="preserve">Iam ꝓbo falſitatē ↄ̨ñtis qm̄ <lb/>in tali caſu corpꝰ cuiꝰ vna medietas auget̄̄ ad du-<lb/>plum ſui acq̇rit ꝓportionē ſexq̇alterã, et aliud acq̇-<lb/>rit ꝓportionē ſuꝑtripartientē quartas q̄ maior eſt / <lb/>igr̄ nõ eque velociter augmentat̄̄, et ꝑ ↄ̨ñs illatum <lb/>falſū. </s>
              <s xml:id="N249C9" xml:space="preserve">Probat̄̄ maior / q2 ſi medietas acq̇ſiuit ꝓpor­<lb/>tionē duplã ſequit̄̄  tale corpꝰ acq̇ſiut tm̄ quantū <lb/>eſt medietas eiꝰ, et ꝑ ↄ̨ñs ſexq̇alterã ꝓportionē. </s>
              <s xml:id="N249D0" xml:space="preserve">Mi­<lb/>nor ꝓbat̄̄: q2 ſi vna quarta alteriꝰ corporis facta <lb/>eſt in q̈druplo maior, ſequit̄̄ qḋ acq̇ſiuit ter tm̄ ſi-<lb/>cut ipſa eſt, et ſic acq̇ſiuit tres quartas totiꝰ, et per <lb/>ↄ̨ñs in fine illud totū componitur ex ſeptem parti-<lb/>bus quaꝝ q̄libet eſt equalis vni quarte totiꝰ corpo­<lb/>ris in principio augmētatiõis, et ſic illud corpꝰ erit <lb/>in ſupratripartiēte quartas maiꝰ quã erat antea / <lb/>qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0209-02" xlink:label="note-0209-02a"/>               </s>
              <s xml:id="N249E8" xml:space="preserve">¶ Cõfirmat̄̄ / q2 ſi iſta poſitio eſſet <lb/>vera, ſeq̄ret̄̄ /  uõ eſſet poſſibile aliq̇d īcipere auge-<lb/>ri a nõ quanto vniformiṫ, aut īfinite tarde ſed ↄ̨ñs <lb/>eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N249F1" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 qḋlibet <lb/>qḋ a nõ quãto īcipit augeri īfinite velociter incipit <lb/>augeri: igr̄ nullū tale / qḋ a nõ quãto incipit augeri               <cb chead="Capitulū ſecundum."/>               incipit vniformiter aut infinitū tarde augeri. </s>
              <s xml:id="N249FB" xml:space="preserve">Con­<lb/>ſequētia ſatis apparet, et añs ꝓbat̄̄ vcꝫ /  quodli-<lb/>bet tale incipit infinite velociter augeri: qm̄ quod-<lb/>libet tale incipit infinitã magnã ꝓportionē acqui-<lb/>rere: igr̄. </s>
              <s xml:id="N24A06" xml:space="preserve">Probat̄̄ tñ falſitas ↄ̨ñtis: q2 aliq̇d incipit <lb/>a nõ quanto augeri īfinite tarde: et illud idē incipit <lb/>a nõ quãto īfinite velociter augeri, et illud idē etiã <lb/>a nõ quanto incipit vniformiter augeri. </s>
              <s xml:id="N24A0F" xml:space="preserve">igr̄ poſſi-<lb/>bile eſt aliq̇d incipere a nõ quãto vniformiter, et in-<lb/>finitū tarde augeri: et ꝑ ↄ̨ñs illud ↄ̨ñs eſt flm̄. </s>
              <s xml:id="N24A16" xml:space="preserve">Pro-<lb/>bat̄̄ añs, et volo /  diuidat̄̄ hora futura in partes <lb/>ꝓportionales ꝓportione dupla, et capio tres ordi­<lb/>nes partiū ꝓportionaliū qui ordines continuo ſe <lb/>habēt in ꝓportione octupla puta pro primo ordīe <lb/>primã partē et quartã: et ſeptimã et decimã / et ſic cõ-<lb/>ſequēter omittendo duas, et ꝓ ſecūdo ordine capio <lb/>ſcḋam, et quintã, et octauã, et vndecimã, et ſic ↄ̨ñter: <lb/>ſimiliter omittēdo duas. </s>
              <s xml:id="N24A29" xml:space="preserve">Et ꝓ tertio ordine capio <lb/>tertiã, ſextã, nonã, duodecimã, et ſic cõſeqnēter etiã <lb/>omittendo duas: et volo /  in qualibet parte ꝓpor­<lb/>tionali primi ordinis vnū pedale perdat ꝓportio-<lb/>nē duplã: et in prima parte ſcḋi ordinis perdat etiã <lb/>duplã: et in ſcḋa eiuſdē ordinis ꝓportiouē in octu-<lb/>plo minorē quã in ſcḋa: et ſic ↄ̨ñter. </s>
              <s xml:id="N24A38" xml:space="preserve">ita  in ſcḋo or­<lb/>dine in ea ꝓportione qua partes ſunt minores in <lb/>ea ↄ̨tinuo ꝓportionē minorē deṗerdat. </s>
              <s xml:id="N24A3F" xml:space="preserve">In prima <lb/>vero parte tertii ordinis idē pedale deꝑdat ꝓpor-<lb/>tionē duplã, et in ſcḋa eiuſdē tertii ordinis in ſexde­<lb/>cuplo minorē, et in tertia eiuſdē ordinis in ſexdecu-<lb/>plo minorē quã in ſcḋa / et ſic ↄ̨ñter. </s>
              <s xml:id="N24A4A" xml:space="preserve">Quo poſito ma­<lb/>nifeſtū eſt /  hoc corpꝰ diminuet̄̄ ad nõ quantñ vſ <lb/>et in īfinitū velociter diminuet̄̄ ad nõ quantū in par­<lb/>tibꝰ ꝓportionabilibꝰ primi ordinis, et in partibus <lb/>ꝓportiõalibꝰ ſcḋi ordīs ↄ̨tinuo vniformiter dimi-<lb/>nuet̄̄ / vt ptꝫ ex caſu et in partibꝰ ꝓportiõalibꝰ tertii <lb/>ordinis in īfinitū tarde diminuit̄̄ ad nõ quantum. <lb/></s>
              <s xml:id="N24A5A" xml:space="preserve">Uolo igr̄ /  cū corpꝰ fuerit ad nõ quantū redactū. <lb/></s>
              <s xml:id="N24A5E" xml:space="preserve">Iteꝝ īcipiat in hora ſeq̄nti augeri a nõ quãto oīno <lb/>eodē mõ ſicut diminuebat̄̄. </s>
              <s xml:id="N24A63" xml:space="preserve">Et argr̄ ſic. </s>
              <s xml:id="N24A66" xml:space="preserve">illud corpꝰ <lb/>īcipit in īfinitū velociter augeri puta in partibꝰ pri­<lb/>mi ordinis, et incipit etiã vniformiter puta in par-<lb/>bꝰ ſcḋi ordīs: et ↄ̨ſimiliter īcipit in īfinitū tarde au-<lb/>geri / vt īdicat diminutio fucta in partibꝰ tertii or-<lb/>dinis: igr̄ aliq̇d īcipit a nõ quãto in īfinitū tarde, et <lb/>īfinitū velociter, et vniformiṫ augeri / qḋ fuit ꝓbãdū</s>
            </p>
            <div xml:id="N24A75" level="5" n="9" type="float">
              <note position="left" xlink:href="note-0209-02a" xlink:label="note-0209-02" xml:id="N24A79" xml:space="preserve">ↄ̨firma°.</note>
            </div>
            <p xml:id="N24A7F">
              <s xml:id="N24A80" xml:space="preserve">Septimo prīcipaliṫ  ↄ̨̨tra aliã partē <lb/>q̄ſtiõis argr̄ ſic. </s>
              <s xml:id="N24A85" xml:space="preserve">Quia ſi velocitas augmētationis <lb/>deberet attēdi penes abſolutã acq̇ſitionē quãtita-<lb/>tia ſeq̄ret̄̄ /  aliq̇d augmētaret̄̄ / qḋ tñ nõ fierit maiꝰ <lb/>ↄ̨ñs eſt falſū: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N24A8E" xml:space="preserve">Seq̄la ꝓbat̄̄: <lb/>et capio vnū bipedale, et volo /  vna medietas eius <lb/>vniformiter acq̇rat vnū ſemipedale, et tm̄ cõtinuo <lb/>deꝑdat alia medietas ſicut altera acq̇rit, q̊ poſito <lb/>argr̄ ſic. </s>
              <s xml:id="N24A99" xml:space="preserve">Illud bipedale nõ ſit maiꝰ vt conſtat: et tñ <lb/>augmentat̄̄: igr̄ ꝓpoſitū. </s>
              <s xml:id="N24A9E" xml:space="preserve">argr̄ minor. </s>
              <s xml:id="N24AA1" xml:space="preserve">Q2 acq̇rit a-<lb/>liquã ̄titatē cū vna medietas eiꝰ acq̇rat ſemipeda­<lb/>lē quãtitatē: igr̄ augmētat̄̄. </s>
              <s xml:id="N24AA8" xml:space="preserve">Ptꝫ ↄ̨ña ꝑ poſitione q̄ <lb/>ponit /  augmētatio d3 attēdi penes abſolutã acq̇­<lb/>ſitionē quãtitatis.               <anchor type="note" xlink:href="note-0209-03" xlink:label="note-0209-03a"/>               </s>
              <s xml:id="N24AB4" xml:space="preserve">¶ Dices et bñ: negãdo ſequelã, et <lb/>ad ꝓbationē admiſſo caſu negãdo /  illud bipeda­<lb/>le augeat̄̄, qm̄ ſemꝑ manet pedale: et cū ꝓbat̄̄ / q2 ac­<lb/>q̇rit aliquã quãtitatē negando illud, ̄uis em̄ vna <lb/>medietas eiꝰ acq̇rit quãtitatē totū nõ. </s>
              <s xml:id="N24ABF" xml:space="preserve">Ad hoc em̄  <lb/>acq̇reret oporteret /  vltra illã quã habet. </s>
              <s xml:id="N24AC4" xml:space="preserve">haberet <lb/>maiorē, hoc eſt  acq̇reret aliquē exceſſum ſuꝑ illã <lb/>qḋ nõ ſit in ꝓpoſito: q2 quãtū vna medietas acq̇rit <lb/>tm̄ alia deꝑdit. </s>
              <s xml:id="N24ACD" xml:space="preserve">¶ Sed ↄ̈ / q2 ſi alia medietas nõ di-<lb/>minueret̄̄: ſequeret̄̄ /  hec medietas que auget̄̄ eque­<lb/>velociter augeretur cum toto: ſed conſequens eſt               <pb chead="De motu augmentationis." file="0210" n="210"/>               falſum: igr̄ ex illud quo ſequit̄̄. </s>
              <s xml:id="N24AD9" xml:space="preserve">Seq̄la ptꝫ / q2 tantã <lb/>quãtitatē ſupra totã p̄habitã acq̇rit medietas: ſic <lb/>totū: igr̄ medietas, et totū eq̄ velociṫ augent̄̄. </s>
              <s xml:id="N24AE0" xml:space="preserve">Ptꝫ <lb/>ↄ̨ña expoſitiõe. </s>
              <s xml:id="N24AE5" xml:space="preserve">Sed ꝓbo falſitatē ↄ̨ñtis. </s>
              <s xml:id="N24AE8" xml:space="preserve">Tū ṗmo <lb/>q2 tūc ſeq̄ret̄̄ /  eq̄ velociṫ augeret̄̄ totū ſicut in īfi-<lb/>nitū modica eiꝰ pars. </s>
              <s xml:id="N24AEF" xml:space="preserve">Sꝫ hoc vr̄ abſurdū: igr̄ illud <lb/>ex q̊ ſequit̄̄. </s>
              <s xml:id="N24AF4" xml:space="preserve">Seq̄la ptꝫ / q2 qñ totū acq̇rit vnū ſemipe­<lb/>dale, medietas eiꝰ acq̇rit tm̄, et octaua et ſexdecima <lb/>termīata ad illã quantitatē acq̇ſitã, et ſic ↄ̨ñter: igr̄. <lb/></s>
              <s xml:id="N24AFC" xml:space="preserve">Tū ſcḋo q2 ſtat /  medietas alicuiꝰ intēdat̄̄ aliq̈liṫ <lb/>velociṫ acq̇rēdo aliquã intēſionē: tñ totū nõ acq̇rit <lb/>tantã. </s>
              <s xml:id="N24B03" xml:space="preserve">ergo eodē mõ ſtat in motu augmētatiõis  <lb/>medietas aliqualiṫ velociṫ augeat̄̄, et totū nõ: et ꝑ <lb/>ↄ̨ñs illatū flm̄. </s>
              <s xml:id="N24B0A" xml:space="preserve">¶ Dices et bene ↄ̨cedēdo illatū in ta­<lb/>li caſu: et ad ꝓbationē falſitatꝪ eiꝰ ↄ̨cedēdo illḋ ↄ̨ñs <lb/>vcꝫ /  ita velociter auget̄̄ totū ſicut īfinite modica <lb/>eiꝰ pars ſignãter ſi hoc fiat ꝑ additionē quãtitatis <lb/>alicui medietati: ſicut ſit qñ aliq̇d addit̄̄ parti aīaĺ: <lb/>et augmētat̄̄ aīal. </s>
              <s xml:id="N24B17" xml:space="preserve">¶ Ad ſcḋam īprobationē cõcedo <lb/><gap/> q2 ſtat  medietas <lb/>alicꝰ ītēdat̄̄ et nõ totū: et ſtat  totū ītēdat̄̄ et vna eiꝰ <lb/>medietas nõ intēdat̄̄. </s>
              <s xml:id="N24B21" xml:space="preserve">Nõ tñ ſtat  pars augmētet̄̄ <lb/>ſine diminutiõe aliq̈ quī totū augmētet̄̄. </s>
              <s xml:id="N24B26" xml:space="preserve">Cõtra tūc <lb/>ſeq̄ret̄̄ /  ſēꝑ eq̄ velociter augmētaret̄̄ aliqua pars <lb/>ſicut totū. </s>
              <s xml:id="N24B2D" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N24B30" xml:space="preserve">Fal­<lb/>ſitas ↄ̨ñtis ꝓbat̄̄. </s>
              <s xml:id="N24B35" xml:space="preserve">Et volo /  vtri medietati vnius <lb/>pedalis addat̄̄ ſemipedale in extremis oppoſitis: <lb/>tūc manifeſtū eſt  totū acq̇rit pedalē quãtitatem <lb/>et nulla ꝑs eiꝰ acq̇rit pedalē quãtitatē: igr̄ nulla ꝑs <lb/>ibi auget̄̄ ita velociṫ ſicut totū: et ꝑ ↄ̨ñs nõ ſēꝑ eque­<lb/>velociṫ etc̈. </s>
              <s xml:id="N24B42" xml:space="preserve">Seq̄la tñ ꝓbat̄̄: q2 ſi nõ ſēꝑ augmētaret̄̄ <lb/>aliq̈ pars ita velociṫ ſicut totū: maxīe eſſet in caſu <lb/>in q̊ ꝓbat̄̄ falſitas ↄ̨ñtis: ſed in illo caſu eque velo-<lb/>citer augetur aliqua pars ſicut totum puta pars <lb/>que cõponitur ex duabꝰ quartis extremis cū parti-<lb/>bus extremalibꝰ q̄ ꝑtes extreme circūferētiales cõ-<lb/>ſtituūt vnū quadratū inṫ qḋ manet aliud vt ptꝫ in <lb/>               <anchor type="figure" xlink:href="fig-0210-01" xlink:label="fig-0210-01a"/>               figura iã ſequenti: igr̄. </s>
              <s xml:id="N24B58" xml:space="preserve">¶ Dices et bñ <lb/>negãdo ſeq̄lã: et ad punctū ꝓbatiõis <lb/>dr̄  etiã in illo caſu eq̄ velociṫ au-<lb/>get̄̄ aliq̈ ꝑs ſicut totū / vt ꝓbat argu-<lb/>mētū: et ſic negat̄̄ /  maxīe eſſet ī illo <lb/>caſu: ſed dico /  eſt in caſu vbi totuꝫ <lb/>ꝑ totū rarefit: tūc em̄ nulla ꝑs ita velociṫ auget̄̄ ſi-<lb/>cut totū / vt ſatꝪ ptꝫ / quī ſi totū aliqḋ qḋ ꝑ totū rare-<lb/>fit rarefiat ad duplū: ipſū totū acq̇rit tantã quãti-<lb/>tatē ſicut ipſū eſt: et nulla ꝑs acq̇rit quãtitatē <lb/>ſicut illud totū eſt. </s>
              <s xml:id="N24B6F" xml:space="preserve">¶ Sed ↄ̈: q2 tūc ſeq̄ret̄̄ /  qñ ali-<lb/>quid augmētaret̄̄ ꝑ rarefactionē q̄ rarefactio eſt ꝑ <lb/>totū ſubiectū quãtitas quã adeq̈te acq̇rit totū eſſet <lb/>mīma quã nõ acq̇rit aliq̄ ꝑs. </s>
              <s xml:id="N24B78" xml:space="preserve">Sed hoc vr̄ flm̄: igr̄ il-<lb/>lud ex quo ſequit̄̄. </s>
              <s xml:id="N24B7D" xml:space="preserve">Seq̄la pꝫ. </s>
              <s xml:id="N24B80" xml:space="preserve">q2 dato /  totū acq̇rat <lb/>pedalē quãtitatē: manifeſtū eſt /  vna medietas eiꝰ <lb/>acq̇ſiuit aliquã partē illiꝰ: et aggregatū ex illa me-<lb/>dietate et ṗma ꝑte ꝓportiõali alteriꝰ medietatꝪ acq̇­<lb/>ſiuit maiorē: et aggregatū ex illa et duabus primis <lb/>ꝑtibꝰ ꝓportiõabilibꝰ alteriꝰ adhuc acq̇ſiuit maiorē / <lb/>et ſic ↄ̨ñter calculando. </s>
              <s xml:id="N24B8F" xml:space="preserve">Ptꝫ /  quãtitas acq̇ſita ipſi <lb/>toti eſt minima quã nõ acquiſiuit aliqua pars.</s>
            </p>
            <div xml:id="N24B94" level="5" n="10" type="float">
              <note position="right" xlink:href="note-0209-03a" xlink:label="note-0209-03" xml:id="N24B98" xml:space="preserve">Dictur</note>
              <figure xlink:href="fig-0210-01a" xlink:label="fig-0210-01" xml:id="N24B9E">
                <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0210-01"/>
              </figure>
            </div>
            <p xml:id="N24BA4">
              <s xml:id="N24BA5" xml:space="preserve">Octauo contra eandē partē q̄ſtionis <lb/>argr̄ ſic. </s>
              <s xml:id="N24BAA" xml:space="preserve">Qm̄ ſi velocitas augmētatiõis attēderet̄̄ <lb/>penes abſolutã acq̇ſitionē quãtitatꝪ: ſeq̄ret̄̄ /  qḋlꝫ <lb/>iſtoꝝ īciperet īfinite velociṫ augeri: et tñ īciperet in-<lb/>finitū tarde augeri aliqḋ iſtoꝝ: ſed ↄ̨ñs videt̄̄ re-<lb/>pugnare: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N24BB5" xml:space="preserve">Seq̄la ptꝫ et volo / <lb/> ſint īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdu­<lb/>pla: ita  primū ſit pedale, ſcḋ3 ſemipedale, tertiū <lb/>q̈rta pedalis / et ſic ↄ̨ñter: et diuidat̄̄ hora ꝑ ꝑtes ꝓ-<lb/>portiõales ꝓportione dupla qḋlibet o illoꝝ diu­               <cb chead="De motu augmentationis."/>               dat̄̄ ꝑ partes ꝓportiõales ꝓportiõe ſexquialtera: et <lb/>qḋlꝫ illoꝝ in q̈libet ꝑte ꝓportiõali hore ꝑdat vnaꝫ <lb/>partē ꝓportionalē ſui ꝓportiõe ſexq̇altera quouſ <lb/>in fine hore deueniat ad nõ quantū: deinde īcipiant <lb/>illa a nõ quãto augeri oīno ſicut diminuebant̄̄ pu-<lb/>ta in q̈libet ꝑte ꝓportiõali hore ꝓportiõe dupla ac­<lb/>quirēdo vna ꝑte ꝓportiõalē ſui ꝓportiõe ſexq̇alte-<lb/>ra q̊ poſito argr̄ ſic: qḋlꝫ illoꝝ īmediate poſt illud <lb/>inſtãs augmētatiõis a nõ quãto in īfinitū velociter <lb/>augmētabit̄̄: et īmediate poſt tale inſtãs in infinitū <lb/>tarde augebit̄̄ aliqḋ illoꝝ: et mõ nullum illoꝝ aug-<lb/>mentat̄̄ igr̄ ꝓpoſitū. </s>
              <s xml:id="N24BD9" xml:space="preserve">Probat̄̄ maior: q2 qḋlꝫ illoꝝ <lb/>īcipit a nõ quãto in qualꝫ ꝑte ꝓportiõali ꝓportiõe <lb/>dupla acq̇rere ꝓportionē ſexq̇alterã: g̊ qḋlꝫ illoꝝ in­<lb/>cipit in īfinitū velociṫ acq̇rere de quãtitate / vt ptꝫ ex <lb/>ſcḋa ↄ̨firmatiõe ſcḋi argumēti huiꝰ q̄ſtiõis et ꝑ ↄ̨ñs <lb/>qḋlꝫ illoꝝ īcipit in īfinitū velociṫ augeri qñ in īfini­<lb/>tū velox augmētatio eſt in īfinitū velox acq̇ſitio quã­<lb/>titatꝪ / vt ptꝫ ex hac poſitionē. </s>
              <s xml:id="N24BEA" xml:space="preserve">Probat̄̄ minor vcꝫ /  <lb/>īmediate poſt hoc in īfinitū tarde acq̇ret aliqḋ iſto­<lb/>rū de quãtitate q2 ↄ̨tinuo in īfinitū minꝰ primo erit <lb/>aliqḋ illoꝝ: ſicut fuit in via diminutiõis: et incipiunt <lb/>oīa illa a nõ quãto in eodē inſtãti augeri: g̊ quocū <lb/>inſtãti dato poſt hoc īter hoc et illud īfinite modicū <lb/>quãtitatē acq̇ſiuit aliqḋ illoꝝ: et ꝑ ↄ̨ñs īfinite tarde <lb/>auget̄̄ aliqḋ illoꝝ. </s>
              <s xml:id="N24BFB" xml:space="preserve">¶ Dices et bñ ↄ̨cedēdo illatū nec <lb/>illud eſt incõueniēs: ſed ſequēs / vt ꝓbat argumentū. <lb/></s>
              <s xml:id="N24C01" xml:space="preserve">Sed ↄ̈ / q2 pari rõne ↄ̨cedendū eſſet / qḋ vnū et idem a <lb/>nõ quãto īciperet in īfinitū velociṫ augmētari: et il-<lb/>lud idē īciperet a nõ quãto in īfinitū tarde augmē-<lb/>tari. </s>
              <s xml:id="N24C0A" xml:space="preserve">ſed ↄ̨ñs eſt flm̄: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N24C0D" xml:space="preserve">Falſi-<lb/>tas ↄ̨ñtis ptꝫ / q2 detur illud et ſit a. / et argr̄ ſic / a. inci­<lb/>pit in īfinitū velociṫ augmētari: g̊ īcipit in infinitū <lb/>velociter acq̇rere de quãtitate: et ꝑ ↄ̨ñs nõ īcipit in <lb/>infinitū velociṫ acq̇rere de quãtitate: et ſic habet̄̄  <lb/>īcipit ī īfinitū velociṫ acq̇rere de quantitate: et nõ <lb/>īcipit ī īfinitū velociṫ acq̇rē de quãtitate / qḋ īplicat <lb/></s>
              <s xml:id="N24C1D" xml:space="preserve">Seq̄la tū ꝓbat̄̄ et volo /  a. īcipiat augeri a nõ quã­<lb/>to in aliqua hora diuiſa ꝑ partes ꝓportiõales ꝓ-<lb/>portiõe dupla ſiĺr  vna medietas eiꝰ in qualꝫ ꝑte <lb/>ꝓportiõali pari acq̇rat ꝓportionē ſexq̇alterã: et al­<lb/>tera medietas in q̈libet īpari acq̇rat octuplã quo <lb/>poſito argr̄ ſic / illud in tali caſu īcipit in īfinitū ve-<lb/>lociter augeri et etiã īcipit in īfinitū tarde augeri et <lb/>hoc a nõ quãto: igr̄ ꝓpoſitū. </s>
              <s xml:id="N24C2E" xml:space="preserve">Argr̄ maior / q2 incipit <lb/>in ꝑtibꝰ ꝓportiõalibꝰ paribꝰ īfinite velociṫ acq̇rere <lb/>de quãtitate / vt ptꝫ ex ſcḋa ↄ̨firmatiõe ſcḋi argumē­<lb/>ti p̄allegati: igr̄ incipit in īfinitū velociter augeri. <lb/></s>
              <s xml:id="N24C38" xml:space="preserve">Probat̄̄ mīor: q2 illud īcipit in īfinitū tarde acq̇re­<lb/>re de quantitate in partibꝰ īparibꝰ / vt ptꝫ ex dedu-<lb/>ctione ṗme ↄ̨firmatiõis ſcḋi argumēti preallegati: <lb/>igr̄ īcipit illud īfinite tarde augeri in ꝑtibꝰ īparibꝰ <lb/>               <anchor type="note" xlink:href="note-0210-01" xlink:label="note-0210-01a"/>               </s>
              <s xml:id="N24C48" xml:space="preserve">¶ Confirmat̄̄. </s>
              <s xml:id="N24C4B" xml:space="preserve">Q2 ſi illn poſito eſſet vera ſeq̇ret̄̄ /  <lb/>nullū quadratū ꝑfectū poſſet vniformiṫ diminui <lb/>ad nõ quãtū qñ trina eiꝰ dimēſio puta lõgitudo la­<lb/>titudo et ꝓfūditas vniformiṫ a nõ quãto diminuūt̄̄ / <lb/>ſed ↄ̨ñs eſt flm̄ / q2 nõ videt̄̄ repugnare tale quadra­<lb/>tū vniformiter ſic diminui ad nõ quantū: igit̄̄ illud <lb/>ex quo ſequit̄̄. </s>
              <s xml:id="N24C5A" xml:space="preserve">Sequela tñ ꝓbatur: quia ſi aliquod <lb/>ſic poteſt diminui detur aliquod quadratū pedalr̄ <lb/>lõgū, pedaliṫ latū, pedaliṫ ꝓfūdū, qḋ ſit a. </s>
              <s xml:id="N24C61" xml:space="preserve">Tūc ar̄ <lb/>ſic / ↄ̨tinuo lõgitudo latitudo et ēt ꝓfūditas huiꝰ q̈-<lb/>drati a. vniformiṫ ī hora diminuit̄̄ vſ ad nõ ̄tū: <lb/>igr̄ in ṗma ꝑte ꝓportiõali hore ꝓportiõe dupla il-<lb/>lud q̈dratū efficit̄̄ in duplo minꝰ logū ī duplo minꝰ <lb/>latū. </s>
              <s xml:id="N24C6E" xml:space="preserve">in duplo minꝰ ꝓfundū: et ſic ꝑ ↄ̨ñs efficit̄̄ ī octu­<lb/>plo minꝰ: et ꝑ ↄ̨ñs in ṗma medietate ꝑdit ſeptē octa­<lb/>uas: et in ſcḋa medietate vnã tm̄: et ꝑ ↄ̨ñs in illa hõ <lb/>cõtinuo diminuit̄̄ vniformiṫ / qḋ fuit probandū</s>
            </p>
            <div xml:id="N24C77" level="5" n="11" type="float">
              <note position="right" xlink:href="note-0210-01a" xlink:label="note-0210-01" xml:id="N24C7B" xml:space="preserve">Confir-<lb/>matio.</note>
            </div>
            <pb chead="Tertii tractatus" file="0211" n="211"/>
            <p xml:id="N24C87">
              <s xml:id="N24C88" xml:space="preserve">Probat̄̄ tñ illa ↄ̨ña: iſtud q̈dratū ꝑfectuꝫ efficit̄̄ in <lb/>duplo minꝰ lõgū, et in duplo minꝰ latū, et in duplo <lb/>minꝰ ꝓfundū. </s>
              <s xml:id="N24C8F" xml:space="preserve">igr̄ efficit̄̄ in octuplo minꝰ: qm̄ coſta <lb/>illiꝰ q̈drati in fine ad coſtã illiꝰ in plīcipio diminu-<lb/>tiõis ſe hꝫ in ꝓportiõe ſubdupla: ita  coſte illiꝰ q̈-<lb/>drati in prīcipio et in fine ſe hñt in ꝓportiõe dupla <lb/>et illa ſunt ꝑfecta q̈drata: igr̄ illa q̈drata ſe hñt in <lb/>ꝓportiõe triplicata ad duplã: et illa ē octupla / vt cõ­<lb/>ſtat ex ſexto capite ſcḋe ꝑtis: igr̄ ꝓpoſitū. </s>
              <s xml:id="N24C9E" xml:space="preserve">Ptꝫ hec <lb/>ↄ̨ña / ꝑ quãdã ↄ̨cluſiõeꝫ ſuperiꝰ ꝓbatã in tractatu de <lb/>motu locali peues effectū capite ſcḋo q̄ ↄ̨cĺo talṫ eſt <lb/></s>
              <s xml:id="N24CA6" xml:space="preserve">Proportio q̊dratoꝝ ꝑfectoꝝ eſt ꝓpor° coſtaꝝ tri-<lb/>plicata. </s>
              <s xml:id="N24CAB" xml:space="preserve">Siĺe argumētū poteris facere de ſuꝑficie <lb/>cuiꝰ latitudo et lõgitudo vnifor̄iṫ diminūt̄̄ ꝑ horã.</s>
            </p>
            <p xml:id="N24CB0">
              <s xml:id="N24CB1" xml:space="preserve">Nono prīcipalr̄ ar̄ ſic: ſi illa poſi° eſſet <lb/>vera ſeq̄ret̄̄: ſi hora diuidat̄̄ ꝑ partes ꝓportiõales <lb/>ꝓportiõe dupla: et in ṗma ꝑte ꝓportiõali īpari pe-<lb/>dale a. aliq̈liṫ velociṫ augeat̄̄: et in ſcḋa īpari in du­<lb/>plo velociꝰ: et in tertia īpari in duplo velociꝰ quã ī <lb/>ſcḋa īpari: et ſic ↄ̨ñter ↄ̨tinuo in q̈lꝫ īpari ſeq̄nte in <lb/>duplo velociꝰ̄ in īpari īmediate p̄cedēte: tūc a. pe­<lb/>dale īfinite velociter augeret̄̄. </s>
              <s xml:id="N24CC2" xml:space="preserve">Cõſequēs eſt flm̄. </s>
              <s xml:id="N24CC5" xml:space="preserve">igr̄ <lb/>illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N24CCA" xml:space="preserve">Seq̄la ptꝫ / q2 ſi illud pedale in q̈lꝫ <lb/>ꝑte ꝓportiõali vniꝰ hore ꝓportiõe dupla ita aug-<lb/>mētaret̄̄  in q̈lꝫ ſeq̄nte in duplo velociꝰ augmēta­<lb/>ret̄̄̄ in īmediate p̄cedēte: ip̄m in q̈lꝫ ꝑte ꝓportiõa­<lb/>li tantã quãtitatē acq̇reret ſicut in ṗma / vt cõſtat: et <lb/>ſic in illa hora in īfinitū velociṫ augmētaret̄̄. </s>
              <s xml:id="N24CD7" xml:space="preserve">igr̄ ſi <lb/>illud idē pedale in q̈lꝫ ꝑte ꝓportiõali ꝓportiõe du­<lb/>pla īpari ſeq̄nte in duplo velociꝰ augeat̄̄̄ in īpari <lb/>īmediate p̄cedēte: ipſum in q̈lꝫ ꝑte tantã quãtitatē <lb/>acquirit quantã in prima. </s>
              <s xml:id="N24CE2" xml:space="preserve">Ptꝫ ↄ̨ña / q2 nõ eſt maior rõ <lb/>de vno ꝙ̄ de alio. </s>
              <s xml:id="N24CE7" xml:space="preserve">Falſitas tñ ↄ̨ñtis argr̄ ſic. </s>
              <s xml:id="N24CEA" xml:space="preserve">qm̄ ille <lb/>ꝑtes īpares ↄ̨tinuo ſe hñt in ꝓportiõe q̈drupla. </s>
              <s xml:id="N24CEF" xml:space="preserve">vt <lb/>ptꝫ: et velocitates augmētationis in illis ꝑtibꝰ ↄ̨ti-<lb/>nuo ſe hñt in ꝓportiõe dupla: g̊ quãtitates acq̇ſite <lb/>ↄ̨tiuuo ſe hñt in ꝓportiõe ſubdupla: et ꝑ ↄ̨ñs aggre­<lb/>gatū ex oībꝰ illis eſt duplū ad primã illaꝝ. </s>
              <s xml:id="N24CFA" xml:space="preserve">oīa iſta <lb/>ſatis patent intelligenti ea que dicta ſunt de velo-<lb/>citate motus localis penes effectum ſuperius.</s>
            </p>
            <p xml:id="N24D01">
              <s xml:id="N24D02" xml:space="preserve">In oppoſitū argr̄ ſic. </s>
              <s xml:id="N24D05" xml:space="preserve">Q2 nõ videt̄̄ alṫ <lb/>modus velocitatꝪ augmētatiõis ab altero illoꝝ co­<lb/>gnoſcende: igitur penes alterum illorum debet ve-<lb/>locitas motus augmentationis attendi.</s>
            </p>
            <p xml:id="N24D0E">
              <s xml:id="N24D0F" xml:space="preserve">Pro ſolutiõe huiꝰ q̄ſtiõis quatuor ſūt <lb/>ordine faciēda. </s>
              <s xml:id="N24D14" xml:space="preserve">Primo em̄ definitiones et declara-<lb/>tiões termīoꝝ ad hãc materiã ſpectãtiū ponētur et <lb/>notant̄̄. </s>
              <s xml:id="N24D1B" xml:space="preserve">Scḋo aliq̈ inducent̄̄ ↄ̨cluſiões. </s>
              <s xml:id="N24D1E" xml:space="preserve">Tertio po-<lb/>nent̄̄ dubitatiões. </s>
              <s xml:id="N24D23" xml:space="preserve">Et poſtremo rõnes ãte oppoſitū <lb/>diſſoluent̄̄. </s>
              <s xml:id="N24D28" xml:space="preserve">Aduertendū igr̄ /  augmētatio ita diffi-<lb/>nit̄̄ a pḣo primo de gñatiõe.               <anchor type="note" xlink:href="note-0211-01" xlink:label="note-0211-01a"/>               </s>
              <s xml:id="N24D32" xml:space="preserve">Augmētatio eſt p̄exi-<lb/>ſtētis magnitudīs additamētū. <lb/>               <anchor type="note" xlink:href="note-0211-02" xlink:label="note-0211-02a"/>               </s>
              <s xml:id="N24D3E" xml:space="preserve">¶ Diminutio vero <lb/>p̄exiſtētꝪ quãtitatꝪ mīoramētū.               <anchor type="note" xlink:href="note-0211-03" xlink:label="note-0211-03a"/>               </s>
              <s xml:id="N24D48" xml:space="preserve">Ex q̊ ↄ̨cludit phūs: <lb/> ex materia ſine magnitudīe nõ p̄t eſſe augmēta° <lb/>               <anchor type="note" xlink:href="note-0211-04" xlink:label="note-0211-04a"/>               </s>
              <s xml:id="N24D54" xml:space="preserve">Textu cõmēti triceſimi ṗmi. </s>
              <s xml:id="N24D57" xml:space="preserve">Hec aūt augmentatio <lb/>duplr̄ fieri p̄t. </s>
              <s xml:id="N24D5C" xml:space="preserve">Uno° ꝓut diſtīguit̄̄ ↄ̈ rarefactionē: et <lb/>ſic fit ꝑ additionē alicuiꝰ rei quãte p̄exñti <lb/>eiuſdē ſpecie<gap/>̀ cū illa ex q̈ re cū p̄exñte fit vnū maiꝰ. <lb/></s>
              <s xml:id="N24D66" xml:space="preserve">Et hec eſt ꝓṗe illa augmētatio de q̈ phūs loquit̄̄ lo­<lb/>cõ p̄allegato. </s>
              <s xml:id="N24D6B" xml:space="preserve">quãuis videat̄̄ ibi ꝓṗe de augmenta-<lb/>tiõe aīati loqui q̄ fit ꝑ intꝰ ſuſceptionē. </s>
              <s xml:id="N24D70" xml:space="preserve">Alio° capit̄̄ <lb/>augmētatio ꝓut eſt idē cū rarefactione. </s>
              <s xml:id="N24D75" xml:space="preserve">Et iſto mõ <lb/>augmētatio p̄t fieri ſine additiõe alicuiꝰ alteriꝰ: ſꝫ <lb/>p̄ciſe ꝑ maiorē extēſionē p̄exiſtētꝪ. </s>
              <s xml:id="N24D7C" xml:space="preserve">Et vtro iſtorū <lb/>modoꝝ loq̇mur in propoſito quãuis de ea ſcḋo mõ <lb/>peculiariṫ dictū ſit in p̄cedēti capite. </s>
              <s xml:id="N24D83" xml:space="preserve">Tu tñ aduer-<lb/>te  ꝓp̄e capiēdo ṫmīos: rarefactio differt ab aug-<lb/>mētatiõe ſaltē diuerſa cõnotant illi duo ṫmini q̇rū               <cb chead="Capitulū ſecundum."/>               termīoꝝ ſignificãtias et ↄ̨notatiões facile ex his q̄ <lb/>circa primū de gñatiõe dicunt̄̄ intelligere poteris. <lb/>               <anchor type="note" xlink:href="note-0211-05" xlink:label="note-0211-05a"/>               </s>
              <s xml:id="N24D96" xml:space="preserve">Utrū aūt augmētatio fiat ſcḋm ꝑtes formales aut <lb/>materiales et q̄ ſint ꝑtes for̄ales aut materiales et <lb/>q̊t ↄ̨ditiões req̇rant̄̄: habes ṗmo de gñatiõe capĺo <lb/>de augmetatiõe               <anchor type="note" xlink:href="note-0211-06" xlink:label="note-0211-06a"/>               </s>
              <s xml:id="N24DA4" xml:space="preserve">Textu cõmēti triceſimi ſcḋi et trice­<lb/>ſimi ſexti videas ibi.               <anchor type="note" xlink:href="note-0211-07" xlink:label="note-0211-07a"/>               </s>
              <s xml:id="N24DAE" xml:space="preserve">Nunc autē ſufficiat ſcire quid <lb/>augmētatio: et q̊tuplex eſt augmētatio: vt ītelligat̄̄ <lb/>penes qḋ velocitas motꝰ augmētatiõis attēdi ha-<lb/>beat. </s>
              <s xml:id="N24DB7" xml:space="preserve">In q̈ materia due ſūt opiniões q̈s calculator <lb/>recitat in capĺo de augmētatiõe: quãuis alii tertiã <lb/>adiiciãt.               <anchor type="note" xlink:href="note-0211-08" xlink:label="note-0211-08a"/>               </s>
              <s xml:id="N24DC3" xml:space="preserve">Uideas Hentiſberū cū cõmētatore ſuo in <lb/>tractatu de motu locali in capĺo de augmētatione <lb/></s>
              <s xml:id="N24DC9" xml:space="preserve">Nūc aūt ſufficiet dicere /  ſcḋm vnã opinionē velo­<lb/>citas motꝰ augmētatiõis attēdit̄̄ penes ꝓportiõa-<lb/>lē quãtitatꝪ acq̇ſitionē. </s>
              <s xml:id="N24DD0" xml:space="preserve">Hoc eſt dicere. </s>
              <s xml:id="N24DD3" xml:space="preserve"> ſi duo aug­<lb/>mētent̄̄ ſiue eq̈lia ſiue ineq̈lia: et eq̈lē ꝓportionē in <lb/>eodē tꝑe adeq̈te acq̇rãt: ipſa eq̄ velociṫ augmētant̄̄ <lb/>et ſi minꝰ in duplo maiorē ꝓportionē acquirit quam <lb/>maiꝰ in eodē tꝑe: vt puta q2 minꝰ acq̇rit q̈druplã: et <lb/>maiꝰ duplã: minꝰ in duplo velociꝰ augmētat̄̄ quam <lb/>maiꝰ. </s>
              <s xml:id="N24DE2" xml:space="preserve">Quare ↄ̨cedit hec poſitio /  ſtat aliq̇d ī q̈̈dru­<lb/>plo velociꝰ augmētari quã illud et in q̈druplo mīo­<lb/>rē quãtitatē acq̇rere adeq̈te.               <anchor type="note" xlink:href="note-0211-09" xlink:label="note-0211-09a"/>               </s>
              <s xml:id="N24DEE" xml:space="preserve">¶ Ex q̊ ſeq̇t̄̄ has ↄ̨ñas <lb/>ſcḋm hãc poſitionē nichil valere: iſta duo in eodem <lb/>tꝑe eq̈lē quãtitatē acq̇rūt: g̊ eq̄ velociṫ augent̄̄ a. in <lb/>duplo velociꝰ acq̇rit de quantitate ꝙ̄ b. / g̊ in duplo <lb/>velociꝰ augmētat̄̄: a. īfinite velociṫ acq̇rit de quãti-<lb/>tate: g̊ īfinite velociṫ augmētat̄̄. </s>
              <s xml:id="N24DFB" xml:space="preserve">Scḋa autē poſitio <lb/>nullo pacto ↄ̨ſiderat ꝓportionē quã illud qḋ auge­<lb/>tur acq̇rit: ſed ſolū quãtitatē. </s>
              <s xml:id="N24E02" xml:space="preserve">Uñ hec ↄ̨ña ſcḋ3 eã eſt <lb/>bona: iſta duo ſiue ſint eq̈lia ſiue inequalia equalē <lb/>quãtitatē acq̇rūt s̈̄titatē p̄habitã ī eodē tꝑe: g̊ eq̄ <lb/>velociṫ augent̄̄. </s>
              <s xml:id="N24E0B" xml:space="preserve">Hiis ãnotatiõibꝰ breuiṫ trãſcurſis: <lb/>reſtat aliq̈s ↄ̨cluſiões īducere. </s>
              <s xml:id="N24E10" xml:space="preserve">Et ṗmo eas īducemꝰ <lb/>q̄ ex ṗori opīiõe ſequūt̄̄: q̄o ex ſcḋa poſteriꝰ ſic / igr̄</s>
            </p>
            <div xml:id="N24E15" level="5" n="12" type="float">
              <note position="left" xlink:href="note-0211-01a" xlink:label="note-0211-01" xml:id="N24E19" xml:space="preserve">q̇d aug-<lb/>mētatio.</note>
              <note position="left" xlink:href="note-0211-02a" xlink:label="note-0211-02" xml:id="N24E21" xml:space="preserve">q̇d dimi-<lb/>nutio.</note>
              <note position="left" xlink:href="note-0211-03a" xlink:label="note-0211-03" xml:id="N24E29" xml:space="preserve">pḣs ṗmo <lb/>de gene.</note>
              <note position="left" xlink:href="note-0211-04a" xlink:label="note-0211-04" xml:id="N24E31" xml:space="preserve">Tex. Cõ-<lb/>mēti .31.</note>
              <note position="right" xlink:href="note-0211-05a" xlink:label="note-0211-05" xml:id="N24E39" xml:space="preserve">pḣs ṗmo <lb/>de gene.</note>
              <note position="right" xlink:href="note-0211-06a" xlink:label="note-0211-06" xml:id="N24E41" xml:space="preserve">Textu cõ­<lb/>mē. 36. et <lb/>32.</note>
              <note position="right" xlink:href="note-0211-07a" xlink:label="note-0211-07" xml:id="N24E4B" xml:space="preserve">Duplex <lb/>opīo de <lb/>augmē-<lb/>tatione.</note>
              <note position="right" xlink:href="note-0211-08a" xlink:label="note-0211-08" xml:id="N24E57" xml:space="preserve">Calcula. <lb/>Hētiſberi</note>
              <note position="right" xlink:href="note-0211-09a" xlink:label="note-0211-09" xml:id="N24E5F" xml:space="preserve">Calcuĺ.</note>
            </div>
            <p xml:id="N24E65">
              <s xml:id="N24E66" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N24E69" xml:space="preserve">Diuiſo corpore per <lb/>ꝑtes ꝓportiõales q̈uis ꝓportiõe: et ṗma ꝑs ꝓpor-<lb/>tiõalis talis corꝑis aliq̈liṫ augmētet̄̄ acq̇rēdo talē <lb/>ꝓportionē q̈lis eſt inṫ ipſam et ſcḋam vel maiorē: et <lb/>ſcḋa in eodē tꝑe augmēter̄ in duplo velociꝰ: et ṫtia <lb/>in triplo velociꝰ quã ṗma: et q̈rta in q̈druplo velociꝰ <lb/>̄ prima in eodē tꝑe: tale corpꝰ efficiṫ īfinitū, et īfi-<lb/>nitã ꝓportionē acquirit, et ſic īfinite velociꝰ augmētat̄̄ <lb/></s>
              <s xml:id="N24E7B" xml:space="preserve">Probar̄ ↄ̨cĺo. </s>
              <s xml:id="N24E7E" xml:space="preserve">q2 ī tali caſu q̄lꝫ ꝑs ꝓportiõalis illiꝰ <lb/>corꝑis ſeq̄ns efficit̄̄ eq̈lis vel maior ꝙ̄ ṗma. </s>
              <s xml:id="N24E83" xml:space="preserve">g̊ ſequit̄̄ / <lb/> illud corpꝰ efficit̄̄ īfinite magnū. </s>
              <s xml:id="N24E88" xml:space="preserve">Probat̄̄ añs: et <lb/>volo /  a. corpꝰ diuidat̄̄ ꝓportiõe h. et ṗma ꝑs ꝓpor­<lb/>tiõalis eiꝰ in hora acq̇rit ꝓportionē h. et ſcḋa duas <lb/>h. et ṫtia tres. et q̈rta q̈tuor . / et ſic ↄ̨ñter. </s>
              <s xml:id="N24E91" xml:space="preserve">Quo poſito <lb/>argr̄ ſic. </s>
              <s xml:id="N24E96" xml:space="preserve">Prima pars diſtat a ſcḋa ꝑ h. ꝓportionē <lb/>adeq̈te in prīcipio augmētatiõis et ip̄a p̄ma acq̇rit <lb/>h. ꝓportionē: et ſcḋa acq̇rit vnã h. ꝓportionē in q̈ <lb/>ṗma excedebat eã: et īſuꝑ tãtã ꝓportiõeꝫ quãtã prīa <lb/>puta vnã aliã ꝓportionē h. / igr̄ efficit̄̄ eq̈lis prime. <lb/></s>
              <s xml:id="N24EA2" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ maximã ſuperiꝰ poſitã. </s>
              <s xml:id="N24EA5" xml:space="preserve">Quãdo due <lb/>quãtitates īequales creſcūt, et mīor illaꝝ acquirit <lb/>illã ꝓportionē q̄ eſt inter maiorē et ipſam, et inſuꝑ <lb/>tantaꝫ proportionē adeq̈te quantã acq̇rit maior in <lb/>fine augmētatiõis tales quãtitates manent eq̈les: <lb/>ſed ſic eſt in ꝓpoſito: igr̄. </s>
              <s xml:id="N24EB2" xml:space="preserve">et ſic ꝓbabis /  ṫtia pars <lb/>effecta eſt eq̈lis ſcḋe q2 acq̇ſiuit duas ꝓportiões h. <lb/>ſicut ſcḋa, et inſuꝑ vnã aliã h. in qua ſcḋa excedebat <lb/>tertiã, et ſiĺr q̈rta acq̇ſiuit tres ꝓportiões h. ſicut et <lb/>tertia et īſuꝑ vnã h. in q̈ tertia excedebat illã: igr̄ ꝑ <lb/>illã maximã oēs ille ꝑtes manēt eq̈les qm̄ ſic ꝓba­<lb/>bis de quibuſcū<gap/> duabꝰ īmeditatis. </s>
              <s xml:id="N24EC3" xml:space="preserve">Et eodē° ꝓba-<lb/>bis  tale corpꝰ acq̇rit infinitã ꝓportionē: ſi prima <lb/>pars eiꝰ acq̇reret maiorē ꝓportionē ꝙ̄ ſit ꝓportio               <pb chead="De motu augmentationis." file="0212" n="212"/>               diuiſiõis patrocinio loci a maiore               <anchor type="note" xlink:href="note-0212-01" xlink:label="note-0212-01a"/>               </s>
              <s xml:id="N24ED4" xml:space="preserve">¶ Ex quo ſequit̄̄ / <lb/> ſtat aliq̈ ꝑ totã vnã horã eq̄ velociṫ augmētari q̊­<lb/>rū in īfinitū minꝰ primo ↄ̨tinuo eſt aliqḋ: et tñ ī fine <lb/>oīa erunt eq̈lia. </s>
              <s xml:id="N24EDD" xml:space="preserve">Probat̄̄ correlariñ et pono /  ſint <lb/>īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdupla: ita <lb/> primū ſit pedale ſcḋm ſemipedale etc̈. </s>
              <s xml:id="N24EE4" xml:space="preserve">Et diuida­<lb/>tur qḋlibet illoꝝ ꝑ partes ꝓportiõales ꝓportione <lb/>dupla: et in hora vniformiter cuiuſlꝫ illoꝝ ṗma ꝑs <lb/>acq̇rat ꝓportionē duplã: et cuiuſlꝫ illoꝝ ſcḋa duas <lb/>et tertia tres, et q̈rta q̈tuor, et ſic ↄ̨ñter. </s>
              <s xml:id="N24EEF" xml:space="preserve">Quo poſito <lb/>manifeſtū eſt ex ↄ̨cluſione,  oīa illa erūt īfinita in <lb/>fine hore / et per ↄ̨ñs eq̈lia, et ꝑ totã horã eq̄ velociter <lb/>augmētabunt̄̄: qm̄ ↄ̨tinuo eq̈les ꝓportiões acq̇rūt / <lb/>vt ↄ̨ſtat, et ↄ̨tinuo in infinitū minꝰ primo erit aliqḋ <lb/>illoꝝ: qm̄ qḋlibet ſequēs in quolꝫ inſtãti intrinſeco <lb/>ſe habebit ad primū in ea ꝓportiõe in q̈ mõ ſe hñt: <lb/>ſed aliqḋ illoꝝ eſt in prīcipio ſubduplū ad primuꝫ <lb/>aliud ſubq̈druplū, aliud ſuboctuplū, aliud ſubſex-<lb/>decuplū / et ſic ↄ̨ñter. </s>
              <s xml:id="N24F04" xml:space="preserve">g̊ ↄ̨tinuo aliqḋ erit ſubduplū, <lb/>ſubq̈druplū, ſuboctuplū, et ſic in infinitū: et ſic patꝫ <lb/>correlariū.               <anchor type="note" xlink:href="note-0212-02" xlink:label="note-0212-02a"/>               </s>
              <s xml:id="N24F10" xml:space="preserve">¶ Sequit̄̄ ſcḋo /  diuiſo corꝑe ꝓportiõe <lb/>ſexq̇altera: et ī vna hora ṗma ꝑs acq̇rat ꝓportiõeꝫ <lb/>duplã, et ſcḋa duas triplas, et tertia tres q̈druplas <lb/>et q̈rta q̈tuor quītuplas, et ſic ↄ̨ñter aſcendēdo tale <lb/>corpꝰ in fine erit īfinitū. </s>
              <s xml:id="N24F1B" xml:space="preserve">Ptꝫ ex ↄ̨cluſiõe.               <anchor type="note" xlink:href="note-0212-03" xlink:label="note-0212-03a"/>               </s>
              <s xml:id="N24F23" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio /  diuiſo corꝑe ꝑ partes ꝓportiõales ꝓpor-<lb/>tiõe dupla, et ṗma ꝑs illiꝰ in vna hora acq̇rat vni-<lb/>formiter proportionē duplã, et ſcḋa duas triplas, <lb/>et tertia tres q̈druplas, et q̈rta quatuor q̈druplas, <lb/>et quīta quī q̈druplas, et ſexta ſexq̈druplas / et ſic <lb/>in īfinitū: tūc tale corpꝰ efficit̄̄ īfinitū. </s>
              <s xml:id="N24F32" xml:space="preserve">Probat̄̄ / qm̄ <lb/>ī tali caſu tertia ꝑs ꝓportiõalis acquirit ſex duplas <lb/>et q̈rta octo duplas et quīta decē, et ſexta duodecī: et <lb/>ſic ↄ̨ñter aſcēdendo ꝑ nūeros pares, et hoc vĺr: igr̄ <lb/>q̄libet ꝑs ꝓportiõalis acquirit tantã quãtitatē ſicut <lb/>ṗma in hora vel maiorē / et ꝑ ↄ̨ñs in fine hore corpus <lb/>eſt īfinitū. </s>
              <s xml:id="N24F41" xml:space="preserve">Ptꝫ hec ↄ̨ña / qm̄ q̄libet acq̇rit maiorē ꝓ-<lb/>portionē ꝙ̄ oporteat vt ſit eq̈lis prime.</s>
            </p>
            <div xml:id="N24F46" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0212-01a" xlink:label="note-0212-01" xml:id="N24F4A" xml:space="preserve">correĺ. 1.</note>
              <note position="left" xlink:href="note-0212-02a" xlink:label="note-0212-02" xml:id="N24F50" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0212-03a" xlink:label="note-0212-03" xml:id="N24F56" xml:space="preserve">.3. correĺ.</note>
            </div>
            <p xml:id="N24F5C">
              <s xml:id="N24F5D" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
              <s xml:id="N24F60" xml:space="preserve">Diuiſo corꝑe ꝑ partes <lb/>ꝓportiõales q̈uis optata ꝓportiõe, et prima pars <lb/>ꝓportiõalis in vna hora acq̇rat aliquã ꝓportionē <lb/>minorē ꝓportiõe diuiſiõis, et ſcḋa acq̇rat duplã ad <lb/>illã, et tertia triplã ad illã, et q̈rta q̈druplã ad illã. <lb/></s>
              <s xml:id="N24F6C" xml:space="preserve">ita  augmētet̄̄ in q̈druplo velociꝰ in eodē tꝑe / et ſic <lb/>ↄ̨ñter: tūc in illo tꝑe illud corpꝰ finite certe velociter <lb/>augmētat̄̄: et ꝑtes q̄ ſe habebãt ī ꝓportiõe diuiſiõis <lb/>ſe habebūt in fine ↄ̨tinuo in ꝓportiõe ꝑ quã ꝓpor° <lb/>diuiſiõis excedit ꝓportionē quã prima acq̇rit. </s>
              <s xml:id="N24F77" xml:space="preserve">Exē-<lb/>plū / vt ſi aliqḋ corpꝰ diuidat̄̄ ꝓportiõe dupla et ī ho­<lb/>ra ṗma ꝑs acq̇rat ꝓportionē ſexq̇alterã et ſcḋa du­<lb/>as et tertia tres, et q̈rta q̈tuor / et ſic ↄ̨ñter, tūc dico /  <lb/>in fine ille ꝑtes q̄ ſe hñt in ꝓportiõe dupla ſe habe-<lb/>būt in ꝓportiõe ſexq̇tertia: qm̄ ꝓportio diuiſiõis q̄ <lb/>eſt dupla excedit ꝓportioneꝫ ſexq̇alterã quã acq̇rit <lb/>ṗma ꝑs ꝓportiõalis ſexq̇alterã quã acq̇rit <lb/>ṗma ꝑs ꝓportiõalis corꝑis ꝑ ꝓportionē ſexq̇tertiã / <lb/>vt ↄ̨ſtat. </s>
              <s xml:id="N24F8C" xml:space="preserve">Probat̄̄ hoc .2. theorema gñaliṫ ſic: et ſit <lb/>ꝓportio diuiſiõis a. corꝑis h. ſit ꝓpor° quã acq̇rit <lb/>in hora ṗma ꝑs ꝓportiõalis f. q̄ ſit mīor h. ꝑ g. pro­<lb/>portionē: ita  h. excedat f. ꝑ g. ꝓportionē. </s>
              <s xml:id="N24F95" xml:space="preserve">Tūc ar̄ <lb/>ſic. </s>
              <s xml:id="N24F9A" xml:space="preserve">Proportio h. q̄ eſt īter ṗma et ſcḋaꝫ ꝑdit f. ꝓpor­<lb/>tionē: et eãdē ꝓportionē f. ꝑdit ꝓpor° q̄ eſt inṫ ſcḋaꝫ <lb/>et tertiã: et inṫ tertiã et q̈rtã: et ſic ↄ̨ñter: et hoc adeq̈te <lb/>et ꝓpor° h. excedit ꝓportionē f. ꝑ ꝓportionē g. / vt ptꝫ <lb/>ex caſu: g̊ ſequit̄̄ /  inṫ primã partē et ſcḋam manet <lb/>g. ꝓpor°. </s>
              <s xml:id="N24FA7" xml:space="preserve">et inṫ ſcḋaꝫ et tertiã: et inṫ tertiã et q̈rtã .etc̈. <lb/></s>
              <s xml:id="N24FAB" xml:space="preserve">Ptꝫ hec ↄ̨ña / ꝑ hãc maximã iã ſuperiꝰ poſitã in ṫtio <lb/>argumēto. </s>
              <s xml:id="N24FB0" xml:space="preserve">Qñcū aliq̇ duo nūeri vel quantitates <lb/>ſe hñt in aliq̈ ꝓportiõe, et eq̈les ꝓportiões acq̇runt <lb/>ſēꝑ manēt in eadē ꝓportionē: et ſi nūerꝰ minor ſiue               <cb chead="De motu augmentationis."/>               quãtitas mīor acq̇rat aliquã ꝓportionē vltra nūeꝝ <lb/>ſiue quãtitatē maiorē: ita tñ  ſēꝑ maneat mīor illã <lb/>proportionē deꝑdit: propor° q̄ a. prīcipio erat inter <lb/>ṫminū maiorē et minorē: ſꝫ ſic eſt in ꝓpoſitio: igr̄. </s>
              <s xml:id="N24FC0" xml:space="preserve">Sꝫ <lb/>tã ꝓbat̄̄ maior / qm̄ ſi ſcḋa ꝑs ꝓportiõalis acq̇reret <lb/>dūtaxat f. ꝓportionē quã adeq̈te acq̇rit ṗma: tunc <lb/>ſēꝑ maneret ī eq̈li ꝓportiõe puta in h. / vt pꝫ ex ma-<lb/>xima ſꝫ mõ ſcḋa ꝑs acq̇rit vltra illã ꝓportiõeꝫ quã <lb/>acq̇rit prima vna ꝓportionē f. et cū hoc manet mīor / <lb/>igr̄ ꝓportionē f. deꝑdit ꝓpor° h. q̄ in prīcipio erat <lb/>inṫ primã et ſcḋaꝫ ꝑte ſꝫ deꝑdita f. ꝓportiõe ab h. nõ <lb/>manet niſi g. ꝓpor° ꝑ quã ꝓpor° h. excedit ꝓpor°nē <lb/>f. / igr̄ inṫ prima et ſcḋaꝫ manebit g. ꝓpor°. </s>
              <s xml:id="N24FD5" xml:space="preserve">Itē ſi ter-<lb/>tia ꝑs ꝓportiõalis acq̇reret duas f. ꝓportiões ſicut <lb/>ſcḋa adeq̈te: tūc adhuc manerēt in h. ꝓportiõe / vt pꝫ <lb/>ex maxīa: ſꝫ mõ ꝑdit tertia vna f. ꝓportionē vltra et <lb/>manet mīor qua ſcḋa: igr̄ ꝓportiõeꝫ f. deꝑdit ꝓpor° <lb/>h. q̄ erat in prīcipio inṫ ſcḋaꝫ et ṫtiã: ſꝫ deꝑdita f. ꝓ-<lb/>portiõe ad h. nõ manet niſi g. ꝓpor° ꝑ qua ꝓpor° h. <lb/>excedit f. ꝓpor°nē: igr̄ iṫ ſcḋaꝫ et ṫtiã manet g. ꝓpor° / <lb/>qḋ fuit ꝓbãdū. </s>
              <s xml:id="N24FE8" xml:space="preserve">Et isto° ꝓbabis de q̇buſcun duabꝰ <lb/>īmediatis  inṫ eas manet g. ꝓpor°. </s>
              <s xml:id="N24FED" xml:space="preserve">Ptꝫ igr̄ ſcḋa <lb/>ꝑs ↄ̨cluſiõis:  vcꝫ in caſu ↄ̨cluſiõnis inṫ partes ma-<lb/>nebit ꝓpor° g. ꝑ quã ꝓpor° diuiſiõis excedit ꝓpor°-<lb/>nē acq̇ſitã ṗme ꝑti ꝓportiõali in toto tꝑe. </s>
              <s xml:id="N24FF6" xml:space="preserve">Et ex hoc <lb/>facile ptꝫ ṗma ꝑs. </s>
              <s xml:id="N24FFB" xml:space="preserve">¶ Sꝫ q̄reret aliq̇s quo cog̊ſci põt <lb/>̄tã ꝓportionē in caſu ↄ̨cluſiõis illud corpꝰ acq̇ſiuit <lb/>ſupra ſe. </s>
              <s xml:id="N25002" xml:space="preserve">¶ Rñdeo et dico ṗmo /  quãuis poſſit dari <lb/>certa rĺa ad hoc vĺr ſciendū: nichilominꝰ q2 illa eſt <lb/>multū ītricata, et intellectu difficilis. </s>
              <s xml:id="N25009" xml:space="preserve">iõ eã nõ pono. <lb/></s>
              <s xml:id="N2500D" xml:space="preserve">Dico 2° /  poterit facile calculari ̄tū illḋ corpꝰ eſt <lb/>ī fine taĺ augmētatiõis ſcita ̄titate ṗme ꝑtꝪ ꝓpor­<lb/>tiõalis in fine augmētatiõis: q̄ ſcita ꝑ regulas di-<lb/>uiſionū poſitas ī q̇nto capite ṗme ꝑtꝪ adīueniet̄̄ to­<lb/>talis corꝑis magnitudo: et tūc hīta ̄titate quã ha­<lb/>buit ī prīcipio augmētatiõis habet̄̄ ꝓpor° acq̇ſita.</s>
            </p>
            <p xml:id="N2501A">
              <s xml:id="N2501B" xml:space="preserve">Tertia ↄ̨̨cĺo. </s>
              <s xml:id="N2501E" xml:space="preserve">Diuiſo corꝑe in ꝑtes ꝓ-<lb/>portiõales q̈cū ꝓportiõe: et ṗma ꝑs ꝓportiõalis <lb/>acq̇rat aliquãtulã ꝓportionē ī hõ: et ſcḋa in duplo <lb/>maiorē ī eadē hõ, et ṫtia ī duplo maiorē quã ſcḋa et <lb/>q̈rta ꝙ̄ ṫtia et ſic in īfinitū: ita  q̈lꝫ ſeq̄ns in duplo <lb/>velociꝰ ↄ̨tinuo augeat̄̄ ī hõ quã īmediate p̄cedēs: ta­<lb/>le corpꝰ īfinite velociṫ auget̄̄ et ſubito acq̇rit īfinitã <lb/>ꝓportionē. </s>
              <s xml:id="N2502F" xml:space="preserve">Probat̄̄ /hec ↄ̨cĺo et ſit ꝓpor° diuiſiõis <lb/>corꝑis g. et ꝓpor° quã acq̇rit ṗma ꝑs ī hõ ſit h. / q̊ po-<lb/>ſito ar̄ ſic: q̇cū īſtãti dato poſt īſtãs īitiatiuū talis <lb/>augmētatiõis dat̄̄ vna ꝑs ꝓportiõalis illiꝰ corꝑis <lb/>cui q̄lꝫ īfinitarū ſeq̄ntiū ē eq̈is vĺ illa maior: g̊ ſeq̇t̄̄ / <lb/> q̊cū īſtãti dato inṫ illḋ et īſtãs īitiatiuū illḋ cor­<lb/>pus acq̇rit īfinitã ꝓportionē / et ꝑ ↄ̨ñs ↄ̨cluſio vera: <lb/></s>
              <s xml:id="N2503F" xml:space="preserve">Cõſequētia ptꝫ: et argr̄ añs: q2 quocū inſtãti da-<lb/>to aliquã ꝓportionē acquiſiuit prima pars ꝓpor­<lb/>tionalis q̄ fit f. gr̄a argumēti et manifeſtū eſt  ali­<lb/>quot f. ꝓportiões cõſtituūt g. ꝓportionē diuiſiõis <lb/>vel maiorē ꝓportionē quã ſit g. ꝓportio diuiſiõis <lb/>et tot f. ꝓportiones in tali inſtanti vel plures acq̇-<lb/>ſiuit aliqua pars q2 in tali inſtãti īfinitas f. ꝓpor-<lb/>tiones acq̇ſiuit aliqua pars, et pars īmeditate ſe-<lb/>quens acq̇ſiuit bis tot f. ꝓportiones: ergo acq̇ſiuit <lb/>tantã ꝓportionē quanta īmediate p̄cedens et cum <lb/>hoc tantã ꝓportionē quãta eſt inter illã et īmedia-<lb/>te p̄cedente vel maiorē / et ꝑ ↄ̨ñs illa pars effecta eſt <lb/>equalis in tali inſtanti īmediate p̄cedenti vel ma-<lb/>ior. </s>
              <s xml:id="N2505C" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ quandã maximã ſuperiꝰ allega­<lb/>tam ad īmediate p̄cedentē concluſione. </s>
              <s xml:id="N25061" xml:space="preserve">Et eodē mõ <lb/>ꝓbabis de īmediate ſequēte illã de qua ꝓbatū eſt / <lb/> erat maior vel equalis īmediate precedenti. </s>
              <s xml:id="N25068" xml:space="preserve">Sit <lb/>em̄ illa gr̄a exēpli quã ꝓbauiꝰ eſſe equalē īmedia­<lb/>te p̄cedenti vel maiorē viceſima pars ꝓportiõalis:               <pb chead="Tertii tractatus" file="0213" n="213"/>               et tūc manifeſtū eſt /  viceſima prima efficitur eq̈-<lb/>lis illi viceſime vel maior qm̄ tot proportiones ac-<lb/>quiſiuit viceſima prima ſicut viceſima et cū hoc ac-<lb/>quiſiuit bis ꝓportionē diuiſionis vel maiorē ea: g̊ <lb/>effecta eſt maior viceſima parte. </s>
              <s xml:id="N2507C" xml:space="preserve">et ſic ꝓbabis de vi-<lb/>ceſima ſcḋa reſpectu viceſime prime.               <anchor type="note" xlink:href="note-0213-01" xlink:label="note-0213-01a"/>               </s>
              <s xml:id="N25086" xml:space="preserve">¶ Ex quo ſe-<lb/>quit̄̄ /  diuiſo corpore quauis ꝓportiõe volueris <lb/>vt ponit̄̄ in caſu ↄ̨cluſiõis nõ eſt poſſibile tale cor-<lb/>pꝰ ſucceſſiue ī tali caſu augmentari. </s>
              <s xml:id="N2508F" xml:space="preserve">Ptꝫ ex ↄ̨cĺone</s>
            </p>
            <div xml:id="N25092" level="5" n="14" type="float">
              <note position="left" xlink:href="note-0213-01a" xlink:label="note-0213-01" xml:id="N25096" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N2509C">
              <s xml:id="N2509D" xml:space="preserve">Quarta ↄ̨̨cluſio. </s>
              <s xml:id="N250A0" xml:space="preserve">Diuiſo corpore qua-<lb/>uis optata ꝓportione, et prima pars ꝓportiõalis <lb/>talis corporis in hora aliqualiter augeat̄̄: et ſcḋa <lb/>velociꝰ prima in ꝓportione in qua eſt minor ea vel <lb/>maiori: et tertia etiã velociꝰ prima in qua eſt minor <lb/>ea vel maiori, et ſic ↄ̨ñter ↄ̨tinuo totū illud corpus <lb/>infinite velociter auget̄̄ in illa hora et ſubito efficit̄̄ <lb/>infinite magnū. </s>
              <s xml:id="N250B1" xml:space="preserve">Probat̄̄ hec ↄ̨cluſio et volo /  di-<lb/>uidat̄̄ aliqḋ corpꝰ ꝓportione a. et incipiant partes <lb/>augmentari: vt ponit̄̄ in ↄ̨cluſione. </s>
              <s xml:id="N250B8" xml:space="preserve">Tunc argr̄ ſic. <lb/></s>
              <s xml:id="N250BC" xml:space="preserve">Quocun inſtanti dato poſt hoc dabit̄̄ vna pars <lb/>ꝓportionalis equalis īmediate p̄cedenti vĺ maior <lb/>et q̄libet ſequēs equalis illi vĺ maior: ergo quocū <lb/>inſtanti dato poſt hoc illud corpꝰ erit infinite ma-<lb/>gnū. </s>
              <s xml:id="N250C7" xml:space="preserve">Cõſequētia ptꝫ et argr̄ añs. </s>
              <s xml:id="N250CA" xml:space="preserve">Qm̄ ſignato aliq̊ <lb/>inſtanti poſt hoc aliqua eſt ꝓportio acq̇ſita prime <lb/>parte ꝓportionali q̄ ſit h. et in īfinitū maior acq̇ſi-<lb/>ta eſt alicui parti / vt ptꝫ ex caſu: qm̄ in īfinitū mīor <lb/>prima eſt aliqua pars, capio igr̄ vnã / que acq̇ſiuit <lb/>vnã ꝓportionē a. vel maiorē vltra ꝓportionē acq̇-<lb/>ſitã parti īmediate p̄cedenti: et ſequit̄̄ /  illa eſt eq̈-<lb/>lis vel maior īmediate p̄cedenti: qm̄ acq̇ſiuit tantã <lb/>ꝓportionē ſicut īmediate p̄cedens: et inſuꝑ illã per <lb/>quã excedebat̄̄ ab īmediate p̄cedenti vel maiorē: et <lb/>ꝑ ↄ̨ñs eſt equalis vel maior / vt ptꝫ ex maxīa ſcḋe cõ-<lb/>cluſionis. </s>
              <s xml:id="N250E3" xml:space="preserve">et ſiĺr pars ſequēs illã eſt eq̈lis īmediate <lb/>p̄cedēti vel maior: qm̄ acquiſiuit tantã ꝓportionē <lb/>quantã īmediate p̄cedens et cū hoc vnã ꝓportionē <lb/>maiorē ꝙ̄ ſic proportio a. per quã excedebatur ab <lb/>īmediate p̄cedēti: et ſic ↄ̨ñter ꝓbabis de q̈libet alia</s>
            </p>
            <p xml:id="N250EE">
              <s xml:id="N250EF" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
              <s xml:id="N250F2" xml:space="preserve">Diuiſo corꝑe quacū-<lb/> proportione volueris: et tn aliquo tꝑe prima pars <lb/>ꝓportionalis acquirat aliquã ꝓportionē: et q̄libet <lb/>ſequēs tantã in eodē tꝑe: tūc oēs ille partes manēt <lb/>in eadē ꝓportione in qua antea ſe habebãt: et totū <lb/>acquirit illã ꝓportionē quã acquirit prima eiꝰ ꝑs <lb/></s>
              <s xml:id="N25100" xml:space="preserve">Probat̄̄ prima pars ↄ̨cluſiõis: qm̄ q̄libet due par­<lb/>tes īmediate ita ſe hñt  quanttã ꝓportionē acq̇ſi-<lb/>uit maior tantã acq̇ſiuit mīor: et ſic manent in eadē <lb/>ꝓportiõe in qua ſe habebãt ãtea. </s>
              <s xml:id="N25109" xml:space="preserve">Ptꝫ ↄ̨ña ex ſcḋa <lb/>parte: et ꝑ ↄ̨ñs oēs ille partes ꝓportiõales ſe hñt in <lb/>ea ꝓportiõe in qua ſe habebant antea. </s>
              <s xml:id="N25110" xml:space="preserve">Scḋa pars <lb/>ꝓbat̄̄ / et ſit h. ꝓportio acq̇ſita primi parti ꝓportio­<lb/>nali. </s>
              <s xml:id="N25117" xml:space="preserve">et argr̄ ſic. </s>
              <s xml:id="N2511A" xml:space="preserve">Quelꝫ ꝑs ꝓportionalis iſtiꝰ corꝑis <lb/>demõſtrato corꝑe ſic diuiſo et augmētato eſt in h. <lb/>ꝓportiõe maior ꝙ̄ ãtea: g̊ totū corpꝰ eſt in h. ꝓpor-<lb/>tiõe maiꝰ: et illa eſt ꝓportio quã acq̇ſiuit ṗma ꝑs ꝓ-<lb/>portiõalis: igr̄ in caſu ↄ̨cluſiõis totū corpꝰ effectuꝫ <lb/>ē maiꝰ in ꝓportiõe quã acq̇ſiuit ṗma ꝑs ꝓportiõa-<lb/>lis. </s>
              <s xml:id="N25129" xml:space="preserve">Probat̄̄ ↄ̨ña: et ſit illud corpꝰ a. in fine augmē-<lb/>tatiõis: et b. in prīcipio. </s>
              <s xml:id="N2512E" xml:space="preserve">Et argr̄ ſic / ṗme ꝑtꝪ ꝓpor-<lb/>tiõalis ipſiꝰ a .h. ꝓportiõe ad primã ipſiꝰ b. eſt ꝓpor­<lb/>tio h. </s>
              <s xml:id="N25135" xml:space="preserve">Et ſcḋe ipſiꝰ a. ad ſcḋaꝫ ipſiꝰ b. eſt etiã ꝓportio <lb/>h. / Et ṫtie ipſiꝰ a. ad ṫtiã ipſiꝰ b. eſt ꝓportio h. / et ſic <lb/>ↄ̨ñter: igr̄ oīm partiū ꝓportionaliū ipſiꝰ a. ad oēs <lb/>ꝑtes ꝓportiõales ipſiꝰ b. eſt ꝓportio h. / ptꝫ hec ↄ̨ña <lb/>qm̄ eadē eſt ꝓpor° ↄ̨iūtoꝝ et diuiſorū / vt ptꝫ ex ſcḋo <lb/>capite ſecunde partis. </s>
              <s xml:id="N25142" xml:space="preserve">Et ex conſequenti totum a. <lb/>eſt in h. proportione maius ipſo b.</s>
            </p>
            <cb chead="Capitulū ſecundum."/>
            <p xml:id="N25149">
              <s xml:id="N2514A" xml:space="preserve">Sexta cõcluſio. </s>
              <s xml:id="N2514D" xml:space="preserve">Partito corpore per <lb/>partes ꝓportionales quacun ꝓportione volue-<lb/>ris et in aliquo tēpore prima pars proportionalis <lb/>acquirat aliquã ꝓportionē et ſecunda acquirat in <lb/>aliqua certa ꝓportione in eodē tēpore ꝓportioneꝫ <lb/>minorē: et tertia in eadē ꝓportione minorē ſecūda: <lb/>et quarta in eadem ꝓportione minorē tertia: et ſic <lb/>ↄ̨ñter. </s>
              <s xml:id="N2515E" xml:space="preserve">tūc ꝓportio inter primã partē et ſcḋam effi-<lb/>citur maior ꝑ primã partē ꝓportionalē ꝓportiõis <lb/>acquiſite prime diuiſe in ea ꝓportione qua ſecūda <lb/>tardius augmētaã prima: et tertia ꝙ̄ ſcḋa: et ſic cõ-<lb/>ſequēter: et ꝓportio īter ſcḋaꝫ et tertiã efficit̄̄ maior <lb/>ꝑ ſcḋam partē ꝓportionalē ꝓportiõis acq̇ſite ṗme <lb/>et ꝓportio īter tertiã et quartã efficit̄̄ maior ꝑ tertiã <lb/>partē ꝓportionalē ꝓportionis acq̇ſite prime: r ſic <lb/>ↄ̨ñter: et (vt opinor) nõ valet finita intellectꝰ capaci­<lb/>tas cõmenſurare ꝓportionē toti corpori acquiſitã <lb/></s>
              <s xml:id="N25174" xml:space="preserve">Exemplū / vt ſi aliqḋ corpꝰ diuidat̄̄ ꝑ partes ꝓpor-<lb/>tionales ꝓportiõe dupla: et prima pars ꝓportiõa­<lb/>lis acq̇rat ꝓportionē ſexquialterã: et ſcḋa ſubqua-<lb/>druplã: et tertia ſubquadruplã ad acquiſitã ſecūde <lb/>et quarta ſubquadruplã ad acquiſitã tertie: et ſic cõ­<lb/>ſequenter: tūc dico /  ꝓportio inter primã partem <lb/>ꝓportionalē et ſcḋam acquiſiuit primã partē ꝓpor­<lb/>tionis ſexq̇altere diuiſe ꝑ partes ꝓportiõales pro­<lb/>portione quadrupla. </s>
              <s xml:id="N25187" xml:space="preserve">Et ꝓportio inter ſcḋaꝫ et ter-<lb/>tiã acq̇ſiuit ſcḋam partē ꝓportionalē ꝓportionis <lb/>ſexq̇altere. </s>
              <s xml:id="N2518E" xml:space="preserve">Et ꝓportio inter tertiã et quartã tertiã <lb/>partē ꝓportionalē ꝓportionis ſexq̇altere. </s>
              <s xml:id="N25193" xml:space="preserve">Et ſi cõ­<lb/>ſequēter. </s>
              <s xml:id="N25198" xml:space="preserve">Probat̄̄ / ſit a. proportio acq̇ſita prime <lb/>parti ꝓportionali: et ſit f. ꝓportio in qua velocius <lb/>auget̄̄ prima ꝙ̄ ſcḋa. </s>
              <s xml:id="N2519F" xml:space="preserve">Et argr̄ ſic. </s>
              <s xml:id="N251A2" xml:space="preserve">Proportiões ac-<lb/>quiſite partibꝰ huiꝰ corporis cõtinuo ſe habent in <lb/>ꝓportione f. / vt ptꝫ ex caſu: ergo exceſſus quibꝰ cõti­<lb/>nuo ſe excedūt etiã ſe hñt ↄ̨tinuo in ꝓportione f. et <lb/>ꝑ primū illoꝝ exceſſuū ꝓportio inter primã et ſcḋaꝫ <lb/>partē efficit̄̄ maior: et ꝑ ſcḋm ꝓportio inter ſcḋaꝫ et <lb/>tertiaꝫ efficit̄̄ maior: et ꝑ tertiū ꝓportio inter tertiã <lb/>et quartã efficit̄̄ maior: et ſic ↄ̨ñter: et primꝰ illoꝝ ex-<lb/>ceſſuū eſt prima pars ꝓportionalis ipſiꝰ a. ꝓpor-<lb/>tionis diuiſe ꝓportiõe f. et ſcḋus ſcḋa: et tertiꝰ tertia / <lb/>et ſic ↄ̨ñter: igr̄ ꝓportio inter primã et ſcḋam partē <lb/>efficit̄̄ maior ꝑ primã partē ꝓportionalē ipſius a. <lb/>ꝓportione f. et ſcḋa ꝑ ſcḋaꝫ: et tertia per tertiã: et ſic <lb/>ↄ̨ñter / qḋ fuit ꝓbandū. </s>
              <s xml:id="N251BF" xml:space="preserve">Ptꝫ tamē prima ↄ̨ña ꝑ hãc <lb/>regulã q̄ ſuperiꝰ demõſtrata eſt in quacun ꝓpor-<lb/>tione ſe hñt aliqua ↄ̨tinuo in eadē ↄ̨tinuo ſe habēt <lb/>exceſſus eoꝝ. </s>
              <s xml:id="N251C8" xml:space="preserve">Sed iã ꝓbo /  ꝑ primū illorū exceſſuū <lb/>ꝓportio inter primã et ſcḋam efficitur maior: et per <lb/>ſcḋm proportio inter ſcḋam et tertiã etc̈. / et hoc ꝑ hãc <lb/>maximã. </s>
              <s xml:id="N251D1" xml:space="preserve">Quãdocū due quãtitates inequales ac­<lb/>quirūt aliquas ꝓportiones: et maior illaꝝ acqui-<lb/>rit maiorē ꝓportionē ꝙ̄ minor: tunc ꝓportio inter <lb/>illas quantitates efficitur maior per exceſſum quo <lb/>ꝓportio acquiſita maiori excedit ꝓportionē acqui­<lb/>ſitam mīori vt in capĺo .8. ſcḋe partis oſtēſum eſt <lb/>ſed ſic eſt in ꝓpoſito: igr̄. </s>
              <s xml:id="N251E0" xml:space="preserve">Sed iam ꝓbat̄̄ /  primꝰ <lb/>illoꝝ exceſſuū eſt prima pars ꝓportionalis ipſius <lb/>a. ꝓportione f. q2 a. ſe habet ad ꝓportionē acquiſi­<lb/>tam prime partiū ꝓportionali in ꝓportione f. / ergo <lb/>exceſſus quo a. excedit ꝓportionē acquiſitã ſecunde <lb/>parti ꝓportionali eſt prima pars proportionalis <lb/>ipſius a. ꝓportione f. </s>
              <s xml:id="N251EF" xml:space="preserve">Ptꝫ ↄ̨ña per hanc regulam. <lb/></s>
              <s xml:id="N251F3" xml:space="preserve">Quandocū aliquod totū excedit aliquid in cer-<lb/>ta ꝓportione tūc excedit illud per primã ſui partē <lb/>ꝓportionalē tali ꝓportione: vt ſi vnū pedale exce-<lb/>dat aliam quantitatē in proportione ſexquialtera <lb/>illud pedale excedit aliud per primã ſui partē pro-<lb/>portionalē ꝓportione ſexquialtera quia per vnaꝫ               <pb chead="De motu augmentationis." file="0214" n="214"/>               tertiã / vt conſtat. </s>
              <s xml:id="N25205" xml:space="preserve">Ex hoc ſequit̄̄ /  ſecundus exceſſus <lb/>eſt ſecūda pars proportionalis proportiõe f. et ter­<lb/>tius tertia / et ſic ↄ̨ſequenter. </s>
              <s xml:id="N2520C" xml:space="preserve">Ex eo  primus illoruꝫ <lb/>eſt prima / et ſic patet prīa ꝑs ↄ̨cluſiõis. </s>
              <s xml:id="N25211" xml:space="preserve">Et ex illa fa­<lb/>cile ꝑſuadetur ſcḋa quoniam ille partes cõtinuo ſe <lb/>habent in alia et alia ꝓportiõe puta minori et mi-<lb/>nori: igit̄̄ impoſſibile eſt intellectui finito illaꝫ inifi­<lb/>nitam ꝓportionū diuerſitatē cõmenſurare: et ꝑ con­<lb/>ſequens impoſſibile eſt ip̄m metiri ꝓportionē quã <lb/>illud corpus adequate acq̇ſiuit: et ſic patet cõcluſio</s>
            </p>
            <p xml:id="N25220">
              <s xml:id="N25221" xml:space="preserve">Septima concluſio diuiſa hora per <lb/>partes proportionales proportione ad libitū ex-<lb/>optata cõſtitutiſ certis ordinibꝰ partiū propor-<lb/>tionaliū inter ſcalariter ſe habentiū: totum cor-<lb/>pus abſoluētiū iuxta tenorē primi ↄ̨cluſionis ſepti­<lb/>mi capitis prime partis: et in prīo illorū aliqḋ cor­<lb/>pus augmētetur acquirendo aliquã proportioneꝫ <lb/>et in ſecundo eque velociter augmētetur: et ita ī quo­<lb/>libet ſi plures fuerint: illud corpus minorē propor­<lb/>tionem acquirit in quolibet ſequenti ꝙ̄ immediate <lb/>precedēti in proportione qua hora diuidit̄̄. </s>
              <s xml:id="N25238" xml:space="preserve">Exem-<lb/>plum / vt ſi hora diuidat̄̄ proportione dupla et con-<lb/>ſtituūtur tres ordines partiū proportionabilium <lb/>interſcalariter ſe habentiū qui ordines totū corpꝰ <lb/>abſoluant: et in primo illorū ordinum vnum pedale <lb/>aliqualiter velociter augmētetur: et in ſecūdo eque <lb/>velociter: et in tertio ſimiliter. </s>
              <s xml:id="N25247" xml:space="preserve">Tūc dico /  ſi in ṗmo <lb/>ordine acquiſiuit proportionē duplam: in ſecundo <lb/>ordine acq̇ſiuit medietatē duple. </s>
              <s xml:id="N2524E" xml:space="preserve">Et in tertio quar­<lb/>tam duple. </s>
              <s xml:id="N25253" xml:space="preserve">Patet / q2 illi ordines cõtinuo. </s>
              <s xml:id="N25256" xml:space="preserve">ſe habēt <lb/>in proportione dupla q̄ eſt proportio diuiſionis: et <lb/>vniuerſaliter patet hec ↄ̨cluſio ex prima cõcluſione <lb/>ſeptimi capitis preallegata.               <anchor type="note" xlink:href="note-0214-01" xlink:label="note-0214-01a"/>               </s>
              <s xml:id="N25264" xml:space="preserve">¶ Ex quo ſequitur pri­<lb/>mo /  cõſciſa hora per partes ꝓportionales q̈uis <lb/>proportione: ſignatiſ certis ordinibus / vt dictum <lb/>eſt in cõcluſione: et in quolibet ſequēti velociꝰ aug-<lb/>mentetur aliquod corpus ꝙ̄ in p̄cedēte in ꝓportiõe <lb/>diuiſionis hore. </s>
              <s xml:id="N25271" xml:space="preserve">Tunc in quolibet illorum ordinū <lb/>tantã proportionē acquirit ſicut in prima: et ſi fue-<lb/>rint quatuor ordines: et in primo acquiſiuit ꝓpor-<lb/>tionē ſexquialterã: in omnibus illis acquiſiuit qua­<lb/>tuor ſexquialteras. </s>
              <s xml:id="N2527C" xml:space="preserve">Patet hoc correlariū / quia illi <lb/>ordines ſe habent in proportione diuiſionis hore <lb/>et in ea proportione in qua ſunt minores corpus ve­<lb/>locius augmentatur in illis: igitur tantã ꝓportio-<lb/>nem acquirit in quolibet ſequēti ſicut in primo.</s>
            </p>
            <div xml:id="N25287" level="5" n="15" type="float">
              <note position="left" xlink:href="note-0214-01a" xlink:label="note-0214-01" xml:id="N2528B" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N25291" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N25295">
              <s xml:id="N25296" xml:space="preserve">¶ Sequitur ſecūdo /  diuiſa hora quacū propor-<lb/>tionem volueris: inſtructiſ ordinibus vt in ↄ̨clu-<lb/>ſione dicitur: et aliquod corpus in quolibet ſequen­<lb/>ti ordine velocius augmētetur ꝙ̄ immediate p̄cedē­<lb/>ti in certa maiori ꝓportiõe cõtinuo ꝙ̄ ſit ꝓportio di­<lb/>uiſionis: tſtc in quolibet ſequēti maiorē proportio­<lb/>nem acquirit ꝙ̄ in primo in ea ꝓportione per quaꝫ <lb/>proportio velocitatū augmētatiõis illius ordinis <lb/>et primi excedit proportionē primi ad ip̄m: vt ſi ho­<lb/>ra diuidat̄̄ proportiõe dupla et ↄ̨ſtituant̄̄ tres ordi­<lb/>nes: et in quolibēt pedale a. in quadruplo velocius <lb/>augmētetur p̄cederte: et tunc dico /  in tertio ordine <lb/>in quadruplo maiorē proportionē acquirit ꝙ̄ ī pri­<lb/>mo q2 ꝓportio primi ad tertiū eſt quadrupla et ve-<lb/>locitas augmentatiõis in tertio ad velocitatem <lb/>augmentatiõis in primo eſt ſexdecupla / vt pꝫ intuē­<lb/>ti, ſexdecupla em̄ excedit quadruplã, ideo in q̈dru-<lb/>plo maiorē proportionē acquirit in tertio ꝙ̄ in pri­<lb/>mo: et in ſecundo in duplo maiorē proportionē quã <lb/>in primo: quia proportio eorū ordinū eſt dnpla: et <lb/>proportio velocitatū quadrupla. </s>
              <s xml:id="N252C1" xml:space="preserve">Modo quadru-<lb/>pla excedit duplam ꝑ duplã. </s>
              <s xml:id="N252C6" xml:space="preserve">Patet ꝓbatio huius               <cb chead="De motu augmentationis."/>               correlarii ex quinta propoſitione ſecundi notabi-<lb/>lis tertii capitis ſecūdi tractatus.               <anchor type="note" xlink:href="note-0214-02" xlink:label="note-0214-02a"/>               </s>
              <s xml:id="N252D3" xml:space="preserve">¶ Sequit̄̄ tertio / <lb/> partita hora per partes proportionales vna cer­<lb/>ta proportione ad libitū ſignata: cõſtructiſ ordi­<lb/>nibus quotcū horã ip̄am abſoluētibꝰ vt in cõclu­<lb/>ſione: et pedale. </s>
              <s xml:id="N252DE" xml:space="preserve">A. in prīo aliquãtulū velociter au-<lb/>geatur: et in quolibet ſequēti ī certa proportiõe mi-<lb/>nore proportiõe diuiſiõis cõtinuo velocius ꝙ̄ in im­<lb/>mediate precedenti: tunc maiorem proportionē ac­<lb/>quirit in precēti ꝙ̄ in ſequēti in ea proportione <lb/>per quã proportio ordinis precedentis ad illum or­<lb/>dinē ſequentē excedit proportionē velocitatis aug-<lb/>mentationis ſequentis et precedentis vt ſi hora di-<lb/>uidatur ꝓportione ſexquialtera et conſtituant̄̄ tres <lb/>ordines. </s>
              <s xml:id="N252F3" xml:space="preserve">Exempli gratia et in quolibet ſequente pe­<lb/>dale. </s>
              <s xml:id="N252F8" xml:space="preserve">A. in ſexquitertio velocius augmentetur ꝙ̄ in <lb/>immediate precedēte. </s>
              <s xml:id="N252FD" xml:space="preserve">Tunc dico /  in primo maio­<lb/>rem proportionem acquirit quam in tertio ordine <lb/>in ea proportione ꝑ quam proportio dupla ſexqui­<lb/>quarta qualis eſt inter primū ex tertiū excedit pro­<lb/>portionem ſuper ſeptipartientē nouas qualis eſt <lb/>inter velocitatem augmentationis tertii ordinis et <lb/>velocitatem primi: et quia proportio dupla ſexqui­<lb/>quarta excedit proportionē ſupra ſeptipartieutem <lb/>nouas per ꝓportionē ſupra decēſeptipartientem <lb/>ſexageſimas quartas. </s>
              <s xml:id="N25312" xml:space="preserve">Ideo in tali ꝓportione ma­<lb/>iorem latitudinē proportionis acquirit tale corpꝰ <lb/>in primo ordine ꝙ̄ in tertio. </s>
              <s xml:id="N25319" xml:space="preserve">Patet probatio huiꝰ <lb/>correlarii ex ſexta ꝓpoſitiõe ſecundi notabilis ter-<lb/>tii capitis ſecundi tractatꝰ preallegati. </s>
              <s xml:id="N25320" xml:space="preserve">Et ſic pote­<lb/>ris inferre infinita alia correlaria ex hac ſeptima <lb/>cõcluſione auxiliãtibus propoſitionibꝰ poſitis in <lb/>notabili preallegato.</s>
            </p>
            <div xml:id="N25329" level="5" n="16" type="float">
              <note position="right" xlink:href="note-0214-02a" xlink:label="note-0214-02" xml:id="N2532D" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N25333">
              <s xml:id="N25334" xml:space="preserve">Octaua concluſio diuiſo corpore per <lb/>partes proportionales qua volueris proportiõe <lb/>aſſumptiſ certis ordinibus partium proportio-<lb/>nabilium interſcalariter ſe habentium qui totum <lb/>corpus abſoluant: et quieſcentibus ceteris ordini-<lb/>bus vnꝰ illorū augeatur taliter  quelibet eiꝰ pars <lb/>acquirat tantam proportionem ſicut prima. </s>
              <s xml:id="N25343" xml:space="preserve">Tunc <lb/>ille ordo acquirat eam proportionem quam acqui­<lb/>rat prima pars eius: et totum corpus minorem pro­<lb/>portionē acquirit </s>
              <s xml:id="N2534C" xml:space="preserve">Quã adinuenies documētis po­<lb/>ſitis in prima parte huius operis capite ſeptimo. <lb/></s>
              <s xml:id="N25352" xml:space="preserve">Prima pars huius concluſionis. </s>
              <s xml:id="N25355" xml:space="preserve">patet ex quinta <lb/>concluſione huius / et ſecunda patet ex tertia cõclu-<lb/>ſione capitis in ea allegati. </s>
              <s xml:id="N2535C" xml:space="preserve">Applica ſi potes.</s>
            </p>
            <p xml:id="N2535F">
              <s xml:id="N25360" xml:space="preserve">Nona concluſio </s>
              <s xml:id="N25363" xml:space="preserve">Diuiſa hora per par­<lb/>tes proportionales qua volueris proportione: et <lb/>in prima a. pedale aliquantulum velociter augea-<lb/>tur: et in ſecunda in duplo velocius: et in tertia in <lb/>triplo ꝙ̄ in prima: et in quarta in quadruplo ꝙ̄ in <lb/>prima: et ſic conſequenter: tunc illud pedale in illa <lb/>hora acquirit maiorem proportionem ꝙ̄ in prima <lb/>parte probortionali hore in proportione duplica­<lb/>ta ad ꝓportionē in qua ſe habet tota illa hora ſic <lb/>diuiſa ad primam partem eius proportionalē. </s>
              <s xml:id="N25378" xml:space="preserve">vt <lb/>diuiſa hora per partes proportionales proportio­<lb/>ne ſexquialtera: et augmentato pedali vt ponitur ī <lb/>concluſione. </s>
              <s xml:id="N25381" xml:space="preserve">Dico /  in tota illa hora illud pedale <lb/>acquirit maiorē proportionē ī nouocuplo ꝙ̄ in pri­<lb/>ma parte proportionali. </s>
              <s xml:id="N25388" xml:space="preserve">Quoniam hora diuiſa <lb/>per partes proportiones proportione ſexquialte-<lb/>ra ſe habet ad primã partē proportionalem pro-<lb/>portionē triplã: et proportio dupla ad triplam eſt <lb/>nouocupla. </s>
              <s xml:id="N25393" xml:space="preserve">Probatur hec concluſio. </s>
              <s xml:id="N25396" xml:space="preserve">¶ Supponē-<lb/>do primo /  ſi in hora diuiſa quauis proportione               <pb chead="Tertii tractatus" file="0215" n="215"/>               volueris cõtinuo illud corpus augeretur ita veloci­<lb/>ter ſicut in prima parte proportionali: in ea ꝓpor-<lb/>tione qua aliqua pars eſt minor prima: in ea mi-<lb/>norem proportionē acquireret in illa quam in pri-<lb/>ma. </s>
              <s xml:id="N253A8" xml:space="preserve">hec ſuppoſitio ex ſe conſtat. </s>
              <s xml:id="N253AB" xml:space="preserve">¶ Secunda ſuppo-<lb/>ſitio. </s>
              <s xml:id="N253B0" xml:space="preserve">Quando iſtud corpus augmentatur in hora <lb/>ſic diuiſa / vt ponitur in concluſione duas propor-<lb/>tiones equales acquirit in ſecunda parte ꝓportio­<lb/>nali equales īquaꝫ illi quã acquireret ſi moueretur <lb/>equeuelociter in ea ſicut in prima quoniam moue-<lb/>tur in duplo velocius ꝙ̄ tunc: et in tertia tres equa-<lb/>les illi quã acquireret ſi moueretur eque velociter <lb/>ſicut in prima: et in quarta quatuor equales illi ̄ <lb/>acquireret ſi moueretur eque velociter ſicut ī prima <lb/>quia modo in quadruplo velocius mouetur ꝙ̄ tunc / <lb/>et ſic in infinitum. </s>
              <s xml:id="N253C7" xml:space="preserve">¶ Tertia ſuppoſitio ſequens ex <lb/>his duabus. </s>
              <s xml:id="N253CC" xml:space="preserve">In caſu concluſionis proportio acqui­<lb/>ſita in prima parte ꝓportionali ſe habet ad vtrã <lb/>illarū duarū acquiſitarū in ſcḋa in proportiõe di-<lb/>uiſionis: et vtra de hiis duabus acquiſitis in ſecū­<lb/>da ad quãlibet illarū triū acquiſitarū in tertia ſe-<lb/>habet etiam in eadem proportione diuiſiõis: et ſic <lb/>conſequēter. </s>
              <s xml:id="N253DB" xml:space="preserve">Patet hec ex prīa ſuppoſitione. </s>
              <s xml:id="N253DE" xml:space="preserve">¶ Ex <lb/>quibus ſequitur /  ibi ſunt infiniti ordines infinito­<lb/>rum continuo ſe habentium in proportiõe diuiſio-<lb/>nis. </s>
              <s xml:id="N253E7" xml:space="preserve">pro primi em̄ ordiuis prima parte capias pro­<lb/>portionem acquiſitam in prima parte proportio-<lb/>nali: et pro ſecunda parte vnã acquiſitarū in ſcḋa <lb/>et pro tertia vnã acquiſitarū in tertia / et ſic in infi-<lb/>nitū. </s>
              <s xml:id="N253F2" xml:space="preserve">Et ꝓ ſecundi ordinis prima parte capias al-<lb/>teram acquiſitam in ſecūda et vnam de acquiſitis <lb/>in tertia pro ſecunda parte illius ſecundi ordinis: <lb/>et pro tertia parte vnã de acquiſitis in quarta: et <lb/>ſic in infinitū. </s>
              <s xml:id="N253FD" xml:space="preserve">Et pro tertii ordinis prima parte ca­<lb/>pias vnam de acquiſitis in tertia que adhuc non <lb/>eſt accepta: et pro ſecūda vnam de acquiſitis ī quar­<lb/>ta / et ſic cõſequenter: ita  nulla maneat acquiſita <lb/>in aliqua parte proportiõali quin ſit aliqua pars <lb/>alicuius illorū ordinū: et manifeſtum eſt  ibi erūt <lb/>infiniti ordines continuo ſe habentes in proportio­<lb/>ne diuiſionis q2 ſemper partes eoꝝ ſe habent adin-<lb/>uicem continuo in proportione diuiſionis: et omni­<lb/>um illorum prime partes etiam ſe habent in ꝓpor­<lb/>tione diuiſionis: et ſecunde: et tertie: et quarte: et ſic <lb/>ſine fine: igitur illi ordines cõtinuo ſe habent in ꝓ-<lb/>portione diuiſionis. </s>
              <s xml:id="N25418" xml:space="preserve">Iam hec ↄ̨ſequentia antea de­<lb/>ducta eſt: et per cõſequens aggregatum ex omnibꝰ <lb/>illis ordinibus ſe habet ad primū illorum in ea ꝓ-<lb/>portione qua ſe habet tota hora diuiſa ad primaꝫ <lb/>partem ꝓportionalem: et primus illorum ordinum <lb/>ſe habet etiam ad primã eius partem que eſt ꝓpor­<lb/>tio acquiſita in prima parte hore etiam in propor­<lb/>tione diuiſionis: igitur aggregatū ex omnibus il-<lb/>lis ordinibus quod eſt proportio acquiſita in tota <lb/>hora ipſi corpori ſe habet ad proportionē acquiſi-<lb/>tam in prima parte ꝓportionali in proportiõe du­<lb/>pla ad proportionem in qua ſe habet tota hora ſic <lb/>diuiſa ad primam eius partem proportionalem.</s>
            </p>
            <p xml:id="N25433">
              <s xml:id="N25434" xml:space="preserve">Patet conſequentia: quia ibi ſunt tres termini cõ­<lb/>tinuo proportionabiles tali proportione quorum <lb/>primus et maximus eſt aggregatum ex omnibꝰ il-<lb/>lis ordininibus: et ſecūdus primus illorū ordinum: et <lb/>tertius proportio acquiſita ī prima parte propor-<lb/>tionali hore: igitur ibi eſt proportio dublicata / vt <lb/>patet intuenti. </s>
              <s xml:id="N25443" xml:space="preserve">Multe alie concluſiones et correla-<lb/>ria ex hac imaginatione et induſtria horū ordinuꝫ <lb/>poſſunt inferri materiam ampliãdo que omnia fa­<lb/>cile inducūtur ex dictis.               <anchor type="note" xlink:href="note-0215-01" xlink:label="note-0215-01a"/>               </s>
              <s xml:id="N25451" xml:space="preserve">Prīcipiuꝫ em̄ pluſ̄ dimi-<lb/>dium totius eſſe videtur ex primis Ethicorum. </s>
              <s xml:id="N25456" xml:space="preserve">Et ce­               <cb chead="Capi. ſecundum"/>               li et mundi: et ex elenchorum et metaphiſices ſecun-<lb/>dis. </s>
              <s xml:id="N2545E" xml:space="preserve">Quandoquidem hiis que circa materiam de <lb/>motu locali difformi quoad tēpus diligēter inſpe­<lb/>ctis facile proprio marte educentur cõcluſiones in <lb/>numere: quoniam omnes que ibi inducuntur mu-<lb/>tatis mutandis hic inferri valent.               <anchor type="note" xlink:href="note-0215-02" xlink:label="note-0215-02a"/>               </s>
              <s xml:id="N2546E" xml:space="preserve">¶ Deinde ponē­<lb/>de ſunt alique cõcluſiones que ex poſitione ſecūda <lb/>naſcuntur. </s>
              <s xml:id="N25475" xml:space="preserve">Prima concluſio: nullū quadratū cuiꝰ <lb/>omnia latera ſunt equalia ſiue ſuperficiale ſit ſine <lb/>ſolidum: poteſt vniformiter ad non quantum dimi-<lb/>nui: vtra eius dimenſione vniformiter ad nõ ̄tū <lb/>diminuta. </s>
              <s xml:id="N25480" xml:space="preserve">Hec concluſio patet ex deductione octa-<lb/>ui argumenti. </s>
              <s xml:id="N25485" xml:space="preserve">Et hanc cõcluſionem ſane intelligas <lb/>capiendo ly poteſt in ſenſu compoſito. </s>
              <s xml:id="N2548A" xml:space="preserve">¶ Ex hac cõ­<lb/>cluſiõe ſequitur /  ſi aliquod quadratuꝫ a non ̄to <lb/>incipit continuo vniformiter acquirere longitudi-<lb/>nem latitudinem et profunditatem: ip̄m infinite tar­<lb/>de incipit augeri. </s>
              <s xml:id="N25495" xml:space="preserve">Probatur / quoniam incipit con­<lb/>tinuo acquirere proportionem octuplam in quali-<lb/>bet parte proportionali proportiõe dupla: igitur <lb/>incipit in infinitum tarde acquirere de quãtitate. <lb/></s>
              <s xml:id="N2549F" xml:space="preserve">Patet conſequentia ex ſecunda confirmatione ſe-<lb/>cundi argumēti huius. </s>
              <s xml:id="N254A4" xml:space="preserve">Probatur antecedēs / quia <lb/>in via dimunitionis quando continuo in qualibet <lb/>parte proportionali dupla proportione latitudo <lb/>longitudo et profunditas perdunt proportionem <lb/>duplam: tunc totum quadratum perdit proportio­<lb/>nem octuplam: g̊ in via augmentationis econuerſo <lb/>augmentando in qualibet parte proportionali ꝓ-<lb/>portione dupla acquiret octuplam proportionem <lb/>illud quadratuꝫ: quod fuit probandū. </s>
              <s xml:id="N254B7" xml:space="preserve">¶ Sequitur <lb/>ſecundo:  ſi a non quanto aliquod quadratū in-<lb/>cipit vniformiter augeri: ſua latitudo et longitudo <lb/>incipiunt infinite velociter augeri. </s>
              <s xml:id="N254C0" xml:space="preserve">Probatur / quia <lb/>longitudo et latitudo incipiunt acquirere in parte <lb/>proportionali pcoportione dupla minorem ꝓpor­<lb/>tionē dupla. </s>
              <s xml:id="N254C9" xml:space="preserve">igitur longitudo et latitudo illiꝰ qua-<lb/>drati incipiunt in infinitū velociter augeri. </s>
              <s xml:id="N254CE" xml:space="preserve">Patet <lb/>hec conſequentia ex ſecunda confirmatione prealle­<lb/>gata. </s>
              <s xml:id="N254D5" xml:space="preserve">Probatur antecedēs / quoniã non augeutur <lb/>hee dimenſiones in proportione dupla: quia tunc <lb/>quadratum non vniformiter augeretur / vt patꝫ ex <lb/>priori correlario: nec in maiori dupla: q2 tunc etiã <lb/>quadratum in maiori quadrupla augeretur: et ſic <lb/>non augeretur vniformiter / vt cõſtat: igitur ille di-<lb/>menſiones in maiori proportiõe dupla augentur <lb/>in partibus proportionalibus temporis propor-<lb/>tione dupla: quod fuit probanduꝫ. </s>
              <s xml:id="N254E8" xml:space="preserve">¶ Sequitur ter­<lb/>tio /  ſi aliquod quadratum incipit a non quanto <lb/>augeri: et in qualibet parte proportionali propor­<lb/>tione dupla ipſius temporis acquirat proportio-<lb/>nem minorem dupla: ipſum incipit infinite veloci-<lb/>ter augeri: et quelibet eius dimenſio incipit in infi-<lb/>nitum velociter augeri: et tamē incipit quelibet eiꝰ <lb/>dimenſio in infinitum velocius augeri ꝙ̄ ip̄m qua-<lb/>dratum. </s>
              <s xml:id="N254FB" xml:space="preserve">Patet hoc correlariuꝫ facile ex ſecunda cõ­<lb/>firmatiõe predicta: hoc addito  ſemper in tali ca-<lb/>ſu quadratum incipit maiorem proportionem ac-<lb/>quirere ꝙ̄ aliqua eius dimēſio / vt patet ex deductio­<lb/>ne octaui argumenti huius paucis facillimis ad-<lb/>ditis.</s>
            </p>
            <div xml:id="N25508" level="5" n="17" type="float">
              <note position="left" xlink:href="note-0215-01a" xlink:label="note-0215-01" xml:id="N2550C" xml:space="preserve">Pḣs .1°. <lb/>ethi. et ce­<lb/>li et mū. et <lb/>elēchoꝝ et <lb/>metha. 2.</note>
              <note position="right" xlink:href="note-0215-02a" xlink:label="note-0215-02" xml:id="N2551A" xml:space="preserve">Cõcluſio­<lb/>nes .2. po­<lb/>ſitionis.</note>
            </div>
            <p xml:id="N25524">
              <s xml:id="N25525" xml:space="preserve">Secunda concluſio ſtat /  a. corpus <lb/>incipit in infinitum velociter augeri et infinite tar-<lb/>de: et vniformiter patet hec concluſio ex deductio-<lb/>ne replice octaui argumenti. </s>
              <s xml:id="N2552E" xml:space="preserve">In hac materia poſ-<lb/>ſunt induci omnes ille concluſiones que indu-<lb/>cte et probate fuerunt tractatu ſecundo capite ter-<lb/>tio de motu locali difformi quoad tēpus. </s>
              <s xml:id="N25537" xml:space="preserve">Uideas <lb/>ibi Cõcluſionibus expeditis et conſequenti ſecun-               <pb chead="De motu augmentationis." file="0216" n="216"/>               da par queſtionis noſtre reſtat ad dubia accedamꝰ</s>
            </p>
            <p xml:id="N25541">
              <s xml:id="N25542" xml:space="preserve">Dubitatur primo. </s>
              <s xml:id="N25545" xml:space="preserve">An ſecundū primã <lb/>opinionem vndecima: duodecima: et tredecima cõ-<lb/>cluſiones calculatoris in capitulo de augmentatio­<lb/>ne ſint concedēde: et an proobationes earum quas <lb/>ipſe calculator adduxit cõcludant et ſint efficaces.</s>
            </p>
            <p xml:id="N25550">
              <s xml:id="N25551" xml:space="preserve">Dubitatur ſecūdo / an ille eedem ſint <lb/>concedende ſecundum poſteriorem opinionem.</s>
            </p>
            <p xml:id="N25556">
              <s xml:id="N25557" xml:space="preserve">Dubitatur tertio / an iuxta ſecūdū op-<lb/>pinionē aliquid poſſit per totum diminui.</s>
            </p>
            <p xml:id="N2555C">
              <s xml:id="N2555D" xml:space="preserve">¶ Ad primū accedendo probo primo /  probatio <lb/>calculatoris ad vndecimã concluſionem nõ valeat <lb/>ſaltem in caſu ſuo: quia in illo caſu illa concluſio <lb/>eſt falſa: igitur non probat eam in tali caſu. </s>
              <s xml:id="N25566" xml:space="preserve">Pro­<lb/>batur antecedēs: quia ipſe ponit caſum  infinita <lb/>incipiant augeri a non quanto: et incipiat primum <lb/>in duplo velocius augeri ſecundo: et ſecundū in du-<lb/>plo velocius tertio: et tertiū quarto: et ſic conſequē­<lb/>ter: in caſu iſta propoſito eſt falſa: in infinitum ve­<lb/>lociter incipit aliquod augeri quod iu infinitū tar­<lb/>de incipit augeri. </s>
              <s xml:id="N25577" xml:space="preserve">Probatur / quia bene ſequitur in­<lb/>finite velociter incipit aliquod iſtoruꝫ augeri quod <lb/>infinite tarde incipit augeri ergo poſt inſtans qḋ <lb/>eſt preſens infinitum velociter augebitur quod in­<lb/>finitum tarde incipit augeri: et ꝑ cõſequēs poſt hoc <lb/>aliqualiter velociter aliquod iſtorum augebit̄̄ qḋ <lb/>infinite tarde incipit augeri: conſequens eſt falſuꝫ / <lb/>igitur et antecedens. </s>
              <s xml:id="N25588" xml:space="preserve">Conſequentie ſunt note et pro­<lb/>batur falſitas conſequentis / quia nullū infinite tar­<lb/>de incipit augeri / vt patet intuenti caſum: igitur.</s>
            </p>
            <p xml:id="N2558F">
              <s xml:id="N25590" xml:space="preserve">¶ Secundo arguitur / ꝓbando inefficaciam proba­<lb/>tionis qua ipſe calculator probat duodecimã con-<lb/>cluſionē. </s>
              <s xml:id="N25597" xml:space="preserve">Ad eam em̄ probandam inducit calcula-<lb/>tor talem caſum ſint infinita quãta quorum primū <lb/>ſit aliquantū: et ſecūdū in quadruplo maius ꝙ̄ pri­<lb/>mū: et tertiū in quadruplo maius ꝙ̄ ſecundū: et ſic <lb/>in infinitū: et augeatur primū aliqualiter velociter <lb/>et ſecundū in duplo minus: et tertiū in duplo minꝰ <lb/>̄ ſecundū: et ſic in infinitum: tunc dicit primã par-<lb/>tem concluſionis ſequi. </s>
              <s xml:id="N255A8" xml:space="preserve">videlicet infinitum tarde <lb/>incipit augeri quod infinitam quãtitatem incipit <lb/>acquirere quia vt inquit: ſecundum in duplo maio­<lb/>rem ̄titatē acquirit ꝙ̄ primū: et tertiuꝫ ꝙ̄ ſecundū / <lb/>et ſic cõſequenter. </s>
              <s xml:id="N255B3" xml:space="preserve">Ad quod probãdū facit hanc cõ­<lb/>ſequentiã: ſi primū illorū preciſe eque velociter au-<lb/>geretur ſicut ſecūdū. </s>
              <s xml:id="N255BA" xml:space="preserve">Secundū in quadruplo velo-<lb/>cius acquireret de quantitate quam primū: ſꝫ nūc <lb/>in duplo velocius incipit primū acquirere de quãti­<lb/>tate quã tnnc: ergo in duplo velocius incipit ſcḋm <lb/>acquirere de quantitate ꝙ̄ primū: et ſic tertiū in du­<lb/>plo velocius ſecūdo: et ſic in infinitū: et per conſe-<lb/>quens ante quodcun inſtans infinita quantitas <lb/>erit acquiſita alicui illorum: et ſic infinitam quan-<lb/>titatem incipit aliquod illoruꝫ acquirere. </s>
              <s xml:id="N255CD" xml:space="preserve">Sed hec <lb/>ratio eſt inefficax quia conſequentia illa quã facit <lb/>nichil valet videlicet hec. </s>
              <s xml:id="N255D4" xml:space="preserve">Si primū eque velociter <lb/>preciſe augeretur ſic ſecundū. </s>
              <s xml:id="N255D9" xml:space="preserve">Secūdum in quadru­<lb/>plo velocius acquireret de quantitate ꝙ̄ primū: ſed <lb/>nunc puta in caſu in duplo velocius incipit primuꝫ <lb/>acquirere de quantitate quã tunc: igitur in duplo <lb/>velocius incipit ſecundū acquirere de quãtitate ̄ <lb/>primum. </s>
              <s xml:id="N255E6" xml:space="preserve">QꝪ autem illa conſequentia nichil valet: <lb/>patet / quia illius conſequentie antecedens eſt verū <lb/>in caſu et conſequens falſum: igitur illa nichil va-<lb/>let. </s>
              <s xml:id="N255EF" xml:space="preserve">Probaiur antecedens: et pono /  in illo caſu <lb/>primum illorum in vna hora acquirat proportio-               <cb chead="De motu augmentationis."/>               nem ſexdecuplam: et ſit illud primū vnum pedale <lb/>et ſecundum in eadem hora acquirat quadruplam <lb/>quod quidem ſecundum eſt quadrupedale. </s>
              <s xml:id="N255FB" xml:space="preserve">quo po-<lb/>ſito antecedens eſt verum et conſequens: igitur con­<lb/>ſequentia nulla. </s>
              <s xml:id="N25602" xml:space="preserve">QꝪ autem antecedens ſit verū pa-<lb/>tet. </s>
              <s xml:id="N25607" xml:space="preserve">quia maior eſt neceſſaria vt conſtat et minor in <lb/>caſu noſtro vera. </s>
              <s xml:id="N2560C" xml:space="preserve">quia incipit in duplo maiorē pro­<lb/>portionem acquirere ꝙ̄ tunc: et continuo in duplo <lb/>maiorem acquiret ꝙ̄ tunc: et ſic continuo in duplo <lb/>maiorem quantitatem acquirit ꝙ̄ tunc: et per con-<lb/>ſequens totum antecedens eſt verum. </s>
              <s xml:id="N25617" xml:space="preserve">Sed iam pro­<lb/>bo falſitatem falſitatē conſequentis quia in quoli­<lb/>bet inſtanti illius hore: primo erit acquiſita maior <lb/>quantitas ꝙ̄ ſubdupla ad quantitatem acquiſitaꝫ <lb/>ipſi ſecundo: igitur in nullo tali inſtanti erit acqui­<lb/>ſita ſecundo dupla quantitas ad quãtitateꝫ acqui­<lb/>ſitam primo: et per cõſequens non incipit in duplo <lb/>velocius acquirere de quantitate ꝙ̄ primū: ex quo­<lb/>nunquam quantitas acquiſita ſecundo erit in du-<lb/>plo maior quam quantitas acquiſita primo. </s>
              <s xml:id="N2562C" xml:space="preserve">Sed <lb/>iam probo /  in quolibet inſtãti illius hore primo <lb/>erit acquiſita maior quautitas ꝙ̄ ſubdupla ad quã­<lb/>titatem acquiſitam primo: quia quocun inſtanti <lb/>dato ſi primū continuo eque velociter augeretur cū <lb/>ſecundo ipſum primum in tali inſtanti haberet ac-<lb/>quiſitam quantitatē ſubquadruplam ad quantita­<lb/>tem acquiſitam ſecundo: ſꝫ modo ſuper illã quanti­<lb/>tatem adhuc acquiſiuit tantam proportionem ſi-<lb/>cut acquiſiuit tunc acquirendo illam quantitatem / <lb/>ergo ſuper illam quantitatem acquiſitam adhuc <lb/>acquiſiuit maioreꝫ illa acquiſita: et ꝑ ↄ̨ñs in tali <lb/>inſtanti quantitas acquiſita eſt maior ꝙ̄ ſubdupla <lb/>ad quantitatem acquiſitam ſecundo / quod fuit pro­<lb/>bandum. </s>
              <s xml:id="N2564B" xml:space="preserve">Patet conſequentia: quia ſi preciſe acqui­<lb/>ſiuiſſet vſ ad illuod inſtans tantam proportionē <lb/>ſicut ſecundū: et ſuper illam ſubquadruplã quanti-<lb/>tatem acquiſitam acquiſiuiſſet adhuc tantam pre-<lb/>ciſe: quantitas ei acquiſita manſiſſet ſubdupla ad <lb/>quantitatem acquiſitam ſecundo: ſed modo in illo <lb/>inſtanti ſuper illa quantitate ſubquadrupla ipſuꝫ <lb/>primū acquirit maiorē: quia acquirit tantam pro­<lb/>portionē ſicut antea et eſt maius: ergo quãtitas ſub­<lb/>dupla ei acquiſita eſt maior ꝙ̄ ſubdupla ad quan-<lb/>titatem acquiſitam ſecundo / qḋ fuit probandum. <lb/></s>
              <s xml:id="N25663" xml:space="preserve">Item ad probandam ſecundam partem eiuſdē cõ-<lb/>cluſionis facit calculator talem conſequētiam. </s>
              <s xml:id="N25668" xml:space="preserve">Si <lb/>primū aliquorum continuo ſe habentium in ꝓpor-<lb/>tione ſubquadrupla puta quorū primū ſit vt qua-<lb/>tuor et ſecundum vt vnum: tertium vt vna quarta: <lb/>et ſic in infinitur eque velociter diminueretur ſicut <lb/>ſecundum in quadruplo velocius deꝑderet de quã-<lb/>titate quam ſecūdum: ſed nunc in duplo tardius in­<lb/>cipit primū deperdere de qqãtitate ꝙ̄ tunc: ergo in <lb/>duplo velocius incipit primum deperdere de quã-<lb/>titate ꝙ̄ ſcḋm. </s>
              <s xml:id="N2567D" xml:space="preserve">Et hec cõſequentia etiaꝫ nichil valet <lb/>quia primū ſpemper deperdit maiorem quantita-<lb/>tem ꝙ̄ duplã ad quãtitatem deperditam a ſecundo <lb/></s>
              <s xml:id="N25685" xml:space="preserve">¶ Ad iſtud dubiū </s>
              <s xml:id="N25688" xml:space="preserve">Reſpondeo ponendo aliquas ꝓ­<lb/>poſitiones. </s>
              <s xml:id="N2568D" xml:space="preserve">¶ Prīa propoſito. </s>
              <s xml:id="N25690" xml:space="preserve">Probationes vnde­<lb/>cime et duodecime concluſiõis calculatoris ſunt in <lb/>efficaces. </s>
              <s xml:id="N25697" xml:space="preserve">Patet hoc ex argumentis nuꝑrime fctīs <lb/></s>
              <s xml:id="N2569B" xml:space="preserve">¶ Secūda ꝓpoſitio </s>
              <s xml:id="N2569E" xml:space="preserve">Ille concluſiones vndecima vi­<lb/>delicet et duodecima in caſibus ibi poſitis ſi ſumã­<lb/>tur in ſenſu cathegorico ſunt falſe. </s>
              <s xml:id="N256A5" xml:space="preserve">Probatur de <lb/>vndecima ex primo argumento contra dubium: de <lb/>duodecima etiam probatur /  ipſa in caſu ibi poſi­<lb/>to ſit falſa: qua nullū illorum corporum infinitam <lb/>quantitatem incipit acquirere: igitur non in infi­               <pb chead="Tertii tractatus" file="0217" n="217"/>              tum tarde incipit aliquod illorum augeri quod in­<lb/>finitã quantitatē acquirere incipit. </s>
              <s xml:id="N256B7" xml:space="preserve">¶ Tertia pro-<lb/>poſitio ille concluſiones capiūtur a calculatore in <lb/>ſenſu hypotetico. </s>
              <s xml:id="N256BE" xml:space="preserve">Ita  ſenſus primi ſit. </s>
              <s xml:id="N256C1" xml:space="preserve">incipit in­<lb/>finitum velociter aliquod iſtorū: et incipit in <lb/>infinitum tarde augeri aliquod iſtorū: et ſenſus ſe-<lb/>cunde ſit iſte incipit infinitū tarde aliquod iſtorum <lb/>augeri: et incipit aliquod eorum infinitam quanti-<lb/>tatē acquirere etc̈. </s>
              <s xml:id="N256CE" xml:space="preserve">¶ Quarta propoſito. </s>
              <s xml:id="N256D1" xml:space="preserve">quelibet <lb/>illarum trium concluſionuꝫ debet tan̄ poſſibilis <lb/>ſecundum hanc primam poſitionem cõcedi. </s>
              <s xml:id="N256D8" xml:space="preserve">Et pri-<lb/>ma puta vndecima. </s>
              <s xml:id="N256DD" xml:space="preserve">Probatur ponendo /  ſit vnuꝫ <lb/>pedale et diuiſa hora per partes proportionales <lb/>proportione dupla. </s>
              <s xml:id="N256E4" xml:space="preserve">Uolo /  in qualibet impari de­<lb/>perdat proportionē octuplam: et in qualibet pari <lb/>ſexq̇alterã vſ ad nõ quãtū: et mãifeſtuꝫ ē /  ī īfinitū <lb/>tarde diminuet̄̄ ī partibus imparibus et in infinitū <lb/>velociter in paribus: volo igitur /  eocontra a non <lb/>quanto incipiat augeri omnino eodem modo quo <lb/>poſito in via augmentationis ſequitur concluſio. <lb/></s>
              <s xml:id="N256F4" xml:space="preserve">¶ Secunda concluſio / que eſt duodecima probatur <lb/>caſu poſito /  aliquod corpus incipit augeri a non <lb/>quanto taliter  in qualibet parte impari acqui-<lb/>rat infinitam quantitatem ſincathegoreumatice: <lb/>et in fine talis partis redigatur ad certã quantita­<lb/>tem finitã ſubito: in qualibet vero pari acquirat ꝓ­<lb/>portionem octuplam quo poſito ſequitur conclu-<lb/>ſio pro prima parte: et ſcḋa ꝓbatur ponendo /  ſint <lb/>infinita continuo ſe habentia in proportiõe dupla <lb/>deſcendendo que in qualibet parte proportionali <lb/>huius hore deperdant proportionem duplam vſ <lb/>ad non quantum: et deinde incipiant eo modo au-<lb/>geri a non quanto. </s>
              <s xml:id="N2570F" xml:space="preserve">Quo poſito patet cõcluſiõis ſe­<lb/>cunda pars dūmodo equiualeat huic: incipit infi-<lb/>uitum velociter aliquod iſtorum augeri. </s>
              <s xml:id="N25716" xml:space="preserve">et incipit <lb/>infinitum tarde continuo aliquod illorum acquire­<lb/>re de quantitate. </s>
              <s xml:id="N2571D" xml:space="preserve">¶ Tertia concluſio / que eſt tredeci­<lb/>ma calculatoris bene ab eo ꝓbata eſt ̄uis uõnū̄ <lb/>abutatur ordine terminorum in eius probatiõe di­<lb/>cendo aliquid illius ordinis fiet ſubito infinitum <lb/>cum deberet dicere infinitū fiet ſubito aliquid illiꝰ <lb/>ordinis etc̈. </s>
              <s xml:id="N2572A" xml:space="preserve">Et per hoc patet reſponſio ad dubium</s>
            </p>
            <p xml:id="N2572D">
              <s xml:id="N2572E" xml:space="preserve">Ad ſecundum dubium reſpondeo po­<lb/>nendo aliquas propoſitiones. </s>
              <s xml:id="N25733" xml:space="preserve">Prima propoſitio <lb/>vndecima cõcluſio calculatoris concedenda eſt ſecū­<lb/>dum opinionem ſecūdam </s>
              <s xml:id="N2573A" xml:space="preserve">Patet hec propoſitio in <lb/>caſu poſito ad probationem eius ſecundū prioreꝫ <lb/>opinionem in dubio precedēti: poſito  in partibꝰ <lb/>in quibus perdit proportionem octuplam ſemper <lb/>ita ſe habeat ac ſi in aliis nichil acquireret.</s>
            </p>
            <p xml:id="N25745">
              <s xml:id="N25746" xml:space="preserve">¶ Secunda propoſitio. </s>
              <s xml:id="N25749" xml:space="preserve">Prima pars duodecime <lb/>concluſionis iuxta opinionem ſecūdam conceden-<lb/>da eſt: in caſu poſito  redigatur in cuiuſlibet par­<lb/>tis imparis principio ad illam quãtitatē quã pre-<lb/>ciſe haberet ſi tantūmodo augeretur in partibus <lb/>paribus acquirendo proportionem octuplam.</s>
            </p>
            <p xml:id="N25756">
              <s xml:id="N25757" xml:space="preserve">¶ Tertia propoſitio. </s>
              <s xml:id="N2575A" xml:space="preserve">Trideciã concluſio etiam cõ-<lb/>cedenda eſt ſed non oportet  concedatur in ſenſu <lb/>conditionali: poſito caſu ſicut ibideꝫ ponitur. </s>
              <s xml:id="N25761" xml:space="preserve">Hoc <lb/>addito /  quodlibet illorum in qualibet parte im-<lb/>pari infinitam quantitatē acquirat: et in qualibet <lb/>pari acquirat proportionem octuplam: et fiat diui­<lb/>ſio temporis proportione dupla. </s>
              <s xml:id="N2576C" xml:space="preserve">Ita tamen ſe ha­<lb/>beat in partibus paribus ac ſi preciſe in illis aug-<lb/>mentaretur. </s>
              <s xml:id="N25773" xml:space="preserve">Et in eodē patet ſecunda pars ſemo-<lb/>uendo ly cõtinuo. </s>
              <s xml:id="N25778" xml:space="preserve">Facile tamē eſt verificare illaꝫ cõ-<lb/>cluſionem ad ſenſum doctoris manente ly cõtinuo <lb/></s>
              <s xml:id="N2577E" xml:space="preserve">Sed iſta ſufficiant pro dubii ſolutione. </s>
              <s xml:id="N25781" xml:space="preserve">Tu ipſe ꝓ-               <cb chead="Capi. ſecundum"/>               pria minerua plura adiicias.</s>
            </p>
            <p xml:id="N25787">
              <s xml:id="N25788" xml:space="preserve">Ad tertiū dubiū reſpõdeo breuiter di­<lb/>ſtinguendo aut illa diminutio fit per condenſatio­<lb/>nem tantum: aut per corruptionē partium ꝑ totum <lb/></s>
              <s xml:id="N25790" xml:space="preserve">Si per condenſationē dubiū eſt bene poſſibile. </s>
              <s xml:id="N25793" xml:space="preserve">Si <lb/>vero per partium corruptionē dubium eſt impoſſi­<lb/>bile: vt bene probat argumentum calculatoris ca-<lb/>pitulo de augmentione verſus finē. </s>
              <s xml:id="N2579C" xml:space="preserve">His poſitis fit.</s>
            </p>
            <p xml:id="N2579F">
              <s xml:id="N257A0" xml:space="preserve">Concluſio reſponſiua huius principa­<lb/>lis cõcluſionis. </s>
              <s xml:id="N257A5" xml:space="preserve">Utra illarum poſitionum de mo­<lb/>tus augmentationis velocitate ſua probilitate ful­<lb/>citur. </s>
              <s xml:id="N257AC" xml:space="preserve">Patet hec ↄ̨cluſio ex ſuperius dictis: et ex his <lb/>que inferius dicentur in argumētorū ſolutionibꝰ.</s>
            </p>
            <p xml:id="N257B1">
              <s xml:id="N257B2" xml:space="preserve">Ad rationes ante oppoſitum. </s>
              <s xml:id="N257B5" xml:space="preserve">Ad pri-<lb/>mam reſponſum eſt ibi vſ ad vltimam replicã ad <lb/>quam reſpondeo cõcedendo illatum vt argumentū <lb/>bene probat ipſum eſſe concedendum. </s>
              <s xml:id="N257BE" xml:space="preserve">Et quia argu­<lb/>mentum in principio ſui videtur querere: an quan-<lb/>do vnum pedale ſecundum eius medietatem perdit <lb/>vnam octauam et ſecundū aliam acquirit vnã quar­<lb/>tam: an concedendum ſit ipſum deperdere aliquaꝫ <lb/>quantitatem. </s>
              <s xml:id="N257CB" xml:space="preserve">¶ Ad quod reſpondeo breuiter /  nõ <lb/>ſed ſimpliciter eſt concedendum quod illud pedale <lb/>acquirit quantitatē: quia quantitas acquiſita vni <lb/>parti excedit quantitatem deperditam ab altera <lb/>parte: et in tali caſu tantam quantitatem acquirit <lb/>illud pedale per quantam quantitas acquiſita vni <lb/>parti excedit quantitatem deperditam ab altera. <lb/></s>
              <s xml:id="N257DB" xml:space="preserve">Et ſi dicas contra demonſtrata quantitate quã de­<lb/>perdit qua pars pedalis. </s>
              <s xml:id="N257E0" xml:space="preserve">arguitur ſic. </s>
              <s xml:id="N257E3" xml:space="preserve">Hec deper­<lb/>dit iſtud pedale: et hoc eſt aliqua quantitas: ergo <lb/>aliquam quantitateꝫ deperdit hoc pedale </s>
              <s xml:id="N257EA" xml:space="preserve">Dico /  <lb/>aliquam quantitateꝫ deperdit hoc pedale: et tamē <lb/>non deperdit aliquam quantitatem: ſicut in rarefa­<lb/>ctione dicimus /  corpus acquirit maiorem quan-<lb/>titatem. </s>
              <s xml:id="N257F5" xml:space="preserve">hoc eſt efficitur maius: et tamen nullã quã-<lb/>titatem acquirit quia nichil acquirit.</s>
            </p>
            <p xml:id="N257FA">
              <s xml:id="N257FB" xml:space="preserve">Ad ſecūdam rationem reſponſum eſt / <lb/>ibi vſ ad vltimam ad quam rñdeo concedendo il­<lb/>latum: vt bene probat argumentum: et uegãdo fal­<lb/>ſitatem conſequentis: et cum probatur concedendo <lb/>illud quod infertur vt poſtea probatur in ſequenti­<lb/>bus confirmationibus. </s>
              <s xml:id="N25808" xml:space="preserve">¶ Ad primam confirmatio­<lb/>nem reſponſum eſt ibi vſ ad replicã: ad quam re-<lb/>ſpondeo concedendo conſequens: et negando  ſit <lb/>falſum et cum probatur </s>
              <s xml:id="N25811" xml:space="preserve">Nego iterum falſitatem <lb/>conſequentis: et ad probationem falſitatis illius <lb/>conſequentis: concedo ſequelam: et nego falſitateꝫ <lb/>illius quod infertur. </s>
              <s xml:id="N2581A" xml:space="preserve">Omnia enim que ibi inferun-<lb/>tur ſequuntur expoſitione vt bene probat argumē­<lb/>tum. </s>
              <s xml:id="N25821" xml:space="preserve">Et illa inducit calculator aliis tamen vtens ꝓ­<lb/>bationibꝰ. </s>
              <s xml:id="N25826" xml:space="preserve">¶ Ad ſecundam confirmationem reſpõ­<lb/>deo concedendo illatum et negando falſitatem cõ-<lb/>ſequentis et ad probationem concedo conſequen-<lb/>tiam: et negando ſimiliter falſitatem conſequcntis <lb/>immo dico /  ſtat duo puta a. et b. incipere in infini­<lb/>tum velociter acquirere quantitatem: et tamen a. in­<lb/>cipit in infinitum velocius acquirere de quantitate <lb/>̄ b. </s>
              <s xml:id="N25837" xml:space="preserve">¶ Ad tertiam confirmationem reſpondeo con­<lb/>cedendo illatum: et negando  illud ſit falſum im-<lb/>mo ſecundum omnem poſitioneꝫ eſt verum. </s>
              <s xml:id="N2583E" xml:space="preserve">Et ideo <lb/>ab vtra poſitione concedendum.</s>
            </p>
            <p xml:id="N25843">
              <s xml:id="N25844" xml:space="preserve">Ad tertiam rationē reſpondeo negan­<lb/>do ſequelam et ad probationem cõcedo antecedēs <lb/>et nego conſequentiam: et cum probatur dico /  ta­<lb/>lis modus arguendi non valet in conditionalibus /               <pb chead="De motu alterationis." file="0218" n="218"/>               vt patet ex dialecticis. </s>
              <s xml:id="N25852" xml:space="preserve">Reſolutio huius argumenti <lb/>habetur ex prima et ſecunda concluſionibus huius <lb/>capitis. </s>
              <s xml:id="N25859" xml:space="preserve">¶ Ad primam confirmationeꝫ patet reſpõ­<lb/>ſio ex tertia concluſione cum ſuo correlario. </s>
              <s xml:id="N2585E" xml:space="preserve">¶ Ad <lb/>ſecūdã cõfirmationē nego ſequelã, et ad ꝓbationeꝫ <lb/>dico:  ſemꝑ illud corpus erit maius in aliqua pro­<lb/>portione rõnali vel irrationali: et cum tu q̄ris ī qua <lb/>ꝓportiõe maius efficitur. </s>
              <s xml:id="N25869" xml:space="preserve">Reſpondeo /  non ſolum <lb/>in iſto caſu verūetiaꝫ in infinitis nõ poſſet ingeniū <lb/>finitum illud diſcutere ꝓpter varietatem ꝓportio-<lb/>num inter partes. </s>
              <s xml:id="N25872" xml:space="preserve">¶ Ad tertiam ↄ̨fimationē cõcedo <lb/>ſequelã ſcḋm hanc poſitionē primã: et nego falſita-<lb/>tem cõſequentis: et ad ꝓbationē nego ſequelam: et <lb/>ad ꝓbationē nego  illud acquirat infinitas ꝓpor­<lb/>tiones equales. </s>
              <s xml:id="N2587D" xml:space="preserve">Proportio em̄ dupla repectu ꝑtis <lb/>non eſt dupla repectu totius.</s>
            </p>
            <p xml:id="N25882">
              <s xml:id="N25883" xml:space="preserve">Ad quartam rationē reſpondeo conce­<lb/>dendo ſequelã et negando falſitatē conſequētis: et <lb/>ad punctū ꝓbationis dico /  illud quod perdit oēs <lb/>ſpecies ꝓportionis ſuꝑparticularis infinitã ꝓpor-<lb/>tionem deperdit: et ꝑ cõſequēs vni ſignate īfinitas <lb/>equales vt optime ꝓbat argumentum.</s>
            </p>
            <p xml:id="N25890">
              <s xml:id="N25891" xml:space="preserve">Ad quintam rationem reſpõdet noua <lb/>concluſio. </s>
              <s xml:id="N25896" xml:space="preserve">¶ Ad cõfirmationem reſpõdeo negando <lb/>ſequelam: et ad probationem concedo antecedens, <lb/>et nego conſequentiã. </s>
              <s xml:id="N2589D" xml:space="preserve">Non eſt em̄ eadē ratio quan­<lb/>do hora diuidit̄̄ ꝓportiõe dupla in illo caſu: et quã­<lb/>do maiori: vt ptꝫ ex tertio capite ſecundi tractatꝰ. <lb/></s>
              <s xml:id="N258A5" xml:space="preserve">¶ Ad ſecundã cõfirmationē nego ſequelã et quum <lb/>querit̄̄ ꝓportio acquiſita. </s>
              <s xml:id="N258AA" xml:space="preserve">dico /  aut illa eſt incõmē­<lb/>ſurabilis: aut a nobis nequa̄ reperibilis</s>
            </p>
            <p xml:id="N258AF">
              <s xml:id="N258B0" xml:space="preserve">Ad ſextam rationem reſpondeo negã­<lb/>do ſequelam: et ad probationē nego cõſequentiam <lb/></s>
              <s xml:id="N258B6" xml:space="preserve">Et q2 argumētū querit modū cognoſcēdi quã pro-<lb/>portionē acquirit totū quãdo pars aliquota acqui­<lb/>rit aliquã ꝓportionē q̄ ſemꝑ reſpectu totius minor <lb/>eſt quam reſpectu partis: ideo dico /  in propoſito <lb/>ad illud cognoſcendū recurrendū eſt ad primã par­<lb/>tem capittulo ſeptimo. </s>
              <s xml:id="N258C3" xml:space="preserve">¶ Ad confirmationē reſpõ-<lb/>deo negando ſequelã: vt bene ꝓbat argumentū eã <lb/>eſſe negandã et ad ꝓbationem nego conſequentiã</s>
            </p>
            <p xml:id="N258CA">
              <s xml:id="N258CB" xml:space="preserve">Ad ſeptimam rationem reſponſuꝫ eſt <lb/>ibi vſ ad vltimam replicam: ad quã reſpõdeo: cõ-<lb/>dendo </s>
              <s xml:id="N258D2" xml:space="preserve">Cõcedēdo illatum: et negando ipſum ipſum <lb/>eſſe falſum.</s>
            </p>
            <p xml:id="N258D7">
              <s xml:id="N258D8" xml:space="preserve">Ad octauam rationem reſponſum eſt <lb/>ibi vſ ad replicam: ad quã reſpõdeo: cõcedēdo il-<lb/>lud qḋ inducit et negando falſitatē cõſequētis: et ad <lb/>punctum probatiõis nego hanc ↄ̨ſequētiã. </s>
              <s xml:id="N258E1" xml:space="preserve">Hoc in-<lb/>cipit in infinitū tarde acquirere de quãtitate: ergo <lb/>non incipit īfinite velociter acquirere de quãtitate <lb/></s>
              <s xml:id="N258E9" xml:space="preserve">¶ Ad cõfirmationē reſpondeo ↄ̨cedendo illatuꝫ / vt <lb/>bene probat argumentum.</s>
            </p>
            <p xml:id="N258EE">
              <s xml:id="N258EF" xml:space="preserve">Ad nonam ratiouem cõcedo ſequelã <lb/>et nego falſitatē conſequētis: et nego  ex illo ſeq̇-<lb/>tur illud corpus infinitam quantitatem acquirere <lb/>nec argumentū intendens illud probare habet ma­<lb/>gnam apparentiã / vt ex dictis pꝫ. </s>
              <s xml:id="N258FA" xml:space="preserve">¶ Et hec de tertio <lb/>Tractatu.</s>
            </p>
            <p xml:id="N258FF">
              <s xml:id="N25900" xml:space="preserve">Finis tertii <lb/>tractatus.</s>
            </p>
          </div>
        </div>
        <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
          <cb chead="De motu alterationis."/>
          <head xml:id="N2590C" xml:space="preserve">Sequitur tractatus quartus in quo <lb/>agitur de motu alterationis.</head>
          <div xml:id="N25911" level="4" n="1" type="chapter" type-free="capitulum">
            <head xml:id="N25916" xml:space="preserve">Capitulum primuꝫ in quo diſputatiue <lb/>inquirit̄̄ penes quid motus alterationis <lb/>velocitas attendi habeat.</head>
            <p xml:id="N2591D">
              <s xml:id="N2591E" xml:space="preserve">COnſummatis documentis co­<lb/>gnoſcende velocitatis motus ad locū et <lb/>ad magnitudinē iam huius operis com­<lb/>plementu doctrinã inueſtigande at menſurande <lb/>velocitatis motus ad qualitatē expoſtulat in qua <lb/>inquiſitione diſputatiue ꝓcedere intendo.</s>
            </p>
            <p xml:id="N2592B">
              <s xml:id="N2592C" xml:space="preserve">Queritur ergo prīo nunquid motus <lb/>alteratiõis velocitatē penes multitudinē graduū <lb/>qualitatis mediante tali motu ꝓducte metiri opor­<lb/>teat. </s>
              <s xml:id="N25935" xml:space="preserve">Et arguit̄̄ primo /  nõ q2 ſi motus alteratiõis <lb/>velocitas eēt mēſurãda penes multitudinē graduū <lb/>qualitatis etc̈. / ſeq̄retur /  ſi a. calidū alteraret paſ-<lb/>ſum pedale ꝑ totū in hora vniformiter ad gradum <lb/>quartum caliditatis et .b. ccalidū in eodē tꝑe alte-<lb/>raret bipedale ꝑ totū ad eundū quartū gradū ca-<lb/>liditatis a. et b. in illa hora eque velociter altera-<lb/>rent illa poſſa / ſed ↄ̨ñs eſt falſuꝫ / igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N25948" xml:space="preserve">Sequela probat̄̄ / q2 tot gradus calidita-<lb/>tis adequate ꝓducit a. ſicut b. in eodē tꝑe q2 tam in­<lb/>tenſam caliditatē ꝓducit a. ſicut b. in illa hora ade-<lb/>quate / igit̄̄ eque velociter a. et b. alterant ſua paſſa <lb/>in illa hora. </s>
              <s xml:id="N25953" xml:space="preserve">Patet ↄ̨ſequētia / q2 penes illud veloci­<lb/>tas alterationis, vt inquis, attendi habet iam ar-<lb/>guitur falſitas ↄ̨ñtis / q2 tunc ſequit̄̄ /  a. agens alte­<lb/>raret bipedale in duabus horis adequate et b. alte­<lb/>raret bipedale in hora adequate et ad eūdem gra-<lb/>dum et tamen a. eque velociter adequate alteraret <lb/>ſuū bipedale ſicut b. / ſed cõſequens ē manifeſte fal-<lb/>ſum / igitur illud ex quo ſeq̇tur. </s>
              <s xml:id="N25964" xml:space="preserve">Sequela ꝓbat̄̄ et po­<lb/>no /  cõpleta hora in qua a. alterauit vnum pedale <lb/>ad gradū vt .4. per totū et .b. ad eundē gradum ca-<lb/>liditatis vi3 alterabit bipedale approximet̄̄ ipſi a. <lb/>vnū aliud pedale qḋ in ſequēti hora alteret ad gra­<lb/>dum vt .4. adequale ꝑ totū b. nichil vlterius alterã­<lb/>te. </s>
              <s xml:id="N25973" xml:space="preserve">Quo poſito ſic argumētor a. in tꝑe illarū duaꝝ <lb/>horarū alterat bipedale ad gradū vt .4. adequate <lb/>per totū et b. in vna hora alterat bipedale ad eun-<lb/>dem gradū ꝑ totū et a. et b. alterãt eque velociter ꝑ­<lb/>te: igitur ſequitur illatū </s>
              <s xml:id="N2597E" xml:space="preserve">Probat̄̄ / tamē minor / q2 a. <lb/>in prima hora eque velociter alterat ſuū paſſum ſi­<lb/>cut b., vt coucedis<gap/> et in ſecūda eque velociter alte-<lb/>rat ſicut in prima / vt cõſtat / igit̄̄ in tꝑe illarū duarū <lb/>horarū eque velociter alterat a. ſuū bipedale ſicut <lb/>b. alterat ſuū in prima illarū ꝑ ↄ̨ñs eque velociter <lb/>alterat a. ſicut b. adequate.               <anchor type="note" xlink:href="note-0218-01" xlink:label="note-0218-01a"/>               </s>
              <s xml:id="N25994" xml:space="preserve">¶ Dices forte negando <lb/>ſequelã </s>
              <s xml:id="N25999" xml:space="preserve">Et ratio eſt / q2 velocitas motus alteratio-<lb/>nis non debet attendi penes qualitatē ſiue multi-<lb/>tudinem graduū qualitatis ꝓducte in eodē tēpore <lb/>abſolute: ſed in ordine ad ſubiectum quod alterat̄̄ <lb/>ita  quãto ſubiectum fuerit maius tãto velocitas <lb/>alterationis erit maior ceteris paribus. </s>
              <s xml:id="N259A6" xml:space="preserve">Sed con­<lb/>tra / q2 tunc ſeq̄retur /  ſi a. alteran ꝓduceret in pri-<lb/>ma parte ꝓportionali vnius hore ꝓportiõe dupla <lb/>diuiſe vnū gradū caliditatis in prima parte ꝓpor­<lb/>tionali vnius pedalis et in ſcḋa ꝓduceret etiã vnum <lb/>gradum in ſcḋa parte ꝓportionali eiuſdē pedalis <lb/>et in tertia vnū alterū in tertia / et ſic cõſequenter b. <lb/>vero in qualibet ꝑte ꝓportionali hore ꝓduceret tã­<lb/>tam formã entitatiue et intenſiue ꝑ totum tamē vnū <lb/>pedale extenſam quãtum in eadē parte hore produ­<lb/>cit a. in parte proportionali pedalis qḋ alterat .b.               <pb chead="Quarti Tractatus" file="0219" n="219"/>               in infinitum velociꝰ alteraret ſuū pedale ꝙ̄ a. / ſꝫ cõ-<lb/>ſequēs eſt falſum / igit̄̄ illud ex quo ſeq̇tur. </s>
              <s xml:id="N259C4" xml:space="preserve">Sequela <lb/>ꝓbatur / q2 in eodē tēpore et in equali ſubiecto in in­<lb/>finitū plures gradus caliditatis ꝓducit b. ꝙ̄ a. per <lb/>alterationē / ergo in infinitū velocius alterat b. ſuū <lb/>paſſum ꝙ̄ a. /  fuit inducēdū </s>
              <s xml:id="N259CF" xml:space="preserve">Iam ꝓbat̄̄ falſitas ↄ̨ſe­<lb/>quētis / q2 equaliter oīno de forma caliditatis pro­<lb/>ducit b. ſicut a. in eodē tꝑe / vt patet ex caſu / igir̄ eque­<lb/>velociter oīno alterat b. ſuū paſſum ſicut a. et ꝑ ↄ̨ñs <lb/>non in infinitū velocius / qḋ eſt oppoſitū ↄ̨ñtis. </s>
              <s xml:id="N259DA" xml:space="preserve">Pa­<lb/>tet ↄ̨ña / q2 velocitas motus vniuerſaliter attendi <lb/>hꝫ penes effectū ꝓductuꝫ ſaltem vbi aliquid ꝑ motuꝫ <lb/>ꝓducitur. </s>
              <s xml:id="N259E3" xml:space="preserve">¶ Itē ſi illa ſolutio eſſet bona ſequeretur / <lb/> ab equalib3 ꝓportionibus alterantiū ad ſua al­<lb/>terabilia inequales velocitates alterationis ꝓue-<lb/>nirēt: ſꝫ cõſequēs eſt manifeſte falſuꝫ / igitur illḋ ex <lb/>quo ſeq̇tur. </s>
              <s xml:id="N259EE" xml:space="preserve">Sequela ꝓbat̄̄ et volo /  a. alteret vnū <lb/>pedale in hora ad gradum vt .4. et b. equale ipſi a. <lb/>in actiuitate alteret vnū bipedale in eadē hora ad <lb/>eundem gradum vt .4. ſemper ītelligo ꝑ totū </s>
              <s xml:id="N259F7" xml:space="preserve">Quo <lb/>poſito manifeſtum eſt ꝑ te  b. in duplo velociꝰ al-<lb/>terat ſuū paſſum ꝙ̄ a. / q2 ſuum paſſum eſt in duplo <lb/>maius et ꝓportio ipſius a. ad ſuum paſſum et b. ad <lb/>ſuū paſſum ſunt equales / igitur ab equalibꝰ ꝓpor-<lb/>tionibus alterãtiū ad ſua alterabilia inequales ve­<lb/>locitates alteratiõis ꝓueniūt / qḋ fuit ꝓbandū </s>
              <s xml:id="N25A06" xml:space="preserve">Pro­<lb/>batur minor / q2 ſi ꝓportio b. ad ſuū paſſuꝫ eſſet ma­<lb/>ior ꝙ̄ ꝓportio a. ad ſuū paſſuꝫ / tūc ſequeret̄̄ /  intē-<lb/>ſiorē caliditatē ꝓduceret b. ī ſuū paſſum ꝙ̄ a. / ſꝫ hoc <lb/>eſt falſuꝫ / vt patet ex caſu / igit̄̄ illud ex quo ſequitur <lb/></s>
              <s xml:id="N25A12" xml:space="preserve">¶ Ideo dices aliter et melius ſicut dicendū eſt ad ar­<lb/>gumentū negando ſequelã et ad ꝓbationē dices /  <lb/>velocitas motus alteratiõis nõ debet attendi ſim-<lb/>pliciter penes multitudinē graduū intēſiõis ipſiꝰ <lb/>qualitatis que mediante tali motu alterationis ꝓ-<lb/>ducitur / ſꝫ penes multitudinē graduū ipſius forme <lb/>ſiue in magno ſubiecto ꝓducat̄̄ ſiue in paruo. </s>
              <s xml:id="N25A21" xml:space="preserve">Ma­<lb/>nifeſtum em̄ eſt /  cū aliqḋ calidū vniformiter rarū <lb/>acquirit ꝑ totū vnū gradū caliditatis intenſiue in <lb/>duplo plus de forma acq̇rit illud totuꝫ calidum ̄ <lb/>vna eius medietas ſicut dictū eſt ſuperiꝰ /  in dēſo <lb/>finite vniforme in duplo plus eſt de materia ꝙ̄ in <lb/>ſua medietate. </s>
              <s xml:id="N25A30" xml:space="preserve">Uolo igitur dicere /  ſicut in denſo <lb/>ſignãtur gradus entitatis materie penes quorum <lb/>multitudinē dēſitas attēdit̄̄ ita in ꝓpoſito dico ve­<lb/>locitatē alteratiõis attēdi debere penes multitudi­<lb/>nē qualitatis in eodē tꝑe ꝓducte nullo pacto cõſide­<lb/>rando intēſionē aut ſubiectū. </s>
              <s xml:id="N25A3D" xml:space="preserve">Sꝫ contra hoc ſic ar­<lb/>guit̄̄ / q2 tunc ſequeret̄̄ /  ſi a. alterans in prīa quar­<lb/>ta vnius hore ꝓducit vnū gradū caliditatis inten-<lb/>ſiue et entitatiue ꝑ totū et in ſecūda quarta tantuꝫ <lb/>et in tertia tantū et in quarta ſimiĺr tantum b. vero <lb/>in primo pedali vnius quadrupedalis ꝓduceret ſi-<lb/>militer vnū gradū caliditatis entitatiue et intenſi-<lb/>ue in prima quarta hore et in ſecūda quarta in ſecū­<lb/>do pedali tantū ꝓduceret et in tertia in tertio peda­<lb/>li et in quarta in quarto pedali tantū gradum ꝓdu­<lb/>ceret / tunc ſeq̇retur /  eque velociter in illa hora b. <lb/>alteraret quadrupedale ſicut a. pedale / ſꝫ ↄ̨ſequens <lb/>eſt falſuꝫ / igit̄̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N25A58" xml:space="preserve">Seq̄la patet faci-<lb/>le ex ſolutiõe / q2 tantū de caliditate entitatiua ꝓdu­<lb/>cit b. ſicut a. adequate </s>
              <s xml:id="N25A5F" xml:space="preserve">Falſitas ↄ̨ſequētis arguitur / <lb/>q2 alteratio ipſius a. qua vcꝫ alterat ſuū paſſuꝫ eſt <lb/>velocior alteratiõe ipſius b. / ergo nõ eque velociter <lb/>in illa hora b. alterat quadrupedale ſicut a. pedale <lb/></s>
              <s xml:id="N25A69" xml:space="preserve">Cõſequētia patet et arguitur añs / q2 intēſio qua a. <lb/>intēdit pedale eſt velocior alteratione ipſius b. et in­<lb/>tenſio qua a. intendit pedale eſt alteratio qua a. al­               <cb chead="Capi. primum"/>               terat pedale: ergo alteratio qua a. alterat pedale <lb/>eſt velocior alteratiõe ipſius b. qua vcꝫ alterat qua­<lb/>drupedale. </s>
              <s xml:id="N25A77" xml:space="preserve">Cõſequētia pꝫ cū minore </s>
              <s xml:id="N25A7A" xml:space="preserve">Nõ em̄, vt ſup­<lb/>pono, alteratio et intēſio diſtinguūtur. </s>
              <s xml:id="N25A7F" xml:space="preserve">et maior ꝓ­<lb/>batur: q2 intēſio qua a. intendit pedale eſt velocior <lb/>intenſione qua b. intēdit quadrupedale et oīs intē-<lb/>ſio qua b. intendit quadrupedale eſt alteratio qua <lb/>b. alterat quadrupedale / igit̄̄ intēſio qua a. intēdit <lb/>pedale eſt velocior alteratione qua b. alterat qua-<lb/>drupedale. </s>
              <s xml:id="N25A8E" xml:space="preserve">Et ſic pꝫ maior.               <anchor type="note" xlink:href="note-0219-01" xlink:label="note-0219-01a"/>               </s>
              <s xml:id="N25A96" xml:space="preserve">¶ Dices et bñ conceden-<lb/>do ſequelã et negãdo ↄ̨ñs eē falſum et ad punctū ꝓ-<lb/>bationis nego / hanc ↄ̨ñam intēſio qua a: intēdit pe­<lb/>dale eſt velocior alteratiõe ipſiꝰ b. et intēſio qua a. <lb/>intēdit pedale eſt alteratio qua a. alterat pedale / g̊ <lb/>alteratio qua a. alterat pedale eſt velocior altera-<lb/>tione ipſius b. </s>
              <s xml:id="N25AA5" xml:space="preserve">Arguit̄̄ em̄ in quatuor termīs. </s>
              <s xml:id="N25AA8" xml:space="preserve">debe­<lb/>ret eī ſic īferri / g̊ alṫatio q̈ a. alṫat pedare ē velocior <lb/>intēſio quã alteratio ipſiꝰ b. </s>
              <s xml:id="N25AAF" xml:space="preserve">Uel aliter rñdēdo ad <lb/>materiã argumēti poterꝪ ſecure dicere motū ītēſio­<lb/>nis nõ eē cõparabilē motui alteratiõis ī velocitate <lb/>et traditate prior tñ ſolutio magis plꝫ. </s>
              <s xml:id="N25AB8" xml:space="preserve">¶ Cõtra q2 <lb/>tūc ſeq̇retur /  velocius alteraret eandē reſiſtētiaꝫ <lb/>vnū pedale vniformiter calidū / vt q̈tuor ꝙ̄ vnū aliḋ <lb/>pedale infinite calidū vniformiter ſine aliqua con­<lb/>trarii ꝑmixtiõe: ſꝫ ↄ̨ñs videt̄̄ manifeſte falſum: igit̄̄ <lb/>illud ex quo ſeq̇tur </s>
              <s xml:id="N25AC5" xml:space="preserve">Falſitas ↄ̨ñtis relinq̇tur nota et <lb/>arguit̄̄ ſeq̄la et pono /  in vno pedali qḋ ſit a. in q̄li­<lb/>bet parte ꝓportionali inducãtur .4. gradus calidi-<lb/>tatis nõ tamē ꝑ totū ſꝫ in parte ꝓportionali ipſius <lb/>a. corrñdēte parti ꝓportionali tꝑis ipſo a. et tēpo-<lb/>re ꝓportione dupla diuiſis pono tamē /  in ea pro­<lb/>portione qua vna pars ꝓportionalis eſt minor al-<lb/>tera minus in tali parte entitatiue inducat̄̄ de cali-<lb/>ditate ſꝑ tamē vt .4. ī'tenſiue in altero vero pedali <lb/>puta b. in qualibet parte ꝓportionali tꝑis induca­<lb/>tur per totū b. medietas caliditatis intēſiue et enti-<lb/>tatiue q̄ in tali parte tꝑis introducit̄̄ in aliqua par­<lb/>te ꝓportionali ipſius a. </s>
              <s xml:id="N25AE0" xml:space="preserve">Quo poſito alterēt a. et b. <lb/>conſimilē reſiſtentiã et ſequit̄̄ /  a. velocius altera-<lb/>bit eandē reſiſtãtiam ꝙ̄ b. et tñ b. eſt infinite caliduꝫ <lb/>vniformiter ſiue cõtrarii admixtiõe: vt ſuppono: et <lb/>a. vniformiter calidū vt .4. / igit̄̄ ꝓpoſitū. </s>
              <s xml:id="N25AEB" xml:space="preserve">Minor fa-<lb/>cile patet ex caſu et minor ꝓbatur / q2 a. eſt in duplo <lb/>maioris põne ꝙ̄ b. / igit̄̄ in dupla velociꝰ alterat eã-<lb/>dem reſiſtentiã ꝙ̄ b. </s>
              <s xml:id="N25AF4" xml:space="preserve">Cõſequētia pꝫ et arguit̄̄ añs / q2 <lb/>a. hꝫ in duplo magis de forma eiuſdē ſpēi  b. / igit̄̄ <lb/>a. eſt in duplo maioris põne ꝙ̄ b. </s>
              <s xml:id="N25AFB" xml:space="preserve">¶ Scḋo ṗncipaĺr <lb/>arguit̄̄ ſic. </s>
              <s xml:id="N25B00" xml:space="preserve">Si pars affirmatiua q̄ſtiõis eēt vera / ſeq̇­<lb/>ret̄̄ /  qḋlibet alterans finitū alterans certã reſiſtē­<lb/>tiã infinitã formã entitatiue in quãtulocū tꝑe ꝓ-<lb/>duceret ſꝫ ↄ̨ñs eſt manifeſte falſum / igit̄̄ illud ex quo <lb/>ſequit̄̄. </s>
              <s xml:id="N25B0B" xml:space="preserve">Probat̄̄ añs / qm̄ qḋlibet alterãs certã reſi-<lb/>ſtētiã infinite velociter adequate agit in quantulo-<lb/>cū tꝑe / igit̄̄ quodlibet alterãs finitū certã alterãs <lb/>reſiſtētiam infinitã formã entitatiue in quãtulocū <lb/>tꝑe ꝓducit. </s>
              <s xml:id="N25B16" xml:space="preserve">Probat̄̄ añs / q2 ſi nõ det̄̄ illud et ſit a. ca­<lb/>lidū vniforme ꝑ totū in forma entitatiue / qḋ alterat <lb/>b. paſſuꝫ certe reſiſtētie ꝑ horam. </s>
              <s xml:id="N25B1D" xml:space="preserve">Et arguit̄̄ ſic / a. īfi­<lb/>nite velociter agit in illa hora adequate alterando <lb/>b. paſſum / igitur propoſitum. </s>
              <s xml:id="N25B24" xml:space="preserve">Probatur antecedēs <lb/>et volo /  a. tangat b. paſſum et diuidatur ipſum a. <lb/>per partes proportionales ꝓportione dupla mi-<lb/>noribus ſus b. paſſum terminatꝪ et arguit̄̄ ſic: pri­<lb/>ma pars proportionalis ipſius a. aliquãtulū agit <lb/>in hora adequate in b. paſſum et ſecunda tantum vĺ <lb/>magis et tertia tantum vel magis ꝙ̄ ſecunda et ſic <lb/>cõſequēter et ſunt infinite: ergo ſequitur /  infinita <lb/>eſt actio ī illa hora adequate. </s>
              <s xml:id="N25B37" xml:space="preserve">Conſequētia patet <gap/>̀ <lb/></s>
              <s xml:id="N25B3D" xml:space="preserve"><pb chead="De motu alterationis quo ad cauſam" file="0220" n="220"/>               Probat̄̄ maior et diuido ṗmã ꝑtē ꝓportionalē ipſiꝰ <lb/>a. in duas medietates / et arguo ſic / ſcḋa pars ꝓpor-<lb/>tionalis ipſiꝰ a. eſt eq̈lis in ponã medietati ṗme re­<lb/>motiori a b. paſſo et eſt pluſ̄ ī duplo meliꝰ appli­<lb/>cata ip̄i b. paſſo ꝙ̄ medietas ṗme remotior a b. paſ­<lb/>ſo et ip̄a ſcḋa ꝑs ꝓportionalis ē eq̈lis ī pone medie­<lb/>tati ṗme ꝓpinquiori ip̄i b. paſſo et eſt ī duplo meliꝰ <lb/>applicata ip̄i b. paſſo ꝙ̄ ip̄a medietas prīe ꝓpinq̇or <lb/>agenti et totalis actio ṗme ꝑtis ꝓportionalis ↄ̨po-<lb/>nitur ex actiõibꝰ ſuaꝝ medietatū: igr̄ ſcḋa ꝑs ꝓpor­<lb/>tionalis plus agit in b. paſſū in eodē tꝑe ꝙ̄ ṗma / qḋ <lb/>fuit probãdū. </s>
              <s xml:id="N25B5A" xml:space="preserve">qm̄ eodē argumēto ꝓbabis tertiã plꝰ <lb/>agere in b. paſſū in eodē tꝑe ꝙ̄ ſcḋa et q̈rtã ꝙ̄ tertia / <lb/>et ſic ↄ̨ñter </s>
              <s xml:id="N25B61" xml:space="preserve">Probat̄̄ tñ ↄ̨ña ꝑ hoc /  ī ea ꝓportiõe q̄ <lb/>aliqḋ agēs ē propīquiꝰ eidē paſſo in ea velociꝰ aget <lb/>ceteris paribꝰ.               <anchor type="note" xlink:href="note-0220-01" xlink:label="note-0220-01a"/>               </s>
              <s xml:id="N25B6D" xml:space="preserve">¶ Dices et bñ negãdo ſequelã et ad <lb/>probationē negãdo añs et cū probat̄̄ admittit̄̄ caſꝰ <lb/>de ip̄o a. et negat̄̄ añs. </s>
              <s xml:id="N25B74" xml:space="preserve">et ad probationē dico ṗmo / <lb/> mīor eſt dubia qm̄ poſſibile eſt /  b. paſſū ſit vltra <lb/>ſpheram actiuitatꝪ medietatꝪ remotioris ṗme par­<lb/>tis proportiõalis a. </s>
              <s xml:id="N25B7D" xml:space="preserve">Stat eī  b. paſſū ſit ītra am-<lb/>bitū actiuitatꝪ totiꝰ a. agētis et tñ ſit vltra ſpherã <lb/>actiuitatꝪ certe partis ipſius a. ita  talis pars nõ <lb/>hēat ibi actionē ꝑ ſe. </s>
              <s xml:id="N25B86" xml:space="preserve">Dico ſcḋo /  eſto  vtra me-<lb/>dietas ṗme partis proportionalis ipſiꝰ a. ſufficiat <lb/>agere ꝑ ſe in ip̄m b. adhuc. </s>
              <s xml:id="N25B8D" xml:space="preserve">tñ negat̄̄ ↄ̨ña et ad proba­<lb/>tionē negat̄̄ propõ / q̄ ibi aſſumit vcꝫ /  in ea propor­<lb/>tione q̈ aliqḋ agēs ē propīquiꝰ eiḋ paſſo / in qḋ ſuffi­<lb/>cit agere in ea velociꝰ agit ceteris ꝑibꝰ / q2 tūc ſeq̄re­<lb/>tur /  in īfinitū velociꝰ in eodē tꝑe ageret agēs īme­<lb/>diatū paſſo ꝙ̄ diſtãs a paſſo cū in īfinitū ſit ei pro-<lb/>pinquiꝰ / qḋ eſt manifeſte falſuꝫ: q2 tūc ſeq̄ret̄̄ ignem <lb/>ſubito calefacere aquã ſibi proximã īducēdo in eaꝫ <lb/>totã caliditatē natã induci ab ip̄o igne. </s>
              <s xml:id="N25BA0" xml:space="preserve">Nec iuuat <lb/>dicere /  cū aliqḋ agēs diſtãs ab aliq̊ paſſo appro­<lb/>ximat̄̄ ei nõ in infinitū meliꝰ applicat̄̄ ei ſcḋm quēli­<lb/>bet eiꝰ pūctū: ſꝫ preciſe ſcḋm vnū pūctū </s>
              <s xml:id="N25BA9" xml:space="preserve">Q2 volo /  <lb/>cõdenſet̄̄ vnū agēs ita  in q̈libet ꝑte proportiona­<lb/>li tꝑis efficiat̄̄ ī duplo propinq̇us ſcḋm ſe et qḋlibet <lb/>eiꝰ punctū ip̄i paſſo ꝙ̄ in parte īmediate p̄cedēti / et <lb/>tūc ſi illa propõ eēt vera ageret illud agens in illo <lb/>tꝑe infinita velocitate / qḋ eſt falſuꝫ / q2 ē agēs finitū <lb/>agēs ī reſiſtētiã. </s>
              <s xml:id="N25BB8" xml:space="preserve">Itē ſi ſic approxīatū reſiſtētie age­<lb/>ret īfinite velociṫ: ageret ī ſibi eq̈lē reſiſtētiã et in īfi-<lb/>nite magnã / quod eſt impoſſibile.</s>
            </p>
            <div xml:id="N25BBF" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0218-01a" xlink:label="note-0218-01" xml:id="N25BC3" xml:space="preserve">Dicitur.</note>
              <note position="right" xlink:href="note-0219-01a" xlink:label="note-0219-01" xml:id="N25BC9" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0220-01a" xlink:label="note-0220-01" xml:id="N25BCF" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N25BD5">
              <s xml:id="N25BD6" xml:space="preserve">Sed ↄ̨̨tra q2 aliquod alterãs finitum <lb/>ſufficit agere īfinita velocitate adeq̈te ī hora q̈libet <lb/>ꝑte eiꝰ ꝓportionali tm̄ agēte ̄tū ṗma rõe ꝓpīqui-<lb/>tatis: igr̄ ſolutio nulla. </s>
              <s xml:id="N25BDF" xml:space="preserve">Probat̄̄ añs et ſigno a. alte­<lb/>rans et b. paſſuꝫ ſicut ī priori caſu et mãifeſtū eſt ex <lb/>ſolutiõe /  ſcḋa pars ꝓportiõalis minꝰ agit ꝙ̄ ṗma <lb/>vel aliq̈ ſequēs ꝙ̄ īmediate p̄cedēs eã et hoc ꝓpṫ de-<lb/>fectū forme: volo igr̄ /  tm̄ de forma addat̄̄ ſcḋe ꝑti <lb/>ꝓportionali quovſ tm̄ ſufficiat agere in b. paſſū <lb/>ſicut prīa adeq̈te in hora ī eadē diſtãtia in q̄ ſe hñt <lb/>ad b. paſſū. </s>
              <s xml:id="N25BF0" xml:space="preserve">et mãifeſtū eſt /  ſcḋa ꝑs ꝓportiõalis nõ <lb/>hꝫ tm̄ de forma ſicut ṗma ſi eī tm̄ hēret (cū ſit in du-<lb/>plo propīquior) plus ageret / qḋ eſt ↄ̈ caſuꝫ. </s>
              <s xml:id="N25BF7" xml:space="preserve">Habeat <lb/>igit̄̄ prima ī f. ꝓportiõe plus de forma ꝙ̄ .2. et pono / <lb/> tertie tm̄ addat̄̄ de forma quouſ ſcḋa hēat pre-<lb/>ciſe in f. proportiõe plus de forma ꝙ̄ ip̄a tertia et ſic <lb/>addatur cuilibet ſequenti de forma taliter  in f. ꝓ­<lb/>portione minus habeat de forma ꝙ̄ immediate pre­<lb/>cedens. </s>
              <s xml:id="N25C06" xml:space="preserve">Quo poſito a. agit infinita velocitate ī ho-<lb/>ra in b. paſſum et eſt finitum finite habēs de forma / <lb/>igitur aliquod alterans finitum ſufficit agere infi-<lb/>nita velocitate in hora adequate etc. / quod fuit pro-<lb/>bandum. </s>
              <s xml:id="N25C11" xml:space="preserve">Patet cõſequētia cū minore / quia forma               <cb chead="De motu alterationis quo ad cauſam"/>               ipſius a. agentis componitur ex infinitis continuo <lb/>ſe habentibus in ꝓportione f. finita deſcēdendo / vt <lb/>patet ex caſu. </s>
              <s xml:id="N25C1B" xml:space="preserve">Et maior probatur / quia ſcḋa pars ꝓ­<lb/>portionalis agit tantū adequate in b. paſſum quã-<lb/>tum prima / q2 in f. proportiõe habet minus de for-<lb/>ma et eſt in duplo propinquior ipſi b. paſſo / igitur <lb/>tertia pars ꝓportionalis tãtū agit adequate quã­<lb/>tum ſecunda et quarta quãtū tertia / et ſic cõſequēter / <lb/>et ꝑ ↄ̨ſequēs a. agit infinita velocitate in hora in b. <lb/>paſſum / quod fuit ꝓbandum. </s>
              <s xml:id="N25C2C" xml:space="preserve">Añs patet ex caſu et cõ­<lb/>ſequentia probat̄̄ / quia ſi ſecūda pars proportio-<lb/>nalis tantū agit in b. paſſum ſicut prima eo  in f. <lb/>proportione minꝰ habet de forma ꝙ̄ prima et eſt <lb/>in duplo propinquior b. paſſo: ſequit̄̄ eadē ratione <lb/>cum tertia habeat in f. proportiõe minus de forma <lb/>̄ ſecūda et ſit in duplo propinquior b. paſſo  ſe-<lb/>cunda  ipſa tantū adequate aget ī hora in b. paſ-<lb/>ſum ſicut ſecunda. </s>
              <s xml:id="N25C3F" xml:space="preserve">Et ſic in ꝓbabis de quibuſcun <lb/>duabus immediatis.               <anchor type="note" xlink:href="note-0220-02" xlink:label="note-0220-02a"/>               </s>
              <s xml:id="N25C49" xml:space="preserve">¶ Dices et bene negando añs <lb/>et ad probationē admiſſo caſu negando iteruꝫ añs <lb/>et ad probationē negatur maior et cū ꝓbatur nega­<lb/>tur añs vcꝫ /  iõ ſecūda tantū agit quantum prima / <lb/>quia habet in f. minus de forma ꝙ̄ prima et eſt ī du­<lb/>plo propinquior b. paſſo. </s>
              <s xml:id="N25C56" xml:space="preserve">Nõ em̄ illa eſt cauſa qua­<lb/>re ſecūda tantū agit in b. paſſuꝫ quãtū prima ſꝫ / q2 <lb/>in tali diſtantia tantã proportionē habet ſecunda <lb/>ad b. paſſum quantū habet prima ad idē b. paſſum. <lb/></s>
              <s xml:id="N25C60" xml:space="preserve">Nã illa cauſalis eſt falſa. </s>
              <s xml:id="N25C63" xml:space="preserve">Tu primo ꝓpter cauſaꝫ <lb/>dictã </s>
              <s xml:id="N25C68" xml:space="preserve">Tū ſecūdo / q2 illa nõ eſt bona ↄ̨ña. </s>
              <s xml:id="N25C6B" xml:space="preserve">nam cū in <lb/>infinitū modicū de forma habet aliqua pars ꝓpor­<lb/>tionalis: deueniēdū eſt ad aliquã partē proportio-<lb/>nalē ipſius a. agentis / que non agit in b. cū ad ip̄m <lb/>habeat proportionē equalitatis vel minoris ineq̈-<lb/>litatis / et tñ illa pars eſt in duplo ꝓpinquior ipſi b. <lb/>paſſo ꝙ̄ pars īmediate precedēs et hꝫ in f. ꝓportiõe <lb/>minus de forma. </s>
              <s xml:id="N25C7C" xml:space="preserve">Et in hoc ↄ̨ſiſtit ſolutio replice /  <lb/>vcꝫ deueniendū eſt ad aliquã partem proportiona­<lb/>lem / q̄ nullo mõ ſufficit ꝑ ſe agere in b. paſſuꝫ ſꝫ ha-<lb/>bet ad illud proportiõeꝫ mīoris inequalitatis.</s>
            </p>
            <div xml:id="N25C85" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0220-02a" xlink:label="note-0220-02" xml:id="N25C89" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N25C8F">
              <s xml:id="N25C90" xml:space="preserve">Sed cõtra et pono /  ſecunde parti ꝓ­<lb/>portionali ipſiꝰ a. alterãtis addatur de forma quo <lb/>vſ agat tm̄ ī b. paſſū ſicut ṗma adeq̈te: et ſiĺr tm̄ <lb/>addat̄̄ tertie de forma /  tantum agat in b. paſſū <lb/>ſicut prima et quarte. / et q̇nte: et ſic ↄ̨ñter ita  queli-<lb/>bet ſequens agat tm̄ ſicut p̄cedens. </s>
              <s xml:id="N25C9D" xml:space="preserve">Quo poſito ſic <lb/>arguit̄̄ a. agit infinite velociter in b. paſſum / vt patꝫ <lb/>ex caſu et a. eſt finitum alterans hoc eſt habēs finitū <lb/>de forma adequate / igit̄̄ aliqḋ alterãs finitū hñs fi­<lb/>nite de forma adeq̈te alterat īfinite velociter certaꝫ <lb/>reſiſtentiã / qḋ eſt negatū. </s>
              <s xml:id="N25CAA" xml:space="preserve">Probat̄̄ minor / q2 ſecūda <lb/>pars proportionalis habet minus de forma ꝙ̄ pri­<lb/>ma adequate et tertia minus ꝙ̄ ſecūda et quarta ̄ <lb/>tertia / et ſic ↄ̨ſequēter: igitur totalis forma ipſius a. <lb/>alterantis eſt finita. </s>
              <s xml:id="N25CB5" xml:space="preserve">Patet iſta ↄ̨ſequētia: q2 for-<lb/>ma totalis ipſius a. vni certe parti date nõ habet <lb/>infinitas equales non cõicantes. </s>
              <s xml:id="N25CBC" xml:space="preserve">Probo tamē an-<lb/>tecedens. </s>
              <s xml:id="N25CC1" xml:space="preserve">quia ſi ſecunda habent tantum ſicut pri-<lb/>ma vel plus cum ſit propinquior ſequeretur /  plꝰ <lb/>ageret ꝙ̄ prima / ſed conſequens eſt falſum et contra <lb/>caſum / igitur et antecedēs </s>
              <s xml:id="N25CCA" xml:space="preserve">Et ſic probabis de qui-<lb/>buſcun immediatis.               <anchor type="note" xlink:href="note-0220-03" xlink:label="note-0220-03a"/>               </s>
              <s xml:id="N25CD4" xml:space="preserve">¶ Et confirmatur / quia ſi q̄-<lb/>ſtio eſſet vera / ſequeretur /  quodlibet alterans fi-<lb/>nitum alteraret certam reſiſtentiam infinita tar-<lb/>ditate / ſꝫ ↄ̨ñs eſt fĺm: igr̄ illud ex q̇ ſeq̇tur. </s>
              <s xml:id="N25CDD" xml:space="preserve">Sequela <lb/>ꝓbat̄̄ / q2 ſi nõ ſignet̄̄ illud et ſit a. / et arguo ſic / a. agit ī­<lb/>finita tarditate: igr̄ propoſitū. </s>
              <s xml:id="N25CE4" xml:space="preserve">Argr̄ añs et volo /  <lb/>in caſu ſuꝑiꝰ poſito b. paſſū diuidat̄̄ ꝑ partes ꝓpor­               <pb chead="Quarti Tractatus" file="0221" n="221"/>               tionales ꝓportiõe dupla minoribꝰ ſus a. alterãs <lb/>terminatis / et argr̄ ſic / b. reſiſtit īfinite ip̄i a. põue fi-<lb/>nite / igit̄̄ a. alterat infinita tarditate. </s>
              <s xml:id="N25CF2" xml:space="preserve">Probat̄̄ añs / <lb/>q2 ṗma ꝑs ꝓportiõalis ip̄ius b. aliquãtulū reſiſtit <lb/>ipſi a. et ſcḋa tm̄ et tertia tm̄ ſicut ſcḋa / et ſic ↄ̨ñter / g̊ <lb/>b. reſiſtit infinite ip̄i a. </s>
              <s xml:id="N25CFB" xml:space="preserve">Probat̄̄ añs. </s>
              <s xml:id="N25CFE" xml:space="preserve">q2 ſcḋa pars ꝓ­<lb/>portionalis eſt in duplo mīor ꝙ̄ prīa et eſt in duplo <lb/>ꝓpinq̇or ipſi agēti ꝙ̄ ṗma g̊ tãtū reſiſtit ſicut prima <lb/></s>
              <s xml:id="N25D06" xml:space="preserve">Et ſic probabis /  tertia tm̄ agit ſicut ſcḋa / et ſic cõ-<lb/>ſequēter. </s>
              <s xml:id="N25D0B" xml:space="preserve">Patet igir̄ antecedens.</s>
            </p>
            <div xml:id="N25D0E" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0220-03a" xlink:label="note-0220-03" xml:id="N25D12" xml:space="preserve">Confir°.</note>
            </div>
            <p xml:id="N25D18">
              <s xml:id="N25D19" xml:space="preserve">Tertio principaliter arguitur ſic </s>
              <s xml:id="N25D1C" xml:space="preserve">Si <lb/>q̄ſtio eēt vera / ſeq̄ret̄̄ aliquod alterãs eque velociter <lb/>alterare partē remotã alicuiꝰ reſiſtētie ſicut partē <lb/>ꝓpinquã ↄ̨ñs eſt falſuꝫ / cū oē agēs naturale velociꝰ <lb/>agat in remotū ꝙ̄ in ꝓpinquū / igit̄̄ illud ex q̊ ſequit̄̄ <lb/></s>
              <s xml:id="N25D28" xml:space="preserve">Seq̄la ꝓbat̄̄ et pono /  alterãs a. alteret reſiſtētiaꝫ <lb/>b. ita difformē  in ea ꝓportiõe in qua ꝑtes ſūt mi­<lb/>nus apte ad ſuſceptionē actionis propṫ diſtantiã <lb/>in ea ꝓportiõe habeat minus de reſiſtētia ita  a. <lb/>ad quodlibet pūctū ip̄ius b. reſiſtētie habeat eãdeꝫ <lb/>proportionē. </s>
              <s xml:id="N25D35" xml:space="preserve">Quo poſito argr̄ ſic / a. alterãs eq̄ ve-<lb/>lociter agit in partē remotã ipſius b. reſiſtētie ſicut <lb/>in partē propinquã igr̄ ꝓpoſitū </s>
              <s xml:id="N25D3C" xml:space="preserve">pꝫ añs / q2 ex caſu <lb/>ab equali proportiõe agit ī remotū et in propīquū <lb/>               <anchor type="note" xlink:href="note-0221-01" xlink:label="note-0221-01a"/>               </s>
              <s xml:id="N25D48" xml:space="preserve">Nec valet dicere ſicut dicit petrus mãtuanꝰ in ſuo <lb/>tractatu de primo et vltīo inſtãti nõ admittēdo caſū <lb/>vcꝫ /  taliter ſit dabilis aliqua reſiſtētia difformis <lb/> ad quēlibet pūctū eiꝰ agens eque velociter agat / <lb/>q2 manifeſtū eſt /  ab aliqua ꝓportiõe agit in c. pū­<lb/>ctū remotū minore ꝙ̄ ſit ꝓportio a q̈ agit in pūctū <lb/>propinquiorē / pono igit̄̄ /  ad punctū c. ſic remitta­<lb/>tur reſiſtētia quovſ ꝓportio a. ad illū punctū c. ſit <lb/>equalis ꝓportioni ipſius a. ad punctū ꝓpinquiorē / <lb/>et tunc manifeſtū eſt /  eque velociter agit in remo-<lb/>tū ſicut in ꝓpinquū </s>
              <s xml:id="N25D5F" xml:space="preserve">Poſſet etiã ꝓbari /  ad punctū <lb/>ꝓpinquiorē addēdo reſiſtētiã ꝓpīquiori pūcto quo <lb/>vſ a. haberet tantã ꝓportionē ad illū punctū ꝓpin­<lb/>quiorē ſicut ad c. pūctū remotiorē.               <anchor type="note" xlink:href="note-0221-02" xlink:label="note-0221-02a"/>               </s>
              <s xml:id="N25D6D" xml:space="preserve">¶ Et ideo aliter <lb/>dices et bñ cõcedēdo ſequelã / qm̄ illud nõ eſt incon-<lb/>ueniēs dūmodo reſiſtētia ſit difformis / īmo ſtat ali­<lb/>quod agēs agere in remotū et nõ in ꝓpinquū quan­<lb/>do vcꝫ ꝓpinquū nõ eſt ſuſceptiuū actionis et remotū <lb/>eſt ſuſceptiuū et ſiĺr cū ad remotū hꝫ ꝓportionē ma­<lb/>ioris ineq̈litatis ad ꝓpīquū o ꝓportionē eq̈litatꝪ</s>
            </p>
            <div xml:id="N25D7C" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0221-01a" xlink:label="note-0221-01" xml:id="N25D80" xml:space="preserve">Petrꝰ ḋ <lb/>mãtua in <lb/>tractatu <lb/>de ṗmo et <lb/>vltimo ī-<lb/>ſtanti.</note>
              <note position="left" xlink:href="note-0221-02a" xlink:label="note-0221-02" xml:id="N25D90" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N25D96">
              <s xml:id="N25D97" xml:space="preserve">Sed contra q2 aliquod alterãs agēs <lb/>in paſſum vniforme eque velociter alterat remotuꝫ <lb/>ſicut ꝓpinquū igr̄ ſolutio nulla. </s>
              <s xml:id="N25D9E" xml:space="preserve">Pro deductiõe ar­<lb/>gumēti ſuppono tria </s>
              <s xml:id="N25DA3" xml:space="preserve">Primū /  oē luminoſum per <lb/>maiorē diſtãtiã agit latitudinē ſui luminis ī medio <lb/>rariori ꝙ̄ in medio minus raro. </s>
              <s xml:id="N25DAA" xml:space="preserve">Secūdū /  oē lumi­<lb/>noſum in medio vniformi ſaltem vbi reflexio nõ eſt <lb/>impedimento ꝓducit totã latitudinē ſui luīs a gra­<lb/>du ſub quo eſt vſ ad nõ gradū. </s>
              <s xml:id="N25DB3" xml:space="preserve">Tertiū /  qḋlibet <lb/>luminoſū ꝓducēs lumē ſuū in medio vniformiter ꝓ­<lb/>portiõalibiliṫ ſicut ſit maioris potētie ita agit ꝑ ma­<lb/>iorē diſtãtiã </s>
              <s xml:id="N25DBC" xml:space="preserve">Quibꝰ ſuppoſitis pono a. luminoſū vt <lb/>4. ꝓducere lumē ī b. mediū pedale vniforme ī rarita­<lb/>te a q̈rto vſ ad nõ g̈dū vniformiṫ difformiter deī-<lb/>de augeat̄̄ a. in ponã ꝑ intēſionē ſui ad duplū puta <lb/>ad octauū medio manēte īuariato. </s>
              <s xml:id="N25DC7" xml:space="preserve">Quo poſito ar­<lb/>guit̄̄ ſic / a. luminoſū tm̄ lumē ꝓducit ī pūcto ſibi ꝓ-<lb/>ximo ipſiꝰ b. medii vniformis ̄tū in pūcto remoto / <lb/>igit̄̄ ꝓpoſitū. </s>
              <s xml:id="N25DD0" xml:space="preserve">Probat̄̄ añs / q2 a. luīnoſū fctã tali in­<lb/>tenſioe producet lumē vniformiter difforme ab .8. <lb/>vſ ad nõ gradū / vt pꝫ ex ſcḋo ſuppoſito et .4. gra-<lb/>dus lūis adeq̈te ꝓducit in pūcto ſibi ꝓximo ſupra <lb/>gradus hītos añ talē intēſionē et .4. ēt gradus ī pū­<lb/>cto in q̊ añ intēſionē lūioſi erat nõ gradus luīs / igr̄               <cb chead="Capi. primum"/>               tm̄ lumem adequate ꝓducit in pūcto ſibi ꝓxīo ſicut <lb/>in puncto remoto / qḋ erat ꝓbandū. </s>
              <s xml:id="N25DE2" xml:space="preserve">Probat̄̄ ṗma <lb/>pars mīoris / q2 vt pꝫ ex ſcḋo ſuppoſito tota latitu-<lb/>do lūis ꝓducti ab a. fctã eius intēſiõe īcipit a gra-<lb/>du ſub quo eſt a. puta ab .8. ꝓpe lūioſū vſ ad non <lb/>gradū et añ intēſionē ipſiꝰ lūioſi ī pūcto ꝓximo ip̄i <lb/>lūioſo erãt .4. gradus lūis p̄ciſe et mõ ſūt .8. / igit̄̄ .4. <lb/>adequate fuerūt ꝓducti fctã intēſione lūioſi in illo <lb/>pūcto ei ꝓxīo. </s>
              <s xml:id="N25DF3" xml:space="preserve">Probat̄̄ ſcḋa pars mīoris / q2 illḋ lu­<lb/>minoſum eſt auctū in ponã ad duplū ex caſu / igr̄ ex <lb/>tertio ſuppoſito ip̄m producit totaꝫ latitudinē ſui <lb/>lūis ꝑ in duplo maiorē diſtãtiã puta ꝑ bipedalē di­<lb/>ſtantiã </s>
              <s xml:id="N25DFE" xml:space="preserve">(Uolo em̄ totū mediū vltra b. eſſe vniforme <lb/>eodē gradu raritatis quo b. ē rarū) et vltra a. ꝓdu-<lb/>cit totã latitudinē ſui lūis vniformiṫ difformiṫ ꝑ in <lb/>duplo maiorē diſtantiã / ꝙ̄ antea igit̄̄ vbi aña erat <lb/>nõ gradus totiꝰ latitudinis ibi mõ eſt gradus me-<lb/>dius totius latitudinis: ſꝫ gradus medius totiꝰ la­<lb/>titudinis eſt vt .4. fctã tali intēſiõe / vt ↄ̨ſtat / igr̄ a. lu-<lb/>minoſuꝫ in pūcto in q̊ aña erat nõ gradus fctã intē­<lb/>ſione ſui ꝓducit .4. g̈dus lūis adeq̈te / qḋ fuit ꝓbãdū <lb/></s>
              <s xml:id="N25E12" xml:space="preserve">¶ Dices et bñ cõcedēdo illatū </s>
              <s xml:id="N25E15" xml:space="preserve">Nec hoc eſt īcõueniēs <lb/>de actiõe partiali lūioſi hoc eſt ꝓducētis lumē ī me­<lb/>dio in quo iã lumē eſt ꝓductū ab ip̄o vel ab altero.</s>
            </p>
            <p xml:id="N25E1C">
              <s xml:id="N25E1D" xml:space="preserve">¶ Sꝫ cõtra: q2 tūc ſeq̇retur /  aliqḋ alterãs velociꝰ <lb/>alteraret remotū ꝙ̄ ꝓpīquum: paſſo exiſtēte vnifor­<lb/>mi: ſꝫ ↄ̨ñs ē falſum: igĺ illḋ ex q̊ ſequit̄̄. </s>
              <s xml:id="N25E24" xml:space="preserve">Seq̄la ꝓbat̄̄ <lb/>et pono /  a. lūioſum vt .8. producat latitudinē ſui <lb/>lūis in b. mediū vniformiter rarū ꝑ totū: deinde ra­<lb/>refiat b. mediū vniformiter ꝑ totuꝫ abſ ̄titatis <lb/>cremēto: ſꝫ ſolū ꝑ materie diminutionē / vt dcm̄ eſt in <lb/>capite de motu rarefactiõis et ↄ̨dēſatiõis. </s>
              <s xml:id="N25E31" xml:space="preserve">Quo po­<lb/>ſito ſic argumētor: fcã tali rarefactiõe a. luminoſuꝫ <lb/>ꝓducit totã latitudinē ſui luīs a gradu ſub q̊ ē puta <lb/>8. vſ ad nõ gradū / vt pꝫ ex ſcḋo ſuppoſito: et ꝑ ma­<lb/>iorē diſtãtiã / vt pꝫ ex ṗmo ſuppoſito: igr̄ in pūcto b. <lb/>medii in q̊ añ rarefactiõeꝫ erat nõ gradus luīs ē ali­<lb/>quis gradus fcã rarefactiõe ꝓductꝰ a luīoſo a. et in <lb/>puncto b. medii propīquiori a. luīoſo minꝰ luīs fuit <lb/>productū: igr̄ velociꝰ a: luīoſuꝫ fcã tali rarefactiõe <lb/>medii agit ī remotū ꝙ̄ ī propīquū paſſo exñte vni-<lb/>formi: qḋ fuit ꝓbãdū. </s>
              <s xml:id="N25E48" xml:space="preserve">Minor ꝓbat̄̄: q2 ꝑ in īfinituꝫ <lb/>mīorē latitudinē diſtat añ talē rarefactionē aliq̇s <lb/>punctꝰ nõ ꝓximꝰ luīoſo ꝓpinq̇or tñ ꝙ̄ punctus vbi <lb/>erat nõ gradus añ rarefactionē a. gradu .8. ꝙ̄ ſit la­<lb/>titudo lūis ꝓducta fctã rarefactiõe ī puncto b. me-<lb/>dii vbi erat nõ gradus et nullꝰ talis punctꝰ efficit̄̄ vt <lb/>8. q2 aĺs nõ eēt latitudo lūis vniformiṫ difformis / <lb/>qḋ eſt ↄ̈ ṗmū ſuppoſitū: igr̄ nullꝰ talis punctꝰ acq̇rit <lb/>tãtã latitudinē luīs ſicut punctꝰ vbi erat nõ gradꝰ: <lb/>et ꝑ ↄ̨ñs ī puncto ꝓpīquior a. luīoſo ꝙ̄ ſit punctꝰ vbi <lb/>erat nõ g̈dꝰ minꝰ luīs fuit ꝓductū ꝙ̄ ī pūcto vbi erat <lb/>nõ g̈dus: qñq̇dē ī q̊libet aliq̇d luīs ꝓducit̄̄ medio ma­<lb/>gis diſpoſito per illã rarefactioneꝫ.</s>
            </p>
            <p xml:id="N25E63">
              <s xml:id="N25E64" xml:space="preserve">¶ Quarto ṗncipaliṫ argr̄ ſic: ſi qõ eēt a ſeq̄ret̄̄ /  <lb/>nullū alterãs poſſꝫ vniformiṫ ↄ̨tinuo corrūpere reſi­<lb/>ſtētiã alicuiꝰ paſſi vſ ad nõ g̈dū: ſꝫ ↄ̨ñs ē fĺm / qm̄ q̄­<lb/>libet reſiſtētiã p̄t vniformiṫ corrūpi ꝑ motū altera­<lb/>tiõis vniformē. </s>
              <s xml:id="N25E6F" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 ſi nõ det̄̄ aliqḋ alte-<lb/>rãs puta a. vniformiṫ ↄ̨tinuo corrūpēs reſiſtētiã c. <lb/>ī hora adeq̈te vſ ad nõ gradū: et arguo ſic / vĺ a. ma­<lb/>net īuariatū: et hoc ñ / vt pꝫ ex ṗma ↄ̨°ne .3. argumēti <lb/>ſexti capitꝪ ṗmi tractatꝰ vĺ ip̄3 a. ↄ̨tinuo variat̄̄: et <lb/>hoc nõ: q2 tūc ip̄3 a. eq̄ ꝓportiõabiĺr corrūꝑet̄̄ vſ <lb/>ad nõ g̈dū / vt pꝫ ex ṗmo et octauo correlariis q̈rte cõ­<lb/>cluſiõis octaui capitꝪ .2. ꝑtis: ſꝫ hoc ē fĺm / q2 tūc eq̄ <lb/>cito reſiſtētia corrūꝑet põnã ſicut ponã r̄ſiſtētiã / igr̄ <lb/>nullo° ab aliq̊ alṫante r̄ſiſtētia v3 vniformiṫ ↄ̨tinuo <lb/>corrūpit. </s>
              <s xml:id="N25E86" xml:space="preserve">Dices et bñ negãdo ſeq̄lã et ad ꝓbatõeꝫ <gap/>̀               <pb chead="De motu alterationis quo ad cauſam" file="0222" n="222"/>               eo  poteſt reſiſtētia vniformiter corrūpi a ponã al­<lb/>terãte variata<gap/> et etiã nõ variata ñ aliūde impedi-<lb/>ta / vt patꝫ ex tertio argumēto paulo ante allegato <lb/></s>
              <s xml:id="N25E97" xml:space="preserve">¶ Sꝫ ↄ̈ / q2 tūc ſeq̄ret̄̄ /  vbicū aliqḋ alterans vni-<lb/>formiter cõtinuo corrūpit aliquã reſiſtētiã ꝑ corru­<lb/>ptionē põne ab ipſa reſiſtētia reagente ceteris im-<lb/>pedimētis et iuuaētis deductꝪ: nulla ponã maior <lb/>eiuſdē ſpēi aut minor valet vniformiter corrūpere <lb/>eãdem reſiſtentiã: ſꝫ ↄ̨ñs eſt falſuꝫ / igit̄̄ illud ex quo <lb/>ſequit̄̄. </s>
              <s xml:id="N25EA6" xml:space="preserve">Falſitas ↄ̨ñtis oſtēdit̄̄: et pono  a. alterãs <lb/>corrūpat cõtinuo vniformiter reſiſtentiã c. vſ ad <lb/>non gradū in hora adeq̈te continuo agendo a pro­<lb/>portione dupla: et ſit b. alterãs eiuſdē ſpēi ī duplo <lb/>maioris põne ipſo a. et cõtinuo cū c. reſiſtentia ꝑdit <lb/>aliquã proportionē ꝑ actionē ipſius b. ꝑdat b. cõſi­<lb/>milē proportionē ꝑ reactionē ipſiꝰ c. reſiſtētie. </s>
              <s xml:id="N25EB5" xml:space="preserve">quo <lb/>poſito continuo manebit eadem ꝓportio inter b. et <lb/>c. / vt pꝫ ex primo correlario quarte cõcluſiõis octa­<lb/>ui capitis ſcḋe partis: igit̄̄ cõtinuo vniformiter b. <lb/>corrūpit c. reſiſtentiã. </s>
              <s xml:id="N25EC0" xml:space="preserve">Sed ſeq̄la ꝓbatur et pono  ī-<lb/>ter a. põnã agentē et c. reſiſtentiã reagentē ↄ̨tinuo <lb/>ſit proportio f. et ſit b. ponã maior eiuſdē ſpēi que <lb/>corrūpat c. reſiſtentiã ad nõ gradū ip̄a reſiſtentia <lb/>reagēte ī ipſã b. põnã. </s>
              <s xml:id="N25ECB" xml:space="preserve">Quo poſito arguit̄̄ b. põnã <lb/>non corrūpere c. reſiſtētiã vniformiter. </s>
              <s xml:id="N25ED0" xml:space="preserve">quia ↄ̨tinuo <lb/>b. ponã aget corrūpēdo c. reſiſtentiã a maiori et ma­<lb/>iori ꝓportione: igr̄ b. ponã nõ vniformiter corrūpit <lb/>c. reſiſtētiã. </s>
              <s xml:id="N25ED9" xml:space="preserve">Probat̄̄ añs / q2 cõtinuo proportio īter <lb/>b. et c. maiorat̄̄: igr̄ ↄ̨tinuo b. agit a maiori et maio-<lb/>ri ꝓportiõe etc̈. </s>
              <s xml:id="N25EE0" xml:space="preserve">Probat̄̄ añs / q2 ↄ̨tinuo reſiſtētia c. / <lb/>q̄ eſt terminꝰ minor ꝑdit maiorē proportionē ꝙ̄ b. <lb/>ponã eiuſdē proportiõis terminꝰ maior: igr̄ ↄ̨tinuo <lb/>proportio īter b. et c. maiorat̄̄. </s>
              <s xml:id="N25EE9" xml:space="preserve">Ptꝫ ↄ̨ña ex ſcḋo cor-<lb/>relario ſcḋe cõcluſiõis octaui capitis ſcḋe ꝑtis. </s>
              <s xml:id="N25EEE" xml:space="preserve">Sꝫ <lb/>añs ꝓbat̄̄ / q2 cõtinuo agēte b. in c. reſiſtentiã ipſa re­<lb/>ſiſtentia maiorē proportionē ꝑdit ꝙ̄ agēte a. in ea-<lb/>dē reſiſtentiã: cū b. ſit maioris põne: et cõtinuo b. per <lb/>reactionē ipſius c. ꝑdit mīorē proportionē ꝙ̄ a. qñ <lb/>c. reagit in a. et cū a. agit in c. et c. reagit in a. cõtinuo <lb/>a. et c. equales deꝑdunt expoſito: g̊ ↄ̨tinuo c. maiorē <lb/>proportionē deꝑdit ꝙ̄ b. </s>
              <s xml:id="N25EFF" xml:space="preserve">Cõſequētia pꝫ: et argr̄ mi-<lb/>nor vcꝫ /  ↄ̨tinuo b. ponã ꝑ reactionē ipſius c. ꝑdit <lb/>minorē proportionē ꝙ̄ a. qñ c. reagit in a. q2 b. eſt <lb/>maioris põne et eſt eiuſdē ſpēi cū a. ceteris aliis iu­<lb/>uamētis et īpedimētis deductis / vt ponitur: igr̄ ma-<lb/>gis reſiſtit ſuo corrūpēti ꝙ̄ a. cū in eadē ſpē q̇cquid <lb/>eſt maioris ponē eſt maioris reſiſtētie ceterꝪ ꝑibus <lb/>et ꝑ conſequens c. tardius corrumpit b. ꝙ̄ a. et b. eſt <lb/>maius ꝙ̄ a. / g̊ cõtinuo b. minorē ꝓportionem deꝑdit <lb/>̄ a. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N25F14" xml:space="preserve">Cõſequētia pꝫ ex octaua ſup-<lb/>põne quarti capitis ſecūde partꝪ auxilio loci a ma­<lb/>iore. </s>
              <s xml:id="N25F1B" xml:space="preserve">Et ſic pꝫ /  nulla maior ꝙ̄ a. vniformiter valet <lb/>corrūpere reſiſtētiã c. </s>
              <s xml:id="N25F20" xml:space="preserve">Sꝫ iã ꝓbo /  nulla mīor: q2 ſi <lb/>ſic det̄̄ illa et ſit e. agēs ī c. reſiſtētiã reagētē. </s>
              <s xml:id="N25F25" xml:space="preserve">et argr̄ <lb/>ſic ↄ̨tinuo e. agit a. mīori et mīori ꝓportiõe corrūpē­<lb/>do b. / igr̄ nõ vniformiṫ corrūpit c. reſiſtētiã </s>
              <s xml:id="N25F2C" xml:space="preserve">Probat̄̄ <lb/>añs: q2 ↄ̨tinuo ꝓportio inṫ e. et c. diminuit̄̄: igr̄ cõti-<lb/>nuo e. agit a. mīori et mīori ꝓportõe etc̈. </s>
              <s xml:id="N25F33" xml:space="preserve">Añs ꝓbat̄̄ / q2 <lb/>c. ṫminꝰ mīor ↄ̨tinuo ꝑ actionē ipſiꝰ e. ꝑdit mīorē ꝓ­<lb/>portionē ꝙ̄ e. ṫminꝰ maior: igr̄ ↄ̨tinuo ꝓportio īter <lb/>e. et c. diminuit̄̄. </s>
              <s xml:id="N25F3C" xml:space="preserve">pꝫ ↄ̨ña ex prīo correlario tertie cõ-<lb/>cluſiõis octaui capitꝪ ſcḋe ꝑtis: et añs ꝓbat̄̄ / q2 cõti-<lb/>nuo e. agēte ī c. reſiſtētiã ip̄a c. reſiſtētia mīorē ꝓpor­<lb/>tionē deꝑdit ꝙ̄ agēte a. ī eãdē reſiſtētiã, cū e. ſit mīo­<lb/>ris ponē ꝙ̄ a. et ↄ̨tinuo e. ꝑ reactionē ipſiꝰ c. ꝑdit ma­<lb/>iorē ꝓportionē ꝙ̄ a. qñ c. reagit ī a. / et ↄ̨tinuo a. et c. <lb/>eq̈les ꝓportões deꝑdūt ex caſu: g̊ ↄ̨tinuo maiorē ꝓ-<lb/>portionē deꝑdit e. ꝙ̄ c. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N25F4D" xml:space="preserve">Ptꝫ ↄ̨ña: et <lb/>arguit̄̄ /  ↄ̨tinuo e. maiorē ꝓportiõeꝫ ꝑdit ꝙ̄ a. et c. / q2               <cb chead="De motu alterationis quo ad cauſam"/>               e. eſt mīoris põne ꝙ̄ a. et eiuſdē ſpēi cū a. ceterꝪ ꝑibꝰ: <lb/>igit̄̄ minꝰ reſiſtit ſuo corrūpēti ꝙ̄ a. et ꝑ ↄ̨ñs c. veloci­<lb/>us corrūpit e. ꝙ̄ a. et e. eſt minꝰ ꝙ̄ a. / g̊ ↄ̨tinuo e. maio­<lb/>rē ꝓportionē deꝑdit ꝙ̄ a. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N25F5B" xml:space="preserve">Cõſequē­<lb/>tia pꝫ ex octaua ſuppõe p̄allegata.               <anchor type="note" xlink:href="note-0222-01" xlink:label="note-0222-01a"/>               </s>
              <s xml:id="N25F65" xml:space="preserve">¶ Dices et bñ cõ­<lb/>cedēdo qḋ īfert̄̄: et negãdo fĺitatē ↄ̨ñtis: et ad ꝓbatio­<lb/>nē nõ addmmittēdo caſū. </s>
              <s xml:id="N25F6C" xml:space="preserve">Nõ eī ſtat  c. reſiſtētia et a. <lb/>ponã eq̄ proportionabiliṫ ↄ̨tinuo ad īuicē corrūpū­<lb/>tur ꝑ mutuas actiões ceṫis deductis: et cū hoc  b. <lb/>ponã maior ꝙ̄ a. et ip̄a c. reſiſtētia ꝑ mutuas earum <lb/>actiões ceteris īpedimētis et iuuamētis deductꝪ eq̄ <lb/>velociter ꝓportionabiliṫ ſe corrūpãt / vt pꝫ ex dedu-<lb/>ctiõe replice. </s>
              <s xml:id="N25F7B" xml:space="preserve">¶ Sed ↄ̈ / q2 tūc ſeq̄ret̄̄ /  vbicū aliqḋ <lb/>alterãs cõtinuo vniformiṫ corrūpit aliquã reſiſten­<lb/>tiã vſ ad nõ g̈dū ꝑ ↄ̨tinuã ipſiꝰ reſiſtētie reactionē <lb/>ceteris iuuamētis et īpedimētis deductis. </s>
              <s xml:id="N25F84" xml:space="preserve">qḋlibet al­<lb/>terãs maioris põne eiuſdē ſpēi agēs in eãdē reſiſtē­<lb/>tiã in īfinitū velociter talē reſiſtētiã corrūpit dūmõ <lb/>nõ īpediat̄̄ ab actiõe quãdiu aliqḋ reſiſtētie fuerit: <lb/>et oīs mīor potēs ī eãdē reſiſtētiã agere īfinitū tar-<lb/>de talē reſiſtētiã corrūpet ceteris deductꝪ: ſꝫ ↄ̨ñs eſt <lb/>falſū: igr̄ illḋ ex q̇ ſeq̇tur. </s>
              <s xml:id="N25F93" xml:space="preserve">Seq̄la ꝓbat̄̄ et pono caſuꝫ <lb/>ſuꝑiꝰ poſitū vcꝫ /  a. vniformiṫ ↄ̨tinuo ī horã corrū­<lb/>pit reſiſtētiã c. etc. </s>
              <s xml:id="N25F9A" xml:space="preserve">Tūc argr̄ /  b. ponã maior in īfini­<lb/>tū velociṫ corrūpet c. reſiſtētiã. </s>
              <s xml:id="N25F9F" xml:space="preserve">Qḋ ſic ꝓbat̄̄ / q2 b. ab <lb/>infinita ꝓportiõe aget ī c. reſiſtentiã: igr̄ in īfinitū ve-<lb/>lociṫ corrūpat c. reſiſtētiã. </s>
              <s xml:id="N25FA6" xml:space="preserve">Cõſeq̄ntia pꝫ: et argr̄ añs / <lb/>q2 reſiſtētia c. deueniet ad nõ g̈dū ꝑ actionē ipſiꝰ b. <lb/>certe põne b. cõtinuo manēte ita  ī īſtãti ī quo c. re-<lb/>ſiſtētia erit totaĺr corrupta adhuc b. manebit certe <lb/>põne: igr̄ infinita erit ꝓportio ipſiꝰ b. põne ad c. re-<lb/>ſiſtētiã: et ꝑ ↄ̨ñs ab īfinita ꝓportiõe aget b. ponã ī c. <lb/>reſiſtētiã: qḋ fuit ꝓbãdū. </s>
              <s xml:id="N25FB5" xml:space="preserve">pꝫ ↄ̨ña ꝑ hoc /  cū īter ali­<lb/>qua duo eſt ꝓportio maioris īeq̈litatꝪ: et vno illorū <lb/>certe quãtitatꝪ ↄ̨tinuo manēte vel maioris reliquū <lb/>vſ ad nõ gradū diminuit̄̄ ꝓportio īter illa ī infini­<lb/>tū augetur. </s>
              <s xml:id="N25FC0" xml:space="preserve">Probatur añs / q2 b. ponã in mīori tꝑe <lb/>corrūpet c. reſiſtētiã vſ ad nõ g̈dū ꝙ̄ a. puta ī mīo-<lb/>ri tꝑe ꝙ̄ ī hora: cū ſit maior ponã: et ip̄a reſiſtētia c. <lb/>ī tali tꝑe mīori ꝙ̄ ſit hora non corrūpet b. põnã vſ <lb/>ad nõ gradū vt ↄ̨ſtat: q2 tūc velociꝰ aget ī b. ꝙ̄ in a. / <lb/>qḋ eſt falſum vt pꝫ ex dictis: igr̄ in fine corruptiõis <lb/>ipſiꝰ c. reſiſtētie ip̄a b. ponã manet ſub certo gradu <lb/>põne ſub q̊ aut maiori cõtinuo aña fuit in tꝑe actio­<lb/>nis: et ꝑ ↄ̨ñs in inſtãti in q̊ c. reſiſtētia erit totaliṫ de­<lb/>ꝑdita adhuc b. manebit certe põne: qḋ fuit ꝓbandū <lb/></s>
              <s xml:id="N25FD6" xml:space="preserve">Sꝫ iã reſtat ꝓbare /  oīs ponã mīor agēs ī eãdē re­<lb/>ſiſtētiã c. ī īfinitū tarde agit illã corrūpēdo. </s>
              <s xml:id="N25FDB" xml:space="preserve">Qḋ pro­<lb/>batur ſic: eſto  illa ponã mīor ſit e. / q2 e. ponã ab ī­<lb/>finite modica proportiõe aget ī ip̄aꝫ reſiſtētiã c. / igr̄ <lb/>in īfinitū tarde aget corrūpēdo illã reſiſtētiã .c. </s>
              <s xml:id="N25FE4" xml:space="preserve">Cõ-<lb/>ſequētia patꝫ et probatur añs / q2 proportio ipſiꝰ e. <lb/>põe ad c. reſiſtētiã ſucceſſiue diminuitur vſ ad pro­<lb/>portionē eq̈litatꝪ: igr̄ e. ponã ab īfinite modica pro­<lb/>portiõe aget in ip̄am reſiſtētiã c. </s>
              <s xml:id="N25FEF" xml:space="preserve">Cõſequētia patꝫ et <lb/>probatur añs / q2 ipſa ponã e. in minori tꝑe corrū-<lb/>petur ab ip̄a c. reſiſtētia ꝙ̄ ip̄a ponã a. puta ī mīori <lb/>tꝑe quã in hora: cū ip̄a e. ponã ſit mīor ꝙ̄ a: et ip̄a e. <lb/>ponã in tali tꝑe nõ corrūpet c. reſiſtētiã vſ ad non <lb/>gradū: q2 tūc velocius ageret ꝙ̄ a. / qḋ eſt falſum: cū <lb/>ſit mīoris põne ꝙ̄ a. / igr̄ in fine corruptiõis ipſius e. <lb/>ponē ad nõ gradum ipſa ponã c. adhuc manet ſub <lb/>certo gradu põne et reſiſtentie: et ꝑ ↄ̨ñs ꝑ aliqḋ tp̄s <lb/>habuit c. proportiõeꝫ maioris īequalitatis ad ip-<lb/>ſam e. põnã et aña e. ponã habuit proportionē ma­<lb/>ioris inequalitatis ad c. reſiſtētiã et illa proportio <lb/>ſucceſſiue diminuebatur cõtinuo: igitur aliqñ c. ha­<lb/>buit proportionē equalitatis ad c. reſiſtentiã / quod <lb/>fuit probandum.</s>
            </p>
            <div xml:id="N2600E" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0222-01a" xlink:label="note-0222-01" xml:id="N26012" xml:space="preserve">Dicitur</note>
            </div>
            <pb chead="Quarti Tractatus" file="0223" n="223"/>
            <p xml:id="N2601C">
              <s xml:id="N2601D" xml:space="preserve">Quinto pricipaliter arguitur ſic. </s>
              <s xml:id="N26020" xml:space="preserve">Si <lb/>queſtio eēt vera / ſeq̇retur /  vbicū aliqua ponã al­<lb/>teratīa et ſua reſiſtētia incipiūt a nõ gradu põne et <lb/>teſiſtētie vniformiter ↄ̨tinuo augeri ponã alteratiã <lb/>cõtinuo velocius creſcēte ſua reſiſtēti: a ip̄a ponã al­<lb/>teratiã ↄ̨tinuo vniformiter alterabit: ſꝫ ↄ̨ñs eſt fĺm / <lb/>igit̄̄ ex quo ſequit̄̄ </s>
              <s xml:id="N2602F" xml:space="preserve">Seq̄la ꝓbat̄̄ / ſit a. ponã alteratiã <lb/>et .c. reſiſtētia q̄ vniformiter incipiãt creſcere a non <lb/>gradu ī iſtã a. ponã alteratiã ↄ̨tinuo ī f. ꝓportiõe ve­<lb/>locius creſcēte ꝙ̄ ip̄a c. reſiſtētia. </s>
              <s xml:id="N26038" xml:space="preserve">Et tūc arguit̄̄ a. po­<lb/>nam cõtinuo vniformiter alterare: q2 cõtinuo ſe ha­<lb/>bebit in f. ꝓportiõe ad c. reſiſtētiã: igit̄̄ cõtinuo alte­<lb/>rabit ab f. ꝓportiõe: et per ↄ̨ñs cõtinuo vniformiter <lb/></s>
              <s xml:id="N26042" xml:space="preserve">Cõſequētia pꝫ: et probatur añs: q2 quocū inſtanti <lb/>dato in toto precedēti tēpore creuit a. ponã in f. ꝓ-<lb/>portiõe velocius a nõ gradu ꝙ̄ c. reſiſtētia: igit̄̄ ī illo <lb/>tēpore adequate in f. ꝓportione maiorē latitudinē <lb/>acq̇ſiuit a non gradu ꝙ̄ c. reſiſtētia: et ꝑ ↄ̨ñs in quoli­<lb/>bet tĺi inſtanti ipſa a. ponã alteratiã eſt in f. ꝓpor-<lb/>tione maior ꝙ̄ ip̄a c. reſiſtētia: et ſic cõtinuo ſe habe­<lb/>bit in f. proportiõe ad c. reſiſtētiã / quod fuit ꝓbandum <lb/></s>
              <s xml:id="N26054" xml:space="preserve">Iam arguit̄̄ falſitas ↄ̨ñtis: q2 tunc ſequeret̄̄ /  vbi-<lb/>cū aliqua ponã alteratiã ita alterat vniformiter <lb/>per ſui vniforme cremētū a nõ gradu ponã etc̈. / vt di­<lb/>ctū eſt: oīs minor ſufficiēs alterare eandē c. reſiſten­<lb/>tiã vniformiter cõtinuo creſcens cū ipſa ponã a. cõ-<lb/>tinuo intēdit motū ſuū alteratiõis: et oīs maior cõ-<lb/>tinuo remittit: ſꝫ ↄ̨ñs videt̄̄ falſuꝫ: igit̄̄ illud ex quo <lb/>ſequit̄̄. </s>
              <s xml:id="N26065" xml:space="preserve">Sequela ꝓbat̄̄ / et ſit b. illa ponã minor ipſa <lb/>a. ponã et vniformiter cõtinuo et eque velociter cre-<lb/>ſcens cū a. et tamē a certo gradu / et arguit̄̄ /  ↄ̨tinuo <lb/>ꝓportio inter b. põnam et c. reſiſtētiã auget̄̄. </s>
              <s xml:id="N2606E" xml:space="preserve">et ꝑ con­<lb/>ſequēs cõtinuo b. intēdit motum ſuū alterationis. <lb/></s>
              <s xml:id="N26074" xml:space="preserve">Cõſequētia pꝫ: et ꝓbatur añs: quia continuo b. ma­<lb/>iorem ꝓportionē acq̇rit ꝙ̄ c. reſiſtētia: igit̄̄ cõtinuo <lb/>proportio inter b. põnã: et c. reſiſtētiam auget̄̄. </s>
              <s xml:id="N2607B" xml:space="preserve">Ptꝫ <lb/>ↄ̨ſequētia ex primo correlario ſecunde cõcluſionis <lb/>octaui capitis ſecunde partis: et añs probat̄̄ / q2 cõ­<lb/>tinuo a. acq̇rit tãta ̄ta c. / vt pꝫ ex primo correlario <lb/>quarte cõcluſionis octaui capitis preallegati. </s>
              <s xml:id="N26086" xml:space="preserve">Nã <lb/>inter a. et c. creſcētes cõtinuo manet eadem propor­<lb/>tio puta f. ꝑ te et b. cõtinuo maiorē proportionem <lb/>acquirit ꝙ̄ a. / vt patet ex octaua ſuppõne quarti ca­<lb/>pitis ſecūde partis (continuo em̄ tantam latitudi-<lb/>nē ponē acquirit b. ponã minor ſicut a. maior) / igit̄̄ <lb/>continuo b. maiorē proportionē acquirit ꝙ̄ c. reſi-<lb/>ſtētia / qḋ fuit probandū. </s>
              <s xml:id="N26097" xml:space="preserve">Et eadē ꝓbatiõe ꝓbabis /  <lb/>oīs ponã alteratiã maior continuo vniformiter et <lb/>eque velociter creſcens ſicut a cõtinuo remittit ſuū <lb/>motū alteratiõis: cū continuo mīorē ꝓportionē ac-<lb/>quirat ex octaua ſuppõne preallegata ꝙ̄ a. et ꝑ ↄ̨ñs <lb/>minorē ꝙ̄ c. reſiſtētia: et ſic cõtinuo ꝓportio inter b. <lb/>et c. diminuitur: vt pꝫ ex ſecūda parte primi correla­<lb/>rii tertie ↄ̨cluſiõis octaui capitis preallegati.</s>
            </p>
            <p xml:id="N260A8">
              <s xml:id="N260A9" xml:space="preserve">Sexto principaliter arguitur ſic </s>
              <s xml:id="N260AC" xml:space="preserve">Si <lb/>queſtio eſſet s: ſeq̇retur aliquod alterans ꝑ infini­<lb/>tam alterationē in determinato tꝑe ꝓducere finitã <lb/>qualitatē: ſꝫ ↄ̨ñs eſt falſum: igit̄̄ ex quo ſequit̄̄. </s>
              <s xml:id="N260B5" xml:space="preserve">Seq̄­<lb/>la ꝓbatur: et volo /  diuidat̄̄ hora ꝑ partes propor­<lb/>tionales ꝓportione dupla: et a. alterans in prima <lb/>parte proportionali alteret b. paſſuꝫ ꝓducēdo qua­<lb/>litatē aliquãtulū velociter: et in ſecūda in duplo ve­<lb/>lociꝰ et ī tertia ī triplo velociꝰ ꝙ̄ in prima: et ī quar­<lb/>ta in quadruplo velociꝰ ꝙ̄ ī ṗma: et ſic ↄ̨ñter ꝓcedē­<lb/>do ſeratim ꝑ oēs ſpēs ꝓportiõis mĺtiplicis. </s>
              <s xml:id="N260C6" xml:space="preserve">Quo <lb/>poſito ſic argumētor a. alterãs īfinite velociṫ alte-<lb/>rat b. paſſū ī illa hora: q2 aliquãtulū velociṫ: et ī du­               <cb chead="Capi. primum"/>               plo: et in triplo: et ſic in īfinitū: vt pꝫ ex caſu: et ſolū in <lb/>illa hora ꝓducit q̈litatē finitã: igit̄̄ aſſumptū verū. <lb/></s>
              <s xml:id="N260D3" xml:space="preserve">Probat̄̄ minor: et pono argumēti gr̄a /  a. in ṗma <lb/>parte ꝓportionali hore mediãte motu alteratiõis <lb/>ꝓducat vnū gradū q̈litatis (loquor de gradibꝰ en-<lb/>titatis for̄e ſꝑ ī hoc maṫia et manifeſtū e  mediãte <lb/>tali motu alteratiõis ꝑ totã horã extenſo ſiue cõti-<lb/>nuato a. ꝓducit duos gradus qualitatis: g̊ mediã-<lb/>te totali illa velocitate difformi adequate ī illa ho-<lb/>ra ꝓducit q̈tuor gradus forme: et ꝑ ↄ̨ñs finitã formã <lb/>qualitatis / qḋ fuit ꝓbandū. </s>
              <s xml:id="N260E6" xml:space="preserve">Cõſequētia et deductio <lb/>pꝫ ex ſcḋa cõcluſiõe tertii capitis ſcḋi tractatꝰ: et ex <lb/>tertio argumēto eiuſdē capitis.               <anchor type="note" xlink:href="note-0223-01" xlink:label="note-0223-01a"/>               </s>
              <s xml:id="N260F2" xml:space="preserve">¶ Dices et bñ ↄ̨cedē­<lb/>do illatū: nec illud eſt incõueniēs capiēdo ly īfinitū <lb/>ſyncathegorematice: et capiēdo ly alterationē ꝓ al­<lb/>teratiõe ꝑtiali. </s>
              <s xml:id="N260FB" xml:space="preserve">Nã ly determīato tꝑe ſtat ↄ̨fuſe tm̄ <lb/></s>
              <s xml:id="N260FF" xml:space="preserve">Quare aliqḋ alterãs ꝑ infinitã alterationē ꝑ aliqḋ <lb/>tp̄s ꝓducit ſolū q̈litatē finitã ̄uis ꝑ nullū tp̄s ꝑ in­<lb/>finita alteratiõeꝫ ꝓducat q̈litatē ſolū finitã. </s>
              <s xml:id="N26106" xml:space="preserve">In ꝓpo­<lb/>ſito eī tota illa velocitas alteratiõis ē finita corrñ­<lb/>des velocitati / q̄ eſt ī ſcḋa ꝑte ꝓportionali tꝑis / vt ſu­<lb/>pra dictū ē de velocitate motꝰ localis q̊ ad effectum <lb/>loco p̄allegato. </s>
              <s xml:id="N26111" xml:space="preserve">Sꝫ ↄ̈ / q2 tunc ſeq̄ret̄̄ /  ſi aliqḋ alte-<lb/>rans alteraret aliqḋ paſſuꝫ aliquãtula velocitate ī <lb/>prīa ꝑte ꝓportionali hore diuiſe ꝑ partes ꝓportio­<lb/>nales ꝓportiõe ſexq̇tertia: et in ſcḋa ꝑte ꝓportiona­<lb/>li alteraret in ſexq̇altero velocius: et in tertia ī ſexq̇­<lb/>altero velociꝰ ꝙ̄ in ſcḋa: et ſic ↄ̨ñter in q̈libet ſequēti <lb/>in ſexq̇altero velocius ꝙ̄ in īmediate p̄cedēti: tūc il-<lb/>lud alterãs ſolū finite velociter alteraret ī tota illa <lb/>hora: finitã qualitatē adequate ī illa hora ꝓduce­<lb/>ret: ſꝫ ↄ̨ñs eſt falſuꝫ: igit̄̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N26126" xml:space="preserve">Seq̄la ꝓ-<lb/>batur: q2 ſi hora eēt diuiſa ꝑ partes ꝓportionales <lb/>ꝓportiõe dupla: et illud alterãs alteraret in q̈libet <lb/>parte ꝓportionali ſeq̄nti in ſexq̇altero velociꝰ ꝙ̄ in <lb/>īmediate p̄cedēti: tūc tota illa velocitas alteratõis <lb/>adequate eſſet finita et finita qualitas mediãte ta-<lb/>li alteratione in illa hora adeq̈te ꝓduceret̄̄ / vt patꝫ <lb/>ex ſeptīa ↄ̨cluſiõe tertii capitis .2. tractatꝰ. </s>
              <s xml:id="N26137" xml:space="preserve">igit̄̄ ī ca­<lb/>ſu propoſito pari rõe finita qualilas adequate ꝓ-<lb/>ducit̄̄ mediãte illa totali alteratiõe in hora adeq̈te <lb/></s>
              <s xml:id="N2613F" xml:space="preserve">Sꝫ falſitas ↄ̨ñtis facile oñdit̄̄ ex ſexta cõcluſione .3. <lb/>capitis preallegati. </s>
              <s xml:id="N26144" xml:space="preserve">hoc addito /  qualitas ꝓducta <lb/>in propoſito eſt ibi ſpacium pertranſitum. </s>
              <s xml:id="N26149" xml:space="preserve">¶ Huic <lb/>propoſito poteris applicare ſecūdū: tertiū: et quar­<lb/>tum argumeutū tertii capitis ſecūdi tractatꝰ. </s>
              <s xml:id="N26150" xml:space="preserve">Ap-<lb/>plica etiã imaginationē ordinū partiū proportio­<lb/>naliū iuxta doctrinam prime et ſecūde cõcluſionem <lb/>ſeptimi capitis prime partis.</s>
            </p>
            <div xml:id="N26159" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0223-01a" xlink:label="note-0223-01" xml:id="N2615D" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N26163">
              <s xml:id="N26164" xml:space="preserve">Septimo principaliter arguitur ſic. <lb/></s>
              <s xml:id="N26168" xml:space="preserve">q2 ſi queſtio eēt a: ſeq̇retur /  qḋlibet alterãs ali-<lb/>quã reſiſtētiã a maiori proportiõe velocius altera-<lb/>ret q̊libet alterãte eãdē reſiſtētiã a minori propor-<lb/>tiõe: ſꝫ ↄ̨ñs eſt falſam: igit̄̄ illud ex q̊ ſeq̇tur. </s>
              <s xml:id="N26171" xml:space="preserve">Seq̄la <lb/>patꝫ: et falſitas ↄ̨ñtis arguit̄̄: q2 qḋlibet alterãs ali­<lb/>quã reſiſtētiã a certa ꝓportiõe difficiliꝰ agit q̊libet <lb/>alterãte eãdem reſtētiã a mīori ꝓportiõe: igit̄̄ qḋlꝫ <lb/>alterans aliquã quolibet alterãte eandē reſiſtentiã <lb/>a minori proportiõe. </s>
              <s xml:id="N2617E" xml:space="preserve">Patꝫ hec ↄ̨ña: q2 omīs pona <lb/>difficilius agens ſiue ꝓducēs aliquid tardius il-<lb/>lud agit ſiue producit. </s>
              <s xml:id="N26185" xml:space="preserve">Et probatur añs: et ſit a. po-<lb/>nã alterãs c. reſiſtentiã ab f. proportiõe: et b. pona <lb/>alterans eandē c. reſiſtentiã ab .h. proportione mi-<lb/>nori: et arguitur /  a. difficilius agit ſiue alterat c. <lb/>reſiſtētiã ꝙ̄ b: q2 difficultas actõis ip̄ius a. ē maior <lb/>̄ difficultas actõis ipſiꝰ b. / igr̄ a. difficiliꝰ agit ꝙ̄ b. <lb/></s>
              <s xml:id="N26193" xml:space="preserve"><pb chead="De motu rarefactionis quo ad cauſam." file="0224" n="224"/>               Probat̄̄ añs, q2 hec actio demõſtrata actiõe ipſiꝰ <lb/>a. eſt maior ꝙ̄ difficultas actõis ipſiꝰ b. et hec actio <lb/>eſt difficultas actiõis ipſiꝰ a. / vt ↄ̨ſtat cū nõ diſtīguã­<lb/>tur (vt ſuppono) / igr̄ difficultas actiõis ipſius a. eſt <lb/>maior ꝙ̄ difficultas actiõis ipſiꝰ b. </s>
              <s xml:id="N261A2" xml:space="preserve">Ptꝫ ↄ̨ña expo-<lb/>ſitorie, et ſiĺr minor: ſed maior ꝓbat̄̄: q2 hec actio-<lb/>demõſtrata actione ipſiꝰ a. eſt maior ꝙ̄ actio ipſiꝰ <lb/>b. et oīs difficultas actiõis ipſiꝰ b. eſt actio ipſiꝰ b. / <lb/>igr̄ hec actio demõſtrata actiõe ipſiꝰ a. eſt maior ̄ <lb/>difficultas actiõis ipſiꝰ b. / qḋ fuit ꝓbandū.                <anchor type="note" xlink:href="note-0224-01" xlink:label="note-0224-01a"/>               </s>
              <s xml:id="N261B4" xml:space="preserve">¶ Dices <lb/>forte cū calculatore in capite de difficultate acti-<lb/>onis, et cū paulo veneto in ſua ſūma pḣie in libro <lb/>de generatõe capĺo .27. ↄ̨cedendo illatū, et negãdo <lb/>falſitatē ↄ̨ñtis, et ad ꝓbationē negãdo illud / qḋ ibi <lb/>aſſumit̄̄: vcꝫ /  quãto aliq̇d difficiliꝰ agit aut ꝓdu-<lb/>cit aliq̇d tãto tardiꝰ agit ſiue ꝓducit illud. </s>
              <s xml:id="N261C3" xml:space="preserve">Nã ḋicit <lb/>calculator /  difficultas actiõis attēdēda eſt penes <lb/>rei potentiã ita  quanto potētia fuerit maior tã-<lb/>to difficultas actionis erit maior.</s>
            </p>
            <div xml:id="N261CC" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0224-01a" xlink:label="note-0224-01" xml:id="N261D0">
                <s xml:id="N261D4" xml:space="preserve">Calcula. <lb/>de diffi. <lb/>actio. <lb/></s>
                <s xml:id="N261DC" xml:space="preserve">Paulus <lb/>venetꝰ in <lb/>ſumma <lb/>pḣie.</s>
              </note>
            </div>
            <note position="left" xml:id="N261E5" xml:space="preserve">ↄ̈ calcuĺ.</note>
            <p xml:id="N261E9">
              <s xml:id="N261EA" xml:space="preserve">Sed cõtra eū arguit̄̄ ſic /  tūc ſeque-<lb/>retur /  difficiliꝰ deꝰ ꝓduceret qḋcū ꝓducibile qḋ <lb/>ꝓducit ꝙ̄ aliqḋ agens creatū ̄tūcū parue potē-<lb/>tie: ſed ↄ̨ñs eſt abſurdū: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N261F3" xml:space="preserve">Se­<lb/>quela ꝓbat̄̄ / q2 deꝰ in īfinitū maioris potentie eſt ̄ <lb/>aliqua creatura. </s>
              <s xml:id="N261FA" xml:space="preserve">Nec valet dicere /  illud intelligr̄ <lb/>de potētia nõ cognitiua / q2 tūc ſeq̄ret̄̄ /  difficilius <lb/>ageret virtꝰ ꝓducēs in hora decē gradꝰ calididatꝪ <lb/>̄ illa q̄ ꝓduceret in eadē hora vnū p̄ciſe, et diffici-<lb/>lius ageret virtus infinita naturalis (ſi que eſſet) <lb/>̄ virtus infinita quo nichil falſius:</s>
            </p>
            <p xml:id="N26207">
              <s xml:id="N26208" xml:space="preserve">In oppoſitū tñ argr̄ ſic. </s>
              <s xml:id="N2620B" xml:space="preserve">Qm̄ veloci-<lb/>tas motus localis attēdit̄̄ penes maiꝰ ſpaciū ꝑtrã­<lb/>ſitū in eodē tꝑe, et velocitas augmētationis penes <lb/>maiorē quãtitatē acq̇ſitã: et velocitas intenſionis <lb/>penes maiorē iutēſionē: igr̄ a ſimili velocitas alte­<lb/>ratiõis d3 attendi penes multitudinē graduū q̈li-<lb/>tatis ꝓducte mediãte motu alterationis. </s>
              <s xml:id="N2621A" xml:space="preserve">Itē nullo <lb/><gap/> <lb/>igitur ſic debet cõmenſurari. </s>
              <s xml:id="N26222" xml:space="preserve">Conſequentia ptꝫ: et <lb/>probabitur antecedens in primo notabili.</s>
            </p>
            <p xml:id="N26227">
              <s xml:id="N26228" xml:space="preserve">Quadruplici mēbro hãc queſtionē ab­<lb/>ſoluere intendo. </s>
              <s xml:id="N2622D" xml:space="preserve">¶ Primo notabilia ponã. </s>
              <s xml:id="N26230" xml:space="preserve">¶ Scḋo <lb/>aliq̈s ↄ̨cluſiones indicaꝫ. </s>
              <s xml:id="N26235" xml:space="preserve">¶ Tertio dubia mouebo <lb/></s>
              <s xml:id="N26239" xml:space="preserve">¶ Quarto ad rationes ante oppoſitū reſpõdebo.</s>
            </p>
            <note position="left" xml:id="N2623C" xml:space="preserve">Triplex <lb/>alṫatio.</note>
            <p xml:id="N26242">
              <s xml:id="N26243" xml:space="preserve">Pro primi expeditione notandum eſt <lb/>primo tagendo materiã primi argumēti:  alte-<lb/>ratio tripliciter accipit̄̄: ſaltem apud eos qui entia <lb/>ſucceſſiua ponūt motū localē, alṫationē, et quēuis <lb/>aliū motū. </s>
              <s xml:id="N2624E" xml:space="preserve">Primo mõ actiue ꝓ ipſo vcꝫ alterante <lb/>ſiue alteratiua potētia. </s>
              <s xml:id="N26253" xml:space="preserve">Scḋo mõ paſſiue ꝓ ſubie-<lb/>cto. </s>
              <s xml:id="N26258" xml:space="preserve">Tertio mõ formaliṫ ꝓ ipſo motu alterationis <lb/>qui ſcḋm reales quedã entitas ſucceſſiua eſt. </s>
              <s xml:id="N2625D" xml:space="preserve">Scḋm <lb/>noīales autē p̄t accipi formalr̄ ꝓ ipſa q̈litate q̄ ſuc­<lb/>ceſſiue ꝓducit̄̄. </s>
              <s xml:id="N26264" xml:space="preserve">Utrūūt alteratio formalis ſit q̄dã <lb/>entitas ſucceſſiua necne ad pñs nõ intēdo diſputa­<lb/>re. </s>
              <s xml:id="N2626B" xml:space="preserve">Id eī diſputatū īuenies ꝑ cõplures ↄ̨mētatores <lb/>pḣi tertio pḣicoꝝ: ſiue em̄ diſtinguat̄̄ ſiue nõ: ſemꝑ <lb/>pari forma ꝓcedent ea q̄ in toto hoc oꝑe dicuntur. <lb/></s>
              <s xml:id="N26273" xml:space="preserve">¶ Tu tñ aduerte /  ſicut alteratio tribꝰ modis dr̄: <lb/>actiue vcꝫ paſſiue, et formalr̄, ita triplr̄ deſcribēda <lb/>eſt eiꝰ velocitas. </s>
              <s xml:id="N2627A" xml:space="preserve">dū tñ primo motꝰ alteratiõis diffi­<lb/>niat̄̄. </s>
              <s xml:id="N2627F" xml:space="preserve">Uñ motꝰ alteratiõis eſt motꝰ ad q̈litatē ꝑ quē <lb/>vcꝫ alicui ſucceſſiue acq̇rit̄̄ aut deꝑdit̄̄ q̈litas / vt ptꝫ <lb/>ꝑ pḣm primo de gñatione textu cõmenti .10. et ī poſt <lb/>p̄dicamēto motꝰ. </s>
              <s xml:id="N26288" xml:space="preserve">Sed velocitas alteratiõis actiue <lb/>eſt potētia alteratiua ſucceſſiue q̈litatē ꝓducēs vel <lb/>corrumpens. </s>
              <s xml:id="N2628F" xml:space="preserve">Uelocitas vero alteratiõis paſſiue               <cb chead="De motu rarefactionis quo ad cauſam."/>               eſt ſubiectū in quo ſucceſſiue ꝓducit̄̄ aut corrūpitur <lb/>q̈litas. </s>
              <s xml:id="N26297" xml:space="preserve">Sed velocitas alteratiõis formalis eſt ip̄a <lb/>q̈litas q̄ ſucceſſiue ꝓducit̄̄, aut corrūpit̄̄ in aliq̊ ſub­<lb/>iecto. </s>
              <s xml:id="N2629E" xml:space="preserve">Nã niſi aliqḋ ſubiectū alteret̄̄ nõ erit motus <lb/>alteratiõis ̄uis qualitas ꝓducat̄̄.               <anchor type="note" xlink:href="note-0224-02" xlink:label="note-0224-02a"/>               </s>
              <s xml:id="N262A8" xml:space="preserve">(Motus em̄ eſt <lb/>actus entis puta ſubiecti tertio phiſicoꝝ textu cõ-<lb/>menti 6.) </s>
              <s xml:id="N262AF" xml:space="preserve">Sꝫ ſi qualitas ſucceſſiue ꝓduceret̄̄ extra <lb/>ſubiectū: poterit dici talis ſucceſſiua ꝓductio mu-<lb/>tatio ad qualitatē. </s>
              <s xml:id="N262B6" xml:space="preserve">Hic vlterius aduerte /  in ipſa <lb/>forma q̈litatis duplices poſſūt gradꝰ ſignari: pu-<lb/>ta gradṫ intēſionis ipſiꝰ forme: et gradus entitatis <lb/>ipſiꝰ forme. </s>
              <s xml:id="N262BF" xml:space="preserve">Nã vt inferiꝰ oſtendemꝰ põt dari quali­<lb/>tas nulliꝰ intēſionis et ſcḋm ſe et ſcḋm quãlꝫ eiꝰ par­<lb/>tē: et ſic in ea reperient̄̄ gradꝰ entitatꝪ forme et non <lb/>gradꝰ intēſiõis: ſicut in materia in capite de motu <lb/>rarefactiõis etc̈. ſignãtur certi gradꝰ ētitatis ipſiꝰ <lb/>materie abſ aliqua intēſione. </s>
              <s xml:id="N262CC" xml:space="preserve">¶ His p̄miſſis dico / <lb/> velocitas alteratiõis nõ attēdit̄̄ aut mēſurari d3 <lb/>penes qualitatē acq̇ſitã in ordine ad ſubiectū maiꝰ <lb/>vel minus in tanto vel tanto tꝑe. </s>
              <s xml:id="N262D5" xml:space="preserve">Probat̄̄ / q2 alias <lb/>nulla alteratio mētalis hoc eſt ipſiꝰ aīe ratiõalis <lb/>eſſet altera velocior aut tardior: qḋ ē manifeſte flm̄ <lb/></s>
              <s xml:id="N262DD" xml:space="preserve">Nec etiã velocitas ipſiꝰ alteratõis mēſurat̄̄ penes <lb/>ꝓportionē qualitatis acq̇ſite ad p̄exiſtentē: q2 tunc <lb/>ſi vnū pedale hñs duos g̈dus caliditas acquireret <lb/>tres gradꝰ in hora, et aliud hñs quatuor acq̇reret <lb/>quī in eadē hora: velociꝰ alteraret̄̄ illud qḋ acq̇-<lb/>rit tres quã illud qḋ acq̇rit quī: q2 inter qualita-<lb/>tē acquiſitã illi qḋ acq̇rit tres et p̄exiſtentē eſt ꝓpor­<lb/>tio ſexq̇altera: ſed iter qualitatē acquiſitã alteri et <lb/>p̄exiſtentē eſt ꝓportio ſexquiq̈rta. </s>
              <s xml:id="N262F0" xml:space="preserve">Itē nec d3 ↄ̨men­<lb/>ſurari penes ꝓportione aggregati ex qualitate ac­<lb/>quiſita et p̄exiſtēte ad qualitate p̄exiſtentem: vt ptꝫ <lb/>eodē exēplo. </s>
              <s xml:id="N262F9" xml:space="preserve">Itē nec velocitas in motu alteratiõis <lb/>d3 attendi penes acq̇ſitionē qualitatis equalis in-<lb/>tenſiõis in eodē tꝑe: q2 tūc ſeq̄ret̄̄ /  eque velociter <lb/>in hora alteraret̄̄ pedale qḋ ꝑ totū acq̇rit .4. gra-<lb/>dus caliditatis: et bipedale qḋ ꝑ totū in eadē hora <lb/>itidē acq̇rit .4. gradus caliditatis: qḋ eſt manifeſte <lb/>falſū / vt ꝓbat primū argumentū ante oppoſitum. <lb/>               <anchor type="note" xlink:href="note-0224-03" xlink:label="note-0224-03a"/>               </s>
              <s xml:id="N2630F" xml:space="preserve">Et hoc eſt ↄ̈ albertū de ſaxonia in ſuo tractatu ꝓ-<lb/>portionū: et ↄ̈ paulū venetū in ſūma pḣie in libris <lb/>phiſicoꝝ capĺo .37. </s>
              <s xml:id="N26316" xml:space="preserve">Et cõfirmat̄̄ hoc / q2 poſſibile eſt <lb/>dare q̈litatē nulliꝰ intēſiõis ſucceſſiue ꝓductã in a-<lb/>liquod ſubiectū / vt inferiꝰ ꝓbat̄̄:               <anchor type="note" xlink:href="note-0224-04" xlink:label="note-0224-04a"/>               et ꝓbat calculator <lb/>in fine capitis de difformibꝰ: et talis ꝓduceret̄̄ per <lb/>motū alteratiõis: q2 nõ ꝑ motū localē, aut augmē­<lb/>tationis, aut aliquē aliū: igr̄ velocitas alteratiõis <lb/>nõ hꝫ attendi penes acq̇ſitionē q̈litatis eq̈lis intē-<lb/>ſionis etc̈. </s>
              <s xml:id="N2632C" xml:space="preserve">Minor ꝓbat̄̄ / q2 illa q̈litas ſucceſſiue a-<lb/>licui acquirit̄̄: igr̄ ꝓducit̄̄ ꝑ motū alteratiõis. </s>
              <s xml:id="N26331" xml:space="preserve">Ptꝫ <lb/>ↄ̨ña ꝑ locū ad diffinitiõe. </s>
              <s xml:id="N26336" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo: q2 quē-<lb/>admodū illud velociꝰ auget qḋ plus de quantitate <lb/>ꝓducit: et illud velociꝰ ꝓdcit ſubſtantiã qḋ plus de <lb/>ſubſtãtia ꝓducit in eodē tꝑe: ita etiã a ſimili dicen-<lb/>dū eſt  illud velociꝰ alterat qḋ in eodē tꝑe plus de <lb/>entitate ipſiꝰ q̈litatꝪ ꝓducit: ſiue illa q̈litas ſit ma­<lb/>ioris intēſionis ſiue minoris nõ eſt cura.               <anchor type="note" xlink:href="note-0224-05" xlink:label="note-0224-05a"/>               </s>
              <s xml:id="N2634A" xml:space="preserve">Et ex hoc <lb/>etiã ptꝫ ↄ̈ paulū venetū /  intenſio nõ eſt eſſentialis <lb/>q̈litati: qm̄ oportet eū cõcedere aliquã qualitatem <lb/>nulliꝰ eſſe intēſiõis. </s>
              <s xml:id="N26353" xml:space="preserve">Mēſurat em̄ intēſionē q̈litatis <lb/>difformis penes reductionē ad vniformitatē, et nõ <lb/>penes gradū ſummū: vt ptꝫ ꝑ eū in libro de gene-<lb/>ratione ſue ſūme capite tertio.               <anchor type="note" xlink:href="note-0224-06" xlink:label="note-0224-06a"/>               </s>
              <s xml:id="N26361" xml:space="preserve">¶ Dico igr̄ /  veloci­<lb/>tas motꝰ alterationis d3 attendi penes multitudi­<lb/>nē graduū entitatis ipſiꝰ q̈litatis: nullo pacto a-<lb/>ſpiciēdo ad intenſionē aut extenſionē. </s>
              <s xml:id="N2636A" xml:space="preserve">Probat̄̄ / q2 <lb/>nõ attendit̄̄ penes intenſionē, nec penes ꝓportionē <lb/>aggregati ex q̈litate acq̇ſita et p̄habita ad q̄litatē               <pb chead="Quarti tractatus" file="0225" n="225"/>               preexiſtentem, nec penes proportionalem qualitateꝫ <lb/>acquiſite ad preexiſtentem, nec penes qualitatem <lb/>acquiſitam in ordine ab ſubiectū maius vel minꝰ <lb/>in tanto tempore: igr̄ debet attendi penes multitu-<lb/>dinē graduū entitatis ipſius q̈litatis nullo pacto <lb/>aſpiciēdo ad intenſionē aut extenſionē. </s>
              <s xml:id="N26380" xml:space="preserve">Añs ptꝫ ex <lb/>dictis, et ↄ̨ña ſiĺr: q2 nõ apparet alter modꝰ quo mē­<lb/>ſurari poſſet motꝰ alterationis velocitas.</s>
            </p>
            <div xml:id="N26387" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0224-02a" xlink:label="note-0224-02" xml:id="N2638B" xml:space="preserve">3°. phiſi. <lb/>tex. q̄ .6.</note>
              <note position="right" xlink:href="note-0224-03a" xlink:label="note-0224-03" xml:id="N26393" xml:space="preserve">ↄ̈ alber-<lb/>tū ḋ ſax. <lb/>et pau. ve.</note>
              <note position="right" xlink:href="note-0224-04a" xlink:label="note-0224-04" xml:id="N2639D" xml:space="preserve">Calcula. <lb/>de diffi.</note>
              <note position="right" xlink:href="note-0224-05a" xlink:label="note-0224-05" xml:id="N263A5" xml:space="preserve">ↄ̈ pauluꝫ <lb/>venetum</note>
              <note position="right" xlink:href="note-0224-06a" xlink:label="note-0224-06" xml:id="N263AD" xml:space="preserve">peues q̇d <lb/>attendit̄̄ <lb/>velocitaſ <lb/>motꝰ al-<lb/>teratiõis</note>
            </div>
            <p xml:id="N263BB">
              <s xml:id="N263BC" xml:space="preserve">Notandū eſt ſcḋo tangendo materiã <lb/>vltime replice primi argumenti:  ponã rei nichil <lb/>aliud eſt ꝙ̄ ipſa res potēs ad agendū. </s>
              <s xml:id="N263C3" xml:space="preserve">Pro quo ad­<lb/>uertendū eſt /  ſicut plus eſt de materia in toto vno <lb/>pedali ꝙ̄ in medietate eiꝰ: et plus etiã de forma eſ-<lb/>ſentiali extēſa ꝙ̄ in medietate eiꝰ: ita etiã pari rõne <lb/>plus eſt de forma accidentali puta de qualitate ex­<lb/>tenſa ꝑ pedale in toto ipſo pedali ꝙ̄ in medietate: <lb/>etiã ſi pedale ſit vniforme: ̄uis eque intēſa eſt q̈li-<lb/>tas in medietate pedalis ſicut ī toto. </s>
              <s xml:id="N263D4" xml:space="preserve">Quare ſignã­<lb/>de ſunt certe portiones / vt ſupra dictum eſt in ipſa <lb/>q̈litate (portiones inquã entitatis forme et nõ intē-<lb/>ſionis) quas vocant pḣi de hac materia loquentes <lb/>gradus forme ſiue entitatis ipſius forme acciden-<lb/>talis. </s>
              <s xml:id="N263E1" xml:space="preserve">Stat em̄ aliquã formã accidentalem puta b. <lb/>eſſe eque extēſam eq̄ intēſam vniformiter ſicut a. et <lb/>tñ in q̈druplo vel in qua volueris ꝓportione minꝰ <lb/>ↄ̨tinere de forma ꝙ̄ a. </s>
              <s xml:id="N263EA" xml:space="preserve">Quod facile demõſtrat̄̄ ſic. <lb/></s>
              <s xml:id="N263EE" xml:space="preserve">Capio em̄ vnū pedale / qḋ ſit b. vniformiter caliduꝫ <lb/>vt .4. / et capio vnū q̈drupedale qḋ ſit a. et ſit qḋlibet <lb/>pedale ipſiꝰ a. calidū oīno eodē mõ ſicut b. et ↄ̨dēſe­<lb/>tur a. nõ variata eiꝰ intēſiõe ad quãtitatē ipſius b. <lb/>quo poſito a. et b. erūt equalis intēſionis et extēſi-<lb/>onis oīno: et tñ a. in q̈druplo plus ↄ̨tinebit de calo­<lb/>re ꝙ̄ b. / igr̄ ſtat aliquã formã accidentalē puta b. eē <lb/>eq̄ intēſam vniformiter ſicut a. et eq̄ extēſam: et tñ in <lb/>q̈druplo minꝰ ↄ̨tinere de forma ꝙ̄ a. / qḋ fuit ꝓbandū <lb/></s>
              <s xml:id="N26402" xml:space="preserve">Probat̄̄ minor / q2 a. ãte ↄ̨dēſationē in quadruplo <lb/>plus ↄ̨tinebat de forma ꝙ̄ b. / vt cõſtat: et ꝑ ↄ̨denſa-<lb/>tionē nichil acq̇ſiuit nec deꝑdit ex caſu: igr̄ facta cõ­<lb/>denſatione in q̈druplo plus cõtinet de forma quã <lb/>b. </s>
              <s xml:id="N2640D" xml:space="preserve">¶ His dictis dico /  poña rei nõ attendit̄̄ penes <lb/>multitudinē materie: q2 tūc ſeq̄ret̄̄ /  vbicun eſſet <lb/>plus de materia ibi plus eſſet de poña actiua ipſiꝰ <lb/>rei. </s>
              <s xml:id="N26416" xml:space="preserve">(De poña .n. actiua loq̇mur) ſed ↄ̨ñs eſt falſum: <lb/>igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N2641B" xml:space="preserve">Falſitas ↄ̨ñtis oſtendit̄̄ / q2 ma­<lb/>ioris actiuitatis eſt pedale ignis quã pedale terre / <lb/>vt experiētia docet: et tñ plus de materia eſt in pe-<lb/>dali terre quã in pedali ignis / vt dicūt pḣi. </s>
              <s xml:id="N26424" xml:space="preserve">Itē paſ­<lb/>ſim ↄ̨cedūt philoſophãtes materiã nulliꝰ eſſe acti-<lb/>uitatis (actiuitatis inquã realis) / igr̄ poña actiua <lb/>rei nõ debet attēdi penes multitudinē materie. </s>
              <s xml:id="N2642D" xml:space="preserve">Itē <lb/>ſi materia eſſet alicuiꝰ actiuitatis ſequeret̄̄ /  ipſa <lb/>eſſet ꝓductiua ↄ̈rioꝝ vel  materia ipſiꝰ aque acti­<lb/>ue cõcurreret ad ꝓducendū formã ignis: et ſic ↄ̨cur­<lb/>reret ad corruptionē ipſiꝰ aque cuiꝰ eſt materia: ſed <lb/>ↄ̨ñs eſt falſuꝫ etc̈. </s>
              <s xml:id="N2643A" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 capta materia ip-<lb/>ſius ignis ſi ipſa eſt actiua: vel ipſa eſt actiua for-<lb/>me ignis: vel forme aque etc̈. vel vtriuſ. </s>
              <s xml:id="N26441" xml:space="preserve">Si tertiū <lb/>ſequit̄̄ ipſam eſſe effectiuã ↄ̈rioꝝ. </s>
              <s xml:id="N26446" xml:space="preserve">Si primū ſequit̄̄: <lb/> cū ipſa fuerit ſub for̄a aque ꝓducet formã ignis <lb/>ſiue nata erit ꝓducere. </s>
              <s xml:id="N2644D" xml:space="preserve">Si ſcḋm ſequit̄̄ /  ipſa exi-<lb/>ſtente ſub forma ignis nata erit cõcurrere ad ꝓdu-<lb/>cendã formã aque etc̈. / et ſic ſequit̄̄ illatū. </s>
              <s xml:id="N26454" xml:space="preserve">Nec etiaꝫ <lb/>poña rei attendenda eſt penes quãtitatē: quia tunc <lb/>quantitas eſſet ꝓductiua ↄ̈rioꝝ vel quãtitas ignis <lb/>cõcurret ad ꝓducendã formã aque vel alicuiꝰ alte-<lb/>rius / qḋ eſt falſuꝫ. </s>
              <s xml:id="N2645F" xml:space="preserve">Ptꝫ ſequela ſicut priꝰ de materia <lb/></s>
              <s xml:id="N26463" xml:space="preserve">Itē ſequit̄̄ /  ſemꝑ caliditas maiorꝪ quãtitatꝪ eſſet <lb/>maioris actiuitatis cuiꝰ falſitas patꝫ manifeſte de <lb/>flãma et ferro ignito. </s>
              <s xml:id="N2646A" xml:space="preserve">¶ Et ꝑ idē ptꝫ /  poña rei non               <cb chead="Capitulū primū."/>               attendit̄̄ penes intenſionē forme: cū ferrū ignitum <lb/>maioris poñe ſit calefactiue quã flãma ignis: et tñ <lb/>nõ eſt maioris intēſiõis.                <anchor type="note" xlink:href="note-0225-01" xlink:label="note-0225-01a"/>               </s>
              <s xml:id="N26479" xml:space="preserve">¶ Dico igr̄ cū calculatore <lb/>in capĺo de poña rei /  poña actiua rei eſſentialis <lb/>attendit̄̄ penes multitudinē forme iu materia. </s>
              <s xml:id="N26480" xml:space="preserve">Qḋ <lb/>ſic ꝓbat̄̄: q2 nõ attendit̄̄ penes multitudinē materie <lb/>intēſionē aut quãtitatē, vt ꝓbatū eſt: igr̄ attendit̄̄ <lb/>penes multitudinē forme in materia. </s>
              <s xml:id="N26489" xml:space="preserve">Patꝫ ↄ̨ña / q2 <lb/>nõ videt̄̄ aliꝰ modꝰ penes quē debeat mēſurari po-<lb/>tentia ipſiꝰ rei.                <anchor type="note" xlink:href="note-0225-02" xlink:label="note-0225-02a"/>               </s>
              <s xml:id="N26495" xml:space="preserve">Et huiꝰ opiniõis etiã eſt paulꝰ vene-<lb/>tus in libro de gñatiõe capite .26. et iacobꝰ forliuiē­<lb/>ſis in expoſitione prime fen primi canonis doctri-<lb/>na tertia capite primo: inquiens oēs cõiter dicere <lb/>potentiã rei attendendã eſſe penes multitudinē for­<lb/>me.               <anchor type="note" xlink:href="note-0225-03" xlink:label="note-0225-03a"/>               </s>
              <s xml:id="N264A7" xml:space="preserve">¶ Ex hac poſitiõe ſequit̄̄ primo a. et b. eq̈lia in <lb/>quãtitate eſſe equãlr̄ intēſa ꝑ totū: et tñ a. eſſe in īfi-<lb/>nitū maioris poñe ꝙ̄ b. </s>
              <s xml:id="N264AE" xml:space="preserve">Probat̄̄ et volo /  a. ſit vnū <lb/>corpꝰ īfinitū in cuiꝰ quolꝫ pedali ſint .4. gradꝰ cali-<lb/>ditatis vniformiter, et etiã .4. g̈dus forme: ita  in <lb/>quolibet pedali ſit equaliter de forma et intēſione: <lb/>et ſit b. vnum pedale habens 4. gradus forme ade-<lb/>quate et intenſionis: et condenſetur a. vſ ad quã-<lb/>titatem b. nulla alia mutatione facta in ipſo. </s>
              <s xml:id="N264BD" xml:space="preserve">Quo <lb/>poſito ſequit̄̄ correlariū / quia a. manebit intenſum <lb/>vt .4. et habebit īfinitos g̈dus forme: q2 īfinitã mul­<lb/>titudinē forme quã ãte ↄ̨dēſationē habebat.               <anchor type="note" xlink:href="note-0225-04" xlink:label="note-0225-04a"/>               </s>
              <s xml:id="N264CB" xml:space="preserve">¶ Se-<lb/>quit̄̄ ſcḋo /  b. eſt īfinite calidū vniformiter: et a. ſo-<lb/>lū finite: et tñ a. eſt in īfinitū maiorꝪ poñe quã b. </s>
              <s xml:id="N264D2" xml:space="preserve">Ptꝫ <lb/>retēto ṗori caſu de a. et  b. diuidat̄̄ ꝑ p̄tes ꝓporti-<lb/>onales ꝓportiõe dupla: et  caliditas exñs in ṗma <lb/>ꝑte ꝓportiõali extēdat̄̄ ꝑ totū b. manēte eadē ītēſiõe <lb/>et ſiĺr fiat de caliditate exñte in ſcḋa parte ꝓporti-<lb/>onali, et in tertia, et in q̈rta / et ſic ↄ̨ñter: ſine additiõe <lb/>alicuiꝰ noue quãtitates. </s>
              <s xml:id="N264E1" xml:space="preserve">Quo poſito b. erit īfinite <lb/>intēſum, et a. ſolū finite vniformiter: et tñ a. erit īfi-<lb/>nite maioris poñe quã b. cū habeat in īfinitū plꝰ de <lb/>forma: igr̄ correlariū verū.               <anchor type="note" xlink:href="note-0225-05" xlink:label="note-0225-05a"/>               </s>
              <s xml:id="N264EF" xml:space="preserve">¶ Ex quo ſequit̄̄ tertio / <lb/> nõ maioris poñe eſt corrūpere caliditatē pedalē <lb/>īfinite intēſam quã corrūpere caliditatē vt .4. peda­<lb/>lem. </s>
              <s xml:id="N264F8" xml:space="preserve">Ptꝫ / q2 tãte reſiſtētie eſt vna ſicut reliq̈. </s>
              <s xml:id="N264FB" xml:space="preserve">Eiuſdē <lb/>em̄ reſiſtētie eſt caliditas ipſiꝰ b. ante̄ fiat infinite <lb/>inteſa: et poſt īfinitã intēſionē acq̇ſitã: cū ſemꝑ ma-<lb/>neat eadē forma oīno.               <anchor type="note" xlink:href="note-0225-06" xlink:label="note-0225-06a"/>               </s>
              <s xml:id="N26509" xml:space="preserve">¶ Ex quo vlteriꝰ ſequit̄̄ q̈rto / <lb/> eque velociter caliditas pedalis finita intēſiue et <lb/>extenſiue. </s>
              <s xml:id="N26510" xml:space="preserve">et poñe vt .8. corrūpet īfinitã caliditatē ſi­<lb/>cut finitã. </s>
              <s xml:id="N26515" xml:space="preserve">Patꝫ ex priori: q2 equaliṫ reſiſtūt finita <lb/>q̈litas et īfinita. </s>
              <s xml:id="N2651A" xml:space="preserve">Et ſic etiã dicendū eſt /  eque veloci­<lb/>ter ꝓducet finite intēſam ſicut īfinite intēſam. </s>
              <s xml:id="N2651F" xml:space="preserve">Con-<lb/>ſequēs igr̄ eſt velocitatē alteratiõīs nõ attendi de-<lb/>bere penes intēſionē q̈litatis. </s>
              <s xml:id="N26526" xml:space="preserve">Quod aduerte.</s>
            </p>
            <div xml:id="N26529" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0225-01a" xlink:label="note-0225-01" xml:id="N2652D">
                <s xml:id="N26531" xml:space="preserve">penes q̇d <lb/>attendi <lb/>hꝫ poña <lb/>rei. <lb/></s>
                <s xml:id="N2653B" xml:space="preserve">Calcu. ḋ <lb/>poña rei</s>
              </note>
              <note position="right" xlink:href="note-0225-02a" xlink:label="note-0225-02" xml:id="N26540">
                <s xml:id="N26544" xml:space="preserve">paulꝰ ve-<lb/>netus de <lb/>gñatiõe. <lb/></s>
                <s xml:id="N2654C" xml:space="preserve">Iacobꝰ <lb/>forliuiē <lb/>ṗma fen <lb/>primi ca­<lb/>nõis do. <lb/>ṗma c. 1.</s>
              </note>
              <note position="right" xlink:href="note-0225-03a" xlink:label="note-0225-03" xml:id="N26559" xml:space="preserve">.1. correĺ.</note>
              <note position="right" xlink:href="note-0225-04a" xlink:label="note-0225-04" xml:id="N2655F" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0225-05a" xlink:label="note-0225-05" xml:id="N26565" xml:space="preserve">.3. correĺ.</note>
              <note position="right" xlink:href="note-0225-06a" xlink:label="note-0225-06" xml:id="N2656B" xml:space="preserve">4. correĺ</note>
            </div>
            <note position="right" xml:id="N26571" xml:space="preserve">5. correĺ.</note>
            <p xml:id="N26575">
              <s xml:id="N26576" xml:space="preserve">¶ Sequit̄̄ quīto / b. eſſe īfinite calidū vniformiter a. <lb/>vero ſolū finite et eſſe equalis quãtitatis: et tñ a. eſſe <lb/>maioris poñe in quacū libuerit ꝓportione. </s>
              <s xml:id="N2657D" xml:space="preserve">Ptꝫ <lb/>facile in caſu primi correlarii. </s>
              <s xml:id="N26582" xml:space="preserve">Nã a. in illo caſu eſt <lb/>in īfinitū maioris poñe quã b: ſi igr̄ velis ipſū fieri <lb/>maioris poñe in aliq̈ ꝓportiõe finita p̄ciſe: demas <lb/>ab eo de forma q̊uſ maneat p̄ciſe maioris poñe <lb/>quã b. in ꝓportione optata.               <anchor type="note" xlink:href="note-0225-07" xlink:label="note-0225-07a"/>               </s>
              <s xml:id="N26592" xml:space="preserve">¶ Sequit̄̄ ſexto /  b. eſt <lb/>īfinite intēſum, et a. īfinite remiſſū ſiue nulliꝰ intēſi-<lb/>onis, et equalis quantitatis cū b. et tñ a. eſt equalis <lb/>poñe cū b. </s>
              <s xml:id="N2659B" xml:space="preserve">Probat̄̄ retento caſu de b. et pono /  a. <lb/>ſit vniformiter calidū vt .4. intēſiue hñs etiã p̄ciſe <lb/>4. g̈dus entitatis ipſiꝰ caliditatis: deinde in prima <lb/>parte ꝓportiõali hore diuidat̄̄ caliditas ipſiꝰ a. in <lb/>duas medietates ſcḋm intēſionē, et vniant̄̄ ſcḋm ex­<lb/>tenſionē et ↄ̨dēſent̄̄ ad pedalē quãtitatē, et in ſcḋa <lb/>parte ꝓportionali tꝑis iteꝝ diuidat̄̄ illa caliditas <lb/>in duas medietates ſcḋm intēſionē, et ↄ̨tinuent̄̄ m <lb/>extēſionē ille due medietatis et reducant̄̄ ad peda­               <pb chead="De motu rarefactionis quo ad cauſam." file="0226" n="226"/>               lem quãtitatē: et ſic ↄ̨ñter: ita  in qualꝫ parte pro-<lb/>portionali tꝑis ſequēti fiat in duplo minꝰ intenſa <lb/>caliditas ipſiꝰ a. ꝙ̄ ī īmediate p̄cedēti: et maneat. </s>
              <s xml:id="N265B7" xml:space="preserve">ſic <lb/>in fine hore nõ reſtituta p̄ſtine intēſioni vel maiori: <lb/></s>
              <s xml:id="N265BD" xml:space="preserve">Quo poſito ſequit̄̄ correlarium. </s>
              <s xml:id="N265C0" xml:space="preserve">Equalis em̄ poñe <lb/>manet a. ſicut ante remiſſionē: cū maneat eadē for-<lb/>ma.               <anchor type="note" xlink:href="note-0226-01" xlink:label="note-0226-01a"/>               </s>
              <s xml:id="N265CC" xml:space="preserve">¶ Sequit̄̄ ſeptimo /  a. et b. ſunt eq̈lis quãtita-<lb/>tis puta pedalis b. īfinite calidū, a. vero īfinite re-<lb/>miſſe calidū: et tñ a. eſt in īfinitū maioris poñe quã <lb/>b. </s>
              <s xml:id="N265D5" xml:space="preserve">Ptꝫ ex priori: et primo.               <anchor type="note" xlink:href="note-0226-02" xlink:label="note-0226-02a"/>               </s>
              <s xml:id="N265DD" xml:space="preserve">¶ Hanc materiã latiꝰ vi-<lb/>dere poteris apud calculatorē capitulo de potētia <lb/>rei. </s>
              <s xml:id="N265E4" xml:space="preserve">et ſic ptꝫ quid poña rei, et penes / q̇d attendi ha-<lb/>beat. </s>
              <s xml:id="N265E9" xml:space="preserve">Et cõſimiliter dicas de reſiſtētia /  ipſa attē-<lb/>di habet penes multitudinem forme. </s>
              <s xml:id="N265EE" xml:space="preserve">Eadem enim <lb/>ratio eſt reſiſtentie et potentie.</s>
            </p>
            <div xml:id="N265F3" level="5" n="10" type="float">
              <note position="right" xlink:href="note-0225-07a" xlink:label="note-0225-07" xml:id="N265F7" xml:space="preserve">6. correĺ.</note>
              <note position="left" xlink:href="note-0226-01a" xlink:label="note-0226-01" xml:id="N265FD" xml:space="preserve">7. correĺ.</note>
              <note position="left" xlink:href="note-0226-02a" xlink:label="note-0226-02" xml:id="N26603" xml:space="preserve">Calcuĺ. ḋ <lb/>poña rei</note>
            </div>
            <p xml:id="N2660B">
              <s xml:id="N2660C" xml:space="preserve">Notandū eſt tertio </s>
              <s xml:id="N2660F" xml:space="preserve">Pro materia ſcḋi <lb/>argumēti /  oē agens ab īfinita latitudine ꝓpor-<lb/>tionis natū eſt agere. </s>
              <s xml:id="N26616" xml:space="preserve">Nã agens vt .2. in reſiſtentiã <lb/>vt vnū agit a ꝓportiõe dupla: in ſubduplã vero re-<lb/>ſiſtentiã a ꝓportiõe in triplo maiori, et in ſubq̈dru­<lb/>plã a ꝓportione in triplo maiori: et in ſuboctuplaꝫ <lb/>a ꝓportiõe in q̈druplo maiori: et ſic in īfinitū. </s>
              <s xml:id="N26621" xml:space="preserve">Ptꝫ <lb/>igr̄ agens vt .2. natū eſſe ab īfinita latitudine ꝓpor­<lb/>tionis agere: ꝑinde at qḋuis alind. </s>
              <s xml:id="N26628" xml:space="preserve">Eadeꝫ em̄ rõ <lb/>cuilibet ſuffragat̄̄ agēti. </s>
              <s xml:id="N2662D" xml:space="preserve">Nec ꝓpoſitū infringit mi­<lb/>nima reſiſtētia per ſe potēs naturaliter reſiſtere ſi <lb/>q̇ſpiã opinet̄̄ talē eſſe dandã. </s>
              <s xml:id="N26634" xml:space="preserve">Et ſi em̄ illa ponatur <lb/>nichilominꝰ agens ſuapte natura ab īfinita ꝓpor-<lb/>tionis latitudine natū eſſe agere nequa̄ ãbigēdū <lb/>eſt. </s>
              <s xml:id="N2663D" xml:space="preserve">Q, o a finita dūtaxat agat ꝓportiõe: ex īpedi­<lb/>mento reſiſtētie ſibi accidit.               <anchor type="note" xlink:href="note-0226-03" xlink:label="note-0226-03a"/>               </s>
              <s xml:id="N26647" xml:space="preserve">Uñ reſiſtere nihil aliud <lb/>eſt quã actionē agētis īpedire totaliter aut partia­<lb/>liter. </s>
              <s xml:id="N2664E" xml:space="preserve">Dico totalr̄ / cū īpedit actiouē a ꝓportiõe eq̈-<lb/>litatis vel maioris ineq̈litatis. </s>
              <s xml:id="N26653" xml:space="preserve">Dico partialr̄ / cnm <lb/>aliquã latitudinē actiõis īpedit ipſa reſiſtētia a ꝓ-<lb/>portione mīoris īeq̈litatis. </s>
              <s xml:id="N2665A" xml:space="preserve">Reſiſtentia .n. vt a pḣis <lb/>diffinitū eſt nichil aliud eſt ꝙ̄ actionis īpedimentū <lb/></s>
              <s xml:id="N26660" xml:space="preserve">Cū o īpedimentū actiõis p̄t agenti ↄ̨tingere du-<lb/>pliciter ex ꝑte vcꝫ paſſi / in qḋ agit ita  paſſū reſi-<lb/>ſtat vel ex parte alicuiꝰ extrinſeci in qḋ nõ agit: q2 <lb/>forte ad illud in tali diſtãtia hꝫ ꝓportionē mīoris <lb/>ineq̈litatꝪ vel ſi forte agit in illud: illud tñ nõ ſolū <lb/>īpedit actionē in ſemet ipſū ſed in aliqḋ etiã extrin­<lb/>ſecū: ideo duplex eſt reſiſtētia: quedã vcꝫ eſſentialis <lb/>q̄dã accidētalis: vt bñ oñdit Suiſeth ī capite de rea­<lb/>ctiõe.                <anchor type="note" xlink:href="note-0226-04" xlink:label="note-0226-04a"/>               </s>
              <s xml:id="N26678" xml:space="preserve">Reſiſtētia eſſētialis eſt reſiſtētia paſſi ī qḋ a-<lb/>gēs agit adeq̈te: vt ſi a. agit in b. et b. ei reſiſtat m <lb/>illã partē inquã agit, talis reſiſtentia illiꝰ partis <lb/>dr̄ eſſentialis.               <anchor type="note" xlink:href="note-0226-05" xlink:label="note-0226-05a"/>               </s>
              <s xml:id="N26686" xml:space="preserve">Sed reſiſtentia accidētalis eſt reſiſtē­<lb/>tia īpediēs actionē agētis in aliqḋ extrinſecū ei vĺ <lb/>ſubiecto in quo eſt: vt ſi a. agit in b. et c. actionē ſiue <lb/>aliquã latitudinē actiõis īpediat in ipſo b. / tūc c. re­<lb/>ſiſtit accidētalr̄ ipſi a.               <anchor type="note" xlink:href="note-0226-06" xlink:label="note-0226-06a"/>               </s>
              <s xml:id="N26696" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  nõnū̄ eadē <lb/>reſiſtētia eſt eſſentialis et accidentalis vt cū a. agit <lb/>in b. et etiã agit in c. et .c. reſiſtit ipſi a. ue tã velociter <lb/>agat in b. ſicut ageret a moto ipſo c. / tūc reſiſtentia <lb/>ipſiꝰ c. eſt accidētalis reſpectu actiõis ipſiꝰ a. in b. <lb/>paſſū, et eſſentialis reſpectu actiõis ipſiꝰ a. in idē c. <lb/>               <anchor type="note" xlink:href="note-0226-07" xlink:label="note-0226-07a"/>               </s>
              <s xml:id="N266AA" xml:space="preserve">¶ Sequit̄̄ ſcḋo /  cõiṫ cū aliqḋ agens agit per totū <lb/>aliqḋ paſſū q̄libet pars ipſiꝰ paſſi reſiſtit eſſentia-<lb/>liter: et q̄libet etiã reſiſtit accidētalr̄. </s>
              <s xml:id="N266B1" xml:space="preserve">Reſiſtit em̄ eſ-<lb/>ſentialiṫ reſpectu actiõis in ipſam: et accidētaliter <lb/>reſpectu actiõis in alterã. </s>
              <s xml:id="N266B8" xml:space="preserve">Et vĺr pars ꝓpinquior <lb/>agenti magis reſiſtit accidētalr̄ ipſi agenti quã re­<lb/>mota reſiſtens. </s>
              <s xml:id="N266BF" xml:space="preserve">Dico reſiſtēs / q2 tm̄ p̄t elongari  <lb/>nõ reſiſtet. </s>
              <s xml:id="N266C4" xml:space="preserve">Intelligas ſēꝑ ceteris paribꝰ.               <anchor type="note" xlink:href="note-0226-08" xlink:label="note-0226-08a"/>               </s>
              <s xml:id="N266CC" xml:space="preserve">¶ Nõ tñ <lb/>in ea ꝓportione in qua pars eſt ꝓpinquior agenti <lb/>ceteris paribꝰ in ea plus reſiſtit: vt bñ ꝓbari põt ex <lb/>deductione ↄ̨firmatiõis ſcḋi argumēti principalis               <cb chead="De motu rarefactionis quo ad cauſam."/>               antc oppoſitã. </s>
              <s xml:id="N266D8" xml:space="preserve">Et ſiĺr dicendū eſt de actione /  cum <lb/>aliqḋ agens agit pars eiꝰ ꝓptnquior magis agit <lb/>quã pars remotior ceteris paribꝰ: nõ tñ in ea ꝓpor­<lb/>tione qua partes ſūt ꝓpinquiores in ea velociꝰ a-<lb/>gūt: vt facile deduci p̄t ex ꝓceſſu ſcḋi argumēti prī-<lb/>cipalis ante oppoſitū.               <anchor type="note" xlink:href="note-0226-09" xlink:label="note-0226-09a"/>               </s>
              <s xml:id="N266EA" xml:space="preserve">¶ Ex q̊ ſequit̄̄ / q̄ ꝓbatio ſiue <lb/>argumentū calculatoris in capite de actiõe lumīo-<lb/>ſi circa principiū quo intēdit ꝓbare /  partes me-<lb/>dii diſtantes a lumīoſo nullo pacto īpediūt actio-<lb/>nē lūinoſi in partibꝰ ꝓpīquioribꝰ eſt īefficax: ̄uis <lb/>ↄ̨cluſio ſit a: īnititur em̄ illa ꝓbatio huic funda-<lb/>mēto: in ea ꝓportiõe qua partes ſūt ꝓpinquiores <lb/>lūinoſo ceteris paribꝰ in ea magis īpedirēt: dūmõ <lb/>ponant̄̄ īpedire / qḋ eſt flm̄ / et negatū ab ipſo calcu-<lb/>latore ī capite de reactiõe iuxta mediū vbi hãc ma­<lb/>teriã ad plenū ꝑ eū digeſtã īuenies.               <anchor type="note" xlink:href="note-0226-10" xlink:label="note-0226-10a"/>               </s>
              <s xml:id="N26706" xml:space="preserve">¶ Sequit̄̄ ſcḋo / <lb/> hec ↄ̨ña nichil valet a. et b. ſūt eq̈les p ↄ̨ñe actiue, <lb/>et a. agit in c. paſſū, et a. eſt in duplo ꝓpīquiꝰ c. paſ-<lb/>ſo quã b. / ergo a. in duplo velocius agit in c. quã b. <lb/>agat in c. </s>
              <s xml:id="N26711" xml:space="preserve">Probat̄̄ quia poſſibile eſt /  c. ſit extra <lb/>ſpherã actiuitatis ipſius b. / et tūc añs eſt veꝝ et ↄ̨ñs <lb/>flm̄: g̊ ↄ̨ña nulla.               <anchor type="note" xlink:href="note-0226-11" xlink:label="note-0226-11a"/>               </s>
              <s xml:id="N2671D" xml:space="preserve">¶ Sequit̄̄ tertio /  hec ↄ̨ña nichil <lb/>valet, a. et b. ſūt eq̈lis poñe actiue, et c. eſt īfra. ſphe-<lb/>ram actiuitatꝪ vtriuſ, et a. eſt in q̈druplo ꝓpīquiꝰ <lb/>ipſe c. ꝙ̄ ip̄m b. / igr̄ a. in q̈druplo velociꝰ agit in c. ̄ <lb/>ip̄m b. </s>
              <s xml:id="N26728" xml:space="preserve">Probat̄̄ / q2 ſi illa ↄ̨ña valeret pari rõne hec <lb/>valeret a. et b. ſūt eq̈lis poñe actiue, et c. eſt ītra ſphe­<lb/>ram actiuitatis vtriuſ, et in īfinitū magis appro­<lb/>ximat̄̄ a. ipſi c. ꝙ̄ īpſū b. approximat̄̄ eidē c. / igr̄ in īfi­<lb/>nitū velociꝰ aget a. in c. quã ipſū b. ſed hec nichil va­<lb/>let: g̊ nec alia. </s>
              <s xml:id="N26735" xml:space="preserve">Seq̄la ſatis ptꝫ, et ꝓbat̄̄ minor: et po­<lb/>no /  a. ſit actiuitatꝪ vt .8. et c. reſiſtētie vt .4. hoc eſt <lb/> maxima ꝓportio a. qua a. põt agere in c. qñ eſt ei <lb/>optīe approxīatū ſicut ei põt approxīari ſit dupla <lb/>(ſemꝑ loquor de optīa approxīatiõe ſimplr̄ poſſi-<lb/>bili) et diſtet a: ab ipſo c. ꝑ pedalē diſtantiã, et in pri­<lb/>ma parte ꝓportiõali hore ꝓportiõe dupla appro-<lb/>ximet̄̄ a. ipſi c. ſcḋm qḋlibet eiꝰ punctū in duplo plꝰ <lb/>ꝑ ↄ̨dēſationē ſiue deꝑditione materie aut forme, et <lb/>in ſcḋa parte ꝓportionali approximetur in duplo <lb/>pluſ̄ in ṗma, et in tertia in duplo pluſ̄ in ſcḋa, et <lb/>ſic ↄ̨ñter: quo poſito añs eſt verū et ↄ̨ñs flm̄ / vt ptꝫ ex <lb/>caſu. </s>
              <s xml:id="N26750" xml:space="preserve">Nã in caſu poſitū eſt /  maxīa ꝓportio a. q̈ a. <lb/>põt agere ſit dupla.               <anchor type="note" xlink:href="note-0226-12" xlink:label="note-0226-12a"/>               </s>
              <s xml:id="N2675A" xml:space="preserve">¶ Sequit̄̄ quarto /  hec ↄ̨ña ni­<lb/>chil valet a. agit in c. et b. eſt in duplo mīoris poñe <lb/>quã a. et in duplo ꝓpinquiꝰ ipſi c. quã a. / g̊ b. tm̄ agi <lb/>in c. ſicut a. </s>
              <s xml:id="N26763" xml:space="preserve">Probat̄̄ eſto /  c. ſit reſiſtētie vt .4. et a. <lb/>poñe vt .8: cū ceterꝪ poſitis in caſu correlarii: tunc <lb/>añs eſt verū et ↄ̨ñs flm̄. </s>
              <s xml:id="N2676A" xml:space="preserve">Nã tūc b. hꝫ ꝓportionē eq̈li­<lb/>tatis ad c. / et ꝑ ↄ̨ñs nõ agit in c.               <anchor type="note" xlink:href="note-0226-13" xlink:label="note-0226-13a"/>               </s>
              <s xml:id="N26774" xml:space="preserve">¶ Sequit̄̄ quinto /  <lb/>paſſū ſimplex vniforme ſcḋm punctū eiꝰ mediū ma­<lb/>xime reſiſtit. </s>
              <s xml:id="N2677B" xml:space="preserve">¶ Hoc eſt  paſſū magis reſiſtit agēti <lb/>ei approxīato ad punctū mediū quã quis alio mõ <lb/>approxīato ceteris paribꝰ.               <anchor type="note" xlink:href="note-0226-14" xlink:label="note-0226-14a"/>               </s>
              <s xml:id="N26787" xml:space="preserve">Illud correlariū eſt cal­<lb/>culatoris in capite de reactione circa mediū. </s>
              <s xml:id="N2678C" xml:space="preserve">Uide­<lb/>as ibi eiꝰ ꝓbationē q̄ pulchra eſt et ſubtilis. </s>
              <s xml:id="N26791" xml:space="preserve">Eam tñ <lb/>nõ pono / q2 nõ apparet michi vĺis. </s>
              <s xml:id="N26796" xml:space="preserve">Et ideo intelli-<lb/>gas eã et ſiĺr correlariū de corꝑe vniformis reſiſtē­<lb/>tie: et omnium dimenſionum vniformium.</s>
            </p>
            <div xml:id="N2679D" level="5" n="11" type="float">
              <note position="left" xlink:href="note-0226-03a" xlink:label="note-0226-03" xml:id="N267A1" xml:space="preserve">q̇d ſit re-<lb/>ſtere.</note>
              <note position="left" xlink:href="note-0226-04a" xlink:label="note-0226-04" xml:id="N267A9">
                <s xml:id="N267AD" xml:space="preserve">Calcula. <lb/></s>
                <s xml:id="N267B1" xml:space="preserve">Reſiſtē-<lb/>tia eſſen-<lb/>tialis.</s>
              </note>
              <note position="left" xlink:href="note-0226-05a" xlink:label="note-0226-05" xml:id="N267B8" xml:space="preserve">Reſiſtē-<lb/>tia acci-<lb/>dentalis</note>
              <note position="left" xlink:href="note-0226-06a" xlink:label="note-0226-06" xml:id="N267C2" xml:space="preserve">.1. correĺ.</note>
              <note position="left" xlink:href="note-0226-07a" xlink:label="note-0226-07" xml:id="N267C8" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0226-08a" xlink:label="note-0226-08" xml:id="N267CE" xml:space="preserve">Aduerte</note>
              <note position="right" xlink:href="note-0226-09a" xlink:label="note-0226-09" xml:id="N267D4" xml:space="preserve">.1. correĺ. <lb/>ↄ̈ calcul.</note>
              <note position="right" xlink:href="note-0226-10a" xlink:label="note-0226-10" xml:id="N267DC" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0226-11a" xlink:label="note-0226-11" xml:id="N267E2" xml:space="preserve">.3. correĺ.</note>
              <note position="right" xlink:href="note-0226-12a" xlink:label="note-0226-12" xml:id="N267E8" xml:space="preserve">4. correĺ.</note>
              <note position="right" xlink:href="note-0226-13a" xlink:label="note-0226-13" xml:id="N267EE" xml:space="preserve">.5. correĺ.</note>
              <note position="right" xlink:href="note-0226-14a" xlink:label="note-0226-14" xml:id="N267F4" xml:space="preserve">Correla. <lb/>calcula.</note>
            </div>
            <p xml:id="N267FC">
              <s xml:id="N267FD" xml:space="preserve">Expeditis notabilibꝰ  ex hoc primo <lb/>mēbro q̄ſtiõis: reſtat ſcḋm mēbrū abſoluere in quo <lb/>ↄ̨cluſiones materiã quarti, quīti, et ſexti argumen­<lb/>toꝝ principaliū ante oppoſitū reſoluētes inducunt̄̄ <lb/>               <anchor type="note" xlink:href="note-0226-15" xlink:label="note-0226-15a"/>               </s>
              <s xml:id="N2680D" xml:space="preserve">Et ṗmo inducã ↄ̨cluſiões tangētes materiã quarti <lb/>et quīti argumenti puta de velocitate motus alte-<lb/>rationis penes cauſam. </s>
              <s xml:id="N26814" xml:space="preserve">Sit igitur.</s>
            </p>
            <div xml:id="N26817" level="5" n="12" type="float">
              <note position="right" xlink:href="note-0226-15a" xlink:label="note-0226-15" xml:id="N2681B" xml:space="preserve">.2. articu­<lb/>lꝰ quõuis</note>
            </div>
            <p xml:id="N26823">
              <s xml:id="N26824" xml:space="preserve">Prima ↄ̨̨cluſio. </s>
              <s xml:id="N26827" xml:space="preserve">Ubicun aliqḋ alte-<lb/>rans vuiformiṫ ↄ̨tinuo corrūpit aliquã reſiſtentiã               <pb chead="Quarti tractatus" file="0227" n="227"/>               ꝑ corruptionē poña ab ipſa reſiſtentia reagēte ce-<lb/>teris īpedimētis et iuuamētis deductis: nulla poña <lb/>alteratiua maior eiuſdē ſpeciei aut mīor valet vni-<lb/>formiṫ corrūpere eandē reſiſtētiã. </s>
              <s xml:id="N26837" xml:space="preserve">Ptꝫ hec ↄ̨cluſio <lb/>ex prima replica q̈rti argumenti ante oppoſitum.</s>
            </p>
            <p xml:id="N2683C">
              <s xml:id="N2683D" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
              <s xml:id="N26840" xml:space="preserve">Ubi aliqḋ alterãs vni­<lb/>formiter ↄ̨tinuo corrūpit̄̄ aliquã reſiſtentiã ꝑ cor-<lb/>ruptionē poñe ab ipſa reſiſtētia reagēte ceterꝪ īpe­<lb/>dimētis et iuuameētis deductis: q̄libet poña altera­<lb/>tiua maior eiuſdē ſpeciei agēs in eandē reſiſtentiã <lb/>in īfinitū velociter talē reſiſtētiã corrūpit: dūmodo <lb/>nõ īpediat̄̄ ab actiõe: quã diu aliquid reſiſtētie fue-<lb/>rit: et oīs minor potens in eadem reſiſtentiam a-<lb/>gere in infinitum tarde talem reſiſtentiam corrum­<lb/>pet ceteris paribus. </s>
              <s xml:id="N26855" xml:space="preserve">Patet hec concluſio ex ſecnn-<lb/>da replica quarti argumenti ante oppoſitum.</s>
            </p>
            <p xml:id="N2685A">
              <s xml:id="N2685B" xml:space="preserve">Tertia ↄ̨̨cluſio. </s>
              <s xml:id="N2685E" xml:space="preserve">Ubicun aliqḋ alte-<lb/>rans īuariatū alterat aliqḋ paſſū cuiꝰ paſſi reſiſtē­<lb/>tia ↄ̨tinuo maioratur: oīs poña alteratiua maior <lb/>eiuſdē ſpeciei: et ſimiliter mīor īuariata alterãs idē <lb/>paſſū cū ↄ̨tinuo et ↄ̨ſimili oīo cremēto reſiſtētie: eq̄ <lb/>velociter ↄ̨tinuo remittit ſuū motū alteratiõis ſicut <lb/>data poña. </s>
              <s xml:id="N2686D" xml:space="preserve">Et ſi reſiſtētia ↄ̨tinuo decreſcat reſpe-<lb/>ctu alicuiꝰ poñe īuariate: et ↄ̨ſiĺr eodē mõ decreſcat <lb/>reſpectu cuiuſuis poñe maioris aut mīoris īuaria­<lb/>te: oīs talis poña maior vel mīor eq̄ velociṫ' ↄ̨tinuo <lb/>intēdit motū ſuū alteratiõis ſicut data poña. </s>
              <s xml:id="N26878" xml:space="preserve">Ptꝫ <lb/>hec ↄ̨cluſio manifeſte ex ſexta ↄ̨cluſiõe quīti capitis <lb/>primi tractatꝰ huiꝰ tertie pattꝪ: hīta poſſibilitate <lb/>caſus ↄ̨cluſiõis  eq̄ velociṫ' vcꝫ ↄ̨tinuo creſcat aut <lb/>decreſcat reſiſtētia reſpectu maioris poñe et mino­<lb/>ris. </s>
              <s xml:id="N26885" xml:space="preserve">Qḋ facile fieri põt adiumēto alicuiꝰ poñe extrī­<lb/>ſece ꝓducētis dictã reſiſtētiã aut corrūpentis. </s>
              <s xml:id="N2688A" xml:space="preserve">Qḋ <lb/>plerū fit in corpore humano cū mala cõplexio a-<lb/>git in bona reſiſtentē: et ꝑ ſubſidiū medicine auget̄̄ <lb/>reſiſtentiã corporis humani. </s>
              <s xml:id="N26893" xml:space="preserve">Aut ꝑ additamentum <lb/>alicuiꝰ cibi diſcõueniētis cõplexioni hūane ↄ̨tinuo <lb/>remittit̄̄ reſiſtentia ipſiꝰ nature: īualeſcente morbo <lb/>et continuo intendente ſuam alterationem.</s>
            </p>
            <p xml:id="N2689C">
              <s xml:id="N2689D" xml:space="preserve">Quarta ↄ̨̨cluſio. </s>
              <s xml:id="N268A0" xml:space="preserve">Quauis poña alte-<lb/>ratiua īuariata alterãte paſſū cuiꝰ paſſi reſiſtentia <lb/>ↄ̨tinuo creſcit ꝑ actionē alicuiꝰ poña. </s>
              <s xml:id="N268A7" xml:space="preserve">cuiꝰ actiõi da­<lb/>ta poña alteratiua reſiſtit: oīs poña maior īuaria­<lb/>ta alterãs idē paſſū cū cremēto reſiſtētie ꝑ actionē <lb/>eiuſdē poñe augmētantis reſiſtentiã ceteris dedu-<lb/>ctis tardiꝰ in quouis tꝑe terminato ad principiuꝫ <lb/>alteratiõis remittit ſuū motū alteratõis: et oīs mi­<lb/>nor alterãs idē paſſū cū cremēto reſiſtētie ꝑ actiõeꝫ <lb/>eiuſdē poñe cuiꝰ etiã actiõi dicta poña mīor reſiſtit <lb/>ceteris īpedimētis et iuuameētis deductis velociꝰ re­<lb/>mittit motū ſuū in quouis tꝑe ad principiū alte-<lb/>ratiõis termīato. </s>
              <s xml:id="N268BE" xml:space="preserve">Exēplū / vt data poña alteratiua <lb/>vt .8. q̄ īuariata alteret g. paſſū cuiꝰ g. paſſi reſiſtē-<lb/>tia ↄ̨tinuo creſcit ꝑ actionē alicuiꝰ poñe puta e. cuiꝰ <lb/>actioni ↄ̨tinuo reſiſtit poña alteratiua vt .8. tūc di­<lb/>cit ↄ̨cluſio /  ſi poña alteratiua vt .12. (ītelligas ſꝑ <lb/>eiuſdē ſpeciei) alteret g. paſſū cuiꝰ reſiſtētia ↄ̨tinuo <lb/>creſcit ꝑ actionē etiã ipſiꝰ e. poñe cui actioni reſiſtit <lb/>ipſa poña alteratiua vt .12. ceteris īpedimentis et <lb/>iuuameētis deductis in quolibet tꝑe terminato ad <lb/>prīcipiū alteratiõis tardiꝰ remittit motū ſuū ꝙ̄ in <lb/>eodē remittat poña vt .8. et ī eodē exēplo ptꝫ de mi-<lb/>nori. </s>
              <s xml:id="N268D7" xml:space="preserve">Probat̄̄ prima pars ↄ̨cluſionis: q2 alterante <lb/>poña maiore illud idē paſſum: reſiſtentia illiꝰ paſſi <lb/>nõ tam velociter creſcit in aliquo tꝑe termīato ad <lb/>inſtans initiatiuū alteratiõis ſicut creſcit in eodeꝫ <lb/>tꝑe alterãte poña mīore: igr̄ alterãte poña maiore               <cb chead="Capitulū primū."/>               in nullo tꝑe termīato ad inſtãs īitiatiuū alteratio­<lb/>nis reſiſtētia tantã ꝓportionē acq̇rit ſicut in eodeꝫ <lb/>tꝑe acq̇rit alterãte poña mīore: et quantã ꝓportio-<lb/>nē in aliq̊ tꝑe acq̇rit reſiſtentia tantã deꝑdit ꝓpor° <lb/>inter reſiſtētiã et potentiã īuariatã agentē in illam <lb/>q̄cū ſit illa: igr̄ in q̊libet tꝑe terminato ad inſtãs <lb/>initiatiuū alteratiõis mīore ꝓportionē deꝑdit pro­<lb/>portio inter potētiã maiorē et reſiſtētiã ꝙ̄ ꝓportio <lb/>inṫ potētiã mīorē: et eandē reſiſtentiã in quã agūt et <lb/>maior et mīor potētia: et ex ↄ̨ñti in q̊libet tali tꝑe mi­<lb/>norē latitudinē motꝰ alteratõis deꝑdit potētia ma­<lb/>ior ꝙ̄ data potētia mīor: et ſic q̈uis potētia altera-<lb/>tiua īuariata alterante paſſū .etc. oīs poña maior <lb/>īuariata alterãs idē paſſū cū cremēto reſiſtentie ꝑ <lb/>actionē potētie augmētantꝪ reſiſtentiã ceteris de-<lb/>ductis tardiꝰ in q̊uis tꝑe termīato ad priucipiū al­<lb/>terationis remittit ſuū motū alterationis / qḋ fuit <lb/>ꝓbandū. </s>
              <s xml:id="N26907" xml:space="preserve">Et eodē modo probat̄̄ eſt ſecunda pars.</s>
            </p>
            <p xml:id="N2690A">
              <s xml:id="N2690B" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
              <s xml:id="N2690E" xml:space="preserve">Ubicū due potentie <lb/>alteratiue īuariate hñt eq̈les ꝓportiones ad duas <lb/>reſiſtētias ineq̈les in quas īcipiūt agere eas corrū­<lb/>pēdo ceteris deduttis: ↄ̨tinuo mīor illaꝝ potētiaꝝ <lb/>velociꝰ alterabit corrūpēdo ſuã reſiſtētiã ꝙ̄ maior. <lb/></s>
              <s xml:id="N2691A" xml:space="preserve">Probat̄̄ / q2 poña maior īcipit tardiꝰ corrūpere ſuã <lb/>reſiſtentiã ꝙ̄ mīor īcipiat corrūpere ſuã: vtra cõti­<lb/>nuo agēte a maiori et maiori ꝓportiõe (vt cõſtat et <lb/>poſt̄ maior tardiꝰ corrūpit ſuã reſiſtentiã nun̄ <lb/>īcipiet equaĺr' corrūpere, vel velociꝰ: igr̄ ↄ̨tinuo tar­<lb/>dius maior poña alterabit corrūpēdo ſuã reſiſten-<lb/>tiã ꝙ̄ mīor ſua: et ex ↄ̨ñti ↄ̨tinuo minor poña velociꝰ <lb/>alterabit corrūpēdo ſuã reſiſtentiã ꝙ̄ maior ſuam / <lb/>qḋ fuit ꝓbandū. </s>
              <s xml:id="N2692D" xml:space="preserve">Cõſequētia ptꝫ, et argr̄ maior / q2 <lb/>poña maior nõ īcipit eq̄ velociter corrūpere ſuã re-<lb/>ſiſtentiã ſicut mīor, nec velociꝰ et incipit: igr̄ incipit <lb/>tardiꝰ. </s>
              <s xml:id="N26936" xml:space="preserve">Ptꝫ ↄ̨ña et ꝓbat̄̄ maior vcꝫ /  nõ īcipit eque <lb/>velociter: q2 ſi ſic ſequit̄̄ /  īmediate poſt īſtãs īitia­<lb/>tiuū alteratiõis ab eq̈li ꝓportiõe aget poña maior <lb/>in ſuã reſiſtentiã ſicut poña mīor (vt ↄ̨ſtat) / et ex ↄ̨ñti <lb/>qualis erit ꝓportio poñe maioris ad ſuã reſiſtētiã <lb/>talis erit ꝓportio mīoris ad ſuã reſiſtentiã: et ꝑ ↄ̨ñs <lb/>q̈lis eſt ꝓportio īmediate poſt inſtãs initiatiuū inṫ <lb/>potentiã maiorē et minorē (q̄ ſit f. / vt pono) talis eſt <lb/>īter reſiſtentiã poñe maioris ad reſiſtentiã potētie <lb/>mīoris vcꝫ f. / vt ptꝫ ꝑ locū a tranſmutata ꝓportione <lb/>et cū a principio alteratiõis et corruptionis illaruꝫ <lb/>duaꝰ reſiſtentiaꝝ īter datas reſiſtētias maiorē vcꝫ <lb/>in quã agit poña maior: et minorē in quã agit po-<lb/>tentia mīor ſit ꝓportio f. vt facile induci põt ꝑ locū <lb/>a ꝑmutata proportiõe: ſeq̇t̄̄ /  illud qḋ corruptū ē a <lb/>maiori reſiſtentia eſt in f. ꝓportione maiꝰ illo quod <lb/>corruptū eſt a reſiſtētia mīore: </s>
              <s xml:id="N26959" xml:space="preserve">Conſequentia ptꝫ ex <lb/>primo correlario quīte ↄ̨cluſionis ſcḋi capitis ſcḋe <lb/>partis: et ex primo correlario q̈rte ↄ̨cluſiõis octa-<lb/>ui capitis eiuſdē partis. </s>
              <s xml:id="N26962" xml:space="preserve">Nã et ſi illa correlaria lo-<lb/>quant̄̄ de termīs ↄ̨tinuo ſe habētibꝰ in eadē ꝓpor-<lb/>tione in qua ſe hñt in principio decremēti nichilo­<lb/>minꝰ demõſtratiões illoꝝ correlarioꝝ vĺr illud pro­<lb/>bãt ꝑ quocū inſtãti illi termiui ſe habeãt in eadē <lb/>proportione in qua ſe hñt in principio decrementi <lb/></s>
              <s xml:id="N26970" xml:space="preserve">Et ꝑ ↄ̨ñs īmediate poſt inſtãs īitiatiuū alteratiõis <lb/>poña maior in f. ꝓportiõe velocius agit corrūpēdo <lb/>ſuã reſiſtentiã ꝙ̄ poña minor. </s>
              <s xml:id="N26977" xml:space="preserve">et ꝑ ↄ̨ñs nõ eq̈liter / qḋ <lb/>fuit ꝓbãdū. </s>
              <s xml:id="N2697C" xml:space="preserve">Et ſi dicas /  ſtat  īmediate poſt hoc <lb/>poña maior corrūpat ſuã reſiſtentiã in f. ꝓportiõe <lb/>velociꝰ ꝙ̄ poña mīor, et etiã eque velociṫ' in diuerſis <lb/>partibꝰ tꝑis. </s>
              <s xml:id="N26985" xml:space="preserve">Argr̄ hoc eſſe flm̄: q2 tūc ſeq̄ret̄̄ /  ſu-<lb/>bito ꝓportio maioris poñe ad ſuam reſiſtētiã q̄ eſt <lb/>eq̈lis ꝓportiõi mīoris potētie ad ſuã reſiſtentiã in               <pb chead="Quarti Tractatus" file="0228" n="228"/>               principio alteratiõis efficiret̄̄ in f. ꝓportiõe maior <lb/>ꝓportiõe mīoris potētie ad mīorē reſiſtentiã vĺ ma­<lb/>ior ꝙ̄ in f. ꝓportiõe maior: ſꝫ iſtḋ ↄ̨ñs eſt falſum: igr̄ <lb/>illud ex q̇ ſequit̄̄. </s>
              <s xml:id="N26997" xml:space="preserve">Sꝫ iã ꝓbo mīorem vcꝫ /  potentia <lb/>maior nõ incipit velocius corrūpere ſuã reſiſtentiã <lb/>̄ potētia minor: q2 ſi potētia maior incipit veloci­<lb/>us corrūpere ſuã reſiſtētia ꝙ̄ mīor: ſeq̇tur /  īmedia­<lb/>te poſt īſtans initiatiuū alteratiõis ſubito ꝓportio <lb/>maioris potētie ad ſuã reſiſtētiã efficit̄̄ pluſ̄ in f. <lb/>ꝓportiõe maior ꝓportiõe minoris potētie ad mīo-<lb/>rē reſiſtētiã / qḋ eſt manifeſte falſum cū ſucceſſiue ille <lb/>ꝓportiões cõtinuo augeãtur et tu prīcipio alteratio­<lb/>nis ſint equales vt caſus ↄ̨°nis indicat. </s>
              <s xml:id="N269AC" xml:space="preserve">Probat̄̄ tñ <lb/>ↄ̨ña / q2 vt paulo ante deductū eſt ſi potētia maior ī­<lb/>ciperet eque velociter corrūpere ſuã reſiſtētiã ſicut <lb/>poña mīor mīorē r̄ſiſtētiã: ꝓportio eiꝰ ad maiorē re­<lb/>ſiſtētiã ſubito efficēt̄̄ ī f. ꝓportõe maior ꝓpor°ne mīo­<lb/>ris poñe ad minorē reſiſtētiã: igit̄̄ cū caſu ſi poten­<lb/>tia maior incipit velocius corrūpere ſuã reſiſtēti3 <lb/>̄ potētia mīor minorē reſiſtētiã: ſeq̇tur /  ꝓportio <lb/>poñe maioris ad ſuã reſiſtētiã ſubito efficit̄̄ maior <lb/>pluſ̄ in f. ꝓportiõe ipſa mīoris poñe ad ſuã reſiſtē­<lb/>tiã. </s>
              <s xml:id="N269C3" xml:space="preserve">Et ſic pꝫ maior prīcipalis argumēti. </s>
              <s xml:id="N269C6" xml:space="preserve">Sꝫ iã reſi-<lb/>ſtat ꝓbare mīorē prīcipalē vcꝫ  poſt̄ poña ma-<lb/>ior tardius corrūpit ſuã reſiſtētiã nū̄ īcipiet eque <lb/>velociter corrūpere vel velociꝰ: q2 ſi ſic detur inſtãs <lb/>in quo īcipit eq̄ velociter corrūpere poſt̄ antea cõ­<lb/>tinuo tardius corrūpebat et ſit illud a. / et argr̄ ſic / in <lb/>a. inſtãti poña maior incipit eq̄ velociter corrūpere <lb/>ſuã reſiſtentiã ſicut poña mīor: et cõtiuuo ante a. in-<lb/>ſtans tardius corrūpebat: ergo ſequit̄̄ /  in a. inſtã­<lb/>ti maior latitudo eſt deꝑdita a. minori reſiſtētia ̄ <lb/>a. maiori: et ꝑ ↄ̨ñs maior ꝓportio eſt deperdita a. re­<lb/>ſiſtētia mīori ꝙ̄ a maiori: vt patꝫ ex octaua ſuppõe <lb/>quarti capitis ſcḋe partis iūcto loco a maiori. </s>
              <s xml:id="N269E1" xml:space="preserve">et ex <lb/>ↄ̨ñti ſequit̄̄ /  in inſtãti a. maior ē ꝓportio poñe mi­<lb/>noris ad reſiſtētiã ꝙ̄ poñe maioris ad maiorē reſi-<lb/>ſtētiã: et ꝑ ↄ̨ñs nõ incipiūt ille due poñe equaliṫ cor­<lb/>rūpere / qḋ fuit ꝓbandū. </s>
              <s xml:id="N269EC" xml:space="preserve">Patet ↄ̨ña: q2 ille ꝓportio­<lb/>nes in prīcipio alteratiõis ſunt equales: et augēt̄̄ p̄-<lb/>ciſe ꝑ decremētū reſiſtētiarū: igitur ſi maiorē ꝓpor-<lb/>tionē deꝑdit reſiſtentia minor ꝙ̄ maior / ſeq̇tur /  in <lb/>illo īſtãti a. maior ꝓportio ē acq̇ſita ꝓportiõi po-<lb/>tētie mīoris ad minorē reſiſtētiã: ꝙ̄ ꝓportioni poñe <lb/>maioris ad maiorē reſiſtētiã: et ꝑ ↄ̨ñs ſeq̇tur /  in in­<lb/>ſtãti a. maior eſt ꝓportio poñe minoris ad ſuã reſi­<lb/>ſtētiã ꝙ̄ poñe maioris ad maiorē reſiſtētiã: et ſic de <lb/>primo ad vltimū ptꝫ ↄ̨ña. </s>
              <s xml:id="N26A01" xml:space="preserve">Sꝫ  poſt̄ poña maior <lb/>tardius corrūpit ſuã reſiſtētiã: nū̄ īcipit velocius <lb/>ſuã reſiſtētiã corrūpere: ꝓbatur / q2 ſi ſic ſequeret̄̄ /  <lb/>poſſet incipere equaliter qm̄ ſucceſſiue cõtinuo cre-<lb/>ſcūt ille ꝓportiões: ſed ↄ̨ñs eſt falſum vt probatum <lb/>eſt: igitur et antecedēs. </s>
              <s xml:id="N26A0E" xml:space="preserve">Et ſic patet totuꝫ antecedēs / <lb/>et per ↄ̨ſequens cõcluſio.               <anchor type="note" xlink:href="note-0228-01" xlink:label="note-0228-01a"/>               </s>
              <s xml:id="N26A18" xml:space="preserve">¶ Ex qua concluſione ſeq̇-<lb/>tur primo /  ſi potentia vt .8. incipiat agere in reſi­<lb/>ſtentiã vt .4. eam corrumpendo ſucceſſiue vſ ad nõ <lb/>gradum: et in eodē inſtanti incipiat potentia vt .6. <lb/>corrūpere reſiſtētiam vt .3. continuo poñis inuaria­<lb/>tis: tūc potentia vt .6. continuo velocius corrumpet <lb/>reſiſtētiã vt .3. ꝙ̄ potentia vt .8. corrūpet reſiſteniaꝫ <lb/>vt .4. quãdiu ſimul corrūpent ceteris deductis: et in <lb/>minori tempore ꝙ̄ ſubſexq̇ṫtio corrūpet potentia vt <lb/>6. reſiſtentiam vt .3. ad non gradum ad tempus in <lb/>quo adequate potentia vt .8. corrūpet reſiſtentiam <lb/>vt .4. quãuis infinite velociter vtra illarum ſuam <lb/>reſiſtentiam corrumpet. </s>
              <s xml:id="N26A33" xml:space="preserve">Prima pars correlarii ī-<lb/>mediate ſequitur ex concluſione: ſed ſecunda pro-<lb/>batur / q2 ſi cõtinuo eque velociter potētia vt .8. cor-               <cb chead="Capi. primum"/>               rūperet reſiſtētiaꝫ vt .4. ſicut potentia vt .6. corrūpit <lb/>reſiſtētia vt .3. tūc potētia vt .6. in ſexq̇tertio minori <lb/>tēpore corrūpēt adequate reſiſtentiã vt .3. ꝙ̄ potētia <lb/>vt .8. corrūperet reſiſtētiã vt .4. ſed mõ ↄ̨tinuo poña <lb/>v. 6. velocius corrūpit reſiſtētiã vt .3. ꝙ̄ poña vt .8. <lb/>reſiſtentiã vt .4. / igitur ī mīori tēpore ꝙ̄ ſubſexq̇tertio <lb/>poña vt .6. corrūpit reſiſtētiam vt .3. adequate ad tē­<lb/>pus in quo adequate poña vt .8. corrūpit reſiſtētiã <lb/>vt .4. / quod fuit ꝓbandū. </s>
              <s xml:id="N26A4D" xml:space="preserve">Tertia pars patꝫ ex dedu­<lb/>ctione ſecunde replice quarti argumēti añ oppoſi-<lb/>tum.               <anchor type="note" xlink:href="note-0228-02" xlink:label="note-0228-02a"/>               </s>
              <s xml:id="N26A59" xml:space="preserve">¶ Sequit̄̄ ſecūdo /  ſi mediciã vt .8. agat in hu­<lb/>morem peccantē reſiſtētie vt .4. et alia mediciã ſub-<lb/>dupla agat in ſubduplū humorē corrūpēte vtra <lb/>malitiã humoris vſ ad nõ gradū vel purgãte ſiue <lb/>euacuãte: ip̄is medicints ↄ̨tinuo manētibꝰ īuariatꝪ <lb/>ceteris deductis: pluſ̄ in duplo velociꝰ minor me­<lb/>dicina corrūpet malitiã humoris in quē agit vſ <lb/>ad nõ gradum aut ip̄m totaliter euacuabit ꝙ̄ alia. <lb/></s>
              <s xml:id="N26A6B" xml:space="preserve">et in infinitū velocius in aliquo tꝑe aget minor me-<lb/>diciã ꝙ̄ maior in eodē tꝑe ̄uis vtra infinite velo­<lb/>citer agit. </s>
              <s xml:id="N26A72" xml:space="preserve">Hoc correlarium eandē cū precedēti ſor-<lb/>titur demõſtrationē: addita poſſibilitate huiꝰ v3  <lb/>ille medicine pñt manere cõtinuo eiuſdē poñe. </s>
              <s xml:id="N26A79" xml:space="preserve">Qḋ <lb/>intelligo cū dico eas manere īuariatas. </s>
              <s xml:id="N26A7E" xml:space="preserve">Id eī poſſi­<lb/>bile eſt fieri ꝑ continuã medicine adminiſtratõ3 ita <lb/> quãtū corrumpit̄̄ de poña medicine reagente hu­<lb/>more: tãtū acq̇ratur ꝑ cõtinuã noue medicine admi­<lb/>nistrationē. </s>
              <s xml:id="N26A89" xml:space="preserve">Aut (quod facilius eſt) ꝑ cõtinuã aliarū <lb/>partium actuationem. </s>
              <s xml:id="N26A8E" xml:space="preserve">Non eī ſubito nec ſimul ip̄a <lb/>tota medicina actuatur.</s>
            </p>
            <div xml:id="N26A93" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0228-01a" xlink:label="note-0228-01" xml:id="N26A97" xml:space="preserve"><gap/>̀. correĺ.</note>
              <note position="right" xlink:href="note-0228-02a" xlink:label="note-0228-02" xml:id="N26A9E" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N26AA4">
              <s xml:id="N26AA5" xml:space="preserve">Sexta concluſio </s>
              <s xml:id="N26AA8" xml:space="preserve">Poſſibile eſt potētiã <lb/>alteratiuã inuariatã cõtinuo manētē aliquod paſ-<lb/>ſum cõtinuo vniformiṫ alterare. </s>
              <s xml:id="N26AAF" xml:space="preserve">Probatur: q2 poſ­<lb/>ſibile eſt  a. potētia cõtinuo manēs potentie vt .8. <lb/>adequate alteret b. paſſum reſiſtēs cõtinuo vt .4. et <lb/>hoc ipſa potentia vt .8. introducēte vnã qualitatem <lb/>et corrūpēte contrariã: igitur poſſibile eſt aliquam <lb/>potentiam alteratiuã continuo inuariatã aliquod <lb/>paſſum continuo vniformiter alterare. </s>
              <s xml:id="N26ABE" xml:space="preserve">Probatur <lb/>antecedēs et pono /  a. potentia vt .8. approximetur <lb/>b. paſſo qḋ quidē paſſum non ſufficit reſiſtere a. po­<lb/>tētie vt .8. reſiſtētiã .4. graduū adequate: ſed appro­<lb/>ximetur c. ipſi b. ita  ſufficiat iuuare ipſum b. ad <lb/>reſiſtendū vt .4. ita  totalis reſiſtētia reſultãs ex <lb/>illis duabus ſit vt .4. et nec b. nec c. ſufficiãt agere in <lb/>a. et incipiat a. corrūpere reſiſtētiã ipſius b. paſſi: et <lb/>in quacun ꝓportiõe minus reſiſtit b. ipſi a. ꝑ ſuaꝫ <lb/>reſiſtētiã intrīſecã in eadē ꝓportiõe cõtinuo c. plus <lb/>iuuet ip̄m b. ad reſiſtēdū ꝙ̄ antea: et hoc ꝑ ipſius c. <lb/>cõtinuã approximationē localē vel ꝑ ſue potētie cõ­<lb/>tinuã intēſionē. </s>
              <s xml:id="N26AD9" xml:space="preserve">Quo poſito patet añs ꝓbandū. </s>
              <s xml:id="N26ADC" xml:space="preserve">Et <lb/>ſic patet concluſio.</s>
            </p>
            <note position="right" xml:id="N26AE1" xml:space="preserve">1. correl.</note>
            <p xml:id="N26AE5">
              <s xml:id="N26AE6" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  poſſibile <lb/>eſt aliquam potentiam alteratiuam continuo ma-<lb/>nentem inuariatam alterare aliquod paſſum con-<lb/>tinuo tardius et tardius. </s>
              <s xml:id="N26AEF" xml:space="preserve">Probatur et pono /  <lb/>a. potentia vt .8. agat in b. paſſum reſiſtentie vt .2. <lb/>et c. approximetur ipſi b. ita  iuuet continuo ip̄m <lb/>b. ad reſiſtendum et ita intendatur c. in potentia  <lb/>continuo plus et plus iuuet ad reſiſtendum: et non <lb/>agat c. ne b. in ipſuꝫ a. </s>
              <s xml:id="N26AFC" xml:space="preserve">Quo poſito ſequitur cor-<lb/>relarium</s>
            </p>
            <note position="right" xml:id="N26B01" xml:space="preserve">2. correl.</note>
            <p xml:id="N26B05">
              <s xml:id="N26B06" xml:space="preserve">¶ Sequitur ſecundo /  poſſibile eſt potentiam al-<lb/>teratiuam agentem in aliquod paſſum continuo <lb/>creſcere aut decreſcere reſiſtentia continuo manen­<lb/>te inuariata et continuo creſcente: et ſimiliter con-<lb/>tinuo decreſcente. </s>
              <s xml:id="N26B11" xml:space="preserve">Patet correlarium ex modo ꝓ-<lb/>bãde concluſionis et proris correlarii.</s>
            </p>
            <pb chead="De motu alterationis quo ad cauſam" file="0229" n="229"/>
            <note position="left" xml:id="N26B1A" xml:space="preserve">3. correĺ.</note>
            <p xml:id="N26B1E">
              <s xml:id="N26B1F" xml:space="preserve">¶ Sequit̄̄ tertio /  non ſtat alterans aliquod paſſū <lb/>inuariatum corumpendo reſiſtentiam continue in­<lb/>tendere motū alterationis vniformiter ceteris de­<lb/>ductis. </s>
              <s xml:id="N26B28" xml:space="preserve">Probatur / quia ſi aliquod alterãs inuaria­<lb/>tum põt vniformiter intendere motū alterationis <lb/>alterãdo aliquod paſſuꝫ corrūpēdo eiuſdē paſſi re­<lb/>ſiſtētiã ceteris deductis ſignet̄̄ illud: et ſit a. alterãs <lb/>c. paſſum / et arguitur ſic / a. alterans inuariatum <lb/>intendit motum ſuuꝫ corrumpendo reſiſtentiam c. <lb/>paſſi ceteris deductis: igitur in quolibet tempore <lb/>ſequenti maiorem latitudinem reſiſtentie corrum-<lb/>pit ꝙ̄ in equali precedente per conſequēs in quoli­<lb/>bet tempore ſequenti maioreꝫ latitudinem propor­<lb/>tionis acquirit proportio ipſius a. ad ſuam reſiſtē­<lb/>tiam ꝙ̄ in ſibi equali precedenti. </s>
              <s xml:id="N26B41" xml:space="preserve">vt patet ex octaua <lb/>ſuppoſitione quarti capitis ſecunde partis iuncto <lb/>loco a maiori et ſic non vniformiter augetur ꝓpor­<lb/>tio ipſius a. ad ſuã reſiſtētiã. </s>
              <s xml:id="N26B4A" xml:space="preserve">Non igr̄ a. vniformiṫ <lb/>intēdit motū ſuū alteratiõis / qḋ eſt oppoſitū cõceſſi. <lb/></s>
              <s xml:id="N26B50" xml:space="preserve">Patet hec ↄ̨ña: qm̄ oīno eodē mõ ſicut ītēdit̄̄ et cre-<lb/>ſcit ꝓportio poñe ad reſiſtētiã: ita ēt ītēditur motꝰ <lb/>iuxta huiꝰ opīonis fundamētū. </s>
              <s xml:id="N26B57" xml:space="preserve">¶ Seq̇t̄̄ .4°. /  qḋlꝫ <lb/>alterãs īuariatū p̄t alterare paſſū eiꝰ reſiſtētiã cor­<lb/>rūpēdo, auxiliãte aliq̊ extrinſeco: ↄ̨tinuo vniformiṫ <lb/>intēdēdo motū alteratõis. </s>
              <s xml:id="N26B60" xml:space="preserve">Probat̄̄ facile / qm̄ vt pꝫ <lb/>ex priori correlario: ſi a ↄ̨tinuo ageret ī c. paſſū eiꝰ <lb/>reſiſtētiã corrūpēdo ceterꝪ deductis ↄ̨tinuo ī q̊lꝫ tꝑe <lb/>alteratõis ſeq̄nti maiorē latitudinē ꝓportiõis acq̇­<lb/>reret ꝓportio eiꝰ ad ſuã reſiſtētiã ꝙ̄ in tꝑe eq̈li p̄ce-<lb/>dēti: pono igr̄ /  approximet̄̄ ip̄i c. aliq̈ poña iuuãs <lb/>ip̄3 c. ad reſiſtēdū ip̄i a taliṫ  ̄tã maiorē latitudi­<lb/>nē ꝓportiõis acq̇rit ꝓportio ip̄ius a ad ip̄m c. ī tꝑe <lb/>alteratiõis ſequēti ꝙ̄ ī ſibi eq̈li p̄cedēti: et hoc ꝑ cor­<lb/>ruptionē reſitētie ītrīſece: tãtã deꝑdat ꝑ iuuamē illi­<lb/>us poñe extrīſece: ita  ſꝑ in q̊lꝫ tꝑe actiõis ſequēte <lb/>tantã latitudinē ꝓportiõis adeq̈te acq̇rat ꝓportio <lb/>ipſiꝰ a. alterãtꝪ ad ip̄3 paſſū b. ſicut ī ſibi eq̈li p̄cedē­<lb/>te. </s>
              <s xml:id="N26B7D" xml:space="preserve">Quo poſito ſeq̇t̄̄ /  ↄ̨tinuo a. vniformiṫ intēdet <lb/>motū ſue alteratiõis alterãdo c. paſſū et corrūpēdo <lb/>eius reſitentiam: quod fuit ꝓbandū. </s>
              <s xml:id="N26B84" xml:space="preserve">¶ Seq̇tur .5°. /  <lb/>qḋlꝫ alterãs īuariatū p̄t alterare paſſū eiꝰ reſiſten­<lb/>tiã corrūpēdo auxiliãte aliq̊ extrīſeco: ↄ̨tīuo vnifor­<lb/>miter remittēdo motum alterationis. </s>
              <s xml:id="N26B8D" xml:space="preserve">Patet hoc <lb/>correlarium ſicut quartum.</s>
            </p>
            <p xml:id="N26B92">
              <s xml:id="N26B93" xml:space="preserve">Septima cõcluſio aliquo </s>
              <s xml:id="N26B96" xml:space="preserve">Alterãte in­<lb/>uariato aliqḋ paſſū alterãdo ↄ̨tinuo vniformiṫ re­<lb/>mittēte motū ſue alteratõis ꝑ cremētū reſiſtētie ex-<lb/>trīſece et accidētaĺ vt ī q̇nto correlario p̄cedētꝪ ↄ̨clu­<lb/>siõis dcm̄ eſt: qḋlꝫ alterãs maioris poñe v3 vniformi­<lb/>ter remitt&lt;/gap&gt; motū ſue alteratõis ꝑ ſui ↄ̨tinuã remiſ-<lb/>ſiõem idē paſſū alterãdo cū eodē iuuamīe reſiſtētie. <lb/></s>
              <s xml:id="N26BA6" xml:space="preserve">Probat̄̄ / ſit a. īuariatū alterãs c. paſſū ↄ̨tinuo vni-<lb/>formiṫ remittēs ſuã alterationē iuuãte aliq̊ extrīſe­<lb/>co c. paſſū ad reſiſtēdū: et ſit b. alterãs maioris po­<lb/>tētie cuiꝰ ꝓportio ad totã reſiſtētiã ipſiꝰ c. ī ṗncipio <lb/>actiõis ſit ī f. ꝓportiõe maior ꝓportione ipſiꝰ a. ad <lb/>eãdē reſiſtētiã: et ita variet̄̄ b. ↄ̨tinuo ī tꝑe alteratõis <lb/>̄ ↄ̨tinuo ī eadē diſtãtia ꝓportio eiꝰ ad ſuã r̄ſiſtētiã <lb/>ſit ī f. ꝓportiõe maior ꝓportiõe a. ad ſuã reſiſtētiã: <lb/>et īcipiãt ī eodē īſtãti alterare ↄ̨ſilia paſſa. </s>
              <s xml:id="N26BB9" xml:space="preserve">Tūc di-<lb/>co /  b. ↄ̨tinuo vniformiṫ remittit motū ſuū altera­<lb/>tiõis et hoc ꝑ ſui ↄ̨tinuã remiſſionē. </s>
              <s xml:id="N26BC0" xml:space="preserve">Qḋ ſic ꝓbat̄̄ / q2 <lb/>b. ↄ̨tinuo vniformiṫ remittit alteratiõeꝫ ſuã / vt pꝫ ex <lb/>ṗma ſuppõe octaui capitꝪ ṗmi tractatꝰ: et hoc cõti-<lb/>nuo remittēdo poñam ſuã igr̄. </s>
              <s xml:id="N26BC9" xml:space="preserve">Minor ꝓbat̄̄ / q2 cõti­<lb/>nuo alteratiõis ip̄ius b. ad alterationē ipſiꝰ a. ē f. ꝓ­<lb/>portio. </s>
              <s xml:id="N26BD0" xml:space="preserve">vt pꝫ ex hypotheſi: et ↄ̨tinuo alteratio ip̄ius               <cb chead="De motu alterationis quo ad cauſam"/>               b. et ipſiꝰ a. decreſcūt / vt pꝫ ex ꝓbatiõe maioris: g̊ cõ­<lb/>tiuuo latitudinis alterationis deperdite ab ipſo <lb/>b. ad latitudinem deperditaꝫ ab ipſo a. eſt propor­<lb/>tio f. / vt patet ex primo correlario quarte cõcluſio. <lb/>8. capitis .2. partis: et per cõſequēs continuo lati-<lb/>tudinis proportiõis deperdite a proportione ipſi­<lb/>us b. ad ſuam reſiſtentiã ad latitudinem propor-<lb/>tionis deperditã a proportione ipſius a. ad ſuam <lb/>reſiſtentiã eſt f. proportio, vt conſtat et ſic continuo <lb/>maiorē proportionē in f. proportiõe deperdit pro-<lb/>portio ipſius b. ad ſuam reſiſtentiam ꝙ̄ proportio <lb/>ipſius a. ad ſuam reſiſtentiã: ſed continuo propor-<lb/>tio ipſius b. ad ſuam reſiſtentiã per augmentū to-<lb/>talis reſiſtentie aggregate vcꝫ ex reſiſtentia intrin-<lb/>ſeca ipſi .c. paſſo et extrīſeca poñe iuuantis minorē <lb/>proportionē perdit ꝙ̄ proportio ipſius a. ad reſiſtē­<lb/>tiã per crementū ſue totalis reſiſtentie cum ↄ̨tinuo <lb/>eque velociter augeatur reſiſtentia ab extrinſeco <lb/>reſpectu a. et b. ex hypotheſi: et velocius continuo <lb/>deſcrescat reſiſtentia intrinſeca per actionem ipſiꝰ <lb/>b. ꝙ̄ ipſius a. / igitur oportet ꝙ̄ continuo reſiduū ꝓ-<lb/>portionis deperdende a ꝓportiõe ipſius b. ad ſuaꝫ <lb/>reſiſtētiã deperdat̄̄ per decrementū ipſius b. alte­<lb/>rantis et ex cõſequenti continuo b. alterans remit-<lb/>titur / qḋ fuit probandum. </s>
              <s xml:id="N26C06" xml:space="preserve">Patet igitur concluſio. <lb/></s>
              <s xml:id="N26C0A" xml:space="preserve">¶ Ex quo ſequitur primo /  aliquo alterante inua­<lb/>riato aliquod paſſum alterando continuo vnifor-<lb/>miter remittente motum ſuum alterationis per iu­<lb/>uamen reſiſtentie extrinſece accidentalis: quodli­<lb/>bet alterans minoris potentie potens agere in idē <lb/>paſſum cum eadem reſiſtentia valet vniformiter re-<lb/>mittere ſuã alterationē per ſui continuä intenſio-<lb/>nem idē paſſum alterando cum eodeꝫ iuuamine re­<lb/>ſiſtentie. </s>
              <s xml:id="N26C1D" xml:space="preserve">Patet hoc correlarium ex modo proban­<lb/>di precedentem cõcluſionem: hoc addito  cõtinuo <lb/>velocius creſcet totalis reſiſtentia reſpectu poten-<lb/>tie minoris ꝙ̄ maioris et ſic continuo per tale cre-<lb/>mentum maiorem proportionem deperderet pro-<lb/>portio potentie minoris ad ſuam reſiſtentiam ̄ <lb/>proportio potentie maioris ad ſuam reſiſtentiam <lb/>niſi potentia minor intenderetur.</s>
            </p>
            <p xml:id="N26C2E">
              <s xml:id="N26C2F" xml:space="preserve">¶ Sequitur ſecundo /  aliquo alterante inuariato <lb/>aliquod paſſum alterando vniformiter intenden-<lb/>te motum ſuū alterationis per iuuamen reſiſtentie <lb/>extrinſece et accidentalis vt in quarto correlario <lb/>ſexte concluſionis declaratum eſt: quodlibet alte-<lb/>rans maioris potentie valet vniformiter intende-<lb/>re motum ſuum alterationis per ſui continuam re­<lb/>miſſionem idem paſſum alterando eodem iuuami-<lb/>ne reſiſtentie: et omne alterans minoris potentie <lb/>potens agere in idem paſſum cum eadem reſiſten-<lb/>tia valet vniformiter intendere motum ſuum alte-<lb/>rationis per ſui continuam intenſionem idem paſ­<lb/>ſum alterando cum eodem iuuamine reſiſtentie.</s>
            </p>
            <p xml:id="N26C4A">
              <s xml:id="N26C4B" xml:space="preserve">Probatur prima pars et ſit a. inuariatū alterãs <lb/>c. paſſum continuo vniformiter intendendo altera­<lb/>tionem ſuam ſit b. alterans maioris potentie <lb/>quod ſic varietur alterando c. paſſum cum conſimi­<lb/>li adiumento  continuo vniformiter et eque velo­<lb/>citer intendat ſuam alterationem ſicut a. </s>
              <s xml:id="N26C58" xml:space="preserve">Tunc di-<lb/>co /  b. alterans maioris potentie continuo inten-<lb/>dit alterationem ſuam: et hoc per ſui continuam <lb/>remiſſionem. </s>
              <s xml:id="N26C61" xml:space="preserve">Quod ſic probatur / quia b. continuo <lb/>vniformiter intendit motum ſuum / vt patet ex hypo­<lb/>theſi: et per nullum tempus per quod erit maioris <lb/>ris potentie ꝙ̄ a. ſtabit inuariatum aut intendetur / <lb/>igitur b. continuo ꝑ tale tempus remittetur conti-               <pb chead="Quarti Tractatus" file="0230" n="230"/>               vniformiṫ intēdēdo alterationē ſuã / qḋ fuit ꝓbãdū <lb/></s>
              <s xml:id="N26C72" xml:space="preserve">Probat̄̄ prīa ꝑs mīoris / ſi ꝑ aliqḋ tale tp̄s ꝑ qḋ vcꝫ <lb/>b. eſt maiorꝪ poñe ꝙ̄ a. ſtat b. īuariatū ſeq̇t̄̄ /  ꝑ illḋ <lb/>tp̄s maiorē ꝓportionē acq̇rit ꝑ decremētū totiꝰ re-<lb/>ſiſtētie ꝓportio ipſiꝰ b. ad ſuã reſiſtētiã ꝙ̄ ꝓportio <lb/>ipſiꝰ a. ad ſuã reſiſtētiã: cum cõtinuo tota reſiſtētia <lb/>ipſius b. ſit mīor ꝙ̄ tota reſiſtētia ip̄ius a. cū ī ṗnci-<lb/>pio fuer̄t eq̈les: et velociꝰ ↄ̨tinuo agit b. corrūpēdo <lb/>reſiētiã ſuã ꝙ̄ a. et ex ↄ̨ñti ſeq̇t̄̄ /  in tali tꝑe b. velociꝰ <lb/>intēdit ſuã alterationē ꝙ̄ a. / qḋ ē ↄ̈ hypotheſim. </s>
              <s xml:id="N26C85" xml:space="preserve">Eo-<lb/>dē mõ ꝓbat̄̄ ſcḋa ꝑs mīoris auxiliãte loco a maiori <lb/></s>
              <s xml:id="N26C8B" xml:space="preserve">Et ſic pꝫ prīa ꝑs correlarii. </s>
              <s xml:id="N26C8E" xml:space="preserve">Secūda vero probatur <lb/>eodem modo paucis mutatis.</s>
            </p>
            <p xml:id="N26C93">
              <s xml:id="N26C94" xml:space="preserve">Octaua concluſio </s>
              <s xml:id="N26C97" xml:space="preserve">Qḋlꝫ alterans ali­<lb/>quod paſſuꝫ cuiꝰ reſiſtētia īcipit vniformiter creſcē <lb/>a nõ gradu: et ↄ̨tinuo vniformiṫ creſcit: ip̄a ēt alterã­<lb/>tis poña īcipiēte a nõ g̈du creſcē vniformiṫ ↄ̨tinuo <lb/>vniformiṫ creſcēte velociꝰ tñ ꝙ̄ reſiſtētia paſſi / vt oꝫ <lb/>cõtinuo vniformiṫ idē paſſū alterat. </s>
              <s xml:id="N26CA4" xml:space="preserve">Probat̄̄ /  cõ­<lb/>tinuo īter poñam et reſiſtētiã erit eadē ꝓportio: igit̄̄ <lb/>ↄ̨tinuo vniformiṫ alterãs alterat reſiſtētiã. </s>
              <s xml:id="N26CAB" xml:space="preserve">Proba­<lb/>tur añs: q2 ↄ̨tinuo inṫ poñaꝫ et reſiſtētiã erit illa ꝓ-<lb/>portio ī q̈ poña alterãtꝪ velociꝰ creſcit reſiſtētia paſ­<lb/>ſi: cū ī eadē ↄ̨tinuo velociꝰ creſcit a nõ g̈du. </s>
              <s xml:id="N26CB4" xml:space="preserve">Si eī īci­<lb/>pit velociꝰ creſcē ī f. ꝓportiõe a nõ g̈du vniformiter <lb/>cõtinuo a ṗncipio cremēti totalis latitudo poñe ac­<lb/>q̇ſita ē ī f. ꝓportiõe maior totali latitudīe reſiſtētie <lb/>in eodē tꝑe acq̇ſita: et ex ↄ̨ñti ↄ̨tinuo īter poñaꝫ et reſi­<lb/>ſtētiã ē f. ꝓportio / qḋ fuit oñdēdū.               <anchor type="note" xlink:href="note-0230-01" xlink:label="note-0230-01a"/>               </s>
              <s xml:id="N26CC6" xml:space="preserve">¶ Ex q̊ ſeq̇t̄̄ ṗmo / <lb/> cõtinuo eq̈lē ꝓportronē acq̇rit reſiſtētia et poña: <lb/>hoc eſt eq̄ velociṫ ꝓportionabilr̄ creſcit reſiſtētia et <lb/>poña: qḋ idē ē. </s>
              <s xml:id="N26CCF" xml:space="preserve">pꝫ hoc correĺ. ex prīo correlario .4. <lb/>ↄ̨°nis .8. capitꝪ .2. ꝑtis.               <anchor type="note" xlink:href="note-0230-02" xlink:label="note-0230-02a"/>               </s>
              <s xml:id="N26CD9" xml:space="preserve">¶ Seq̇t̄̄ 2° /  alterãte aliqua <lb/>poña aliqḋ paſſū ↄ̨tinuo vniformiṫ ꝑ ↄ̨tinuū et vni-<lb/>for̄e cremētū a nõ gradu poñe et reſiſtētie: oīs poña <lb/>mīor ↄ̨tinuo eq̄ velociṫ' creſcēs cum maiori alterãs <lb/>idē paſſum cū eodē cremēto reſiſtētie ↄ̨tinuo ītēdit <lb/>motū ſuū. </s>
              <s xml:id="N26CE6" xml:space="preserve">ꝓbat̄̄ / q2 ↄ̨tinuo ꝓportio īter talē poñam <lb/>mīorē et illã reſiſtētiã auget̄̄: igr̄ ↄ̨tinuo talis poña <lb/>ītēdit motū ſuū. </s>
              <s xml:id="N26CED" xml:space="preserve">Coña pꝫ: et ꝓbat̄̄ añs: q2 ↄ̨tinuo ma­<lb/>iorē ꝓportionē acq̇rit illa poña mīor ꝙ̄ ſua reſiſtē-<lb/>tia / igr̄ continuo ꝓportio īter talē poñaꝫ mīorē et il­<lb/>lã reſiſtētiã auget̄̄. </s>
              <s xml:id="N26CF6" xml:space="preserve">Coña ptꝫ ex ṗmo correlario ſcḋe <lb/>ↄ̨°nis .8. capitꝪ p̄allegati: et añs ꝓbat̄̄: q2 ↄ̨tinuo ma­<lb/>iorē ꝓportiõe acq̇rit poña illa mīor ꝙ̄ maior / vt ptꝫ <lb/>ex .8. ſuppõe .4. capitꝪ .2. ꝑtꝪ cū ↄ̨tinuo ſit mīor: et eã­<lb/>dē latitudinē poñe acq̇rit ex caſu correlarii: et poña <lb/>maior ↄ̨tinuo eq̈lē ꝓportionē acq̇rit ſicut reſiſtētia / <lb/>vt patꝫ ex precedēti correlario: igr̄ continuo maio­<lb/>rē ꝓportionē acq̇rit poña illa mīor ꝙ̄ reſiſtētia: qḋ <lb/>fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0230-03" xlink:label="note-0230-03a"/>               </s>
              <s xml:id="N26D0E" xml:space="preserve">¶ Sequit̄̄ tertio /  alterãte aliq̈ poña ali­<lb/>qḋ paſſū ↄ̨tinuo vniformiṫ etc̈. oīs poña maior ↄ̨ti-<lb/>nuo eq̄ velociṫ' creſcēs cū poña illa mīori ↄ̨tinuo re­<lb/>mittit motū ſuū alterãdo idē paſſū cū eodē cremen­<lb/>to reſiſtētie. </s>
              <s xml:id="N26D19" xml:space="preserve">Hoc correlariū ſiĺem cū p̄cedēdi exigit <lb/>demõſtratiõeꝫ: adiumēto ṗmi correlarii .3. ↄ̨°nis .8. <lb/>capitꝪ p̄allegati.               <anchor type="note" xlink:href="note-0230-04" xlink:label="note-0230-04a"/>               </s>
              <s xml:id="N26D25" xml:space="preserve">¶ Seq̇t̄̄ .4°. /  alterãte aliq̈ poña <lb/>aliqḋ paſſū ↄ̨tinuo vniformiṫ ꝑ ↄ̨tinuū et vnifor̄e cre­<lb/>mētū poñe et reſiſtētie a nõ g̈du ī eodē inſtãti īcipiē­<lb/>do: oē alterãs incipiēs a nõ g̈du ītēdē poñaꝫ ſuã añ <lb/>illḋ īſtãs: et ↄ̨tinuo vniformiṫ et eq̄ velociṫ creſcēs ſic̃ <lb/>datū alterãs: ↄ̨tīuo remittet motū ſuū idē paſſū al­<lb/>terãdo: et oē īcipiēs creſcē a nõ gradu poſt illḋ īſtãs <lb/>ↄ̨tinuo eq̄ velociṫ creſcēs ſicut datū alterãs: cū alte­<lb/>rat idē paſſū: ↄ̨tinuo ītēdit alterationē ſuã. </s>
              <s xml:id="N26D38" xml:space="preserve">pꝫ hoc <lb/>correlariū ex ṗori hoc addito /  oē alterãs īcipiēs <lb/>creſcē a ñ g̈du añ datū īſtãs ↄ̨tinuo erit maiꝰ ꝙ̄ illḋ <lb/>qḋ alterat vniformiṫ: q2 eq̄ velociṫ oīno creſcit cū il­<lb/>lo: et oē alterãs īcipiēs poſt idē īſtãs ↄ̨tinuo erit mi­<lb/>nus eq̄ velociṫ creſcēs cū alterãte vniformiter.</s>
            </p>
            <div xml:id="N26D45" level="5" n="14" type="float">
              <note position="left" xlink:href="note-0230-01a" xlink:label="note-0230-01" xml:id="N26D49" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0230-02a" xlink:label="note-0230-02" xml:id="N26D4F" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0230-03a" xlink:label="note-0230-03" xml:id="N26D55" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0230-04a" xlink:label="note-0230-04" xml:id="N26D5B" xml:space="preserve">4. correĺ.</note>
            </div>
            <cb chead="Capi. primum"/>
            <p xml:id="N26D63">
              <s xml:id="N26D64" xml:space="preserve">Nona cõcluſio </s>
              <s xml:id="N26D67" xml:space="preserve">Creſcētibꝰ a nõ gradu <lb/>alterãte reſiſtētia ſui paſſi: alterãte ↄ̨tinuo velociꝰ <lb/>et velociꝰ ītēdete poñaꝫ ſuã reſiſtētia o ↄ̨tinuo vni­<lb/>formiṫ: ip̄m alterãs ↄ̨tinuo ītēdit alterationē ſuaꝫ <lb/></s>
              <s xml:id="N26D71" xml:space="preserve">Probat̄̄ / q2 ↄ̨tinuo ꝓportio īter alterãs et ſuã reſi­<lb/>ſtētiã auget̄̄: igr̄ ↄ̨tinuo alterãs ītēdit alterationē <lb/>ſua. </s>
              <s xml:id="N26D78" xml:space="preserve">Coña pꝫ: et ar̄ añs / q2 ↄ̨tinuo maiorē ꝓportiõeꝫ <lb/>acq̇rit alterãs ꝙ̄ reſiſtētia paſſi: igit̄̄ ↄ̨tinuo ꝓpor-<lb/>tio īter alterãs et ſuã reſiſtētiã auget̄̄. </s>
              <s xml:id="N26D7F" xml:space="preserve">pꝫ ↄ̨ña ex pri­<lb/>mo correlario .2. ↄ̨°nis .8. capitꝪ .2. ꝑtꝪ. </s>
              <s xml:id="N26D84" xml:space="preserve">Probat̄̄ tñ <lb/>añs / q2 ſi nõ ſignet̄̄ aliqḋ tp̄s ꝑ qḋ acq̇rit minorē ꝓ-<lb/>portionē alterãs ꝙ̄ reſiſtētia paſſi vel eq̈lē: et capio <lb/>inſtãs īitiatiuū eiꝰ: et ſigno gradū cremēti q̊ ī tali ī-<lb/>ſtãti īcipit creſcere ſaltē ad quē ṫmīat̄̄ eiꝰ cremētū ī <lb/>tali īſtãti: q̇ ſit c. et pono /  a prīcipio actiõis hoc eſt <lb/>in īſtãti in q̊ a nõ gradu īcipiunt alterãs et reſiſtētia <lb/>creſcē (velociꝰ tñ creſcēte alterãte ꝙ̄ reſiſtētia vt oꝫ) <lb/>incipiat vna alia potētia creſcere a nõ gradu poñe <lb/>ↄ̨tinuo vniformiṫ c. g̈du alterãdo ſꝑ eãdē reſiſtētiã <lb/>vniformiṫ / vt oꝫ ex .8. ↄ̨°ne. </s>
              <s xml:id="N26D9B" xml:space="preserve">Quo poſito ſic argumē-<lb/>tor ꝑ datū tp̄s ↄ̨tinuo poña vniformiṫ creſcēs eq̈lē <lb/>ꝓportionē acq̇rit ꝓportiõi quã acq̇rit reſiſtētia ad-<lb/>equate: et ꝑ idē tp̄s vel ſaltē ꝑ aliquã ꝑtē eiꝰ terīatã <lb/>ad īſtãs īitiatiuū eiuſdē tꝑis: poña ↄ̨tinuo velociꝰ et <lb/>velociꝰ creſcēs maiorē ꝓportionē acq̇rit ꝙ̄ poña cõ­<lb/>tinuo vniformiṫ creſcēs: igit̄̄ ꝑ eadē partē dati tꝑis <lb/>maiorē ꝓportionē acq̇rit poña velociꝰ et velociꝰ cre­<lb/>ſcēs ꝙ̄ reſiſtētia paſſi: et ex ↄ̨ñti nõ ꝑ illḋ tp̄s acq̇rit <lb/>mīorē ꝓportiõeꝫ alterãs datū ꝙ̄ reſiſtētia paſſi aut <lb/>eq̈lē: qḋ ē oppoſitū dati. </s>
              <s xml:id="N26DB2" xml:space="preserve">Maior pꝫ ex ṗmo correla-<lb/>rio .8. ↄ̨°nis: et mīor probat̄̄: q2 ꝑ aliquã ꝑtē illiꝰ tꝑis <lb/>terīatã ad īſtãs īitiatiuū eiuſdē: poña velociꝰ et velo­<lb/>ciꝰ eſt mīor poña vniformiṫ creſcēte (cū cõti-<lb/>nuo añ īſtãs īitiatiuū illiꝰ tꝑis ſig̈ti creſcit illa po­<lb/>tētia c. g̈du et poña velociꝰ et velociꝰ creſcēs īcipiēs ī <lb/>eodē inſtãti cõtinuo creſcit remiſſiori gradu / vt patꝫ <lb/>aſpiciēti) et cõtinuo ꝑ eandē partē tꝑis maiorēre la-<lb/>titudinē acq̇rit poña velociꝰ et velociꝰ creſcēs ꝙ̄ potē­<lb/>tia creſcēs vniformiṫ / vt pꝫ aſpiciēti: igr̄ ꝑ eãdē ꝑteꝫ <lb/>tꝑis poña velociꝰ et velociꝰ creſcēs maiorē ꝓportio­<lb/>tionē acq̇rit ꝙ̄ poña vniformiṫ creſcēs / qḋ fuit ꝓbã­<lb/>dū. </s>
              <s xml:id="N26DCD" xml:space="preserve">Coña pꝫ ex .8. ſuppõe .4. capitꝪ .2. ꝑtis. </s>
              <s xml:id="N26DD0" xml:space="preserve">Et ſic ptꝫ <lb/>cõcluſio.               <anchor type="note" xlink:href="note-0230-05" xlink:label="note-0230-05a"/>               </s>
              <s xml:id="N26DDA" xml:space="preserve">¶ Ex q̊ ſequit̄̄ prīo /  creſcētibꝰ a nõ gradu <lb/>reſiſtētia alicuiꝰ paſſi et poña alterãtis ip̄m incipiē­<lb/>do ī eodē īſtanti reſiſtētia cõtinuo vniformiṫ creſcē­<lb/>te poña o alterãtis ↄ̨tinuo tardiꝰ et tardius velo-<lb/>ciꝰ tñ ip̄a reſiſtētia: ip̄m alterãs ↄ̨tinuo motū ſuū al­<lb/>teratiõis remittet. </s>
              <s xml:id="N26DE7" xml:space="preserve">Probat̄̄ hoc correlariū īſtar cõ­<lb/>cluſiõis ſignãdo vcꝫ ī q̊uis īſtãti gradū cremēti ipſi­<lb/>us poñe et capiēdo poñam q̄ a prīcipio alteratiõis <lb/>ↄ̨tinuo vniformiṫ illo gradu creuerit: et ſic reꝑietur <lb/>talis poña ↄ̨tinuo vniformiṫ creſcēs cõtinuo maio­<lb/>rē ꝓportionē acq̇rē ꝑ aliqḋ tp̄s ꝙ̄ poña ↄ̨tinuo tar­<lb/>dius et tardiꝰ creſcēs: q2 ꝑ tale tp̄s erit mīor velociꝰ <lb/>creſcēs: et ip̄a poña vniformiṫ creſcēs equalē ꝓpor­<lb/>tionē acq̇rit ꝓportioni acq̇ſite ab ip̄a reſiſtētia. </s>
              <s xml:id="N26DFA" xml:space="preserve">Ma­<lb/>iorē igit̄̄ ꝓportionē acq̇ret ꝑ illḋ tp̄s reſiſtētia ꝙ̄ po­<lb/>tētia illa ↄ̨tinuo tardiꝰ et tardiꝰ creſcēs. </s>
              <s xml:id="N26E01" xml:space="preserve">pꝫ igr̄ cor­<lb/>relariū.               <anchor type="note" xlink:href="note-0230-06" xlink:label="note-0230-06a"/>               </s>
              <s xml:id="N26E0B" xml:space="preserve">¶ Seq̇t̄̄ 2° /  creſcētibꝰ a nõ gradu reſiſtē-<lb/>tia alicuiꝰ paſſi et pon alterãtis ip̄m īcipiēdo ī eo-<lb/>dē īſtãti reſiſtētia ↄ̨tinuo velociꝰ et velociꝰ creſcēte, <lb/>tardiꝰ tñ ↄ̨tinuo ꝙ̄ ponã data ↄ̨tinuo vniformiṫ cre­<lb/>ſcēs ip̄3 alterãs cõtinuo remittet motū ſuū. </s>
              <s xml:id="N26E16" xml:space="preserve">Hoc cor­<lb/>relariū eadē cū p̄cedēti ↄ̨°ne oñdit̄̄ demõſtratione. <lb/></s>
              <s xml:id="N26E1C" xml:space="preserve">Quouis eī īſtãti dato ſignet̄̄ g̈dus cremēti ad quē <lb/>ṫīat̄̄ cremētū eiꝰ ī tĺi īſtãti et põat̄̄ reſiſtētia a princi­<lb/>pio alteratiõis ↄ̨tinuo vniformiṫ creuiſſe illo g̈du <lb/>et ↄ̨tinuo eodē poſtea creſcē et habebit̄̄ illã reſiſten-<lb/>tiam ſic vniformiter creſcentē per aliqḋ tp̄s ſequēs <lb/>īſtãs ſignatã ↄ̨tinuo eq̈lē ꝓportõeꝫ adeq̈te acq̇rere               <pb chead="De motu alterationis quo ad cauſam" file="0231" n="231"/>               ꝓportiõi quã in eodē tꝑe acq̇rit poña, mīorē tñ ̄ <lb/>reſiſtētia ↄ̨tinuo velociꝰ creſcēs / vt pꝫ aſpiciēti. </s>
              <s xml:id="N26E30" xml:space="preserve">Qui­<lb/>bus īſpectis facile ptꝫ correlariū.               <anchor type="note" xlink:href="note-0231-01" xlink:label="note-0231-01a"/>               </s>
              <s xml:id="N26E3A" xml:space="preserve">¶ Seq̇t̄̄ tertio /  <lb/>creſcētibꝰ a nõ gradu reſiſtētia alicuiꝰ paſſi et ponã <lb/>alterãtis ip̄m īcipiēdo ī eodē īſtãti: reſiſtētia ↄ̨tinuo <lb/>tardius et tardiꝰ, et cõtinuo tardiꝰ ꝙ̄ ponã data cõ­<lb/>tinuo vniformiṫ creſcēs: ip̄m alterãs ↄ̨tinuo intēdit <lb/>motū ſuū. </s>
              <s xml:id="N26E47" xml:space="preserve">Probat̄̄ hoc correlariū ſicut ṗmū.</s>
            </p>
            <div xml:id="N26E4A" level="5" n="15" type="float">
              <note position="right" xlink:href="note-0230-05a" xlink:label="note-0230-05" xml:id="N26E4E" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0230-06a" xlink:label="note-0230-06" xml:id="N26E54" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0231-01a" xlink:label="note-0231-01" xml:id="N26E5A" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N26E60">
              <s xml:id="N26E61" xml:space="preserve">Decima ↄ̨̨cluſio </s>
              <s xml:id="N26E64" xml:space="preserve">Creſcētibꝰ a nõ gra-<lb/>du reſiſtētia alicuiꝰ paſſi et ponã alterãtis ip̄m inci­<lb/>piēdo ī eodē inſtãti et ponã et reſiſtētia ↄ̨tinuo velo-<lb/>cius et velociꝰ creſcētibꝰ: aut vtra ↄ̨tinuo creſcēte <lb/>tardius et tardiꝰ: ſtat alterãs ↄ̨tinuo vniformiter al­<lb/>terare: ſtat etiã ip̄m ↄ̨tinuo velociꝰ et velociꝰ altera-<lb/>re: ſtat ſiĺr ip̄3 alterare cõtinuo tardiꝰ et tardiꝰ: ſtat <lb/>etiã etc̈. miſceas mēbra. </s>
              <s xml:id="N26E75" xml:space="preserve">Ptꝫ ↄ̨° facile. </s>
              <s xml:id="N26E78" xml:space="preserve">¶ Inferas tua <lb/>induſtria concluſioues his ſiĺes a certis gradibus <lb/>ponã et reſiſtentia creſcere incipientibus.</s>
            </p>
            <p xml:id="N26E7F">
              <s xml:id="N26E80" xml:space="preserve">Undecima cõcluſio materiã ſexti ar-<lb/>gumēti tangēs. </s>
              <s xml:id="N26E85" xml:space="preserve">Diuiſa hora ꝑ partes ꝓportiona-<lb/>les ꝓportiõe ſexq̇altera ↄ̨ſtitutiſ tribꝰ ordinibꝰ <lb/>ꝑtiū ꝓportionaliū īterſcalariṫ ſe hñtiū ꝑ ṗmo ordīe <lb/>capiēdo ṗmã .4.7.10. / et ſic ↄ̨ñr omiſſis ↄ̨tinuo dua-<lb/>bus ꝑ 2° o capiēdo ſcḋam .5.8.11. / et ſic ↄ̨ñter omiſ­<lb/>ſis duabꝰ: ꝓ tertio o capiēdo tertiã .6.9.12. / et ſic <lb/>ↄ̨ñter omiſſis ſiĺr ↄ̨tinuo duabꝰ: et in ṗmo illoꝝ or­<lb/>dinū aliqḋ alterãs alteret aliqḋ paſſuꝫ certa veloci­<lb/>tate: et in ſcḋo tãta: et in tertio tãta adeq̈te: tūc qua­<lb/>litas ꝓducta mediãte totali velocitate in illis tribꝰ <lb/>ordinibꝰ ſe hꝫ ad q̈litatē ꝓductã in prīo illoꝝ ordi-<lb/>nū ī ꝓportiõe dupla ſexq̇nona: q̈lis eſt .19. ad 9. </s>
              <s xml:id="N26E9E" xml:space="preserve">pꝫ <lb/>ↄ̨cluſio eſto gr̄a argumēti /  ī prīo illoꝝ ordinū ꝓ-<lb/>duxerit nouē gradus q̈litatꝪ. </s>
              <s xml:id="N26EA5" xml:space="preserve">Tūc eī mãifeſtū ē /  in <lb/>ſcḋo ꝓduxit ſex et in tertio q̈tuor: ꝰ ſic oēs gradus ꝓ­<lb/>ducti in tribꝰ orbinibꝰ ſūt decē et nouē. </s>
              <s xml:id="N26EAC" xml:space="preserve">Mõ. ig. ad <lb/>6. eſt dctã ꝓportio dupla ſexq̇noua. </s>
              <s xml:id="N26EB1" xml:space="preserve">pꝫ igr̄ ꝓbatio <lb/>ↄ̨°nis additis his / q̄ dctã ſunt in ſeptīo capitis ṗme <lb/>partis. </s>
              <s xml:id="N26EB8" xml:space="preserve">¶ Inducas ſiĺes ↄ̨°nes īnitēdo doctrine ca-<lb/>pitis p̄allegati quot volueris.</s>
            </p>
            <p xml:id="N26EBD">
              <s xml:id="N26EBE" xml:space="preserve">Duodecima ↄ̨̨cluſio. </s>
              <s xml:id="N26EC1" xml:space="preserve">diuiſa hora qua­<lb/>uis ꝓportiõe: et ī prīa parte ꝓportionali cuiꝰ aliqḋ <lb/>alteras alteret aliqḋ paſſuꝫ ab aliq̈ ꝓportiõe ade-<lb/>quate: et in ſcḋa a ꝓportiõe ī duplo maiori: et ī ṫtia <lb/>in triplo maiori ꝙ̄ in prīa: et ſic ↄ̨ñter: q̈litas ꝓdu-<lb/>cta mediãte totali velocitate ī illa hora ſe hꝫ ad q̈li­<lb/>tatē ꝓductã ī prīa ꝑte ꝓportionali in ꝓportiõe du-<lb/>pla ad ꝓportionē q̈ totū ſic diuiſū ſe hꝫ ad ṗmã ſui <lb/>ꝑtem ꝓportionalē. </s>
              <s xml:id="N26ED4" xml:space="preserve">pꝫ hec ↄ̨cluſio ex ꝓbatiõe q̈rte <lb/>ↄ̨°nis tertii capitis ſcḋi tractatꝰ. </s>
              <s xml:id="N26ED9" xml:space="preserve">¶ Addas his oēs <lb/>cõcluſiões ꝓbatas tertio capite p̄allegato mutatꝪ <lb/>mutandis.               <anchor type="note" xlink:href="note-0231-02" xlink:label="note-0231-02a"/>               </s>
              <s xml:id="N26EE5" xml:space="preserve">¶ Ad tertiū huius q̄ſtionis articulū ac-<lb/>cedēdo. </s>
              <s xml:id="N26EEA" xml:space="preserve">¶ Dubitatur prīo. </s>
              <s xml:id="N26EED" xml:space="preserve">Utrū luminoſū ꝓducat <lb/>in oē mediū in qḋ agit totã latitudinē luīs quã na-<lb/>tū eſt ꝓducere a gradu vcꝫ ſue lucis vſ ad nõ gra-<lb/>dū: dūmõ nõ ſit reflixio. </s>
              <s xml:id="N26EF6" xml:space="preserve">¶ Dubitat̄̄ ſcḋo. </s>
              <s xml:id="N26EF9" xml:space="preserve">Penes q̇d <lb/>hēat attēdi difficultas actionis. </s>
              <s xml:id="N26EFE" xml:space="preserve">¶ Dubitat̄̄ tertio. <lb/></s>
              <s xml:id="N26F02" xml:space="preserve">Utrū alterãs aliqḋ paſſū reſiſtēs valeat eq̄ velociter <lb/>alterare ꝑtē ꝓpinquã et remotã. </s>
              <s xml:id="N26F07" xml:space="preserve">¶ Ad ṗmū dubium <lb/>argr̄ ꝓbãdo /  luīoſū nõ agit totã latitudinē ſui lu­<lb/>minis ī qḋcū mediū q̈litercū diſpoſitū: ſꝑ ītelli­<lb/>go dūmõ ſit luīs ſuſceptiuū: q2 tūc ſeq̄ret̄̄ /  luīoſuꝫ <lb/>vt .8. tãtã latitudinē luīs ꝓduceret ī mediū bñ diſpo­<lb/>ſitū ̄tã ī mediū ñ ita bñ diſpoſitū ad luīs ſuſceptio­<lb/>nē: ſꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄. </s>
              <s xml:id="N26F16" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 ſꝑ <lb/>ꝑ te ꝓducit ī qḋlꝫ mediū ī qḋ agit latitudinē ab .8. <lb/>vſ ad nõ g̈dū dūmõ nõ ſit reflexio īpediēs </s>
              <s xml:id="N26F1D" xml:space="preserve">(Impe­<lb/>diēs inquã ne fiat ꝓductio vſ ad nõ g̈du) / igr̄ tãtã <lb/>latitudinē luīs ꝓducit ī medio bñ diſpoſitio ̄tã in               <cb chead="De motu alterationis quo ad cauſam"/>               medio non eq̄ bñ diſpoſito. </s>
              <s xml:id="N26F27" xml:space="preserve">Fĺitas ↄ̨ñtis ꝓbat̄̄ qm̄ <lb/>qḋlibet agēs naturale ſuapte natura velociꝰ agit ī <lb/>paſſum meliꝰ diſpoſitū ꝙ̄ in paſſuꝫ nõ eque bñ di-<lb/>ſpoſitū: igr̄ luīnoſū velociꝰ agit ī mediū meliꝰ diſpo-<lb/>ſitū ꝙ̄ in mediū nõ eq̄ bñ diſpoſitū: et ſic in eodē tꝑe <lb/>maiorē latitudinē luīs ꝓducit ī mediū meliꝰ diſpo-<lb/>ſitū ꝙ̄ minꝰ bñ diſpoſitū </s>
              <s xml:id="N26F36" xml:space="preserve">Et ↄ̨fir̄at̄̄ / q2 aĺs ſeq̄ret̄̄ /  <lb/>diſpõ medii nullo pacto ad īductionē luīs cõferret / <lb/>qḋ irrõnabĺr ē dctm̄.               <anchor type="note" xlink:href="note-0231-03" xlink:label="note-0231-03a"/>               </s>
              <s xml:id="N26F42" xml:space="preserve">¶ Dices forte cū calculatore <lb/>ↄ̨cedēdo illatū et negãdo fĺitatē ↄ̨ñtis: et ad ꝓbatio­<lb/>nē dr̄ /  illḋ verū ē de agēte cū reſiſtētia. </s>
              <s xml:id="N26F49" xml:space="preserve">Nichil em̄ <lb/>luī reſiſtit / q2 nulla q̈litas ei ↄ̈ria. </s>
              <s xml:id="N26F4E" xml:space="preserve">Et ſi tñ diſpõ me­<lb/>dii nichil ↄ̨ferat ad maiorē latitudinē luīs ītrodu-<lb/>cēdã: nichilominꝰ vt inq̇t idē calculator ↄ̨fert ad ꝓ-<lb/>ductionē luīs ꝑ maiorē diſtãtiã. </s>
              <s xml:id="N26F57" xml:space="preserve">In ea eī ꝓportione <lb/>in q̈ mediū efficit̄̄ rariꝰ ī ea luīoſuꝫ ꝑ maiorē diſtan­<lb/>tiã ſui luīs latitudinē ꝓducit vt īq̇t. </s>
              <s xml:id="N26F5E" xml:space="preserve">¶ Sꝫ ↄ̨tra / q2 tūc <lb/>ſeq̄ret̄̄ /  qḋlꝫ luīoſuꝫ ̄tūcū paruū ſue naturali <lb/>diſpõi relictã poſſet ꝑ ̄tūcū diſtãtiã agere: ſed <lb/>ↄ̨ñs ē flm̄: igr̄ etc̈. </s>
              <s xml:id="N26F67" xml:space="preserve">Seq̄la ꝓbat̄̄: et volo /  luīoſuꝫ a. <lb/>agat latitudinē ſui luīs ꝑ mediū pedalis ̄titatis <lb/>deiñ rarefiat mediū ad raritatē ī millecuplo maio­<lb/>iorē. </s>
              <s xml:id="N26F70" xml:space="preserve">Quo poſito ſeq̇t̄̄ a. luīoſuꝫ agė latitudinē ſui <lb/>luīs ad diſtãtiã ī millecuplo maiorē ex ſolu°ne: et ſi <lb/>iterū rarefiat ad duplū adhuc aget ꝑ ī duplo maio­<lb/>rē diſtãtiã: et ſic in īfinitū. </s>
              <s xml:id="N26F79" xml:space="preserve">Sꝫ ar̄ fĺitas ↄ̨ñtꝪ: q2 tūc ſe­<lb/>q̄ret̄̄ qḋlꝫ lūioſū / qḋ p̄t videri ī ꝓpinq̊ a certa poña <lb/>finita poſſe ab eadē poña a ̄tacū diſtãtiã videri / <lb/>qḋ eſt mãifeſte falſū: cū poña ſit finita: et ſiĺr luīoſum <lb/></s>
              <s xml:id="N26F83" xml:space="preserve">pꝫ ſeq̄la / q2 ̄tã latitudinē luīs ꝓducit ī ꝓpīquū tã­<lb/>tã v3 ꝓducē ī ̄tãcū diſtãtiã / et ꝑ ↄ̨ñs videri cū lumē <lb/>ſit ſpēs lucis ſiue luīoſi vĺ eã ſꝑ ↄ̨comitet̄̄. </s>
              <s xml:id="N26F8A" xml:space="preserve">¶ Dices <lb/>forte ↄ̨cedēdo id qñ īfert̄̄: et negãdo fĺitatē ↄ̨ñtis et <lb/>ad ꝓbatiõeꝫ ↄ̨cedēdo qḋ iteꝝ īfert̄̄: et negãdo fĺitatē <lb/>ↄ̨ñtis. </s>
              <s xml:id="N26F93" xml:space="preserve">¶ Sꝫ ↄ̈ / quaꝫ tūc ſeq̄ret̄̄ /  luīoſū vt .8. ꝓducens <lb/>lum̄ vniformiṫ diffor̄e ab .8. vſ ad nõ g̈dū nõ varia­<lb/>tū ī poña: īfinitã formã luīs poſſꝫ ꝓducē ſꝫ ↄ̨ñs ē fĺ3 / <lb/>igr̄ illḋ ex q̊ ſeq̇t̄̄. </s>
              <s xml:id="N26F9C" xml:space="preserve">Fĺitas ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄retur <lb/>qḋlꝫ luīoſū eē īfinite poñe: cū īfinitã mĺtitudinē for̄e <lb/>valeat ꝓducē. </s>
              <s xml:id="N26FA3" xml:space="preserve">Seq̄la tñ ꝓbat̄̄ et pono /  luīoſuꝫ vt .8. <lb/>agat latitudinē ſui luīs vniformiṫ difforme ab .8. <lb/>ad nõ g̈dū ꝑ aliquã ꝑtã alicuiꝰ medii īfiniti puta bi­<lb/>pedalē. </s>
              <s xml:id="N26FAC" xml:space="preserve">Deīde rarefiat totū illḋ mediū īfinitū vni-<lb/>formiṫ ꝑ totū et hoc ſine acq̇ſitiõe ̄titatꝪ: ſꝫ ꝑ ſolam <lb/>deꝑditionē maṫie (vt corr̄ ī hac mä opꝫ imaginari) <lb/>ad cētuplū: et mãifeſtū ē ex ſolutõe luīoſū vt .8. ꝓdu­<lb/>cere totã latitudinē ſui luīs ꝑ ducēta pedalia: ſigno <lb/>igr̄ / g̈dū mediū puta vt .4. ī fīe cēteſimi pedaĺ (vt oꝫ) <lb/>tūc uotū ē ī q̊lꝫ illoꝝ cētū pedaliū eē .4. g̈dꝰ luīs vni-<lb/>formis. </s>
              <s xml:id="N26FBD" xml:space="preserve">et cū hoc alcq̇d vltra: g̊ iã illḋ luīoſū vt .8. in <lb/>cãu dato ꝓducit latitudinē luīſ vuiformē vt .4. ꝑ .100 <lb/>pedalia: et ſi iteꝝ rarefiat illḋ mediū infinitū ad du­<lb/>plū iã ꝓducet ī duplo maiorē mĺtitudinē for̄e: q2 la­<lb/>titudinē luīs vniformē vt .4. ꝑ ducēta pedalia: et ſic <lb/>in īfinitū: ſeq̇t̄̄ g̊ /  luīoſū vt .8. ꝓducēs lumē vnifor-<lb/>miṫ diffor̄e etc̈. nõ variatū ī poña īfinitã formã luīs <lb/>p̄t ꝓducē: qḋ fuit ꝓbãdū. </s>
              <s xml:id="N26FCE" xml:space="preserve">¶ Dices negãdo ſeq̄lã et ad <lb/>ꝓbationē admiſſo cãu ↄ̨cedēdo /  fcã tĺi rarefactõe <lb/>dat̄̄ ibi lumē cētipedaĺ ̄titatꝪ vnifor̄e vt .4. ſꝫ illud <lb/>nõ plꝰ ↄ̨tinet de for̄a ꝙ̄ ↄ̨tinebat lumē pedale vnifor­<lb/>me vt .4. qḋ ꝓducebat̄̄ añ medii rarefactionē ꝑ ṗmū <lb/>pedale illiꝰ ꝑtis bipedalis in quã ꝑtē bipedalē lu-<lb/>minoſū agebat añ rarefactionē quēadmodum de-<lb/>claratū eſt in ſecundo notabili.</s>
            </p>
            <div xml:id="N26FDF" level="5" n="16" type="float">
              <note position="left" xlink:href="note-0231-02a" xlink:label="note-0231-02" xml:id="N26FE3" xml:space="preserve">3. articu-<lb/>lꝰ. q̄ſtionis</note>
              <note position="right" xlink:href="note-0231-03a" xlink:label="note-0231-03" xml:id="N26FEB" xml:space="preserve">Cal. de <lb/>acti. luīo.</note>
            </div>
            <p xml:id="N26FF3">
              <s xml:id="N26FF4" xml:space="preserve">Sed ↄ̨̨tra / q2 tūc ſequeretur /  in lati-<lb/>tudinē luīs vniformiter intēſi vt .4. eſſet in infini-<lb/>tū parū de forma adequate: ſꝫ ↄ̨ñs īplicat: igit̄̄ il-<lb/>lud ex quo ſequit̄̄. </s>
              <s xml:id="N26FFD" xml:space="preserve">Sequela ꝓbat̄̄: et volo /  illud me­<lb/>diū infinitū rarefiat in infinitū. </s>
              <s xml:id="N27002" xml:space="preserve">Quo poſito ibi re-<lb/>perietur infinita latitudo luīs quãtitatiue vnifor-               <pb chead="Quarti Tractatus" file="0232" n="232"/>               miter ītēſa vt 4. ſigno / igr̄ primū pedale eius: et ar-<lb/>guo ſic /vel in illo pedali adeq̈te eſt aliq̇d de forma, <lb/>vel īfinite modica nõ primū, q2 tūc ſequeret̄̄ /  ī quo­<lb/>libet pedali eēt tm̄ de forma: et ſic illud lūioſū ꝓdu­<lb/>ceret infinitã multitudinē forme / quod eſt negatum <lb/></s>
              <s xml:id="N27015" xml:space="preserve">Relinquit̄̄ igr̄ /  in quolibet tali pedali intenſa vt <lb/>4. ſit adeq̈ta in īfinitū parū de for̄a / qḋ fuit ꝓbãdū.</s>
            </p>
            <p xml:id="N2701A">
              <s xml:id="N2701B" xml:space="preserve">Secūdo ad idē arguit̄̄ ſic / q2 ſi dubiū <lb/>eſſet verū ſeq̄ret̄̄ quodlibet luminoſū īfinitū lumen <lb/>poſſe ꝓducere in quãtūcū paruo tꝑe: ſed ↄ̨ñs eſt <lb/>flm̄ igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N27024" xml:space="preserve">Seq̄la ꝓbat̄̄ et pono ca­<lb/>ſum /  lumīoſum vt .8. ſubito approximetur alicui <lb/>medio, qḋ etiã p̄t fieri naturalr̄ ponēdo mīmū na-<lb/>turale, et ſit hec approximatio in īſtanti a. / quo po-<lb/>ſito argr̄ ſic / luīoſum vt .8. in inſtanti a. ꝓducit totã <lb/>latitudinē ſui luīs: et in quolibet inſtãti ſequēti ꝓ-<lb/>ducit tantã latitudinē luīs ſicut in a. / igr̄ in quãtūcū­<lb/> paruo tꝑe īfinitã latitudinē luīs ꝓducit intēſiue / <lb/>qḋ fuit probandū. </s>
              <s xml:id="N27037" xml:space="preserve">Ptꝫ ↄ̨ña: et ꝓbat̄̄ minor / q2 in q̊lꝫ <lb/>inſtãti ſeq̄nti a. luīoſum eſt eq̄ approxīatū medio et <lb/>eq̄ potēs ad agendū ſicut in a. et nõ īpedit̄̄: igr̄ ī q̊lꝫ <lb/>tali ꝓducit tantã latitudinē luīs ſicut in a. </s>
              <s xml:id="N27040" xml:space="preserve">¶ Dices <lb/>et bñ negãdo ſeq̄lã: et ad ꝓbationē admiſſo caſu ne­<lb/>gãdo mīorē: et ad ꝓbationē negãdo  illud luīoſū <lb/>nõ ſit īpeditū īmo / vt bñ dicit Gregoriꝰ de arimīo in <lb/>ṗmo ſnīaꝝ diſ. 17.  ilḋ luīoſū īpedit̄̄ in q̊lꝫ īſtãti ſe-<lb/>q̄nti a. ↄ̨uãdo lumē ꝓductū ab eo in ipſo īſtanti a. <lb/></s>
              <s xml:id="N2704E" xml:space="preserve">Nã tãta t<gap/> req̇rit̄̄ ad ↄ̨uãdū aliq̇d ſiċ ad ꝓducēdū <lb/>illḋ. </s>
              <s xml:id="N27055" xml:space="preserve">Et ꝓpṫea luīoſū vlṫiꝰ nõ v3 ꝓducē aliqḋ lumen</s>
            </p>
            <p xml:id="N27058">
              <s xml:id="N27059" xml:space="preserve">Sed ↄ̨̨tra / q2 in caſu luminoſū vt octo <lb/>ꝓducens certã latitudinē luīs in aliqḋ mediū valet <lb/>ꝓducere maiorē luīs latitudinē nõ aucta eiꝰ poña / <lb/>igr̄ ſolutio nulla. </s>
              <s xml:id="N27062" xml:space="preserve">Probat̄̄ ſeq̄la, et pono caſū /  cã­<lb/>dela a. illumīet totū vnū ↄ̨claue clauſū in qḋ ꝓdu-<lb/>cat lumē b. deīde īuariata cãdela et medio, aꝑīat̄̄ fe­<lb/>neſtra, et manifeſtū eſt /  aget vltra ꝑ feneſtrã. </s>
              <s xml:id="N2706B" xml:space="preserve">(Uo­<lb/>lo em̄ /  ſit prīa fedeſtre) / igr̄ in tali caſu candela a. <lb/>vltra lumē b. ꝓductū in ↄ̨claue adhuc ꝓducit aliqḋ <lb/>lumen et ſic maius lumen ꝙ̄ b. ipſa et medio inua-<lb/>riatis: quod fuit probandum.</s>
            </p>
            <p xml:id="N27076">
              <s xml:id="N27077" xml:space="preserve">Tertio ad idē argr̄ ſic / q2 ſi ꝑs affirma­<lb/>tiua dubii eſſet a ſeq̄ret̄̄ /  nullū luīoſū poſſet ꝓ-<lb/>ducere latitudinē ſui lumīs vniformiṫ difformiṫ in <lb/>medio difformi: ſꝫ ↄ̨ñs eſt flm̄ cū ad hoc nullū īcõue-<lb/>niēs ſeq̇ videat̄̄: igr̄ etc̈. </s>
              <s xml:id="N27082" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 ſi aliqḋ lu-<lb/>mīoſū poſſet ꝓducere latitudinē ſue luīs vniformiṫ <lb/>difformiṫ in medio difformi: ſeq̄ret̄̄ /  ip̄m nõ poſſꝫ <lb/>ꝓducere latitudinē ſui luīs vniformiṫ difformiṫ in <lb/>medio vniformi: ſꝫ ↄ̨ñs eſt falſum: igr̄ .etc̈. </s>
              <s xml:id="N2708D" xml:space="preserve">Falſitas huiꝰ <lb/>ↄ̨ñtis ptꝫ / q2 tūc nullū luīoſum poſſet latitudinē ſui <lb/>luīs ꝓducere vniformiṫ difformiṫ in medio vnifor­<lb/>mi, cū nõ ſit maior rõ de vno ꝙ̄ de alio. </s>
              <s xml:id="N27096" xml:space="preserve">Probat̄̄ tñ <lb/>ſeq̄la / q2 ſi ſic ſit a luminoſum quod producit lati-<lb/>tudinē ſui luīs vniformiter difformiter in c. mediuꝫ <lb/>difforme, et eandē latitudinē ſui lumīs ꝓducat vni­<lb/>formiter difformiter in b. mediū vniforme, et arguo <lb/>ſic / vel b. mediū eſt maiꝰ ipſo c. vel minus vel equale: <lb/>ſi maiꝰ: ↄ̨dēſet̄̄ q̊uſ ſit eq̈le ip̄i c. ſi minꝰ rarefiat q̊-<lb/>uſ ſit eq̈le ip̄i c. ſꝑ b. manēte vniformi in dēſitate <lb/></s>
              <s xml:id="N270A8" xml:space="preserve">Quo poſito iã ſequit̄̄ /  idē luīoſū eq̈lē latitudinē <lb/>luīs intenſiue et extēſiue agit ꝑ mediū minus raꝝ et <lb/>magis raꝝ: ↄ̨ñs eſt manifeſte flm̄: igr̄ .etc̈. </s>
              <s xml:id="N270AF" xml:space="preserve">Seq̄la ꝓ-<lb/>bat̄̄: et ſig̊ vnã ꝑtē in c. medio difformi ṫmīatū ad a. <lb/>luīoſū: et arguo ſic, vel illa ꝑs eſt eq̄ rara oīno ſicut <lb/>eq̈lis ꝑs ei corrñdens in b. medio, vel magis rara, <lb/>vĺ miuꝰ rara: ſi magis. </s>
              <s xml:id="N270BA" xml:space="preserve">iã ſequit̄̄ ꝓpoſitū, vcꝫ  idē <lb/>luīoſū eq̈lē latitudinē luīs intēſiue et extēſiue agit ꝑ <lb/>mediū minꝰ raꝝ et magis raꝝ. </s>
              <s xml:id="N270C1" xml:space="preserve">In corrñdentibꝰ em̄               <cb chead="Capi. primum"/>               ꝑtibꝰ illoꝝ duoꝝ medioꝝ b. et c. eq̈les latitudīes luīs <lb/>ſūt extēſiue et ītēſiue. </s>
              <s xml:id="N270C9" xml:space="preserve">Sūt .n. ille latitudīes totales <lb/>luīs vniformiṫ difformes eq̈les extēſiue et intēſue. <lb/></s>
              <s xml:id="N270CF" xml:space="preserve">Sꝫ minꝰ: idē ſeq̇tur: vt ↄ̨ſtat. </s>
              <s xml:id="N270D2" xml:space="preserve">ſi eq̄ rara oīno: vĺ igr̄ <lb/>q̈lꝫ ꝑs illiꝰ ṫmīata ad luīoſū ē rara ſicut pars ſibi <lb/>corrñdēs ī b. vel nõ. </s>
              <s xml:id="N270D9" xml:space="preserve">Si m iã ſequit̄̄ idē qḋ priꝰ. </s>
              <s xml:id="N270DC" xml:space="preserve">Si <lb/>ṗmū iã ſeq̇tur illã ꝑtē eē vniformē ꝑ totū, capio igr̄ <lb/>ex reſiduo aliquã ꝑtē difformē īmediatã ip̄i ꝑti vni­<lb/>formi </s>
              <s xml:id="N270E5" xml:space="preserve">(Nõ .n. totū eſt vniforme ꝑ te) et manifeſtū ē / <lb/> ꝑs aggregata ex illa vniformi et difformi nõ ē eq̄ <lb/>rara m ſe et quãlꝫ eiꝰ ꝑtē ṫmīatã ad luīoſū ſicut ꝑs <lb/>corrñdēs ī b. q2 tūc illa ꝑs aggregata eēt vniformis <lb/>ſicut ꝑs ſibi corrñs in b. et a. ꝑ illã ꝑtē et ꝑ quãlꝫ eius <lb/>ꝑtē tantã latitudinē luīs intēſiue et extenſiue ꝓducit <lb/>ſicut ꝑ ↄ̨ſimilē partē corrñdēte in b. / igr̄ ꝓpoſitum.</s>
            </p>
            <p xml:id="N270F4">
              <s xml:id="N270F5" xml:space="preserve">In oppoſitū argr̄ ſic. </s>
              <s xml:id="N270F8" xml:space="preserve">Q2 ſi luīoſū nõ <lb/>in qḋcū mediū in qḋ agit ꝓduceret totã latitudi-<lb/>nē ſui luīs ad ſenſū datū: ſeq̄ret̄̄ /  in nullum medi­<lb/>um illã introducere valeret vel  tantã latitudineꝫ <lb/>adeq̈te intēſiue ꝓduceret in mediū meliꝰ diſpoſitū <lb/>quantã in minꝰ bene diſpoſitū: ſed ↄ̨ñs eſt flm̄: igit̄̄ <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N27107" xml:space="preserve">Falſitas ↄ̨ñtis ſatis ptꝫ ꝓ ṗma <lb/>parte, et ꝓ ſcḋa ꝓbat, q2 tūc ſeq̈ret̄̄ /  in diſpoſitio <lb/>medii nichil cõduceret ad maiorē vel minorē inten­<lb/>ſionē latitudinis lumīs, et ex ↄ̨ñti tã qḋlꝫ lūioſum ī <lb/>qḋcū mediū in qḋ agit totã latitudinē ſui luīs ꝓ-<lb/>duceret, qḋ eſt oppoſitū añtis. </s>
              <s xml:id="N27114" xml:space="preserve">Seq̄la tñ ꝓbat̄̄ / q2 ſi <lb/>ſit aliqḋ luīoſum in aliqḋ mediū ꝓducēs totã lati-<lb/>tudinē ſui luīs: ſignet̄̄ illud et ſit a. / et arguo ſic / a. ꝓ-<lb/>ducit totã latitudinē ſui luīs in aliqḋ mediū diſpo­<lb/>nat̄̄ / igr̄ in duplo meliꝰ mediū ꝑ rarefactionē: et tūc <lb/>ſequit̄̄ /  a. tantã latitudinē luīs adeq̈te intēſiue ꝓ-<lb/>ducit in illud mediū qñ eſt meliꝰ diſpoſitū quantaꝫ <lb/>ꝓducit in illud qñ eſt minꝰ bñ diſpoſitū: qḋ erat al-<lb/>tera pars ↄ̨ñtis. </s>
              <s xml:id="N27127" xml:space="preserve">Patꝫ tñ hec ↄ̨ña / q2 nõ põt ꝓducere <lb/>maioreꝫ ꝙ̄ ſit tota latitudo ſui luminis / vt conſtat.</s>
            </p>
            <p xml:id="N2712C">
              <s xml:id="N2712D" xml:space="preserve">Pro deciſiõe huiꝰ dubitatiõis:  ītro-<lb/>ductiõe aliquaꝝ ↄ̨cluſionū ſupponenduꝫ eſt. </s>
              <s xml:id="N27132" xml:space="preserve">Quid <lb/>eſt lux, quid lumē, quid q̈litas vniformiṫ difformis <lb/>vt cognofcitt̄̄ quid lumen vniformiter difforme. </s>
              <s xml:id="N27139" xml:space="preserve">Eſt <lb/>aūt lux forma accidentalis corꝑis luīoſi qua aliq̇d <lb/>lucidū ſiue luīoſū dr̄. </s>
              <s xml:id="N27140" xml:space="preserve">Perſpectiui aūt ita diffiniūt <lb/>lucē. </s>
              <s xml:id="N27145" xml:space="preserve">Lux eſt lucidoꝝ corpoꝝ ſpecies. </s>
              <s xml:id="N27148" xml:space="preserve">Uel lux eſt oīm <lb/>viſibiliū primū q̄ ꝑ ſe ceteroꝝ viſibiliū ſpecies viſui <lb/>ꝓfert. </s>
              <s xml:id="N2714F" xml:space="preserve">Lumē vero eſt actus dyaphani, ſcḋm  dya-<lb/>phanū. </s>
              <s xml:id="N27154" xml:space="preserve">ſcḋo de aīa Tex. cõme. 69. q̄ autē differētia <lb/>ſit īter lumen et lucē, et an lumen ſit ſpecies lucis: vi-<lb/>deas Paulū vene. libro de aīa capĺo .13. </s>
              <s xml:id="N2715B" xml:space="preserve">Qualitas <lb/>vero vniformiter difformis eſt illa q̄ ſic ſe hꝫ  in ea <lb/>ꝓportione in qua q̄uis pūcta eiꝰ intrinſeca magis <lb/>diſtant quãtitatie a g̈du eiꝰ ſūmo: in ea ꝑ maiorē la­<lb/>titudinē diſtãt intenſiue ab eodē g̈du ſūmo. </s>
              <s xml:id="N27166" xml:space="preserve">Ex quo <lb/>īmediate ſequit̄̄ q̇d ſit lumen vniformiter difforme <lb/></s>
              <s xml:id="N2716C" xml:space="preserve">Hiis adde q̈tuor / q̄ calcu. ſupponit in capĺo de acti­<lb/>one lumīoſi. </s>
              <s xml:id="N27171" xml:space="preserve">Primū qḋlꝫ luīoſum in qḋlꝫ mediū in <lb/>qḋ ſufficit agere totã latitudinē ſui luīs ꝓducit: ita <lb/> nõ intēſius lumen ꝓducit in vno medio ꝙ̄ in alio. <lb/>               <anchor type="note" xlink:href="note-0232-01" xlink:label="note-0232-01a"/>               </s>
              <s xml:id="N2717F" xml:space="preserve">Hoc ipſe ꝓbat ꝑ argumētum in oppoſitū huiꝰ du-<lb/>bii. </s>
              <s xml:id="N27184" xml:space="preserve">Scḋm qḋlꝫ luīoſū ꝓduces lumē in medium vni-<lb/>forme ꝓducit ipſum vniformiter difforme. </s>
              <s xml:id="N27189" xml:space="preserve">Tertiuꝫ <lb/>in ea ꝓportiõe in q̈ mediū efficit̄̄ rariꝰ: in eo luīoſuꝫ <lb/>ꝑ maiorē diſtãtiã lumē ꝓducit q̈rtū ꝓportiõabilr̄ ſi­<lb/>cut luīoſū fiet maiorꝪ poñe, ita ꝑ maiorē diſtãtiã lu­<lb/>men ꝓducit. </s>
              <s xml:id="N27194" xml:space="preserve">Utrū autē hee .3. ſuppoſitiones ſint e: <lb/>et q̄ ſint rõnes ad eas: ſeq̄ntes ꝓpoſitiões oſtēdunt.</s>
            </p>
            <div xml:id="N27199" level="5" n="17" type="float">
              <note position="right" xlink:href="note-0232-01a" xlink:label="note-0232-01" xml:id="N2719D" xml:space="preserve">4. ſuppo­<lb/>ſita q̇bꝰ ī­<lb/>itit̄̄ tota <lb/>deductio <lb/>cal. ī c. de <lb/>ac. lu.</note>
            </div>
            <p xml:id="N271AD">
              <s xml:id="N271AE" xml:space="preserve">Expedito notabili pono aliquas pro-<lb/>poſitiones ad dubium reſponſiuas.</s>
            </p>
            <pb chead="De motu alterationis quo ad cauſam." file="0233" n="233"/>
            <p xml:id="N271B7">
              <s xml:id="N271B8" xml:space="preserve">Prima ꝓpoſitio. </s>
              <s xml:id="N271BB" xml:space="preserve">Nõ eſt ꝓbabile lumi­<lb/>noſū tam intēſaꝫ latitudinē luīs ꝓducere in mediū <lb/>minꝰ diſpoſitū ſicut in magis diſpoſitū </s>
              <s xml:id="N271C2" xml:space="preserve">¶ Et cõ­<lb/>firmat̄̄ / q2 lumīoſū intēſiꝰ lumē partiale ꝓducit in <lb/>mediū magis diſpoſitū ꝙ̄ minꝰ diſpoſitū: vt Cal. <lb/>ipſe tenēs oppoſitū ↄ̨cedit: igr̄ pari rõne intēſiꝰ lu-<lb/>men totale ꝓducit in mediū magis diſpoſitū ꝙ̄ in <lb/>minꝰ diſpoſitū. </s>
              <s xml:id="N271CF" xml:space="preserve">Cõfirmat̄̄ ſcḋo / q2 pari rõne ſeq̇ret̄̄ <lb/>ſolē equalē latitudinē luīs ꝓducere in aquã et in a-<lb/>ciē dūmõ equalr̄ ſibi approximent̄̄ quãuis illã lati­<lb/>tudinē ꝓducat ꝑ minorē diſtãtiã in aquã, ꝙ̄ in aerē / <lb/>ſed hoc eſt manifeſte flm̄: vt experiētia ſatis docet: <lb/>igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N271DC" xml:space="preserve">Seq̄la tñ ꝓbat̄̄: q2 in diſpo° <lb/>medii nõ īpedit a ꝓductiõe intēſiõis: ſed extēſionis <lb/>vt īquit: igr̄. </s>
              <s xml:id="N271E3" xml:space="preserve">¶ Cõfirmat̄̄ tertio / q2 approxīato lu-<lb/>minoſo aque: in nulla parte ipſiꝰ aque eſt tm̄ luīs <lb/>ſicut in aere: vt viſus docet: g̊ nõ ſemꝑ lumīoſū ꝓdu­<lb/>cit in qḋlibet mediū in qḋ agit totã latitudinē ſui <lb/>luīs. </s>
              <s xml:id="N271EE" xml:space="preserve">Idē etiã apparet ſi candela ponat̄̄ in nebula: <lb/>et ſic ptꝫ ꝓpoſitio </s>
              <s xml:id="N271F3" xml:space="preserve">Ad rationē tñ calcu. q̄ eſt in oppo­<lb/>ſitū. </s>
              <s xml:id="N271F8" xml:space="preserve">Reſpõdeo negãdo ſequelã. </s>
              <s xml:id="N271FB" xml:space="preserve">Et ad ꝓbationē nõ <lb/>admitto  meliꝰ valeat illud mediū diſponi ad lu-<lb/>minis ſuſceptionē a tali luīoſo natã ꝓduci. </s>
              <s xml:id="N27202" xml:space="preserve">Nec ſēꝑ <lb/>maior raritas eſt cauſa maioris luīs ſuſceptionis <lb/>vt īmediate ꝓbabit̄̄. </s>
              <s xml:id="N27209" xml:space="preserve">Sicut em̄ aer req̇rit certã rari­<lb/>tatē ad ↄ̨ſeruandū gradū ſummū humiditatis: ita <lb/> maior aut mīor eſt ei iſta ī diſpoſitio: ita ſiĺr dicēduꝫ <lb/>eſt in ꝓpoſito  maior raritas eſt illi luīoſo indi-<lb/>ſpoſitio vel nõ eſt maior diſpoſitio ad illã luīs ſu-<lb/>ſcipiēdã latitudinē. </s>
              <s xml:id="N27216" xml:space="preserve">Itē opꝫ calcu. ↄ̨cedere luīoſum <lb/>eq̈le lumen ꝓducere intēſiue et extēſiue in mediū ma­<lb/>gis diſpoſitū ſaltē ſcḋm eū et minus diſpoſitū., <lb/></s>
              <s xml:id="N2721E" xml:space="preserve">ptꝫ dato luīe vniformi in ↄ̨claui qḋ ipſe ↄ̨cedit dari <lb/>poſſi vel ſaltē dubitat .30. ↄ̨cluſiõe de actione lumi: <lb/>et rarefiat mediū ad duplū. </s>
              <s xml:id="N27225" xml:space="preserve">Tūc em̄ nõ ꝓducet̄̄ in-<lb/>tenſius lumen in conclaue: quia luminoſum nõ pro­<lb/>ducit lumen vltra ſuum gradum.</s>
            </p>
            <p xml:id="N2722C">
              <s xml:id="N2722D" xml:space="preserve">Scḋa ꝓpoſitio. </s>
              <s xml:id="N27230" xml:space="preserve">Quēadmodū ꝓbabi­<lb/>le eſt qḋlibet luīoſum agens in mediū vniforme ꝓ-<lb/>ducere lumē vniformiter difforme: ita etiã ꝓbabile <lb/>eſt oppoſitū vel ſaltē apparēter defenſari p̄t. </s>
              <s xml:id="N27239" xml:space="preserve">Pri-<lb/>ma pars ꝓbat̄̄ argumēto calcu. ad .12. ↄ̨cluſionē in <lb/>capĺo de actiõe lumi. / q2 capto a. luīoſo agente in <lb/>mediū vniforme manifeſtū eſt /  ad oēm punctū me­<lb/>dii natū eſt luīoſum ꝓducere tm̄ gradū luīs quãtū <lb/>producit ad punctū ſibi ꝓximū: dūmodo ad talem <lb/>punctū ponat̄̄. </s>
              <s xml:id="N27248" xml:space="preserve">Et modo nõ ad quēlibet pūctū agit <lb/>gradū equalē: ergo tota cauſa inequalis actionis <lb/>eſt ratione maioris diſtantie vniꝰ puncti ꝙ̄ alteriꝰ / <lb/>ergo in ea ꝓportione in qua diſtantia alicuiꝰ pun-<lb/>cti ab ipſo a. luīoſo eſt maior in ea ꝓportione īpe-<lb/>dimentū eſt maius: et ꝑ ↄ̨ñs in ea ꝓportione in qua <lb/>puncta magis diſtant in ea ꝑ maiorē latitudinem <lb/>īpedit̄̄ actio a. lumīoſi ad ipſa. </s>
              <s xml:id="N27259" xml:space="preserve">Sequit̄̄ ergo lumē <lb/>ꝓductū ab a. eſſe vniformiter difforme in medio vni­<lb/>formi. </s>
              <s xml:id="N27260" xml:space="preserve">Ptꝫ hec vltīa ↄ̨ña ex diffinitiõe q̈litatis vni­<lb/>formiter difformis poſita in notabili: et ſic ptꝫ pri-<lb/>ma pars. </s>
              <s xml:id="N27267" xml:space="preserve">Scḋa ꝓbat̄̄: q2 ſi oppoſitū eſſet ↄ̨cedendū <lb/>maxīe eſſet ꝓpter rationē factã: ſed illa facile et ap­<lb/>parenter īpedit̄̄: negando hanc ↄ̨ñam. </s>
              <s xml:id="N2726E" xml:space="preserve">Tota cauſa <lb/>ineq̈lis actiõis eſt ratiõe maioris dīſtantie vniꝰ pū­<lb/>cti ꝙ̄ alteriꝰ: ergo in ea ꝓportiõe in qua diſtantia <lb/>alicuiꝰ pūcti ab ipſo a. luīoſo eſt maior in ea īpedi­<lb/>mentū eſt maiꝰ. </s>
              <s xml:id="N27279" xml:space="preserve">quãuis em̄ maioritas diſtantie īpe­<lb/>diat actionē pluſ̄ minoritas: nõ tñ eque ꝓportio-<lb/>nabiliter ſicut diſtantia eſt maior ita plus īpedit. <lb/></s>
              <s xml:id="N27281" xml:space="preserve">et hoc eſt ꝓbabile. </s>
              <s xml:id="N27284" xml:space="preserve">Quēadmodū in materia quaſi               <cb chead="De motu alterationis quo ad cauſam."/>               ſiĺi: iſta ↄ̨ña negat̄̄. </s>
              <s xml:id="N2728A" xml:space="preserve">agens velociꝰ agit in idē paſſū <lb/>a propīquio ꝙ̄ a remoto: ergo ꝓportionabilr̄ ſicut <lb/>paſſū eſt ꝓpinquiꝰ: ita velociꝰ agit: vtra igr̄ pars <lb/>ſuam habet ꝓbabilitatē. </s>
              <s xml:id="N27293" xml:space="preserve">Patet ergo propoſitio.</s>
            </p>
            <p xml:id="N27296">
              <s xml:id="N27297" xml:space="preserve">Tertia ꝓpoſitio. </s>
              <s xml:id="N2729A" xml:space="preserve">Nõ eſt michi ꝓbbbi­<lb/>le. </s>
              <s xml:id="N2729F" xml:space="preserve">Qḋlꝫ lumīoſum in ea ꝓportiõe agere ꝑ maiorē <lb/>diſtãtiã ī q̈ mediū rariꝰ efficit̄̄. </s>
              <s xml:id="N272A4" xml:space="preserve">Probr̄ / q2 tūc ſeq̄ret̄̄ <lb/>qḋlꝫ luīoſū ſue naturali diſpoſitiõi relictū poſſe ꝑ <lb/>īfinitã diſtantiã agere / vt ptꝫ ex deductiõe primi ar­<lb/>gumēti: ſed ↄ̨ñs eſt flm̄: g̊ illud ex quo ſequit̄̄ </s>
              <s xml:id="N272AD" xml:space="preserve">¶ Et cõ­<lb/>firmat̄̄ / q2 dicere oppoſitū eſt velle aſſerere  in ea <lb/>ꝓportiõe in qua aliqḋ mediū eſt magis rarum eſt <lb/>magis diſpoſitū vt ꝑ illud lumē diffundat̄̄. </s>
              <s xml:id="N272B6" xml:space="preserve">Sꝫ hoc <lb/>eſt flm̄: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N272BB" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄ / <lb/>q2 rariꝰ eſt lignū ꝙ̄ vitrū vel criſtallꝰ: et tñ nõ eſt ma­<lb/>gis diſpoſitū vt ꝑ illud lumē diffundat̄̄: igr̄. </s>
              <s xml:id="N272C2" xml:space="preserve">¶ Itē <lb/>pluſ̄ in decuplo denſor eſt criſtallꝰ ꝙ̄ aer et tamen <lb/>nõ pluſ̄ in decuplo eſt minꝰ depoſitū vt ꝑ illud lu­<lb/>men diffundat̄̄ vt experiētia docet. </s>
              <s xml:id="N272CB" xml:space="preserve">Itē multo den-<lb/>ſior eſt criſtallꝰ et birilꝰ ꝙ̄ aqua: et tñ meliꝰ (vt appa­<lb/>ret ſenſui) diffundit̄̄ lumē per cristallū ꝙ̄ per aquã. <lb/></s>
              <s xml:id="N272D3" xml:space="preserve">¶ Ampliꝰ multo dēſiꝰ eſt vitrū ꝙ̄ nebula: et tñ meliꝰ <lb/>diffundit̄̄ lumen per vitrum ꝙ̄ per nebulã: vt cõſtat</s>
            </p>
            <p xml:id="N272D8">
              <s xml:id="N272D9" xml:space="preserve">Quarta ꝓpoſitio. </s>
              <s xml:id="N272DC" xml:space="preserve">Dubiū eſt an in ea <lb/>ꝓportiõe q̈ luīoſū efficit̄̄ ītēſiꝰ in forma, in ea agat <lb/>ꝑ maiorē diſtantiã medio vniformi exñte: ad hoc <lb/>em̄ nõ video rationē nec ad oppoſitū .etc̈. </s>
              <s xml:id="N272E5" xml:space="preserve">¶ Hiis tñ <lb/>nõ obſtantibꝰ admiſſis illis q̈tuor ſuppoſitiõibꝰ po­<lb/>ſitis in notabili infero aliq̈s ↄ̨cluſiões de mēte cal.</s>
            </p>
            <p xml:id="N272EC">
              <s xml:id="N272ED" xml:space="preserve">Prima ↄ̨̨cluſio. </s>
              <s xml:id="N272F0" xml:space="preserve">Nullū luīoſū ꝓduce-<lb/>re v3 totã latitudinē ſui luīs a ſuo g̈du vſ ad non <lb/>g̈dū vniformiṫ difformiṫ' ī medio difformi. </s>
              <s xml:id="N272F7" xml:space="preserve">Probr̄ / <lb/>q2 ſi aliq̇d luīoſuꝫ valet ꝓducere totã latitudinē ſui <lb/>lumīs vniformiter difformiter in medio vniformi: <lb/>nullū valet ꝓducere ſuã latitudinē vniformiter dif­<lb/>formiter in medio difformi / vt ptꝫ ex deductione .3. <lb/>argumēti ãte oppoſitū huiꝰ dubii. </s>
              <s xml:id="N27304" xml:space="preserve">Sꝫ qḋlibet valꝫ <lb/>ꝓducere totã latitudinē ſui luīs vniformiter diffor­<lb/>miter in medio vniformi: igr̄ nullū valet producere <lb/>totã latitudinē ſui luīs etc̈. in medio difformi. </s>
              <s xml:id="N2730D" xml:space="preserve">Cõſe­<lb/>quētia pꝫ ꝑ ſillogiſmū hypotheticū ad ↄ̨ditiõali etc̈. <lb/>et minor ptꝫ ꝑ rationē ad primã partē ſcḋe propo-<lb/>ſitiouis huius dubii. </s>
              <s xml:id="N27316" xml:space="preserve">Patet ergo concluſio.</s>
            </p>
            <p xml:id="N27319">
              <s xml:id="N2731A" xml:space="preserve">Scḋa ↄ̨̨cĺo. </s>
              <s xml:id="N2731D" xml:space="preserve">Qḋlꝫ luīoſū ꝓducēs lati­<lb/>tudiuē ſui luīs vniformiṫ difformiṫ ad nõ g̈dū vſ <lb/>in mediū vniforme creſcēs in g̈du lucis ſtãte quãti-<lb/>tate tm̄ luīs g̈du ꝓducit in punctū remotū ab eo in <lb/>q̊ erat nõ g̈dꝰ ãte crementū ꝙ̄ tū ꝓpe ſe in pūctū ſibi <lb/>ꝓximū. </s>
              <s xml:id="N2732A" xml:space="preserve">Probat̄̄: ſit a. luīoſū ꝓducēs lumē vnifor­<lb/>miter difforme vt in caſu ↄ̨cluſiõis in b. mediū: et ſit <lb/>nõ g̈dꝰ luīs in c. pūcto ipſiꝰ b. medii: et augeat̄̄ a. in <lb/>gradu acq̇rēdo d. g̈dū luīs: ita  efficiat̄̄ in f. ꝓpor­<lb/>tiõe intēſiꝰ ſtante ̄titate. </s>
              <s xml:id="N27335" xml:space="preserve">Tūc dico /  a. tm̄ gradū <lb/>lumīs ꝓducit in punctū remotū ab eo in quo ante <lb/>erat nõ gradus quantū in punctum ſibi proximū. <lb/></s>
              <s xml:id="N2733D" xml:space="preserve">Quod ſic oſtendit̄̄ / q2 d. gradū luminis producit in <lb/>punctū ſibi proximū: et d. gradū luminis producit <lb/>adequate in pūctū c. in quo añ cremētū erat nõ gra­<lb/>dus luminis: igit̄̄ propoſitū. </s>
              <s xml:id="N27346" xml:space="preserve">Maior ptꝫ et minor ꝓ-<lb/>bat̄̄. </s>
              <s xml:id="N2734B" xml:space="preserve">q2 luminoſū a. effectū eſt in .f. proportione ītē­<lb/>ſius ſtante quantitate: igit̄̄ a. ꝓducit ſuum lumen ꝑ <lb/>diſtantiam in f. proportione maiorem / vt ptꝫ ex ter­<lb/>tia ſuppoſitiõe: et vltra ſequit̄̄ /  in f. proportiõe a. <lb/>plus diſtat a pūcto ī quo eſt nõ gradꝰ luminis poſt <lb/>crementū ꝙ̄ a c. puncto: et ex cõſequēti ſequit̄̄ /  in f. <lb/>proportione gradus ſūmꝰ ꝑ minorē latitudinē exce­<lb/>dit lumē ad c. punctū ꝙ̄ ad punctū in quo poſt cremē­               <pb chead="Quarti Tractatus" file="0234" n="234"/>               tum eſt nõ gradus luminis: vt pꝫ ex diffinitione q̈li­<lb/>tatis vniformiter difformis: et excedit nõ gradū ip­<lb/>ſe gradꝰ ſūmus per totã ſuam latitudinem: vt con-<lb/>ſtat: g̊ excedit lumen ad c. punctum ꝑ latitudineꝫ in <lb/>f. minorē ꝙ̄ ſit tota latitudo ipſius gradꝰ ſummi ꝓ-<lb/>ducti prope luminoſum: et gradus ſummꝰ luminis <lb/>ante crementū eſt in f. proportione minor ꝙ̄ pꝰ cre­<lb/>mentū: ex hypotheſi et prima ſuppoſitione: g̊ per to­<lb/>tam illam latitudinem ſummi gradꝰ añ intenſionē <lb/>gradꝰ ſummꝰ poſt intēſionem excedit lumen ad pun­<lb/>ctū c. et per illã ēt ille gradꝰ ſummꝰ poſt intēſionē ex­<lb/>cedit lumē productū in pūcto proximo luminoſo cū <lb/>ex ea latitudine et illo lumine producto adequate il­<lb/>le gradus ſummꝰ ↄ̨ponat̄̄: igr̄ lumē productū ad c. <lb/>punctum eſt equale lumini producto ī punctū proxi­<lb/>mū luminoſo. </s>
              <s xml:id="N2737F" xml:space="preserve">pꝫ ↄ̨ña ꝑ hoc /  ea que eq̈liter ab eo­<lb/>dē 3° excedunt̄̄ ſunt eq̈lia: </s>
              <s xml:id="N27384" xml:space="preserve">Et luminoſū producit d. <lb/>gradū luminis in punctū ſibi proximū: vt pꝫ ex hy-<lb/>potheſi et prima ſuppoſitione: ergo d. gradū lumi-<lb/>nis producit adeq̈te in punctū c. in quo erat nõ gra­<lb/>dus luminis ante cremētū: qḋ fuit probandū: ptꝫ g̊ <lb/>cõcluſio. </s>
              <s xml:id="N27391" xml:space="preserve">¶ Ex hac ↄ̨cluſione ſequit̄̄ /  cū luminoſuꝫ <lb/>auget̄̄ in gradu: ſtante quãtitate: medio vniformi ce­<lb/>teris paribꝰ: ꝑ totū mediū ꝑ qḋ añ cremētū agebat <lb/>ꝓducit lumē vniforme, tm̄ vcꝫ in pūctū remotū ſicut <lb/>in quodlꝫ propinquiꝰ. </s>
              <s xml:id="N2739C" xml:space="preserve">Probat̄̄ ſupponēdo /  nun̄ <lb/>ex qualitate difformiṫ difformi et vniformiter dif-<lb/>formi fit q̈litas vniformiṫ difformis adequate. </s>
              <s xml:id="N273A3" xml:space="preserve">quo <lb/>poſito arguit̄̄ ſic: in caſu correlarii tm̄ lumē ꝓducit <lb/>luminoſū in punctum vbi ante crementuꝫ luminoſi <lb/>erat non gradꝰ ſicut in punctū ſibi ꝓximū / vt patet <lb/>ex precedenti concluſione: igit̄̄ totalis qualitas pro­<lb/>ducta ꝑ cremētū luminoſi eſt vniformis: et ꝑ ↄ̨ñs tm̄ <lb/>lumē ꝓducit luminoſuꝫ in remotū ſicut in quolib3 ꝓ-<lb/>pinquum: pꝫ tñ ↄ̨ña. </s>
              <s xml:id="N273B4" xml:space="preserve">q2 totalis qualitas producta ꝑ <lb/>crementū luminoſi nõ ē vniformiṫ difformis cū ex-<lb/>trema eiꝰ ſint eque intenſa: </s>
              <s xml:id="N273BB" xml:space="preserve">Nec etiã ē difformiṫ dif­<lb/>formis: q2 ex ſuppoſito ex qualitate difformiṫ dif­<lb/>formi et vniformtter difformi nõ fit qualitas vnifor­<lb/>mis: igr̄ eſt vniformis: quod fuit probandum. </s>
              <s xml:id="N273C4" xml:space="preserve">Pa-<lb/>tet igitur correlarium.</s>
            </p>
            <p xml:id="N273C9">
              <s xml:id="N273CA" xml:space="preserve">Tertia ↄ̨̨cluſio </s>
              <s xml:id="N273CD" xml:space="preserve">Luminoſiori ageres ī <lb/>medſū vniforme deductis īpedimētis ꝑ ſui cremētū <lb/>in quãtitate: et nõ ī gradu: aut ꝑ vniformē medii ra­<lb/>refactionem: maiorē latitudinē luminis ꝓducit ī re­<lb/>motū ꝙ̄ in ꝓpinquū. </s>
              <s xml:id="N273D8" xml:space="preserve">Patet hec cõcluſio ex dedutio­<lb/>ne tertii argumenti ṗncipalis añ oppoſitū queſtio­<lb/>nis.               <anchor type="note" xlink:href="note-0234-01" xlink:label="note-0234-01a"/>               </s>
              <s xml:id="N273E4" xml:space="preserve">Ex hac cõcluſione ſequit̄̄ /  luminoſū creſcēs <lb/>in gradu et in quãtitate ſimul: velociꝰ agit in remo-<lb/>tum ꝙ̄ in ꝓpinquū. </s>
              <s xml:id="N273EB" xml:space="preserve">Patet: q2 ratione cremēti ī gra­<lb/>du eq̄uelociṫ agit in ꝓpinquuꝫ ſicut in remotū. </s>
              <s xml:id="N273F0" xml:space="preserve">et ra­<lb/>tione cremēti in quãtitate velociꝰ in remotū ꝙ̄ in ꝓ-<lb/>pinquum: igr̄ rõe cremēti in gradu et in quãtitate ſi­<lb/>mul: velociꝰ agit in remotū ꝙ̄ ī ꝓpinquum / ptꝫ er-<lb/>go correlarium.               <anchor type="note" xlink:href="note-0234-02" xlink:label="note-0234-02a"/>               </s>
              <s xml:id="N27400" xml:space="preserve">¶ Sequit̄̄ ſcḋo /  decreſcente lumi-<lb/>noſo ī quãtitate: vel medio vniformi vniformiter ſe <lb/>condenſante: velociꝰ corrūpit̄̄ lumē in remotu ꝙ̄ in <lb/>ꝓpinquum. </s>
              <s xml:id="N27409" xml:space="preserve">patet / quia ſemper lumen eſt equale pro­<lb/>pe luminoſum. </s>
              <s xml:id="N2740E" xml:space="preserve">vt patet ex prima ſuppoſitione poſi­<lb/>ta in notabili: et continuo agit luminoſū ꝑ minoreꝫ <lb/>diſtantiã / vt pꝫ ex tertia ſuppoſitione: et lumē conti-<lb/>nuo manet vniformiter difforme pꝫ ex ſecūda ſup­<lb/>poſitione: igr̄ velocius lumē corrūpitur in remotum <lb/>̄ in propinquum. </s>
              <s xml:id="N2741B" xml:space="preserve">Patet ergo correlarium.</s>
            </p>
            <div xml:id="N2741E" level="5" n="18" type="float">
              <note position="left" xlink:href="note-0234-01a" xlink:label="note-0234-01" xml:id="N27422" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0234-02a" xlink:label="note-0234-02" xml:id="N27428" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N2742E">
              <s xml:id="N2742F" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N27432" xml:space="preserve">Stat luminoſum <lb/>inuariatuꝫ in quãtate in īfinitū creſcere in gradu <lb/>et tñ continuo agere ꝑ equalē diſtantiam. </s>
              <s xml:id="N27439" xml:space="preserve">Probat̄̄ /               <cb chead="Capi. primum"/>               ponēdo  eque velociter ꝓportionabiliter ſicut lu-<lb/>minoſuꝫ auget̄̄ in gradu ita mediū ↄ̨denſetur. </s>
              <s xml:id="N27441" xml:space="preserve">quo <lb/>poſito cõtinuo aget per equalē diſtantiã / vt ptꝫ ex .3. et <lb/>4. ſuppõnibꝰ: igit̄̄ cõcluſio vera. </s>
              <s xml:id="N27448" xml:space="preserve">¶ Ex quo ſequitur / <lb/> vbicū luminoſum agit in mediū vniforme cuiꝰ <lb/>vna medietas īmediata agenti rarefit: reliqua ma­<lb/>nēte inuariata, et luminoſuꝫ minorat̄̄ in ̄titate ita <lb/> ad extremū partis rarefacte idem gradus lumi-<lb/>nis ↄ̨̨ſeruet̄̄: ad oēm pūctū citra talē ↄ̨tinuo idē gra­<lb/>dus luminis conſeruabit̄̄: et ad oēm vltra remittet̄̄. <lb/></s>
              <s xml:id="N27458" xml:space="preserve">Probatur / q2 ad extremū partis rarefacte equali­<lb/>ter facit rarefactio ad ꝓductionē luminis ſiue con-<lb/>ſeruationē ſicut remiſſio quãtitatis ad luminis di­<lb/>minutionē et pari ratione ad quodlibet pūctū citra <lb/>cū lumē ↄ̨tinuo maneat vniformiṫ difforme / vt pꝫ ex <lb/>ſcḋa ſuppõne / q2 mediū continuo maneat vniforme <lb/>vt ſuppono: ergo ad oēm punctū citra idē gradus <lb/>luminis conſeruatur. </s>
              <s xml:id="N27469" xml:space="preserve">Et ad puncta remotiora plꝰ <lb/>facit minoratio quãtitatꝪ ad remiſſionē luminis ̄ <lb/>ad ꝓpīq̇ora / vt pꝫ ex .3. correlario .3. ↄ̨cluſiõis: igr̄ ad <lb/>pūcta remotiora remittitt̄̄ lumē: et ſic pꝫ correlariū.</s>
            </p>
            <p xml:id="N27472">
              <s xml:id="N27473" xml:space="preserve">Quinto concluſio. </s>
              <s xml:id="N27476" xml:space="preserve">agētibus lumino-<lb/>ſis equalibus ītenſiue et quantitatiue in media vni-<lb/>formis inequalia in raritate: et rarefientibꝰ datis <lb/>mediis vniformiter īuariata quãtitate taliter ꝙ̄ cõ­<lb/>tinuo quilꝫ gradus luminis in vno medio moueat̄̄ <lb/>ita velociter ſicut gradus correſpõdēs ī altero me-<lb/>dio. </s>
              <s xml:id="N27485" xml:space="preserve">Tunc cõtinuo velociꝰ fiet intenſio ad puncta ī <lb/>medio denſiori in quod lumē ꝑ minorē diſtantiam <lb/>ꝓducitur ꝙ̄ ad puncta correspõdentia in medio ra­<lb/>riori. </s>
              <s xml:id="N2748E" xml:space="preserve">Probat̄̄ / q2 ſignatis in vtro medio duobꝰ <lb/>punctis ineq̈lis intēſionis: correſpõdentibꝰ tamen <lb/>quorū remiſſior aliqñ erit ita intenſus ſicut inten-<lb/>ſior: manifeſtū eſt  citius gradus q̇ eſt in intenſio­<lb/>ri puncto deueniet ad pūctū remiſſiorē in medio dē­<lb/>ſiori ꝙ̄ ↄ̨ſimilis punctꝰ intēſior deueniet ad ↄ̨ſimilē <lb/>punctū remiſſiorē in medio rariori. </s>
              <s xml:id="N2749D" xml:space="preserve">cū in medio dē-<lb/>ſiori illa puncta ſint ꝓximiora: et gradus luminis <lb/>exiſtens in illis eque velociter in vtro medio mo­<lb/>uentur. </s>
              <s xml:id="N274A6" xml:space="preserve">g̊ velocius fiet intenſio luminis ad puncta ī <lb/>medio denſiori ꝙ̄ ad cõſiĺia puncta in medio rario­<lb/>ri. </s>
              <s xml:id="N274AD" xml:space="preserve">¶ Ex quo ſequit̄̄ / ꝙ̄ luminoſo agente ī mediū vni­<lb/>forme creſcente continuo in quãtitate: ita  ↄ̨tinuo <lb/>gradus luminis moueant̄̄ vniformiter: ad omnem <lb/>punctū medii ad quē lumē intēdet̄̄ cõtinuo tardius <lb/>et tardiꝰ intendet̄̄. </s>
              <s xml:id="N274B8" xml:space="preserve">Probat̄̄ ex cõcluſione / q2 cõtinuo <lb/>illa latitudo luminis eſt maior et cõtinuo gradus <lb/>eius eque velociter mouētur: igit̄̄ cõtinuo tardius et <lb/>tardius lumē intendet̄̄: cõtinuo em̄ equalis latitu-<lb/>do luminis magis diſtabit ab eodē puncto ꝙ̄ ante / <lb/>vt pꝫ aſpicienti: et ↄ̨tinuo mouet̄̄ talis latitudo ver­<lb/>ſus idē punctū tardiꝰ et tardius. </s>
              <s xml:id="N274C7" xml:space="preserve">Nã tardius mo-<lb/>uent̄̄ in tali latitudine lumīs pūcta ſiue gradꝰ ma-<lb/>gis intenſi ꝙ̄ minꝰ intenſi / vt ↄ̨ſtat pꝫ igr̄ correlari­<lb/>um. </s>
              <s xml:id="N274D0" xml:space="preserve">¶ Seq̇tur ſcḋo /  ſi cõtinuo aliq̈s hõ eſſet ad pū­<lb/>ctū mediū latitudinis talis luminis ↄ̨tinuo minus <lb/>minus calefieret a tali lumine dūmodo tale lumen <lb/>natum ſit calefacere et cõtinuo minus et minus vide­<lb/>ret ceteris īpedimentis et iuuameētis deductis. </s>
              <s xml:id="N274DB" xml:space="preserve">patꝫ / <lb/>q2 continuo infinita puncta iuuãtia ad productio-<lb/>nē caliditatis et viſionis magis diſtãt a tali homi-<lb/>ne. </s>
              <s xml:id="N274E4" xml:space="preserve">igit̄̄ cõtinuo minuus iuuant. </s>
              <s xml:id="N274E7" xml:space="preserve">ſeq̇tur g̊ correlariū</s>
            </p>
            <p xml:id="N274EA">
              <s xml:id="N274EB" xml:space="preserve">Sexte concluſio. </s>
              <s xml:id="N274EE" xml:space="preserve">luminoſo agente in <lb/>mediū vniforme: ad omnē punctū intrinſecū medii <lb/>cõſeruatur idē gradus luminis intenſiue et extenſi-<lb/>ue ſicut ſi ad illum punctū eēt luminoſum vniforme <lb/>gradu tali puncto correſpõdente et equalis quãti-               <pb chead="De motu alterationis quo ad cauam" file="0235" n="235"/>               tatis cū luminoſo agente. </s>
              <s xml:id="N274FE" xml:space="preserve">Probat̄̄. </s>
              <s xml:id="N27501" xml:space="preserve">Sit a. lumino­<lb/>ſum gradu c. agēs latitudinem luminis a .c. gradu <lb/>vſ ad non gradū: ſit .d. gradus in f. ꝓportione <lb/>remiſſior c. et ſit b. luminoſum equale ipſi a. quãtita­<lb/>tiue in f. tamē ꝓportiõe remiſſius. </s>
              <s xml:id="N2750C" xml:space="preserve">Tūc dico /  ſi b. <lb/>ponatur in puncto in quo eſt d. gradus: cõſeruabit̄̄ <lb/>idem gradus q̇ cõſeruat̄̄ ab a. extenſiue et intenſiue <lb/></s>
              <s xml:id="N27514" xml:space="preserve">QꝪ ſic oſtēditur / q2 d. eſt in f. ꝓportiõe remiſſior ip̄o <lb/>c. et latitudo luminis eſt vniformiter difformis: igr̄ <lb/>d. in f. ꝓportõe minus diſtat a nõ gradu /  c. pꝫ hec <lb/>cõſequētia aſpicienti naturã qualitatis vniformiṫ <lb/>difformis ad nõ gradum terminate. </s>
              <s xml:id="N2751F" xml:space="preserve">Et ex ↄ̨ſequēti <lb/>ſeq̇tur /  diſtãtia ꝑ quam agit a. eſt in f. ꝓportione <lb/>maior ꝙ̄ diſtantia inter d. et nõ gradū totius lumi­<lb/>nis ꝓducti ab a. </s>
              <s xml:id="N27528" xml:space="preserve">Et b. eſt equalis quãtitatis cū ip̄o <lb/>a. et in f. ꝓportiõe remiſſius: g̊ ſi ponatur b. ad pun-<lb/>ctum ī quo eſt d. gradus luminis ↄ̨ſeruabit̄̄ idē gra­<lb/>dus luminis q̇ ↄ̨ſeruatur ab a. intenſiue et extenſiue <lb/>patet ↄ̨ña / q2 aget latitudinē a .d. vſ ad nõ gradū <lb/>per diſtantiã in f. ꝓportiõe minorē ꝙ̄ a. / vt ptꝫ ex .4. <lb/>fuppõne: et talis eſt diſtautia inter d. et nõ gradū lu­<lb/>minis: igr̄ etc̈. </s>
              <s xml:id="N27539" xml:space="preserve">Ptꝫ g̊ cõcluſio. </s>
              <s xml:id="N2753C" xml:space="preserve">plura in hac materia <lb/>dicerē niſi tota ip̄a in īteret̄̄ illis ſuppõnibꝰ q̈rū i-<lb/>tas ē ſuſpecta. </s>
              <s xml:id="N27543" xml:space="preserve">vt ptꝫ ex dictis. </s>
              <s xml:id="N27546" xml:space="preserve">Et ꝑ hoc pꝫ rḋſio ad <lb/>dubiū eſt em̄ prīa ꝓpõ cõcluſio reſponſiua.               <anchor type="note" xlink:href="note-0235-01" xlink:label="note-0235-01a"/>               </s>
              <s xml:id="N27550" xml:space="preserve">¶ Ad ra­<lb/>tiones ante oppoſitum patet reſpõſio ex dictis ſūt <lb/>enim pro ꝑte dubii quã ſuſtineo. </s>
              <s xml:id="N27557" xml:space="preserve">¶ Ad rationem in <lb/>oppoſitū pꝫ ſolutio ex dictis.</s>
            </p>
            <div xml:id="N2755C" level="5" n="19" type="float">
              <note position="left" xlink:href="note-0235-01a" xlink:label="note-0235-01" xml:id="N27560" xml:space="preserve">Soluit̄̄ <lb/>2. dubiū.</note>
            </div>
            <note position="left" xml:id="N27568" xml:space="preserve">Quid eſt <lb/>difficul-<lb/>tas actio­<lb/>nis.</note>
            <p xml:id="N27572">
              <s xml:id="N27573" xml:space="preserve">Ad ſecundū dubiū ſoluenduꝫ </s>
              <s xml:id="N27576" xml:space="preserve">Aduer-<lb/>tēdū eſt nõ eſt  difficultas actiõis aliſi ꝙ̄ agēs vel <lb/>effectꝰ ſiue actio ipſiꝰ agētis. </s>
              <s xml:id="N2757D" xml:space="preserve">p̄t aūt ſic diffiniri diffi­<lb/>cultas actõis eſt actio q̄ ꝓducit̄̄ cū reſiſtētia ab agē­<lb/>te a finita ꝓportiõe.               <anchor type="note" xlink:href="note-0235-02" xlink:label="note-0235-02a"/>               </s>
              <s xml:id="N27589" xml:space="preserve">¶ Ex hoc ſeq̇t̄̄ /  deꝰ nõ ꝓducit <lb/>difficultatē actionis niſi vt forte cõcurrit cū creatu­<lb/>ris q2 nichil duo reſiſtit.               <anchor type="note" xlink:href="note-0235-03" xlink:label="note-0235-03a"/>               </s>
              <s xml:id="N27595" xml:space="preserve">¶ Sequit̄̄ ſcḋo luminoſum <lb/>nõ facere difficultatē actiõis / q2 nõ agit cū reſiſtētia <lb/></s>
              <s xml:id="N2759B" xml:space="preserve">Itē nec aīa intelligēdo ꝓpter eandē rõnem.               <anchor type="note" xlink:href="note-0235-04" xlink:label="note-0235-04a"/>               </s>
              <s xml:id="N275A3" xml:space="preserve">¶ Seq̇-<lb/>tur tertio difficultatē actiõis nõ ꝓuenire a ꝓportio­<lb/>ne equalitatis: nec minoris equalitatis. </s>
              <s xml:id="N275AA" xml:space="preserve">nulla em̄ <lb/>actio ꝓducit̄̄ mediãte ꝓportiõe equalitatis aut mi­<lb/>noris ineq̈litatis: igit̄̄ nec difficultas actõis cū dif­<lb/>ficultas actõis ſit actio.               <anchor type="note" xlink:href="note-0235-05" xlink:label="note-0235-05a"/>               </s>
              <s xml:id="N275B8" xml:space="preserve">¶ Siq̇tur .4. /  difficultas <lb/>actionis nõ eſt attēdenda penes potentiã agētis ſe­<lb/>cundū vltimū. </s>
              <s xml:id="N275BF" xml:space="preserve">q2 tunc ſeq̄retur deū agentē in inſtã­<lb/>ti facultatē in agendo: īmo maximã poſſibilē / quod <lb/>eſt abſurdū. </s>
              <s xml:id="N275C6" xml:space="preserve">Et miror de cal. quomõ nolluit cõcede­<lb/>re difficultatē actionis intēdi cū diminuit̄̄ ꝓportio <lb/>cū vocabulū illud videat̄̄ importare: nec vn̄ vidi <lb/>aliquē in tali ſignificantia vtētē illo vocabulo: pau­<lb/>lū venetū et ip̄m excipio. </s>
              <s xml:id="N275D1" xml:space="preserve">Itē dicit facilitatē defectū <lb/>poñe cõſignificare. </s>
              <s xml:id="N275D6" xml:space="preserve">Sꝫ ꝓfecto plurimū abuſus ē ter­<lb/>mino.               <anchor type="note" xlink:href="note-0235-06" xlink:label="note-0235-06a"/>               </s>
              <s xml:id="N275E0" xml:space="preserve">Nã facilitas ſiue facultas qḋ idem eſt facili-<lb/>tatē ſiue poteſtatē agendi ſignificat vnde 2.11. q. vi. <lb/>c. biduū et eſt verbū Marci imperatoris .ff. quando <lb/>appellandū ſit. </s>
              <s xml:id="N275E9" xml:space="preserve">Si q̇s ipſius a quo appelauit ad-<lb/>eundi facultatē nõ habuit etc. capitur facultas ꝓ co­<lb/>pia et poteſtate aliq̇d faciēdi hinc diuitie facultates <lb/>dicuntur et ſimiliter poſſeſſiões:               <anchor type="note" xlink:href="note-0235-07" xlink:label="note-0235-07a"/>               q2 illis mediãtibꝰ <lb/>magna facile poſſumus et ꝑ clara pḣs .1. ethi. impo­<lb/>ſibile eī eſt vtis res ꝑ claras agat cui facultates de­<lb/>ſunt inde facultates eccĺe. xiti. q. ii. huic cõtrariū eſt <lb/>verbū difficultas quaſi nõ facultas ſiue labore ope­<lb/>randi.               <anchor type="note" xlink:href="note-0235-08" xlink:label="note-0235-08a"/>               </s>
              <s xml:id="N27606" xml:space="preserve">inde difficile quod nõ ſiue labore fieri poteſt <lb/>Mantuanꝰ omne qḋ excellens etc. </s>
              <s xml:id="N2760B" xml:space="preserve">Difficiles ortus <lb/>incremēta tarda hꝫ.               <anchor type="note" xlink:href="note-0235-09" xlink:label="note-0235-09a"/>               </s>
              <s xml:id="N27615" xml:space="preserve">Et virgiliꝰ difficiles primuꝫ <lb/>terre colleſ maligni.               <anchor type="note" xlink:href="note-0235-10" xlink:label="note-0235-10a"/>               </s>
              <s xml:id="N2761F" xml:space="preserve">hinc difficile quod aliqñ ca-<lb/>pitur pro nõ vt in calce. d.c. biduū: nõnū̄ vero pro <lb/>vix eccle. primo preuerſi difficile corriguntur etc.</s>
            </p>
            <div xml:id="N27626" level="5" n="20" type="float">
              <note position="left" xlink:href="note-0235-02a" xlink:label="note-0235-02" xml:id="N2762A" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0235-03a" xlink:label="note-0235-03" xml:id="N27630" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0235-04a" xlink:label="note-0235-04" xml:id="N27636" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0235-05a" xlink:label="note-0235-05" xml:id="N2763C" xml:space="preserve">4. correĺ.</note>
              <note position="left" xlink:href="note-0235-06a" xlink:label="note-0235-06" xml:id="N27642" xml:space="preserve">Marcus <lb/>īperator</note>
              <note position="left" xlink:href="note-0235-07a" xlink:label="note-0235-07" xml:id="N2764A" xml:space="preserve">phūs pri­<lb/>mo ethi.</note>
              <note position="left" xlink:href="note-0235-08a" xlink:label="note-0235-08" xml:id="N27652" xml:space="preserve">baptiſta <lb/>1. per the. <lb/>mari.</note>
              <note position="left" xlink:href="note-0235-09a" xlink:label="note-0235-09" xml:id="N2765C" xml:space="preserve">Uirgiliꝰ</note>
              <note position="left" xlink:href="note-0235-10a" xlink:label="note-0235-10" xml:id="N27662" xml:space="preserve">2. geor. <lb/>Eccle. 1.</note>
            </div>
            <cb chead="De motu alterationis quo ad cauam"/>
            <p xml:id="N2766C">
              <s xml:id="N2766D" xml:space="preserve">Sed q2 diſputatio de ſignificãtis dictionum ad <lb/>grãmaticū ſpectat non ad pḣm: ſuperſedeo.</s>
            </p>
            <note position="right" xml:id="N27672" xml:space="preserve">Soluit̄̄ <lb/>2. dubiū</note>
            <p xml:id="N27678">
              <s xml:id="N27679" xml:space="preserve">Sit igitur cõcluſio reſponſiua ad du­<lb/>bium. </s>
              <s xml:id="N2767E" xml:space="preserve">Difficultas actionis menſuranda eſt penes <lb/>paruitaten proportionis maioris inequalitatis: <lb/></s>
              <s xml:id="N27684" xml:space="preserve">Ita  quanto proportio agētis ad paſſum eſt mi-<lb/>nor tanto difficultas actionis eſt maior. </s>
              <s xml:id="N27689" xml:space="preserve">Nec ob-<lb/>ſtat argumentum calculataoris: et pauli ve. inferen-<lb/>tium /  tunc ſeq̄retur /  tãte difficultatis eſſet ꝓta-<lb/>re vnū granū milli ſicut vnum magnuꝫ molare: qm̄ <lb/>illud nõ eſt incõueniēs: imo verum reſpectu potētie <lb/>maioris et minoris. </s>
              <s xml:id="N27696" xml:space="preserve">Hec concluſio ex īprobationi-<lb/>bus aliorum modorum cõmēſurande difficultatis <lb/>actionis patet. </s>
              <s xml:id="N2769D" xml:space="preserve">illis em̄ īpugnatis ſolus hic relin-<lb/>quitur poſſibilis. </s>
              <s xml:id="N276A2" xml:space="preserve">Et ꝑ hoc patet ad dubium.</s>
            </p>
            <note position="right" xml:id="N276A5" xml:space="preserve">Soluit̄̄ <lb/>3. dubiū.</note>
            <p xml:id="N276AB">
              <s xml:id="N276AC" xml:space="preserve">Ad tertium dubium. </s>
              <s xml:id="N276AF" xml:space="preserve">Reſpondetur ꝑ <lb/>talem concluſionem </s>
              <s xml:id="N276B4" xml:space="preserve">Agens naturale poteſt equeu­<lb/>lociter agere in remotum et ꝓpinquum. </s>
              <s xml:id="N276B9" xml:space="preserve">hec conclu­<lb/>ſio patet ex deductione tertii argumenti principa-<lb/>lis ante oppoſitum.               <anchor type="note" xlink:href="note-0235-11" xlink:label="note-0235-11a"/>               </s>
              <s xml:id="N276C5" xml:space="preserve">Et hec cõcluſio eſt cõtra petruꝫ <lb/>mantuanū: et iohãnem de caſali. </s>
              <s xml:id="N276CA" xml:space="preserve">Sed contra / eã ſic <lb/>arguitur ioannes de caſali. </s>
              <s xml:id="N276CF" xml:space="preserve">Sit paſſum ita diſpoſi­<lb/>tum vt per te agens d. equeuelociter agat in pun-<lb/>ctum eius a. propinquiorem et b. remotiorem. </s>
              <s xml:id="N276D6" xml:space="preserve">Et ſit <lb/>c. agens minus cuius actio in idem paſſū ṫminetur <lb/>ad a. punctū ita ꝓpinquiū ipſi c. ſicut d. </s>
              <s xml:id="N276DD" xml:space="preserve">Et augeat̄̄ <lb/>ↄ̨tinuo c. quouſ ſit equale ipſi d. ita tñ  ſemꝑ eiꝰ <lb/>actio terminet̄̄ ad nõ gradū quouſ deueniat eiꝰ <lb/>actio ad b. punctū. </s>
              <s xml:id="N276E6" xml:space="preserve">quo poſito argr̄ ſic / c. ↄ̨tinuo a-<lb/>get velociꝰ in ꝓpinquū ꝙ̄ in remotū quouſ actio <lb/>eiꝰ deueniat ad b. </s>
              <s xml:id="N276ED" xml:space="preserve">Et deinde ↄ̨tinuo aget in a. ꝓpī-<lb/>quū velociꝰ ꝙ̄ in b. remotū, et erit equale aliquãdo <lb/>ipſi d. agens ↄ̨tinuo in equalē reſiſtētiã oīno cete-<lb/>ris paribꝰ: igr̄ d. ↄ̨tinuo agit velociꝰ in a. ꝙ̄ in b. / qḋ <lb/>eſt oppoſitū dati: ↄ̨ña ptꝫ cū maiore ex hypotheſi. <lb/></s>
              <s xml:id="N276F9" xml:space="preserve">Et minor ꝓbat̄̄ / q2 ↄ̨tinuo erit c. ꝓpinquiꝰ a. quã b. <lb/>et ↄ̨tinuo habebit maiꝰ iuuamē ex ꝑte effectꝰ ꝓducti <lb/>ad a. ꝙ̄ ad b. / igr̄ ↄ̨tinuo velociꝰ agit c. ad a. ꝙ̄ ad b. / <lb/>qḋ fuit ꝓbandū: hec eſt ferme vtriꝰ rationis ioãnis <lb/>de caſali. </s>
              <s xml:id="N27704" xml:space="preserve">Ad hanc rationē rñdeo admiſſo caſu cõ-<lb/>cedēdo maiorem: et negando  c. ↄ̨tinuo agat in eq̈­<lb/>lem reſiſtentiam reſiſtentie in quã agit d. q2 cū c. in­<lb/>cipit agere in tale paſſum: cū incipiat fortius age-<lb/>re in ꝓpinquū ꝙ̄ ī remotū ex hypotheſi: iã illud pa­<lb/>ſum in quod agit c. incipit eſſe diſſimile illi in quod <lb/>d. natū eſt eque velociter agere reſpectu propinqui <lb/>et remoti. </s>
              <s xml:id="N27715" xml:space="preserve">Et ſi dicas volo /  iuuamime extrinſeco fi­<lb/>at  continuo tm̄ reſiſtat adequate paſſum ī quod <lb/>agit c. ſicut paſſum in qod agit d. admitto illud: et <lb/>tunc dico ad argumentū negando minorē vcꝫ  cū <lb/>actio c. deuenerit ad b. continuo aget c. velociꝰ in a. <lb/>̄ in b. ymo cuꝫ c. fuerit equale ipſi d. incipiet agere <lb/>q̈liter ad a. et b. eſto  aliqñ tardiꝰ cõtinuo egerit. <lb/></s>
              <s xml:id="N27725" xml:space="preserve">Nã cū primo eſt eq̈le ipſi d. incipit habere equalem <lb/>proportionē ad quolꝫ punctū. </s>
              <s xml:id="N2772A" xml:space="preserve">Stat eī platonē cõ-<lb/>tinuo per horã velociꝰ ſorte moueri: et tñ in fine eq̈li­<lb/>ter moueri et ad ꝓbationeꝫ nego iſtã ↄ̨ñam cõtinuo <lb/>erit c. ꝓpinquiꝰ a. ꝙ̄ b. et ↄ̨tinuo habebit maius iu-<lb/>uamen ex parte effectus ꝓducti ad a. ꝙ̄ ad b. / igit̄̄ cõ­<lb/>tinuo velocius agit c. ad a ꝙ̄ ad b. q2 ſicut iuuameu­<lb/>tum eſt maius ad a. ꝙ̄ ad b. ita reſiſtentia eſt minor <lb/>ad b. ꝙ̄ ad a. / nec obſtat /  cõtinuo equaliter corrum­<lb/>pitur de reſiſtētia in ꝓpinquū et remotū: reſiſtentia <lb/>eſt minoris in remotū ꝙ̄ in ꝓpinquū: et qñ idem exceſ-<lb/>ſus demptꝰ ē a maiori et minori etc. q2 totalis reſi-<lb/>ſtentia intrinſeca videlicet et extrinſeca ad quodli-<lb/>bet pūctū eſt equalis: eſto  intrīſeca ſit inequalis <lb/></s>
              <s xml:id="N27746" xml:space="preserve">Et ꝑ hoc pꝫ rñſio ad tertium dubium.</s>
            </p>
            <div xml:id="N27749" level="5" n="21" type="float">
              <note position="right" xlink:href="note-0235-11a" xlink:label="note-0235-11" xml:id="N2774D" xml:space="preserve">Cõtra pe­<lb/>trū ḋ mã­<lb/>tua: et Iõ­<lb/>hannē de <lb/>caſali.</note>
            </div>
            <pb chead="Quarti tractatus." file="0236" n="236"/>
            <p xml:id="N2775F">
              <s xml:id="N27760" xml:space="preserve">Concluſio reſponſiua ad queſtionem <lb/>patet ex primo notabili queſtionis.</s>
            </p>
            <p xml:id="N27765">
              <s xml:id="N27766" xml:space="preserve">Ad rationes queſtionis reſtat dicere. <lb/></s>
              <s xml:id="N2776A" xml:space="preserve">¶ Ad primam rationem reſponſum eſt ibi vſ ad <lb/>vltimam replicã: ad quã reſpondeo cõcedendo illa­<lb/>tum: et neganda falſitatem conſequentis: vt patet ex <lb/>ſecundo notabili.</s>
            </p>
            <p xml:id="N27773">
              <s xml:id="N27774" xml:space="preserve">Ad ſecundam rationem reſponſum ē <lb/>ibi vſ ad vltimam replicam: ad quam reſpondeo <lb/>admiſſo caſu: negando minorem: </s>
              <s xml:id="N2777B" xml:space="preserve">Et ad ꝓbationeꝫ <lb/>minoris: nego conſequentiam: et cū probatur nego / <lb/> forma totalis ipſius a. vni certe parti date nõ hꝫ <lb/>infinitas equales non cõmunicantes: et ratio eſt q2 <lb/>quelibet habet tantam formam aut maiorem ꝙ̄ ſit <lb/>forma habens ꝓportionem equalitatis ad reſiſtē-<lb/>tiam b. paſſi: vt conſtat quoniã alias non ageret.</s>
            </p>
            <p xml:id="N2778A">
              <s xml:id="N2778B" xml:space="preserve">¶ Ad confirmationem patet reſpoſio ex tertio no-<lb/>tabili.</s>
            </p>
            <p xml:id="N27790">
              <s xml:id="N27791" xml:space="preserve">Ad tertiam rationem reſponſum ē ibi <lb/>vſ ad vltimam replicam: </s>
              <s xml:id="N27796" xml:space="preserve">Ad quã reſpondeo con-<lb/>cedendo illatū: </s>
              <s xml:id="N2779B" xml:space="preserve">Nec hoc ē incõueniēs / vt patet ex ter­<lb/>tia concluſione primi dubii: ex quinta cõcluſione cū <lb/>primo et ſecundo correlariis: quibus adde in ca-<lb/>ſu oculū aquile optime diſpoſitum non videre obie­<lb/>ctum ſibi debite approximatū in quantocū inten­<lb/>ſo lumine. </s>
              <s xml:id="N277A8" xml:space="preserve">quod ſic probatur poſito /  ſit oculus aq̇­<lb/>le bene diſpoſitus vbi eſt gradus .4. latitudinis lu­<lb/>minis vniformiṫ difformis. </s>
              <s xml:id="N277AF" xml:space="preserve">obiecto pedali ſibi de-<lb/>bite approximato. </s>
              <s xml:id="N277B4" xml:space="preserve">rarefiat ergo. </s>
              <s xml:id="N277B7" xml:space="preserve">illa latitudo lumi­<lb/>nis: quouſ latitudo luminis circunſtãs pedale ſit <lb/>tam parue potentie  non ſufficiat īmutare oculuꝫ <lb/>aquile: quo poſito oculus aquile nõ videbit / ergo ꝓ­<lb/>poſitum (volo enim quod ſemper oculus aquile et <lb/>pedale ſint ꝓpe gradū .4.) et ſicut arguit̄̄ de lumine <lb/>vt .4. arguas tu de quouis alio. </s>
              <s xml:id="N277C6" xml:space="preserve">Adde ſecundo /  a. <lb/>luminoſum poteſt naturaliter producere lumen vni­<lb/>forme. </s>
              <s xml:id="N277CD" xml:space="preserve">Quod ſic oſtenditur. </s>
              <s xml:id="N277D0" xml:space="preserve">pono /  a. <lb/>ꝓducat latitudinem luminis ab octauo vſ ad nõ <lb/>gradum et  vndiqua circa luminoſum in puncto <lb/>vbi eſt gradus .4. ponatur obſtaculum cauſans re-<lb/>flexionem luminis. </s>
              <s xml:id="N277DB" xml:space="preserve">quo poſito iam luminiuoſum ꝑ li­<lb/>neam reflexam ꝓducet verſus ſe lumen a .4. vſ ad <lb/>non gradum. </s>
              <s xml:id="N277E2" xml:space="preserve">et iam in illo medio ante reflexionem <lb/>erat latitudo a .4. vſ ad .8. / igitur manebit latitu-<lb/>do vniformis. </s>
              <s xml:id="N277E9" xml:space="preserve">Et ſi dicas  nõ ꝓducet luminoſuꝫ lu­<lb/>men a quarto vſ ad non gradū ꝑ tantam diſtan-<lb/>tiam per lineam reflexam ꝑ quantã per lineam re-<lb/>ctam. </s>
              <s xml:id="N277F2" xml:space="preserve">Tunc volo /  obſtaculum approximetur cor-<lb/>pori luminoſo et habebitur propoſitum.</s>
            </p>
            <p xml:id="N277F7">
              <s xml:id="N277F8" xml:space="preserve">Ad quartam rationem reſponſum eſt <lb/>vbi vſ ad vltimam replicam. </s>
              <s xml:id="N277FD" xml:space="preserve">Ad quam reſpõdeo <lb/>concedendo quod infertur: nec illud eſt incõueniens</s>
            </p>
            <p xml:id="N27802">
              <s xml:id="N27803" xml:space="preserve">Ad quintam rationem reſpondeo con­<lb/>cedendo illatum. </s>
              <s xml:id="N27808" xml:space="preserve">vt patet ex concluſionibus queſtio­<lb/>nis illud eſſe concedendum: et nego  illud ſit falſuꝫ</s>
            </p>
            <p xml:id="N2780D">
              <s xml:id="N2780E" xml:space="preserve">Ad ſextam rationem reſponſum ē ibi <lb/>vſ ad vltimam replicam ad quam reſpondeo ne-<lb/>gando ſequelam. </s>
              <s xml:id="N27815" xml:space="preserve">Et ad probationem nego conſe-<lb/>quentiam.</s>
            </p>
            <p xml:id="N2781A">
              <s xml:id="N2781B" xml:space="preserve">Ad ſeptimam rationem reſpondet ſe-<lb/>cundum dubium huius queſtionis.</s>
            </p>
          </div>
          <div xml:id="N27820" level="4" n="2" type="chapter" type-free="capitulum">
            <head xml:id="N27825" xml:space="preserve">Capitulum ſecundum in quo <lb/>agitur de intenſione et remiſ-<lb/>ſione formarum.</head>
            <cb chead="Capitulum ſecundum."/>
            <p xml:id="N2782E">
              <s xml:id="N2782F" xml:space="preserve">QUoniam intenſio forme ſeque­<lb/>la eſt alterationis naturaliter, aut for-<lb/>me ꝓductionis: </s>
              <s xml:id="N27836" xml:space="preserve">Queritur an forma poſ­<lb/>ſit intendi.</s>
            </p>
            <p xml:id="N2783B">
              <s xml:id="N2783C" xml:space="preserve">Et arguitur primo  non. </s>
              <s xml:id="N2783F" xml:space="preserve">quia ſi for-<lb/>ma poſſet intendi: hoc maxime fieret ꝑ cõtrarii de-<lb/>purationē. </s>
              <s xml:id="N27846" xml:space="preserve">ſed conſequens eſt falſum: igitur illḋ ex <lb/>quo ſequitur. </s>
              <s xml:id="N2784B" xml:space="preserve">Sequela patet per phm̄ tertio topi-<lb/>coꝝ dicētem illa que ↄ̨trariis ſuis ſunt in ꝑmixtio-<lb/>ra: magis ſunt alia. </s>
              <s xml:id="N27852" xml:space="preserve">vt illud eſt albius quod ē nigro <lb/>impermixtiꝰ: igitur intenſio forme fit ꝑ depuratio­<lb/>nem a contrario. </s>
              <s xml:id="N27859" xml:space="preserve">Itē aurum ꝑ maiorem depuratio­<lb/>nem fit magis fuluū vt experientia docet: igit̄̄ intē-<lb/>ſio coloris auri fit ꝑ cõtrarii depurationē. </s>
              <s xml:id="N27860" xml:space="preserve">Sed fal­<lb/>ſitas ↄ̨ñtis arguit̄̄ / q2 aliqua forma intenditur: et nõ <lb/>per depurationem a cõtrario: igitur ītenſio forme <lb/>non fit ꝑ contrarii depurationeꝫ. </s>
              <s xml:id="N27869" xml:space="preserve">Añs arguitur de <lb/>charitate q̄ nõ intēditur per depurationem a con-<lb/>trario / vt patet auctoritate theologorū. </s>
              <s xml:id="N27870" xml:space="preserve">Patet etiã <lb/>de lumine quod non intenditur per contrarii depu­<lb/>rationē: cum lumen non habeat contrariū.               <anchor type="note" xlink:href="note-0236-01" xlink:label="note-0236-01a"/>               </s>
              <s xml:id="N2787C" xml:space="preserve">¶ Di-<lb/>ces diſtinguendo /  aliqua forma non intendatur ꝑ <lb/>contrarii depurationē. </s>
              <s xml:id="N27883" xml:space="preserve">aut forma habens contra-<lb/>rium: et ſic negatur. </s>
              <s xml:id="N27888" xml:space="preserve">aut non habens contrarium et <lb/>ſic conceditur.</s>
            </p>
            <div xml:id="N2788D" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0236-01a" xlink:label="note-0236-01" xml:id="N27891" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N27897">
              <s xml:id="N27898" xml:space="preserve">Sed contra / quia aliqua forma habēs <lb/>contrarium non intenditur depuratione contrarii / <lb/>igitur ſolutio nulla. </s>
              <s xml:id="N2789F" xml:space="preserve">Añs probatur et pono caſū /  <lb/>aliq̇s non habituatꝰ habitu ↄ̈rio caſtitatis acq̇rat <lb/>hītū caſtitatꝪ ꝑ actꝰ freq̄tatos. </s>
              <s xml:id="N278A6" xml:space="preserve">Quo poſito talis <lb/>intendit habitū caſtitatis: et tamen nõ intendit illū <lb/>a contrario ipſū depurãdo cū nõ habeat eius cõtra­<lb/>rium ex caſu: igitur aliqua forma habens contrari­<lb/>um non intenditur depuratione cõtrarii / quod fuit <lb/>ꝓbandum. </s>
              <s xml:id="N278B3" xml:space="preserve">Item aſſenſus alicuiꝰ ꝓpoſitionis intē-<lb/>ditur abſ depuratione aſſenſus ſui cõtradictorii: <lb/>cum aſſenſus duarū contradictoriarū impoſſibili-<lb/>ter ſe cõpatiuntur vt inferius videbitur: igitur.</s>
            </p>
            <p xml:id="N278BC">
              <s xml:id="N278BD" xml:space="preserve">¶ Et confirmatur / q2 ſi forma ſic intenderetur: ſeq̄-<lb/>retur non poſſe caliditatē intendi quin ſimul ī eiuſ-<lb/>dē caliditatis ſubiecto frigiditas intendatur. </s>
              <s xml:id="N278C4" xml:space="preserve">ↄ̨ñs <lb/>eſt falſum et cõtra experientiam: igitur illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N278CB" xml:space="preserve">Sequela ꝓbatur / q2 ſi caliditas intendi­<lb/>tur: ipſa (per te) minꝰ ꝑmiſcetur frigiditati. </s>
              <s xml:id="N278D0" xml:space="preserve">et vltra <lb/>ipſa caliditas minus ꝑmiſcetur frigiditati: igit̄̄ fri­<lb/>giditas minus ꝑmiſcetur caliditati. </s>
              <s xml:id="N278D7" xml:space="preserve">et vltra: frigidi­<lb/>tas minus permiſcetur caliditati: igitur frigiditas <lb/>intenditur quandoquidē ſecundum opinionem fri­<lb/>giditatem intendi nihil eſt aliud ꝙ̄ frigiditatē a ca­<lb/>liditate depurari et minus caliditati ꝑmiſceri: igit̄̄ <lb/>de primo ad vltimū ſi caliditas intenditur: frigidi­<lb/>tas intenditur: quod fuit probandum.</s>
            </p>
            <p xml:id="N278E6">
              <s xml:id="N278E7" xml:space="preserve">Secundo ad idē arguitur ſic / q2 ſi for-<lb/>ma poſſet intendi: maxime intenderetur ꝑ uoue for­<lb/>me additionē priore manēte cū poſteriore penetra­<lb/>tiue et vnitiue. </s>
              <s xml:id="N278F0" xml:space="preserve">ſed conſequens eſt falſum: igitur illḋ <lb/>ex quo ſequitur. </s>
              <s xml:id="N278F5" xml:space="preserve">Sequela patet / q2 alis ſequeretur <lb/>qualitatem ſimpliciter eſſe indiuiſibilem quo ad in­<lb/>tenſionem. </s>
              <s xml:id="N278FC" xml:space="preserve">et per conſequens alteram alterationem non eē <lb/>intenſiorem quod eſt falſum. </s>
              <s xml:id="N27901" xml:space="preserve">Sed falſitas conſeq̄n­<lb/>tis arguitur. </s>
              <s xml:id="N27906" xml:space="preserve">q2 ſi forma intenderetur per noue for­<lb/>me additionem etc. / ſequeretur quãlibet albedinem <lb/>eſſe infinite perfectionis: ſed conſequens eſt manife­<lb/>ſte īpoſſibile / igitur illud ex quo ſequitur /. </s>
              <s xml:id="N2790F" xml:space="preserve">Sequela <lb/>ꝓbatur et ſuppoſito /  quelib3 albedo ſit perfectior <lb/>nigredine: pono /  in a. ſubiectum intendatur albe­<lb/>do a non gradu in hora per continuam noue albe-               <pb chead="De intenſione  remiſſione formarum." file="0237" n="237"/>               dinis additionē etc. / (vt dictis) et ſit albedo adequate <lb/>in illa hora in a. ſubiectū ꝓducta b. / et arguo ſic / b. cõ­<lb/>tinet īfinitas ꝑfectiones non cõmunicantes vna cer­<lb/>ta perfectione maiores: igitur b. eſt infinite perfec-<lb/>tionis. </s>
              <s xml:id="N27925" xml:space="preserve">Conſequentia patet / q2 illud dicitur īfinitū: <lb/>quod continet infinita vni certo equalia non cõmu­<lb/>nicantia vel vno certo infinita nõ cõmunicantia ma­<lb/>iora. </s>
              <s xml:id="N2792E" xml:space="preserve">Sed antecedens probat̄̄: q2 in qualibet parte <lb/>ꝓportionali illiꝰ hore ꝓducta eſt in a ſubiectum ꝑ­<lb/>te aliqua albedo manēs cum precedenti. </s>
              <s xml:id="N27935" xml:space="preserve">et quelibet <lb/>albedo qualibet nigredine eſt ꝑfectior ex ſuppoſitio <lb/>et ſunt infinite partes ꝓportionales illiꝰ hore / igit̄̄ <lb/>b. tota albedo a. ſubiecti in fine hore continet infini­<lb/>tas perfectiones albedinis nõ cõicantes quacun <lb/>nigredine ſignata perfectiores / quod fuit ꝓbandū. <lb/>               <anchor type="note" xlink:href="note-0237-01" xlink:label="note-0237-01a"/>               </s>
              <s xml:id="N27949" xml:space="preserve">¶ Et confirmatur. </s>
              <s xml:id="N2794C" xml:space="preserve">quia dabilis eſt aliqua albedo <lb/>non habēs partes graduales / (vt poſtea videbitur) / <lb/>igitur non quelibet qualitas eſt intenſa ad ſenſum <lb/>tuum et ex hoc forma non intēnditur ꝑ noue forme <lb/>additionem etc. </s>
              <s xml:id="N27957" xml:space="preserve">¶ Item ſi forma intenditur per no-<lb/>ue forme additionē etc. / ſequitur penetratio dimen-<lb/>ſionum / quod eſt contra phm̄ 4. phi. </s>
              <s xml:id="N2795E" xml:space="preserve">Sequela patet / <lb/>q2 forma addita et forma p̄exiſtentens ī corꝑe ſūt duo <lb/>corpora: et per te ī ītenſione vniunt̄̄ penetratiue igr̄</s>
            </p>
            <div xml:id="N27965" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0237-01a" xlink:label="note-0237-01" xml:id="N27969" xml:space="preserve">confir̄a°.</note>
            </div>
            <p xml:id="N2796F">
              <s xml:id="N27970" xml:space="preserve">Tertio principalr̄ arguit̄̄ ſic / q2 ſi for-<lb/>ma poſſet intendi: hoc maxime fieret per continuaꝫ <lb/>alterius et alterius perfectioris forme ſucceſſionem / <lb/>ſed conſequens eſt falsum: igitur illud ex quo ſequi­<lb/>tur. </s>
              <s xml:id="N2797B" xml:space="preserve">Sequela ꝓbatur: q2 ſi forma poteſt intendi (cuꝫ <lb/>ꝑ auctorē ſex principioꝝ forma ſit ſimplex et ſimpli­<lb/>ci et in variabili eēntia cõſiſtens) non videtur quo <lb/>alio mõ forma intenderetur </s>
              <s xml:id="N27984" xml:space="preserve">Sed falſitas ↄ̨ñtis oſtē­<lb/>ditur / quia tunc ſequeretur caliditatem corrūpi et a <lb/>nullo corrūpi. </s>
              <s xml:id="N2798B" xml:space="preserve">ſꝫ ↄ̨ñs eſt falſum igr̄. </s>
              <s xml:id="N2798E" xml:space="preserve">, ↄ̨ñs ſit fal-<lb/>ſum patet: q2 bene ſequitur .a. corrūpitur: ergo ali-<lb/>quid corrūpit a. a paſſiuo ad actiuū etc. et vltra. </s>
              <s xml:id="N27995" xml:space="preserve">ali-<lb/>quid corrūpit a. / ergo a. corrūpit̄̄ ab aliquo ab acti­<lb/>uo ad paſſiuum etc. / et ꝑ ↄ̨ñs ſi a. corrūpit̄̄ a. corrum-<lb/>pitur ab aliquo / quod fuit ꝓbandū. </s>
              <s xml:id="N2799E" xml:space="preserve">Sequela tñ pro­<lb/>bat̄̄: et pono /  a. calido approximetur b. frigidū po­<lb/>tens agere in caliditatem ipſius a. per ſuam frigi-<lb/>ditatem et incipiat b. agere in a. reagens in inſtanti <lb/>quod eſt preſens per remotionem de preſenti: et ar-<lb/>guo ſic. </s>
              <s xml:id="N279AB" xml:space="preserve">caliditas que mõ eſt in ipſo a. corrūpitur. <lb/></s>
              <s xml:id="N279AF" xml:space="preserve">et a nullo corrūpitur: igitur. </s>
              <s xml:id="N279B2" xml:space="preserve">Minor ꝓbatur. </s>
              <s xml:id="N279B5" xml:space="preserve">q2 cali­<lb/>ditas que modo ē ī ipſo a non corumpitur a frigi-<lb/>ditate q̄ modo eſt in ipſo b. cuꝫ eque cito deſinat eē <lb/>ſicut caliditas que modo eſt in ipſo a. </s>
              <s xml:id="N279BE" xml:space="preserve">Nec calidi-<lb/>tas que modo eſt in ipſo a. corrūpitur ab aliq̈ frigi­<lb/>ditate ipſius b. ſequente: q2 q̄libet ſequens produce­<lb/>tur poſt corruptionē huius caliditatꝪ per tempus. <lb/></s>
              <s xml:id="N279C8" xml:space="preserve">igitur a nullo corrumpitur hec caliditas / quod fuit <lb/>probandum.               <anchor type="note" xlink:href="note-0237-02" xlink:label="note-0237-02a"/>               </s>
              <s xml:id="N279D2" xml:space="preserve">¶ Dices forte concedendo ſequelã cuꝫ <lb/>ↄ̨ñte: et ad probationem falſitatis conſequentis ne­<lb/>gando illam ſequelam. </s>
              <s xml:id="N279D9" xml:space="preserve">et ad probationem admittē­<lb/>do caſum dices /  caliditas illa corrumpitur a fri-<lb/>giditate que mõ eſt in ipſo b: </s>
              <s xml:id="N279E0" xml:space="preserve">Et  non eſt incõueni-<lb/>ens /  eque cito deſinant eſſe caliditas et frigiditas <lb/>et tamen vna alteram corrnmpat et econtra.</s>
            </p>
            <div xml:id="N279E7" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0237-02a" xlink:label="note-0237-02" xml:id="N279EB" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N279F1">
              <s xml:id="N279F2" xml:space="preserve">Sed contra / q2 tunc ſeq̄ret̄̄ in caſu na­<lb/>turaliter poſſibili aliquam caliditatem ab aliquo <lb/>corrumpi et tamen nec corrumpi ab aliquo quod ē: <lb/>nec ab aliquo quad fuit, nec quod erit, ↄ̨ñs īplicat <lb/>q2 ſi ab aliquo corrumpitur. </s>
              <s xml:id="N279FD" xml:space="preserve">ab aliquo quod eſt vel <lb/>fuit corrūpitur: vt conſtat logico. </s>
              <s xml:id="N27A02" xml:space="preserve">igitur ſolutio nul­<lb/>la </s>
              <s xml:id="N27A07" xml:space="preserve">Sequela probatur. </s>
              <s xml:id="N27A0A" xml:space="preserve">et pono /  b. frigidū alicuius <lb/>actiuitatis et a. calidū tante reſiſtentie omnino ſint <lb/>in debita diſtantia ad agendū: ita  vtrū ſit ītra               <cb chead="De intenſione  remiſſione formarum."/>               ſpheram actiuitatis alterius et incipiat frigiditas <lb/>ipſius b. intendi per remotionē de pñti / (vt oportet) <lb/>et agere in caliditatem ipſius a. </s>
              <s xml:id="N27A18" xml:space="preserve">Quo poſito ſic ar-<lb/>gumentor caliditas ipſius a. carrūpit̄̄: et hoc ab aii­<lb/>quo (per te) et tamen non corrumpitur ab aliquo qḋ <lb/>eſt: q2 maxime a frigiditate que eſt in inſtãti quod eſt <lb/>preſens in ip̄o b. ſed hoc nõ: q2 eſt equalis actiuita-<lb/>tis ſicut caliditas q̄ mõ eſt in ipſo a. reſiſtentie ex ca­<lb/>ſu </s>
              <s xml:id="N27A27" xml:space="preserve">Nec ab aliquo quod erit, q2 quelibet frigiditas <lb/>in b. q̄ poſt illaꝫ erit erit poſt illã ꝑ tempꝰ id eſt poſt <lb/>corruptionē eiꝰ. </s>
              <s xml:id="N27A2E" xml:space="preserve">Nec corrūpitur ab aliqno qḋ fuit / <lb/>vt conſtat (imp̄ſentiarū em̄ de corrūpēte ꝑticulari <lb/>agitur) / igitur illa caliditas corrumpitur ab aliquo <lb/>quo non eſt nec fuit nec erit / quod fuit probandum <lb/>               <anchor type="note" xlink:href="note-0237-03" xlink:label="note-0237-03a"/>               </s>
              <s xml:id="N27A3E" xml:space="preserve">¶ Dices / igitur aliter ad argumentum cõcedendo ſe­<lb/>quelam cū ↄ̨ñte. </s>
              <s xml:id="N27A43" xml:space="preserve">et ad ꝓbationē falſitatis ↄ̨ñtis: cõ-<lb/>cedo qḋ infertur vcꝫ  caliditas corrūpitur et a nul­<lb/>lo corrūpitur. </s>
              <s xml:id="N27A4A" xml:space="preserve">ſed in caſu poſito illa caliditas cor-<lb/>rūpitur a quibuſcū infinitis frigiditatibꝰ ꝓduc-<lb/>tis in tꝑe verſus inſtans initiatiuū actionis termi­<lb/>natis. </s>
              <s xml:id="N27A53" xml:space="preserve">Et ad ꝓbationem falſitatis huius ↄ̨ñtis: di-<lb/>cas negando iſtam ↄ̨ñam a. corrūpit̄̄ / ergo aliquid <lb/>corrūpit a. </s>
              <s xml:id="N27A5A" xml:space="preserve">Sed oportet īferre / ergo aliquid vel ali­<lb/>qua corrumpunt a. qḋ concedo.               <anchor type="note" xlink:href="note-0237-04" xlink:label="note-0237-04a"/>               </s>
              <s xml:id="N27A64" xml:space="preserve">¶ Ex quo ſequitur / <lb/> aliquid corrūpitur: et tñ non p̄t determīri corru­<lb/>ptiuū eiꝰ ꝑticulare.               <anchor type="note" xlink:href="note-0237-05" xlink:label="note-0237-05a"/>               </s>
              <s xml:id="N27A70" xml:space="preserve">¶ Sequitur ſcḋo /  a. caliditas <lb/>corrūpit̄̄ ab infinitis frigiditatibus: et tamē nõ ab <lb/>infinitis frigiditatibꝰ a. corrūpitur. </s>
              <s xml:id="N27A77" xml:space="preserve">Patet / q2 nec <lb/>a duabus nec a tribus: nec a .100. nec a .1000. / vt patꝫ <lb/>intuenti. </s>
              <s xml:id="N27A7E" xml:space="preserve">Nã quelibet due: tres: 100. et quelibet mille <lb/>frigiditatis ꝓduceut̄̄ poſt corruptionē illiꝰ calidi-<lb/>tatis.</s>
            </p>
            <div xml:id="N27A85" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0237-03a" xlink:label="note-0237-03" xml:id="N27A89" xml:space="preserve">Dicitur.</note>
              <note position="right" xlink:href="note-0237-04a" xlink:label="note-0237-04" xml:id="N27A8F" xml:space="preserve">1. correl.</note>
              <note position="right" xlink:href="note-0237-05a" xlink:label="note-0237-05" xml:id="N27A95" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N27A9B">
              <s xml:id="N27A9C" xml:space="preserve">Sed contra / quia eodem pacto ſeque-<lb/>retur /  aliq̇d generaret̄̄ et nõ ab aliquo: ſed ↄ̨ñs vi­<lb/>detur falſum cum cuiuſlibet entis ꝓducti ꝓductiõe <lb/>naturali ſit cã ꝑticularis ꝓductiua: igitur ſolutio <lb/>nulla. </s>
              <s xml:id="N27AA7" xml:space="preserve">Sequela ꝓbat̄̄ et pono /  aliq̈ aq̈ reagens ca­<lb/>lefiat a ſuppoſitio igne et capio caliditatē exñntem <lb/>in aqua ī d. inſtanti / et arguo ſic. </s>
              <s xml:id="N27AAE" xml:space="preserve">hec caliditas nõ eſt <lb/>producta ab aliq̈ caliditate ignis que prefuit ante <lb/>d. inſtans: nec a caliditate ignis q̄ erit poſt d. inſtãs / <lb/>vt patet ex dictis nec a caliditate ignis que ꝓducit̄̄ <lb/>ſimul cū hac caliditate in d. iuſtanti. </s>
              <s xml:id="N27AB9" xml:space="preserve">igit̄̄ hec calidi­<lb/>tas aq̄ a nullo eſt ꝓducta / quod fuit ꝓbandõ. </s>
              <s xml:id="N27ABE" xml:space="preserve">Mīor <lb/>probatur / q2 ſi hec caliditas aq̄ ꝓducit̄̄ a caliditate <lb/>ignis que ꝓducitur ſimul cum hac caliditate aque ī <lb/>d. inſtanti: caliditas ignis que ꝓducitur ſimul cum <lb/>hac caliditate aque in d. inſtanti: ꝓducitur ab eadē <lb/>caliditate aq̄ eadē ratioue: et ſic ſequit̄̄ /  caliditas <lb/>illa ignis eſt cauſa et effectus reſpectu eiuſdem pu-<lb/>ta caliditas aque in eodē genere cauſe puta efficien­<lb/>tis. </s>
              <s xml:id="N27AD1" xml:space="preserve">ſed hoc īplicat cum īpoſſibile ſit idem eē natura <lb/>prius altero et eodem eſſe natura poſterius: igitur <lb/>illa caliditas nõ ꝓducitur a caliditate ignis que ſi­<lb/>mul ꝓducitur cū ea in d. inſtanti / quod fuit ꝓbãduꝫ <lb/></s>
              <s xml:id="N27ADB" xml:space="preserve">Nec valet dicere /  caliditas ignis non ꝓducitur in <lb/>illo caſu a caliditate aque in eodē inſtanti: ſed a fri­<lb/>giditate aque: et  vnū contrarioꝝ per ſe producit <lb/>reliquū tan̄ terminū nõ vltimate intentū: et  mi-<lb/>nus perfectū plerū ꝓducit perfectū vt cū frigidi-<lb/>tas vt .6. agit in caliditatē vt .8. vel minorē eã remit­<lb/>tendo / q2 ſequitur bene frigiditas q̄ ē in aqua in d. <lb/>inſtanti ꝓducit caliditatē ignis in eodē inſtanti: et <lb/>caliditas ignis in eodē d. inſtanti: igit̄̄ caliditas <lb/>ignis in d. inſtanti eſt cauſa et effectus reſpectu eiuſ­<lb/>dē puta frigiditatis exiſtentis in aqua pro eodē in­<lb/>ſtanti in eodem genere cauſe efficientis: quod inten­               <pb chead="Quarti tractatus." file="0238" n="238"/>               debam: </s>
              <s xml:id="N27AF9" xml:space="preserve">¶ Et confirmat̄̄ / q2 ſi intenſio fieret per con­<lb/>tinuã alteriꝰ et alteriꝰ forme perfectioris ſucceſſio-<lb/>nē: ſequeret̄̄ /  vnū lumē corrūperet aliud lumē: ſed <lb/>ↄ̨ñs eſt falſum: igitur illud ex quo ſequit̄̄. </s>
              <s xml:id="N27B02" xml:space="preserve">Sequela <lb/>ꝓbat̄̄ et pono caſum corpꝰ luminoſū vt .4. illumi-<lb/>net aliquod mediū: et adueniat luminoſū vt octo lu­<lb/>mē illiꝰ medii ītēdēs. </s>
              <s xml:id="N27B0B" xml:space="preserve">Quo poſito arguit̄̄ ſſc / lumen <lb/>ꝓductū a corpore luminoſo vt .4. corrūpit̄̄: et nõ ni­<lb/>ſi a lumīe ꝓducto a luminoſo vt .8. igit̄̄. </s>
              <s xml:id="N27B12" xml:space="preserve">Añs ꝓbat̄̄ / <lb/>quia ſi non corrūpitur (cū lumen illud intendat̄̄ ex <lb/>caſu) tã ſequēs lumē manet cū precedente: et per con­<lb/>ſeq̄ns intenſio non fit per continuam alterius et al­<lb/>terius forme ꝑfectioris ſucceſſionem / qḋ fuit ꝓban­<lb/>dū               <anchor type="note" xlink:href="note-0238-01" xlink:label="note-0238-01a"/>               </s>
              <s xml:id="N27B24" xml:space="preserve">¶ Dices forte cū auctore huius opinationīs cõ-<lb/>cedendo qḋ infertur. </s>
              <s xml:id="N27B29" xml:space="preserve">vel ſaltē  vnū lumīoſum de-<lb/>ſtruit lumen alterius.</s>
            </p>
            <div xml:id="N27B2E" level="5" n="5" type="float">
              <note position="left" xlink:href="note-0238-01a" xlink:label="note-0238-01" xml:id="N27B32" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N27B38">
              <s xml:id="N27B39" xml:space="preserve">Sed contra / quia in medio illumina-<lb/>to adueniente alio luminoſo vt octo percipimꝰ lu-<lb/>men perfectiꝰ et maius ꝙ̄ ſit lumen luminoſi vt octo / <lb/>igitur lumē ꝓductū a luminoſo vt .4. non corrūpit̄̄ <lb/>ſed manet cū lumine ꝓducto a lūinoſo vt octo.</s>
            </p>
            <note position="left" xml:id="N27B44" xml:space="preserve">Dicitur.</note>
            <p xml:id="N27B48">
              <s xml:id="N27B49" xml:space="preserve">¶ Dices negando ↄ̨ñam. </s>
              <s xml:id="N27B4C" xml:space="preserve">ymo corrūpitur lumē pro­<lb/>ductū a luminoſo vt .4. et ꝓducit̄̄ ꝑfectius et intēſiꝰ <lb/>lumen ꝙ̄ lumē corporis luminoſi vt octo. </s>
              <s xml:id="N27B53" xml:space="preserve">(hoc eſt ̄ <lb/>per ſe ꝓduceret luminoſū vt octo) a duobꝰ illis cor­<lb/>poribus luminoſis et a neutro illorum.</s>
            </p>
            <p xml:id="N27B5A">
              <s xml:id="N27B5B" xml:space="preserve">Sed contra / q2 in illo caſu ſūt due vm­<lb/>bre duorum corporum luminoſorum: igitur ibi ſūt <lb/>duo lumina remiſſa: et ꝑ ↄ̨ñs adueniente vno lumi-<lb/>ne aliḋ nõ corrūpitur. </s>
              <s xml:id="N27B64" xml:space="preserve">Patet / q2 vtra vmbrarū ē <lb/>lumē diminutiuū.               <anchor type="note" xlink:href="note-0238-02" xlink:label="note-0238-02a"/>               </s>
              <s xml:id="N27B6E" xml:space="preserve">¶ Dices et bene negando ↄ̨ñaꝫ / q2 <lb/>vtra illaꝝ vmbraꝝ eſt lumē diminutuꝫ qḋ ab vno <lb/>luminoſo per ſe tantum ꝓducit̄̄ ymaginandum eſt <lb/>em̄ /  qñ opacū opponitur luminoſo: tunc totuꝫ lu­<lb/>men ꝓductū ab illo ī medio in quo ſit vmbra corrū­<lb/>pitur. </s>
              <s xml:id="N27B7B" xml:space="preserve">et ſi ex parte oppoſita luminoſo ſit aliud cor-<lb/>pus luminoſum: et corpus opacū interponat̄̄ illis lu­<lb/>minoſis: etiã lumē eiuſdē lumīoſi corrūpit̄̄ </s>
              <s xml:id="N27B82" xml:space="preserve">In vtro­<lb/> tamen medio in quo cauſatur vmbra producitur <lb/>lumē diminutū ab vno tm̄ luīoſo: (diminutū inquã <lb/>et remiſſius ꝙ̄ in medio vbi non cauſatur vmbra) eo <lb/> in medio vbi cauſatur vmbra vnum luminoſum <lb/>alterum non iuuat.</s>
            </p>
            <div xml:id="N27B8F" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0238-02a" xlink:label="note-0238-02" xml:id="N27B93" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N27B99">
              <s xml:id="N27B9A" xml:space="preserve">Sed contra: quia ſi ſolutio eſſet bona <lb/>ſequeretur /  quantulūcū paruū luminoſum cor­<lb/>rūperet lumē ꝓductū a quantocū lūinoſo ītenſio­<lb/>ri: ſed ↄ̨ñs eſt falſum / igr̄ illḋ ex quo ſequitur. </s>
              <s xml:id="N27BA3" xml:space="preserve">Falſi-<lb/>tas ↄ̨ñtis pꝫ: q2 tūc corpus luminoſū nullius eēt ­<lb/>tutis in conſeruando: et nullius virtutis reſiſtiue in <lb/>reſiſtendo corrūpēti effectū ſuū: cū quacū reſiſten­<lb/>tia alicuius luminoſi ſignata luminoſum minoris <lb/>actiuitatis ſuū lumē ſufficeret corrūpere per te. </s>
              <s xml:id="N27BB0" xml:space="preserve">Sꝫ <lb/>ſeq̄la ꝓbat̄̄: q2 dato quãtocū corpore luminoſo: <lb/>lumen eiꝰ maiorat̄̄ per te adueniente lūinoſo quan­<lb/>tūcū paruo: igit̄̄ quãtulūcū paruū luminoſum <lb/>corrūpit lumē ꝓductū a quãtocū luminoſo inten­<lb/>ſiori. </s>
              <s xml:id="N27BBD" xml:space="preserve">Patet conſequentia ex poſitiõe.               <anchor type="note" xlink:href="note-0238-03" xlink:label="note-0238-03a"/>               </s>
              <s xml:id="N27BC5" xml:space="preserve">¶ Confirma­<lb/>tur ſcḋo / q2 ſi intenſio fieret eo mõ. </s>
              <s xml:id="N27BCA" xml:space="preserve">ſeq̄ret̄̄ nullã intē-<lb/>ſionē eſſe motū: nec eſſe poſſe.               <anchor type="note" xlink:href="note-0238-04" xlink:label="note-0238-04a"/>               </s>
              <s xml:id="N27BD4" xml:space="preserve">et ꝑ ↄ̨ñs ad q̈litatē non <lb/>poſſet eē motꝰ qḋ eſt impoſſibile et cõtra phm̄ tertio <lb/>phiſicoꝝ. </s>
              <s xml:id="N27BDB" xml:space="preserve">Sequela ꝓbat̄̄: q2 qñ ſubiectū intenditur: <lb/>nulla q̈litas durat niſi per inſtans: ergo illa talis <lb/>non acquiritur per motum. </s>
              <s xml:id="N27BE2" xml:space="preserve">Nichil enim quod <lb/>acquiritur indiuiſibiliter: acquiritur per motum. <lb/></s>
              <s xml:id="N27BE8" xml:space="preserve">Nec valet dicere /  illa qualitas acq̇ritur ꝑ motū <lb/>infinitarū qualitatū p̄cedētiū: q2 tales nõ compo-<lb/>nunt nec compoſuerunt vnam qualitatē per te: nec               <cb chead="Capitulum ſecundum."/>               fuerunt cõtinue: igit̄̄ eaꝝ nõ potuit eſſe vnus motus <lb/>potius ꝙ̄ vnius hominis et vnius equi.</s>
            </p>
            <div xml:id="N27BF4" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0238-03a" xlink:label="note-0238-03" xml:id="N27BF8" xml:space="preserve">Cõfir̄a°: <lb/>ſcḋa.</note>
              <note position="left" xlink:href="note-0238-04a" xlink:label="note-0238-04" xml:id="N27C00" xml:space="preserve">phūs .3. <lb/>phi.</note>
            </div>
            <p xml:id="N27C08">
              <s xml:id="N27C09" xml:space="preserve">Quarto principaliter arguit̄̄ ſic / quia <lb/>ſi forma poſſet intendi: hoc maxime eſſet per maio-<lb/>rem et maiorem radicationē in ſubiecto. </s>
              <s xml:id="N27C10" xml:space="preserve">ſꝫ ↄ̨ñs ē fal­<lb/>ſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N27C15" xml:space="preserve">Sequela patꝫ iux­<lb/>ta ponētes illã opinionē. </s>
              <s xml:id="N27C1A" xml:space="preserve">Sed falſitas conſequētis <lb/>arguit̄̄. </s>
              <s xml:id="N27C1F" xml:space="preserve">q2 vel quando forma intenditur aliq̇d ꝓdu­<lb/>citur in ea vel in ſubiecto eius vel nihil. </s>
              <s xml:id="N27C24" xml:space="preserve">ſi ſecunduꝫ <lb/>ſequitur /  ipſa non intēditur vel efficitur perfectiꝰ / <lb/>ut conſtat. </s>
              <s xml:id="N27C2B" xml:space="preserve">Si primū: vel illud eſt eiuſdem ſpeciei cū <lb/>forma vel nõ ſi eſt eiuſdeꝫ ſpeciei: iã ſequitur /  duo <lb/>accidentia eiuſdē ſpeciei eſſent ī eodem ſubiecto / qḋ <lb/>eſt contra phm̄ quinto methaphiſices et contra te-<lb/>nentes hanc poſitionem. </s>
              <s xml:id="N27C36" xml:space="preserve">Item iam tunc fieret ꝑ ad­<lb/>ditionem et non per maiorem radicationē / qḋ eſt cõ­<lb/>tra opinantes. </s>
              <s xml:id="N27C3D" xml:space="preserve">Si eſt alterius ſpeciei: iaꝫ ſequitur / <lb/> illa forma ꝑꝑ ꝓductionē illiꝰ nõ efficitur ꝑfectior <lb/>nec intenſior. </s>
              <s xml:id="N27C44" xml:space="preserve">Probat̄̄ ſequela / q2 alias pari ratio­<lb/>ne diceretur /  propṫ ꝓductionē albedinis in lacte <lb/>dulcedo efficiret̄̄ ꝑfectior et intenſior: qḋ nemo com­<lb/>pos mētis diceret. </s>
              <s xml:id="N27C4D" xml:space="preserve">Relinq̇tur ergo /  forma nõ intē­<lb/>ditur ꝑ maiorem radicationem in ſubiecto.</s>
            </p>
            <note position="right" xml:id="N27C52" xml:space="preserve">Dicitur.</note>
            <p xml:id="N27C56">
              <s xml:id="N27C57" xml:space="preserve">¶ Dices et bñ ſecundū hanc opinionē q̄ eſt beati tho­<lb/>me concedendo illatum: et negando falſitatem ↄ̨ñtꝪ <lb/>et ad pūctū ꝓbationis: dices intenſionē fieri ꝑ ꝓdu­<lb/>ctionē alicuius alterius tertii alterius ſpeciei a for­<lb/>ma. </s>
              <s xml:id="N27C62" xml:space="preserve">et cum ꝓbat̄̄ /  non q2 tunc pari ratione dulce-<lb/>do in lacte intenderet̄̄ ꝑ productionem albedinis: <lb/></s>
              <s xml:id="N27C68" xml:space="preserve">Negatur illud. </s>
              <s xml:id="N27C6B" xml:space="preserve">Non em̄ eſt ſimile: q2 per ꝓductio-<lb/>nem albedinis dulcedo nõ habet ꝑfectius eſſe ꝙ̄ an­<lb/>tea. </s>
              <s xml:id="N27C72" xml:space="preserve">Quando vero forma intenditur ipſa continuo <lb/>habet perfectius et ꝑfectius eē. </s>
              <s xml:id="N27C77" xml:space="preserve">Quod quidē eſſe nõ <lb/>eſt pars eius: nec eiuſdē ſpeciei cum illa. </s>
              <s xml:id="N27C7C" xml:space="preserve">ſed ei acci-<lb/>dit ymaginatur em̄ hec opinio quãlibet formã et qḋ­<lb/>libet cõpoſitum, habere eē et eēntiam. </s>
              <s xml:id="N27C83" xml:space="preserve">Et quamuis <lb/>vna forma nõ poteſt eſſe ꝑfectior altera eiuſdē ſpe-<lb/>ciei eēntialiter: tñ efficitur ꝑfectior accidētaliter et <lb/>intenſior per acq̇ſitionē ꝑfectioris et perfectioris eē</s>
            </p>
            <p xml:id="N27C8C">
              <s xml:id="N27C8D" xml:space="preserve">Sed contra / quia illud eſſe forme acci­<lb/>dentalis eſt accñs. </s>
              <s xml:id="N27C92" xml:space="preserve">et cõtinuo per te efficit̄̄ illud esse ꝑ­<lb/>fectius qñ forma accidentalis intendit̄̄: ergo ſequit̄̄ / <lb/> ipſum eſſe intenditur. </s>
              <s xml:id="N27C99" xml:space="preserve">et nõ ꝑ additionē ſecundum <lb/>hanc opinionem / ergo fit per acquiſitionē ꝑfectio-<lb/>ris eſſe ipſi eſſe / qḋ eſt falſum cum ſic eēt ꝓceſſus ī in­<lb/>finitū in differentibus ſpecie cū aliqua forma inten­<lb/>ditur.               <anchor type="note" xlink:href="note-0238-05" xlink:label="note-0238-05a"/>               </s>
              <s xml:id="N27CA9" xml:space="preserve">¶ Dices et bñ concedendo maiorem: et negan-<lb/>do minorem. </s>
              <s xml:id="N27CAE" xml:space="preserve">q2 quãuis forma quando intendit̄̄ ha­<lb/>bet continuo perfectiius et ꝑfectius eſſe: non tñ aliqḋ <lb/>tale eē efficitur intenſius q2 nullū illorū manet niſi <lb/>ꝑ inſtans in tꝑe intenſionis. </s>
              <s xml:id="N27CB7" xml:space="preserve">Quare eē non intendi­<lb/>tur: ſed bene eſt illud quo forma accñtalis intēdit̄̄.</s>
            </p>
            <div xml:id="N27CBC" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0238-05a" xlink:label="note-0238-05" xml:id="N27CC0" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N27CC6">
              <s xml:id="N27CC7" xml:space="preserve">Sed contra: quia ſi forma intenditur <lb/>ꝑ continuã acquiſitionē alterius et alteriꝰ eē ꝑfectio­<lb/>ris: ſequitur /  in quãtulocū paruo tꝑe intēſiõis <lb/>infinite entitatis ꝓducunt̄̄ a forma intendēte / qḋ eſt <lb/>impoſſibile: q2 tus creata et fiuita nõ p̄t produce-<lb/>re infinita in tempore finito. </s>
              <s xml:id="N27CD4" xml:space="preserve">infinita quidē quorum <lb/>quodlibet vno ſignato ſit ꝑfectiꝰ.               <anchor type="note" xlink:href="note-0238-06" xlink:label="note-0238-06a"/>               </s>
              <s xml:id="N27CDE" xml:space="preserve">¶ Et ↄ̨firmatur / <lb/>q2 tunc ſequeret̄̄ /  forma intenſior haberet eſſe al-<lb/>terius ſpeciei ab eē forme minꝰ intenſe / qḋ eſt falſuꝫ <lb/></s>
              <s xml:id="N27CE6" xml:space="preserve">Sequela ꝓbat̄̄ /  eē albedinis intenſioris eſt perfe­<lb/>ctius eē albedinis remiſſioris (ꝑ te) / igitur eſt alteri­<lb/>us ſpeciei. </s>
              <s xml:id="N27CED" xml:space="preserve">Nec valet dicere /  ē ꝑfectiꝰ nõ tñ eēntia-<lb/>liter ſed accidentaliter q2 tūc ſequeretur /  poſſꝫ ef-<lb/>fici eē remiſſioris albedinis ita ꝑfectū ſicut eē inten­<lb/>ſioris. </s>
              <s xml:id="N27CF6" xml:space="preserve">et hoc non niſi per intenſioneꝫ: ergo ſequitur /               <pb chead="De intenſione  remiſſione formarum." file="0239" n="239"/>                ipſum eē poſſet intendi / qḋ ē contra opinionem et <lb/>paulo ante improbatū. </s>
              <s xml:id="N27D00" xml:space="preserve">Nec valꝫ iterū dicere /  vnū <lb/>eē eſt perfectius altero accidentaliter: et non p̄t eē ꝑ­<lb/>fectius. </s>
              <s xml:id="N27D07" xml:space="preserve">q2 tūc ſequeretur /  darent̄̄ aliq̈ duo eiuſdē <lb/>ſpeciei quoꝝ vnū per nullã poñam poſſet eē ita ꝑfe­<lb/>ctū accidentaliṫ ſicut reliquū et quorū neutrū poſſꝫ <lb/>eē minus perfectū accidētaliṫ ꝙ̄ ſit nec magꝪ. </s>
              <s xml:id="N27D10" xml:space="preserve">quod <lb/>eſt manifeſte falſum </s>
              <s xml:id="N27D15" xml:space="preserve">Si em̄ ſic eēt: iã illa ꝑfectio nõ <lb/>eēt ei accidentalis.               <anchor type="note" xlink:href="note-0239-01" xlink:label="note-0239-01a"/>               </s>
              <s xml:id="N27D1F" xml:space="preserve">¶ Confirmat̄̄ ſcḋo. / quia tunc ſeq̄­<lb/>retur /  dabilis eēt albedo infinite remiſſionis: ſed <lb/>ↄ̨ñs eſt falſū / igit̄̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N27D26" xml:space="preserve">Sequela ꝓba­<lb/>tur et pono /  cū albedo remittit̄̄ ad nõ gradū in in­<lb/>ſtanti terminatiuo remiſſionis conſeruet deus albe­<lb/>dinem non cõcurrendo ad ꝓductionē alicuiꝰ eiꝰ eſſe <lb/>in ipſam vel ſuum ſubiectū: </s>
              <s xml:id="N27D31" xml:space="preserve">Quo poſito iam ipſa <lb/>albedo erit infinite remiſſionis vel nullius intenſio­<lb/>nis quod idem eſt: igitur.</s>
            </p>
            <div xml:id="N27D38" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0238-06a" xlink:label="note-0238-06" xml:id="N27D3C" xml:space="preserve">Cõfir̄a°.</note>
              <note position="left" xlink:href="note-0239-01a" xlink:label="note-0239-01" xml:id="N27D42" xml:space="preserve">confir̄a <lb/>ſcḋa</note>
            </div>
            <p xml:id="N27D4A">
              <s xml:id="N27D4B" xml:space="preserve">¶ In opoſitum tamen eſt communis ſcola philoſo­<lb/>phorum.</s>
            </p>
            <p xml:id="N27D50">
              <s xml:id="N27D51" xml:space="preserve">Pro ſolutione huius queſtionis tres <lb/>erunt articuli. </s>
              <s xml:id="N27D56" xml:space="preserve">in primo ponentur notabilia ex qui-<lb/>bus patebit concluſio reſponſiua ad queſitū. </s>
              <s xml:id="N27D5B" xml:space="preserve">in ſe-<lb/>cundo diſſoluentur quedã dubia huic materie anne­<lb/>xa. </s>
              <s xml:id="N27D62" xml:space="preserve">in tertio ſoluentur rationes ante oppoſitum</s>
            </p>
            <p xml:id="N27D65">
              <s xml:id="N27D66" xml:space="preserve">Pro primi expeditione notandum eſt <lb/>quotuplex ſit forma: et quid intenſio: et quomõ ſit in­<lb/>tenſio. </s>
              <s xml:id="N27D6D" xml:space="preserve">Unde quadruplex eſt forma: intenſa tm̄ vcꝫ <lb/>extenſa tm̄: intenſa et extenſa ſimul: et nec ītenſa nec <lb/>extenſa. </s>
              <s xml:id="N27D74" xml:space="preserve">Sed tu aduerte ꝓ declaratione terminorū <lb/>huiꝰ diuiſionis et eorum que ↄ̨ñter dicētur inſequē-<lb/>tibus: triplicē eſſe opinionē de formarum intenſio­<lb/>ne: </s>
              <s xml:id="N27D7D" xml:space="preserve">Quedã eſt opinio ſcoti in ſecundo ſententiaruꝫ <lb/>               <anchor type="note" xlink:href="note-0239-02" xlink:label="note-0239-02a"/>               </s>
              <s xml:id="N27D87" xml:space="preserve">Et oīm noīaliū: que conſiſtit in hac ꝓpoſitione. </s>
              <s xml:id="N27D8A" xml:space="preserve">For­<lb/>ma intenditur per additionē gradus ad gradū: nul­<lb/>la forma eſt intenſa niſi in ea plures partes ſe pe­<lb/>netrēt vnitiue: vt cū aliquid calefit in aliqua parte <lb/>temporis priori introducit̄̄ aliqua caliditas in illḋ <lb/>quod calefit: et in parte poſteriori temporis intro-<lb/>ducitur aliqua alia que preexiſtentē penetrat et cuꝫ <lb/>ea vnitur, et vnam qualitatē intenſiorē ↄ̨ſtituit. </s>
              <s xml:id="N27D9B" xml:space="preserve">Hec <lb/>poſitio in ſequenti notabili amplius declarabitur <lb/>               <anchor type="note" xlink:href="note-0239-03" xlink:label="note-0239-03a"/>               </s>
              <s xml:id="N27DA7" xml:space="preserve">Alia eſt opinio burlei et ſuorum ſequaciū que ī hac <lb/>ꝓpoſitione conſiſtit. </s>
              <s xml:id="N27DAC" xml:space="preserve">Nulla forma habet partes ſe <lb/>penetrantes vnitiue. </s>
              <s xml:id="N27DB1" xml:space="preserve">Imo quelibet eſt indiuiſibilis <lb/>gradualiter. </s>
              <s xml:id="N27DB6" xml:space="preserve">Quapropṫ cõcedit ipſe burleus nul-<lb/>lã qualitatē eē intenſam: quãius ſubiectū cui inhe-<lb/>ret intenſum denominet. </s>
              <s xml:id="N27DBD" xml:space="preserve">Ex quo infertur /  m hãc <lb/>opinionē duo membra illius diuiſionis p̄poſite ſūt <lb/>reiicienda. </s>
              <s xml:id="N27DC4" xml:space="preserve">Nec m hanc opinionē ſunt diffinienda <lb/></s>
              <s xml:id="N27DC8" xml:space="preserve">Hanc opinionē latius tertiū notabile declarabit.</s>
            </p>
            <div xml:id="N27DCB" level="5" n="10" type="float">
              <note position="left" xlink:href="note-0239-02a" xlink:label="note-0239-02" xml:id="N27DCF" xml:space="preserve">opīo no-<lb/>minaliū.</note>
              <note position="left" xlink:href="note-0239-03a" xlink:label="note-0239-03" xml:id="N27DD7" xml:space="preserve">opinio <lb/>burlei</note>
            </div>
            <note position="left" xml:id="N27DDF" xml:space="preserve">opīo btī <lb/>thome</note>
            <p xml:id="N27DE5">
              <s xml:id="N27DE6" xml:space="preserve">Tertia eſt opinio beati thome: que in tali ꝓpoſitio­<lb/>ne conſiſtit. </s>
              <s xml:id="N27DEB" xml:space="preserve">Nulla forma intenditur ꝑ additionē ꝑ-<lb/>tis ad partē in eodem ſitu penetratiue et vnitiue: ſꝫ <lb/>dūtaxat iutenditur per maiorē radicationē in ſub­<lb/>iecto. </s>
              <s xml:id="N27DF4" xml:space="preserve">Quid aūt ſit illa radicatio. </s>
              <s xml:id="N27DF7" xml:space="preserve">quartū notabile <lb/>explicabit. </s>
              <s xml:id="N27DFC" xml:space="preserve">Et ſecundū / hanc tertiã et primã opinio-<lb/>nes diuerſi mode diffinienda eſt forma intenſa: et ēt <lb/>ipſius forme intenſio.               <anchor type="note" xlink:href="note-0239-04" xlink:label="note-0239-04a"/>               </s>
              <s xml:id="N27E08" xml:space="preserve">Secundū primaꝫ opinionem <lb/>forma intenſa eſt illa que habet plures gradus ſiue <lb/>partes eiuſdem ſpeciei cum ipſa penetratiue et vni-<lb/>tiue: quoꝝ graduū quelibet pars habet plures gra­<lb/>dus penetratiue et vnitiue. </s>
              <s xml:id="N27E13" xml:space="preserve">Gradus aūt eſt certa por­<lb/>tio ſiue pars qualitatis intenſe ex qua cū alia vni-<lb/>tiue et penetratiue ſe habentibus nata eſt conſtitui q̈­<lb/>litas intenſior. </s>
              <s xml:id="N27E1C" xml:space="preserve">Aliqñ tñ capit̄̄ gradus ꝓ ipſa tota­<lb/>li qualitate: ſicut capit̄̄ cū dicimꝰ: pono /  in ſubiec-<lb/>to pedale ſit gradus ſummus caliditatis. </s>
              <s xml:id="N27E23" xml:space="preserve">Unde la-<lb/>titudo qualitatis idem eſt / quod ipſa qualitas intē-               <cb chead="De intenſione  remiſſione formarum."/>               ſa. </s>
              <s xml:id="N27E2B" xml:space="preserve">Realis tñ diceret /  gradus eſt quoddã indiuiſi-<lb/>bile continuans partes intenſiuas qualitatis pene­<lb/>tratiue et vnitiue ſe habentes. </s>
              <s xml:id="N27E32" xml:space="preserve">Et plerū noīales et <lb/>calculatores vtunt̄̄ gradibus ſic ſūptis. </s>
              <s xml:id="N27E37" xml:space="preserve">Forte ꝓpṫ <lb/>breuiloquiū: cū dicunt: ſignet̄̄ pūctus in quo ſit gra­<lb/>dus quartus etc. </s>
              <s xml:id="N27E3E" xml:space="preserve">Et hinc apparet quid ſit non gra-<lb/>dus. </s>
              <s xml:id="N27E43" xml:space="preserve">Unde non gradus forme eſt priuatio talis for­<lb/>me hoc eſt ſubiectū priuatū tali forma. </s>
              <s xml:id="N27E48" xml:space="preserve">Supponit <lb/>em̄ non gradꝰ alicuius forme pro ſubiecto cõnotan­<lb/>do  priuetur tali forma. </s>
              <s xml:id="N27E4F" xml:space="preserve">Forma igr̄ intenſa tm̄ m <lb/>hanc opinionē eſt forma intenſa cuius quelibet ꝑs <lb/>cuilibet alteri cõtinuat̄̄ penetratiue et vnitiue.               <anchor type="note" xlink:href="note-0239-05" xlink:label="note-0239-05a"/>               </s>
              <s xml:id="N27E5B" xml:space="preserve">Nec <lb/>ex hoc ſequit̄̄ quãtitatē corporis chriſti in ſacramē­<lb/>to altaris (eſto  diſtinguat̄̄ ipſa quãtitas a re quã­<lb/>ta) eē formã intenſã tm̄. </s>
              <s xml:id="N27E64" xml:space="preserve">Quãuis eī quelib3 pars eiꝰ <lb/>quãlibet aliã penetret: nõ tñ cuilibet vnit̄̄. </s>
              <s xml:id="N27E69" xml:space="preserve">Et ſi enim <lb/>ibi m ſcotū nõ ſit diſtãtia ſituationis: eſt tamē di-<lb/>ſtantia continuationis.               <anchor type="note" xlink:href="note-0239-06" xlink:label="note-0239-06a"/>               </s>
              <s xml:id="N27E75" xml:space="preserve">Hanc diſtantiã ↄ̨tinuatio-<lb/>nis appellat ſcotus poſitionē / que eſt dnr̄a quãtita­<lb/>tis: ſine qua quãtitas non poteſt eē: in .4. ſen: diſ: 10: <lb/>9. prima.               <anchor type="note" xlink:href="note-0239-07" xlink:label="note-0239-07a"/>               </s>
              <s xml:id="N27E83" xml:space="preserve">Forma aūt extenſa tm̄ eſt forma diuiſibi-<lb/>lis non intenſa: vt forma ſubſtantialis aſini               <anchor type="note" xlink:href="note-0239-08" xlink:label="note-0239-08a"/>               </s>
              <s xml:id="N27E8D" xml:space="preserve">For-<lb/>ma vero intenſa et extenſa ſimul eſt illa q̄ habet plu­<lb/>res gradus ſiue partes eiuſdē ſpeciei cū ipſa pene-<lb/>tratiue et vnitiue: quoꝝ graduū quelibet pars ha-<lb/>bet plures gradus penetratiue et vnitiue: et non que­<lb/>libet pars illius forme cuilibet alteri vnit̄̄. </s>
              <s xml:id="N27E9A" xml:space="preserve">vt albe-<lb/>do caliditas: et vĺr oīs qualitas permanens corpo­<lb/>ralis.               <anchor type="note" xlink:href="note-0239-09" xlink:label="note-0239-09a"/>               </s>
              <s xml:id="N27EA6" xml:space="preserve">Forma aūt nõ intenſa ne extenſa eſt forma <lb/>indiuiſibilis ſimpĺr. </s>
              <s xml:id="N27EAB" xml:space="preserve">vt aīa rõalis.               <anchor type="note" xlink:href="note-0239-10" xlink:label="note-0239-10a"/>               </s>
              <s xml:id="N27EB3" xml:space="preserve">¶ Ex diffinitiõe <lb/>forme intenſe et extenſe ſimul ſequitur /  dabilis eſt <lb/>qualitas intenſa et extenſa cuius vna medietas ē ex­<lb/>tenſa tantum. </s>
              <s xml:id="N27EBC" xml:space="preserve">Probat̄̄ eſto /  in primo pedali vniꝰ <lb/>bipedalis ponatur qualitas vniformiter intenſa vt <lb/>octo et in alia medietate ponatur qualitas eiuſdeꝫ <lb/>ſpeciei que priori vniat̄̄ extenſiue: et illa ſit nulliꝰ in­<lb/>tenſionis vt poſtea ꝓbabo eē poſſibile. </s>
              <s xml:id="N27EC7" xml:space="preserve">Quo poſito <lb/>habetur veritas correlarii.               <anchor type="note" xlink:href="note-0239-11" xlink:label="note-0239-11a"/>               </s>
              <s xml:id="N27ED1" xml:space="preserve">¶ Sequitur ſecundo /  <lb/>aliq̈ q̈litas ē ītēſa et vna eiꝰ medietas ē extēſa tm̄: re­<lb/>liq̈ o ītēſa tm̄ (et loq̊r de medietatibꝰ entitatis for­<lb/>me). </s>
              <s xml:id="N27EDA" xml:space="preserve">Probatur priori caſu retento hoc addito /  tã­<lb/>ta entitas ipſius for̄e ſit in pedali non intenſo quã­<lb/>ta eſt in pedali intenſo. </s>
              <s xml:id="N27EE1" xml:space="preserve">et reducatur qualitas exñs ī <lb/>pedali intenſo ad non quãtū oībus partibus eius <lb/>ſe penetrantibus vnitiue. </s>
              <s xml:id="N27EE8" xml:space="preserve">Quo poſito ſequitur cor­<lb/>relarium. </s>
              <s xml:id="N27EED" xml:space="preserve">¶ Sed ſecundū opinionē burlei forma ex­<lb/>tenſa eodem mõ definitur ſicut apud priorē opinio­<lb/>nem: et ſiĺr forma nec intenſa nec extenſa. </s>
              <s xml:id="N27EF4" xml:space="preserve">¶ Secun-<lb/>dum vero opinionē beati thome forma intenſa tm̄ <lb/>eſt forma indiuiſibilis extenſiue nata magis et ma-<lb/>gis radicari in ſubiecto. </s>
              <s xml:id="N27EFD" xml:space="preserve">vt ſcientia tus etc: </s>
              <s xml:id="N27F00" xml:space="preserve">Forma <lb/>vero extenſa tantum eſt forma diuiſibilis extēſiue <lb/>non nata magis et magis radicari in ſubiecto. </s>
              <s xml:id="N27F07" xml:space="preserve">vt <lb/>quantitatis que a ſubiecto diſtinguitur ſecundū hãc <lb/>opinionē. </s>
              <s xml:id="N27F0E" xml:space="preserve">paternitas: filiatio. </s>
              <s xml:id="N27F11" xml:space="preserve">et ſic de reſiduis for­<lb/>mis non ſuſcipientibꝰ magis et minus. </s>
              <s xml:id="N27F16" xml:space="preserve">Forma intē-<lb/>ſa et extenſa ſimul eſt forma nata per motuꝫ magis <lb/>et magis radicari in ſubiecto habens parteꝫ extra <lb/>partē vt albedo caliditas etc. </s>
              <s xml:id="N27F1F" xml:space="preserve">Forma nec extēſa nec <lb/>intenſa ē forma ſubſtantialis indiuiſibilis. </s>
              <s xml:id="N27F24" xml:space="preserve">Eſt aūt <lb/>forma ſubſtantialis ex qua cum materia prima cõ-<lb/>ſtituit̄̄ ſubſtantia. </s>
              <s xml:id="N27F2B" xml:space="preserve">Sed forma accidētalis eſt illa ex <lb/>qua et ſuo ſubiecto nõ conſtituitur ſubſtantia ſꝫ ens <lb/>per accidens.</s>
            </p>
            <div xml:id="N27F32" level="5" n="11" type="float">
              <note position="left" xlink:href="note-0239-04a" xlink:label="note-0239-04" xml:id="N27F36" xml:space="preserve">m opīo­<lb/>nē noīali­<lb/>uꝫ q̇d for­<lb/>ma ītēſa</note>
              <note position="right" xlink:href="note-0239-05a" xlink:label="note-0239-05" xml:id="N27F42" xml:space="preserve">q̇d for̄a ī­<lb/>tēſa tãtū</note>
              <note position="right" xlink:href="note-0239-06a" xlink:label="note-0239-06" xml:id="N27F4A" xml:space="preserve">ſcotꝰ ī .4. <lb/>d. 10.9. 1.</note>
              <note position="right" xlink:href="note-0239-07a" xlink:label="note-0239-07" xml:id="N27F52" xml:space="preserve">q̇d for̄a <lb/>extēſa tm̄</note>
              <note position="right" xlink:href="note-0239-08a" xlink:label="note-0239-08" xml:id="N27F5A" xml:space="preserve">q̇d for̄a ī­<lb/>tēſa et ex­<lb/>tenſa.</note>
              <note position="right" xlink:href="note-0239-09a" xlink:label="note-0239-09" xml:id="N27F64" xml:space="preserve">q̇d for̄a <lb/>nec ītēſa <lb/>nec extē-<lb/>ſa.</note>
              <note position="right" xlink:href="note-0239-10a" xlink:label="note-0239-10" xml:id="N27F70" xml:space="preserve">1. correl</note>
              <note position="right" xlink:href="note-0239-11a" xlink:label="note-0239-11" xml:id="N27F76" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N27F7C">
              <s xml:id="N27F7D" xml:space="preserve">Notandum eſt ſecundo /  intenſio ca­<lb/>pitur dupliciter. </s>
              <s xml:id="N27F82" xml:space="preserve">Primo modo ꝓ alteratione me-<lb/>diante qua qualitas acquiritur: et ſic loquendo: in-<lb/>tenſio ē motꝰ de quo motu dictū eſt in q̄ſtiõe p̄cedēti <lb/></s>
              <s xml:id="N27F8A" xml:space="preserve"><pb chead="Quarti Tractatus" file="0240" n="240"/>               Secuudo mõ dicit̄̄ iutenſio q̈litas mediãte qua ali-<lb/>q̇d eſt intenſū. </s>
              <s xml:id="N27F93" xml:space="preserve">Et p̄t addi tertiꝰ modus quo dicit̄̄ in­<lb/>tenſio motus quo qualitas aut ſubiectū efficitur in­<lb/>tenſius.               <anchor type="note" xlink:href="note-0240-01" xlink:label="note-0240-01a"/>               </s>
              <s xml:id="N27F9F" xml:space="preserve">Hec diſtinctio eſt calculatoris capite de in­<lb/>tenſione et remiſſione. </s>
              <s xml:id="N27FA4" xml:space="preserve">De prīo aūt mēbro diſtīctio-<lb/>nis dictum eſt capite p̄cedēti: </s>
              <s xml:id="N27FA9" xml:space="preserve">Scḋm vero declara-<lb/>bit .4. caput </s>
              <s xml:id="N27FAE" xml:space="preserve">Et de tertio eſt pñs conſideratio. </s>
              <s xml:id="N27FB1" xml:space="preserve">Un-<lb/>de aduertendū eſt /  differētia eſt inter motū inten-<lb/>ſionis et motum alterationis ſiue inter intenſioneꝫ <lb/>prīo mõ: et tertio°: et ↄ̨ſiĺr diſcrimē eſt inter illoꝝ mo-<lb/>tuum velocitates. </s>
              <s xml:id="N27FBC" xml:space="preserve">Nã velocitas alterationis atten­<lb/>ditur / vt dictū eſt p̄cedēti capite penes maioris qua­<lb/>litatis acq̇ſitionē: ſiue magis denoīet ſubiectū ſiue <lb/>minꝰ: </s>
              <s xml:id="N27FC5" xml:space="preserve">Sed velocitas intenſionis tertio mõ attēdit̄̄ <lb/>penes ſucceſſiuã acquiſitioneꝫ maioris denoīatio-<lb/>nis.               <anchor type="note" xlink:href="note-0240-02" xlink:label="note-0240-02a"/>               </s>
              <s xml:id="N27FD1" xml:space="preserve">¶ Ex quo ſequit̄̄ /  iſti duo termini motꝰ altera­<lb/>tionis ſiue motus acquiſitionis q̈litatis et motꝰ in­<lb/>tenſionis tertio°: ſunt ṫmini īꝑtinētes. </s>
              <s xml:id="N27FD8" xml:space="preserve">Quod ſic ꝓ­<lb/>batur: q2 ſtat aliquod corpꝰ alterari acq̇rendo ali-<lb/>quã qualitatē: et eadē q̈litate nullo mõ intēdi. </s>
              <s xml:id="N27FDF" xml:space="preserve">vt po­<lb/>ſito  vua medietas pedalis ſit calida vt .8. ſine ad­<lb/>mixtione contrarii: et alia medietas ſit frigida vt .2 <lb/>et incipiat ſucceſſiue acq̇rere frigiditatē. </s>
              <s xml:id="N27FE8" xml:space="preserve">Tūc em̄ il-<lb/>lud pedale alterat̄̄ acquirendo frigiditatē: et medi-<lb/>ante ea nõ intendit̄̄: </s>
              <s xml:id="N27FEF" xml:space="preserve">Item poteſt aliquod ſubiectuꝫ <lb/>intendi: et nullo pacto alterari vt poſito  vniꝰ pe­<lb/>dalis vna medietas ſit alba vt .8. et alia nigra vt .8 <lb/>et rarefiat medietas nigra ſucceſſiue nullã q̈litateꝫ <lb/>acquirēdo. </s>
              <s xml:id="N27FFA" xml:space="preserve">q̇eſcēte altera medietate. </s>
              <s xml:id="N27FFD" xml:space="preserve">Quo poſito: iã <lb/>illud ſubiectū intendit̄̄. </s>
              <s xml:id="N28002" xml:space="preserve">vt poſtea patebit et tñ nullo <lb/>mõ alterat̄̄ cū nullã q̈litatem acq̇rat aut deperdat: <lb/>igit̄̄ iſti duo termini motꝰ alteratiõis ſiue acq̇ſitio-<lb/>nis qualitatis: et motꝰ intenſionis. </s>
              <s xml:id="N2800B" xml:space="preserve">tertio mõ dictus <lb/>ſunt īpertinētes.               <anchor type="note" xlink:href="note-0240-03" xlink:label="note-0240-03a"/>               </s>
              <s xml:id="N28015" xml:space="preserve">¶ Sequit̄̄ ſcḋo aliq̇d cõtinuo ſucceſ­<lb/>ſiue alterari ad caliditatē: et ip̄m cõtinuo remitti in <lb/>caliditate ſiue effici minus calidum. </s>
              <s xml:id="N2801C" xml:space="preserve">Probatur et ſi­<lb/>gno vnū pedale cuiꝰ vna medietas ſit calida vt .7. ſi­<lb/>ne admixtione coutrarii: et alia frigida vt .2. et acq̇­<lb/>rat medietas calita vt .7. mediū gradū caliditatis <lb/>ipſa quieſcente a rarefactione et ↄ̨dēſatione: medie­<lb/>tas vero frigida ſine acq̇ſitione qualitatis rarefiat <lb/>acquirendo ſemipedalē quãtitatē. </s>
              <s xml:id="N2802B" xml:space="preserve">Quo poſito ī tē­<lb/>pore illiꝰ rarefactionis et alterationis pedale illud <lb/>alterat̄̄ acq̇rēdo caliditatē: nihilominꝰ remittit̄̄ ſiue <lb/>efficit̄̄ minꝰ calidū: igr̄ ꝓpoſitū: </s>
              <s xml:id="N28034" xml:space="preserve">Mīor ꝓbat̄̄ / q2 ī prī­<lb/>cipio alteratiõis illḋ pedale ē calidū vt .2. cū dimi­<lb/>dio: in fine o erit calidū vt vnū cū ſexta vt pꝫ calcu­<lb/>lanti. </s>
              <s xml:id="N2803D" xml:space="preserve">additis his q̄ dicent̄̄ capite .4. / igr̄ mīor vera. <lb/>               <anchor type="note" xlink:href="note-0240-04" xlink:label="note-0240-04a"/>               </s>
              <s xml:id="N28047" xml:space="preserve">¶ Sequit̄̄ tertio /  ſtat aliq̇d in infinitū velociter ac­<lb/>quirere caliditatē in hora. </s>
              <s xml:id="N2804C" xml:space="preserve">et in eadē hora in infini-<lb/>tū velociter effici minꝰ calidū. </s>
              <s xml:id="N28051" xml:space="preserve">Probat̄̄ hoc correla­<lb/>riū priori caſu retēto hoc addito /  in q̈lꝫ ꝑte ꝓpor-<lb/>tionali hore diuiſe ꝓportione dupla acq̇rat̄̄ vna ꝑs <lb/>ꝓportionalis illiꝰ dimidii gradus acq̇rēdi diuiſi ꝑ <lb/>pertes ꝓportionales ꝓportione ſexq̇altera et in q̈lꝫ <lb/>tali ꝑte ꝓportiõali hore deꝑdat̄̄ vna pars ꝓportio­<lb/>nalis totiꝰ illiꝰ denoīatiõis deꝑdende ſiĺr diuiſe ꝓ-<lb/>portione ſexq̇altera. </s>
              <s xml:id="N28062" xml:space="preserve">Quo poſito ſeq̇t̄̄ correlarium / <lb/>vt pꝫ ex dictꝪ circa primã et ſcḋaꝫ ↄ̨fir̄atiões ſcḋi ar­<lb/>gumēti ſcḋi capitꝪ tertii tractatꝰ. </s>
              <s xml:id="N28069" xml:space="preserve">Et iſta correlaria <lb/>ex q̈lꝫ illaꝝ triū opīonū ſequūt̄̄ / vt pꝫ debite inq̇rēti. <lb/></s>
              <s xml:id="N2806F" xml:space="preserve">Põt aūt q̈litas m opīonē doctoris ſubtilis et no­<lb/>mīaliū et ēt ſubiectū dupliciṫ intendi ꝑ rarefactiõeꝫ / <lb/>vcꝫ aut cõdenſationē et ꝑ acq̇ſitionē g̈duū aut remiſ­<lb/>ſionē cõtrarii. </s>
              <s xml:id="N28078" xml:space="preserve">Exēplum primi / vt ſi ſit vnum pedale <lb/>cuiꝰ vna medietas ſit calida vt .4. et alia vt .8. et ↄ̨dē­<lb/>ſet̄̄ medietas remiſſior alia q̇eſcente aut ſe rarefaci­<lb/>ente aut ſe tardiꝰ cõdenſante aut rarefiat intenſior               <cb chead="Capi. primum"/>               condenſante ſe aut quieſcente remiſſiori vel tardiꝰ <lb/>ſe rarefaciente. </s>
              <s xml:id="N28086" xml:space="preserve">Tūc em̄ et q̈litas et ſubiectum inten­<lb/>dunt̄̄. </s>
              <s xml:id="N2808B" xml:space="preserve">Qñquidē difformiū intenſio penes reductio­<lb/>nē ad vniformitatē attendi habeat (vt ſuppono) </s>
              <s xml:id="N28090" xml:space="preserve">Ex­<lb/>emplū ſcḋi / vt eſto  calidū ꝑ totū vt .6. acquirat in <lb/>ſuper duos gradus caliditatis: aut calidū vt tria ī <lb/>quo ē ꝑmixtio frigiditatis ꝑdat duos gradus fri-<lb/>giditatis nõ acq̇rēdo caliditatē: aut acq̇rēdo calidi­<lb/>tatē aut tardiꝰ deperdendo caliditatem ꝙ̄ frigidi-<lb/>tatē ī ꝑte equali tūc em̄ ſubiectum illud intendit̄̄ in <lb/>caliditate: </s>
              <s xml:id="N280A1" xml:space="preserve">¶ Hinc palã eſt nõ ſꝑ intenſionē quali-<lb/>tatis aut ſubiecti fieri ex graduali q̈litatis addita­<lb/>mēto aut noue q̈litatis additione: ſed nõnū ex ra­<lb/>refactione aut condenſatione plerū o ex cõtra­<lb/>rie qualitatis remiſſione. </s>
              <s xml:id="N280AC" xml:space="preserve">¶ Naſcit̄̄ inde intēſioneꝫ <lb/>tertio mõ nõ bñ ſic / definiri intenſio ē ſucceſſiua addi­<lb/>tio gradus ad gradū poſteriore priorē vnitiue pe-<lb/>netrãte: </s>
              <s xml:id="N280B5" xml:space="preserve">Fit enim ſepius nulla additione facta: ſed <lb/>adiutorio condenſationis ꝑtis remiſſioris aut ra-<lb/>refactioris intenſioris mõ iã expoſito. </s>
              <s xml:id="N280BC" xml:space="preserve">Tunc eī ſub-<lb/>iectum ſucceſſiue magis tale denoīat̄̄ a q̈litate cõti­<lb/>nuo magis et magis eodē° intenſa. </s>
              <s xml:id="N280C3" xml:space="preserve">Hoc igr̄ tibi ſi-<lb/>gnū erit fidē faciet ītēſione 3° mõ dictã eē ſucceſſi-<lb/>uã alicuiꝰ q̈litatis maioris et maioris denoīatiõis <lb/>acq̇ſitionē. </s>
              <s xml:id="N280CC" xml:space="preserve">pꝫ igr̄ / q̇d intēſio et quõ intenſio fiat.</s>
            </p>
            <div xml:id="N280CF" level="5" n="12" type="float">
              <note position="left" xlink:href="note-0240-01a" xlink:label="note-0240-01" xml:id="N280D3" xml:space="preserve">Calcula.</note>
              <note position="left" xlink:href="note-0240-02a" xlink:label="note-0240-02" xml:id="N280D9" xml:space="preserve">1. correl.</note>
              <note position="left" xlink:href="note-0240-03a" xlink:label="note-0240-03" xml:id="N280DF" xml:space="preserve">2. correl.</note>
              <note position="left" xlink:href="note-0240-04a" xlink:label="note-0240-04" xml:id="N280E5" xml:space="preserve">.3. correl.</note>
            </div>
            <note position="right" xml:id="N280EB" xml:space="preserve">opīo bur­<lb/>lei.</note>
            <p xml:id="N280F1">
              <s xml:id="N280F2" xml:space="preserve">Notandū eſt / tertio declarãdo ſecūdã <lb/>opinionē q̄ burlei eſt in ſuo tractatu de intenſiõe et <lb/>remiſſione for̄aꝝ. </s>
              <s xml:id="N280F9" xml:space="preserve">tres eē concluſiones in q̇bꝰ totam <lb/>ſuã opinionē fūdauit. </s>
              <s xml:id="N280FE" xml:space="preserve">et ſuis rõibꝰ ſtabiliuit.</s>
            </p>
            <p xml:id="N28101">
              <s xml:id="N28102" xml:space="preserve">Prīa ↄ̨̨cluſio / ī oī motu ad formã acqui­<lb/>rit̄̄ aliq̇d noui qḋ eſt forma vel ꝑs for̄e. </s>
              <s xml:id="N28107" xml:space="preserve">Probat̄̄ / qm̄ <lb/>alias motꝰ ad formã nõ eēt ꝓprie motꝰ. </s>
              <s xml:id="N2810C" xml:space="preserve">ſubiectū em̄ <lb/>niſi aliquid acquireret aut deꝑderet nõ mutaretur: <lb/></s>
              <s xml:id="N28112" xml:space="preserve">Nõ em̄ aliter ſe haberet reſpectu forme ꝙ̄ priꝰ et ſic <lb/>nequa̄ ad formam mutaretur </s>
              <s xml:id="N28117" xml:space="preserve">Conſequens igitur <lb/>eſt ī omni motu ad formã nouū aliq̇d acquiri / quod <lb/>eſt forma aut ꝑs forme.</s>
            </p>
            <p xml:id="N2811E">
              <s xml:id="N2811F" xml:space="preserve">Scḋa ↄ̨̨cluſio / per oē3 motū ad formã <lb/>corrūpit̄̄ tota forma p̄cedēs a q̄ ē ꝑ ſe motꝰ: et acq̇rit̄̄ <lb/>vna for̄a totaliṫ noua cuiꝰ nihil p̄fuit. </s>
              <s xml:id="N28126" xml:space="preserve">Probat̄̄ / qm̄ <lb/>ſi forma adueniens maneret cum p̄cedēte: iam talis <lb/>for̄a eēt cõpoſita / quod eſt ↄ̈ auctorē ſex ṗncipiorum <lb/>diffiniētē formã iſto° </s>
              <s xml:id="N2812F" xml:space="preserve">For̄a ē cõpõni ↄ̨tīgēs ſimplici <lb/>et īuariabili eſſentia conſiſtens. </s>
              <s xml:id="N28134" xml:space="preserve">Itē motꝰ ad formã <lb/>non ſit ꝑ additionē g̈dꝰ ad g̈dū: q2 tūc ītenſio fieret <lb/>ꝑ additionē g̈dꝰ ad g̈dū puta ꝑtis poſterius ꝓducte <lb/>ad ꝑtem priꝰ ꝓductã: ſꝫ hoc ē falſum: igr̄. </s>
              <s xml:id="N2813D" xml:space="preserve">Falſitas <lb/>ↄ̨ñtis ꝓbat̄̄: q2 tūc q̈lꝫ for̄a ſbãlis diuiſibilis poſſet <lb/>ītēdi: q2 cuilꝫ p̄t fieri additio g̈dꝰ ad g̈dū penetrati-<lb/>ue et vnitiue. </s>
              <s xml:id="N28146" xml:space="preserve">Poſſunt eī due for̄e ſbãles eiuſdē ſpēi­<lb/>ſe penetrare. </s>
              <s xml:id="N2814B" xml:space="preserve">vt paſſi theologi ↄ̨cedūt cū igr̄ ſe pene­<lb/>trãt vniat eis deꝰ et tūc hēt̄̄ for̄as ſbãles eē ītēſas </s>
              <s xml:id="N28150" xml:space="preserve">Fi­<lb/>et eī /  q̄lꝫ ꝑs cuilibeꝫ quã penetret vniat̄̄. </s>
              <s xml:id="N28155" xml:space="preserve">Et hec ē ḋ <lb/>potioribꝰ rõibꝰ q̄ adduci pñt ad hãc opīonē corro-<lb/>borãdū et ad reliq̈s duas opugnãdas et firmandas <lb/></s>
              <s xml:id="N2815D" xml:space="preserve">Dicit enim / burleus neutram aliarum põnum ſuffi-<lb/>ciētē cauſã aſſignare q̈re vna forma diuiſibilis intē­<lb/>ſibilis ſit et alia nõ: quare etiã vna magis et minꝰ ſu­<lb/>uꝫ ſubiectū denoīet reliq̈ o nõ </s>
              <s xml:id="N28166" xml:space="preserve">Ip̄e vero cauſã aſſi­<lb/>gnans ḋt /  rõ for̄a aliq̈ magis et minus nata ē ſub­<lb/>iectū denoīare / q2 ipſa in ſua ſpecie habet latitudi-<lb/>nē ſpecificã: vt q2 eadē ſpēs for̄e p̄t ſaluari ī forma <lb/>magis ꝑfecta et minus perfecta. </s>
              <s xml:id="N28171" xml:space="preserve">ymagīat̄̄ em̄ /  ī q̈lꝫ <lb/>ſpē forme accidētalis nate ſubiectū denoīare magꝪ <lb/>et minꝰ reperiūt̄̄ infinita indiuidua diuerſaꝝ perfe-<lb/>ctionū nõ q̇dē ſpecificaꝝ ſꝫ īdiuidualiū ita  dantur <lb/>duo indiuidua albedinis quoꝝ vnum eſt perfectius               <pb chead="De intenſione et remiſſione formarum" file="0241" n="241"/>               altero: nec alius minus perfectum poteſt eqnari ſue <lb/>perfectioni. </s>
              <s xml:id="N28183" xml:space="preserve">Iſte vero ꝑfectiones nequa̄ excedunt <lb/>perfectioneꝫ ſpecificã, </s>
              <s xml:id="N28188" xml:space="preserve">Et q2 in formis ſubſtantiali-<lb/>bus non reperitur talis latitudo perfectionis ſpeci­<lb/>fice. </s>
              <s xml:id="N2818F" xml:space="preserve">ideo nulla talis eſt intenſibilis aut nata ſuū ſub­<lb/>iectum magis aut minꝰ denoīare. </s>
              <s xml:id="N28194" xml:space="preserve">¶ Ex quo ſequit̄̄ / <lb/> inter omnem albedinem et quãuis aliã minꝰ per­<lb/>fectam mediant infinite albedines quarum nulla ē <lb/>eque perfecta cuꝫ reliqua </s>
              <s xml:id="N2819D" xml:space="preserve">¶ Et ſi querat̄̄ / quare vna <lb/>albedo denoīet intenſius ſubiectum ꝙ̄ altera ceterꝪ <lb/>paribus. </s>
              <s xml:id="N281A4" xml:space="preserve">Dico /  hoc ideo ē quia ipſa eſt perfectior <lb/>et eſt excellentius indiuiduū in ſpecie albedinis ꝙ̄ re­<lb/>liqua et hoc non ꝑꝑ maiorē multitudinē graduū: ſꝫ <lb/>hanc perfectionē habet ex propria natura</s>
            </p>
            <p xml:id="N281AD">
              <s xml:id="N281AE" xml:space="preserve">Tertia concluſio </s>
              <s xml:id="N281B1" xml:space="preserve">Nulla forma inten-<lb/>ditur: aut remittit̄̄: ſed ſubiectū intenditur et remit-<lb/>titur m formã ita  forma eſt illud ſecundū quod <lb/>ſubiectū intenditur aut remittit̄̄. </s>
              <s xml:id="N281BA" xml:space="preserve">Probat̄̄. </s>
              <s xml:id="N281BD" xml:space="preserve">q2 cū ſub­<lb/>iectum intenditur in quolibet inſtanti habet aliam <lb/>et aliam formã cuiꝰ nihil antea fuit in ſubiecto: igit̄̄ <lb/>nulla talis forma intendit̄̄: </s>
              <s xml:id="N281C6" xml:space="preserve">Patet ↄ̨ña / q2 intenſio ē <lb/>motus et nulla talis forma mouetur cū non maneat <lb/>niſi ꝑ inſtans / igr̄ nulla talis forma intenditur: </s>
              <s xml:id="N281CD" xml:space="preserve">Te-<lb/>net ↄ̨ña a ſuperiori diſtributo ad ſuum inferius ne­<lb/>gatiue: </s>
              <s xml:id="N281D4" xml:space="preserve">Sꝫ  ſubiectū intendat̄̄ patet / quia contiuuo <lb/>manēs idē habet ꝑfectiorē et perfectiorē formã / igit̄̄ <lb/>continuo mouetur et intenditur.               <anchor type="note" xlink:href="note-0241-01" xlink:label="note-0241-01a"/>               </s>
              <s xml:id="N281E0" xml:space="preserve">¶ Ex his cõcluſioni­<lb/>bus inferunt̄̄ aliqua correlaria que idē burleꝰ cõce-<lb/>dit: </s>
              <s xml:id="N281E7" xml:space="preserve">Primū /  in tꝑe alterationis in quolibet inſtau­<lb/>ti eſt alia et alia forma totalis cuiꝰ nihil prefuit: et ta­<lb/>lis forma durat preciſe ꝑ inſtans: ̄uis poſſit dura-<lb/>re per tempus ceſſante alteratione. </s>
              <s xml:id="N281F0" xml:space="preserve">Prima pars ſe­<lb/>quit̄̄ ex ſecunda concluſione et ſecunda probat̄̄ / quia <lb/>alias nulla qualitas eēt ens permanens ſi non poſ­<lb/>ſet durare niſi ꝑ inſtans.               <anchor type="note" xlink:href="note-0241-02" xlink:label="note-0241-02a"/>               </s>
              <s xml:id="N281FE" xml:space="preserve">¶ Scḋm correlarium in in-<lb/>diuiduis eiuſdem ſpeciei qualitatis vnum eſt perfec­<lb/>tius altero eſſentialiṫ ita  dantur duo quoruꝫ vnū <lb/>ita eſt perfectius altero  nõ pñt eē eq̄ perfecta </s>
              <s xml:id="N28207" xml:space="preserve">Sed <lb/>hoc etiam concedit opinio nomīaliū </s>
              <s xml:id="N2820C" xml:space="preserve">Hec enim per-<lb/>fectio indiuidualis eſt.               <anchor type="note" xlink:href="note-0241-03" xlink:label="note-0241-03a"/>               </s>
              <s xml:id="N28216" xml:space="preserve">¶ Tertium correlarium. </s>
              <s xml:id="N28219" xml:space="preserve">Nõ <lb/>eſt poſſibile tranſire a caliditate minꝰ perfecta ad <lb/>perfectiorem in eodē ſubiecto adequate niſi tranſe­<lb/>undo ꝑ omnes qualitates medias in eadem ſpecie et <lb/>hoc naturaliter: q2 alias ſubiectum non moueretur <lb/>ſucceſſiue ad q̈litatē.               <anchor type="note" xlink:href="note-0241-04" xlink:label="note-0241-04a"/>               </s>
              <s xml:id="N2822B" xml:space="preserve">¶ Quartū correlariū. </s>
              <s xml:id="N2822E" xml:space="preserve">Unū cõ-<lb/>trarioꝝ ꝓducit ꝑ ſe reliquū tau̄ tñ terminū non vl­<lb/>timate intentū. </s>
              <s xml:id="N28235" xml:space="preserve">Probat̄̄ / q2 cū caliditas corrumpit <lb/>frigiditatē cõtinuo ē remiſſior frigiditas cuius ni-<lb/>hil antea fuit: et nõ videt̄̄ a quo ꝓducat̄̄ illa frigidi­<lb/>tas niſi a caliditate: igr̄ caliditas per ſe ꝓducit fri-<lb/>giditatē. </s>
              <s xml:id="N28240" xml:space="preserve">et ſic vnum ↄ̈riorū per ſe ꝓducit alterum.</s>
            </p>
            <div xml:id="N28243" level="5" n="13" type="float">
              <note position="left" xlink:href="note-0241-01a" xlink:label="note-0241-01" xml:id="N28247" xml:space="preserve">.1. correl.</note>
              <note position="left" xlink:href="note-0241-02a" xlink:label="note-0241-02" xml:id="N2824D" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0241-03a" xlink:label="note-0241-03" xml:id="N28253" xml:space="preserve">.3. correl.</note>
              <note position="left" xlink:href="note-0241-04a" xlink:label="note-0241-04" xml:id="N28259" xml:space="preserve">4. correl.</note>
            </div>
            <p xml:id="N2825F">
              <s xml:id="N28260" xml:space="preserve">Itē ſecūdū hanc opinionē remittere frigiditatē ē cõ­<lb/>tinuo ꝓducere minꝰ et minus perfectã frigiditatē: ſꝫ <lb/>caliditas per ſe remittit frigiditatē: g̊ ꝑ ſe producit <lb/>minus et minus perfectã frigiditatē ſucceſſiue: et per <lb/>ↄ̨ñs vnū ↄ̈rioꝝ ꝑ ſe ꝓducit reliquū. </s>
              <s xml:id="N2826B" xml:space="preserve">QꝪ vero nõ ꝓdu­<lb/>cat tan̄ terminū vltimate intētū: pꝫ / q2 vltimate in­<lb/>tendit producere ſibi ſimile.               <anchor type="note" xlink:href="note-0241-05" xlink:label="note-0241-05a"/>               </s>
              <s xml:id="N28277" xml:space="preserve">¶ Quītū correlariū q̈-<lb/>litas corrūpit̄̄ ꝑ motū ſequētē: et a nullo corrūpitur <lb/>nec ab aliquibꝰ finitis ſed ab infinitis. </s>
              <s xml:id="N2827E" xml:space="preserve">Probat̄̄ / et ſit <lb/>forma a. in aliquo īſtãti alterationis in ſubiecto et <lb/>manifeſtū ē /  īmediate pꝰ illud inſtans non erit: ſed <lb/>corrūpit̄̄ et nõ per motū p̄cedentē / vt ↄ̨ſtat nec ꝑ mo­<lb/>tū qui ē cū uullꝰ motꝰ ſit in inſtanti: igit̄̄ ꝑ motū ſeq̄n­<lb/>tē corrūpit̄̄. </s>
              <s xml:id="N2828B" xml:space="preserve">Sꝫ  a. nullo corrūpat̄̄ pꝫ ex tertio ar-<lb/>gumēto añ oppoſitū               <anchor type="note" xlink:href="note-0241-06" xlink:label="note-0241-06a"/>               </s>
              <s xml:id="N28295" xml:space="preserve">¶ Sextū correlariū </s>
              <s xml:id="N28298" xml:space="preserve">Aliqua q̈-<lb/>litas a nullo generat̄̄ īmediate nec ab aliquibus fi-<lb/>nitis: ſed ab infinitis </s>
              <s xml:id="N2829F" xml:space="preserve">Patet ex tertio argumēto.</s>
            </p>
            <div xml:id="N282A2" level="5" n="14" type="float">
              <note position="left" xlink:href="note-0241-05a" xlink:label="note-0241-05" xml:id="N282A6" xml:space="preserve">.5. correl.</note>
              <note position="left" xlink:href="note-0241-06a" xlink:label="note-0241-06" xml:id="N282AC" xml:space="preserve">6. correl.</note>
            </div>
            <p xml:id="N282B2">
              <s xml:id="N282B3" xml:space="preserve">¶ Septimū correlariū. </s>
              <s xml:id="N282B6" xml:space="preserve">Aliqua qualitas ꝓducit q̈li­               <cb chead="De intenſione et remiſſione formarum"/>               tatē ꝑfectiorē ſe eēntialiṫ et ſpecifice generatione eq̇­<lb/>uoca: et ēt corrūpit ꝑfectiorē ſe </s>
              <s xml:id="N282BE" xml:space="preserve">Patet ponēdo /  fri­<lb/>giditas remittit caliditatē. </s>
              <s xml:id="N282C3" xml:space="preserve">quo poſito auxilio pro­<lb/>bationis .4. correlarii pꝫ hoc correlarium.               <anchor type="note" xlink:href="note-0241-07" xlink:label="note-0241-07a"/>               </s>
              <s xml:id="N282CD" xml:space="preserve">¶ Octa­<lb/>uum correlariū. </s>
              <s xml:id="N282D2" xml:space="preserve">Ad qualitatē nõ eſt motus / q̇ ſit ip-<lb/>ſa qualitas (vt dicunt noīales) vel fundat̄̄ in ipſa q̈-<lb/>litate (vt dicūt reales) ſꝫ bñ ē motꝰ qui eſt ipſū ſub-<lb/>iectū vel fundat̄̄ in illo. </s>
              <s xml:id="N282DB" xml:space="preserve">Probat̄̄: q2 forma non ma-<lb/>net niſi ꝑ inſtans nec ſcḋm ſe nec m aliquid eiꝰ: igit̄̄ <lb/>ipſa forma nõ eſt motꝰ nec motꝰ in ea fundat̄̄. </s>
              <s xml:id="N282E2" xml:space="preserve">¶ Ad-<lb/>uerte tñ  et ſi g alterꝰ burleꝰ concedat vnum ↄ̈riorū <lb/>ꝑ ſe ꝓducere reliquū: illḋ tñ non ē neceſſe (meliori iu­<lb/>dicio ſꝑ excepto) </s>
              <s xml:id="N282EB" xml:space="preserve">Cū em̄ querit̄̄ a quo ꝓducit̄̄ frigi-<lb/>ditas ipſius aque in remiſſiõe frigiditatis qñ iguis <lb/>agit in aquã: dico /  ꝓducit̄̄ ab ipſa aq̄: vel ab ipſa <lb/>natura vĺi vt ſeruetur ordo nat̄̄alis ī productione q̈­<lb/>litatū. </s>
              <s xml:id="N282F6" xml:space="preserve">Nã ſu apte natura inditū eſt naturalibꝰ enti­<lb/>bus in operationibꝰ ſuis ſaltem neq̈ committere <lb/>iuxta ſnīam phī. 7. de hiſtoriis aīaliū dicētis natu-<lb/>rã nõ cõmittere ſaltū in operationibus ſuis ſed gra­<lb/>datī ꝓcedē. </s>
              <s xml:id="N28301" xml:space="preserve">Et ſi dicas /  remittere frigiditatē nõ ē <lb/>niſi ꝓducere remiſſiorē, nego illud ſed dico /  remit­<lb/>tere frigiditatē eſt corrumpere illã: ita  poſt corru­<lb/>ptionē eiꝰ īmediate introducat̄̄ ab aliquo agente ī­<lb/>ꝑfectior ſiue remiſſior frigiditas. </s>
              <s xml:id="N2830C" xml:space="preserve">¶ Adhuc tñ poſ-<lb/>ſunt aliqua correlaria inferri.               <anchor type="note" xlink:href="note-0241-08" xlink:label="note-0241-08a"/>               </s>
              <s xml:id="N28316" xml:space="preserve">¶ Quoꝝ primū eſt. </s>
              <s xml:id="N28319" xml:space="preserve">Cū <lb/>caliditas agit per totum aliquod ſubiectū: ſubito <lb/>corrūpit totã frigiditatē ſubiecti. </s>
              <s xml:id="N28320" xml:space="preserve">Hoc patet ex dic-<lb/>tis.               <anchor type="note" xlink:href="note-0241-09" xlink:label="note-0241-09a"/>               </s>
              <s xml:id="N2832A" xml:space="preserve">¶ Ex quo ſeq̇tur 2°. /  aliqñ caliditas maiorē fri-<lb/>giditatē ſiue ꝑfectiorē corrūpit ī remotū ꝙ̄ in ꝓpin-<lb/>quū </s>
              <s xml:id="N28331" xml:space="preserve">Probat̄̄ eſto  agat ī aliquod frigidū ꝑ totuꝫ / <lb/>quod ſit frigidiꝰ ī ꝑte diſtãtiori ꝙ̄ ꝓpīquiori.               <anchor type="note" xlink:href="note-0241-10" xlink:label="note-0241-10a"/>               </s>
              <s xml:id="N2833B" xml:space="preserve">¶ Se­<lb/>quit̄̄ tertio /  aliq̈ caliditas finita agens a finita ꝓ­<lb/>portiõe in quãtocū paruo tempore alterationis <lb/>infinitas frigiditates totales corrūpit. </s>
              <s xml:id="N28344" xml:space="preserve">pꝫ ex p̄dic­<lb/>tis hoc addito /  calidū agat in frigidū et nulla fi-<lb/>at reactio.               <anchor type="note" xlink:href="note-0241-11" xlink:label="note-0241-11a"/>               </s>
              <s xml:id="N28350" xml:space="preserve">¶ Sequit̄̄ .4°. /  cõtinuo ī motu alteratio­<lb/>nis dat̄̄ vltimū inſtans eē rei ꝑmanētis ymo idē in-<lb/>ſtans eſt ṗmū eē et vltimū eē. </s>
              <s xml:id="N28357" xml:space="preserve">pꝫ / q2 nulla q̈litas du­<lb/>rat niſi ꝑ inſtans in tali tp̄e.               <anchor type="note" xlink:href="note-0241-12" xlink:label="note-0241-12a"/>               </s>
              <s xml:id="N28361" xml:space="preserve">¶ Seq̇t̄̄ quīto /  aliqḋ <lb/>agens corrūpit ſuã reſiſtētiã ſubito in quaꝫ tñ agit <lb/>a finita ꝓportõe. </s>
              <s xml:id="N28368" xml:space="preserve">Qḋ mihi videt̄̄ mirabile: niſi vĺis <lb/>oīm cauſaꝝ cõcurrat efficientia. </s>
              <s xml:id="N2836D" xml:space="preserve">Probatur in caſu <lb/>tertii correlarii.               <anchor type="note" xlink:href="note-0241-13" xlink:label="note-0241-13a"/>               </s>
              <s xml:id="N28377" xml:space="preserve">¶ Sequit̄̄ ſexto /  qualitas corrū­<lb/>pit q̈litatē eiuſdē ſpeciei. </s>
              <s xml:id="N2837C" xml:space="preserve">Probat̄̄ hoc magis cali-<lb/>do agēte in minꝰ calidū: </s>
              <s xml:id="N28381" xml:space="preserve">Poſſet tñ dici /  hoc fit vel <lb/>a forma ſubſtãtiali vel a toto ↄ̨poſito vel a. cã vĺi.</s>
            </p>
            <div xml:id="N28386" level="5" n="15" type="float">
              <note position="right" xlink:href="note-0241-07a" xlink:label="note-0241-07" xml:id="N2838A" xml:space="preserve">8. correl.</note>
              <note position="right" xlink:href="note-0241-08a" xlink:label="note-0241-08" xml:id="N28390" xml:space="preserve">.1. correl.</note>
              <note position="right" xlink:href="note-0241-09a" xlink:label="note-0241-09" xml:id="N28396" xml:space="preserve">2. correl.</note>
              <note position="right" xlink:href="note-0241-10a" xlink:label="note-0241-10" xml:id="N2839C" xml:space="preserve">.3. correl.</note>
              <note position="right" xlink:href="note-0241-11a" xlink:label="note-0241-11" xml:id="N283A2" xml:space="preserve">4. correl.</note>
              <note position="right" xlink:href="note-0241-12a" xlink:label="note-0241-12" xml:id="N283A8" xml:space="preserve">.5. correl.</note>
              <note position="right" xlink:href="note-0241-13a" xlink:label="note-0241-13" xml:id="N283AE" xml:space="preserve">6. correl.</note>
            </div>
            <p xml:id="N283B4">
              <s xml:id="N283B5" xml:space="preserve">Dic vt libet               <anchor type="note" xlink:href="note-0241-14" xlink:label="note-0241-14a"/>               </s>
              <s xml:id="N283BD" xml:space="preserve">¶ Sequit̄̄ 7°. /  ſi deꝰ poneret infinitas <lb/>caliditates penetratiue in eodē ſubiecto ex his non <lb/>reſultaret vna caliditas nec reſultare poſſet ītēſi-<lb/>ue: q2 iã tūc aliqua for̄a poſſꝫ intēdi ꝑ additionē g̈-<lb/>dus ad g̈dū / qḋ hec põ negat. </s>
              <s xml:id="N283C8" xml:space="preserve">¶ Seq̇t̄̄ 8°. Burleū nõ <lb/>cõuenienṫ inſcripſiſſe tractatū ſuū ī ſcriptū de inten­<lb/>ſiõe et remiſſiõe for̄aꝝ. </s>
              <s xml:id="N283CF" xml:space="preserve">pꝫ / q2 m eū nulla ē ītēſio aut <lb/>remiſſio for̄e: cū for̄a nec ītēdat̄̄ nec remittat̄̄ ex .3. ↄ̨­<lb/>cluſiõe titulꝰ: igr̄ ille falſus m eū. </s>
              <s xml:id="N283D6" xml:space="preserve">Diceret tñ nõ eē ī­<lb/>cõuenies falſo titulo librū īſcribere. </s>
              <s xml:id="N283DB" xml:space="preserve">Nã ouidiꝰ fal-<lb/>ſo ſuū librū ſine titulo īſcripſit. </s>
              <s xml:id="N283E0" xml:space="preserve">Aliṫ titulꝰ ↄ̈riū illiꝰ <lb/>qḋ ba p̄tēdūt ſig̈t: </s>
              <s xml:id="N283E5" xml:space="preserve">Exēplū habes familiare extra <lb/>de cohabitatione clericorum et mulierum.</s>
            </p>
            <div xml:id="N283EA" level="5" n="16" type="float">
              <note position="right" xlink:href="note-0241-14a" xlink:label="note-0241-14" xml:id="N283EE" xml:space="preserve">7. correl.</note>
            </div>
            <p xml:id="N283F4">
              <s xml:id="N283F5" xml:space="preserve">Notãdū ē quarto tãgendo opinioneꝫ <lb/>beati thome /  quelꝫ forma diſtinguit̄̄ a ſuo eſſe qḋ­<lb/>quidem eē vocat̄̄ eſſe exiſtentie: </s>
              <s xml:id="N283FC" xml:space="preserve">Eſſe vero eſſentie eſt <lb/>idem cū ipſa forma. </s>
              <s xml:id="N28401" xml:space="preserve">Uñ m hãc opinioneꝫ quelibet <lb/>forma eſt nata habere infinita eē qnoruꝝ ↄ̨tinuo vnū <lb/>eſt ꝑfectius altero: et quãto forma accidentalis ha-<lb/>bet perfectius eſſe in ſubiecto tm̄ dr̄ magis radica-<lb/>ri in ſubiecto. </s>
              <s xml:id="N2840C" xml:space="preserve">Et hoc eſt / quod intēdit hec opinio di­<lb/>cere cum dicit formã intendi ꝑ maiorē radicationē               <pb chead="Quarti Tractatus" file="0242" n="242"/>               in ſubiecto </s>
              <s xml:id="N28416" xml:space="preserve">Et ſic p̄t definiri ſcḋm hanc poſitionē in­<lb/>tenſio forme,  ipſa eſt cõtinuo maior et maior radi­<lb/>catio in ſubiecto ſucceſſiua: id eſt intēſio forme ē cõ-<lb/>tinuo et ſucceſſiua acq̇ſitio ꝑfectioris et ꝑfectioris eē <lb/>in quãtulūcū eī ꝑua intenſione ſiue alteratiõe ip-<lb/>ſa forma infinita eē acquirit in ſuo cõpoſito et deꝑ­<lb/>dit. </s>
              <s xml:id="N28425" xml:space="preserve">in quolibet em̄ inſtanti īntrinſeco intenſiõis ha­<lb/>bet ꝑfectiꝰ et perfectiꝰ eē: quia hoc eſt ſuum intendi: <lb/>et nun̄ duo eē manent ſimul. </s>
              <s xml:id="N2842C" xml:space="preserve">Et eodē mõ ymaginã­<lb/>dū eſt de corruptione et generatione iſtoꝝ eē ſecūdū <lb/>hanc opinionē: ſicut de generatione et corruptione <lb/>forme in motu alterationis ſcḋm opinionē burlei.</s>
            </p>
            <note position="left" xml:id="N28435" xml:space="preserve">1. correl.</note>
            <p xml:id="N28439">
              <s xml:id="N2843A" xml:space="preserve">¶ Ex hac opinione ſequitur primo /  formã inten-<lb/>di non eſt ipſã aliquē gradū acquirere: aut effici eſ-<lb/>ſentialiter perfectiorē: ſed eſt ipſam cõtinuo habe-<lb/>re perfectius et ꝑfectiꝰ eē / qḋ eē ab eã diſtinguitur.</s>
            </p>
            <p xml:id="N28443">
              <s xml:id="N28444" xml:space="preserve">Hoc correlariū pꝫ ex diffinitione intenſionis.               <anchor type="note" xlink:href="note-0242-01" xlink:label="note-0242-01a"/>               </s>
              <s xml:id="N2844C" xml:space="preserve">¶ Se­<lb/>quitur ſcḋo /  nulla forma intenſibilis, ſucceſſiue ꝓ­<lb/>ducit̄̄: ſed ſubito: ſucceſſiue tñ intēditur. </s>
              <s xml:id="N28453" xml:space="preserve">Nõ loquor <lb/>de ſucceſſiua productione ſecundum extenſionem.</s>
            </p>
            <div xml:id="N28458" level="5" n="17" type="float">
              <note position="left" xlink:href="note-0242-01a" xlink:label="note-0242-01" xml:id="N2845C" xml:space="preserve">2. correl.</note>
            </div>
            <p xml:id="N28462">
              <s xml:id="N28463" xml:space="preserve">Patet hoc correlarium / quia ipſa non habet ꝑtes ī­<lb/>tenſionales ſecundum / quas poſſet ſucceſſiue ꝓduci. <lb/>               <anchor type="note" xlink:href="note-0242-02" xlink:label="note-0242-02a"/>               </s>
              <s xml:id="N2846F" xml:space="preserve">¶ Sequitur tertio /  ſortes ꝑ primū actū ſuum me-<lb/>ritoriū meret̄̄ totam beatitudinem quã habebit: et <lb/>per ſequētes actus meritorios ſolum meretur perfe­<lb/>ctius eſſe talis beatitudinis. </s>
              <s xml:id="N28478" xml:space="preserve">Patet hoc correlariuꝫ / <lb/>quia per ſequentes actus ſortes intendit meritum <lb/>et per conſequens continuo meretur habere beatitu­<lb/>dinē ſub perfectiori eē ſed totam eſſentiam beatitu-<lb/>dinis per primū opus meritoriū meruit.               <anchor type="note" xlink:href="note-0242-03" xlink:label="note-0242-03a"/>               </s>
              <s xml:id="N28488" xml:space="preserve">Et hoc ē  <lb/>voluit dicere Robertus holkot in ſua prīa q̄ſtione <lb/>quando dixit /  primus actꝰ meritoriꝰ eſt longe ma­<lb/>gis meritorius ꝙ̄ aliquis ſequens quãtūcū perfe­<lb/>ctus ſit: quia per nullum ſequētem homo meret̄̄ bea­<lb/>titudinem: ſed meretur eē ꝑfectius ipſius beatitudi­<lb/>nis: quod quidē eē diſtinguit̄̄ realiter ad ipſa beati­<lb/>tudine.               <anchor type="note" xlink:href="note-0242-04" xlink:label="note-0242-04a"/>               </s>
              <s xml:id="N2849E" xml:space="preserve">¶ Sequitur quarto /  cū aliquod ſubiectum <lb/>calidum ſit magis calidū per alterationem: termi-<lb/>nus a quo eſt ipſa caliditas, et terminꝰ ad quē eſt ea­<lb/>dem caliditas: ſed tñ ſub ꝑfectiori eē. </s>
              <s xml:id="N284A7" xml:space="preserve">Patet / q2 ex ſe­<lb/>cundo correlario ipſa forma non ſucceſſiue ꝓducit̄̄: <lb/>ſed continuo eadē manens mutatur ab eſſe īperfec-<lb/>ctiori ad eē perfectius.               <anchor type="note" xlink:href="note-0242-05" xlink:label="note-0242-05a"/>               </s>
              <s xml:id="N284B5" xml:space="preserve">¶ Sequit̄̄ quīto /  cū forma <lb/>īcipit intendi a non gradu ipſa incipit ſubito eſſe, <lb/>et nullum eē incipit ſubito habere ymo quocū eſſe <lb/>dato in infinitum imperfectius habuit quãuis inci­<lb/>piat habere aliqḋ eē. </s>
              <s xml:id="N284C0" xml:space="preserve">Prīa pars pꝫ ex ſecundo cor-<lb/>relario: et ſecūda ꝓbat̄̄: q2 ſi aliqḋ eē inciperet habe­<lb/>re iã non inciperet intēdi a nõ gradu: igr̄ ſi īcipit a <lb/>nõ gradu intēdi iã nullū eē incipit habere.               <anchor type="note" xlink:href="note-0242-06" xlink:label="note-0242-06a"/>               </s>
              <s xml:id="N284CE" xml:space="preserve">¶ Sequi­<lb/>tur ſexto /  ſortes nullam charitatē per actū ſequē­<lb/>tē primū meret̄̄: ſed ſolū meret̄̄ intenſionē illius q̈li­<lb/>tatis queq̇dē intēſio nõ eſt niſi habere perfectius et <lb/>perfectius eē manēte eadē charitate oīno.               <anchor type="note" xlink:href="note-0242-07" xlink:label="note-0242-07a"/>               </s>
              <s xml:id="N284DE" xml:space="preserve">¶ Sequi­<lb/>tur ſeptīo /  for̄a ſubſtãtialis nõ ītenditur. </s>
              <s xml:id="N284E3" xml:space="preserve">Hoc cor­<lb/>relariū ꝓbat ſic capreolus: q2 ſi forma aſini intēde-<lb/>ret̄̄ oportet eiꝰ eē corrūpi: ſed ad corruptionē eē ip-<lb/>ſius ſequit̄̄ corruptio aſini: et ad corruptionē ipſius <lb/>aſini: ſeq̇tur corruptio forme ipſius aſini / et ex ↄ̨ñti <lb/>ſequitur ipſam nõ acq̇rere ꝑfectiꝰ eē et per ↄ̨ñs nõ in­<lb/>tendi. </s>
              <s xml:id="N284F2" xml:space="preserve">Et hec eſt ratio / quã aſſignat reſpondeo ar­<lb/>gumentis contrarii: quare eſt /  forma ſubſtantia-<lb/>lis non intenditur: cū ſecundū eum et etiam beatum <lb/>thomam forma ſubſtantialis poſſit habere perfec­<lb/>tius eſſe ꝙ̄ hab3 eſto  materia melius diſponatur <lb/>vel vt magis loquar ad eorum intenſionem poſito / <lb/> a principio ꝓductionis forme ipſa forma fuerit <lb/>ꝓducta in materia melius diſpoſita.               <anchor type="note" xlink:href="note-0242-08" xlink:label="note-0242-08a"/>               </s>
              <s xml:id="N28508" xml:space="preserve">¶ Sed contra <lb/>hoc ſic argumētor / quia ſi hoc eſſet veruꝫ ſequeretur               <cb chead="Capi. primum"/>               animã rationalem naturaliter poſſe intendi: ſed <lb/>conſequens eſt falſum. </s>
              <s xml:id="N28512" xml:space="preserve">igitur illud ex quo ſequitur, <lb/>videlicet /  nõ repugnat forme ſubſtantiali habere <lb/>perfectius eē eſto ꝙ̄ fuiſſet producta in materia me-<lb/>lius diſpoſita. </s>
              <s xml:id="N2851B" xml:space="preserve">Sequela ꝓbatur / q2 materia ſortis <lb/>poteſt melius diſponi ſorte manente.               <anchor type="note" xlink:href="note-0242-09" xlink:label="note-0242-09a"/>               </s>
              <s xml:id="N28525" xml:space="preserve">Poteſt enim <lb/>mutari complexio ſortis fleugmatica ī perfectioreꝫ <lb/>complexionem puta ſanguineam que quidem com­<lb/>plexio eſt accidens proprium et diſpoſitio per quaꝫ <lb/>materia ſit apta ad formam ſuſcipiendam / vt dicit <lb/>beatus thomas in .4°. diſ. 44. q̄ſ. prīa ar. primo in <lb/>reſponſione ad quartum / et hoc manente ſorte vt di­<lb/>cunt medici et ſignanter conciliator differentia .22. / <lb/>igitur anima rationalis tūc perfectius eē acquiret <lb/>in illa materia magis diſpoſita / et quia illa diſpoſi­<lb/>tio ſit ſucceſſiue ſequitur /  anima rationalis ſuc-<lb/>ceſſiue habebit perfectius et perfectius eē / et per con­<lb/>ſequens intendetur / vt patet ex definitione intenſio­<lb/>nis.               <anchor type="note" xlink:href="note-0242-10" xlink:label="note-0242-10a"/>               </s>
              <s xml:id="N28547" xml:space="preserve">¶ Sed ad hoc diceret beatus thomas nõ admit­<lb/>tendo /  complexio īnata poſſit mutari in alteram <lb/>meliorē, aut peioreꝫ vt multi medicorum tenent nec <lb/>aliqua complexio mutata mutat eſſe / et ſic ceſſat ar­<lb/>gumentum. </s>
              <s xml:id="N28552" xml:space="preserve">Nihilominus ſupernaturaliter loquen­<lb/>do pono tale correlarium. </s>
              <s xml:id="N28557" xml:space="preserve">ſecundum hanc viam id <lb/>eſt / quod mihi videtur ſequi ex hac poſitione forma <lb/>ſubſtantialis poteſt intendi. </s>
              <s xml:id="N2855E" xml:space="preserve">Probatur / quia ipſa <lb/>poteſt habere ꝑfectius et perfectius eē ſucceſſiue: igi­<lb/>tur poteſt intendi </s>
              <s xml:id="N28565" xml:space="preserve">Patet conſequentia ex diffinitio­<lb/>ne intenſionis. </s>
              <s xml:id="N2856A" xml:space="preserve">probatur antecedens et pono /  deꝰ <lb/>cõſeruet formã brunelli in materia ipſius brunelli: <lb/>et diſponat continuo materiam ipſius brunelli ma­<lb/>gis et magis. </s>
              <s xml:id="N28573" xml:space="preserve">Quo poſito forma brunelli acquiret <lb/>continuo perfectius et perfectius eē: igitur intendet̄̄ <lb/></s>
              <s xml:id="N28579" xml:space="preserve">Nec hoc ſolum ſequitur ad hanc poſitionē btī tho-<lb/>me: ſed etiam ad põnem noīalium. </s>
              <s xml:id="N2857E" xml:space="preserve">Unde ſecundum <lb/>illam poſitionē pono talē concluſioneꝫ.               <anchor type="note" xlink:href="note-0242-11" xlink:label="note-0242-11a"/>               </s>
              <s xml:id="N28588" xml:space="preserve">Forma ſub­<lb/>iſtantialis corporea poteſt intendi. </s>
              <s xml:id="N2858D" xml:space="preserve">Probat̄̄ / q2 po-<lb/>teſt habere plures gradus ſiue partes eiuſdem ſpe­<lb/>ciei cum ipſa penetratiue et vnitiue quorū graduum <lb/>quelibet pars habet plures gradus penetratiue et <lb/>vnitiue: igitur poteſt eſſe intenſa et intendi. </s>
              <s xml:id="N28598" xml:space="preserve">Patet <lb/>ↄ̨ña ex diffinitione: et probatur añs et capio vnã for­<lb/>mã aſini pedalem / et volo /  in prīa ꝑte ꝓportionali <lb/>hore future vna medietas eius penetret alteram: et <lb/>vniatur ei m penetrationē, rarefiat tamen ſic  cõ­<lb/>tinuo maneat pedalis: et in ſecunda parte ꝓportio­<lb/>nali iterū vna medietas illiꝰ forme penetret alterã <lb/>et vniat̄̄ ei m penetrationē / et ī tertia ꝑte iterū vna <lb/>medietas penetret alteram: et ſic in īfinitū: et mane-<lb/>at ſic ī īſtãti terminatiuo pedalis q̈litatis. </s>
              <s xml:id="N285AD" xml:space="preserve">Quo po­<lb/>ſito ſequitur /  illa forma aſini hꝫ plures gradus ſi­<lb/>ue partes eiuſdē ſpecie cum ipſa penetratiue et vni-<lb/>tiue etc. / igr̄ ꝓpoſitū. </s>
              <s xml:id="N285B6" xml:space="preserve">Et hec breuiter ſufficiãt ꝓ decla­<lb/>ratione opīonis btī thome.               <anchor type="note" xlink:href="note-0242-12" xlink:label="note-0242-12a"/>               </s>
              <s xml:id="N285C0" xml:space="preserve">Recurras ad plura in <lb/>hac opinione vidēda ad ſcḋam ſcḋe queſ. 24. et ad <lb/>primū ſen: diſtinc. 17. / et videas ibidē capreolū q̇ſtio-<lb/>ne ſcḋa </s>
              <s xml:id="N285C9" xml:space="preserve">¶ Expeditis notabilibus et ex ↄ̨ñti prima ꝑ­<lb/>te q̄ſtionis: reſtūt ad dubia deſcendamus.</s>
            </p>
            <div xml:id="N285CE" level="5" n="18" type="float">
              <note position="left" xlink:href="note-0242-02a" xlink:label="note-0242-02" xml:id="N285D2" xml:space="preserve">.3. correl.</note>
              <note position="left" xlink:href="note-0242-03a" xlink:label="note-0242-03" xml:id="N285D8" xml:space="preserve">Robertꝰ <lb/>holkot.</note>
              <note position="left" xlink:href="note-0242-04a" xlink:label="note-0242-04" xml:id="N285E0" xml:space="preserve">4. correl.</note>
              <note position="left" xlink:href="note-0242-05a" xlink:label="note-0242-05" xml:id="N285E6" xml:space="preserve">5. correl.</note>
              <note position="left" xlink:href="note-0242-06a" xlink:label="note-0242-06" xml:id="N285EC" xml:space="preserve">6. correl.</note>
              <note position="left" xlink:href="note-0242-07a" xlink:label="note-0242-07" xml:id="N285F2" xml:space="preserve">7. correl.</note>
              <note position="left" xlink:href="note-0242-08a" xlink:label="note-0242-08" xml:id="N285F8" xml:space="preserve">obicit̄̄ ca. <lb/>preolo.</note>
              <note position="right" xlink:href="note-0242-09a" xlink:label="note-0242-09" xml:id="N28600" xml:space="preserve">tho. 4. d. <lb/>44. q. ṗ.</note>
              <note position="right" xlink:href="note-0242-10a" xlink:label="note-0242-10" xml:id="N28608" xml:space="preserve">ſoluit̄̄ ob­<lb/>iectio</note>
              <note position="right" xlink:href="note-0242-11a" xlink:label="note-0242-11" xml:id="N28610" xml:space="preserve">for̄a ſub­<lb/>ſtãtiaĺ p̄t <lb/>intendi</note>
              <note position="right" xlink:href="note-0242-12a" xlink:label="note-0242-12" xml:id="N2861A" xml:space="preserve">tho. 2.2. <lb/>capreolꝰ</note>
            </div>
            <p xml:id="N28622">
              <s xml:id="N28623" xml:space="preserve">¶ Dubitat̄̄ prīo. </s>
              <s xml:id="N28626" xml:space="preserve">Utrū cuiuſlibet forme q̄ ſucceſſiue <lb/>acq̇rit̄̄ dat̄̄ primū inſtans ſui eſſe. </s>
              <s xml:id="N2862B" xml:space="preserve">¶ Dubitat̄̄ ſecūdo <lb/></s>
              <s xml:id="N2862F" xml:space="preserve">Utrū id quod ſucceſſiue calefit vel aliq̈ qualitate q̈­<lb/>lificat̄̄: ſucceſſiue incipit calefieri aut eē tale, vel põt <lb/>incipere eē tale. </s>
              <s xml:id="N28636" xml:space="preserve">¶ Dubitat̄̄ tertio. </s>
              <s xml:id="N28639" xml:space="preserve">Utrū aliq̈ res na­<lb/>turalis p̄t naturalr̄ p̄ciſe ꝑ inſtans durare. </s>
              <s xml:id="N2863E" xml:space="preserve">¶ Dubi­<lb/>tat̄̄ q̈rto. </s>
              <s xml:id="N28643" xml:space="preserve">Utrū ꝓbabile ſit creatura nullo mõ poſſe <lb/>agere in inſtanti. </s>
              <s xml:id="N28648" xml:space="preserve">¶ Dubitat̄̄ quīto. </s>
              <s xml:id="N2864B" xml:space="preserve">Utrū deꝰ p̄t ꝓdu­<lb/>cere vnum angelū īmediate poſt aliū: et quot īmedi­<lb/>ate poteſt producere.</s>
            </p>
            <p xml:id="N28652">
              <s xml:id="N28653" xml:space="preserve">Ad primum dubium arguitur /  non               <pb chead="De intenſione et remiſſione formarum" file="0243" n="243"/>               et pono /  albedo a. poſſibilis acquirat̄̄ illa hora fu­<lb/>tura iſto mõ, ita  prīa pars ꝓportionalis acqui-<lb/>ratur in prima parte proportionali hore: et in ſe­<lb/>cunda acquiratur ſecūda et in tertia acq̇rat̄̄ tertia: <lb/>et ſic ↄ̨ñter: taliter tñ  dū acquirat̄̄ ſcḋa ſucceſſiue <lb/>corrūpat̄̄ adequate prīa et dū acq̇ritur tertia corrū­<lb/>pat̄̄ ſecunda et nihil eiꝰ denuo acquiratur. </s>
              <s xml:id="N28667" xml:space="preserve">Quo po­<lb/>ſito ſic argumētor a. albedo ſucceſſiue acquiritur: et <lb/>tamen eius non dat̄̄ primū inſtans ſui eē: igir̄ pars <lb/>dnbii affirmatiua falſa: </s>
              <s xml:id="N28670" xml:space="preserve">Maior ꝓbat̄̄: q2 q̄lib3 ꝑs. <lb/>ꝓportiõalis illiꝰ albedinis acquirit̄̄ ſueceſſiue: igit̄̄ <lb/>illa albedo producitur ſucceſſiue. </s>
              <s xml:id="N28677" xml:space="preserve">Et mīor patet: q2 <lb/>non habet primū inſtans ſui eē in fine hore: nec an-<lb/>te finem cum in nullo inſtanti habebit ſuas ꝑtes ſi­<lb/>mul: igitur nõ datur primū inſtans ſui eſſe.               <anchor type="note" xlink:href="note-0243-01" xlink:label="note-0243-01a"/>               </s>
              <s xml:id="N28685" xml:space="preserve">¶ Dicit <lb/>vnus /  in tali caſu a. albedo erit et tñ non ꝓducetur <lb/></s>
              <s xml:id="N2868B" xml:space="preserve">Et ad h°  aliquid ſucceſſiue productū habeat pri-<lb/>mū inſtans ſui eē: oportet  illud ſit in aliquo īſtã-<lb/>ti: vel aliquando erit.</s>
            </p>
            <div xml:id="N28692" level="5" n="19" type="float">
              <note position="left" xlink:href="note-0243-01a" xlink:label="note-0243-01" xml:id="N28696" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2869C">
              <s xml:id="N2869D" xml:space="preserve">Sed contra / quia bene ſequit̄̄ hec albe­<lb/>do producetur: ergo hec albedo que eſt vel erit ꝓdu­<lb/>cetur: et ex hoc ſequitur /  hec albedo eſt vel erit </s>
              <s xml:id="N286A4" xml:space="preserve">Pa­<lb/>tet ↄ̨ña / a ꝓportõe de termino ampliato ad propoſi­<lb/>tionem explicãtē ſenſū ampliatiõis. </s>
              <s xml:id="N286AB" xml:space="preserve">¶ Ideo dices <lb/>aliter et bene ad hoc argumētuꝫ petri de mãtua nõ <lb/>admittendo caſum q2 caſus īplicat. </s>
              <s xml:id="N286B2" xml:space="preserve">Ex eo em̄ ſequi­<lb/>tur /  illa albedo nun̄ erit cum nun habebit oēs <lb/>ſuas partes ſimul: et ſequitur /  erit: quia ponitur / <lb/> illa albedo ita producatur in hora futura ꝙ̄ pri­<lb/>ma pars proportionalis eius producatur in pri-<lb/>ma parte ꝓportionali hore etc. </s>
              <s xml:id="N286BF" xml:space="preserve">Cū em̄ dicit̄̄ /  hu-<lb/>ius albedinis prima pars ꝓportionalis ꝓducetur ly <lb/>albedinis ſupponit pro illo quod eſt vel erit.</s>
            </p>
            <p xml:id="N286C6">
              <s xml:id="N286C7" xml:space="preserve">Sed ↄ̨̨tra pono /  illa albedo ſit pꝰ de­<lb/>cē annos et in hora futura partes eius eo mõ ꝓducan­<lb/>tur et corrūpant̄̄ ſicut in priori caſu. </s>
              <s xml:id="N286CE" xml:space="preserve">Tunc illa albe-<lb/>do ꝓducetur in hora futura: cum quelibet pars eius <lb/>proportionalis producet̄̄, et tamē huius productiõis <lb/>nõ habebit primū inſtans ſui eſſe cum nec in fine hu-<lb/>uis hore, nec ante / vt ꝓbatum eſt: igr̄ ꝓpoſitum. </s>
              <s xml:id="N286D9" xml:space="preserve">Nec v3 <lb/>dicere /  nichil põt ꝓduci quin habeat qñ oēs ſuas <lb/>partes ſimul: q2 tempus et ſonus et vox (m noīales) <lb/>ꝓducūtur et tamen nun̄ habent omnes ſuas ꝑtes <lb/>ſimul nec poſſunt.</s>
            </p>
            <p xml:id="N286E4">
              <s xml:id="N286E5" xml:space="preserve">Secundo ad idem arguit̄̄ ſic pono /  <lb/>ſortes incipiat alterari a non gradu in hora futura: <lb/>ita  in prima parte ꝓportionali acq̇rat .2. gradꝰ al-<lb/>bedinis et in ſcḋa vnum, et in tertia dimidiuꝫ et ſic ſine <lb/>fine: et non maneat ſortes in inſtanti terminatiuo ho­<lb/>re: ſed maneat eius albedo. </s>
              <s xml:id="N286F2" xml:space="preserve">Quo poſito illa albedo <lb/>ſucceſſiue acquirit̄̄: et erit vt .4. et tñ non dat̄̄ primuꝫ <lb/>inſtans ſui eē: igr̄. </s>
              <s xml:id="N286F9" xml:space="preserve">Maior eſt nota / q2 nõ erit mino-<lb/>ris intenſionis: et minor probat̄̄ / q2 illa albedo erit <lb/>añ finē illiꝰ hore: igr̄ non dat̄̄ primū inſtans ſui eſſe <lb/></s>
              <s xml:id="N28701" xml:space="preserve">Conſequētia pꝫ: q2 ſi daret̄̄ maxīe eēt inſtãs ṫmīa-<lb/>tiuū illiꝰ hore. </s>
              <s xml:id="N28706" xml:space="preserve">Añs tñ ꝓbat̄̄: q2 illa albedo erit acq̇-<lb/>ſita añ finē illiꝰ hore: ergo erit añ finē huiꝰ hore. </s>
              <s xml:id="N2870B" xml:space="preserve">Au-<lb/>tecedēs pꝫ / q2 illa albedo acquiret̄̄ ante finē illiꝰ ho­<lb/>re. </s>
              <s xml:id="N28712" xml:space="preserve">Conſequentia pꝫ a reſolubili ad ſuã reſoluenteꝫ <lb/>               <anchor type="note" xlink:href="note-0243-02" xlink:label="note-0243-02a"/>               </s>
              <s xml:id="N2871C" xml:space="preserve">¶ Dices et bñ negando /  illa albedo erit añ finem <lb/>illius hore et negãdo /  erit acq̇ſita ante finē illius <lb/>hore: et ad ꝓbationē negãdo ↄ̨ñam: et cū ꝓbat̄̄ nega­<lb/>tur /  illa ſit ſua reſoluens: ſꝫ ē iſta: illa albedo erit <lb/>acquiſitio añ finē illius hore. </s>
              <s xml:id="N28727" xml:space="preserve">Alio mõ diſtinguitur <lb/>iſta propõ illa albedo erit acquiſita ante finem il-<lb/>lius hore aut capiēdo ly acq̇ſita noīaliṫ vt tm̄ v3 ſi-<lb/>cut acq̇ſitio ſiue qḋ acq̇rit̄̄: et ſic coucedit̄̄ illa propõ,               <cb chead="De intenſione et remiſſione formarum"/>               aut capiēdo ꝑticipialiter p̄teritiue, et ſic negat̄̄. </s>
              <s xml:id="N28733" xml:space="preserve">Ad <lb/>hoc em̄  aliq̇d ſit lta acq̇ſitū: req̇rit̄̄ /  ipſum ſit vĺ <lb/>fuerit in aliquo īſtãti, loquēdo de re permanenti.</s>
            </p>
            <div xml:id="N2873A" level="5" n="20" type="float">
              <note position="left" xlink:href="note-0243-02a" xlink:label="note-0243-02" xml:id="N2873E" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N28744">
              <s xml:id="N28745" xml:space="preserve">Sed contra / quia quelibet pars ꝓpor­<lb/>tionalis eiꝰ añ finem illiꝰ hore erit acq̇ſita: et qñ vna <lb/>fuerit acq̇ſita altera nõ corrūpit̄̄: g̊ illa albedo ante <lb/>finē illiꝰ hore erit acq̇ſita. </s>
              <s xml:id="N2874E" xml:space="preserve">Coña ꝓbat̄̄: q2 bñ ſequit̄̄ / <lb/>quelibet ꝑs erit ꝓportionals huiꝰ albedinis añ finē <lb/>huius hore erit acq̇ſita. </s>
              <s xml:id="N28755" xml:space="preserve">(ſaltē m certã diuiſionē) / g̊ <lb/>oēs ꝑtes ꝓportionales huiꝰ albedīs añ finē huiꝰ ho­<lb/>re erūt ꝓducta. </s>
              <s xml:id="N2875C" xml:space="preserve">Patet prīa ↄ̨ña a ſimili: q2 bñ ſeq̇t̄̄ <lb/>oīs homo currit: ergo omnes homines currunt: et <lb/>ſic vĺr a ſingulari ad ſuum plurale.               <anchor type="note" xlink:href="note-0243-03" xlink:label="note-0243-03a"/>               </s>
              <s xml:id="N28768" xml:space="preserve">¶ Et cõfirmatur / <lb/>q2 bene ſequit̄̄ hec albedo ante finem huius hore ꝓ­<lb/>ducetur: ergo hec albedo que eſt vel erit ante finem <lb/>huius hore aliquando producetur: et per conſeq̄ns <lb/>hec albedo eſt vel erit ante finem huius hore: et ſic eq̄ <lb/>cito ſicut ꝓducetur erit producta. </s>
              <s xml:id="N28775" xml:space="preserve">et ex hoc ſequitur / <lb/> non dabitur inſtans in quo primo erit.               <anchor type="note" xlink:href="note-0243-04" xlink:label="note-0243-04a"/>               </s>
              <s xml:id="N2877F" xml:space="preserve">¶ Dices et <lb/>bene diſtinguendo hanc ꝓpoſitionem hec albedo <lb/>ante finem huius hore producet̄̄: quia vel illa deter­<lb/>minatio ante finem huius hore determinat ſubie-<lb/>ctum, aut copulam, aut predicatum. </s>
              <s xml:id="N2878A" xml:space="preserve">Si determinat <lb/>ſubiectū aut copulaꝫ negatur: </s>
              <s xml:id="N2878F" xml:space="preserve">Si vero determiuat <lb/>predicatum conceditur. </s>
              <s xml:id="N28794" xml:space="preserve">Nec tunc ly albedo ſuppo­<lb/>nit pro eo quod eſt vel erit ante finē huius hore: ſed <lb/>bene pro eo quod producetur ante finē huius hore. <lb/></s>
              <s xml:id="N2879C" xml:space="preserve">Determinatio em̄ p̄dicati nullo modo reſtrīgit co-<lb/>pulam aut ſubiectum: licet determinatio copule re­<lb/>ſtringat et ſubiectū et predicatum </s>
              <s xml:id="N287A3" xml:space="preserve">Pari forma diſtī­<lb/>guas conſequens et conſequentiam</s>
            </p>
            <div xml:id="N287A8" level="5" n="21" type="float">
              <note position="right" xlink:href="note-0243-03a" xlink:label="note-0243-03" xml:id="N287AC" xml:space="preserve">cõfir̄atio</note>
              <note position="right" xlink:href="note-0243-04a" xlink:label="note-0243-04" xml:id="N287B2" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N287B8">
              <s xml:id="N287B9" xml:space="preserve">Sed contra / quia hec albedo producit̄̄ <lb/>in iſta hora. </s>
              <s xml:id="N287BE" xml:space="preserve">ergo ꝓducetur ante finem huiꝰ hore vel <lb/>in fine vel poſt finē: ſed nõ poſt finē nec in fine: igitur <lb/>hoc albedo ante finē huius hore ꝓducetur (vt illa de­<lb/>termīatio ſꝑ determinat copulã) / et ꝑ ↄ̨ñs hec albe-<lb/>do eſt vel erit ante finem huius hore / quod fuit ꝓbã­<lb/>dū. </s>
              <s xml:id="N287CB" xml:space="preserve">Patet ↄ̨ña vltima: q2 ſꝑ determinatio reſtrin-<lb/>gens copulã reſtringit vtrū extremum / vt patet ex <lb/>dialectis.               <anchor type="note" xlink:href="note-0243-05" xlink:label="note-0243-05a"/>               </s>
              <s xml:id="N287D7" xml:space="preserve">¶ Cõfirmatur ſecundo: q2 tota illa albe­<lb/>do erit acquiſita alicui ſubiecto: et nõ niſi ſorti et nõ <lb/>in inſtanti termīatiuo hore: cū tūc ſortes nõ erit. </s>
              <s xml:id="N287DE" xml:space="preserve">igi­<lb/>tur ante inſtans terminatiuū hore erit tota illa al-<lb/>bedo acquiſita ſorti: et ꝑ ↄ̨ñs añ illḋ īſtans ipſa erit <lb/></s>
              <s xml:id="N287E6" xml:space="preserve">Nec v3 dicere /  illa acquiritur materie ſortis ma-<lb/>nenti in inſtanti terminatiuo: q2 volo /  ſiĺr mate-<lb/>ria non maneat: ſed maneat preciſe albedo illa: tūc <lb/>illa albedo nõ erit alicui acquiſita ante inſtans ter­<lb/>minatiuū hore: et erit acquiſita alicui: igitur alicui <lb/>erit acquiſita ante inſtans terminatiuuꝫ hore. </s>
              <s xml:id="N287F3" xml:space="preserve">Nec <lb/>valet dicere /  in tali caſu illa albedo nulli erit acq̇­<lb/>ſita: q2 volo /  ſortes actione īmanēte ꝓducat in ſe <lb/>talem qualitatē cū ceteris ꝑticulis caſus: tunc illa <lb/>qualitas a nullo ꝓducet̄̄ niſi a ſorte et a nullo erit ꝓ­<lb/>ducta ꝙ̄ a ſorte: igit̄̄ talis qualitas erit acq̇ſita ſor­<lb/>ti. </s>
              <s xml:id="N28802" xml:space="preserve">Nec valet iterū dicere /  illa qualitas erit ꝓduc­<lb/>ta prīo in inſtanti terminatiuo a ſorte qui tunc non <lb/>eſt: q2 tunc aliquid primo eēt ꝓductū: et tamē nõ ha­<lb/>beret ꝓ tunc cauſam ſue ꝓductionis: quod videtur <lb/>abſurdum.               <anchor type="note" xlink:href="note-0243-06" xlink:label="note-0243-06a"/>               </s>
              <s xml:id="N28812" xml:space="preserve">¶ Confirmatur tertio et pono /  corrum­<lb/>patur tota illa albedo que ſic fuit ꝓducta in inſtan­<lb/>ti terminatiuo illius hore. </s>
              <s xml:id="N28819" xml:space="preserve">Quo poſito arguit̄̄ ſic / ī <lb/>illo inſtanti deſinet eē adequate aliqua albedo to­<lb/>talis ipſius ſortis ꝑ remotionē de pñti: et nõ niſi .4. <lb/>graduū: igr̄ talis albedo aliqñ erit: et nõ niſi añ in­<lb/>ſtãs termīatiuū illiꝰ hore / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N28824" xml:space="preserve">Mīor tã ꝓ-<lb/>bat̄̄ / q2 totalis albedo ꝓducta in ſorte nõ eſt intēſior               <pb chead="Quarti tractatus." file="0244" n="244"/>               4. gradibꝰ, nec minus intēſa / vt patet aſpiciēti: igr̄ <lb/>eſt adequate .4. graduum.</s>
            </p>
            <div xml:id="N28830" level="5" n="22" type="float">
              <note position="right" xlink:href="note-0243-05a" xlink:label="note-0243-05" xml:id="N28834" xml:space="preserve">Cõfir̄a°. <lb/>ſcḋa</note>
              <note position="right" xlink:href="note-0243-06a" xlink:label="note-0243-06" xml:id="N2883C" xml:space="preserve">3. ↄ̨firma.</note>
            </div>
            <p xml:id="N28842">
              <s xml:id="N28843" xml:space="preserve">Tertio principaliter arguitur ſic. </s>
              <s xml:id="N28846" xml:space="preserve">Si <lb/>pars affirmatiua dubii eſſet a ſeq̄retur /  ſortes <lb/>et plato ab eadē ꝓportione et eq̄ velociter cõtinuo <lb/>alterarent̄̄ ꝑ idē tp̄s: et tñ nõ equalē qualitatē acq̇-<lb/>rerēt: ſꝫ ↄ̨ñs eſt impoſſibile igit̄̄. </s>
              <s xml:id="N28851" xml:space="preserve">Seq̄la ꝓbat̄̄ et po-<lb/>no vt ſupra /  ſortes et plato incipiãt alterari a nõ <lb/>gradu ab equali ꝓportione: et eque velociter et con­<lb/>tinuo in iſta hora eq̄ velociter alterētur eandē qua­<lb/>litatē acq̇rēdo: et maneat plato in inſtãti termiuati­<lb/>uo ſortes o nõ. </s>
              <s xml:id="N2885E" xml:space="preserve">Quo poſito argr̄ ſic / in īſtãti termi­<lb/>natiuo aliquã determinatã qualitatē habebit pla­<lb/>to: et tantã nõ habebit ſortes tūc: nec ante: et alterã­<lb/>tur ꝑ idē tēpus ab equali ꝓportiõe. </s>
              <s xml:id="N28867" xml:space="preserve">igitur ꝓpoſitū <lb/>               <anchor type="note" xlink:href="note-0244-01" xlink:label="note-0244-01a"/>               </s>
              <s xml:id="N28871" xml:space="preserve">¶ Dices et bene negãdo mīorē / vcꝫ  ſortes et plato <lb/>per idē tēpus adequate ab equali ꝓportiõe alterã-<lb/>tur: q2 plato alterabitur ꝑ horã ſortes vero nõ: q2 <lb/>ſortes nõ manebit ꝑ horã. </s>
              <s xml:id="N2887A" xml:space="preserve">Nõ em̄ manebit in inſtã­<lb/>ti terminatiuo hore. </s>
              <s xml:id="N2887F" xml:space="preserve">nec v3 iſta ↄ̨ña ſortes et plato cõ­<lb/>tinuo in eodē tēpore adequate alterãtur ab eadē ꝓ-<lb/>portiõe: igr̄ ille ꝓportiões in illo tꝑe adequate ī ſor­<lb/>tē et in platonē equalē effectū oīno ꝓducūt. </s>
              <s xml:id="N28888" xml:space="preserve">¶ Sed <lb/>contra / q2 in inſtãti terminatiuo hore erit verū dice­<lb/>re de totali qualitate manēte in cadauere ſortis  <lb/>illã ꝓduxit ſortes / ē ꝑ ↄ̨ñs erit verū dicere /  illa <lb/>fuit.               <anchor type="note" xlink:href="note-0244-02" xlink:label="note-0244-02a"/>               </s>
              <s xml:id="N28898" xml:space="preserve">¶ Dices et bñ cõcedēdo añs et negãdo ↄ̨ñaꝫ. </s>
              <s xml:id="N2889B" xml:space="preserve">In <lb/>illo iſtãti em̄ verū eſt dicere /  illã albedinē ſortes <lb/>ꝓduxit: ſed ſortes nõ ꝓduxit illã albedinē / q2 illa nõ <lb/>erit ante illud inſtans. </s>
              <s xml:id="N288A4" xml:space="preserve">¶ Sꝫ contra / q2 ſi ſolutio eēt <lb/>bona ſequeret̄̄ /  in caſu ſortes habebit maiꝰ meri­<lb/>tum ꝙ̄ habebit plato: et tñ nõ magis p̄miabit̄̄ īmo <lb/>equaliter p̄miarētur / ↄ̨ñs eſt falſum: et cõtra ꝓpõnē <lb/>theologã. inequaliter merētes ineq̈liter p̄miabunt̄̄ / <lb/>igit̄̄ et illḋ ex quo ſeq̇tur. </s>
              <s xml:id="N288B1" xml:space="preserve">Seq̄la ꝓbat̄̄ et pono /  ſor­<lb/>tes et plato incipiãt mereri a nõ gradu cõtinuo vni-<lb/>formiter in hora ſequēti: ita  ſi vter illoꝝ mane­<lb/>ret in inſtanti termīatiuo hore vter haberet meri­<lb/>tum vt .4. decedat tñ ſortes ꝑ remotionē de pñti in <lb/>gr̄a pĺone manēte q̇ decedat ꝑ põnem de pñti. </s>
              <s xml:id="N288BE" xml:space="preserve">Quo <lb/>poſito arguit̄̄ ſic / in tali caſu ſortes p̄miabit̄̄: et nõ <lb/>maiori p̄mio ꝙ̄ plato nec minori: igit̄̄ p̄miabit̄̄ eq̈li <lb/>p̄mio. </s>
              <s xml:id="N288C7" xml:space="preserve">et tñ nun̄ habebit tãtum meritū: igitur. </s>
              <s xml:id="N288CA" xml:space="preserve">QꝪ <lb/>nõ premiabit̄̄ maiori p̄mio notū eſt: ſed  nõ mīori <lb/>premio totali p̄miabit̄̄: argr̄ ſic: ſignetur illud tota­<lb/>le premiū: et ſit a: et arguo /  nõ: q2 plato p̄miabit̄̄ <lb/>premio vt .4. et ſortes habebit quodlibet meritum <lb/>citra .4. / ergo habebit premiū vt .4. / et ꝑ ↄ̨ñs ſortes <lb/>et plato equali premio p̄miãtur et nõ minori ſortes <lb/>̄ plato. </s>
              <s xml:id="N288DB" xml:space="preserve">Coña tenet / q2 ſi hꝫ qḋlibet meritū citra .4. <lb/>ipſe habebit quodlibet p̄miū citra .4. et ſi hꝫ quod-<lb/>libet p̄miū citra .4. iã hꝫ p̄miū vt .4. cū nemo p̄t ha-<lb/>bere quãlibet ̄titatē citra quãtitatē quadrupeda-<lb/>lē quī habeat quãtitatē quadrupedalē: igit̄̄ de prīo <lb/>ad vltimū ſi ſortes hꝫ qḋlibet meritū citra .4. ſorteſ <lb/>hēbit p̄miū vt .4. / quod fuit ꝓbandū.               <anchor type="note" xlink:href="note-0244-03" xlink:label="note-0244-03a"/>               </s>
              <s xml:id="N288EF" xml:space="preserve">¶ Dices forte <lb/>admiſſo caſu negãdo añs / q2 ad hoc  ſortes vĺ pĺo <lb/>dicat̄̄ habere meritū vt .4. ſatis eſt  aīa eius ali-<lb/>quãdo habeat illud. </s>
              <s xml:id="N288F8" xml:space="preserve">Mõ in caſu et ſi ſortes nõ ma-<lb/>neat in inſtãti terminatiuo tamē aīa eiꝰ manet qḋ <lb/>ſufficit. </s>
              <s xml:id="N288FF" xml:space="preserve">¶ Sed cõtra / q2 volo /  ſimul deſinat eē aīa <lb/>cum ſorte in poſterū tamē re producēda: et ſcḋ3 ̄ti­<lb/>tatē meritorū p̄miēda. </s>
              <s xml:id="N28906" xml:space="preserve">Quo poſito ſeq̇t̄̄ intētū igit̄̄</s>
            </p>
            <div xml:id="N28909" level="5" n="23" type="float">
              <note position="left" xlink:href="note-0244-01a" xlink:label="note-0244-01" xml:id="N2890D" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0244-02a" xlink:label="note-0244-02" xml:id="N28913" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0244-03a" xlink:label="note-0244-03" xml:id="N28919" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2891F">
              <s xml:id="N28920" xml:space="preserve">In oppoſitū tamē eſt philoſophus ſex­<lb/>to phiſicoꝝ ponēs talē ↄ̨cluſionē. </s>
              <s xml:id="N28925" xml:space="preserve">in quo res primo <lb/>eſt athomū et īpartibile eē neceſſe eſt. </s>
              <s xml:id="N2892A" xml:space="preserve">Innuēs ꝙ̄ oīs <lb/>res ꝑmanēs hꝫ vel habuit primū inſtans ſui eē ante <lb/>quod nõ fuit. </s>
              <s xml:id="N28931" xml:space="preserve">Et intelligit de re generabili.</s>
            </p>
            <cb chead="Capitulum ſecundum."/>
            <p xml:id="N28936">
              <s xml:id="N28937" xml:space="preserve">Pro deciſione huius dubitationis no­<lb/>tandū eſt primo ſuppoſita diſtīctione inſtantiū de­<lb/>clarata circa materiã de incipit et deſinit  duplex <lb/>eſt primum inſtans eē alicuiꝰ forme vcꝫ primū īſtãs <lb/>cõpletū et primū inſtãs nõ cõpletū. </s>
              <s xml:id="N28942" xml:space="preserve">Primū inſtans <lb/>alicuiꝰ forme cõpletū eſt inſtans ī quo res primo eſt <lb/>añ qḋ nichil eiuſdē forme p̄fuit. </s>
              <s xml:id="N28949" xml:space="preserve">Et iſto modo īcipit <lb/>eē per primū eſſe aīa rõnalis et oē qḋ indiuiſibiliter <lb/>in inſtanti ꝓducit̄̄. </s>
              <s xml:id="N28950" xml:space="preserve">Sed primū inſtãs eē alicuius for­<lb/>me incõpletū eſt in quo illa forma primo eſt et tamē <lb/>aliquid eiꝰ prefuit. </s>
              <s xml:id="N28957" xml:space="preserve">Et iſto mõ forma q̄ ſucceſſiue ac-<lb/>quiritur hꝫ primū inſtans ſui eſſe incõpletū. </s>
              <s xml:id="N2895C" xml:space="preserve">Eodeꝫ <lb/>modo poteſt fieri diſtīctio de primo inſtãti non eſſe <lb/>et de vltimo eē et de vltimo non eſſe.               <anchor type="note" xlink:href="note-0244-04" xlink:label="note-0244-04a"/>               </s>
              <s xml:id="N28968" xml:space="preserve">Et hanc diſtin­<lb/>ctionē ponit Gregorius de arimīo .q. 3. d. 17. primi <lb/>ſen. ſubiūgens aliã diſtīctionē de formis: q2 quedã <lb/>ſunt que ꝓducūtur indiuiſibiliter vt aīa rõnalis et <lb/>minimū naturale: alie partim ſucceſſiue et partim ī­<lb/>stantanee: ſicut forma aſini cuiꝰ datur minimū natu-<lb/>rale / qḋ ſubito ꝓducit̄̄ et poſt ꝓductionē illius vna <lb/>pars reſidue forme ſucceſſiue gñatur: quedã o ſuc­<lb/>ceſſiue tãtum de quibus iã exēplificatū eſt. </s>
              <s xml:id="N2897B" xml:space="preserve">¶ Quibꝰ <lb/>intellectis aduertendū eſt  de hac dubitatiõe due <lb/>ſūt opiniones famate.               <anchor type="note" xlink:href="note-0244-05" xlink:label="note-0244-05a"/>               </s>
              <s xml:id="N28987" xml:space="preserve">Prīa eſt gregorii arimenē <lb/>loco preallegato: et cõiter eã inſequunt pḣi paripa­<lb/>thetici que põ tan̄ in baſi et fundamento in vnica <lb/>cõſiſtit ꝓpõne que talis eſt. </s>
              <s xml:id="N28990" xml:space="preserve">Oīs res ꝑmanēs natu-<lb/>raliter ꝓducta habet vel habuit ṗmū inſtãs ſui eē <lb/>añ qḋ nec ī tꝑe nec in inſtãti fuit. </s>
              <s xml:id="N28997" xml:space="preserve">¶ Ex q̊ infert̄̄  oīs <lb/>res ſucceſſiue ꝓducta prius ꝓducebat quã ſit vĺ fue­<lb/>rit ꝓducta: ita  ſi aliqua albedo acquirat̄̄ ſucceſſi­<lb/>ue per horã futurã adequate cõcedēdū eſt  talis <lb/>albedo ꝓducet̄̄ ante finē hore future: ſꝫ nõ erit ꝓdu-<lb/>cta ante finē hore future: ſꝫ erit ꝓducta in inſtãti ter­<lb/>minatiuo talis hore in quo primo erit. </s>
              <s xml:id="N289A6" xml:space="preserve">¶ Ex quo in­<lb/>fert bec opinio /  ſi totū qḋ in iſta hora ꝓducebat̄̄ <lb/>de albedine in iſtãti termīatiuo hore corrūperet̄̄ et <lb/>nun̄ vlterius reproducat̄̄ tunc nõ eſt dabilis albe­<lb/>do adequate ꝓducta in illa hora. </s>
              <s xml:id="N289B1" xml:space="preserve">Et in vniuerſū ad <lb/>hoc  aliquid quod ponit̄̄ ſucceſſiue ꝓduci ſit: opꝰ <lb/>eſt tale manere in īſtãti termīatiuo ſue ꝓductionis <lb/></s>
              <s xml:id="N289B9" xml:space="preserve">Alias nullo pacto cõcedēdum eſt ipſum produci.</s>
            </p>
            <div xml:id="N289BC" level="5" n="24" type="float">
              <note position="right" xlink:href="note-0244-04a" xlink:label="note-0244-04" xml:id="N289C0" xml:space="preserve">Gregoriꝰ <lb/>in primo <lb/>ſen.</note>
              <note position="right" xlink:href="note-0244-05a" xlink:label="note-0244-05" xml:id="N289CA" xml:space="preserve">Opinio <lb/>gregorii</note>
            </div>
            <note position="right" xml:id="N289D2" xml:space="preserve">opīo mã­<lb/>tuanti.</note>
            <p xml:id="N289D8">
              <s xml:id="N289D9" xml:space="preserve">¶ Alia eſt opinio. </s>
              <s xml:id="N289DC" xml:space="preserve">Petri de mantua quã poſuit in <lb/>ſuo tractatu de inſtãti capite 2° et cõſiſtit pūctualiṫ <lb/>in hac ꝓpõe. </s>
              <s xml:id="N289E3" xml:space="preserve">Oīs res ſucceſſiue ꝓducta prius fuit ī <lb/>tp̄e inadequate ꝙ̄ in aliquo inſtãti. </s>
              <s xml:id="N289E8" xml:space="preserve">¶ Ex quo infert / <lb/> oīs res ſucceſſiue ꝓducta nõ citiꝰ ꝓducetur ꝙ̄ erit <lb/>ꝓducta. </s>
              <s xml:id="N289EF" xml:space="preserve">¶ Ex quo infert vlterius / ꝙ̄ oīs res ſucceſſi-<lb/>ue ꝓducenda dūmõ ſit ꝑmanēs habebit primū in-<lb/>ſtans ſui eſſe añ quod in nullo inſtanti erit: ̄uis añ <lb/>illud erit in tēpore. </s>
              <s xml:id="N289F8" xml:space="preserve">Et ꝑ hoc differt a prima opinio­<lb/>ne: et cõuenit ſiĺr cū illa. </s>
              <s xml:id="N289FD" xml:space="preserve">Cõuenit quidē: q2 dicit talē <lb/>rem habere primū inſtãs ſui eē in quo eſt velerit (nõ <lb/>facio differētiã in pñti p̄terito aut futuro. </s>
              <s xml:id="N28A04" xml:space="preserve">In hoc eī <lb/>nõ ſtat difficultas) et añ illud iſtãs in nullo inſtan­<lb/>ti fuit. </s>
              <s xml:id="N28A0B" xml:space="preserve">Sꝫ differt a prima / q2 prima dicit /  nec ante <lb/>illud inſtãs fuit in tꝑe nec in inſtãti. </s>
              <s xml:id="N28A10" xml:space="preserve">Hec vero mãtua­<lb/>ni dicit ꝓ ante illud fuit in tꝑe: et tamē in nullo īſtã­<lb/>ti. </s>
              <s xml:id="N28A17" xml:space="preserve">¶ Ex quo ſequitur tertio /  oīs res ſucceſſiue ꝓ-<lb/>ducenda erit in aliquo tēpore aña ꝙ̄ ſit in aliquo ī­<lb/>ſtanti: et ſic prius erit in tēpore ꝙ̄ in inſtanti: et dicit / <lb/>hoc non eſſe incõueniēs de illo qḋ erit in tēpore in­<lb/>diuiſibiliter. </s>
              <s xml:id="N28A22" xml:space="preserve">¶ Ex quo infert .4. /  aliqua res ante <lb/>primū inſtans ſui eſſe erit in aliquo tēpore: et tamē <lb/>illa ꝑ nullū tēpus erit ante primū inſtans ſui eſſe <lb/></s>
              <s xml:id="N28A2A" xml:space="preserve">Patet prima pars ex correlario p̄cedēti: et ſecūda <lb/>probatur / q2 ad hoc  aliquid ſit ꝑ aliquod tempꝰ <lb/>requirit̄̄  ſit in quolibet inſtanti illius ſaltē intrī­<lb/>ſeco. </s>
              <s xml:id="N28A33" xml:space="preserve">¶ Ex hac põe ſequitur quīto /  hec albedo erit               <pb chead="De intenſione  remiſſione formarum." file="0245" n="245"/>               et tamē in nullo inſtãti erit. </s>
              <s xml:id="N28A3B" xml:space="preserve">Probat̄̄ et pono /  albe­<lb/>do vt .4. in iſta hora adequate ꝓducat̄̄ ſucceſſiue: et <lb/>corrūpat̄̄ in inſtãti termīatiuo hore / et deſinat eſſe ꝑ <lb/>primū nõ eſſe. </s>
              <s xml:id="N28A44" xml:space="preserve">Quo poſito patet correlariū. </s>
              <s xml:id="N28A47" xml:space="preserve">¶ Seq̇­<lb/>tur ſexto /  hec albedo iã nõ eſt et aliquãdo erit: et tñ <lb/>hec albedo: nec incipiet eē nec in tēpore nec in inſtã­<lb/>ti. </s>
              <s xml:id="N28A50" xml:space="preserve">pꝫ ex caſu ſuꝑioris correlarii in nullo eī inſtan-<lb/>ti incipit eē in tēpore vel inſtãti / vt pꝫ intuēti. </s>
              <s xml:id="N28A55" xml:space="preserve">¶ Seq̇­<lb/>tur ſeptimo /  licet nulla res ſucceſſiue ꝓducēda in-<lb/>cipit vel incipiet eſſe: q̄libet tñ res ſucceſſiue ꝓducē-<lb/>da ꝑmanēs in inſtãti termīatiuo ſue ꝓductiõis inci­<lb/>pit vel incipiet eē in inſtãti. </s>
              <s xml:id="N28A60" xml:space="preserve">Prima pars pꝫ / q2 ante <lb/>quodlibet inſtãs in quo verū eſt dicere hec qualitas <lb/>ſucceſſiue ꝓducta eſt: fuit ī tēpore p̄cedēti in quo ſuc­<lb/>ceſſiue ꝓducebat̄̄: igit̄̄ talis res nõ incipit vel īcipiet <lb/>eſſe. </s>
              <s xml:id="N28A6B" xml:space="preserve">Secūda pars ꝓbat̄̄ / q2 in inſtanti termīatiuo <lb/>ſue ꝓductiõis talis res incipit eſſe in inſtãti: q2 licet <lb/>antea fuerit in tēpore ī nullo tñ īſtãti profuit: igit̄̄ <lb/></s>
              <s xml:id="N28A73" xml:space="preserve">¶ Sequit̄̄ octauo ſortē ꝑ totã vnã horã eē in gr̄a: et <lb/>et tamē in eadē hora eē in pctõ. </s>
              <s xml:id="N28A78" xml:space="preserve">Probat̄̄ et pono /  <lb/>deus p̄cipiat ſorti exñti in gr̄a /  nun̄ diligat pla­<lb/>tonē gradu dilectionis vt .4. cõcedat tñ ei  abſ <lb/>peccato poſſit eū diligere quolibet gradu citra .4. <lb/></s>
              <s xml:id="N28A82" xml:space="preserve">Quo poſito īcipiat ſortes intēdere dilectionē pla-<lb/>tonis ꝑ iſtã horã ita  ſi maneret ī inſtãti termina-<lb/>tiuo haberet prīo ī illo dilectionē vt .4. ſꝫ tã nec ip̄e <lb/>ſortes nec ſua aīa illã habeãt in inſtãti terminatīo <lb/></s>
              <s xml:id="N28A8C" xml:space="preserve">Quibꝰ poſitis: argr̄ ſic / ſortes ꝑ totã illã horã erit <lb/>in gr̄a et in eadē hora erit in pctõ: igitur correlariū <lb/>verū. </s>
              <s xml:id="N28A93" xml:space="preserve">Maior ꝓbat̄̄ / q2 in quolibet inſtãti intrinſeco <lb/>illius hore ſortes erit in gr̄a cū in nullo illoꝝ com-<lb/>mittat aut omittat </s>
              <s xml:id="N28A9A" xml:space="preserve">(In nullo enim inſtanti intrin-<lb/>ſeco diligit pĺonē dilectõe vt .4.) / igit̄̄ ſortes ꝑ totaꝫ <lb/>illã horã erit in gr̄a. </s>
              <s xml:id="N28AA1" xml:space="preserve">Sꝫ minor ꝓbat̄̄ / q2 in illa hora <lb/>.4. gradus dilectiõis erūt a ſorte producti ꝑ opīonē <lb/>et cū primū fuerūt ꝓducti ſortes erit ī pctõ: igit̄̄ ſor-<lb/>tes in illa hora erit in pctõ. </s>
              <s xml:id="N28AAA" xml:space="preserve">Et ſic pꝫ correlarium.</s>
            </p>
            <p xml:id="N28AAD">
              <s xml:id="N28AAE" xml:space="preserve">¶ Sequit̄̄ .9. /  ſortes dãpnabit̄̄: et tamē ꝑ totã vitã <lb/>ſuã fuit in gr̄a. </s>
              <s xml:id="N28AB3" xml:space="preserve">pꝫ in caſu ſuꝑioris corelarii. </s>
              <s xml:id="N28AB6" xml:space="preserve">Sor-<lb/>tes dãpnabit̄̄ cum fuerit in peccato / vt pꝫ ex dictis. <lb/></s>
              <s xml:id="N28ABC" xml:space="preserve">¶ Hec oīa cõcedēda ſunt tã̄ correlaria huiꝰ põnis <lb/></s>
              <s xml:id="N28AC0" xml:space="preserve">Nec ea videri debēt abſurda: quãdoquidē ea omīa <lb/>aduerſa opinio cogitur cõcedere. </s>
              <s xml:id="N28AC5" xml:space="preserve">Diuidat̄̄ em̄ vnū <lb/>pedale vniformiṫ in hora futura ita  in īſtanti ter­<lb/>minatiuo prīo totū erit diuiſū et ſit linea terminãs <lb/>illud pedale ī extremo poſterius diuidēdo a. </s>
              <s xml:id="N28ACE" xml:space="preserve">Quo <lb/>poſito a. linea ī iſta hora adeq̈te erit diuiſo et tamē <lb/>per nullū tp̄s nec in aliquo inſtãti erit diuiſio a. li-<lb/>nea </s>
              <s xml:id="N28AD7" xml:space="preserve">Itē a linea mõ nõ diuidit̄̄ et aliqñ diuidet̄̄ et tñ <lb/>nec īcipit nec īcipiet diuidi. </s>
              <s xml:id="N28ADC" xml:space="preserve">Itē a. linea ꝑ totam illã <lb/>horã eſt integra q2 in quolibet inſtãti intrinſeco il­<lb/>lius: et tamē in eadē hora diuidet̄̄ et erit diuiſio. </s>
              <s xml:id="N28AE3" xml:space="preserve">Et <lb/>ſi dicas /  in illo caſu a. linea ñ ꝑ totã illã horã eſt ī­<lb/>tegra: q2 nõ eſt ītegra in īſtãti termīatiuo eiꝰ. </s>
              <s xml:id="N28AEA" xml:space="preserve">Mo-<lb/>do ſecūdū aliam põnem ad hoc  aliq̇d ſit aliqua-<lb/>le ꝑ aliqḋ tēpus: requirit̄̄ /  ſit tale ī quolibet inſtã­<lb/>ti illius tēporis: et intrīſeco et extrīſeco. </s>
              <s xml:id="N28AF3" xml:space="preserve">Ponat̄̄ tūc / <lb/> in īſtanti termīatiuo reproducat̄̄ ſubito illud pe­<lb/>dale cum oībꝰ ſuis lineis / quo poſito a. linea erit in­<lb/>tegra ī quolibet īſtanti illius hore et intrīſeco et ex-<lb/>trinſeco / vt pꝫ dicet tñ opinãs /  in tali caſu nõ diui­<lb/>detur linea. </s>
              <s xml:id="N28B00" xml:space="preserve">Ideo ponatur /  deꝰ precipiat ſorti  <lb/>diligat eū in aliquo inſtãti intrīſeco huiꝰ hore fu-<lb/>ture et ſit ſortes ī gr̄a et nichil cõmittat ꝑ horã futu­<lb/>ram: ſed omittat diligere deū et decedat ī inſtãti ter­<lb/>minatiuo ꝑ primū nõ eē. </s>
              <s xml:id="N28B0B" xml:space="preserve">Quo poſito ſortes erit in <lb/>iſta hora futura adequate in pctõ: et tamē ꝑ nullum <lb/>tēpus nec in aliquo inſtãti. </s>
              <s xml:id="N28B12" xml:space="preserve">Sortes nūc nõ eſt ī pctõ: <lb/>et aliquãdo erit in pctõ: et tñ nec incipit nec īcipiet eē               <cb chead="De intenſione  remiſſione formarum."/>               in pctõ. </s>
              <s xml:id="N28B1A" xml:space="preserve">Sortes per totã vitam ſuã erit in gr̄a et fine <lb/>peccato ſaltē in quolibet īſtanti intrīſeco ſue vite: et <lb/>tamē ſortes dãpuabit̄̄. </s>
              <s xml:id="N28B21" xml:space="preserve">¶ Hinc igr̄ cõſtat ea oīa / que <lb/>hec opīo puta mãtuani ↄ̨cedit tan̄ ſequētia ſuam <lb/>opīonem: oportet opinionē aduerſaꝫ itidem cõcede­<lb/>re: et ea nec abſurda eē: nec pḣie diſſona.</s>
            </p>
            <p xml:id="N28B2A">
              <s xml:id="N28B2B" xml:space="preserve">His notatis ponūtur due cõcluſiões <lb/>pro prīa opīone. </s>
              <s xml:id="N28B30" xml:space="preserve">¶ Prīa ↄ̨cluſio </s>
              <s xml:id="N28B33" xml:space="preserve">Cuiuſlibet rei que <lb/>ſucceſſiue ꝓducit̄̄ datur primū inſtãs ſui eē in q̊ ip̄a <lb/>primo erit: et ante qḋ ip̄a nullo pacto erit: tamē cu-<lb/>iuſlibet illius / quod erit in illo īſtãti aliquid erit añ <lb/>idem inſtãs. </s>
              <s xml:id="N28B3E" xml:space="preserve">Prima pars ꝓbat̄̄ argumēto in op-<lb/>poſituꝫ: et ꝑ ea q̄ dicta ſunt declarãdo hanc opinio­<lb/>nē. </s>
              <s xml:id="N28B45" xml:space="preserve">Sed ſcḋa pars ꝓbat̄̄ / q2 cuiuſlibet illius qḋ erit <lb/>in illo inſtãti aliq̈ pars erit añ idem inſtans: q2 qḋ­<lb/>libet illiꝰ ꝓducit̄̄ ſucceſſiue: et nõ in illo inſtanti: nec <lb/>poſt igr̄ añ illud inſtans: et per ↄ̨ñs cuiuſlibet eius ali­<lb/>quid erit añ illud īſtans. </s>
              <s xml:id="N28B50" xml:space="preserve">Iteꝫ dato oppoſito ſeq̄re­<lb/>tur /  aliquid eius ſubito ꝓduceret̄̄ in inſtãti termi-<lb/>natiuo: et ſic totū nõ ſucceſſiue produceret̄̄. </s>
              <s xml:id="N28B57" xml:space="preserve">¶ Secun­<lb/>da cõcluſio. </s>
              <s xml:id="N28B5C" xml:space="preserve">Quelibet res ſucceſſiue corrūpēda ha-<lb/>bebit primū inſtãs nõ eē in quo primo nõ erit ſecun­<lb/>dum ſe et qḋlibet eius: et añ qḋ ip̄a erit ſcḋm ſe vĺ ali­<lb/>quid eiꝰ et habebit ſiue habet vltimū eē ī quo vcꝫ ip̄a <lb/>eſt tota: et poſt quod nun̄ erit ſcḋm ſe totã. </s>
              <s xml:id="N28B67" xml:space="preserve">Hec cõ­<lb/>cluſio ꝓbat̄̄ eo modo quo prima</s>
            </p>
            <p xml:id="N28B6C">
              <s xml:id="N28B6D" xml:space="preserve">Sed pro ſecūda opinione ponitur ta-<lb/>lis concluſio. </s>
              <s xml:id="N28B72" xml:space="preserve">Oīs res ſucceſſiue ꝓducenda erit eq̄ <lb/>cito ſicut ꝓducetur: nec habebit ṗmū inſtãs ſui eſſe <lb/>ante quod nullo modo erit: ſꝫ bñ habebit primum <lb/>(ſaltem haberi p̄t) añ qḋ in nullo inſtãti erit. </s>
              <s xml:id="N28B7B" xml:space="preserve">Et oīs <lb/>res ſucceſſiue corrūpenda nõ hꝫ vltimū inſtãs ſui eē <lb/>poſt quod nullo mõ erit: ſꝫ bñ habet vltimū inſtans <lb/>ſui eē poſt quod in nullo inſtãti erit. </s>
              <s xml:id="N28B84" xml:space="preserve">Probat̄̄ prīa <lb/>pars ↄ̨cluſiõis / q2 aliqua res eque cito erit produ-<lb/>cta ſicut ꝓducet̄̄ q̄ ꝓducet̄̄ ſucceſſiue: et nõ eſt maior <lb/>ratio de vna ꝙ̄ de alia: igr̄ quelibet ſucceſſiue ꝓdu-<lb/>cenda eque cito erit ꝓducta ſicut ꝓducet̄̄. </s>
              <s xml:id="N28B8F" xml:space="preserve">Minor eſt <lb/>nota: et maior ꝓbatur de ſono aut voce ꝓducenda <lb/></s>
              <s xml:id="N28B95" xml:space="preserve">Uox em̄ ꝓducēda eq̄ cito erit ſic ꝓducet̄̄. </s>
              <s xml:id="N28B98" xml:space="preserve">iteꝫ ſicut de­<lb/>us poteſt creare vnū angelū in īſtanti pñti et vnum <lb/>īmediate poſt inſtãs quod eſt pñs: ita põt ꝓducere <lb/>vnū īmediate añ inſtãs / quod eſt pñs: et corrumpere <lb/>eū in inſtãti qḋ eſt pñs: ita  in inſtanti / quod ē pñs <lb/>non ſit: et tūc ille angelus ꝓductꝰ immediate añ in-<lb/>ſtans qḋ eſt pñs erit eq̄ cito ſicut ꝓducet̄̄ etc. / igit̄̄ illḋ <lb/>non eſt incõueniēs. </s>
              <s xml:id="N28BA9" xml:space="preserve">Añs tñ pꝫ / q2 non videt̄̄ maior rõ / <lb/> deus põt vnū et nõ reliquū. </s>
              <s xml:id="N28BAE" xml:space="preserve">Eodē modo ꝓbabis <lb/>ſecūdam partem. </s>
              <s xml:id="N28BB3" xml:space="preserve">Item oīa q̄ ſequūtur ex iſta põne <lb/>debēt cõcedi ab aduerſario: et incõueniētia que cõ-<lb/>cedit aduerſariꝰ iſta põ minime admittit: igit̄̄ iſta <lb/>opīo ꝓbabilior eſt et vera. </s>
              <s xml:id="N28BBC" xml:space="preserve">Añs patuit ex his / q̄ di-<lb/>cta ſunt declarãdo iſtam põnem</s>
            </p>
            <p xml:id="N28BC1">
              <s xml:id="N28BC2" xml:space="preserve">Ad rõnes ante oppoſitū. </s>
              <s xml:id="N28BC5" xml:space="preserve">Ad primam <lb/>dictum eſt ibi vſ ad vltimaꝫ replicã: ad quã reſpõ­<lb/>deo diſtinguēdo /  aliquid põt ꝓduci qḋ nun̄ ha-<lb/>bebit oēs ſuas partes ſimul: aut aliqḋ ſucceſſiuum <lb/>et ſic ego cõcedo: aut ꝑmanēs et ſic ego nego. </s>
              <s xml:id="N28BD0" xml:space="preserve">illḋ eī <lb/>repugnat nature rei permanentis.</s>
            </p>
            <p xml:id="N28BD5">
              <s xml:id="N28BD6" xml:space="preserve">Ad ſecūdam rõnem reſponſum eſt / ibi <lb/>vſ ad vltimã replicã ad quã reſpondeo negando <lb/>iſtam ↄ̨ñam q̄libet pars ꝓportionalis ſecūdū hãc <lb/>diuiſionē fuit producta ante finem huius hore: er-<lb/>go oēs partes ꝓportionales fuerūt ꝓducte añ finē <lb/>huius hore. </s>
              <s xml:id="N28BE3" xml:space="preserve">Nec valet talis ↄ̨ña a ſingulari ad pĺe <lb/>ſignanter in extrinſecis tꝑibus vt logica docet.</s>
            </p>
            <p xml:id="N28BE8">
              <s xml:id="N28BE9" xml:space="preserve">¶ Ad primã cõfirmationē rñſum eſt ibi vſ ad re-               <pb chead="Quarti tractatus." file="0246" n="246"/>               plicam: rñdeo negãdo hac ↄ̨ñam hec albedo pro­<lb/>ducet̄̄: ergo hec albedo añ finē huius hore ꝓducetur <lb/>vel in fine huiꝰ hore ꝓducet̄̄ vel poſt finē (eſto  ſem­<lb/>per determinatio determīet copulã) </s>
              <s xml:id="N28BF7" xml:space="preserve">Tñ prīo /  de­<lb/>mõſtrãdo in ↄ̨ñti vnã horã q̄ nun̄ erit nec fuit nec ē <lb/>datur añs verū: et ↄ̨ñs fĺm. </s>
              <s xml:id="N28BFE" xml:space="preserve">Tñ ſcḋo / q2 poſita a ꝑte <lb/>añtis cõſtãtia illius hore future adhuc añs ē verum <lb/>et ↄ̨ñs falſum ex eo /  determīatio determīas copu­<lb/>lã determinat et reſtrīgit vtrū extremū ſubiectum <lb/>et predicatū vcꝫ. </s>
              <s xml:id="N28C09" xml:space="preserve">Si tñ talis determīatio ſubiectum <lb/>aut predicatū determinet cū cõſtãtia illiꝰ hore futu-<lb/>re: illi ↄ̨ñe annuēdū cenſeo. </s>
              <s xml:id="N28C10" xml:space="preserve">¶ Ad ſecundã ↄ̨firmatio­<lb/>nē dictū eſt ibi vſ ad īprobationē: ad quam rñdeo <lb/>cõcedēdo /  in illo inſtãti illa albedo eſt primo ꝓdu­<lb/>cta ab aliq̊: et cuꝫ addit̄̄: et nõ niſi a ſorte negat̄̄ illa <lb/>mīor. </s>
              <s xml:id="N28C1B" xml:space="preserve">Imo dico /  eſt tūc prīo ꝓducta ab illo q̇ aña <lb/>ꝓducebat eã cū ip̄o ſorte puta ab aliqua cã ſuꝑiori <lb/>cõcurrēte cū ſorte agēte actiõe īmanēte. </s>
              <s xml:id="N28C22" xml:space="preserve">Nec opor-<lb/>tet dare cãm particularē ſui ꝓducti eē: ſꝫ bñ dat̄̄ cã <lb/>particularis ſue ſucceſſiue ꝓductiõis puta ip̄e ſor-<lb/>tes. </s>
              <s xml:id="N28C2B" xml:space="preserve">¶ Ad tertiã ↄ̨firmationem rñdeo admiſſo caſu <lb/>negãdo maiorē: q2 nõ datur tota albedo q̄ fuit ī ſor­<lb/>te / ſꝫ dat̄̄ miuima albedo quã ſortes nõ hēbit in illa <lb/>hora: et illa eſt .4. graduū q2 nun̄ hēbit albedinem <lb/>4. graduū: et quēlibet minorē hēbit aliquãdo vel q̈­<lb/>libet mīori data hēbit maiorē aliqñ minorē tñ al-<lb/>bedine vt .4.</s>
            </p>
            <p xml:id="N28C3A">
              <s xml:id="N28C3B" xml:space="preserve">Ad tertiam rõnem reſponſum eſt ibi <lb/>vſ ad replicã ad quã rñdeo cõcedēdo qḋ infertur <lb/>v.  ſortes et pĺo in illo cãu equaliter p̄miabunt̄̄ etc̈. <lb/></s>
              <s xml:id="N28C43" xml:space="preserve">Nec illud eſt incõueniēs: aut cõtra maximã theolo-<lb/>gorū / qñ vnꝰ meret̄̄ adequatū p̄miū vĺ habuit adeq̈­<lb/>tū meritū: alter vero quodlibet citra illud habuit. <lb/></s>
              <s xml:id="N28C4B" xml:space="preserve">Uñ ad hoc  aliq̇s premiet̄̄ vt .4. adequate ſatis eſt <lb/> ip̄e quodlibet meritū citra .4. habuerit. </s>
              <s xml:id="N28C50" xml:space="preserve">Nec req̇­<lb/>ritur /  ip̄e vel aīa eiꝰ aliqḋ habuerit merituꝫ vt .4. <lb/>vt bene ꝓbat replica. </s>
              <s xml:id="N28C57" xml:space="preserve">Et hec de dubio ꝓ cuius prin­<lb/>cipali ↄ̨cluſiõe teneo ſcḋaꝫ opīonē puta mantuani <lb/>eſſe probabiliorem.</s>
            </p>
            <p xml:id="N28C5E">
              <s xml:id="N28C5F" xml:space="preserve">Ad ſecundum dubiū arguitur ad par­<lb/>tem negatiuã et ſuppono duo. </s>
              <s xml:id="N28C64" xml:space="preserve">Primū /  in propo­<lb/>ſito loquor de ſucceſſiua calefactõe tã intēſiua quã <lb/>extenſiua. </s>
              <s xml:id="N28C6B" xml:space="preserve">Secūdū  ad hoc /  aliqḋ dicat̄̄ albū vel <lb/>alia qualitate qualificatū in ſpē: requirit̄̄ /  maior <lb/>pars ꝙ̄ eius medietas ſic ſcḋ3 ſe et quãlibet eiꝰ par­<lb/>tem ſaltē ſuꝑficiãlē tali qualitate qualificata. </s>
              <s xml:id="N28C74" xml:space="preserve">Qui­<lb/>bus ſuppoſitis ſic argumētor illud / qḋ ſucceſſiue ca­<lb/>lefiet nec īcipiet eē calidū per primū eē nec ꝑ vltimū <lb/>nõ eſſe: igitur nõ incipiet eē calidū. </s>
              <s xml:id="N28C7D" xml:space="preserve">Añs ꝓbatur et vo­<lb/>lo /  a. pedale īcipiat in inſtãti pñti acq̇rere ſucceſſi­<lb/>ue caliditatē qua aliqñ denoīabit̄̄ calidū: et arguo <lb/>ſic a. in nullo inſtãti intrīſeco alteratiõis īcipiet eē <lb/>calidū: nec ī aliquo extrīſeco ꝑ primū eē aut vltimū <lb/>nõ eſſe: igit̄̄ nõ incipiet eē calidū. </s>
              <s xml:id="N28C8A" xml:space="preserve">Añs ꝓbatur / quia <lb/>de extrīſeco notū eſt: et de intrīſeco arguit̄̄ ſic / quia <lb/>ſi in aliquo intrīſeco inciperet maxime eēt in inſtã­<lb/>ti in quo ṗmo ṗma medietas ipſiꝰ a. eſt ſecūdum ſe <lb/>et quodlibet ſui calefacta: ſꝫ hoc nõ: igit̄̄. </s>
              <s xml:id="N28C95" xml:space="preserve">Probat̄̄ <lb/>minor / q2 nullū tale inſtãs eſt dabile: igit̄̄ in tali nõ <lb/>incipit calefieri. </s>
              <s xml:id="N28C9C" xml:space="preserve">Añs ꝓbat̄̄ / q2 ſi ſit dabile: ſignetur <lb/>illud: et ſit b. / et arguit̄̄ ſic in b. inſtãti prīa medietas <lb/>ipſius a. eſt ſecūdū ſe et quodlibet ſui calefacta: igr̄ <lb/>in extremitate eiꝰ eſt aliqua qualitas termīata ad <lb/><gap/> <lb/>igitur in parte diſtãtiori ab agēte eſt qualitas mi-<lb/>noris intēſioris: et qñ illa ꝓducebatur ſucceſſiue iã <lb/>maior pars ꝙ̄ medietas erat calefacta: igr̄ ante b. <lb/>inſtans illud corpus erat calefactū: et ꝑ ↄ̨ñs in illo               <cb chead="Capitulum ſecundum."/>               inſtãti nõ incipit calefieri / qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0246-01" xlink:label="note-0246-01a"/>               </s>
              <s xml:id="N28CB8" xml:space="preserve">¶ Dices <lb/>forte bñ admiſſis ſuppõnibꝰ negãdo añs: et ad pū­<lb/>ctum ꝓbatiõis dices /  in īſtãti in quo prīo eſt verū <lb/>dicere primã medietatē eē calefactã ſecūdū ſe et qḋli­<lb/>let ſui a. incipit calefieri ꝑ vltimū nõ eſſe. </s>
              <s xml:id="N28CC3" xml:space="preserve">Et cū ꝓba­<lb/>tur /  nõ q2 nõ eſt dabile tale inſtãs negat̄̄ illud et <lb/>ad ꝓbatiouē q2 q̈litas termīata ad medietatē non <lb/>calefactã eſt aliqualis intēſiõis ↄ̨cedas illud: q2 in­<lb/>tēſionis difformis terminate ad nõ gradū: et cū in­<lb/>fertur: igr̄ in parte remotiori ab agēte eſt iam ꝓdu­<lb/>cta qualitas minoris intēſiõis: negabis illã ↄ̨ñam <lb/>ſed oporteret ſic argumētari qualitas terminata <lb/>ad ſecundã medietatē eſt aliqualis intēſionis: et ter­<lb/>minatur verſus ſecundã medietatē ad certū gradū <lb/>et nõ fuit impedimētū vlterioris ꝓductiõis: igr̄ iam <lb/>aliqua pars vlterior eſt tali qualificata. </s>
              <s xml:id="N28CDC" xml:space="preserve">Mõ nõ eſt <lb/>ſic in ꝓpoſito </s>
              <s xml:id="N28CE1" xml:space="preserve">Imaginãdū eſt em̄ /  prīo agens ca-<lb/>lefactiuū ꝑ ſucceſſiuã approximationē ꝓduxit qua­<lb/>litatē vniformiter difformē vel difformiter diffor-<lb/>mē (nõ eſt cura) ſucceſſiue a certo gradu vſ ad nou <lb/>gradū ꝑ primã medietatē adequate: et quãdo ṗmo <lb/>verū eſt dicere /  talis caliditas eſt ꝓducta per pri­<lb/>mã medietatē adequate a certo gradu ī extremo ꝓ­<lb/>pinquiori vſ ad nõ gradū ī remiſſiori ipſius ṗme <lb/>medietatis / tunc tale corpus incipit calefieri ꝑ vlti-<lb/>mum non eſſe.</s>
            </p>
            <div xml:id="N28CF6" level="5" n="25" type="float">
              <note position="right" xlink:href="note-0246-01a" xlink:label="note-0246-01" xml:id="N28CFA" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N28D00">
              <s xml:id="N28D01" xml:space="preserve">Sed contra / q2 ſi daretur tale inſtans <lb/>in quo vcꝫ eſſet verū dicere in hoc prima medietas <lb/>huiꝰ corꝑis eſt calida ſecūdū ſe et quodlibet ſui: et <lb/>nõ īmediate añ hoc etc. / ſeq̇retur talē caliditatem nõ <lb/>fuiſſe ſucceſſiue ꝓductã: et ſic nun̄ daret̄̄ inceptio <lb/>denoīatiõis calidi cuius caliditas ſucceſſiue ꝓducit̄̄ / <lb/>qḋ fuit ꝓbandū. </s>
              <s xml:id="N28D10" xml:space="preserve">Seq̄la tñ ꝓbat̄̄: et pono /  ſimꝰ ī illo <lb/>inſtãti: et arguo ſic / caliditas huiꝰ medietatis cū ſit <lb/>alicuius intēſionis hꝫ duas medietates in quas di­<lb/>uiſibilis eſt ſcḋm intēſionē: et vna nõ fuit ꝓducta añ <lb/>alterã: igit̄̄ nõ ſucceſſiue ꝓducebatur talis caliditas <lb/></s>
              <s xml:id="N28D1C" xml:space="preserve">Coña eſt nota et mīor ꝓbatur: q2 ſi vna illarum me­<lb/>dietatū fuit ꝓducta añ alterã ſignetur prius produ­<lb/>cta et ſit a. / et arguo ſic / qñ a. fuit ꝓducta tã prima me­<lb/>dietas illius corꝑis erat totaliter calida: q2 illa ex­<lb/>tenditur ꝑ totam primã medietatē: et illa medietas <lb/>caliditatis eſt ꝓducta añ ſecūdã medietatē: g̊ aña ̄ <lb/>caliditas cõpoſita ex his duabꝰ medietatibꝰ ſit ꝓ­<lb/>ducta tã medietas prima illius corporis erat cale­<lb/>facta / quod fuit negatū: igr̄ ſi illa ꝓducit̄̄ ſucceſſiue <lb/>iã nõ dabitur inſtãs in quo tale corpus īcipit deno­<lb/>minari calidū.               <anchor type="note" xlink:href="note-0246-02" xlink:label="note-0246-02a"/>               </s>
              <s xml:id="N28D38" xml:space="preserve">¶ Dices et bene negando ſeq̄lam: et <lb/>ad ꝓbationē cõcedes /  vna medietas intēſiua non <lb/>fuit prius ꝓducta ꝙ̄ altera et cū infertur: ergo non <lb/>ſucceſſiue ꝓducebatur illa caliditas nego illã ↄ̨ñaꝫ <lb/></s>
              <s xml:id="N28D42" xml:space="preserve">Et rõ eſt / q2 ̄uis vna medietas intēſius nõ ṗus fuit <lb/>ꝓducta ꝙ̄ altera tñ ſignabiles ſunt infinite partes <lb/>illius caliditatis quarū prima ꝓducta eſt ante ſecū­<lb/>dã: et ſecunda añ tertiã et tertia añ quartã et ↄ̨ñter <lb/>et talis partes ſe penetrãt vt ſignãdo pro prīa par­<lb/>te totã caliditatē ꝓductã in prima parte ꝓportio-<lb/>nali tꝑis: et pro ſecunda ꝓductã in ſcḋa parte ꝓpor­<lb/>tionali tꝑis / et ſic ↄ̨ñter. </s>
              <s xml:id="N28D53" xml:space="preserve">¶ Sed cõtra q2 de rõne illiꝰ <lb/>quod ſucceſſiue ꝓdncitur eſt /  q̄libet eius pars añ <lb/>alterã ꝓducatur: igr̄ ſi alicuius rei due partes eq̄ <lb/>primo ſint ꝓducte illud nõ ſucceſſiue ꝓducitur: et ꝑ <lb/>ↄ̨ñs talis caliditas nõ ſucceſſiue producitur / quod <lb/>fuit probandum.</s>
            </p>
            <div xml:id="N28D60" level="5" n="26" type="float">
              <note position="right" xlink:href="note-0246-02a" xlink:label="note-0246-02" xml:id="N28D64" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N28D6A">
              <s xml:id="N28D6B" xml:space="preserve">Secundo ad idē arguitur ſic. </s>
              <s xml:id="N28D6E" xml:space="preserve">Nulla <lb/>qualitas poteſt ſucceſſiue produci / igr̄ titulus dubii <lb/>ſupponit falſum. </s>
              <s xml:id="N28D75" xml:space="preserve">Aſſumptū probatur / q2 ſi aliqua <lb/>qualitas poſſet ſucceſſiue produci: citiꝰ producere­               <pb chead="De intenſione  remiſſione formarum." file="0247" n="247"/>               tur vnꝰ gradus ꝙ̄ alter. </s>
              <s xml:id="N28D7F" xml:space="preserve">Coña eſt nota / q2 alias nõ <lb/>ſucceſſiue ꝓduceretur illa qualitas: et falſitas ↄ̨ñtis <lb/>oñditur / q2 ſi citiꝰ ꝓduceret̄̄ vnꝰ gradus ꝙ̄ alter citiꝰ <lb/>ꝓduceretur gradus medius ꝙ̄ gradus vltramediꝰ / <lb/>ſꝫ ↄ̨ñs eſt falſuꝫ / igit̄̄ illud ex quo ſeq̇tur. </s>
              <s xml:id="N28D8A" xml:space="preserve">Sequela vi­<lb/>detur apparēs: q2 ſi vnꝰ gradus ꝓduceret̄̄ añ alte-<lb/>rū: et mediꝰ nõ ꝓducit̄̄ poſt gradum vltramediū: ſe-<lb/>quitur /  ꝓduceretur ante. </s>
              <s xml:id="N28D93" xml:space="preserve">Sꝫ falſitas ↄ̨ñtis ꝓba-<lb/>tur / q2 nullus gradus medius citiꝰ producetur ſuc-<lb/>ceſſiue ꝙ̄ gradus vltramedius: igr̄ nõ citiꝰ ꝓducetur <lb/>gradus mediꝰ ꝙ̄ gradus vltramedius. </s>
              <s xml:id="N28D9C" xml:space="preserve">Coña pꝫ ab <lb/>equiualētibꝰ: et añs ꝓbat̄̄: q2 da oppoſitū: et ſignet̄̄ <lb/>ille gradus medius et ſit a. / et arguo ſic. </s>
              <s xml:id="N28DA3" xml:space="preserve">aliq̇s gradꝰ <lb/>vltramediꝰ ita cito ꝓducetur ſicut a. / igr̄ a. nõ citius <lb/>ꝓducetur ꝙ̄ gradus vltramediꝰ. </s>
              <s xml:id="N28DAA" xml:space="preserve">Coña pꝫ: et ꝓbatur <lb/>añs: et capio b. inſtãs in quo nondū erit ꝓductꝰ gra­<lb/>dus medius: et ſigno gradū vnū vltramediū adhuc <lb/>ꝓducendū cuiꝰ tñ q̈litas ꝓducta in b. inſtanti eſt ꝑs / <lb/>et arguo ſic / iſte gradus vltramedius ſignatus ita <lb/>cito ꝓducetur ſicut a. cū īmediate poſt inſtans īitia­<lb/>tiuū alteratiõis ꝓducetur aliqua eiꝰ pars puta illa <lb/>que erit producta in b. inſtanti: et a. nõ põt citiꝰ pro­<lb/>duci cū caſu ꝙ̄ īmediate poſt idē inſtãs: igr̄ aliquis <lb/>gradus vltramedius ita cito ꝓducitur ſicut a. / quod <lb/>fuit probanduꝫ. </s>
              <s xml:id="N28DC1" xml:space="preserve">Tota deductio patet intuenti.</s>
            </p>
            <p xml:id="N28DC4">
              <s xml:id="N28DC5" xml:space="preserve">¶ Dices et bñ negando añs: et ad ꝓbationē nego ſe­<lb/>quelam: q2 ly alter diſtribuitur: et ad probationeꝫ <lb/>nego /  alias nõ ſucceſſiue ꝓduceret̄̄ talis qualitas <lb/></s>
              <s xml:id="N28DCD" xml:space="preserve">ad hoc em̄ /  aliquid habēs partes ſucceſſiue ꝓdu­<lb/>catur req̇rit̄̄ et ſufficit /  ip̄m producat̄̄: et nulla eiꝰ <lb/>pars ſubito producatur. </s>
              <s xml:id="N28DD4" xml:space="preserve">¶ Ex quo ſeq̇tur /  in pro­<lb/>ductiõe ſucceſſiua qualitatis vſ ad ſūmū ante quē­<lb/>libet gradū mediū productꝰ eſt medius: et añ quēli­<lb/>bet gradū mediū productꝰ eſt gradus vltramedius <lb/>et añ quēlibet gradū vltramediū ꝓductꝰ eſt gradꝰ <lb/>vltramedius etc̈. </s>
              <s xml:id="N28DE1" xml:space="preserve">Probatur / q2 ante quēlibet gradū <lb/>productū ꝑ aliquã partē ſubiecti ꝓductꝰ eſt gradus <lb/>equalis intēſiõis ꝑ minorē partē propīquiorē agē­<lb/>ti: et cuiuſcū intēſionis gradu ſignato in pūcto ꝓ­<lb/>pinquiori citiꝰ productus eſt gradus eiuſdē intēſio­<lb/>nis ꝙ̄ ille ſignatꝰ: et ſic ante̄ productꝰ eſt ille gra-<lb/>dus ſignatꝰ productꝰ eſt in puncto illo ꝓpinquiori <lb/>gradus maioris intēſionis: igit̄̄ correlariū verum. <lb/></s>
              <s xml:id="N28DF3" xml:space="preserve">¶ Seq̇tur ſcḋo /  in ſucceſſiua ꝓductiõe qualitatis <lb/>a nõ gradu vſ ad ſummū quocū gradu ſignato <lb/>cuius vis intēſiõis gradus ita cito producit̄̄ ſicut il­<lb/>le ſignatus. </s>
              <s xml:id="N28DFC" xml:space="preserve">pꝫ hoc aſpiciēti /  cuiuſcū intēſiõis <lb/>gradus in īfinitū parua intēſio eſt pars: hoc addi-<lb/>to /  ꝙ̄ cito alicuius aliqua pars ꝓducit̄̄ tã cito ip̄m <lb/>producit̄̄. </s>
              <s xml:id="N28E05" xml:space="preserve">¶ Seq̇tur tertio /  in tali ꝓductiõe ſucceſ­<lb/>ſiua quo ad ſubiectū nõ citiꝰ ꝓducet̄̄ gradus mediꝰ <lb/>̄ gradus vltramedius. </s>
              <s xml:id="N28E0C" xml:space="preserve">Probat̄̄ ex exponētibus: et <lb/>correlario priori. </s>
              <s xml:id="N28E11" xml:space="preserve">¶ Sed cõtra et ſuppono intēſio-<lb/>nē difformiū debere attēdi penes gradū ſummum <lb/>aut minimū quē nõ hꝫ: et arguo ſic / in inſtãti in quo <lb/>primū eſt verū dicere /  in paſſo eſt ꝓducta qualitas <lb/>a gradu medio vſ ad certū g̈dū minorē vel nõ g̈dū <lb/>in illo productꝰ eſt gradus medius ex ſuppoſito: et <lb/>adhuc nullus gradus vltramediꝰ: igr̄ citiꝰ produ-<lb/>ctus eſt gradus mediꝰ ꝙ̄ gradus vltramedius: et ꝑ <lb/>ↄ̨ñs primū correlariū fĺm. </s>
              <s xml:id="N28E24" xml:space="preserve">Itē vt ſuꝑius dictū ē poſ­<lb/>ſibile eſt agens naturale eq̄ velociter agere in ꝓpī­<lb/>quū ſicut in remotū: igit̄̄ ſtat gradū mediū produci <lb/>ante quēlibet vltramediū. </s>
              <s xml:id="N28E2D" xml:space="preserve">Nã in aliquo īſtanti erit <lb/>primo gradus mediꝰ in aliq̊ pūcto ſubiecti: et ī eo-<lb/>dē inſtãti erit in quolibet puncto: et nullꝰ vltrame-<lb/>dius vt cõſtat igr̄.</s>
            </p>
            <p xml:id="N28E36">
              <s xml:id="N28E37" xml:space="preserve">In oppoſituꝫ arguitur ſic / quodlibet <lb/>corpus quod ſucceſſiue calefiet incipiet eſſe caliduꝫ:               <cb chead="fehlt"/>               igitur. </s>
              <s xml:id="N28E3F" xml:space="preserve">Aſſumptū probat̄̄: et ſit a. corpus qḋ ſucceſ-<lb/>ſiue calefit: et per talē calefactionē ſucceſſiuã aliqñ <lb/>erit calidū: et argr̄ ſic / iſte due ↄ̈dictiorie a. eſt calidū <lb/>a. nõ eſt calidū ſucceſſiue ificãt̄̄ capio / igr̄ totū tem­<lb/>pus ꝑ quod ficabit̄̄ affirmatiua: et totū ꝑ qḋ ifi-<lb/>cabit negatiua: et arguo ſic / vel in inſtãti medio illo­<lb/>rum duoꝝ tp̄m affirmatiua eſt a vĺ negatīa. </s>
              <s xml:id="N28E4E" xml:space="preserve">Si af­<lb/>firmatiua: ſeq̇tur /  a. incipit eē calidū ꝑ primū eſſe / <lb/>q2 in illo eſt calidū et nõ ante. </s>
              <s xml:id="N28E55" xml:space="preserve">Si negatiua: manife­<lb/>ſtum eſt /  a. incipit eē calidū ꝑ vltimū nõ eē: igitur <lb/>ſi a. ſucceſſiue calefiet et denoīabit̄̄ calidū: ipſum in­<lb/>cipiet eē calidum / qḋ fuit probãdum.</s>
            </p>
            <p xml:id="N28E5E">
              <s xml:id="N28E5F" xml:space="preserve">Pro ſolutione huiꝰ dubii ſciendū eſt / <lb/> propriū eſt qualitati ſuū ſubiectū denoīare qua­<lb/>le. </s>
              <s xml:id="N28E66" xml:space="preserve">Uñ phūs in p̄dicamētis. </s>
              <s xml:id="N28E69" xml:space="preserve">Qualitas eſt ſcḋm quã <lb/>quales eē dicimur. </s>
              <s xml:id="N28E6E" xml:space="preserve">Sꝫ eū nõ quãtulacū qualitas ī <lb/>ſubiecto videat̄̄ ſufficere ad denoīandū illḋ ſubie-<lb/>ctum quale: cū albedo dentiū ethiopis non ſufficit <lb/>ethiopē denoīare albū: dubiū eſt quãta albedo re-<lb/>quirit̄̄ in ſubiecto vt ſubiectū dicatur album. </s>
              <s xml:id="N28E79" xml:space="preserve">Unde <lb/>de hoc due ſunt opīones. </s>
              <s xml:id="N28E7E" xml:space="preserve">Prima eſt calculatoris ī <lb/>multis locis īnuentis ex ſuo modo argumētandi /  <lb/>̄tūcū parua qualitas ſufficit denoīare ſuū ſub­<lb/>iectū quale ſpecifice ſaltē in corpore finito: dūmo-<lb/>do nõ impediat̄̄ a ſuo ↄ̈rio in eodē ſubiecto.               <anchor type="note" xlink:href="note-0247-01" xlink:label="note-0247-01a"/>               </s>
              <s xml:id="N28E8E" xml:space="preserve">Alia ē <lb/>pauli veneti in ſcḋo dubio ſue q̈drature capite .13°. <lb/>dicentis  ad hoc /  hõ ſit albus ſufficit  maior <lb/>pars ſuꝑficialis ſue faciei ꝙ̄ medietas ſit alba: et ēt <lb/>hoc requirit̄̄. </s>
              <s xml:id="N28E99" xml:space="preserve">et ad hoc  aīatū nõ hõ piloſuꝫ vel pē-<lb/>noſum ſit album req̇rit et ſufficit maiorem partē ex­<lb/>tremalē piloꝝ vel pēnarū ſcḋm ſe totã eē albam: et <lb/>ad hoc  brutū nec piloſum nec pēnoſum ſiue aliḋ <lb/>in aīatum ſeu aīatū ſolū vegetatiue ſit albū req̇rit̄̄ <lb/>et ſufficit maiorē partē ſuꝑficialē ſcḋm ſe totã eē al­<lb/>bam. </s>
              <s xml:id="N28EA8" xml:space="preserve">Et vt id dicã / qḋ ſentio totū hoc ſtat ad nomē: <lb/>et ad placitū potētis imponere iſtū terīm albuꝫ ad <lb/>ſig̈ndū. </s>
              <s xml:id="N28EAF" xml:space="preserve">Nã poteſt imponi /  nichil dicatur album <lb/>niſi hēat albedinē vltra medietatē non habēdo re-<lb/>ſpectum ad ſuꝑficieꝫ. </s>
              <s xml:id="N28EB6" xml:space="preserve">vel niſi habeat albedinē ꝑ to­<lb/>tum vel  ſufficit habere ̄tūcun parū de albedi­<lb/>ne. </s>
              <s xml:id="N28EBD" xml:space="preserve">Imo ſcḋm opīonē pauli aliq̇d diceretur album <lb/>cuiꝰ nulla pars eſt alba. </s>
              <s xml:id="N28EC2" xml:space="preserve">Nã olor hñs pēnas albas <lb/>cuius tamē cutis eſt nigerrīa dr̄ albus ꝓpter albe-<lb/>dinem ſuaꝝ pēnarū q̄ non ſunt partes oloris: et ſic <lb/>põt ſignari vna pars oloris alba q̄ nichil habet al­<lb/>bedinis in ſe: ſꝫ dr̄ alba /  ſue plume ſint albe.</s>
            </p>
            <div xml:id="N28ECD" level="5" n="27" type="float">
              <note position="right" xlink:href="note-0247-01a" xlink:label="note-0247-01" xml:id="N28ED1" xml:space="preserve">Paulus <lb/>venetus.</note>
            </div>
            <p xml:id="N28ED9">
              <s xml:id="N28EDA" xml:space="preserve">His ſuppoſitis reſpõdeo ad dubiū ꝑ <lb/>4. cõcluſiones. </s>
              <s xml:id="N28EDF" xml:space="preserve">¶ Prīa cõcluſio. </s>
              <s xml:id="N28EE2" xml:space="preserve">Tenēdo opīonem <lb/>calculatoris oē corpus / qḋ q̈lificabit̄̄ ſucceſſiue non <lb/>habēs ↄ̈riū forme inducēde incipiet qualificari ſiue <lb/>eſſe qualificatū ſpecifice ꝑ vltimū inſtãs nõ eē. </s>
              <s xml:id="N28EEB" xml:space="preserve">Pro­<lb/>batur hec ↄ̨cluſio / qm̄ qḋlibet tale corpus īmediate <lb/>poſt inſtãs initiatiuū actiõis habebit aliquã talem <lb/>qualitatē: igit̄̄ īmediate poſt illḋ inſtãs quodlibet <lb/>tale erit calidū. </s>
              <s xml:id="N28EF6" xml:space="preserve">Patet / q2 ex opīone quãtulacun <lb/>qualitas nõ ꝑmixta ↄ̨trario ſufficit ad denoīatio-<lb/>nem. </s>
              <s xml:id="N28EFD" xml:space="preserve">¶ Secunda cõcluſio. </s>
              <s xml:id="N28F00" xml:space="preserve">Tenēdo req̇ri partē ma-<lb/>iorē medietate ſcḋm ſe et qḋlibet ſui ſaltē ſuꝑficiale <lb/>debere eē q̈lificatã ad hoc  totū corpꝰ dicat̄̄ q̈lifi-<lb/>tū ſpecifice: qḋlꝫ corpꝰ ſucceſſiue calefiēdū et denoīan­<lb/>dū calidū īcipit aut īcipiet eē calidū ꝑ vltimū nõ eē. <lb/></s>
              <s xml:id="N28F0C" xml:space="preserve">Hec ↄ̨° ſatis pꝫ ex prīo argumēto añ oppoſituꝫ / q2 ī <lb/>īſtanti in quo primo veꝝ eſt dicere vnã medietatē ſu­<lb/>perficialē eſſe calidã m ſe et qḋlibet ſui: in illo veꝝ <lb/>eſt dicere /  totum corpus nõ eſt calidum et īmedia-<lb/>te poſt illud inſtans totum corpus erit calidum cuꝫ <lb/>maior pars ſuꝑficialis ꝙ̄ medietas īmediate poſt <lb/>hoc erit calida ſcḋm quodlibet ſui.</s>
            </p>
            <pb chead="Quarti Tractatus" file="0248" n="248"/>
            <p xml:id="N28F1F">
              <s xml:id="N28F20" xml:space="preserve">¶ Tertia ↄ̨cluſio. </s>
              <s xml:id="N28F23" xml:space="preserve">Tenēdo qualitates ↄ̈rias ſe ↄ̨pa­<lb/>ti in gradibus remiſ id qḋ ſucceſſiue calefit ꝑ ītro­<lb/>ductionē caliditatis: et eq̄ velocē corruptionē frigi-<lb/>ditatis incipit vocari calidū ꝑ vltimū inſtãs nõ eſſe <lb/></s>
              <s xml:id="N28F2D" xml:space="preserve">Probatur hec ↄ̨cluſio / q2 in tꝑe illo alteratiõis de-<lb/>ueniēdū eſt ad aliquod inſtãs in quo adeq̈te tantuꝫ <lb/>nata eſt denoīare caliditas ſicut frigiditas. </s>
              <s xml:id="N28F34" xml:space="preserve">ſit igr̄ <lb/>illud inſtaus a. et argr̄ ſic / in inſtãti a. illud corpus <lb/>nec eſt calidū nec frigidū: q2 qualitates ↄ̈rie ſe mu-<lb/>tuo adequate impediūt in a. inſtanti in denoīatio-<lb/>nibus ſuis: et īmediate poſt a. inſtãs illud corpꝰ erit <lb/>calidū cū īmediate poſt a. inſtãs ītroducet̄̄ aliquid <lb/>calididatꝪ: igr̄ in inſtãti a. illud corpꝰ incipit eē cali­<lb/>dū per vltimū nõ eē / qḋ fuit ꝓbandū. </s>
              <s xml:id="N28F45" xml:space="preserve">Aſſumptū ta-<lb/>men ꝓbat̄̄ vcꝫ /  deueniendū ſit ad aliquod inſtans <lb/>in quo adeq̈te tm̄ nata eſt denoīare caliditas ſicut <lb/>frigiditas: q2 in prīcipio alteratõis frigiditas ma­<lb/>gis denoīat ꝙ̄ nata ſit denoīare caliditas / vt pꝫ cū <lb/>in infinitū parua ſit caliditas in prīcipio alteratio­<lb/>nis et denoīatio caliditatis cõtinuo ſucceſſiue cre-<lb/>ſcit ↄ̨tinuo: et denoīatio frigiditatis ſucceſſiue cõti­<lb/>nuo decreſcit / igr̄ ad aliqḋ inſtans veniunt ad equa­<lb/>litatē / qḋ fuit ꝓbandū. </s>
              <s xml:id="N28F5A" xml:space="preserve">Patet ↄ̨ña / q2 minꝰ ſuo ma-<lb/>iori ſucceſſiue cõtinuo nõ põt fieri maius quī aliqñ <lb/>ſit equale illi qḋ mõ eſt maius eo. </s>
              <s xml:id="N28F61" xml:space="preserve">ſiue maius q̇eſcat <lb/>ſiue nõ: igitur. </s>
              <s xml:id="N28F66" xml:space="preserve">¶ Quarta ↄ̨cluſio.               <anchor type="note" xlink:href="note-0248-01" xlink:label="note-0248-01a"/>               </s>
              <s xml:id="N28F6E" xml:space="preserve">Si aliquod infi-<lb/>nitū calefiat ſucceſſiue calefieri ipſum calefiet hoc ē <lb/>incipiet eē calidū ꝑ primū inſtãs eē etiã ſecūdū opi­<lb/>nionē Suiſeth. </s>
              <s xml:id="N28F77" xml:space="preserve">Probat̄̄ / q2 in quolꝫ inſtãti intrīſe-<lb/>co alteratiõis aña ꝙ̄ ꝑ totū ſit qualitas p̄ciſe fini-<lb/>ta pars illius erit q̈leficata: et reſtabit infinita q̈lifi­<lb/>canda: igr̄ in nullo tali inſtãti intrīſeco illud corpꝰ <lb/>infinitū incipiet eē colidū. </s>
              <s xml:id="N28F82" xml:space="preserve">pꝫ ↄ̨ña / q2 etiã vt opīat̄̄ <lb/>Suiſeth qualitas corꝑis infiniti exñs in parte fini­<lb/>ta nichil facit ad totius denoīationē: et per ↄ̨ñs in in-<lb/>ſtauti in quo primo erit verū dicere /  qualitas eſt <lb/>ꝑ totū illud corpꝰ infinitū: illud corpꝰ infinitū inci-<lb/>piet eē calidū p primū inſtãs eē / qḋ fuit ꝓbandum. <lb/></s>
              <s xml:id="N28F90" xml:space="preserve">Poſſnt hic inferri multa et diuerſa correlaria ſecū­<lb/>dū diuerſitatē põnū de denoīationibꝰ ꝑtiū de ꝑtiū <lb/>denoīationū inceptiõe et multa alia q̄ infert paulꝰ <lb/>venetus loco preallegato:               <anchor type="note" xlink:href="note-0248-02" xlink:label="note-0248-02a"/>               et hētiſber in illo ſopbiſ­<lb/>mate.. 5°. oīs hõ qui eſt albus currit: et ſiĺr ſuus cõ-<lb/>mentator: ſed gr̄a breuitatis ſuꝑſedeo facile em̄ pa­<lb/>tent perſpiciori ingenio. </s>
              <s xml:id="N28FA4" xml:space="preserve">Et per hoc patꝫ ſufficiēter <lb/>reſponſio ad dubium.</s>
            </p>
            <div xml:id="N28FA9" level="5" n="28" type="float">
              <note position="left" xlink:href="note-0248-01a" xlink:label="note-0248-01" xml:id="N28FAD" xml:space="preserve">Suiſeth.</note>
              <note position="left" xlink:href="note-0248-02a" xlink:label="note-0248-02" xml:id="N28FB3" xml:space="preserve">hētiſber.</note>
            </div>
            <p xml:id="N28FB9">
              <s xml:id="N28FBA" xml:space="preserve">Ad rõnes dubii ante oppoſitū. </s>
              <s xml:id="N28FBD" xml:space="preserve">Ad pri­<lb/>mã reſpõſum eſt ibi vſ ad vltimã replicã ad quaꝫ <lb/>reſpondeo dupĺr. </s>
              <s xml:id="N28FC4" xml:space="preserve">Primo negando añs / q2 motus <lb/>ſaltē ſcḋm diſtinguētes eū a mobili et ſonus ꝓduci­<lb/>tur ſucceſſiue: et tñ nõ quelibet eiꝰ pars ꝓducit̄̄ an-<lb/>te quãlibet aliam / q2 alique ptes ſcḋm extēſionē ꝓ-<lb/>ducūtur ſiĺ. </s>
              <s xml:id="N28FCF" xml:space="preserve">Duplices nã ſunt partes motus ſecū­<lb/>dum extenſionem ſubiecti et ſecundū ſucceſſionem. <lb/></s>
              <s xml:id="N28FD5" xml:space="preserve">Primo em̄ ſunt ſimul: licet nõ ſecūde. </s>
              <s xml:id="N28FD8" xml:space="preserve">Dico tñ ſcḋo <lb/>concedēdo añs et negando ↄ̨ñam. </s>
              <s xml:id="N28FDD" xml:space="preserve">Et rõ eſt / q2 nõ eſt <lb/>de rõne ſucceſſiue ꝓductiõis /  q̄libet pars ſit ꝓdu-<lb/>cta ante alterã vt oſtenſum eſt: ſed de rõne ſucceſſi-<lb/>ue ꝓductiõis eſt  nõ ſit dabilis aliqua pars que <lb/>ſubito producatur. </s>
              <s xml:id="N28FE8" xml:space="preserve">Unde id dr̄ ſucceſſiue ꝓduci / qḋ <lb/>ꝓducitur habēs partes et cuius nulla pars ꝓducit̄̄ <lb/>ſubito. </s>
              <s xml:id="N28FEF" xml:space="preserve">¶ Et ex hoc ſequit̄̄ /  aliqua qualitas ſucceſ­<lb/>ſiue producit̄̄ et tamen quelibet pars ꝓportiona-<lb/>lis ſecundū extenſionē certa diuiſione erit eque ci-<lb/>to adequate ꝓducta ſicut ṗma. </s>
              <s xml:id="N28FF8" xml:space="preserve">Patet hoc correla-<lb/>riuꝫ poſito /  ſemꝑ agens agat in ꝓpinquū agēdo <lb/>in remotū: et nõdū ceſſet agė in ꝓpīquū ꝓpṫ debitã               <cb chead="Capi. Tertium"/>               aſſimilationē. </s>
              <s xml:id="N29002" xml:space="preserve">Idē aĺr ꝓbatur certo mõ diuidēdo.</s>
            </p>
            <p xml:id="N29005">
              <s xml:id="N29006" xml:space="preserve">Ad ſecūdam rõnem reſponſuꝫ eſt ibi <lb/>vſ ad replicã: ad quã rñdeo ↄ̨cedēdo /  illo ſuppo­<lb/>ſito citiꝰ ꝓducit̄̄ gradus mediꝰ ꝙ̄ gradus vltra me-<lb/>dius: ſed correlariū cū dictis intelligit̄̄ dūmõ fiat <lb/>ſucceſſiue ꝓductio qualitatis q̊ ad ſubiectū: et  q̈li­<lb/>tas difformis nõ corrñdeat ſuo gradu ſummo etc̈. <lb/></s>
              <s xml:id="N29014" xml:space="preserve">Et hec de ſecundo dubio.</s>
            </p>
            <p xml:id="N29017">
              <s xml:id="N29018" xml:space="preserve">Ad tertium dubium arguitur ad par­<lb/>tem negatiuã: q2 tūc ſeq̄ret̄̄ aliquã creaturã eſſe in-<lb/>finite actiuitatis: ſꝫ ↄ̨ñs eſt falſum: igr̄. </s>
              <s xml:id="N2901F" xml:space="preserve">Seq̄la pro-<lb/>batur et ſit a forma p̄ciſe durãs ꝑ inſtans: et arguit̄̄ <lb/>ſic / a. corrūpit̄̄ per vltimū inſtans eſſe ſecundū ſe et <lb/>quodlibet ſui (q2 de tali corruptõe ītelligit dubiū) <lb/>et talis forma reſiſtit: igit̄̄ corrūpit̄̄ ab agēte īfinite <lb/>virtutis. </s>
              <s xml:id="N2902C" xml:space="preserve">Patet / q2 nullius finiti ad finitū eſt infini­<lb/>ta ꝓportio. </s>
              <s xml:id="N29031" xml:space="preserve">¶ Et cõfirmat̄̄ / q2 reſiſtētia eſt cauſa ſuc-<lb/>ceſſõis reſpectu tutis finite: igit̄̄ vbicū eſt reſiſtē­<lb/>tia et agēs finitū ibi eſt ſucceſſio. </s>
              <s xml:id="N29038" xml:space="preserve">¶ Confirmat̄̄ ſcḋo / <lb/>q2 alias eq̄ cito corrūperetur illa reſiſtētia a mīori <lb/>virtute ſicut a maiori. </s>
              <s xml:id="N2903F" xml:space="preserve">imo a finita ſicut ab infinita / <lb/>ſed ↄ̨ñs eſt falſum / igitur illud ex quo ſequitur.</s>
            </p>
            <p xml:id="N29044">
              <s xml:id="N29045" xml:space="preserve">In oppoſitū tamen arguitur ſic / q2 in­<lb/>ſtantiū indiuiſibiliū qḋlibet preciſe durat ꝑ inſtãs <lb/>igit̄̄.               <anchor type="note" xlink:href="note-0248-03" xlink:label="note-0248-03a"/>               </s>
              <s xml:id="N29051" xml:space="preserve">¶ Reſpõdet huic dubio Gregorius de arimīo <lb/>in ṗmo d. 17. q̄ .2. ponedo talē ↄ̨cluſionē. </s>
              <s xml:id="N29056" xml:space="preserve">Nulla res <lb/>naturaliṫ põt preciſe durare ꝑ inſtans. </s>
              <s xml:id="N2905B" xml:space="preserve">Nõ adducit <lb/>tñ efficacē rõnem. </s>
              <s xml:id="N29060" xml:space="preserve">¶ Et iõ ↄ̈ eū et ex dictis eius ſic ar­<lb/>gumētor. </s>
              <s xml:id="N29065" xml:space="preserve">Capio aliquod mīmū naturale ꝓductum <lb/>in inſtanti cuiꝰ materia per remotionē de pñti inci­<lb/>piat cõdēſari in eodē inſtãti: totum hoc eſt poſſibi-<lb/>le naturaliter. </s>
              <s xml:id="N2906E" xml:space="preserve">Quo poſito illud minimū naturale <lb/>immediate poſt primū inſtãs ſui eſſe nõ erit: igitur <lb/>preciſe durabit per inſtans. </s>
              <s xml:id="N29075" xml:space="preserve">Non video / quid poſſet <lb/>dicere huic rationi. </s>
              <s xml:id="N2907A" xml:space="preserve">maxime: q2 ipſe tenet tale mini­<lb/>mū naturale poſſe ſic ꝓduci: et tenet ipſum corrum­<lb/>pi per cõdenſationem. </s>
              <s xml:id="N29081" xml:space="preserve">¶ Et confirmatur / quia ſcḋ3 <lb/>eū viſio p̄t ꝓduci inſtanti. </s>
              <s xml:id="N29086" xml:space="preserve">Uolo igitur /  ſit in in-<lb/>ſtanti preſenti aliquod minimū naturale in preſen­<lb/>tia ſortis ad quod primo ſortes aduertit et īcipiat <lb/>illud mīmū in eodem inſtanti corrumpi ꝑ remotio-<lb/>nē de preſenti. </s>
              <s xml:id="N29091" xml:space="preserve">Quo poſito viſio in prīo inſtãti ſui <lb/>eſſe deſinit eē per remotioneꝫ de preſenti: igr̄ preci­<lb/>ſe per inſtans durabit. </s>
              <s xml:id="N29098" xml:space="preserve">Totus caſus eſt poſſibilis <lb/>naturaliter. </s>
              <s xml:id="N2909D" xml:space="preserve">¶ Confirmatur ſcḋo et volo /  aliquis <lb/>angelus prīo aduertat ad ſortem in inſtanti preſē­<lb/>ti cū quo ſit parrhiſius in eodē inſtanti: et habeat <lb/>noticiam intuitiuã eius: et ſubito mutetur vſ rho­<lb/>mã vel ad tantū ſpaciū  ex illo non ſufficit videre <lb/>ſortē intuitiue:               <anchor type="note" xlink:href="note-0248-04" xlink:label="note-0248-04a"/>               totū hoc eſt poſſibile angelo ex pro­<lb/>priis naturalibus / vt cõcedit idē Gregorius in ſcḋo <lb/></s>
              <s xml:id="N290B2" xml:space="preserve">Quo poſito ſequit̄̄ /  illa viſio nõ erit poſt primum <lb/>inſtans ſui eſſe: igitur preciſe durabit per inſtãs na­<lb/>turaliter.</s>
            </p>
            <div xml:id="N290B9" level="5" n="29" type="float">
              <note position="right" xlink:href="note-0248-03a" xlink:label="note-0248-03" xml:id="N290BD" xml:space="preserve">Grego. ī <lb/>1. ſen.</note>
              <note position="right" xlink:href="note-0248-04a" xlink:label="note-0248-04" xml:id="N290C5" xml:space="preserve">grego. in <lb/>2. ſen.</note>
            </div>
            <p xml:id="N290CD">
              <s xml:id="N290CE" xml:space="preserve">Et ideo aliter reſpondeo ad dubiū po-<lb/>nendo talem concluſionem. </s>
              <s xml:id="N290D3" xml:space="preserve">Aliqua res naturalis <lb/>ponendo minimum naturale poteſt preciſe dura-<lb/>re per inſtans: et ſimiliter non ponendo minimum <lb/>naturale: ſed ponendo angelum poſſe ſubito muta­<lb/>ri de loco ad locum. </s>
              <s xml:id="N290DE" xml:space="preserve">Prima pars huius concluſio­<lb/>nis probatur per argumentum poſt oppoſitum: et <lb/>ſecūda per vltimam eius cõfirmationē. </s>
              <s xml:id="N290E5" xml:space="preserve">Et ſi queras <lb/>vtrum dato /  angelus non poſſet ſubito mutari <lb/>nec ponatur mīmū naturale aliq̇d poſſit durare p̄-<lb/>ciſe per inſtans. </s>
              <s xml:id="N290EE" xml:space="preserve">Reſpondeo /  ſic poſito  ad quã-<lb/>libet formam naturalem coſeruandam in materia               <pb chead="De intenſione et remiſſione formarum" file="0249" n="249"/>               requiratur certa diſpõ cū qua põt ſtare et cuꝫ nulla <lb/>minori põt ſtare. </s>
              <s xml:id="N290FA" xml:space="preserve">Tūc poſito /  in aliquo inſtanti <lb/>ṗmo gñetur forma aq̄ cū illa diſpõe neceſſario req̇­<lb/>ſita ad ↄ̨ſeruationē forme aq̄ in materia et incipiat <lb/>dicta diſpõ corrūpi ꝑ totum ꝑ vltimū eē: ita  aña <lb/>agens bñ approximatū ad agēdū ꝑ totã illã diſpõ­<lb/>nem īpediebat̄̄ ab aliquo in ꝓportiõe equalitatis: <lb/>et iã illud incipiat remoueri ita  nõ tm̄ impediat <lb/>immediate poſt inſtãs / qḋ eſt pñs. </s>
              <s xml:id="N2910B" xml:space="preserve">Quo poſito ſeq̇t̄̄ <lb/>tale agens p̄ciſe durare ꝑ inſtans </s>
              <s xml:id="N29110" xml:space="preserve">Et hic eſt modus <lb/>opinãdi doctoris ſubtilis in .4. ī materia de actio­<lb/>ne accidētiū in euchariſtie ſacramēto. </s>
              <s xml:id="N29117" xml:space="preserve">¶ His poſitꝪ <lb/>rñdendū eſt ad rõnē ante oppoſitū. </s>
              <s xml:id="N2911C" xml:space="preserve">Ad quaꝫ rñdeo <lb/>cõcedēdo añs, et negãdo hanc ↄ̨ñam hec reſiſtentia <lb/>corrūpit̄̄ ſubito ſuo cõtrario: igit̄̄ corrūpitur ab <lb/>agēte infinite tutis. </s>
              <s xml:id="N29125" xml:space="preserve">Et rõ eſt / q2 talis reſiſtētia nõ <lb/>poteſt durare ꝑ tp̄s quatulacū ꝑte talis reſiſtētie <lb/>corrupta. </s>
              <s xml:id="N2912C" xml:space="preserve">Hoc em̄ nõ ideo eſt. </s>
              <s xml:id="N2912F" xml:space="preserve">q2 agēs hꝫ infinitaꝫ ꝓ­<lb/>portionē ad illã reſiſtentiã: ſed q2 illa reſiſtētia non <lb/>nata eſt ſucceſſiue corrumpi. </s>
              <s xml:id="N29136" xml:space="preserve">Imo ̄tūcun parua <lb/>parte corrupta reliqua pars nullo mõ nata eſt re-<lb/>ſiſtere: q2 nullo pacto nata eſt eſſe: cū tunc daret̄̄ mi­<lb/>nus mīmo. </s>
              <s xml:id="N2913F" xml:space="preserve">¶ Ad primã cõfirmationē diſtinguo cõ-<lb/>ſequēs aut intelligis de reſiſtētia cuiꝰ vna pars na­<lb/>ta eſt manere poſt corruptionē alteriꝰ: et ſic cõcedo <lb/>aut de reſiſtētia cuiꝰ nulla pars nata eſt manere ſo­<lb/>litarie, et ſic negatur. </s>
              <s xml:id="N2914A" xml:space="preserve">Mõ ſic eſt in ꝓpoſito. </s>
              <s xml:id="N2914D" xml:space="preserve">Et ſi tu <lb/>arguas de noticia ītuitiua angeli cuius vna pars <lb/>nata eſt manere ſolitarie et tñ illa ſubito corrūpit̄̄ / <lb/>vt ꝓbabat ſecūda ↄ̨firmaiio poſt oppoſitū. </s>
              <s xml:id="N29156" xml:space="preserve">Reſpõ­<lb/>deo /  illud nõ fit a ↄ̈rio corrūpēte et reſiſtentiã ſu-<lb/>perante: ſꝫ fit a ſubita cauſe abſentia </s>
              <s xml:id="N2915D" xml:space="preserve">Et ſi iterū ar­<lb/>guas de forma aq̄ que ſubito corrūpit̄̄ a corruptio­<lb/>ne ſue mīme diſpõnis ipſam cõſeruantis et tamen <lb/>ipſa corr pitur a cõtrario. </s>
              <s xml:id="N29166" xml:space="preserve">Reſpondeo /  illud fit <lb/>ꝓpter ſubitã abſentiã cõſeruantis et nõ ſimpliciter <lb/>ꝓpter actionē ↄ̈rii. </s>
              <s xml:id="N2916D" xml:space="preserve">¶ Ad aliã ↄ̨firmationē concedo <lb/>quod infertur: nec illud eſt incõueniēs de reſiſtētia <lb/>cuius nulla pars nata eſt manere ſolitarie. </s>
              <s xml:id="N29174" xml:space="preserve">Et hec <lb/>de tertio dubio.</s>
            </p>
            <p xml:id="N29179">
              <s xml:id="N2917A" xml:space="preserve">Ad quartū dubiū arguitur /  nõ quia <lb/>ſol põt ꝓducere lume in inſtanti cū nichil ei reſiſtat <lb/>in ꝓducēdu lumine: igit̄̄ creatura põt agere in inſtã­<lb/>ti.               <anchor type="note" xlink:href="note-0249-01" xlink:label="note-0249-01a"/>               </s>
              <s xml:id="N29188" xml:space="preserve">¶ Dices forte negãdo añs et ad ꝓbationē negã-<lb/>do ↄ̨ñam: q2 talis eſt natura rei create  nõ ſufficit <lb/>ſubito agere. </s>
              <s xml:id="N2918F" xml:space="preserve">¶ Sed contra / q2 mīmū naturale in in­<lb/>ſtanti ꝓducitur a re creata: igit̄̄. </s>
              <s xml:id="N29194" xml:space="preserve">Nec valet negare <lb/>tale minimū naturale eo /  ꝓbabiliꝰ ſit nõ ponere <lb/>q2 ſaltē volūtas p̄t velle in inſtãti: et eſt agens crea­<lb/>tū: igitur. </s>
              <s xml:id="N2919D" xml:space="preserve">Añs ꝓbatur: q2 angelus peccauit in prīo <lb/>inſtãti ſui eē: q2 ſi dicas /  omiſit habeo intētū vcꝫ / <lb/> potuit cõmiſiſſe. </s>
              <s xml:id="N291A4" xml:space="preserve">Nõ em̄ precepiſſet deus īpoſſibi­<lb/>le. </s>
              <s xml:id="N291A9" xml:space="preserve">Sꝫ añs pꝫ per illud ioãnis. </s>
              <s xml:id="N291AC" xml:space="preserve">Ab initio ī itate nõ <lb/>ſtetit.               <anchor type="note" xlink:href="note-0249-02" xlink:label="note-0249-02a"/>               </s>
              <s xml:id="N291B6" xml:space="preserve">¶ Dices negãdo añs et ad pūctū ꝓbatõis / qḋ <lb/>conſiſtit in auctoritate: dr̄  intelligit̄̄ illa auctori­<lb/>tas de ſtatu ꝑ tp̄s et nõ ꝑ inſtans.</s>
            </p>
            <div xml:id="N291BD" level="5" n="30" type="float">
              <note position="left" xlink:href="note-0249-01a" xlink:label="note-0249-01" xml:id="N291C1" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0249-02a" xlink:label="note-0249-02" xml:id="N291C7" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N291CD">
              <s xml:id="N291CE" xml:space="preserve">¶ Contra / q2 experiētia docet /  ſi in turri diſtãte ꝑ <lb/>3. aut .4. leucas in aliqua certa hora adequate oſtē­<lb/>datur aliquod corpus luīoſū puta teda aut cãdela <lb/>in eodē tp̄e adequate videt̄̄ ab exiſtentibus ī medio <lb/>illius ſpacii puta in diſtãtia .2. leucaꝝ et ab exiſten­<lb/>tibꝰ in extremo puta in diſtantia .4. leucarū: igitur <lb/>nõ citiꝰ vr̄ a ꝓpīquioribꝰ ꝙ̄ a remotioribꝰ et ꝑ ↄ̨ñs <lb/>nulla ē ibi ſucceſſio ī ꝓducēda tali viſiõe. </s>
              <s xml:id="N291DF" xml:space="preserve">¶ Et cõfir­<lb/>mat̄̄ et ſuppono formã ſubſtãtialē hr̄e mīmã diſpõ­<lb/>nem cū qua põt ſtare ī materia. </s>
              <s xml:id="N291E6" xml:space="preserve">Quo ſuppoſito ca­<lb/>pio paſſū vniformiter tali diſpõe qualificatū et ſit <lb/>agens debite approximatum ad agendum per to-               <cb chead="De intenſione et remiſſione formarum"/>               tum illud paſſum ſit tñ in parte oppoſita ↄ̈riū im-<lb/>pediens totaliter agēs ne agat: ita  totiꝰ potētie <lb/>ad totã reſiſtētiã ſit ꝓportio equalitatis et incipiat <lb/>in inſtãti pñti remoueri illud impediens. </s>
              <s xml:id="N291F6" xml:space="preserve">Quo po-<lb/>ſito argr̄ ſic / forma illius paſſi ſubito corrumpitur / <lb/>igitur alia forma a creatura ſubito gñatur. </s>
              <s xml:id="N291FD" xml:space="preserve">Añs ꝓ­<lb/>batur / q2 īmediate poſt inſtãs pñs aget illud agēs <lb/>ꝑ totū illud paſſū: cū agat et ſit debite approxima­<lb/>tū ad agendū ꝑ totū illud paſſū ex caſu: igit̄̄ ꝑ totū <lb/>illḋ paſſuꝫ īmediate poſt inſtãs / qḋ eſt pñs corrūpi-<lb/>tur aliquid de illa diſpõne: et per ↄ̨ñs cū illa ſit mi­<lb/>nima cū qua põt ſtare: īmediate poſt inſtãs quod ē <lb/>pñs per nullã partē illius paſſi erit aliq̇d illius for­<lb/>me ſubſtãtialis: et per ↄ̨ñs ſubito corrumpit̄̄ / quod <lb/>fuit probandum.</s>
            </p>
            <p xml:id="N29212">
              <s xml:id="N29213" xml:space="preserve">Secundo ad idem argr̄ ſic  hoc theo­<lb/>logice / q2 ſi agēs creatū non poſſet agere in inſtan­<lb/>ti: ſequeret̄̄ beatam ginē nõ fuiſſe verã matrē nr̄i <lb/>redēptoris: ſed ↄ̨ñs eſt fĺm et hereticū: igit̄̄. </s>
              <s xml:id="N2921C" xml:space="preserve">Seque-<lb/>la ꝓbatur / q2 corpus xp̄i fuit organiſatū et ꝓductū <lb/>in inſtãti / vt dicūt oēs doctores theologi ī .3°. / ſꝫ btã <lb/>virgo in tali inſtanti nichil potuit agere: igr̄ nullo <lb/>pacto cõcurrebat ad ꝓductionē talis corporis et ꝑ <lb/>ↄ̨ñs nõ fuit vera mr̄ / qḋ fuit ꝓbandū.               <anchor type="note" xlink:href="note-0249-03" xlink:label="note-0249-03a"/>               </s>
              <s xml:id="N2922E" xml:space="preserve">¶ Dices negã­<lb/>do ↄ̨ñaꝫ: q2 vt dicit phūs in libro de aīalibꝰ: et Aui­<lb/>cenna ṗmo .c. ṗma. f.d. quī a. et de gña: aliū Mulier <lb/>nullo mõ ↄ̨currit actiue ad prolis gñationē: ſꝫ ſolū <lb/>mīſtrat materiã: ̄uis Galienꝰ et medicorū maior <lb/>pars oppoſitū aſtruat. </s>
              <s xml:id="N2923B" xml:space="preserve">¶ Cõtra ſaltē ſequit̄̄ /  ali-<lb/>quãdo btã virgo fuit vel ſaltē aīa eius poſt ſepara­<lb/>tionē a corpore qñ nõ fuit btã: ſꝫ ↄ̨ñs eſt fĺm: igr̄. </s>
              <s xml:id="N29242" xml:space="preserve">Se­<lb/>quela ꝓbat̄̄ / q2 in primo inſtãti ſeꝑatiõis aīe ip̄a nõ <lb/>fuit btã: q2 ꝑ te in illo inſtãti nõ põt ꝓduxiſſe actum <lb/>volūtatꝪ aut ītellectꝰ. </s>
              <s xml:id="N2924B" xml:space="preserve">Fĺitas tñ ↄ̨ñtis ꝓbat̄̄: q2 tūc <lb/>ſequeret̄̄ aliqñ eē aīam nec viatricem nec btãm: nec <lb/>dãpnatã: nec eē in purgatorio / qḋ eſt fĺm. </s>
              <s xml:id="N29252" xml:space="preserve">¶ Dices / <lb/> nõ eſt incõueniēs quod infert̄̄: et ad ꝓbationē fal-<lb/>ſitatis eiꝰ dr̄ /  nõ eſt incõueniēs: nec ↄ̈ ſacrã doctri­<lb/>nã /  detur talis aīa ꝑ inſtãs: ſed incõueniens eſſet <lb/>per tempus:</s>
            </p>
            <div xml:id="N2925D" level="5" n="31" type="float">
              <note position="right" xlink:href="note-0249-03a" xlink:label="note-0249-03" xml:id="N29261" xml:space="preserve">phūs de <lb/>anima. <lb/>Auicē. <lb/>Galienꝰ.</note>
            </div>
            <p xml:id="N2926D">
              <s xml:id="N2926E" xml:space="preserve">Cõtra q2 tūc ſeq̄retur aīam btē virgi-<lb/>nis fuiſſe ꝑ aliquod tēpus ꝑ quod nõ habebat tãtã <lb/>btītudinē ſicut mīmꝰ btūs: ſed ↄ̨ñs eſt fĺm: igr̄. </s>
              <s xml:id="N29275" xml:space="preserve">Seq̄­<lb/>la deducit̄̄: et capio totã btītudinē quã habet beata <lb/>virgo: et ſit vt .10. et capio beatitudinē minimi bea­<lb/>ti et ſit vt .2. / et arguo ſic / beatitudo beate virginis <lb/>ſucceſſiue ꝓducebat̄̄: ergo quando ꝓducebatur ſuc-<lb/>ceſſiue primus gradus et in toto illo tempore ipſa <lb/>erat minus beata ꝙ̄ ille minimꝰ beatus </s>
              <s xml:id="N29284" xml:space="preserve">Probatur / <lb/>quia ille habebat vt .2. ipſa vero vt vnū. </s>
              <s xml:id="N29289" xml:space="preserve">Sed falſi-<lb/>tas ↄ̨ſequentis probatur: quia pari ratione ſeque­<lb/>retur /  chriſtus ſcḋm aīam / hoc eſt aīa eius nõ fuit. <lb/></s>
              <s xml:id="N29291" xml:space="preserve">beata in primo inſtanti ſui eſſe: et  vno tēpore fuit <lb/>beatior ꝙ̄ in altero: ſed vtrū iſtorū eſt manifeſte <lb/>falſum et hereticū: igitur. </s>
              <s xml:id="N29298" xml:space="preserve">Sequela patet / quia per <lb/>te in primo inſtanti ſui eſſe ipſa anima nõ potuit ꝓ­<lb/>ducere beatitudinē: igitur nõ potuit eē beata.</s>
            </p>
            <p xml:id="N2929F">
              <s xml:id="N292A0" xml:space="preserve">¶ Et coufirmatur /  omnis ſucceſſio ꝓuenit aut ra­<lb/>tione reſiſtētie: aut ſucceſſiue approximationis aut <lb/>ſucceſſiue intentionis agētis aut rõne ſucceſſiue di­<lb/>ſpoſitionis: aut ratione libertatis agentis: igitur <lb/>vbi nulla iſtarum cauſarum reperitur ibi non po-<lb/>terit eſſe ſucceſſio: ſed dabilis eſt actio naturalis ī <lb/>qua nulla dictarum cauſarum reperitur: igitur p̄t <lb/>eſſe actio naturalis ſubita. </s>
              <s xml:id="N292B1" xml:space="preserve">Minor ꝓbatur de actu <lb/>intelligendi non habente contrarium naturaliter <lb/>producto. </s>
              <s xml:id="N292B8" xml:space="preserve">In productione enim talis actus nulla <lb/>dictarū cauſarum concurrit.</s>
            </p>
            <pb chead="Quarti Tractatus" file="0250" n="250"/>
            <p xml:id="N292C1">
              <s xml:id="N292C2" xml:space="preserve">In oppoſituꝫ arguitur ſic / quia alias <lb/>ſequeretur /  non velocius poſſet agens infinitum <lb/>ꝓducere aliquē effectū ꝙ̄ agēs finitū poſſit ꝓducere <lb/>eundē: ſꝫ ↄ̨ñs videtur abſurdū: igr̄ probabile ē crea­<lb/>turam nullo pacto poſſe agere in inſtãti. </s>
              <s xml:id="N292CD" xml:space="preserve">Seq̄la pꝫ / <lb/>quia tam agens finitū quã infinitum ꝓduceret ſuū <lb/>effectū in inſtanti</s>
            </p>
            <note position="left" xml:id="N292D4" xml:space="preserve">Hollrot. <lb/>hiberni-<lb/>cus.</note>
            <p xml:id="N292DC">
              <s xml:id="N292DD" xml:space="preserve">Huic dubio reſpondet Hollrot et hi-<lb/>bernicus et q̇ eos ſequunt̄̄ /  nulla creatura põt age­<lb/>re in inſtanti. </s>
              <s xml:id="N292E4" xml:space="preserve">Et mouētur aliq̈bus rõnibꝰ theologi­<lb/>cis quarū precipua eſt hec. </s>
              <s xml:id="N292E9" xml:space="preserve">Si creatura poſſet age-<lb/>re ī inſtãti: ſequeret̄̄ /  homo poſſet naturaliter pec­<lb/>care infinitꝪ pctīs vni certo dato eq̈libꝰ nõ cõicanti­<lb/>bus: ſed ↄ̨ñs eſt impoſſibile: igit̄̄ illud ex quo ſequit̄̄ <lb/></s>
              <s xml:id="N292F3" xml:space="preserve">Sequela probat̄̄ / q2 ſi ſortes põt peccare hoc eſt elice­<lb/><gap/> <lb/>igitur in eē et cõtinuet ſortes illud peccatū ꝑ aliqḋ <lb/>tempus. </s>
              <s xml:id="N292FD" xml:space="preserve">Quo poſito ſic arguit̄̄ ſortes in illo inſtã-<lb/>ti peccat aliquo peccato: et tantum peccat in quoli-<lb/>bet inſtanti tēporis ſequētis ꝑ quod continuat illū <lb/>actū: et ſunt infinita inſtantia in eo: ergo peccat infi­<lb/>nitis peccatis etc. / qḋ fuit probandū. </s>
              <s xml:id="N29308" xml:space="preserve">Hec tñ rõ nõ eſt <lb/>multum efficax / q2 innitit̄̄ falſo fundamēto: puta  <lb/>quelibet ſequēs cõtinuatio et cuiuſlibet gradus illi­<lb/>us actus ſit libera cõtinuatio / qḋ tamē eſt falſuꝫ etc. <lb/></s>
              <s xml:id="N29312" xml:space="preserve">Et ſic ſoluit Adam in prīo hanc rõnem. </s>
              <s xml:id="N29315" xml:space="preserve">Uide hoc <lb/>latius apud theologos.</s>
            </p>
            <p xml:id="N2931A">
              <s xml:id="N2931B" xml:space="preserve">Sit igitur concluſio reſpõſiua ad du­<lb/>bium. </s>
              <s xml:id="N29320" xml:space="preserve">Et ſi ſuſtētabile creaturã in inſtãti poſſe ef­<lb/>ctū producere nullū: nichilominus (meliori iudicio <lb/>ſemper excepto) id ꝓbabile eē exiſtimo nequaquã. <lb/></s>
              <s xml:id="N29328" xml:space="preserve">Prima pars cõcluſiõis ꝓbatur. </s>
              <s xml:id="N2932B" xml:space="preserve">q2 rõnes ad oppo­<lb/>ſitum abſ cõtradictione ſolui pñt: igitur illa opi­<lb/>nio valet ſuſtētari. </s>
              <s xml:id="N29332" xml:space="preserve">Añs ꝓbatur ſoluēdo rõnes pro <lb/>parte oppoſita. </s>
              <s xml:id="N29337" xml:space="preserve">Secunda probatur rationibꝰ ante <lb/>oppoſitum factis.</s>
            </p>
            <p xml:id="N2933C">
              <s xml:id="N2933D" xml:space="preserve">Ab primam rõnem ante oppoſitū di-<lb/>ctum eſt / ibi vſ ad vltimã replicã ad quã poteſt di-<lb/>ci negãdo /  illud corpus luminoſum eque cito vi-<lb/>deatur a remotiori ſicut a ꝓpinquiori. </s>
              <s xml:id="N29346" xml:space="preserve">et cum addu­<lb/>citur experientia dicitur /  illa eſt fallax. </s>
              <s xml:id="N2934B" xml:space="preserve">Quãuis <lb/>em̄ ita appareat: non tamen ita eſt. </s>
              <s xml:id="N29350" xml:space="preserve">¶ Ad confirma­<lb/>tionem dico primo admiſſo caſu et ſuppoſitio nego / <lb/> īmediate poſt inſtans / qḋ eſt pñs illud agēs agat <lb/>in totū / q2 nullū agēs naturali p̄t incipere agere eq̈ <lb/>cito ī propriū ſicut in remotū. </s>
              <s xml:id="N2935B" xml:space="preserve">Quãtūcū eī agēs <lb/>approximetur alicui paſſo ꝑ quod debeat agere ci­<lb/>tius aget in ṗmã medietatē ꝙ̄ in ſcḋam. </s>
              <s xml:id="N29362" xml:space="preserve">Dico ſcḋo <lb/>admittendo /  agens naturale põt incipere eq̄ cito <lb/>agere per totū paſſum admiſſo caſu cum ſuppoſi-<lb/>to: negando añs: et cū probatur nego aſſumptū, et <lb/>ad ꝓbationem cõcedo /  eſt debite approximatum <lb/>ad agendū ꝑ totū tñ non agit ꝑ totum q2 īmediate <lb/>poſt inſtaus / qḋ eſt pñs nõ agit in pūctū in extremo <lb/>remotiori q2 immediate poſt hoc reſtētia illiꝰ pūcti <lb/>habebit ꝓportionē maioris ineq̈litatꝪ ad totaꝫ po­<lb/>tentiam agētis: q2 aña habuit et nõ ſubito illã ꝑdit <lb/></s>
              <s xml:id="N29378" xml:space="preserve">QꝪ aña habuit patet / q2 aña tota reſiſtētia puncti <lb/>in extremo ꝓpīquiori habuit ꝓportionē eq̈litatis <lb/>ad poñam vel maioris īeq̈litatꝪ (nõ ē cura) q2 alias <lb/>fuiſſꝫ actio ad illū pūctū / qḋ ē ↄ̈ caſū: igr̄ aña reſiſtē­<lb/>tia pūcti ī remotiori extremo habuit ꝓportionem <lb/>maioris inequalitatis / quod fuit probandum.</s>
            </p>
            <p xml:id="N29385">
              <s xml:id="N29386" xml:space="preserve">Ad ſecūdam rõnem reſponſuꝫ eſt ibi <lb/>vſ ad p̄mã replicã: ad quã dicēdū ē negãdo ſeq̄lã <lb/></s>
              <s xml:id="N2938C" xml:space="preserve">Et rõ eſt / q2 aduerſariꝰ opiniabit̄̄: nec aīaꝫ btē gīs               <cb chead="Capi. Tertium"/>               nec alicuius alteriꝰ btī ↄ̨currere actiue ad ꝓductio­<lb/>nē ſue btītudinis imo deꝰ ſe ſolo ꝓducit illã btītu-<lb/>dinē: et ꝑ ↄ̨ñs põt illã in īſtãti ꝓducere cū ſit agēs in­<lb/>finitū. </s>
              <s xml:id="N29398" xml:space="preserve">Hec em̄ fuit imaginatio aliq̊rū theologorū. <lb/></s>
              <s xml:id="N2939C" xml:space="preserve">Si o teneat̄̄ /  deꝰ nõ põt ſe ſolo ꝓducere actū vo­<lb/>lūtatis aut ītellectꝰ vt imaginat̄̄ hollrot: et de alia <lb/>co: tunc diſtinguēdū eſt /  creatura poſſit agere in ī­<lb/>ſtanti aut cū adiutorio infinito: et ſic ↄ̨cedit̄̄ aut ad-<lb/>iuta ſolū finite: et ſic negatur. </s>
              <s xml:id="N293A7" xml:space="preserve">¶ Ad ↄ̨firmationē ſo­<lb/>lutionē q̄re.               <anchor type="note" xlink:href="note-0250-01" xlink:label="note-0250-01a"/>               </s>
              <s xml:id="N293B1" xml:space="preserve">Nõ em̄ video vñ poſſit talis ſucceſſio ꝓ­<lb/>cedere niſi dicas cuꝫ doctore ſubtili in .2°. ſen. /  eſt <lb/>aliqua reſiſtētia intrīſeca: et talis reſiſtētia intrinſe­<lb/>ca eſt finitas ipſius agētis creati cui ꝓpter ſuã fini­<lb/>tatē repugnat ſubito aliquid efficere. </s>
              <s xml:id="N293BC" xml:space="preserve">Et ſcḋm hoc <lb/>cõcedēdū eſt /  agens creatū reſiſtit ſibi ipſi. </s>
              <s xml:id="N293C1" xml:space="preserve">Et iſto <lb/>mõ iam dabitur aliqua dictarū cauſarū ſucceſſio-<lb/>nis puta reſiſtētia. </s>
              <s xml:id="N293C8" xml:space="preserve">Nec aliter potuit doctor ſubti-<lb/>lis ſoluere rõnē pḣi ꝓbantis graue in vacuo ſubito <lb/>moueri niſi ponēdo hãc intrīſecã reſiſtentiã. </s>
              <s xml:id="N293CF" xml:space="preserve">Et cõ-<lb/>formiṫ ↄ̨cedēdū eſt /  eq̄ velociṫ ꝓportionabilr̄ ſicut <lb/>tus agētis finiti auget̄̄ et intēdit̄̄ reſiſtētia intrin-<lb/>ſeca eiuſdē diminuit̄̄.               <anchor type="note" xlink:href="note-0250-02" xlink:label="note-0250-02a"/>               </s>
              <s xml:id="N293DD" xml:space="preserve">Ex q̊ ſequit̄̄ vlteriꝰ /  ſi effice-<lb/>retur talis tus infinita: iã nullo pacto eſſet in tali <lb/>agēte reſiſtētia intrīſeca cū nichil aliud ſit illa reſi­<lb/>ſtētia intrinſeca ꝙ̄ ip̄m agēs finitaꝫ habens actiui-<lb/>tatē. </s>
              <s xml:id="N293E8" xml:space="preserve">Supponit em̄ hic terminꝰ reſiſtētia intrinſeca <lb/>ꝓ aliquod agēte cõnotando ip̄m habere adequate fi­<lb/>nita tutē agendi. </s>
              <s xml:id="N293EF" xml:space="preserve">Quare repugnat deo cū intrīſe­<lb/>ca reſiſtentia aliq̇d efficere. </s>
              <s xml:id="N293F4" xml:space="preserve">Et ſi nõ placeat hec ītrī­<lb/>ſeca reſiſtētia q̄ras aliaꝫ cãm. </s>
              <s xml:id="N293F9" xml:space="preserve">¶ Sed q2 dubiuꝫ ad <lb/>vtrã partē defenſat̄̄ ſoluende ſunt rões in oppoſi­<lb/>tū adducte. </s>
              <s xml:id="N29400" xml:space="preserve">Ad rõnē ī oppoſitū rñdeo cõcedēdo ali­<lb/>quē effectū non poſſe velocius ꝓduci ab agēte infini­<lb/>to cuiuſmodi eſt deꝰ ꝙ̄ ab agente finito cuiuſmõi eſt <lb/>creatura: nec illud ē incõueniēs. </s>
              <s xml:id="N29409" xml:space="preserve">Nõ eī ex hoc ſeq̇tur <lb/>deū et creaturã eē equalis tutꝪ actiue. </s>
              <s xml:id="N2940E" xml:space="preserve">Nã iſta ↄ̨ña <lb/>nichil valet iſta duo agētia equa cito ꝓducūt eūdē <lb/>effectū vel ſiĺem: igr̄ ſūt eq̈lis actiue. </s>
              <s xml:id="N29415" xml:space="preserve">Sꝫ oꝫ ſic argu-<lb/>mētari cū eq̈li reſiſtētia eq̄ velociter ceterꝪ ꝑibꝰ iſta <lb/>agētia ſiĺe effectū ꝓducūt: igr̄ ſūt eq̈lis virtutꝪ actīe <lb/>vbi eī nulla ē reſiſtētia: ꝑfectionē actīe tutꝪ ſubita <lb/>ꝓductio mīme arguit. </s>
              <s xml:id="N29420" xml:space="preserve">Ad aliã rõnē hollrot et hiber­<lb/>nici rñſū ē aliq̈ĺr in corꝑe dubii. </s>
              <s xml:id="N29425" xml:space="preserve">Et hec de .4. dubio</s>
            </p>
            <div xml:id="N29428" level="5" n="32" type="float">
              <note position="right" xlink:href="note-0250-01a" xlink:label="note-0250-01" xml:id="N2942C" xml:space="preserve">Reſiſten-<lb/>tia inttī-<lb/>ſeca.</note>
              <note position="right" xlink:href="note-0250-02a" xlink:label="note-0250-02" xml:id="N29436" xml:space="preserve">Correla.</note>
            </div>
            <p xml:id="N2943C">
              <s xml:id="N2943D" xml:space="preserve">Ad quintū dubium arguitur ad par-<lb/>tē negatiuã / q2 ſi deꝰ poſſet ꝓducē michaelē īmedia­<lb/>te poſt gabrielē maxīe eēt ꝓducēdo gabrielē ꝑ ṗmū <lb/>īſtãs eē et michaelē ꝑ vltimū nõ eē: ſꝫ ↄ̨ñs ē fĺm / igr̄ il­<lb/>lud ex q̊ ſeq̇tur. </s>
              <s xml:id="N29448" xml:space="preserve">Seq̄la pꝫ: ſꝫ fĺitas ↄ̨ñtꝪ oñdit̄̄: q2 bñ <lb/>ſequit̄̄ michael ꝓducet̄̄: g̊ ſucceſſiue vel ſubito: ſꝫ nõ <lb/>ſucceſſiue cū nõ hēat partes: igr̄ ſubito et ꝑ ↄ̨ñs in in­<lb/>ſtanti: ſꝫ ↄ̨ñs ē fĺm / q2 erit añ qḋlꝫ inſtãs futurū: et nõ <lb/>ꝓducit̄̄ ī īſtãti pñti. </s>
              <s xml:id="N29453" xml:space="preserve">Itē oē qḋ ꝓducit̄̄ qñ tp̄s ē ꝓducit̄̄ <lb/>in tꝑe vel in īſtãti: igr̄ ſi michael ſic ꝓducat̄̄ poſt ga­<lb/>brielē ip̄e ꝓducet̄̄ in tꝑe vel ī inſtãti: ſꝫ nõ ī tꝑe: g̊ in ī-<lb/>ſtãti / qḋ īprobatū ē.               <anchor type="note" xlink:href="note-0250-03" xlink:label="note-0250-03a"/>               </s>
              <s xml:id="N29461" xml:space="preserve">¶ Dices cõcedēdo ſeq̄lã: et negã­<lb/>do falſitatē ↄ̨ñtis: et ad punctū probationis nego <lb/>iſtã ↄ̨ñam ꝓducit̄̄ ſubito: ergo in inſtãti: ſicut aliq̇d <lb/>diuiditur ſubito hoc eſt nõ ꝑ partē ante partē tñ in <lb/>nullo inſtanti: ſꝫ ante qḋlibet inſtãs futurū diuidet̄̄ <lb/>et erit diuiſū vt caſu poſito /  vniformiter in hora <lb/>futura adeq̈te diuidat̄̄ aliqḋ pedale / tunc ſuꝑficies <lb/>ſiue linea īitians tale pedale ſubito diuidet̄̄ et ī nul­<lb/>lo inſtãti: ſꝫ añ qḋlibet inſtans futurū erit diuiſa. <lb/></s>
              <s xml:id="N29475" xml:space="preserve">Nec valet iſta ↄ̨ña aliquid ꝓducitur: ergo illud ꝓ-<lb/>ducitur ſucceſſiue vel in inſtãti. </s>
              <s xml:id="N2947A" xml:space="preserve">Ad aliud nego /  nõ <lb/>producitur in tempore licet inadequate tamen per <lb/>nullum tempus producitur / quia eſt ante quodlibet <lb/>inſtans illius temporis productus.</s>
            </p>
            <div xml:id="N29483" level="5" n="33" type="float">
              <note position="right" xlink:href="note-0250-03a" xlink:label="note-0250-03" xml:id="N29487" xml:space="preserve">Dicitur.</note>
            </div>
            <pb chead="De intenſione et remiſſione formarum" file="0251" n="251"/>
            <note position="left" xml:id="N29491" xml:space="preserve">Correĺ.</note>
            <p xml:id="N29495">
              <s xml:id="N29496" xml:space="preserve">¶ Ex quo ſeq̇tur /  michael põt eē et tamē in nullo ī-<lb/>ſtanti. </s>
              <s xml:id="N2949B" xml:space="preserve">Hoc eſt iſta eſt poſſibilis michael erit et ī nul­<lb/>lo inſtanti erit. </s>
              <s xml:id="N294A0" xml:space="preserve">Probat̄̄. </s>
              <s xml:id="N294A3" xml:space="preserve">q2 ex q̊ michael erit ante <lb/>quodlibet inſtãs futurū volo /  deus ꝓducat illuꝫ <lb/>immediate poſt hoc: et corrūpat illū añ qḋlibet in-<lb/>ſtans futurū. </s>
              <s xml:id="N294AC" xml:space="preserve">Quo poſito patet correlarium.</s>
            </p>
            <p xml:id="N294AF">
              <s xml:id="N294B0" xml:space="preserve">¶ Sed cõtra q2 ſi hoc eſſet verū ſeq̄ret̄̄ /  deꝰ poſſet <lb/>ꝓducere .3. angelos vnū immediate poſt aliū: ſꝫ ↄ̨ñs <lb/>eſt flm̄ igit̄̄. </s>
              <s xml:id="N294B7" xml:space="preserve">Seq̄la ꝓbatur / q2 ſi deꝰ põt ꝓducere vnū <lb/>angelū: in inſtanti pñti: et vnū aliū immediate poſt <lb/>inſtans / qḋ eſt pñs: pari rõe poterit ꝓducere vnū an­<lb/>gelū in inſtãti qḋ eſt pñs et vnū aliū īmediate añ in-<lb/>ſtans quod eſt preſens. </s>
              <s xml:id="N294C2" xml:space="preserve">Quo habito iã poterit pro­<lb/>ducere .3. vnū immediate poſt aliuꝫ. </s>
              <s xml:id="N294C7" xml:space="preserve">vnū vcꝫ īmedia­<lb/>te ante inſtans quod eſt preſens: et aliū in inſtanti <lb/>preſenti et aliū immediate poſt inſtans quod eſt p̄-<lb/>ſens: igitur aſſumptū verm.               <anchor type="note" xlink:href="note-0251-01" xlink:label="note-0251-01a"/>               </s>
              <s xml:id="N294D5" xml:space="preserve">¶ Dices ſicut dicenduꝫ <lb/>eſt concedendo quod infert̄̄: nec illud eſt incõueniēs <lb/>               <anchor type="note" xlink:href="note-0251-02" xlink:label="note-0251-02a"/>               </s>
              <s xml:id="N294E1" xml:space="preserve">¶ Ex quo ſeq̇tur /  angelus ꝓductus īmediate ante <lb/>inſtans quod eſt pñs creatur: et tamē nõ incipit eſſe <lb/></s>
              <s xml:id="N294E7" xml:space="preserve">Patet / q2 nec incipit eē per primum inſtans ſui eē: <lb/>nec per vltimū non eē: igitur. </s>
              <s xml:id="N294EC" xml:space="preserve">Antecedens probatur / <lb/>quia non incipit per primū eē cuꝫ nullū ſit primum <lb/>inſtans ſui eē: quia maxime eēt inſtans quod ē pre­<lb/>ſens ſed hoc nõ: cum in illo ſit et ante illud fuerit ex <lb/>caſu: nec incipit per vltimū non eē cum nullū ſit da­<lb/>bile in quo nõ ſit: et immediate poſt quod erit.               <anchor type="note" xlink:href="note-0251-03" xlink:label="note-0251-03a"/>               </s>
              <s xml:id="N294FE" xml:space="preserve">¶ Se­<lb/>quitur ſecūdo /  licet ſimpliciter nõ incipiat eē: inci­<lb/>pit tamē eē in aliquo inſtanti puta in īſtanti quod <lb/>eſt preſens. </s>
              <s xml:id="N29507" xml:space="preserve">Patet intuenti.</s>
            </p>
            <div xml:id="N2950A" level="5" n="34" type="float">
              <note position="left" xlink:href="note-0251-01a" xlink:label="note-0251-01" xml:id="N2950E" xml:space="preserve">Dicitur.</note>
              <note position="left" xlink:href="note-0251-02a" xlink:label="note-0251-02" xml:id="N29514" xml:space="preserve">Correla.</note>
              <note position="left" xlink:href="note-0251-03a" xlink:label="note-0251-03" xml:id="N2951A" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N29520">
              <s xml:id="N29521" xml:space="preserve">Sed contra / quia tunc ſequeretur /  <lb/>angelus īmediate ante inſtans quod eſt preſens ꝓ­<lb/>ductus nec incipiet eſſe in tempore nec in inſtãti: ſed <lb/>cõſequēs eſt falſum: igit̄̄. </s>
              <s xml:id="N2952A" xml:space="preserve">Falſitas ↄ̨ñtis patet / quia <lb/>tunc aliq̇d eēt quod ī nullo inſtãti eēt / qḋ eſt impoſ-<lb/>ſibile. </s>
              <s xml:id="N29531" xml:space="preserve">Seq̄la tamē probatur: et pono /  angelus ꝓ­<lb/>ductus immediate ante inſtans quod eſt pñs deſi-<lb/>nat eſſe per primū inſtans nõ eē in inſtãti quod eſt <lb/>pñs. </s>
              <s xml:id="N2953A" xml:space="preserve">Quo poſitio iam ille angelus eſt productus <lb/>et tñ nullo modo incipit aut incepit eē nec in tempo­<lb/>re nec in inſtanti / quod fuit ꝓbandum.</s>
            </p>
            <p xml:id="N29541">
              <s xml:id="N29542" xml:space="preserve">In oppoſitū tamē arguitur ſic. </s>
              <s xml:id="N29545" xml:space="preserve">Omē <lb/>illud eſt deo poſſibile quod nõ implicat ↄ̨tradictio­<lb/>nem: ſed .2. angelos aut .3. vnū immediate poſt aliã <lb/>ꝓducere nõ implicat ↄ̨tradictionē: igit̄̄. </s>
              <s xml:id="N2954E" xml:space="preserve">Maior eſt <lb/>nota: et minor ꝓbatur rñdendo ad rõnes pro par­<lb/>te oppoſita nitētes inferre impoſſibile.</s>
            </p>
            <p xml:id="N29555">
              <s xml:id="N29556" xml:space="preserve">Pro ſolutiõe dubii breuiter pono du­<lb/>as cõcluſiones.               <anchor type="note" xlink:href="note-0251-04" xlink:label="note-0251-04a"/>               </s>
              <s xml:id="N29560" xml:space="preserve">¶ Prima cõcluſio. </s>
              <s xml:id="N29563" xml:space="preserve">Poſſibile ē deū <lb/>producere duos angelos vnū immediate poſt alte-<lb/>rum, vnū vcꝫ per põnem de pñti et alterum ꝑ remo-<lb/>tionem. </s>
              <s xml:id="N2956C" xml:space="preserve">Hanc cõcluſionē nõ aliter ꝓbo ꝙ̄ ratione in <lb/>oppoſitū facta.               <anchor type="note" xlink:href="note-0251-05" xlink:label="note-0251-05a"/>               </s>
              <s xml:id="N29576" xml:space="preserve">¶ Secūda concluſio. </s>
              <s xml:id="N29579" xml:space="preserve">Poſſibile eſt <lb/>deū ꝓducere .3. angelos vnū īmediate poſt aliū vnū <lb/>vcꝫ in īſtãti pñti: et alterū īmediate añ inſtãs qḋ eſt <lb/>pñs: et tertiū immediate poſt inſtãs qḋ eſt preſens <lb/></s>
              <s xml:id="N29583" xml:space="preserve">Probatur nec concluſio / q2 ſicut deus põt ꝓducere <lb/>vnū angelū in īſtãti qñ eſt pñs: et vnū īmediate poſt <lb/>inſtans qḋ eſt pñs: ita põt ꝓducere vnū in inſtãti qḋ <lb/>eſt pñs: et alium īmediate añ inſtãs qḋ eſt pñs. </s>
              <s xml:id="N2958C" xml:space="preserve">Quo <lb/>poſito ineē pꝫ itas ↄ̨cluſiõis.               <anchor type="note" xlink:href="note-0251-06" xlink:label="note-0251-06a"/>               </s>
              <s xml:id="N29596" xml:space="preserve">¶ Ex his ſeq̇tur ṗmo / <lb/> poſſibile eſt aliquid fore qḋ mõ non eſt: et tñ nū̄ <lb/>incipere eē. </s>
              <s xml:id="N2959D" xml:space="preserve">Patet poſito /  vnus angelus īmedia­<lb/>te añ īſtãs terminatiuū hore ꝓducat̄̄. </s>
              <s xml:id="N295A2" xml:space="preserve">tunc manife-<lb/>ſtum eſt /  talis angelus nec incipit nec incipiet eē. <lb/>               <anchor type="note" xlink:href="note-0251-07" xlink:label="note-0251-07a"/>               </s>
              <s xml:id="N295AE" xml:space="preserve">¶ Sequitur ſcḋo /  poſſibile eſt aliquid quod mo-<lb/>do non eſt incipere eē: et poſtea nõ eē ꝑ tempus nec               <cb chead="De intenſione et remiſſione formarum"/>               per inſtans. </s>
              <s xml:id="N295B6" xml:space="preserve">Patet de tertio angelo ponēdo /  ꝓ-<lb/>ducatur īmediate poſt inſtãs qḋ eſt pñs et corrūpat̄̄ <lb/>ante qḋlibet inſtãs futurū. </s>
              <s xml:id="N295BD" xml:space="preserve">Quo poſito ſequit̄̄ veri­<lb/>tas correlarii.               <anchor type="note" xlink:href="note-0251-08" xlink:label="note-0251-08a"/>               </s>
              <s xml:id="N295C7" xml:space="preserve">¶ Sequitur tertio /  aliquid erit qḋ <lb/>modo nõ eſt: et tamen ipſum nõ incipit nec incipiet <lb/>eſſe nichilominus ipſum deſinet eē. </s>
              <s xml:id="N295CE" xml:space="preserve">Probatur cor-<lb/>relarium ponēdo /  īmediate ante inſtans termīa­<lb/>tiuū hore future ꝓducat deus b. angelum: et corrum­<lb/>pat illū in inſtanti terminatiuo ꝑ primum non eſſe <lb/></s>
              <s xml:id="N295D8" xml:space="preserve">Quo poſito ſequitur propoſitum.               <anchor type="note" xlink:href="note-0251-09" xlink:label="note-0251-09a"/>               </s>
              <s xml:id="N295E0" xml:space="preserve">¶ Sequit̄̄ quar­<lb/>to /  aliquid incipiet eē et poſt modum nõ erit: et tñ <lb/>nun̄ deſinet eē. </s>
              <s xml:id="N295E7" xml:space="preserve">Probat̄̄. ponēdo /  īmediate poſt <lb/>inſtans quod eſt pñs ꝓducat deus c. angelū et cor-<lb/>rumpat illū ante qḋlibet inſtãs futurū. </s>
              <s xml:id="N295EE" xml:space="preserve">Quo poſi-<lb/>to habetur itas correlarii. </s>
              <s xml:id="N295F3" xml:space="preserve">¶ Tu tñ aduerte /  nõ­<lb/>nulli non admittūt caſum iſtius quarti correlarii. <lb/>               <anchor type="note" xlink:href="note-0251-10" xlink:label="note-0251-10a"/>               </s>
              <s xml:id="N295FF" xml:space="preserve">Nec memini me legiſſe aliquē dempto Paulo vene­<lb/>to q̇ in .4. dubio ſue quadrature capite .38°. in ṗmo <lb/>correlario ſcḋe ↄ̨cluſionis in ꝓpria forma illud ad­<lb/>mittit et cõcedit. </s>
              <s xml:id="N29608" xml:space="preserve">Et ſic pꝫ rñſio ad dubium</s>
            </p>
            <div xml:id="N2960B" level="5" n="35" type="float">
              <note position="left" xlink:href="note-0251-04a" xlink:label="note-0251-04" xml:id="N2960F" xml:space="preserve">1. conclu.</note>
              <note position="left" xlink:href="note-0251-05a" xlink:label="note-0251-05" xml:id="N29615" xml:space="preserve">2. conclu.</note>
              <note position="left" xlink:href="note-0251-06a" xlink:label="note-0251-06" xml:id="N2961B" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0251-07a" xlink:label="note-0251-07" xml:id="N29621" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0251-08a" xlink:label="note-0251-08" xml:id="N29627" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0251-09a" xlink:label="note-0251-09" xml:id="N2962D" xml:space="preserve">4. correĺ.</note>
              <note position="right" xlink:href="note-0251-10a" xlink:label="note-0251-10" xml:id="N29633" xml:space="preserve">Paulus <lb/>venetus ī <lb/>4. du. c. <lb/>38°.</note>
            </div>
            <p xml:id="N2963F">
              <s xml:id="N29640" xml:space="preserve">Ad rationem ante oppoſitū reſponſū <lb/>eſt vſ ad vltimã replicã: ad quã reſpondeo conce­<lb/>dendo qḋ infertur vt iam cõceſſum eſt: et ad proba-<lb/>tionem falſitatꝪ ↄ̨ñtis concedo quod infertur: et ne­<lb/>go /  illud ſit impoſſibile. </s>
              <s xml:id="N2964B" xml:space="preserve">Et hoc de dubio .5.</s>
            </p>
            <p xml:id="N2964E">
              <s xml:id="N2964F" xml:space="preserve">¶ Concluſio reſponſiua ad queſitū patet ex 2.3.4. <lb/>notabilibus.</s>
            </p>
            <p xml:id="N29654">
              <s xml:id="N29655" xml:space="preserve">Ad rões ante oppoſitū q̄ſtiõis. </s>
              <s xml:id="N29658" xml:space="preserve">Ad pri­<lb/>mã rñdeo negando ſequelã vt bene probat repli-<lb/>ca. </s>
              <s xml:id="N2965F" xml:space="preserve">Dico tamē /  ſi in ſubiecto in quo fiet intēſio q̈li­<lb/>tatis ſit ſuum cõtrariū ipſa intendit̄̄ ꝑ depuratio­<lb/>nem a cõtrario: ſꝫ nõ preciſe ſed cum hoc per addi-<lb/>tionem gradus ad gradum, aut acquiſitionē ꝑfe-<lb/>ctioris eē ſcḋm beatum Thomã etc. </s>
              <s xml:id="N2966A" xml:space="preserve">Et per hoc patꝫ <lb/>reſponſio ad ↄ̨firmationē: nõ eī ſcḋm illam opinio­<lb/>nē intēdi ē preciſe minꝰ ꝑmiſceri ſuo ↄ̈rio: ſꝫ cū hoc <lb/>requiritur aliquid aliud / vt dictum eſt.</s>
            </p>
            <p xml:id="N29673">
              <s xml:id="N29674" xml:space="preserve">Ad ſecundam rationem cõcedendo ſe­<lb/>quelam: et nego falſitatem ↄ̨ñtis: et ad probationē <lb/>nego ſeq̄lam: et cum probat̄̄ admiſſo caſu cum ſup-<lb/>poſito: nego ↄ̨ſequentiam. </s>
              <s xml:id="N2967D" xml:space="preserve">Et ratio eſt quia ad hoc <lb/> aliquid ſit infinite perfectionis nõ ſufficit / qḋ ibi <lb/>dicitur: ſed cum hoc requiritur /  cõtineat omnē ꝑ-<lb/>fectionē poſſibile. </s>
              <s xml:id="N29686" xml:space="preserve">¶ Ad ↄ̨firmationeꝫ rñdeo /  eſto <lb/> dabilis ſit qualitas nullius intenſionis: non ta-<lb/>men propter hoc ſequitur /  forma non intendatur <lb/>per additionem gradus ad gradum. </s>
              <s xml:id="N2968F" xml:space="preserve">¶ Ad aliḋ di­<lb/>co /  phūs intelligit dictū ſuum de dimēſione ſub­<lb/>ſtantie compoſite ex materia et forma.</s>
            </p>
            <p xml:id="N29696">
              <s xml:id="N29697" xml:space="preserve">Ad tertiam rationē reſponſum eſt / ibi <lb/>vſ ad vltimã replicã: ad quã rñdeo cõcedendo qḋ <lb/>infertur: et dico /  infinita ꝓducētia ſunt vna cauſa <lb/>particularis. </s>
              <s xml:id="N296A0" xml:space="preserve">Accipitur em̄ cauſa collectiue. </s>
              <s xml:id="N296A3" xml:space="preserve">¶ Ad <lb/>primã confirmationē reſponſnm eſt / ibi vſ ad vlti­<lb/>mã replicaꝫ: ad quã rñdeo concedendo qḋ infertur: <lb/>et nego /  ꝓpterea lumīoſum nulliꝰ ſit virtutis in <lb/>conſeruãdo ſuū lumē ſꝫ ideo nõ cõſeruat vt ꝑfectius <lb/>ꝓducat. </s>
              <s xml:id="N296B0" xml:space="preserve">¶ Ad ſecūdã cõfirmationē patet ſolutio ex <lb/>.8. correlario burlei tertii notabilis.</s>
            </p>
            <p xml:id="N296B5">
              <s xml:id="N296B6" xml:space="preserve">Ad quartam rationem reſpõſū eſt / <lb/>ibi vſ ad vltimam replicam ad quam reſpondeo <lb/>concedendo quod infertur: et negando falſitatem <lb/>conſequentis et cum probatur ↄ̨cedo /  virtus crea­<lb/>ta et finita poteſt producere infinita in tꝑe finito qñ <lb/>ad ꝓductionē vniꝰ req̇ritur infinitorum productio <lb/></s>
              <s xml:id="N296C4" xml:space="preserve"><pb chead="Quarti Tractatus" file="0252" n="252"/>               ¶ Ad confirmationem reſpondeo negando ſeque-<lb/>lam: et ad probationē cõcedo antecedēs: et nego cõ-<lb/>ſequentiam: quēadmodū negant nominales de al­<lb/>bedine vbi eſt plus de forma ꝙ̄ in altera: et ad īpro­<lb/>bationē vltimã concedo / qḋ infertur ſicut concedūt <lb/>alie due opiniones. </s>
              <s xml:id="N296D5" xml:space="preserve">¶ Ad ſecūdam confirmationeꝫ <lb/>dico primo negando ſequelã et ad ꝓbationē nõ ad­<lb/>mitto caſum: q2 albedo non poteſt eſſe ſine aliquo <lb/>eſſe. </s>
              <s xml:id="N296DE" xml:space="preserve">Dico ſcḋo concedendo quod infertur: nec illud <lb/>eſt inconueniens. </s>
              <s xml:id="N296E3" xml:space="preserve">Et hec de q̄ſtiõe et capite ſcḋo.</s>
            </p>
          </div>
          <div xml:id="N296E6" level="4" n="3" type="chapter" type-free="capitulum">
            <head xml:id="N296EB" xml:space="preserve">Caput .3.4. tractatus inquireas diſpu­<lb/>tatiue. An qualitates contrarie ſe com-<lb/>patiantur.</head>
            <p xml:id="N296F2">
              <s xml:id="N296F3" xml:space="preserve">QUeritur vtrum forme contra-<lb/>rie ſe inuicē compatiantur ſecundum idē <lb/>ſubiectum adequate.</s>
            </p>
            <p xml:id="N296FA">
              <s xml:id="N296FB" xml:space="preserve">Et arguitur primo /  non auctoritate <lb/>beati Auguſtini in libro enchiridion capite .17. di-<lb/>centis. </s>
              <s xml:id="N29702" xml:space="preserve">Nullus cibus ſimul dulcis eſt et amarꝰ: nul­<lb/>lum corpus vbi albū ibi nigrū eſt.               <anchor type="note" xlink:href="note-0252-01" xlink:label="note-0252-01a"/>               </s>
              <s xml:id="N2970C" xml:space="preserve">Et exemplicat de <lb/>aliis contrariis volēs ꝓbare contraria eidē ineſſe <lb/>non poſſe: igitur de intētione beati Augu. eſt cõtra­<lb/>ria ſe compari mīme. </s>
              <s xml:id="N29715" xml:space="preserve">¶ Secundo auctoritate phi-<lb/>loſophi in predicamēto ̄titatis dicentis. </s>
              <s xml:id="N2971A" xml:space="preserve">Nichil <lb/>eſt qḋ videatur ſimul contraria ſuſcipere. </s>
              <s xml:id="N2971F" xml:space="preserve">Et ꝑ hoc <lb/>vult probare /  cõtraria nõ poſſunt ſimul eidē ineē: <lb/>et exēplificat de albo et nigro: igitur illud eſt de mē­<lb/>te eius. </s>
              <s xml:id="N29728" xml:space="preserve">¶ Tertio auctoritate eiuſdem philoſophi <lb/>primo phiſicorum tex. 9.20. / vbi dicit cõtra anaxa-<lb/>gorã ponētem vnum cõtrarium fieri ex altero:  cõ­<lb/>traria poſſunt eſſe in eodem in potentia: ſed non in <lb/>actu ſimul: igitur illud eſt de intēſione philoſophi. <lb/>               <anchor type="note" xlink:href="note-0252-02" xlink:label="note-0252-02a"/>               </s>
              <s xml:id="N2973A" xml:space="preserve">¶ Dtces et bene ad omnes has auctoritates diſtin­<lb/>guendo /  cõtraria non poſſunt eſſe ſimul in eodem <lb/>aut capiēdo ly cõtraria primo intētionaliter et ſimi­<lb/>liter ly eſſe in eodē: et ſic negatur. </s>
              <s xml:id="N29743" xml:space="preserve">aut ſecunde inten­<lb/>tionaliter pro terminis cõtrariis et predicari acci­<lb/>dentaliter: et ſic cõcedo contraria nõ poſſe eſſe natu­<lb/>raliter in eodē ſubiecto. </s>
              <s xml:id="N2974C" xml:space="preserve">Quod beatus Aug. ſubti-<lb/>liter innuit cū inquit. </s>
              <s xml:id="N29751" xml:space="preserve">Nullum corpus vbi eſt album <lb/>ibi nigrū eſt. </s>
              <s xml:id="N29756" xml:space="preserve">Et hec eſt intētio eius. </s>
              <s xml:id="N29759" xml:space="preserve">Similiter phi-<lb/>loſophus in predicamēto quantitatis loquitur de <lb/>contrarietate ſecundo intentionaliter. </s>
              <s xml:id="N29760" xml:space="preserve">Uult em̄ lo­<lb/>co preallegato probare /  magnum et paruum nõ <lb/>ſunt termini contrarii: dicens /  termini contrarii <lb/>non poſſunt ſimul de eodem verificari: paruum ve-<lb/>ro et magnum de eo verificãtur. </s>
              <s xml:id="N2976B" xml:space="preserve">Et ſic intelligitur <lb/>eius auctoritas vbicun de hac materia loquitur.</s>
            </p>
            <div xml:id="N29770" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0252-01a" xlink:label="note-0252-01" xml:id="N29774" xml:space="preserve">Auguſti. <lb/>enchi.</note>
              <note position="left" xlink:href="note-0252-02a" xlink:label="note-0252-02" xml:id="N2977C" xml:space="preserve">dicitur.</note>
            </div>
            <p xml:id="N29782">
              <s xml:id="N29783" xml:space="preserve">Contra / quia philoſophus quarto me­<lb/>thaphiſices .t. 9.27. volens ꝓbare cõtra heraclitū / <lb/> nemo poteſt aſſentire duabus cõtradictoriis ſic <lb/>arguit. </s>
              <s xml:id="N2978C" xml:space="preserve">Nemo poteſt habere ſimul et ſemel q̈litates <lb/>ↄ̈rias. </s>
              <s xml:id="N29791" xml:space="preserve">igit̄̄ nemo põt habere ſimul duarum ↄ̈dicto­<lb/>riarū aſſenſus. </s>
              <s xml:id="N29796" xml:space="preserve">Supponit phūs antecedēs tã̄ ma­<lb/>nifeſtum: et ꝓbat ↄ̨ñam. </s>
              <s xml:id="N2979B" xml:space="preserve">quia aſſenſus ↄ̈dictoriarū <lb/>ſunt qualitates ↄ̈rie: ergo ſeq̇tur /  phūs habuit ꝓ <lb/>incõueniēti cõtraria primo intentionaliter eē ī eo-<lb/>dem.               <anchor type="note" xlink:href="note-0252-03" xlink:label="note-0252-03a"/>               </s>
              <s xml:id="N297A9" xml:space="preserve">¶ Dices et bene diſtinguendo /  phūs opīatꝰ <lb/>fuerit qualitates contrarias eſſe incõpoſſibiles: aut <lb/>corporales / et ſic nego: aut ſpirituales et ī extenſas <lb/>cuiuſmodi eſt volitio et nolitio: aſſenſus vnius con-<lb/>tradictorii et diſſenſus eiuſdem: ſcīa actualis et opi­<lb/>nio actualis reſpectu eiuſdē: et ſic bene concedo / q2 <lb/>tales in quibuſcun gradibus repugnant: corpo-<lb/>rales vero minime. </s>
              <s xml:id="N297BA" xml:space="preserve">Et in hoc experientiã conſulen-<lb/>dum eſt que ī naturali philoſophia doctrix et in grã <lb/>cõprobatur.</s>
            </p>
            <div xml:id="N297C1" level="5" n="2" type="float">
              <note position="left" xlink:href="note-0252-03a" xlink:label="note-0252-03" xml:id="N297C5" xml:space="preserve">dicitur</note>
            </div>
            <cb chead="Capi. Tertium"/>
            <p xml:id="N297CD">
              <s xml:id="N297CE" xml:space="preserve">Sed contra / q2 vel qū phūs aſſumit <lb/>īpoſſibile eē qualitates ↄ̈rias ſe cõpati ītelligit vlr <lb/>vel ſolum dementalibus. </s>
              <s xml:id="N297D5" xml:space="preserve">Si primū habetur inten­<lb/>tum. </s>
              <s xml:id="N297DA" xml:space="preserve">Si ſecundū adhuc nichil probaret: quia aſſu­<lb/>meret falſum. </s>
              <s xml:id="N297DF" xml:space="preserve">Nã qualitates mētales et habituales <lb/>ↄ̈rie ſe cõpatiūtur. </s>
              <s xml:id="N297E4" xml:space="preserve">Et ſi ſolū intelligeret de actua-<lb/>libus: tunc aſſumeret ꝓbandum et ſic argumentum <lb/>philoſophi eēt inefficax.               <anchor type="note" xlink:href="note-0252-04" xlink:label="note-0252-04a"/>               </s>
              <s xml:id="N297F0" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi due for­<lb/>me accidētales cõtrarie ſe cõpatiunt̄̄ in eodē: ſeque­<lb/>retur duas formas ſubſtantiales ſe cõpati in eadē <lb/>materia: ſed ↄ̨ñs manifeſte falſuꝫ: igit̄̄ illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N297FB" xml:space="preserve">Sequela ꝓbatur: q2 ſi illa q̄ repugnãt et <lb/>naturaliter cõtrariãtur ſunt naturaliter cõpoſſibi­<lb/>lia: a fortiori ea q̄ nõ cõtrariãtur erunt ↄ̨poſſibilia <lb/>cuiuſmodi ſunt forme ſubſtantiales.</s>
            </p>
            <div xml:id="N29804" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0252-04a" xlink:label="note-0252-04" xml:id="N29808" xml:space="preserve">Confir°</note>
            </div>
            <p xml:id="N2980E">
              <s xml:id="N2980F" xml:space="preserve">Secundo ad idem argr̄ ſic / quia nulle <lb/>forme īcompoſſibiles ſe compatiūtur: ſed omēs for­<lb/>me contrarie ſunt incõpoſſibiles: ergo nulle forme <lb/>contrarie ſe compatiuntur.               <anchor type="note" xlink:href="note-0252-05" xlink:label="note-0252-05a"/>               </s>
              <s xml:id="N2981D" xml:space="preserve">Maior eſt nota cum cõ­<lb/>ſequentia et minor probatur / quia forme contrarie <lb/>ſunt que ſub eodem genere poſite ſunt, et eidem ſu-<lb/>ſceptibili viciſſim inſunt: et mutuo ſe expellunt.</s>
            </p>
            <div xml:id="N29826" level="5" n="4" type="float">
              <note position="right" xlink:href="note-0252-05a" xlink:label="note-0252-05" xml:id="N2982A" xml:space="preserve">diffi° q̈li­<lb/>tatuꝫ con­<lb/>trariarū.</note>
            </div>
            <note position="right" xml:id="N29834" xml:space="preserve">dicitur.</note>
            <p xml:id="N29838">
              <s xml:id="N29839" xml:space="preserve">¶ Dices diſtinguēdo minorem aut  ſint incõpoſ-<lb/>ſibiles ſcḋm quoſcū gradus, et ſic negatur, aut ſe­<lb/>cundum aliquos et aliquos non, et ſic cõceditur. </s>
              <s xml:id="N29840" xml:space="preserve">Nã <lb/>ſecundū gradus ſummos ſunt incõpoſſibiles, et ſe-<lb/>cundū certos remiſſos ſe cõpatiuntur. </s>
              <s xml:id="N29847" xml:space="preserve">¶ Sed cõtra / <lb/>q2 tunc ſequeretur aliquã frigiditatem alicui cali-<lb/>ditati non eſſe contrariam: ſed conſequens eſt fal-<lb/>ſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N29850" xml:space="preserve">Falſitas cõſequē­<lb/>tis oſtenditur: quia quando aliqua ſunt eiuſdē ſpe­<lb/>ciei quicquid cõtrariatur vni cõtrariat̄̄ et alteri: ſꝫ <lb/><gap/> <lb/>igitur ſi aliqua frigiditas alicui caliditati contra­<lb/>riatur: quelibet frigiditas contrariabitur cuilibet <lb/>caliditati: quod eſt contrarium ↄ̨ñtis. </s>
              <s xml:id="N29860" xml:space="preserve">Sequela tñ <lb/>probatur / quia per te frigiditas remiſſa et calidi-<lb/>tas remiſſa ſe cõpatiuntur: et per cõſequens nõ mu­<lb/>tuo ſe expellūt: et ſi non mutuo ſe expellūt: nõ ſunt <lb/>forme cõtrarie. </s>
              <s xml:id="N2986B" xml:space="preserve">Prima ↄ̨ña patet et ſecūda ꝓbatur <lb/>per diffinitionē q̈litatū cõtrariuꝫ.               <anchor type="note" xlink:href="note-0252-06" xlink:label="note-0252-06a"/>               </s>
              <s xml:id="N29875" xml:space="preserve">¶ Dices forte / <lb/>ſicut videtur dicere iacobus de forlinio cõcedendo <lb/>quod infertur vcꝫ  caliditas remiſſa et frigiditas <lb/>remiſſa non ſunt cõtrarie qualitates ꝓpter rõnem <lb/>adductã: et cū probatur oppoſitū negatur illa pro­<lb/>poſitio vniuerſalis quãdocū aliqua ſunt eiuſdem <lb/>ſpeciei quicquid cõtrariatur vni cõtrariatur et al-<lb/>teri. </s>
              <s xml:id="N29886" xml:space="preserve">Imo (vt inquit) cuilibet frigiditati ↄ̨trariatur <lb/>caliditas ſumma: et tamen caliditas remiſſa nõ cõ­<lb/>riatur ei. </s>
              <s xml:id="N2988D" xml:space="preserve">Si quereret̄̄ ratio diceret forte /  talis eſt <lb/>natura rei ſicut dicit gregoriꝰ de armino de incõ-<lb/>poſſibilitate quorūcū ↄ̨trariorū in quãtuliſcū <lb/>gradibus.               <anchor type="note" xlink:href="note-0252-07" xlink:label="note-0252-07a"/>               </s>
              <s xml:id="N2989B" xml:space="preserve">Dico tamen aliter negando ſequelam: et <lb/>ad punctum probationis: nego hanc ↄ̨ſequentiam <lb/>non mutuo ſe expellūt: ergo non cõtrariantur. </s>
              <s xml:id="N298A2" xml:space="preserve">Et <lb/>ad probationem dicit̄̄ /  illa non eſt totalis defini­<lb/>tio: ſed d3 addi mutuo ſe expellūt ſecundū ſe vel ali­<lb/>quas illi eiuſdem ſpeciei. </s>
              <s xml:id="N298AB" xml:space="preserve">Mõ ̄uis ille ſe nõ expel-<lb/>lant: alique eiuſdē ſpeciei cum illis ſe expellunt / qḋ <lb/>ſufficit vt dicantur contrarie.</s>
            </p>
            <div xml:id="N298B2" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0252-06a" xlink:label="note-0252-06" xml:id="N298B6" xml:space="preserve">dr̄ <lb/>ṗmo.</note>
              <note position="right" xlink:href="note-0252-07a" xlink:label="note-0252-07" xml:id="N298BE" xml:space="preserve">dr̄ ſcḋo.</note>
            </div>
            <p xml:id="N298C4">
              <s xml:id="N298C5" xml:space="preserve">Cõtra quia tūc ſequeretur quoſcū <lb/>gradus remiſſe caliditatis et remiſſe frigiditatis <lb/>eē compoſſibiles: ſed conſequens eſt falſum: igitur <lb/>illud ex quo ſequitur. </s>
              <s xml:id="N298CE" xml:space="preserve">Sequela ꝓbat̄̄: quia nõ videt̄̄ <lb/>maior rõ de aliq̇bꝰ ꝙ̄ de aliis </s>
              <s xml:id="N298D3" xml:space="preserve">Sꝫ fĺitas ↄ̨ñtis ꝓbat̄̄ / <lb/>q2 ſi q̊tcū frigiditatꝪ remiſſe et calididatꝪ remiſſe <lb/>ſṫ ↄ̨poſſibĺes ſeq̇t̄̄ g̈dꝰ calididatꝪ vt .6. et frigiditatꝪ               <pb chead="De intenſione et remiſſione formarum" file="0253" n="253"/>               vt ſex eſſe compoſſibiles: ſꝫ ↄ̨ſequēs eſt falſum: igit̄̄ <lb/></s>
              <s xml:id="N298E0" xml:space="preserve">Sequela eſt nota et falſitas conſequentis oſtendi-<lb/>tur ſupponēdo totã latitudinē coliditatis eē vt .8. <lb/>et  ſemꝑ ad inductionē vniꝰ gradus caliditatis <lb/>in ſubiecto in quo eſt frigiditas ſequitur corruptio <lb/>vnius gradus frigitatis p̄ciſe: ita  ̄tum inducit̄̄ <lb/>de vno ↄ̈rio tm̄ de altero corrūpatur. </s>
              <s xml:id="N298ED" xml:space="preserve">Quo ſuppo­<lb/>ſito volo /  illi corpori approximet̄̄ ſumme caliduꝫ <lb/>inducēs in illḋ caliditatē ſummã </s>
              <s xml:id="N298F4" xml:space="preserve">Quo poſito argr̄ <lb/>ſic / qñ inducitur gradus .7. caliditatis corrumpitur <lb/>6. frigiditatis: et qñ inducitur .8. caliditatis corrū-<lb/>pitur .5. p̄ciſe ipſius frigiditatꝪ: igr̄ manet g̈dus .8. <lb/>caliditatis / q̇ eſt ſummꝰ ex ſuppoſito cū frigiditate <lb/>vt .4. / ſꝫ ↄ̨ñs eſt īpoſſibile: igr̄ illḋ ex quo ſequitur / vcṫ <lb/>quotcū gradus remiſſos caliditatis et frigidita­<lb/>tis eē cõpoſſibiles. </s>
              <s xml:id="N29905" xml:space="preserve">Nec iuuat dicere /  illi .4. g̈dus <lb/>frigiditatis ſubito corrūpuntur: et  nõ ſemper ad <lb/>inductionē vniꝰ gradus caliditatis ſeq̇tur indutio <lb/>vnius gradus frigiditatis p̄ciſe: q2 tunc illi .4. gra­<lb/>dus corrūperētur et nõ ꝑ motū: et agēs finitū cū reſi­<lb/>ſtentia ſubito et infinite velociter agēt: quo nichil <lb/>abſurdius.               <anchor type="note" xlink:href="note-0253-01" xlink:label="note-0253-01a"/>               </s>
              <s xml:id="N29919" xml:space="preserve">¶ Ideo dices aliter et bñ negãdo ſeq̄laꝫ <lb/></s>
              <s xml:id="N2991D" xml:space="preserve">Imo dico /  in aliq̇bus g̈dibus remiſſis ſe cõpatiū­<lb/>tur: et in aliq̇bus non: et ad ꝓbationē nego /  nõ ſit <lb/>maior rõ de aliq̇bꝰ quã de aliis. </s>
              <s xml:id="N29924" xml:space="preserve">Uñ in hac mä po-<lb/>nitur ꝓ baſi et fundamēto talis ꝓpõ. </s>
              <s xml:id="N29929" xml:space="preserve">Oēs g̈dꝰ q̈lita­<lb/>tū ↄ̈riarū q̊rum nūerꝰ nõ excedit totalē latitudineꝫ <lb/>alteriꝰ illaꝝ ſe ↄ̨patiunt̄̄. </s>
              <s xml:id="N29930" xml:space="preserve">Exēpluꝫ vt g̈dus calidita <lb/>vt .6. nõ ↄ̨patitur ſecum g̈dus frigiditatꝪ vt .3. quia <lb/>aggregatū ex .3. et .6. excedūt .8. ſꝫ bñ .5. g̈dus calidi­<lb/>tatis ſecū patiunt̄̄ .3. frigiditatꝪ: q2 aggregatū ex <lb/>illis nõ excedit nūeꝝ octauū. </s>
              <s xml:id="N2993B" xml:space="preserve">Gradꝰ o excedentes <lb/>totalem latitudinem alterius illaꝝ ſe cõpatiuntur <lb/>minime.</s>
            </p>
            <div xml:id="N29942" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0253-01a" xlink:label="note-0253-01" xml:id="N29946" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2994C">
              <s xml:id="N2994D" xml:space="preserve">Sed contra / quia ſi ſex gradus cali-<lb/>ditatis non ſecum patiuntur tres frigiditatis: igi-<lb/>tur nec .6. gradus caliditatis ſecum patiuntur du­<lb/>os gradus frigiditattis / quod eſt contra ſolutio-<lb/>nē. </s>
              <s xml:id="N29958" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 tm̄ repugnãt duo g̈dus frigidi-<lb/>tatis .6. g̈dibꝰ calididatꝪ ̄tū .6. g̈dibꝰ caliditatis <lb/>repugnãt .3. frigiditatis: igr̄ ſi .3. g̈dus frigiditatis <lb/>ſūt īcõpoſſibiles .6. g̈dibꝰ calididatꝪ: ēt et duo. </s>
              <s xml:id="N29961" xml:space="preserve">Añs <lb/>ꝓbat̄̄ / q2 ſunt eiuſdē ſpēi / igr̄ nõ vr̄ q̈re magis .3. gra­<lb/>dus frigiditatꝪ repugnãt .6. g̈dibꝰ calididatꝪ ꝙ̄ duo <lb/></s>
              <s xml:id="N29969" xml:space="preserve">Itē ſi caliditas vt .6. nõ ↄ̨patit̄̄ frigiditatē vt .3. / g̊ nec <lb/>mīorē. </s>
              <s xml:id="N2996E" xml:space="preserve">Patꝫ ꝑ locū a maiori.               <anchor type="note" xlink:href="note-0253-02" xlink:label="note-0253-02a"/>               </s>
              <s xml:id="N29976" xml:space="preserve">¶ Dices et bñ negãdo <lb/>hãc ↄ̨ñaꝫ nõ cõpatit̄̄ ſecū frigiditatē vt .3. / g̊ nec vt .2. <lb/>et ad ꝓbationē q̄ eſt inq̇ſitiua rõis. </s>
              <s xml:id="N2997D" xml:space="preserve">Dico /  hoc iõ ē <lb/>q2 ex tali ↄ̨poſſibilitate triū graduū frigiditatꝪ cū <lb/>6. calididatꝪ ſequit̄̄ ↄ̨poſſibilits ſūme calididatꝪ cuꝫ <lb/>aliq̈ frigiditate </s>
              <s xml:id="N29986" xml:space="preserve">Et iõ .6. calididatꝪ ſūt īcõpoſſibiles <lb/>3. frigiditatis.</s>
            </p>
            <div xml:id="N2998B" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0253-02a" xlink:label="note-0253-02" xml:id="N2998F" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N29995">
              <s xml:id="N29996" xml:space="preserve">Contra / quia nec duos frigiditatis ſe­<lb/>cū patit̄̄ caliditas vt .6. / igr̄ ſolutio nulla. </s>
              <s xml:id="N2999B" xml:space="preserve">Añs ꝓba­<lb/>tur / q2 ille due q̈litates ſūt ↄ̈rie actiue et paſſiue ad <lb/>īuicē optīe approximate et actiuitas vniꝰ excedit re­<lb/>ſiſtētiã alterius: igitur continuo caliditas corrum­<lb/>pit frigiditatem cum excedat illaꝫ: et per conſequēs <lb/>non ſe compatiuntur caliditas vt ſex et frigiditas <lb/>ſaltem per tempus cuius: oppoſitum fatetur opi-<lb/>nio. </s>
              <s xml:id="N299AC" xml:space="preserve">Sequela tamen probatur / quia caliditas et fri­<lb/>giditas vniuerſaliter exiſtens in diuerſis ſubie-<lb/>ctis debite ad inuicem approximatis ſemper agūt <lb/>et patiuntur ab inuicem vel vna agit et alia pati-<lb/>tur dummodo actiuitas vnius excedit reſiſtentiam <lb/>alterius: igitur a fortiori quando ſunt ſimul cum               <cb chead="De intenſione et remiſſione formarum"/>               in infinitū melius applicentur ad inuicem vna illa­<lb/>rum patitur ab altera.               <anchor type="note" xlink:href="note-0253-03" xlink:label="note-0253-03a"/>               </s>
              <s xml:id="N299C3" xml:space="preserve">¶ Reſpondet de forlino ne-<lb/>gando antecedens: et ad punctum probationis ne­<lb/>gat /  omnes qualitates cõtrarie exiſtentes in di-<lb/>uerſis ſubiectis debite applicate agunt et patiun-<lb/>tur ab inuicem: aut  vna illarum agat in alteram <lb/></s>
              <s xml:id="N299CF" xml:space="preserve">Et dat inſtantiam ponendo caſum /  ſint duo pe-<lb/>dalia in quorum quolibet ſint quatuor gradus ca­<lb/>liditatis et quatuor frigiditatis: et  approximen­<lb/>tur ab inuicē. </s>
              <s xml:id="N299D8" xml:space="preserve">Tunc manifeſtum eſt /  vnum illorum <lb/>non agit in relinquū: et tamē ibi eſt caliditas ī ſub­<lb/>iectis extrinſecis cuꝫ debita approximatione: igit̄̄. <lb/></s>
              <s xml:id="N299E0" xml:space="preserve">¶ Sed (meliori indicio ſemper excepto) hec reſpon­<lb/>ſio non ſatiſfacit: quia illa duo pedalia ſunt oīno <lb/>ſimilia: ita  quanta eſt actiuitas vnius tanta eſt <lb/>reſiſtentia alterius. </s>
              <s xml:id="N299E9" xml:space="preserve">Sed vbi vnum excederet reli-<lb/>quum regula ſiue propoſitio nequa̄ videtur ha-<lb/>bere inſtantiam.               <anchor type="note" xlink:href="note-0253-04" xlink:label="note-0253-04a"/>               </s>
              <s xml:id="N299F5" xml:space="preserve">¶ Et ideo dices aliter ad argumē­<lb/>tum concedendo gradum caliditatis vt ſex ſecum <lb/>pati duos gradus frigiditatis: et cum probatur  <lb/>non: quia ille calitates agunt et patiuntur ab in-<lb/>uicem, vel vna patitur ab altera: negatur illud: et <lb/>ad probationem conceditur antecedens, et nega-<lb/>tur conſequētia.               <anchor type="note" xlink:href="note-0253-05" xlink:label="note-0253-05a"/>               </s>
              <s xml:id="N29A09" xml:space="preserve">Et ratio eſt / quia vt dicit Scotus <lb/>2. ſen. </s>
              <s xml:id="N29A0E" xml:space="preserve">Nulla res naturalis intendit primo et prin-<lb/>cipaliter corrumpere aliquam aliam: ſed principa­<lb/>liter intendit aſſimilare ſibi paſſum, et producere <lb/>formam ei ſimilem, et quãdo in paſſo in quod agit <lb/>eſt forma ei incompoſſibilis corrumpit illam: ſꝫ nõ <lb/>corrumpit eam ſi fuerit ei compoſſibilis. </s>
              <s xml:id="N29A1B" xml:space="preserve">¶ Ex quo <lb/>infertur /  nulla qualitas corrumpit qualitateꝫ ſi­<lb/>bi contrariam in aliquo ſubiecto niſi ſuam intro-<lb/>ducat in idem ſubiectum. </s>
              <s xml:id="N29A24" xml:space="preserve">Et quia caliditas vt ſex <lb/>exiſtens cum frigiditate vt duo in aliquo ſubiecto <lb/>non poteſt in eodem ſubiecto producere aliquem <lb/>gradum caliditatis: quia ſubiectum eſt debite aſ-<lb/>ſimilitatuꝫ per illam caliditatem vt ſex ideo non cor­<lb/>rumpit frigiditatem. </s>
              <s xml:id="N29A31" xml:space="preserve">¶ Ex quo ſequitur /  iſta con­<lb/>ſequentia nichil valet iſte duo qualitates cõtrarie <lb/>ſunt debite approximate non impedite et actiui-<lb/>tas vnius excedit reſiſtentiam alterius / igitur vna <lb/>illaruꝫ agit in reliquam </s>
              <s xml:id="N29A3C" xml:space="preserve">Sꝫ oportet addere ex par­<lb/>te antecedentis et paſſum non eſt complete omni­<lb/>no aſſimilatum.</s>
            </p>
            <div xml:id="N29A43" level="5" n="8" type="float">
              <note position="right" xlink:href="note-0253-03a" xlink:label="note-0253-03" xml:id="N29A47" xml:space="preserve">Iaco. de <lb/>for.</note>
              <note position="right" xlink:href="note-0253-04a" xlink:label="note-0253-04" xml:id="N29A4F" xml:space="preserve">Dicitur.</note>
              <note position="right" xlink:href="note-0253-05a" xlink:label="note-0253-05" xml:id="N29A55" xml:space="preserve">Doctor <lb/>ſubti ī .2</note>
            </div>
            <p xml:id="N29A5D">
              <s xml:id="N29A5E" xml:space="preserve">Sed contra hanc ſolutionem replico <lb/>ſic / quia ſi eſſet vera / ſequeretur corpus calidum <lb/>poſſe agere in frigidum nullo pacto corrumpen-<lb/>do frigiditatem: ſꝫ bene inducendo caliditatem: ſꝫ <lb/>conſequens eſt contra vnum fundamentum opinio­<lb/>nis: igitur ſolutio nulla </s>
              <s xml:id="N29A6B" xml:space="preserve">Ponit em̄ ad inductionē <lb/>vnius gradus cõtrarie qualitatis ſequi corruptio­<lb/>nem alterius qualitatis ſibi oppoſite. </s>
              <s xml:id="N29A72" xml:space="preserve">Probatur <lb/>tamen ſequela: et pono caſum /  ſit vnum pedale <lb/>frigidum vt tria: et nullo pacto ſit ī illo frigiditas <lb/>permixta ſuo contrario: et approximetur ei cali-<lb/>ditas vt quin agens in eam. </s>
              <s xml:id="N29A7D" xml:space="preserve">Quo poſito argui­<lb/>tur ſic caliditas vt quin inducet quin gradus <lb/>caliditatis in illud frigidum vt tria: et nullum gra­<lb/>dum frigiditatis corrumpet (cum tres gradus fri­<lb/>giditatis ſint compoſſibiles quin caliditatis: et <lb/>nullum agens naturale corrumpit aliquam formã <lb/>niſi propter incompoſſibilitatem illius cuꝫ forma <lb/>inducenda ex ſolutione) / igitur aſſumptum verum. <lb/>               <anchor type="note" xlink:href="note-0253-06" xlink:label="note-0253-06a"/>               </s>
              <s xml:id="N29A95" xml:space="preserve">¶ Et confirmatur / quia aliqui gradus remiſſi qua­<lb/>litatum contrarium ſe compatiuntur: et aliqui nõ: <lb/>igitur dabiles ſunt maximi gradus remiſſi qui ſe <lb/>compatiuntur vel minimi q̇ non vel maximi q̇ nõ vel <lb/>mīmi q̇ ſe ↄ̨patiuntur nullū iſtoꝝ eſt dicendum: igr̄. <lb/></s>
              <s xml:id="N29AA1" xml:space="preserve"><pb chead="Quarti tractatus." file="0254" n="254"/>               Item caliditas remiſſa cū aliqua frigiditate p̄t ſta­<lb/>re et cum aliqua nõ: igr̄ dabilis eſt maxima frigidi­<lb/>tas cum qua caliditas remiſſa p̄t ſtare vel minima <lb/>cum qua nõ vel maxima cū qua nõ vel minima cum <lb/>qua poteſt ſtare nullū iſtoꝝ ē dicendum: igitur.</s>
            </p>
            <div xml:id="N29AB0" level="5" n="9" type="float">
              <note position="right" xlink:href="note-0253-06a" xlink:label="note-0253-06" xml:id="N29AB4" xml:space="preserve">Confir°.</note>
            </div>
            <p xml:id="N29ABA">
              <s xml:id="N29ABB" xml:space="preserve">Tertio prīcipaliter arguitur ſic / quia <lb/>ſi qualitates cõtrarie ſe cõpatiunt̄̄: ſequit̄̄ calidita-<lb/>tem eque ꝓportionabiliter intēdi in ſubiecto ī quo <lb/>eſt ſuo permixta contrario ſicut friditas remittitur / <lb/>ſed ↄ̨ñs eſt falſum: igitur illud ex quo ſequit̄̄. </s>
              <s xml:id="N29AC6" xml:space="preserve">Seq̄-<lb/>la patet / q2 quantū de caliditate inducit̄̄ tm̄ de fri-<lb/>gididate corrūpitur ex opinione: igr̄ eque ꝓportio-<lb/>nabiliter ſicut caliditas intēditur frigiditas remit­<lb/>tit̄̄. </s>
              <s xml:id="N29AD1" xml:space="preserve">Probo tñ falſitatem ↄ̨ñtis / quia poſito  in a. <lb/>corpore ſit media latitudo caliditatis et media fri-<lb/>giditatis: et approximetur ſūme calidum corrum-<lb/>pens frigiditatem vſ ad non graduꝫ arguit̄̄ ſic in­<lb/>finite velociter ꝓportionabiliṫ corrumpitur frigi-<lb/>ditas et finite velociter ſolum intenditur caliditas <lb/>puta in ꝓportione dupla a quarto vſ ad 8. / igitur <lb/>non eque ꝓportionabiliter ſicut īducitur caliditas <lb/>corrumpitur frigiditas / quod fuit ꝓbãdum. </s>
              <s xml:id="N29AE4" xml:space="preserve">Maior <lb/>patet / q2 in tempore finito infinitã ꝓportionem per­<lb/>dit frigiditas: q2 a certo gradu vſ ad nõ graduꝫ <lb/>corrumpitur: igitur infinite velociter ꝓportionabi­<lb/>liter corrūpitur frigiditas: </s>
              <s xml:id="N29AEF" xml:space="preserve">Conſequentia patet in­<lb/>telligenti ſecundam ꝑtem huius operis.               <anchor type="note" xlink:href="note-0254-01" xlink:label="note-0254-01a"/>               </s>
              <s xml:id="N29AF9" xml:space="preserve">¶ Et cõfir­<lb/>matur / q2 mollicies et duricies ſunt forme ↄ̈rie: et ta­<lb/>men non ſe compatiunt̄̄ in aliquibns gradibus igr̄ <lb/></s>
              <s xml:id="N29B01" xml:space="preserve">Antecedens ꝓbat̄̄ / q2 ad ipſas eſſe in eodem ſubiec­<lb/>to adequato ſequitur ↄ̈dictio: igitur ſe non com-<lb/>patiiuntur. </s>
              <s xml:id="N29B08" xml:space="preserve">Probat̄̄ añs / q2 bene ſequitur ī iſto ſub­<lb/>iecto eſt mollicies: ergo eſt mobile. </s>
              <s xml:id="N29B0D" xml:space="preserve">in iſto ſubiecto ē <lb/>duricies: ergo eſt durum: et vltra ipſum eſt molle et <lb/>durum: ergo ipſum cedit comprimēti: et ipſum nõ ce­<lb/>dit comprimēti: qḋ eſt ↄ̈dictio. </s>
              <s xml:id="N29B16" xml:space="preserve">Prima conſequētia <lb/>patet / q2 nihil aliud eſt habere duriciē ꝙ̄ eē durum et <lb/>habere molliciē ꝙ̄ eſſe molle. </s>
              <s xml:id="N29B1D" xml:space="preserve">Et ſecunda probatur <lb/>a definito ad diffinionem. </s>
              <s xml:id="N29B22" xml:space="preserve">Durum em̄ ſcḋ3 phm̄ .2°: <lb/>de generatione eſt illud qḋ non facile cedit ↄ̨primē-<lb/>ti. </s>
              <s xml:id="N29B29" xml:space="preserve">Et molle quod facile cedit comprimenti.               <anchor type="note" xlink:href="note-0254-02" xlink:label="note-0254-02a"/>               </s>
              <s xml:id="N29B31" xml:space="preserve">¶ Confir­<lb/>matur ſecundo / quia ſi qualitates contrarie ſe com­<lb/>patiunt̄̄: ſequitur /  idem naturaliṫ eſſet albuꝫ et ni­<lb/>grum calidum et frigidū: diuiſiue: ſed ↄ̨ñs eſt falſuꝫ / <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N29B3C" xml:space="preserve">Sequela probat̄̄: quia <lb/>per te poſſibile eſt .4. gradus caliditatis eē cum .4. <lb/>gradibus frigiditatis in eodem ſubiecto et .4. albe­<lb/>dinis et .4. nigredinis: et quelibet. </s>
              <s xml:id="N29B45" xml:space="preserve">illarum qualita-<lb/>tum denoīat ſuū ſubiectū: igr̄ idem erit album et ni­<lb/>grum, calidum et frigidum / quod fuit probandum. <lb/></s>
              <s xml:id="N29B4D" xml:space="preserve">Nec valet dicere /  nec albedo nec nigredo ſuū ſub-<lb/>iectum denoīat: q2 manifeſtum eſt illud ſubiectū eſſe <lb/>coloratum. </s>
              <s xml:id="N29B54" xml:space="preserve">igitur aliquo colore vel aliquibꝰ et ſi ali­<lb/>quibus: ſequit̄̄ /  quolibet illorum denominatur co­<lb/>loratum: et ſic quodlibet illorū ſuum ſubiectum de-<lb/>nominat. </s>
              <s xml:id="N29B5D" xml:space="preserve">¶ Confirmatur tertio / quia ſi qualitates <lb/>contrarie ſe cõpatiuntur ſequit̄̄ gradum mediū gra­<lb/>uitatis et gradum medium leuitatis ſe cõpati: ſꝫ cõ-<lb/>ſequens eſt falſum / igitur illud ex quo ſequitur. </s>
              <s xml:id="N29B66" xml:space="preserve">Se­<lb/>quela probatur et capio ſūme graue quod per vni-<lb/>formē acquiſitionē leuitatis fiat ſūme leue ī aliquo <lb/>tꝑe: et ſequitur /  illud in inſtanti medio illiꝰ tempo­<lb/>ris habebit medium gradum grauitatis et mediuꝫ <lb/>leuitatis: igitur medius gradus grauitatis et me-<lb/>dius frigiditatis ſe cõpatiuntur. </s>
              <s xml:id="N29B75" xml:space="preserve">Sed falſitas con-<lb/>ſequentis probat̄̄ / q2 īpoſſibile ē duo ↄ̈ria inſtrumē­<lb/>ta eidē principali agenti et particulari forme equa­<lb/>liter eē conuenientia: igitur in nullo ſubiecto gradꝰ               <cb chead="Capitulum ſecundum."/>               medius grauitatis ſecū patit̄̄ medium gradum le-<lb/>uitatis / quod eſt oppoſitum ↄ̨ñtis. </s>
              <s xml:id="N29B83" xml:space="preserve">Antecedens patꝫ / <lb/>quia contraria inſtrumenta neceſſario ſunt diuerſo­<lb/>rum generum perfectionis: igit̄̄ principale agens et <lb/>particularis forma magis ſibi determīat de vno ̄­<lb/>dē alio: et per conſequens non ſibi equaliter conue-<lb/>niunt / qnod fuit probandum.</s>
            </p>
            <div xml:id="N29B90" level="5" n="10" type="float">
              <note position="left" xlink:href="note-0254-01a" xlink:label="note-0254-01" xml:id="N29B94" xml:space="preserve">ↄ̨firma. 1.</note>
              <note position="left" xlink:href="note-0254-02a" xlink:label="note-0254-02" xml:id="N29B9A" xml:space="preserve">2. ↄ̨fir̄a°.</note>
            </div>
            <p xml:id="N29BA0">
              <s xml:id="N29BA1" xml:space="preserve">Quarto prīcipaliter arguitur ſic </s>
              <s xml:id="N29BA4" xml:space="preserve">Si <lb/>qualitates ↄ̈rie ſe compatiuntur. </s>
              <s xml:id="N29BA9" xml:space="preserve">ſequitur ſcīam et <lb/>opinionem reſpectu eiuſdē ꝓpõnis eſſe compoſſibi­<lb/>les in eodem intellectu: ſed conſequens eſt falſū igr̄ <lb/></s>
              <s xml:id="N29BB1" xml:space="preserve">Sequela pater / q2 ſcientia et opinio ſūt qualitates <lb/>contrarie perinde ac caliditas et frigiditas. </s>
              <s xml:id="N29BB6" xml:space="preserve">Sꝫ fal­<lb/>ſitas ↄ̨ñtis oſtenditur: et ſit ꝓpoſitio reſpectu cuiꝰ hꝫ <lb/>ſcientiam et opinionem idem intellectꝰ puta ſortis <lb/>oīs hõ eſt riſibilis / et arguo ſic: bene ſequitur ſortes <lb/>ſcit hanc propoſitionem: ergo aſſentit ei firmiter et <lb/>opinatur / ergo non ſentit ei firmiter ſꝫ iſta duo con­<lb/>ſequentia repugnant: igitur et eorum anteceden-<lb/>tia: et per conſequens illud ex quo ſequuntur eſt im­<lb/>poſſibile. </s>
              <s xml:id="N29BC9" xml:space="preserve">¶ Dices forte concedendo / quod infertur et <lb/>ad improbationem negatur hec conſequentis: ſor-<lb/>tes opinatur hanc ꝓpoſitionem: igitur non firmi-<lb/>ter aſſentit ei: ſed oportet inferre / ergo aſſentit ei ali­<lb/>quo aſſenſu non firmo.</s>
            </p>
            <p xml:id="N29BD4">
              <s xml:id="N29BD5" xml:space="preserve">Sed contra / quia pari ratione ſeque-<lb/>retur aſſenſus duarum contradictoriarū eē cõpoſ-<lb/>ſibiles: ſed ↄ̨ñs eſt falſum: igitur ſolutio nulla:               <anchor type="note" xlink:href="note-0254-03" xlink:label="note-0254-03a"/>               </s>
              <s xml:id="N29BE1" xml:space="preserve">Se-<lb/>quela patet / quia aſſenſus contradictoriarum ſūt q̈­<lb/>litates contrarie: vt patet ꝑ phm̄ .4. methaphi. loco <lb/>allegato in prīo argumēto. </s>
              <s xml:id="N29BEA" xml:space="preserve">Falſitas tamen conſe-<lb/>quentis probat̄̄: q2 tunc ſequeretur aliquem poſſe <lb/>aſſentire ꝓpoſitioni per ſe note in falſitate / qḋ nul-<lb/>lus ſani capitis diceret. </s>
              <s xml:id="N29BF3" xml:space="preserve">Sequela ꝓbat̄̄ / quia omīs <lb/>copulatiua ex contradictoriis compoſita eſt per ſe <lb/>nota in falſitate cum ſua contradictoria diſiuncti­<lb/>ua ſit per ſe nota in veritate. </s>
              <s xml:id="N29BFC" xml:space="preserve">Iſta enim ſe notificat <lb/>ſortes eſt vel ſortes non eſt.               <anchor type="note" xlink:href="note-0254-04" xlink:label="note-0254-04a"/>               </s>
              <s xml:id="N29C06" xml:space="preserve">¶ Et confirmatur / quia <lb/>pari ratione ſequeretur virtus et vicium eſſe compo­<lb/>ſibilia in eodem reſpectu eiuſdē: ſed conſequens eſt <lb/>falſum. </s>
              <s xml:id="N29C0F" xml:space="preserve">igitur </s>
              <s xml:id="N29C12" xml:space="preserve">Falſitas conſequentis oſteuditur: q2 <lb/>ſi virtus et vicium etc. puta tēperantia et intemperã­<lb/>tia ſunt in eodem: ſequeretur illud eē temperatuꝫ et <lb/>intemperatum: ſed conſequens implicat contradi-<lb/>ctionem: igitur. </s>
              <s xml:id="N29C1D" xml:space="preserve">Sequela ꝓbatur / q2 ſi in illo eſt tem­<lb/>perantia illud eſt temperatum: et ſi in illo eſt īempe­<lb/>rantia ipſum eſt intēperatum. </s>
              <s xml:id="N29C24" xml:space="preserve">igr̄.               <anchor type="note" xlink:href="note-0254-05" xlink:label="note-0254-05a"/>               </s>
              <s xml:id="N29C2C" xml:space="preserve">¶ Confirmat̄̄ ſe­<lb/>cundo / quia ſequeretur ſanitatem et egritudinē poſ­<lb/>ſe eſſe in eodem ſubiecto adequate: ſed conſequens <lb/>eſt falſum: igit̄̄. </s>
              <s xml:id="N29C35" xml:space="preserve">Sequela patet / q2 ſunt qualitates <lb/>contrarie quēadmodū caliditas et frigiditas. </s>
              <s xml:id="N29C3A" xml:space="preserve">Sed <lb/>falſitas conſequentis probatur </s>
              <s xml:id="N29C3F" xml:space="preserve">Tum primo / q2 op­<lb/>poſitū aſſerit phūs in poſt predicamētis. </s>
              <s xml:id="N29C44" xml:space="preserve">Tum ſecū­<lb/>do / q2 bene ſequitur in iſto mēbro eſt ſanitas: ergo <lb/>in iſto mēbro eſt diſpoſitio naturalis ex qua opera­<lb/>tiones eius naturales et ꝓportionate ꝓueniunt: et ī <lb/>iſto mēbro ē egritudo: ergo ī iſto mēbro eſt diſpoſi-<lb/>tto ex qua non proueniunt operationes eius natu-<lb/>rales et proportionate: ſed iſtã ↄ̨ña implicãt cõtra-<lb/>dictionē / igit̄̄ illud ex quo ſequitur eſt impoſſibile.</s>
            </p>
            <div xml:id="N29C55" level="5" n="11" type="float">
              <note position="right" xlink:href="note-0254-03a" xlink:label="note-0254-03" xml:id="N29C59" xml:space="preserve">phūs .4. <lb/>metha.</note>
              <note position="right" xlink:href="note-0254-04a" xlink:label="note-0254-04" xml:id="N29C61" xml:space="preserve">1. cõfir̄a°</note>
              <note position="right" xlink:href="note-0254-05a" xlink:label="note-0254-05" xml:id="N29C67" xml:space="preserve">2. ↄ̨firma</note>
            </div>
            <note position="right" xml:id="N29C6D" xml:space="preserve">3. cõfir̄a°.</note>
            <p xml:id="N29C71">
              <s xml:id="N29C72" xml:space="preserve">¶ Confirmatur tertio / quia termini motus ſunt in-<lb/>compoſſibiles per phm̄ quinto phiſicorū ſed cali-<lb/>ditas et frigiditas albedo et nigredo ſunt termini <lb/>motus: igitur ſunt īcõpoſſibiles. </s>
              <s xml:id="N29C7B" xml:space="preserve">Minor patet / q2 in <lb/>motu calefactionis frigiditas eſt vnus terminꝰ pu-<lb/>ta a quo. </s>
              <s xml:id="N29C82" xml:space="preserve">et caliditas alter puta terminꝰ ad quē igr̄.</s>
            </p>
            <p xml:id="N29C85">
              <s xml:id="N29C86" xml:space="preserve">Quinto principaliter arguitur ſic </s>
              <s xml:id="N29C89" xml:space="preserve">Si               <pb chead="De formis contrariis." file="0255" n="255"/>               qualitates contrarie ſe cõpaterent̄̄ ſequeret̄̄ /  mix­<lb/>tio non eſſet poſſibilis: ſed conſequens eſt falſum: <lb/>igitur. </s>
              <s xml:id="N29C95" xml:space="preserve">Sequela ꝓbat̄̄ / q2 ſi q̈litates contrarie ſe cõ­<lb/>patiuntur cõplexio non ē poſſibilis: igitur nec mix­<lb/>tio cum cõplexio formã mixti conſeruat ſine q̈ for̄a <lb/>mixti non poſſet in materia prīa durare. </s>
              <s xml:id="N29C9E" xml:space="preserve">Probat̄̄ <lb/>ſequela / q2 cõplexio eſt qualitas ſecūda reſultãs ex <lb/>actione q̈litatū primaꝝ etc. / vt patet ꝑ auicēnã prima <lb/>fen primi canonis .d. tertia: ſed talis q̈litas ſecūda <lb/>non eſt poſſibilis: igr̄ nec cõplexio. </s>
              <s xml:id="N29CA9" xml:space="preserve">Añs ꝓbat̄̄ / quia <lb/>agentibꝰ et patientibus elementis ad inuicē ꝑ te ī ele­<lb/>mentum frigidum ꝓducit̄̄ caliditas in calidū frigi­<lb/>ditas in ſiccū humiditas in humidū ſiccitas tantuꝫ­<lb/>modo. </s>
              <s xml:id="N29CB4" xml:space="preserve">igr̄ agētibꝰ et patientibus elementis ad inui­<lb/>cē nõ videtur quomodo ibi generat̄̄ vna q̈litas ſecū­<lb/>da. </s>
              <s xml:id="N29CBB" xml:space="preserve">Patet conſequentia / q2 vbi corrūpit̄̄ aliq̈ quali­<lb/>tas prima ibi ita cito adequate ꝓducitur ſua cõtra­<lb/>ria quõ ibi igr̄ producetur qualitas illa ſecunda.</s>
            </p>
            <note position="left" xml:id="N29CC2" xml:space="preserve">auicēna. <lb/>ṗma ṗmi</note>
            <p xml:id="N29CC8">
              <s xml:id="N29CC9" xml:space="preserve">¶ Et confirmatur / q2 ſi qualitates contrarie ſe com­<lb/>patiunt̄̄: ſequeret̄̄ /  ad ꝑmutationē complexionis ī­<lb/>di in complexionem ſclaui non ſequeret̄̄ mors vel ī-<lb/>firmitas / quod eſt contra Auicēnã prima fen .pri. c. <lb/>d. 3. </s>
              <s xml:id="N29CD4" xml:space="preserve">Sequela probatur / q2 cū introducētia cõplexio­<lb/>nem indi agūt in complexioneꝫ ſclaui: cõplexio ſcla­<lb/>ui temperat̄̄. </s>
              <s xml:id="N29CDB" xml:space="preserve">et poſt totalem corruptionem cõplexio­<lb/>nis ſclaui introducta ē cõplexio indi cum qua anīa <lb/>rationalis eque bene poteſt ſtare et exercere opera-<lb/>tiones ſibi naturales ſicut cū complexione ſclaui vĺ <lb/>melius: igitur ad ꝑmutationem cõplexionis ſclaui ī <lb/>complexionem indi non ſequitur neceſſario mors <lb/>vel infirmitas / quod fuit probandū </s>
              <s xml:id="N29CEA" xml:space="preserve">Antecedens pro­<lb/>batur / q2 introducentia cõplexionē indi corrūpēdo <lb/>complexionē ſclaui ſucceſſiue et eque velociter ꝓdu-<lb/>cūt cõplexionē indi ꝑ te cum ſint qualitates contra­<lb/>rie: et complexio indi et complexio ſclaui ſunt extre-<lb/>ma: igitur per mixtionē complexionis ſclaui cū cõ-<lb/>plexione indi tota complexio redditur temperãtior <lb/>et temperantius homo ab illo aggregato mutatur <lb/>et alteratur / quod fuit probandum.</s>
            </p>
            <p xml:id="N29CFD">
              <s xml:id="N29CFE" xml:space="preserve">In oppoſitum tamē arguit̄̄ ſic / in qua­<lb/>libet parte aque tepide eſt caliditas et frigiditas: <lb/>igitur forme contrarie ſe compatiuntur. </s>
              <s xml:id="N29D05" xml:space="preserve">Antecedēs <lb/>patet / q2 in quolibet tepido eſt caliditas et frigidi-<lb/>tas et quelibet pars tepidi ē tepida: igitur in quali­<lb/>bet parte aque tepide eſt caliditas et frigiditas.</s>
            </p>
            <p xml:id="N29D0E">
              <s xml:id="N29D0F" xml:space="preserve">¶ Dices forte negando antecedens et ad ꝓbationeꝫ <lb/>negando minorē. </s>
              <s xml:id="N29D14" xml:space="preserve">Imo dices /  aliqua pars aq̄ te­<lb/>pide eſt totaliter frigida et  tūc aqua dicitur tepi-<lb/>da cum particule quedam ipſius aque totaliter <lb/>calide ꝙ̄ plurimis particulis frigidis ſimpliciter <lb/>commiſcentur.</s>
            </p>
            <p xml:id="N29D1F">
              <s xml:id="N29D20" xml:space="preserve">Sed contra / quia quelibet ꝑs aque te­<lb/>pide calefacit et frigefacit: igitur in qualibet eſt ca-<lb/>liditas et frigiditas. </s>
              <s xml:id="N29D27" xml:space="preserve">Antecedens probatur / quia ſi ī <lb/>quauis parte aque tepide ponatur aliquod corpus <lb/>valde calidum illḋ frigefit vel ſaltem eius caliditas <lb/>remittitur: et nõ niſi a frigiditate: igit̄̄ ibi eſt frigi-<lb/>ditas intenſa: et ſi in eadē parte ponat̄̄ frigidū illḋ <lb/>calefiet vel ſaltē eius frigiditas remitteret̄̄ et nõ niſi <lb/>a caliditate: ergo in eadem parte eſt caliditas. </s>
              <s xml:id="N29D36" xml:space="preserve">Nec <lb/>valet dicere ſicut videtur dicere. </s>
              <s xml:id="N29D3B" xml:space="preserve">Gregorius de ari-<lb/>mino  in qualibet parte tepidi eſt caliditas et fri-<lb/>giditas: ſed inadequate q2 capio a. partem et tota-<lb/>lem eius caliditatem que (vt conſtat) ē aliqualis ex­<lb/>tenſionis adequate. </s>
              <s xml:id="N29D46" xml:space="preserve">tunc arguo ſic vel ſub illa extē-<lb/>ſione caliditatis eſt aliqua frigiditas vel nulla. </s>
              <s xml:id="N29D4B" xml:space="preserve">ſi ṗ­<lb/>mum ſigno adequatã illius frigiditatis extenſionē <lb/>et ſequitur /  in eodē adequate ſunt caliditas et fri-               <cb chead="De formis contrariis."/>               giditas. </s>
              <s xml:id="N29D55" xml:space="preserve">ſi ſecundum ſequitur /  aliqua pars tepide <lb/>eſt in qua non eſt caliditas et frigiditas </s>
              <s xml:id="N29D5A" xml:space="preserve">Omnis em̄ <lb/>qualitas corpores ſuum adequatum habet ſubiec-<lb/>tum et adequatam extenſionem. </s>
              <s xml:id="N29D61" xml:space="preserve">Item in qualib3 ꝑ­<lb/>te tepidi eſſe caliditatē et frigiditatē et in nulla ade-<lb/>quate adeo eſt īmaginabile ſicut  quelꝫ pars po-<lb/>roſi eſt poroſa. </s>
              <s xml:id="N29D6A" xml:space="preserve">Quod probat̄̄ īpoſſibile primo de <lb/>generatione. </s>
              <s xml:id="N29D6F" xml:space="preserve">Analogia patet ſubtilius rimãti. </s>
              <s xml:id="N29D72" xml:space="preserve">Si­<lb/>cut enim dicis /  in qualibet parte tepidi eſt calidi­<lb/>tas et frigiditas: ſed inadequate equa ratione dice­<lb/>retur /  in qualibet parte corporis poroſi eſt poro-<lb/>ſitas et non poroſitas ſiue continuatas: ſꝫ nullibi ē <lb/>non poroſitas adequate.</s>
            </p>
            <p xml:id="N29D7F">
              <s xml:id="N29D80" xml:space="preserve">Pro diſſolutione huius queſtionis er̄t <lb/>tres articuli in primo ponentur notanda ex quibꝰ <lb/>concluſio reſponſiua ad queſitum elicietur. </s>
              <s xml:id="N29D87" xml:space="preserve">In ſecū­<lb/>do dubia </s>
              <s xml:id="N29D8C" xml:space="preserve">In tertio rationes ante oppoſituꝫ diſſol­<lb/>uentur.</s>
            </p>
            <p xml:id="N29D91">
              <s xml:id="N29D92" xml:space="preserve">Notandum eſt /  de hac queſtiõe due <lb/>ſunt extreme opiniones et famate.               <anchor type="note" xlink:href="note-0255-01" xlink:label="note-0255-01a"/>               </s>
              <s xml:id="N29D9C" xml:space="preserve">Prima eſt quaꝫ <lb/>inſequitur et defendit Gregorius de arimino in pri­<lb/>mo ſententiarum diſ. 17. vcꝫ  qualitates cõtrarie <lb/>in nullis gradibus ſe compatiunt̄̄. </s>
              <s xml:id="N29DA5" xml:space="preserve">Imo a tota ſpē <lb/>ſe expellunt. </s>
              <s xml:id="N29DAA" xml:space="preserve">Secunda eſt opinio doctoris ſubtilis. <lb/></s>
              <s xml:id="N29DAE" xml:space="preserve">ſecundo ſententiarum et iacobi forliuiēſis in ſuo tra­<lb/>ctatu de intenſione et remiſſione formarum:  vcꝫ q̈­<lb/>litates contrarie ſe compatiuntnr in aliquibꝰ gra­<lb/>dibus remiſſis </s>
              <s xml:id="N29DB7" xml:space="preserve">Pro declaratione huius opinionis <lb/>pono tres concluſiones.</s>
            </p>
            <div xml:id="N29DBC" level="5" n="12" type="float">
              <note position="right" xlink:href="note-0255-01a" xlink:label="note-0255-01" xml:id="N29DC0" xml:space="preserve">gre. i: ſen <lb/>d. 17</note>
            </div>
            <p xml:id="N29DC8">
              <s xml:id="N29DC9" xml:space="preserve">Prima concluſio </s>
              <s xml:id="N29DCC" xml:space="preserve">Et ſi impoſſibile eſt <lb/>duas qualitates cõtrarias ſūmas: aut vnã ſummã <lb/>et aliam remiſſam ſe cõpati: nihilominus duas q̈li-<lb/>tates contrarias in gradibus remiſſis compoſſibi­<lb/>les eē in eodem ſubiecto adequato ambigendum ē <lb/>minime. </s>
              <s xml:id="N29DD9" xml:space="preserve">Prīa pars huius concluſionis ꝓbatur / q2 <lb/>ſi alique qualitates contrarie in gradibus ſūmis ſe <lb/>compatiuntur et etiam in gradibus remiſſis: ille ne­<lb/>qua̄ eſſent contrarie: cum nec ſecundum ſe nec m <lb/>aliquas eiuſdē ſpeciei cum illis ſe expellūt: ſed aliq̄ <lb/>ſunt contrarie: igit̄̄ ſaltē in gradibus ſummis ſe ex­<lb/>pellūt. </s>
              <s xml:id="N29DE8" xml:space="preserve">Secunda pars probatur argumēto facto ī <lb/>oppoſitū et ꝓbabitur in primo dubio per argumen­<lb/>ta in aduerſam opinionem adducenda.</s>
            </p>
            <p xml:id="N29DEF">
              <s xml:id="N29DF0" xml:space="preserve">Secunda concluſio </s>
              <s xml:id="N29DF3" xml:space="preserve">Poſſibile eſt qua­<lb/>litates contrarias in gradibus remiſſioribꝰ mediis <lb/>gradibus ſuarum latitudinum ſe compati in eodē <lb/>ſubiecto adeq̈te.               <anchor type="note" xlink:href="note-0255-02" xlink:label="note-0255-02a"/>               </s>
              <s xml:id="N29E01" xml:space="preserve">Hanc concluſionem ꝓbabiliter po­<lb/>no contra iacobum de forliuio. </s>
              <s xml:id="N29E06" xml:space="preserve">Quam ſic ꝓbo / q2 <lb/>poſſibile eſt dare corpus ī quo eſt remiſſa caliditas <lb/>ſuo neqna̄ permixta contrario: igitur poſſibile ē <lb/>qualitates contrarias in gradibus remiſſioribus <lb/>gradibus mediis ſuarum latitudinum ſe compati ī <lb/>eodem ſubiecto adequate. </s>
              <s xml:id="N29E13" xml:space="preserve">Probat̄̄ conſequentia / <lb/>que aduerſario ē manifeſta / q2 ſit illḋ corpꝰ a. ī quo <lb/>eſt caliditas remiſſa ī ꝑmixta contrario: 4. graduū <lb/>caliditatis: et agat in illud ſumme frigidum: et ar-<lb/>guo ſic tale frigidum introducendo primum gradū <lb/>frigiditatis corrumplt adequate. </s>
              <s xml:id="N29E20" xml:space="preserve">quartum calidi-<lb/>tatis: et introducendo ſcḋm gradum frigiditatꝪ cor­<lb/>rūpit tertiū caliditatis: igr̄ tunc in illo corpore ma­<lb/>nent adequate duo gradus caliditatis duobꝰ fri-<lb/>giditatis admixti: et per conſequens dantur quali­<lb/>tates contrarie ſe compatientes ī remiſſioribꝰ gra­<lb/>dibus mediis ſuarum latitudinum gradibus: ſi ca­<lb/>liditas remiſſa in aliquo ſubiecto ſuo ſit impermix­<lb/>ta contrario. </s>
              <s xml:id="N29E33" xml:space="preserve">Non enim ſubito 4. gradus frigidi-<lb/>tatis inducitur aut .4. caliditatis corrumpitur / igr̄               <pb chead="Quarti tractatus." file="0256" n="256"/>               immediate poſt hoc caliditas et frigiditas non con­<lb/>ſtituēt numerū totalis latitudinis. </s>
              <s xml:id="N29E3F" xml:space="preserve">Sed iam probo <lb/>antecedens / quia dabilis eſt aer in ſua naturali diſ­<lb/>poſitione: et talis habet humiditatē ſummã: et cali-<lb/>ditatem remiſſam non permixtam contrario cum ī <lb/>ſua naturali diſpoſitione non exigat aliquam fri-<lb/>giditatem: igitur eſt dare corpus in quo eſt remiſſa <lb/>caliditas ſuo ī ꝑmixta ↄ̈rio / quod fuit ꝓbanduꝫ. </s>
              <s xml:id="N29E4E" xml:space="preserve">An­<lb/>tecedens patet / q2 naturalis diſpoſitio aeris p̄t ab <lb/>aliquibus cauſis naturalibus produci </s>
              <s xml:id="N29E55" xml:space="preserve">(Alias enim <lb/>non eēt illa diſpoſitio aeri naturalis cum nõ poſſꝫ <lb/>eē aut a rerum natura produci) / igit̄̄ aliquando fuit <lb/>naturaliter loquendo: aut aliquãdo erit: vel modo <lb/>eſt               <anchor type="note" xlink:href="note-0256-01" xlink:label="note-0256-01a"/>               </s>
              <s xml:id="N29E65" xml:space="preserve">Nulla enim potentia eſt fruſtra in natura primo <lb/>celi </s>
              <s xml:id="N29E6A" xml:space="preserve">Ponatur igitur / illud ineſſe et habebitur propo­<lb/>ſitū </s>
              <s xml:id="N29E6F" xml:space="preserve">Itē ignis ſūme calidus poteſt remitti a ſummo <lb/>frigido maiori ſine inductione contrarie forme ī ip­<lb/>ſo igne: cum ignis a tota ſpecie nullū gradū frigidi­<lb/>tatis patiat̄̄: igitur in igne reperibilis eſt aliqua ca­<lb/>liditas remiſſa contrarii expers </s>
              <s xml:id="N29E7A" xml:space="preserve">Item ſortes q̇ nū-<lb/>̄ fuit temperatus vel habuit habitum temperãtie <lb/>p̄t habere habitū intēperantie remiſſum ſine habi-<lb/>tu contrario: igitur ꝓpoſitum. </s>
              <s xml:id="N29E83" xml:space="preserve">Antecedens patꝫ: q2 <lb/>alias ſortes q̇ nun̄ habuit habitum temperantie <lb/>non poſſet a non gradu acquirere habitum intēpe-<lb/>rantie: quin eum ſubito acquireret vſ ad gradum <lb/>ſummū: vel ſi ſucceſſiue acquireret: per aliquod tp̄s <lb/>plus produceretur in eo de habitu temperantie ̄ <lb/>intemperantie et ſic ſortes q̇ nun̄ habuit habitum <lb/>temperantie nec intemperantie non poſſet prīo eē <lb/>ītēꝑatꝰ nec tēꝑatꝰ. </s>
              <s xml:id="N29E96" xml:space="preserve">Imo neceſſario priꝰ per magnuꝫ <lb/>tempus eēt temperatus cum per magnū tempꝰ ha-<lb/>bitus temperantie maior eēt et intenſior  habitꝰ <lb/>intemperantie acquiſitꝰ ſucceſſiue a non gradu: quo <lb/>nihil abſurdius. </s>
              <s xml:id="N29EA1" xml:space="preserve">Item ſortes poteſt opinari remiſ-<lb/>ſe abſ ſcientia: igitur propoſitum. </s>
              <s xml:id="N29EA6" xml:space="preserve">Antecedens pꝫ <lb/>facile / q2 põt ꝓpoſitionē nū̄ antea apprehenſam: <lb/>ꝑꝑ rationem aliquã topicã opinari non habita de-<lb/>monſtratione aliqua: igitur ſortes poteſt opinari <lb/>remiſſe abſ ſcientia. </s>
              <s xml:id="N29EB1" xml:space="preserve">Antecedēs patet / q2 in tali ca­<lb/>ſu eſt cauſa ꝓducens ſcīam vt conſtat: igr̄ </s>
              <s xml:id="N29EB6" xml:space="preserve">Item ali­<lb/>as idem ſequeretur quod ſupra.</s>
            </p>
            <div xml:id="N29EBB" level="5" n="13" type="float">
              <note position="right" xlink:href="note-0255-02a" xlink:label="note-0255-02" xml:id="N29EBF" xml:space="preserve">ↄ̈ ia. ḋ for­<lb/>liuio.</note>
              <note position="left" xlink:href="note-0256-01a" xlink:label="note-0256-01" xml:id="N29EC7" xml:space="preserve">phūs. 1. c.</note>
            </div>
            <p xml:id="N29ECD">
              <s xml:id="N29ECE" xml:space="preserve">Tertia concluſio. </s>
              <s xml:id="N29ED1" xml:space="preserve">Omnes gradꝰ dua­<lb/>rum qualitatum contrariarum non excedentes nu-<lb/>merum totalis latitudinis alterius illarum ſūt ī eo­<lb/>dem ſubiecto adequato compoſſibiles: excedentes <lb/>vero: ſe cõpatiuntur minime. </s>
              <s xml:id="N29EDC" xml:space="preserve">Prima pars huiꝰ cõ-<lb/>cluſionis probatur / q2 in aliquibus gradibus qua-<lb/>litates contrarie ſe cõpatiunt̄̄ / vt probatum eſt ar-<lb/>gumento in oppoſitū facto: et non in gradibus tota­<lb/>lem latitudinem excedentibus / vt probabitur: cū ſe-<lb/>cunda pars concluſionis probabit̄̄: igitur in omni­<lb/>bus non excedentibus ſe ↄ̨patiunt̄̄. </s>
              <s xml:id="N29EEB" xml:space="preserve">Secunda ꝑs ꝓ-<lb/>batur ſuppoſito /  ad inductionem vnius gradus q̈­<lb/>litatis contrarie ſequitur adequate vniꝰ gradus al­<lb/>terius corruptio ſi contraria ſit in ſubiecto </s>
              <s xml:id="N29EF4" xml:space="preserve">Et ar-<lb/>guo ſic: ſi gradus qualitatum contrariarum excedē­<lb/>tes totalē latitudinem alterius illaꝝ ſe compatiun­<lb/>tur: ponat̄̄ /  in aliquo corpore ſint ſex gradus cali­<lb/>ditatis: tribꝰ frigiditatis admixti. </s>
              <s xml:id="N29EFF" xml:space="preserve">et approximetur <lb/>ſumme calidū introducēs caliditatē in tale corpus <lb/>et eius remittens frigiditatem. </s>
              <s xml:id="N29F06" xml:space="preserve">Quo poſito arguit̄̄ <lb/>ſic / per inductionem ſeptimi gradus caliditatis cor­<lb/>rumpitur tertius frigiditatis: et ad inductionē octa­<lb/>ui corrumpit̄̄ ſecūdus frigiditatis adequate ex ſup­<lb/>poſito: igitur manet caliditas ſumma cum vno gra­<lb/>du frigiditatis: conſequens eſt impoſſibile per pri-<lb/>mam concluſionem: igitur illud ex quo ſequitur. </s>
              <s xml:id="N29F15" xml:space="preserve">et ꝑ               <cb chead="Capitulum ſecundum."/>               conſequens eius oppoſitum verum / quod fuit ꝓbã-<lb/>dum.               <anchor type="note" xlink:href="note-0256-02" xlink:label="note-0256-02a"/>               </s>
              <s xml:id="N29F22" xml:space="preserve">¶ Ex quo ſequitur primo /  iſta ↄ̨ña nihil valꝫ <lb/>iſte due qualitates ſunt contrarie: igitur ſe mutuo <lb/>expellunt: </s>
              <s xml:id="N29F29" xml:space="preserve">Iſta tamen eſt bona iſte qualitates ſunt <lb/>contrarie / igitur mutuo ſe expellunt ſecundum ſe vĺ <lb/>ſibi ſimiles in ſpecie. </s>
              <s xml:id="N29F30" xml:space="preserve">Patet correlarium ex dictis ī <lb/>ſecundo argumēto ante oppoſitum. </s>
              <s xml:id="N29F35" xml:space="preserve">Nolo enim di-<lb/>cere gradus caliditatis frigiditatis ſe compatien-<lb/>tes nõ eē contrarios qm̄ ad eoꝝ contrarietatē ſuf­<lb/>ficit /  poſſint eē partes qualitatum ſe mutuo expel­<lb/>lentium puta ſūmarum.               <anchor type="note" xlink:href="note-0256-03" xlink:label="note-0256-03a"/>               </s>
              <s xml:id="N29F45" xml:space="preserve">¶ Sequitur ſecundo /  in <lb/>diffinitione qualitatum contrarium debet addi <lb/>hec ꝑticula ſecundum ſe vel ſibi ſimiles in ſpecie: ita <lb/>vt totalis diffinitio ſit iſta </s>
              <s xml:id="N29F4E" xml:space="preserve">Contraria ſunt que ab <lb/>eodem genere poſita ſunt: et maxime a ſe inuicem di­<lb/>ſtant et eidem ſuſceptibili viciſſim īſunt: et mutuo ſe <lb/>expellunt: m ſe vel ſibi ſimiles in ſpecie.               <anchor type="note" xlink:href="note-0256-04" xlink:label="note-0256-04a"/>               </s>
              <s xml:id="N29F5C" xml:space="preserve">¶ Sequit̄̄ <lb/>tertio /  quãuis gradus qualitatuꝫ contrariarum <lb/>quorum numerus excedit totalem latitudinem al-<lb/>terius illarum non ſint cõpoſſibiles: tamē gradus <lb/>qualitatum ↄ̈riarum quorū totalis numerus ē mi-<lb/>nor totali numero latitudinis graduum alterius il-<lb/>larum bene ſe admittūt et ſe in eodē adequate ſub-<lb/>iecto cõpatiuntur vt .3. gradus caliditatis tribꝰ fri-<lb/>giditatis. </s>
              <s xml:id="N29F6F" xml:space="preserve">Patet correlarium ex ſecunda cõcluſiõe.</s>
            </p>
            <div xml:id="N29F72" level="5" n="14" type="float">
              <note position="right" xlink:href="note-0256-02a" xlink:label="note-0256-02" xml:id="N29F76" xml:space="preserve">1. correla.</note>
              <note position="right" xlink:href="note-0256-03a" xlink:label="note-0256-03" xml:id="N29F7C" xml:space="preserve">2. correlã</note>
              <note position="right" xlink:href="note-0256-04a" xlink:label="note-0256-04" xml:id="N29F82" xml:space="preserve">.3. correl.</note>
            </div>
            <p xml:id="N29F88">
              <s xml:id="N29F89" xml:space="preserve">Dubitatur primo vtrum ſit probabile <lb/>contraria in omnibus gradibus ſe expellere.</s>
            </p>
            <p xml:id="N29F8E">
              <s xml:id="N29F8F" xml:space="preserve">¶ Dubitatur ſecundo vtrum cõplexio ſit qualitas <lb/>producta ex actione qualitatum primaꝝ ↄ̈riarum. <lb/></s>
              <s xml:id="N29F95" xml:space="preserve">¶ Dubitatur tertio vtrum complexio indi põt mu-<lb/>tari in complexionem ſclaui ſine morte aut egritu-<lb/>dine.</s>
            </p>
            <p xml:id="N29F9C">
              <s xml:id="N29F9D" xml:space="preserve">Ad primum dubium </s>
              <s xml:id="N29FA0" xml:space="preserve">Arguitur primo <lb/>ratione doctoris ſubtilis ſecundo ſen. d. 2. q̄ſ. 9. </s>
              <s xml:id="N29FA5" xml:space="preserve">Si <lb/>contraria in quibuſcun gradibus ſunt incõpoſſi­<lb/>bilia: ſequitur ſubiectū aliqñ eē denudatū ab vtro-<lb/> contrariorum, aut nun̄ dari aliquã totalem al­<lb/>terationem ſucceſſiuam: ſed conſequens eſt falſum / <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N29FB2" xml:space="preserve">Falſitas conſequentis <lb/>pro ſecunda parte probatur. </s>
              <s xml:id="N29FB7" xml:space="preserve">q2 nulla totalis alte-<lb/>ratio eēt motus / quod eſt ↄ̈ phm̄. </s>
              <s xml:id="N29FBC" xml:space="preserve">Pro prima parte <lb/>ſimiliter probatur: q2 nun̄ vnū contrariorum cor­<lb/>rumpitur: niſi vt aliud inducatur: ergo cū primum <lb/>fuerit corruptū aliud inducitur: et ſic nū̄ non denu­<lb/>datum ab vtro contrarioruꝫ. </s>
              <s xml:id="N29FC7" xml:space="preserve">Sequela tñ ꝓbat̄̄ / q2 <lb/>per te in nullo tempore caliditas eſt ſimul cum fri-<lb/>gidate. </s>
              <s xml:id="N29FCE" xml:space="preserve">incipiat igitur calidum agere in frigidum <lb/>remittittendo eius frigiditatem: vſ ad non gra-<lb/>dum: deinde introducendo caliditatem. </s>
              <s xml:id="N29FD5" xml:space="preserve">Quo poſi­<lb/>to capio inſtans medium copulans tempus in quo <lb/>nihil eſt caliditatis in illo paſſo cum tempore ī quo <lb/>nihil eſt frigiditatis puta inſtans in quo primū fri­<lb/>giditas eſt vſ ad non gradum remiſſa / et arguo ſic / <lb/>vel in illo inſtanti eſt aliquid frigiditatꝪ in paſſo vĺ <lb/>aliquid caliditatis: vel ne caliditas ne frigidi-<lb/>tas. </s>
              <s xml:id="N29FE6" xml:space="preserve">Non primum q2 ex caſu illud inſtans eſt ṗmuꝫ <lb/>non eē frigiditatis cõpletum: et in illo frigiditas eſt <lb/>primum remiſſa complete ad non gradum: igit̄̄ dã-<lb/>dum eſt ſecundum vel tertium: et ſic vel ſubito induc­<lb/>ta eſt in paſſum aliquãta caliditas: vel in eo nec eſt <lb/>caliditas nec frigiditas / ex quo ſequitur ꝓbandum <lb/></s>
              <s xml:id="N29FF4" xml:space="preserve">¶ Dices forte ſicut dicit quidã concedendo ſequelaꝫ <lb/>et negando falſitatem conſequentis. </s>
              <s xml:id="N29FF9" xml:space="preserve">imo in inſtan­<lb/>ti illo medio in paſſo illo nec eſt caliditas nec frigi-<lb/>ditas. </s>
              <s xml:id="N2A000" xml:space="preserve">Et dicit /  non eſt inconueuiēs  maneat ſub­<lb/>iectum per inſtans denudatum ab vtro contrario­<lb/>rum. </s>
              <s xml:id="N2A007" xml:space="preserve">Et cum arguitur illud eē falſum / quia tunc nõ               <pb chead="De formis contrariis." file="0257" n="257"/>               darentur contraria immediata: </s>
              <s xml:id="N2A00F" xml:space="preserve">Negat conſequen­<lb/>tiam </s>
              <s xml:id="N2A014" xml:space="preserve">Dicit enim /  non ideo dicuntur contraria im­<lb/>mediata / q2 ſubiectum nec per tempus nec per īſtãs <lb/>non poteſt eē ſine altero illoruꝫ: ſed ideo ſunt imme­<lb/>diata / q2 ſubiectum per tempus non põt eē ſine alte­<lb/>ro illorum quãuis poſſit per inſtans.</s>
            </p>
            <p xml:id="N2A01F">
              <s xml:id="N2A020" xml:space="preserve">Sed contra hoc arguitur ſic / quia ſi ſo­<lb/>lutio eēt bona ſequeretur /  etiam per tempus poſ­<lb/>ſet eē nec ſanum nec egrum: ſed conſequens eſt falſū / <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N2A029" xml:space="preserve">Sequela probat̄̄ et po­<lb/>no caſum /  alicui animali egro adhibeatur medi-<lb/>cina remittens per horam egritudinem ad non gra­<lb/>dum: ita  in inſtanti terminatiuo nihil ſit egritudi­<lb/>nis et ſucceſſiue per eandem horam approximet̄̄ ali­<lb/>quod agens contrarium inductioni ſanitatis / qḋ <lb/>primo medicinam inductiuam ſanitatis et impedia­<lb/>tur adequate ab ea. </s>
              <s xml:id="N2A03A" xml:space="preserve">Quo poſito manentibus illis <lb/>ſic per tempus in tali animali nec erit ſanitas nec <lb/>egritudo: igitur per tempus erit aliquod anīal de­<lb/>nudatum ab vtro īmeditatorum contrarioruꝫ / qḋ <lb/>fuit probandum </s>
              <s xml:id="N2A045" xml:space="preserve">Nec valet dicere /  tūc animal de­<lb/>ſinit eē. </s>
              <s xml:id="N2A04A" xml:space="preserve">Tum primo  tunc aliquod animal deſine­<lb/>ret eſſe ſine aliqua egritudine / quod eſt falſum.               <anchor type="note" xlink:href="note-0257-01" xlink:label="note-0257-01a"/>               </s>
              <s xml:id="N2A054" xml:space="preserve">¶ Di-<lb/>ces ſicut dicendum eſt negando ſequelam. </s>
              <s xml:id="N2A059" xml:space="preserve">ymo di-<lb/>ces /  tunc illud morietur. </s>
              <s xml:id="N2A05E" xml:space="preserve">Et cū probat̄̄ /  nõ quia <lb/>tunc aliquod animal deſineret eē ſine aliqua egri-<lb/>tudine: nego ſequelam. </s>
              <s xml:id="N2A065" xml:space="preserve">Et ratio ē / q2 illud agens cõ­<lb/>trarium ſanitati vel qualitas mediante qua agit ē <lb/>illi animali egritudo. </s>
              <s xml:id="N2A06C" xml:space="preserve">Unde egritudo eſt queuis diſ­<lb/>poſitio ſenſibiliter ledens operationes animalis. <lb/></s>
              <s xml:id="N2A072" xml:space="preserve">vt etc̈. infra dicetur ex quo ſequitur /  non omne il-<lb/>lnd in quo eſt egritudo ſubiectiue eſt egrum. </s>
              <s xml:id="N2A077" xml:space="preserve">plerū <lb/>eni3 denominat̄̄ animal egrū per egritudinem que <lb/>non eſt iu ipſo:               <anchor type="note" xlink:href="note-0257-02" xlink:label="note-0257-02a"/>               </s>
              <s xml:id="N2A083" xml:space="preserve">Et hoc eſt correlarium de forliuio <lb/>prima primi .9.4.</s>
            </p>
            <div xml:id="N2A088" level="5" n="15" type="float">
              <note position="left" xlink:href="note-0257-01a" xlink:label="note-0257-01" xml:id="N2A08C" xml:space="preserve">dicitur.</note>
              <note position="left" xlink:href="note-0257-02a" xlink:label="note-0257-02" xml:id="N2A092" xml:space="preserve">de forli.</note>
            </div>
            <p xml:id="N2A098">
              <s xml:id="N2A099" xml:space="preserve">Sed contra / quia tunc homo deſine-<lb/>ret eē per vltimum inſtans ſui eſſe. </s>
              <s xml:id="N2A09E" xml:space="preserve">Sed conſequens <lb/>eſt falſum: igitur illud ex quo ſequitur. </s>
              <s xml:id="N2A0A3" xml:space="preserve">Sequela pa­<lb/>tet aſpicienti. </s>
              <s xml:id="N2A0A8" xml:space="preserve">¶ Reſpondeo /  non habeo illud ī ta­<lb/>li caſu pro inconuenienti.</s>
            </p>
            <p xml:id="N2A0AD">
              <s xml:id="N2A0AE" xml:space="preserve">Pro epilogo autem huius materie ad­<lb/>uerte hanc diſtīctionē forme introducēde abiicien­<lb/>de. </s>
              <s xml:id="N2A0B5" xml:space="preserve">q2 vel talis forma abiiciēda requiritur ad cõſer-<lb/>uationem paſſi. </s>
              <s xml:id="N2A0BA" xml:space="preserve">Et ſic dico /  in inſtanti corruptio-<lb/>nis talis forme corrumpitur paſſum: </s>
              <s xml:id="N2A0BF" xml:space="preserve">Et introducit̄̄ <lb/>ſubito contraria forma in materia ſi nulla ſit paſ-<lb/>ſi reſiſtentia. </s>
              <s xml:id="N2A0C6" xml:space="preserve">Si vero non requiritur forma expellē­<lb/>da ad conſeruationem paſſi aut forma introducen­<lb/>da eſt paſſo conſentanea et naturalis: aut non. </s>
              <s xml:id="N2A0CD" xml:space="preserve">Si <lb/>primum ſnbito introducitur dummõ non ſit contra­<lb/>rium circunſtans aut aliquod īpediens. </s>
              <s xml:id="N2A0D4" xml:space="preserve">Si nõ tunc <lb/>manet paſſum per inſtans vel per tempus ſi natum <lb/>ſit manere ab vtro contrariorum denudatum ꝓ-<lb/>pter reſiſtentiam. </s>
              <s xml:id="N2A0DD" xml:space="preserve">Sed tamen non manebit per tem­<lb/>pus ſi contraria ſint īmediata.</s>
            </p>
            <p xml:id="N2A0E2">
              <s xml:id="N2A0E3" xml:space="preserve">Sed contra / quia ſubiectum contrari­<lb/>orum īmediatorum ſtat naturaliter ſine altero illo­<lb/>rum / quod eſt ſibi conueniens et cum ſibi diſconueni­<lb/>enti: igitur poteſt ſtare naturaliter ſine conuenien-<lb/>ti et ſine diſconuenienti ſimul. </s>
              <s xml:id="N2A0EE" xml:space="preserve">Patet conſequentia / <lb/>quia alias propter deſitionē diſpoſitionis diſcon­<lb/>uenientis ſubiectum deſineret eē / quod eſt abſurduꝫ <lb/>in philoſophia.</s>
            </p>
            <p xml:id="N2A0F7">
              <s xml:id="N2A0F8" xml:space="preserve">Secundo arguitur </s>
              <s xml:id="N2A0FB" xml:space="preserve">Et pono minimū <lb/>naturale inter calidum et frigidum in equali diſtan­               <cb chead="De formis contrariis."/>               tia ita  calidū et frigidum nata ſint agere ab eq̈li <lb/>ꝓportione in illud minimū naturale et ſit illud mi-<lb/>nimū naturale ita natū ſuſcipere actionem vnius ſi­<lb/>cut alṫi. </s>
              <s xml:id="N2A109" xml:space="preserve">Quo poſito ſic argumētor calidū agit ī il-<lb/>lud minimū naturale cum habeat ꝓportionem ma­<lb/>ioris īequalitatis ad ipſuꝫ. </s>
              <s xml:id="N2A110" xml:space="preserve">Et ſimiliter frigidū: et <lb/>non per diuerſas partes cum illud ſit minimū natū <lb/>ſuſcipere caliditatem et frigiditatem que per ſe po­<lb/>teſt exiſtere: igitur in illo minimo naturali eſt ſimul <lb/>caliditas et frigiditas: et per conſequens contraria <lb/>ſe compatiuntur. </s>
              <s xml:id="N2A11D" xml:space="preserve">Nec valet dicere /  vnum illorum <lb/>agentium impedit aliud: et ſic neutrum agit: q2 po-<lb/>no /  tota reſiſtentia paſſi cum adiutorio calidi iu-<lb/>uantis ipſum ne frigidū agat in illud ſit minor acti­<lb/>uitate frigidi. </s>
              <s xml:id="N2A128" xml:space="preserve">et ſic dicat̄̄ de actiuitate calidi etc. / quo <lb/>poſito vtrun illorum habebit ꝓportionem maio-<lb/>ris inequalitatis ad paſſum et per conſeq̄ns aget.</s>
            </p>
            <p xml:id="N2A12F">
              <s xml:id="N2A130" xml:space="preserve">Tertio principaliter ad idem arguit̄̄ <lb/>ſic argumēto pauli veneti in libro de generatiõe ca­<lb/>pite: 25°. </s>
              <s xml:id="N2A137" xml:space="preserve">Sit a. calidū et b. frigidum agentia et patiē­<lb/>tia ab inuicē et cū b. incipit introducere frigiditatē <lb/>ſit vna parua pars ipſius a. repaſſa ꝓpinquior fri­<lb/>gido a quo recipit frigiditatem: et ſit d. pars maior <lb/>non repaſſa in eodem inſtanti. </s>
              <s xml:id="N2A142" xml:space="preserve">Quo poſito ſic ar-<lb/>guo d. pars repaſſa agit in b. ꝓducendo caliditatē / <lb/>igitur agit in c. etiam producendo caliditatem et b. <lb/>frigidum agit in c. ꝓducendo frigiditatem ex caſu / <lb/>igitur in c. parte eſt caliditas et frigiditas in eodem <lb/>ſubiecto adequate. </s>
              <s xml:id="N2A14F" xml:space="preserve">Prima conſequentia ptꝫ / q2 om­<lb/>ne agens in remotum ceteris paribus agit in ꝓpin­<lb/>quum </s>
              <s xml:id="N2A156" xml:space="preserve">Item melius applicatur d. pars ipſi c. ꝙ̄ ipſi <lb/>b. et non tm̄ reſiſtit ei c. ſicut b. / igit̄̄ d. pars agit in c. <lb/>               <anchor type="note" xlink:href="note-0257-03" xlink:label="note-0257-03a"/>               </s>
              <s xml:id="N2A162" xml:space="preserve">¶ Et confirmatur / q2 in corpore medio colore colo-<lb/>rato puta viridi croceo etc. ſunt qualitates contra-<lb/>rie / igitur contraria ſe cõpatiunt̄̄.               <anchor type="note" xlink:href="note-0257-04" xlink:label="note-0257-04a"/>               </s>
              <s xml:id="N2A16E" xml:space="preserve">Antecedens patet <lb/>ꝑ phm̄ in libro de ſen. et ſēſa. dicētē colores medios <lb/>cõponi ex extremis. </s>
              <s xml:id="N2A175" xml:space="preserve">Patꝫ etiam hoc ꝑ pictores qui <lb/>ex cõmixtione albedinis et nigredinis faciunt colo-<lb/>res medios.               <anchor type="note" xlink:href="note-0257-05" xlink:label="note-0257-05a"/>               </s>
              <s xml:id="N2A181" xml:space="preserve">¶ Confirmat̄̄ ſecundo / q2 aliquid moue­<lb/>tur motibus contrariis / igitur contraria ſe compa­<lb/>tiuntur. </s>
              <s xml:id="N2A188" xml:space="preserve">Antecedens patet de anima rationali aſcē­<lb/>dente in vno brachio et deſcendente in alio </s>
              <s xml:id="N2A18D" xml:space="preserve">¶ Dices <lb/>et bene diſtinguendo antecedens aut per ſe et ſic ne-<lb/>gatur aut per accidens / et ſic conceditur. </s>
              <s xml:id="N2A194" xml:space="preserve">¶ Contra <lb/>aliquid mouetur per ſemotibus contrariis / igitur <lb/>ſolutio nulla. </s>
              <s xml:id="N2A19B" xml:space="preserve">Antecedens probatur et volo /  deſcē­<lb/>dat lancea in aere et aſcendat muſca per lã­<lb/>ceam. </s>
              <s xml:id="N2A1A2" xml:space="preserve">Quo poſito illa muſca aſcendit per lanceam <lb/>et ſimiliter deſcendit cū lancea / igitur ſimul aſcendit <lb/>et deſcendit cum lancea per ſe / quod fuit probanduꝫ</s>
            </p>
            <div xml:id="N2A1A9" level="5" n="16" type="float">
              <note position="right" xlink:href="note-0257-03a" xlink:label="note-0257-03" xml:id="N2A1AD" xml:space="preserve">1. cõfir̄a°.</note>
              <note position="right" xlink:href="note-0257-04a" xlink:label="note-0257-04" xml:id="N2A1B3" xml:space="preserve">phūs de <lb/>ſen. et ſē.</note>
              <note position="right" xlink:href="note-0257-05a" xlink:label="note-0257-05" xml:id="N2A1BB" xml:space="preserve">2. confir.</note>
            </div>
            <p xml:id="N2A1C1">
              <s xml:id="N2A1C2" xml:space="preserve">In oppoſitum ſunt rationes  aucto­<lb/>ritates contra aliam rationem aducte.</s>
            </p>
            <p xml:id="N2A1C7">
              <s xml:id="N2A1C8" xml:space="preserve">Sit igitur concluſio reſpõſiua ad du­<lb/>bium: probabile eſt qualitates contrarias in q̇buſ­<lb/>cun gradibus ſe excludere. </s>
              <s xml:id="N2A1CF" xml:space="preserve">hec concluſio patet ſol­<lb/>uendo rationes ad oppoſitum factas</s>
            </p>
            <p xml:id="N2A1D4">
              <s xml:id="N2A1D5" xml:space="preserve">Ad rationes ante oppoſitum </s>
              <s xml:id="N2A1D8" xml:space="preserve">Ad pri-<lb/>mam dico ſicut dictum eſt / ibi vſ ad vltimaꝫ repli­<lb/>cam. </s>
              <s xml:id="N2A1DF" xml:space="preserve">Ad quam reſpondeo /  nulla egritudo eſt ita <lb/>diſcouueniens quin ſit quodam mõ naturalis. </s>
              <s xml:id="N2A1E4" xml:space="preserve">diſ-<lb/>poſitio. </s>
              <s xml:id="N2A1E9" xml:space="preserve">Hoc videtur dicere iacobus de forliuio ī ṗ-<lb/>mo tegni .9:11.</s>
            </p>
            <p xml:id="N2A1EE">
              <s xml:id="N2A1EF" xml:space="preserve">Ad ſecundam rationcm dico /  agen-<lb/>tia illa producunt in illud minimum naturale qua­<lb/>litatem ſecundam virtualiter continentem calidita­<lb/>tem et frigiditatem: </s>
              <s xml:id="N2A1F8" xml:space="preserve">Et talis qualitas eſt tepiditas               <pb chead="Quarti tractatus." file="0258" n="258"/>               ipſius aque: eſt in manu cuꝫ apparet frigefieri a po­<lb/>mo: et ſimiliter in pomo etc. </s>
              <s xml:id="N2A202" xml:space="preserve">Et ſic ſoluuntur omnia <lb/>talia.</s>
            </p>
            <p xml:id="N2A207">
              <s xml:id="N2A208" xml:space="preserve">Ad tertiam rationem reſpondeo ſicut <lb/>reſponſum eſt ibi vcꝫ negando /  d. agat in c. </s>
              <s xml:id="N2A20D" xml:space="preserve">Et ra­<lb/>tio eſt /  talis eſt natura agentis vt prius reducat <lb/>paſſum ad impoſſibilitatem reactionis ꝙ̄ reſtituat <lb/>ſe priſtine integritati / vt bene dicit paulus vene. ī li-<lb/>bro de genera. </s>
              <s xml:id="N2A218" xml:space="preserve">¶ Ad primam confirmationem dico / <lb/> phūs loquitur de compoſitione virtuali et nõ for­<lb/>mali ſicut dicimus mixtum ↄ̨poni ex: 4. elementis <lb/></s>
              <s xml:id="N2A220" xml:space="preserve">¶ Ad aliam confirmationem dictum eſt ibi vſ ad <lb/>replicam ad quã dico /  ſi muſca in ordine ad lance­<lb/>am ita velociter mouetur ſicut lancea / tunc non aſcē­<lb/>dit nec deſcendit ſi tardius dico /  deſcendit: ſi vero <lb/>velocius dico /  aſcendit.</s>
            </p>
            <p xml:id="N2A22B">
              <s xml:id="N2A22C" xml:space="preserve">Ad ſecundum dubium arguit̄̄ primo / <lb/> complexio non ſit qualitas proueniens ex actio­<lb/>ne qualitatum contrariaꝝ elementoruꝫ. </s>
              <s xml:id="N2A233" xml:space="preserve">Quia ſi eēt <lb/>q̈litas etc. ſequeretur /  virtualiter contineret in ſe <lb/>quattuor qualitates primas: ̄uis non equaliter.</s>
            </p>
            <p xml:id="N2A23A">
              <s xml:id="N2A23B" xml:space="preserve">Sed conſequens eſt falſum: igitur illud ex quo ſeq̇-<lb/>tur. </s>
              <s xml:id="N2A240" xml:space="preserve">Sequela eſt nota apud ponētes hanc opinionē <lb/></s>
              <s xml:id="N2A244" xml:space="preserve">Sed falſitas conſequentis ꝓbatur: q2 tunc ſequere­<lb/>tur /  non poſſet fieri diſtemperamētū in cõplexiõe <lb/>per lapſum in caliditatem quin etiam fierit diſtēpe­<lb/>ramētum per lapſum ad ſiccitatē aut econtra. </s>
              <s xml:id="N2A24D" xml:space="preserve">Sed <lb/>conſequens eſt falſum: igitur illud ex quo ſequitur. <lb/></s>
              <s xml:id="N2A253" xml:space="preserve">Falſitas conſequentis patet de puero tendente ver­<lb/>ſus iuuentutiem qui (vt cõmuuiter dicūt medici) no­<lb/>tabiliter exiccatur abſ hoc /  notabiliter calefiat <lb/>aut frigefiat.               <anchor type="note" xlink:href="note-0258-01" xlink:label="note-0258-01a"/>               </s>
              <s xml:id="N2A261" xml:space="preserve">Patet etiam falſitas conſequentis ꝑ <lb/>Gali. in .2. tegni: </s>
              <s xml:id="N2A266" xml:space="preserve">Iaꝫ ꝓbo ſequelam. </s>
              <s xml:id="N2A269" xml:space="preserve">Et volo /  fiat <lb/>diſtēperamētū ꝑ actionē calidi in cõplexione ſortis <lb/>ita quod ipſa ſortis complexio per ſuperhabundã­<lb/>tiam alicuius calidi agentis in eam ſucceſſiue cor-<lb/>rumpatur. </s>
              <s xml:id="N2A274" xml:space="preserve">Quo poſito. </s>
              <s xml:id="N2A277" xml:space="preserve">arguitur ſic complexio ſor­<lb/>tis corrumpitur: ergo non eſt tam intenſa quãtum <lb/>antea: et ante erat virtualiter ſicca: hoc eſt ꝓducti-<lb/>ua ſiccitatis: ergo modo non eſt tam ſicca virtuali-<lb/>ter: cum non ſit tam intenſa: et per conſequens tam <lb/>potens ad exiccandū.               <anchor type="note" xlink:href="note-0258-02" xlink:label="note-0258-02a"/>               </s>
              <s xml:id="N2A289" xml:space="preserve">¶ Dices forte cum iacobo de <lb/>forliuio in .5.9. ſuper prīa fen .pri. cano. </s>
              <s xml:id="N2A28E" xml:space="preserve"> ꝓpter iſtḋ <lb/>argumentum oportet ponere duas complexiones: <lb/>vnã vcꝫ: inter qualitates actiuas caliditatē ſ. et fri-<lb/>giditatem: et aliam inter qualitates paſſiuas humi­<lb/>didatē vcꝫ et ſiccitatem: et agregatū ex illis eſt vna cõ­<lb/>plexio totalis colectiua: et iſto modo ſtabit diſtem-<lb/>peramētū in cõplexione qualitatum actiuarum nul­<lb/>lo modo facto diſtēperamēto inter qualitates paſ­<lb/>ſiuas.</s>
            </p>
            <div xml:id="N2A2A1" level="5" n="17" type="float">
              <note position="left" xlink:href="note-0258-01a" xlink:label="note-0258-01" xml:id="N2A2A5" xml:space="preserve">Gali.</note>
              <note position="left" xlink:href="note-0258-02a" xlink:label="note-0258-02" xml:id="N2A2AB" xml:space="preserve">ia. de for</note>
            </div>
            <p xml:id="N2A2B1">
              <s xml:id="N2A2B2" xml:space="preserve">Sed cõtra quia adhuc ponendo illas <lb/>duas cõplexiões eē qualitates: ſequitur /  nõ ē poſ­<lb/>ſet fieri diſtēperamentū per remiſſionem calidita-<lb/>tis quin etiam fiat per remiſſionem frigiditatis:</s>
            </p>
            <p xml:id="N2A2BB">
              <s xml:id="N2A2BC" xml:space="preserve">Sed conſequens eſt falſum: igitur illud ex quo ſeq̇-<lb/>tur: </s>
              <s xml:id="N2A2C1" xml:space="preserve">Falſitas conſequentis patet manifeſte: </s>
              <s xml:id="N2A2C4" xml:space="preserve">Et ar-<lb/>guitur ſequela. </s>
              <s xml:id="N2A2C9" xml:space="preserve">Et pono /  frigidum agat in cõple-<lb/>xionem ſortis intenſam vt ſex corrumpendo duos <lb/>gradus eius. </s>
              <s xml:id="N2A2D0" xml:space="preserve">Quo poſito ſic argumentor: cõplexio <lb/>ſortis ante remiſſionem eius eſt aliqualiter frigida <lb/>virtualiter: et pꝰ eſt remiſſior ꝙ̄ añ: ergo eſt minus fri­<lb/>gida virtualiter ꝙ̄ ante actionem frigidi in ipſam / <lb/>et ſic eſt diſtēperamētum in complexione ſortis pro­<lb/>pter remiſſionē frigiditatis et per conſequens nõ p̄t <lb/>fieri diſtēperamentum in ſorte ꝑ remiſſionem cali-<lb/>ditatis: quin fiat etiam diſtēperamētū per remiſ-               <cb chead="Capitulum tertium"/>               ſionem frigiditatis. </s>
              <s xml:id="N2A2E4" xml:space="preserve">¶ Dices forte et bene negando <lb/>ſequelam: et ad probationem concedēdo antecedēs <lb/>et negando hanc conſequentiam cõplexio ſortis tē­<lb/>perata ante remiſſionem eſt aliqualiter virtualiter <lb/>frigida: et eſt minus frigida virtualiter ꝙ̄ ãte actio­<lb/>nem frigidi in ipſam: ergo eſt diſtēperamētū in cõ-<lb/>plexione ſortis propter remiſſionem frigiditatis: <lb/></s>
              <s xml:id="N2A2F4" xml:space="preserve">Et ratio eſt / q2 quãuis cõplexio ſortis ſit remiſſior  <lb/>ante nihilominus eius virtualis frigiditas iuuatur <lb/>a frigiditate corrumpentis ipſam: et ſic corpus ſor­<lb/>tis eſt frigidius ꝙ̄ ante et minus calidū: vel ſaltē nõ <lb/>habet tantum de caliditate et habet magis de fri-<lb/>giditate. </s>
              <s xml:id="N2A301" xml:space="preserve">¶ Aliter et melius. </s>
              <s xml:id="N2A304" xml:space="preserve">dices /  non poteſt fieri <lb/>diſtēperamentū in cõplexione ſortis tēperata (ſal-<lb/>tē valde notabile) ꝑ remiſſionē caliditatis virtua-<lb/>lis: quin etiã fiat diſtēperamētū ꝑ remiſſionē frigi-<lb/>ditatis in eadē cõplexione / q2 ipſa ī tali caſu remit­<lb/>tit̄̄ et ſic virtualiter in omni ſua qualitate virtuali. <lb/></s>
              <s xml:id="N2A312" xml:space="preserve">remittitur. </s>
              <s xml:id="N2A315" xml:space="preserve">Sed ex hoc non ſequitur /  ī corpore ſor­<lb/>tis fiat diſtēperamētū ꝑ remiſſionem frigiditatis ī <lb/>tali caſu ymo potius ꝑ augmentū. </s>
              <s xml:id="N2A31C" xml:space="preserve">iuuant em̄ ſe fri­<lb/>giditas īducta et tualis ipſius complexionis.</s>
            </p>
            <p xml:id="N2A321">
              <s xml:id="N2A322" xml:space="preserve">Sed contra / quia tunc ſequeret̄̄ /  cõ-<lb/>plexio ſortis tēꝑata nunc eēt oīno ſimilis cõplexio­<lb/>ni platonis: et cõtinuo vſ ad diē craſtinū incluſiue <lb/>erit oīno ei ſimilis. </s>
              <s xml:id="N2A32B" xml:space="preserve">Et tamē ꝑ totū diem craſtinum <lb/>ſortes et plato habebunt cõplexiones diſtēperatas <lb/>et hoc per morbos oīno oppoſitos. </s>
              <s xml:id="N2A332" xml:space="preserve">Sed conſequēs <lb/>videt̄̄ repugnare: igit̄̄ illud ex quo ſequitur. </s>
              <s xml:id="N2A337" xml:space="preserve">Seque­<lb/>la ꝓbat̄̄: </s>
              <s xml:id="N2A33C" xml:space="preserve">Et pono /  cõplexiones ſortis et platonis <lb/>ꝓuenientes ex actione q̈litatū primaꝝ ſint oīno ſi-<lb/>miles intenſe vt .6. vt poſtea ꝓbabo eē poſſibile. </s>
              <s xml:id="N2A343" xml:space="preserve">Et <lb/>deiñ approxīet̄̄ ſorti frigifactiuū corrūpēs vſ ad <lb/>craſtinum diem duos gradus ſue complexiõis: pla­<lb/>toni vero apprometur calidum corrumpens eq̄ue-<lb/>lociter continuo duos gradus ſue cõplexionis quo <lb/>poſito ſequitur ꝓpoſitum: igitur.</s>
            </p>
            <p xml:id="N2A350">
              <s xml:id="N2A351" xml:space="preserve">Secundo arguit̄̄ ſic / ſi complexio eſſet <lb/>qualitas generata ex actione qualitatum primarū <lb/>etc. ſequeretur /  ꝓduceretur ꝑ actionē ad inuicē cali­<lb/>di et frigidi: humidi et ſicci cū ad inuicē miſcentur.</s>
            </p>
            <p xml:id="N2A35A">
              <s xml:id="N2A35B" xml:space="preserve">Sed conſequens eſt falſum: igitur illud ex quo ſeq̇tur <lb/></s>
              <s xml:id="N2A35F" xml:space="preserve">Sequela patet: et ꝓbat̄̄ falſitas conſequentis: quia <lb/>vel calida et ſicca excedunt humida et frigida vel ecõ­<lb/>tra: vel ſunt equalia: </s>
              <s xml:id="N2A366" xml:space="preserve">Sed nullū iſtorū eſt dicendum / <lb/>igitur ↄ̨plexio non producitur per actionem ad in-<lb/>uicē calidi et frigidi etc. ꝓbatur minor: q2 non eſt di-<lb/>cendum primū: q2 tunc calida et ſicca ↄ̨uerterent hu­<lb/>mida et frigida in ſui naturam: et non fieret mixtio <lb/>et ſic non produceretur cõplexio / vt patet per phūm <lb/>primo de genera. Textu. com. 88. </s>
              <s xml:id="N2A375" xml:space="preserve">Nec :2. q2 tūc ideꝫ <lb/>ſequeretur. </s>
              <s xml:id="N2A37A" xml:space="preserve">Nec .3. q2 tunc non fieret actio: cū a pro-<lb/>portione equalitatis non fiat actio. </s>
              <s xml:id="N2A37F" xml:space="preserve">¶ Nec valet di­<lb/>cere:  debent eē calida et ſicca equalia humidis et <lb/>frigidis: nõ quidē  tanta ſit actiuitas illorū ſicut <lb/>reſiſtentia horum et eocontra: </s>
              <s xml:id="N2A388" xml:space="preserve">Sed q2 ab eadē pro-<lb/>portione calida et ſicca agunt in frigida et humida <lb/>et eocontra / vt videtur dicere phūs prīo de genera. <lb/>Tex. com. 89. </s>
              <s xml:id="N2A391" xml:space="preserve">Quia tunc ſequeretur /  ſemper pro-<lb/>duceretur in omni mixtione ↄ̨plexio equalis ad põ-<lb/>dus / quod eſt falſuꝫ. </s>
              <s xml:id="N2A398" xml:space="preserve">Sequela patet / q2 ibi equaliter <lb/>agerent contrarie qualitates: et per conſequens cõ­<lb/>plexio ex actione illarum producta equaliter virtu­<lb/>aliter quãlibet contineret: et ſic eſſet cõplexio equa-<lb/>lis ad pondus: vt patet ex diffinitione qualitatis <lb/>equalis ad pondus probatur tamen falſitas conſe­<lb/>q̄ntis auctoritate auicene prima fen .pri. cano. doc-               <pb chead="De formis contrariis." file="0259" n="259"/>               ctrina .3. c. prīo. </s>
              <s xml:id="N2A3AC" xml:space="preserve">Itē non videt̄̄ aliquod mixtum exi-<lb/>gere qualitates contrarias equaliter: igit̄̄ nullius <lb/>mixti ↄ̨plexio equalis ad põdus ſignari p̄t. </s>
              <s xml:id="N2A3B3" xml:space="preserve">¶ Ideo <lb/>aliter dices concedendo ſequelam: et negando falſi­<lb/>tatē ↄ̨ñtis. </s>
              <s xml:id="N2A3BA" xml:space="preserve">Et ad ꝓbationē: dicit̄̄ /  aliquando exce­<lb/>dunt calida et ſicca: aliqñ vero ecõtra. </s>
              <s xml:id="N2A3BF" xml:space="preserve">Opꝫ em̄ in oī <lb/>mixto vnū elemētū dominari / vt patet / qm̄ alias ta­<lb/>le mixtū nõ eēt ens naturale: q2 nõ eēt mobile.               <anchor type="note" xlink:href="note-0259-01" xlink:label="note-0259-01a"/>               </s>
              <s xml:id="N2A3CB" xml:space="preserve">et hec <lb/>eſt ſentētia phī primo celi et mūdi. </s>
              <s xml:id="N2A3D0" xml:space="preserve">dicentis quodli-<lb/>bet mixtū moueri ſcḋm naturã elemēti p̄dominan-<lb/>tis </s>
              <s xml:id="N2A3D7" xml:space="preserve">Non tñ in mixtione ita debet aliqḋ elementū do­<lb/>minari vt tãte potētie ſit /  valeat alia in ſuã natu-<lb/>rã ↄ̨uertere: et  ex tali nullo mõ generet̄̄ ex actione <lb/>qualitatum primaꝝ qualitas .2. ↄ̨plexionalis pre-<lb/>parans ad formã mixti materiam elementi </s>
              <s xml:id="N2A3E2" xml:space="preserve">Sed  <lb/>ita concurrant illa elementa in agendo ad inuicem <lb/> ex actionibꝰ eorū ꝓducat̄̄ qualitas .2. ↄ̨plexiona­<lb/>lis in materias elementorum taliter /  cū talis for­<lb/>ma accidentalis fuerit in materiis elementorū pro­<lb/>ducator forma ſubſtantialis mixti.</s>
            </p>
            <div xml:id="N2A3EF" level="5" n="18" type="float">
              <note position="left" xlink:href="note-0259-01a" xlink:label="note-0259-01" xml:id="N2A3F3" xml:space="preserve">Phūs .1. <lb/>celi.</note>
            </div>
            <p xml:id="N2A3FB">
              <s xml:id="N2A3FC" xml:space="preserve">Sed contra / quia tunc ſequeret̄̄ /  for­<lb/>me ſubſtantiales elementoꝝ manerent in mixto. </s>
              <s xml:id="N2A401" xml:space="preserve">Sꝫ <lb/>conſequēs eſt falſum: igit̄̄ illud ex quo ſequitur. </s>
              <s xml:id="N2A406" xml:space="preserve">Fal­<lb/>ſitas ↄ̨ñtis oſtendit̄̄ / q2 tunc nõ quelibet pars mixti <lb/>eēt mixta / qḋ eſt cõtra rationeꝫ mixtionis primo de <lb/>gene. </s>
              <s xml:id="N2A40F" xml:space="preserve">ſequela patet: q2 in illa parte in qua eēt ignis <lb/>non eēt aqua: et per ↄ̨ñs illa ꝑs nõ eſſet mixta.               <anchor type="note" xlink:href="note-0259-02" xlink:label="note-0259-02a"/>               </s>
              <s xml:id="N2A419" xml:space="preserve">Si ve­<lb/>ro velis dicere /  illa elemēta ſunt ſimul: iã duo cor­<lb/>pora eēnt in eodē loco: qḋ eſt īpoſſibile naturaliter / <lb/>vt pꝫ per phm̄ .4. phiſicorū. </s>
              <s xml:id="N2A422" xml:space="preserve">Sed iã ꝓbat̄̄ ſequela / q2 <lb/>forma mixti ītroducit̄̄ priꝰ ꝙ̄ corrūpant̄̄ diſpoſitio­<lb/>nes elementoꝝ vſ ad nõ gradū: et quãdiu manent <lb/>diſpoſitiones elementoꝝ tãdiu manēt forme elemē­<lb/>toꝝ: ergo ſequit̄̄ /  forme elemētoꝝ manent ī mixto <lb/>ꝓbatur maior: q2 quodlꝫ elemētū requirit certã diſ­<lb/>poſitionē: puta certã latitudinem qualitatū prima­<lb/>rū ſine qua nequit eē: ergo ante̄ qualitas prīa ad <lb/>non gradū corrūpit̄̄ forma mixti introducit. </s>
              <s xml:id="N2A435" xml:space="preserve">quod <lb/>fuit ꝓbandū.               <anchor type="note" xlink:href="note-0259-03" xlink:label="note-0259-03a"/>               </s>
              <s xml:id="N2A43F" xml:space="preserve">¶ Dices et bñ negãdo ſequelã: </s>
              <s xml:id="N2A442" xml:space="preserve">Et ad ꝓ­<lb/>bationē nego minorē: et rõ ē / q2 quãuis forme elemē­<lb/>torū nõ ſemper corrūpant̄̄ ꝓpter defectū diſpoſitio­<lb/>nis requiſite: corrūpuut̄̄ tñ ꝓpter ītroductioneꝫ for­<lb/>me ↄ̨plexionalis formis elemētorū repugnantis cū <lb/>qua non p̄t ſtare forma elemēti: ſed bñ forma mixti.</s>
            </p>
            <div xml:id="N2A44F" level="5" n="19" type="float">
              <note position="left" xlink:href="note-0259-02a" xlink:label="note-0259-02" xml:id="N2A453" xml:space="preserve">phūs .4. <lb/>phiſi.</note>
              <note position="left" xlink:href="note-0259-03a" xlink:label="note-0259-03" xml:id="N2A45B" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2A461">
              <s xml:id="N2A462" xml:space="preserve">Sed contra: quia tunc ſequeretur /  <lb/>in quodlibet mixto ſaltē per aliqḋ tempꝰ īmediate <lb/>poſt eius generationē manent quatuor qualitates <lb/>prime. </s>
              <s xml:id="N2A46B" xml:space="preserve">Sed ↄ̨ñs eſt falſum: igit̄̄ illḋ ex quo ſequitur <lb/>ſequela pꝫ: q2 nõ valent ab aliqua potētia finita ſu­<lb/>bito corrūpi: cū ſue corruptioni reſiſtant: vt conſtat <lb/>et per conſequens per aliqḋ tp̄s manēt: </s>
              <s xml:id="N2A474" xml:space="preserve">Iam ꝓbat̄̄ <lb/>falſitas conſequentis: q2 tūc ſeq̈ret̄̄ /  infinite poſ-<lb/>ſent eſſe naturaliter ſpēs cõplexionis: </s>
              <s xml:id="N2A47B" xml:space="preserve">Sed cõſeq̄ns <lb/>eſt falſum: igit̄̄ illud ex quo ſequit̄̄ ſequela ꝓbat̄̄ q2 <lb/>infinitis modis: et infinitis proportionibus valent <lb/>ↄ̨binari in mixtione q̈litates prīe: igit̄̄ infinite ſpe-<lb/>cies cõplexionū valent ex eaꝝ actione ad inuicē pro­<lb/>creari.               <anchor type="note" xlink:href="note-0259-04" xlink:label="note-0259-04a"/>               </s>
              <s xml:id="N2A48D" xml:space="preserve">Itē infinita poſſunt eē indiuidua ſpeciei hu-<lb/>mane ſucceſſiue: et tñ nõ eſt poſſibile duo eē eiuſdē cõ­<lb/>plexionis: vt inquit Auicena prīa. fen .pri. ca. d. 3. c. 1. <lb/></s>
              <s xml:id="N2A495" xml:space="preserve">Et prīo theoretice .c. 7. ↄ̨plexionū quãtitates corpoꝝ <lb/>ſcribuntur infinite igitur.               <anchor type="note" xlink:href="note-0259-05" xlink:label="note-0259-05a"/>               </s>
              <s xml:id="N2A49F" xml:space="preserve">Iã ꝓbo falſitatem ↄ̨ñtis / <lb/>q2 tunc infinite poſſent eē ſpecies naturaliter / quod <lb/>eſt contra phm̄ primo poſteriorum.</s>
            </p>
            <div xml:id="N2A4A6" level="5" n="20" type="float">
              <note position="left" xlink:href="note-0259-04a" xlink:label="note-0259-04" xml:id="N2A4AA" xml:space="preserve">auicē. i. f. <lb/>p c. d. 3. c. 1</note>
              <note position="left" xlink:href="note-0259-05a" xlink:label="note-0259-05" xml:id="N2A4B2" xml:space="preserve">Phus .1. <lb/>poſte.</note>
            </div>
            <p xml:id="N2A4BA">
              <s xml:id="N2A4BB" xml:space="preserve">Tertio argnitur ſic: </s>
              <s xml:id="N2A4BE" xml:space="preserve">Si complexio eēt <lb/>qualitas ex actione et paſſione primaꝝ qualitatum <lb/>producta: ſequeretur  plura poſſent eſſe indiuidua­               <cb chead="De formis contrariis."/>               eiuſdem ſpeciei eodē modo ↄ̨plexionata. </s>
              <s xml:id="N2A4C8" xml:space="preserve">Sed ↄ̨ñs ē <lb/>falſuꝫ: igitur illḋ ex quo ſequitur               <anchor type="note" xlink:href="note-0259-06" xlink:label="note-0259-06a"/>               </s>
              <s xml:id="N2A4D2" xml:space="preserve">Falſitas ↄ̨ñtis pꝫ <lb/>per auice. vbi ſupra: </s>
              <s xml:id="N2A4D7" xml:space="preserve">Sed ſequela ꝓbat̄̄ / q2 poſſibi-<lb/>le eſt elementa in eadē oīno ꝓportione cõcurrere ad <lb/>generationē ſortis et platonis: igitur tunc ſimiles <lb/>cõplexiones oīno ꝓducent. </s>
              <s xml:id="N2A4E0" xml:space="preserve">Item vel ↄ̨plexio ſortis <lb/>excedit cõplexionē platonis ī caliditate et ſiccitate, <lb/>aut in caliditate et humiditate: aut in frigiditate et <lb/>humiditate etc. / quocū iſtoruꝫ modorū excedat aut <lb/>excedat̄̄ p̄t ꝑ remiſſionē aut intenſionē efficl equa-<lb/>lis: cū poſſit effici maior aut minor: igit̄̄ propoſituꝫ <lb/>               <anchor type="note" xlink:href="note-0259-07" xlink:label="note-0259-07a"/>               </s>
              <s xml:id="N2A4F4" xml:space="preserve">Itē recitat Auguſtinꝰ .5. de ciui. dei duos fuiſſe ge-<lb/>mellos quoꝝ vter ſemper triſtabatur cū alter tri­<lb/>ſtabat̄̄ et eſuriebat egrotabat̄̄ etc. / cuiꝰ cauſam dixit <lb/>ypocras fuiſſe ſiĺitudinē regiminis et nutritiõis poſ­<lb/>ſidoni vero aſtrologus id aſtris aſcripit. </s>
              <s xml:id="N2A4FF" xml:space="preserve">Et hec ſi­<lb/>militudo non proueniebat niſi ex idētitate cõplexio­<lb/>nis: igit̄̄ poſſibile ē reperire duo indiuidua eiuſdeꝫ <lb/>cõplexionis.               <anchor type="note" xlink:href="note-0259-08" xlink:label="note-0259-08a"/>               </s>
              <s xml:id="N2A50D" xml:space="preserve">¶ Et confirmat̄̄: q2 ſi ↄ̨plexio eēt quali-<lb/>tas proueniens ex actione ad inuicē qualitatum pri­<lb/>marum. </s>
              <s xml:id="N2A514" xml:space="preserve">Sequeretur / q2 poſſet dari complexio equa­<lb/>lis ad pondus. </s>
              <s xml:id="N2A519" xml:space="preserve">Sed ↄ̨ñs eſt falſum: et contra medi-<lb/>corū primo res: igr̄ illud ex quo ſequit̄̄. </s>
              <s xml:id="N2A51E" xml:space="preserve">Seq̄la ꝓba­<lb/>tur: et pono /  qualitates excedentes diminuantur <lb/>ſucceſſiue. </s>
              <s xml:id="N2A525" xml:space="preserve">quouſ excedant̄̄: quo poſito aliquando <lb/>venient ad equalitatē: igr̄ tunc dabit̄̄ ↄ̨plexio equa­<lb/>lis ad pondus. </s>
              <s xml:id="N2A52C" xml:space="preserve">¶ Nec valet dicere /  cū caliditas et <lb/>frigiditas equant̄̄: et ſiĺr humiditas et ſiccitas: ñ tñ <lb/>ex hoc ſequit̄̄ /  humiditas et caliditas ſint equales / <lb/>q2 pono /  oēs efficiant̄̄ ad inuicē equales. </s>
              <s xml:id="N2A535" xml:space="preserve">¶ Nec v3 <lb/>dice /  ſi fiãt eq̈les in g̈du nõ tñ fiūt eq̈les ī poña / q2 <lb/>nõ req̇rit̄̄ ad cõplexionē eq̈lē ad põdus eq̈litas gra­<lb/>dualis. </s>
              <s xml:id="N2A53E" xml:space="preserve">Sed equalitas in poña. </s>
              <s xml:id="N2A541" xml:space="preserve">¶ Nec valet dicere / <lb/> talis cõplexio nõ durabit niſi per inſtans: ꝓpter <lb/>conſtellationē iuuantē vnam q̈litatem et alteraꝫ: q2 <lb/>volo  quãtū celū iuuat vnã: tm̄ approximatio ali­<lb/>cuius ſimilis alteri iuuet alteram: quo poſito mane­<lb/>bit per tempus talis cõplexionis:</s>
            </p>
            <div xml:id="N2A54E" level="5" n="21" type="float">
              <note position="right" xlink:href="note-0259-06a" xlink:label="note-0259-06" xml:id="N2A552" xml:space="preserve">Auicen.</note>
              <note position="right" xlink:href="note-0259-07a" xlink:label="note-0259-07" xml:id="N2A558" xml:space="preserve">Auguſti. <lb/>5. de ciui.</note>
              <note position="right" xlink:href="note-0259-08a" xlink:label="note-0259-08" xml:id="N2A560" xml:space="preserve">Cõfir̄a°.</note>
            </div>
            <p xml:id="N2A566">
              <s xml:id="N2A567" xml:space="preserve">In oppoſitum arguitur / quia ex actio­<lb/>ne qualitatū primaꝝ ad inuicē ꝓducitur qualitas .2 <lb/>et in omni mixtione ſit mutua actio īter qualitates <lb/>primas: ergo in omni mixtione elementorū genera­<lb/>tur quedam qualitas ex mutua actione qualitatuꝫ <lb/>primarū: et illa a phīs vocatur complexio: igitur cõ­<lb/>plexio eſt qualitas.               <anchor type="note" xlink:href="note-0259-09" xlink:label="note-0259-09a"/>               </s>
              <s xml:id="N2A57B" xml:space="preserve">Item auicena .12. de animalibꝰ <lb/></s>
              <s xml:id="N2A57F" xml:space="preserve">Cõplexio eſt res accidens ex qualitatum contraria­<lb/>rum operatione etc. </s>
              <s xml:id="N2A584" xml:space="preserve">Itē auic. prīa .pri: </s>
              <s xml:id="N2A587" xml:space="preserve">Cõplexio eſt <lb/>qualitas etc.</s>
            </p>
            <div xml:id="N2A58C" level="5" n="22" type="float">
              <note position="right" xlink:href="note-0259-09a" xlink:label="note-0259-09" xml:id="N2A590" xml:space="preserve">Auicē. 2. <lb/>de aīa.</note>
            </div>
            <p xml:id="N2A598">
              <s xml:id="N2A599" xml:space="preserve">Pro ſolutione huius dubii tangendo <lb/>matcriã primi argumēti ante oppm̄. </s>
              <s xml:id="N2A59E" xml:space="preserve">dico. </s>
              <s xml:id="N2A5A1" xml:space="preserve"> comple­<lb/>xio vt inquit Aui. loco preallegato eſt qualitas que <lb/>ex actione ad inuicē et paſſione contrarium qua-<lb/>litatum in elementis inuentarum: quorum partes <lb/>ad tantã paruitatē redacte ſunt: vt cuiuſ earū plu­<lb/>rimū contingat plurimū alteriꝰ prouenit: hoc eſt cõ­<lb/>plexio eſt qualitas ꝓueniens ex actione et reactione <lb/>qualitatū primaꝝ in elementis repertarum quoruꝫ <lb/>pares ad tantã paruitatē extenuate ſunt / vt ſecun-<lb/>dū plurimas et minutas partes ad inuicē ſe contin-<lb/>gant. </s>
              <s xml:id="N2A5B8" xml:space="preserve">hoc tamen non obſtante etiaꝫ poteſt mix­<lb/>tio et complexio ſine tali diuiſione vide .2. de genera­<lb/>tione. </s>
              <s xml:id="N2A5BF" xml:space="preserve">Ad videndū vero an cõplexio ſit qualitas.</s>
            </p>
            <p xml:id="N2A5C2">
              <s xml:id="N2A5C3" xml:space="preserve">¶ Supponitur quãlꝫ formã ſubſtantialem require-<lb/>re certã diſpoſitionem in materia ad ſui conſerua-<lb/>tionem ſine qua materiã non informat hanc paſſim <lb/>admittunt omnes naturaliter loquētes. </s>
              <s xml:id="N2A5CC" xml:space="preserve">¶ Ex quo <lb/>ſequitur quãlibet formã mixti req̇rere certã diſpõeꝫ <lb/>in materia ſine qua non poteſt materiaꝫ informare               <pb chead="Quarti Tractatus" file="0260" n="260"/>               quam complexionem appellamus. </s>
              <s xml:id="N2A5D8" xml:space="preserve">¶ Ex quo ſequi­<lb/>tur ſecūdo /  facile et ſatis apparēter teneri poteſt <lb/>complexionem non eſſe aliquam vel aliquas qua-<lb/>litates ſecundas. </s>
              <s xml:id="N2A5E1" xml:space="preserve">Sed dumtaxat aggregatum ex <lb/>4. qualitatibus primis refractis et certa proporti-<lb/>one ꝓportionatis. </s>
              <s xml:id="N2A5E8" xml:space="preserve">Probatur / quia eque bene ſal-<lb/>uantur omnia ponendo illud aggregatum eſſe cõ-<lb/>plexionem ſicut ponendo illam eſſe qualitatem .2. <lb/>               <anchor type="note" xlink:href="note-0260-01" xlink:label="note-0260-01a"/>               </s>
              <s xml:id="N2A5F6" xml:space="preserve">¶ Sequitur tertio /  probabile eſt complexionem <lb/>non eſſe vnam qualitatem .2.               <anchor type="note" xlink:href="note-0260-02" xlink:label="note-0260-02a"/>               </s>
              <s xml:id="N2A600" xml:space="preserve">Sed duas vt opina-<lb/>tur Iacobus de for. ſuper prima fē .primi cap. q̄ .5. <lb/>               <anchor type="note" xlink:href="note-0260-03" xlink:label="note-0260-03a"/>               </s>
              <s xml:id="N2A60C" xml:space="preserve">Probatur hoc correlarium ex argumento primo <lb/>ante oppoſitum. </s>
              <s xml:id="N2A611" xml:space="preserve">¶ Sequitur quarto /  non minus <lb/>probabile eſt complexionem vnam eſſe qualitatem <lb/>2. iuxta diffinitionem auicene poſitam. </s>
              <s xml:id="N2A618" xml:space="preserve">Probatur / <lb/> ſi oporteret ponere duas: hoc maxime eſſet / quia <lb/>vnam ponendo non poſſet defenſari diſtempera-<lb/>mentū in vna qualitate quin fieret in duabus. </s>
              <s xml:id="N2A621" xml:space="preserve">Sed <lb/>hoc non obſtat: igitur. </s>
              <s xml:id="N2A626" xml:space="preserve">Minor ꝓbatur: quia poſſet <lb/>dici ſicut de facto dicendum puto /  cum membro <lb/>approximatur aliquod frigidum corrūpens com-<lb/>plexionē eius virtualiter calidam: ex actione com-<lb/>plexionis membri et actione frigidi ei approximati <lb/>producitur alia complexio non tam virtualiter ca­<lb/>lida propter impedimentum frigidi: ſed bene tam <lb/>humida aut ſicca: quia nichil impedit illam cõple-<lb/>xionem producere complexionē ſibi ſimilem in ſicci­<lb/>tate. </s>
              <s xml:id="N2A63B" xml:space="preserve">Nec valet dicere /  illa ſemper erit remiſſior <lb/>et ſic non producet tam ſiccam complexionē virtua-<lb/>liter ſicut ipſa iam eſt: q2 et ſi illa non ſit adeo ſicca <lb/>ſicut precedens nichilominus illud tamen mēbrum <lb/>habet tantum de ſiccitate quantum antea: quia cõ-<lb/>plexio producta iuuat preexiſtentem: quia aliqua-<lb/>liter cõueniunt.               <anchor type="note" xlink:href="note-0260-04" xlink:label="note-0260-04a"/>               </s>
              <s xml:id="N2A64F" xml:space="preserve">¶ Ex quo ſequitur quinto illud di-<lb/>ctum philoſophi .5. de phiſi. auditu /  non eſt eadē <lb/>ſanitas veſpere et mane. </s>
              <s xml:id="N2A656" xml:space="preserve">Quod ſic probatur: quia <lb/>quodlibet comeſtibile natuꝫ agere in complexionē <lb/>incipit producere aliam complexionem: et ſimiliter <lb/>alter celi aſpectus aliter agit mane in complexio-<lb/>nē et veſpere. </s>
              <s xml:id="N2A661" xml:space="preserve">Et ſic alia eſt ſanitas veſpere et mane <lb/></s>
              <s xml:id="N2A665" xml:space="preserve">Non tamen ītelligas /  ſemper egritudo eſt mala <lb/>complexio aut remiſſio bona cõplexio / īmo plerū <lb/>eſt egritudo ſine aliquo iſtorum. </s>
              <s xml:id="N2A66C" xml:space="preserve">vt eſto /  membro <lb/>bene complexionato approximetur aliquod ei con­<lb/>trarium: nõ tamen ſufficiat agere in mēbrum. </s>
              <s xml:id="N2A673" xml:space="preserve">Sed <lb/>bene ſufficiat impedire ne membrū notabiliter ita <lb/>bene digerat et nutriatur ſicut ãte: quo poſito iam <lb/>eſt egritudo ſine inductione male cõplexionis etc̈. <lb/>               <anchor type="note" xlink:href="note-0260-05" xlink:label="note-0260-05a"/>               </s>
              <s xml:id="N2A683" xml:space="preserve">¶ Ex quo ſequitur .6. /  bona cõplexio non eſt ſem-<lb/>per ſanitas denominans ſanū / quia habens bonã <lb/>complexionem non ſemper eſt ſanus / vt pꝫ ex dictis <lb/>igitur.               <anchor type="note" xlink:href="note-0260-06" xlink:label="note-0260-06a"/>               </s>
              <s xml:id="N2A691" xml:space="preserve">¶ Sequitur ſeptimo /  aliquid eſt egrum cui <lb/>non inheret egritudo. </s>
              <s xml:id="N2A696" xml:space="preserve">Patet ex dictis: et eſt de mē-<lb/>te Iacobi forli. prima primi queſtione quarta:</s>
            </p>
            <div xml:id="N2A69B" level="5" n="23" type="float">
              <note position="left" xlink:href="note-0260-01a" xlink:label="note-0260-01" xml:id="N2A69F" xml:space="preserve">Correĺ.</note>
              <note position="left" xlink:href="note-0260-02a" xlink:label="note-0260-02" xml:id="N2A6A5" xml:space="preserve">Iacobꝰ <lb/>de for.</note>
              <note position="left" xlink:href="note-0260-03a" xlink:label="note-0260-03" xml:id="N2A6AD" xml:space="preserve">Correĺ.</note>
              <note position="left" xlink:href="note-0260-04a" xlink:label="note-0260-04" xml:id="N2A6B3" xml:space="preserve">pḣus .5. <lb/>pḣi.</note>
              <note position="left" xlink:href="note-0260-05a" xlink:label="note-0260-05" xml:id="N2A6BB" xml:space="preserve">6. correĺ.</note>
              <note position="left" xlink:href="note-0260-06a" xlink:label="note-0260-06" xml:id="N2A6C1" xml:space="preserve">7. correĺ.</note>
            </div>
            <p xml:id="N2A6C7">
              <s xml:id="N2A6C8" xml:space="preserve">Notandū eſt ſecundo tangendo ſcḋi <lb/>argumenti materiam /  duplex eſt complexio que-<lb/>dã eſt equalis ad pondus. </s>
              <s xml:id="N2A6CF" xml:space="preserve">alia vero eſt equalis ad <lb/>iuſticiam.               <anchor type="note" xlink:href="note-0260-07" xlink:label="note-0260-07a"/>               </s>
              <s xml:id="N2A6D9" xml:space="preserve">Complexio equalis ad iuſticiã ſiue equa­<lb/>litate iuſticie eſt complexio tēperata per quam vnū­<lb/>quod membrum debite excercet ſiue natum eſt ex­<lb/>cercere ſuã oꝑationē:               <anchor type="note" xlink:href="note-0260-08" xlink:label="note-0260-08a"/>               et ideo vocat̄̄ eq̈lis eq̈litate iu­<lb/>ſticie / q2 ſicut iuſticia ↄ̨ſiſtit ī q̈dã eq̈litate geometri­<lb/>ca et ꝑ illã redit̄̄ vnicui / qḋ ſuū eſt .5. ethicoꝝ: ita ꝑ <lb/>hanc ↄ̨plexionē qḋlibet mēbrū capit / qḋ ſuū eſt. </s>
              <s xml:id="N2A6ED" xml:space="preserve">Cõ-<lb/>plexio aūt ad pondꝰ eſt illa in q̈ oēs q̈litates prime <lb/>ſūt eq̈les: põt aut ymagīari duobꝰ modis primo, <lb/>vcꝫ / q̈ ad q̈litates motiuas et q̊ ad alteratiuas. </s>
              <s xml:id="N2A6F6" xml:space="preserve">Itē <lb/>q̊ ad q̈litates alteratiuas põt tripliciṫ ymaginari. <lb/></s>
              <s xml:id="N2A6FC" xml:space="preserve">Primo° /  in ea ſiut tualiṫ oēs q̈litates equales <lb/>in actiuitate et poña. </s>
              <s xml:id="N2A701" xml:space="preserve">Scḋo° /  ſit ꝓportio eq̈litatꝪ               <cb chead="Capi. Tertium"/>               īter quãlꝫ actiuã et ſuã paſſiuã. </s>
              <s xml:id="N2A707" xml:space="preserve">Tertio° /  ſit equali-<lb/>tas ṗmo° et ſcḋo°.               <anchor type="note" xlink:href="note-0260-09" xlink:label="note-0260-09a"/>               </s>
              <s xml:id="N2A711" xml:space="preserve">¶ Tunc ſit ṗma ↄ̨° </s>
              <s xml:id="N2A714" xml:space="preserve">Poſſibile eſt da­<lb/>re eq̈le ad põdus q̊ ad q̈litates motiuuas. </s>
              <s xml:id="N2A719" xml:space="preserve">Probat̄̄ <lb/>ſit a. corpꝰ hñs plus g̈uitatꝪ ꝙ̄ leuitatis: et incipiat <lb/>acq̇rere leuitatē: et deꝑdere g̈uitatē vniformiṫ et eq̄ue­<lb/>lociṫ. </s>
              <s xml:id="N2A722" xml:space="preserve">q̊ poſito qñ medietas exceſſus g̈uitatis fuerit <lb/>deꝑdita: tūc g̈uitas et leuitas ipſiꝰ a. ſunt eq̈les vt cõ­<lb/>ſtat: igr̄ dabile eſt eq̈le ad põdus q̊ ad q̈litates moti­<lb/>uas localiṫ. </s>
              <s xml:id="N2A72B" xml:space="preserve">¶ Ex hac ↄ̨°ne ſequit̄̄ ṗmo /  a. moueret̄̄ <lb/>ꝑ aerē et ignē. </s>
              <s xml:id="N2A730" xml:space="preserve">pꝫ / q2 in igne oīa alia elemēta moue­<lb/>rēt deorſū et ignis nõ īpediret: q2 in ꝓpria regione <lb/>nõ hꝫ leuitatē actualē: et ſiĺr cū mouet̄̄ in aere ignis <lb/>ſolū īpedit, et aq̈ et ṫra mouēt deorſū.               <anchor type="note" xlink:href="note-0260-10" xlink:label="note-0260-10a"/>               </s>
              <s xml:id="N2A73E" xml:space="preserve">¶ Seq̇t̄̄ ſcḋo / <lb/> tale corpꝰ moueret̄̄ q̊uſ medietas eiꝰ eēt in aere: <lb/>alia o in aq̈. </s>
              <s xml:id="N2A745" xml:space="preserve">pꝫ / q2 quãdiu maior pars ꝙ̄ medie-<lb/>tas eſt ſuꝑ aquã maior eſt tꝰ ad deſcēdendū ꝙ̄ ad <lb/>aſcēdendum: igitur continuo deſcendet donec ſit ſi­<lb/>tuatum equaliter inter illa duo elementa.               <anchor type="note" xlink:href="note-0260-11" xlink:label="note-0260-11a"/>               </s>
              <s xml:id="N2A753" xml:space="preserve">¶ Sequi­<lb/>tur tertio /  tale corpꝰ ſic ſituatū equaliter in aere <lb/>et aqua: continuo moueretur circulariter deducta <lb/>reſiſtentia extrinſeca. </s>
              <s xml:id="N2A75C" xml:space="preserve">Probatur: quia continuo le­<lb/>uitas ignis et aeris medietatis inferioris trahunt <lb/>ſurſum: et grauitas terre et aque trahunt deorſum <lb/>et non poſſunt trahere recte (vt conſtat) trahunt cir­<lb/>culariter: et ad ſic trahendum iuuant ſe medietas <lb/>inferior et ſuperior per granitatem terre et aque, et <lb/>leuitatem aeris et ignis: et ſolum impedit leuitas <lb/>ignis in medietate ſuperiori et granitas terre in in­<lb/>feriori .etc̈.               <anchor type="note" xlink:href="note-0260-12" xlink:label="note-0260-12a"/>               </s>
              <s xml:id="N2A774" xml:space="preserve">¶ Secūda concluſio. </s>
              <s xml:id="N2A777" xml:space="preserve">Dabile eſt mixtum <lb/>complexionatum ad pondus qua ad qualitates al­<lb/>teratiuas primo modo. </s>
              <s xml:id="N2A77E" xml:space="preserve">Et etiã ſecūdo modo. </s>
              <s xml:id="N2A781" xml:space="preserve">Pro­<lb/>batur hec concluſio per argumentum .3. ante oppo­<lb/>ſitum.               <anchor type="note" xlink:href="note-0260-13" xlink:label="note-0260-13a"/>               </s>
              <s xml:id="N2A78D" xml:space="preserve">¶ Tertia concluſio. </s>
              <s xml:id="N2A790" xml:space="preserve">Nõ eſt poſſibile dare cõ-<lb/>plexionatū complexione equali tertio modo. </s>
              <s xml:id="N2A795" xml:space="preserve">Pro­<lb/>batur: quia ſi caliditas et frigiditas ſunt equales <lb/>in potentiis: ſequitur /  maioris reſiſtentie eſt fri-<lb/>giditas ꝙ̄ caliditas: quia ceteris paribus magis <lb/>reſiſtit frigiditas ꝙ̄ caliditas vt omnes naturali-<lb/>ter loquentes dicunt: et ſic ſequitur /  iam frigidi-<lb/>tas agit in caliditatem vel  non eſt ibi proportio <lb/>equalitatis inter qualitatem actiuam et ſuam paſ-<lb/>ſiuam niſi dicatur reſiſtentiam equari potētie aut <lb/>excedere. </s>
              <s xml:id="N2A7AA" xml:space="preserve">Sed illud eſt falſum: et per conſequens nõ <lb/>eſt illud complexionatum complexione ad pondus <lb/>tertio modo.               <anchor type="note" xlink:href="note-0260-14" xlink:label="note-0260-14a"/>               </s>
              <s xml:id="N2A7B6" xml:space="preserve">De hac materia plura videas apud <lb/>Iacobum de forli. prima primi queſtione ſexta.               <anchor type="note" xlink:href="note-0260-15" xlink:label="note-0260-15a"/>               </s>
              <s xml:id="N2A7C0" xml:space="preserve">Et <lb/>apud marſilium ſecundo de gene. queſt. 15.</s>
            </p>
            <div xml:id="N2A7C5" level="5" n="24" type="float">
              <note position="left" xlink:href="note-0260-07a" xlink:label="note-0260-07" xml:id="N2A7C9" xml:space="preserve">q̇d cõple-<lb/>xio eq̈lis <lb/>eq̈litate <lb/>iuſticie</note>
              <note position="left" xlink:href="note-0260-08a" xlink:label="note-0260-08" xml:id="N2A7D5" xml:space="preserve">pḣus .5. <lb/>ethi. <lb/>q̇d cõple-<lb/>xio ad <lb/>põdus</note>
              <note position="right" xlink:href="note-0260-09a" xlink:label="note-0260-09" xml:id="N2A7E3" xml:space="preserve">ṗma ↄ̨°</note>
              <note position="right" xlink:href="note-0260-10a" xlink:label="note-0260-10" xml:id="N2A7E9" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0260-11a" xlink:label="note-0260-11" xml:id="N2A7EF" xml:space="preserve">.3. correĺ.</note>
              <note position="right" xlink:href="note-0260-12a" xlink:label="note-0260-12" xml:id="N2A7F5" xml:space="preserve">2. ↄ̨cluſio</note>
              <note position="right" xlink:href="note-0260-13a" xlink:label="note-0260-13" xml:id="N2A7FB" xml:space="preserve">3. ↄ̨cluſio</note>
              <note position="right" xlink:href="note-0260-14a" xlink:label="note-0260-14" xml:id="N2A801" xml:space="preserve">Iacobꝰ <lb/>de for. q. <lb/>6. prima <lb/>primi</note>
              <note position="right" xlink:href="note-0260-15a" xlink:label="note-0260-15" xml:id="N2A80D" xml:space="preserve">marſiliꝰ <lb/>2° de ge. <lb/>q. 15.</note>
            </div>
            <p xml:id="N2A817">
              <s xml:id="N2A818" xml:space="preserve">Notanduꝫ eſt tertio tangendo adhuc <lb/>materiã .2. argumēti: quõ vcꝫ generat̄̄ ↄ̨plexio et for­<lb/>ma ſubſtãtialis ipſiꝰ mixti. </s>
              <s xml:id="N2A81F" xml:space="preserve">Q, cū aliq̈ q̈litate .2. cõ­<lb/>plexiõali põt ſtare for̄a elemēti: et cū aliq̈ nõ. </s>
              <s xml:id="N2A824" xml:space="preserve">Pro-<lb/>bat̄̄ ṗma ꝑs: q2 ñ ſubito corrūpūt̄̄ elemēta cū ex eis <lb/>fit mixtū nec ēt ſubito ↄ̨plexio diſponēs ad ītrodu-<lb/>ctionē for̄e mixti ꝓducit̄̄. </s>
              <s xml:id="N2A82D" xml:space="preserve">Sꝫ ſucceſſiue: g̊ ꝑ illḋ tēpꝰ <lb/>ꝓductiõis ↄ̨plexiõis ante̄ for̄a mixti ītroducat̄̄: <lb/>for̄e elemētoꝪ ſtant cū tali ↄ̨plexiõe / qḋ fuit ꝓbandū <lb/></s>
              <s xml:id="N2A835" xml:space="preserve">Scḋa ꝑs ꝓbat̄̄: q2 aliq̄ mixtoꝝ ↄ̨plexiões multū re-<lb/>pugnãt elemētis / vt ptꝫ de ↄ̨plexiõe aceti q̄ multū re­<lb/>pugnat igni: igr̄ tales nõ ſtãt cū formis elemētorū. <lb/></s>
              <s xml:id="N2A83D" xml:space="preserve">¶ Scḋa ſuppõ q̄lꝫ for̄a ſubſtãtialis q̄ corrūpit̄̄: aut <lb/>corrūpit̄̄ ꝓpṫ defectū ↄ̨uatis diſpõnis: aut ꝓpter <lb/>īductã ↄ̈riã diſpõnē. </s>
              <s xml:id="N2A844" xml:space="preserve">Ptꝫ. </s>
              <s xml:id="N2A847" xml:space="preserve">q2 nõ videt̄̄ ꝓpṫ q̇d aliud <lb/>deſinat materiã īfor̄are. </s>
              <s xml:id="N2A84C" xml:space="preserve">¶ Tertia ſuppõ qḋlꝫ ele-<lb/>mētuꝫ req̇rit ad ſui ↄ̨uationē certos g̈dus q̈litatū <lb/>ṗmaꝝ: vĺ ſaltē vniꝰ q̈litatis ṗme: hec pꝫ a cõi natu-<lb/>turaliū auctoritate               <anchor type="note" xlink:href="note-0260-16" xlink:label="note-0260-16a"/>               </s>
              <s xml:id="N2A85A" xml:space="preserve">¶ Tūc ſit ṗma ↄ̨°. </s>
              <s xml:id="N2A85D" xml:space="preserve">In oī gñatiõe <lb/>mixti et ↄ̨plexiõis necc̈ie eſt vt nullū elemētū ſic ex-<lb/>cedat vt reliqua in ſui naturam conuertere valeat. <lb/></s>
              <s xml:id="N2A865" xml:space="preserve">alias enim non eſſet mixtio. </s>
              <s xml:id="N2A868" xml:space="preserve">Patet hoc primo de <lb/>generatione. </s>
              <s xml:id="N2A86D" xml:space="preserve">Tex. cõi. octauum et ibi bene proba-               <pb chead="De formis contrariis." file="0261" n="261"/>               tur.               <anchor type="note" xlink:href="note-0261-01" xlink:label="note-0261-01a"/>               </s>
              <s xml:id="N2A87A" xml:space="preserve">¶ Secunda concluſio: licet detur aliquod mi-<lb/>xtum equale ad pondus. </s>
              <s xml:id="N2A87F" xml:space="preserve">Non tamen talis comple-<lb/>xio eſt ei naturalis. </s>
              <s xml:id="N2A884" xml:space="preserve">Sed eſt via ad aliam vel ad cor-<lb/>ruptionem. </s>
              <s xml:id="N2A889" xml:space="preserve">Prima pars patet ex priori notabili. <lb/></s>
              <s xml:id="N2A88D" xml:space="preserve">Et .2. ꝓbatur: q2 tunc tale mixtū nõ eſſet ens natu-<lb/>rale: cū naturaliter nõ eſſet mobile. </s>
              <s xml:id="N2A892" xml:space="preserve">vt ptꝫ ex dedu-<lb/>ctione .3. argumenti etc̈.               <anchor type="note" xlink:href="note-0261-02" xlink:label="note-0261-02a"/>               </s>
              <s xml:id="N2A89C" xml:space="preserve">¶ Ex quo ſequitur /  vbicū­<lb/> elementa concurrunt ad generationem natura-<lb/>lem alicuius mixti: ſemper vnū illorū excelit et do-<lb/>minatur. </s>
              <s xml:id="N2A8A5" xml:space="preserve">Patet ex priori concluſione. </s>
              <s xml:id="N2A8A8" xml:space="preserve">quia alias <lb/>aliquod mixtum naturaliter eſſet complexio natū <lb/>ad pondus.               <anchor type="note" xlink:href="note-0261-03" xlink:label="note-0261-03a"/>               </s>
              <s xml:id="N2A8B4" xml:space="preserve">¶ Tertia concluſio / vbicun per acti-<lb/>onē qualitatum primarū in elementis repertarū <lb/>corrumpuntur diſpoſitiones requiſite ad formas <lb/>elementoꝝ: ipſa elementa corrumpuntur: et forma <lb/>mixti in eoꝝ materias introducitur. </s>
              <s xml:id="N2A8BF" xml:space="preserve">Prima pars <lb/>pꝫ ex prima parte .2. ſuppoſitionis. </s>
              <s xml:id="N2A8C4" xml:space="preserve">Et ſecūda ꝓ-<lb/>batur: q2 alias materie elementoꝝ manerent ſiue <lb/>forma: oportet igitur /  corruptis formis elemen-<lb/>torum introducator forma mixti. </s>
              <s xml:id="N2A8CD" xml:space="preserve">oīs em̄ forma na­<lb/>turalis, aut eſt mixti, aut elemēti.               <anchor type="note" xlink:href="note-0261-04" xlink:label="note-0261-04a"/>               </s>
              <s xml:id="N2A8D7" xml:space="preserve">¶ Et ſi dicas: po­<lb/>no /  corrumpantur diſpoſitiones requiſite ad for­<lb/>mas elementorum ante̄ in materia ſit complexio <lb/>requiſita ad introductionē forme mixti. </s>
              <s xml:id="N2A8E0" xml:space="preserve">Tunc ma­<lb/>nifeſtum eſt /  nõ introducetur forma mixti: igr̄ cõ-<lb/>cluſio falſa. </s>
              <s xml:id="N2A8E7" xml:space="preserve">Reſpondeo primo nõ admittendo ca-<lb/>ſum: q2 ad illum ſequitur materiam manere ſine <lb/>forma. </s>
              <s xml:id="N2A8EE" xml:space="preserve">Dico .2. /  in inſtanti: in quo debet introdu­<lb/>ci forma mixti cauſa vniuerſalis que nõ vult mate-<lb/>riam eſſe ſiue forma: ſubito producet diſpoſitionē <lb/>ipſi forme mixti. </s>
              <s xml:id="N2A8F7" xml:space="preserve">Nam illud opud mixtionis eſt o-<lb/>pus ipſius prime cauſe.               <anchor type="note" xlink:href="note-0261-05" xlink:label="note-0261-05a"/>               </s>
              <s xml:id="N2A901" xml:space="preserve">Dicente proculo. </s>
              <s xml:id="N2A904" xml:space="preserve">oīs cauſa <lb/>prima plus agit in cauſatū ſuū: ꝙ̄ vniuerſalis cau­<lb/>ſa .2.               <anchor type="note" xlink:href="note-0261-06" xlink:label="note-0261-06a"/>               </s>
              <s xml:id="N2A910" xml:space="preserve">Quare non abſre dicit pḣs .12. metha. a tali <lb/>principio dependet celum et natura. </s>
              <s xml:id="N2A915" xml:space="preserve">Tex. con. 38. <lb/></s>
              <s xml:id="N2A919" xml:space="preserve">Ipſe em̄ omnipotens. </s>
              <s xml:id="N2A91C" xml:space="preserve">quaſdam rationes ſemina-<lb/>les rebus indidit vt mediantibus illis poſſint di-<lb/>uerſa mixta generari vt inquit.               <anchor type="note" xlink:href="note-0261-07" xlink:label="note-0261-07a"/>               </s>
              <s xml:id="N2A928" xml:space="preserve">Ma. in .2. d. 18.               <anchor type="note" xlink:href="note-0261-08" xlink:label="note-0261-08a"/>               </s>
              <s xml:id="N2A930" xml:space="preserve">Qḋ <lb/>admirans Galienus .2. certicorū inquit. </s>
              <s xml:id="N2A935" xml:space="preserve">Omne bo­<lb/>nū pulchrū: et omne quod ordini vni adheret et vie: <lb/>et oſtenditur in eo veſtigium ſapientie non eſt illud <lb/>niſi de ſurſum: reccurre igr̄ ad cauſam vniuerſalē <lb/>vel nõ admittas caſum.               <anchor type="note" xlink:href="note-0261-09" xlink:label="note-0261-09a"/>               </s>
              <s xml:id="N2A945" xml:space="preserve">¶ Quarta concluſio aliqñ <lb/>prius corrūpuntur forme elementorū ꝙ̄ corrūpan­<lb/>tur diſpoſitiones requiſite ad conſeruationē ſuaꝝ <lb/>formarū. </s>
              <s xml:id="N2A94E" xml:space="preserve">Probatur: quia vt ſenſus docet in mar-<lb/>more eſt maior ſicitas et frigiditas ꝙ̄ terra requi-<lb/>rat ad ſui conſeruationē: cū nõnun̄ ſit magis hu­<lb/>mida ꝙ̄ marmor: igr̄ nõ corrumpitur forma ſubſtã­<lb/>tialis terre cū ex ea generatur marmor ꝓpter de-<lb/>fectum diſpoſitionis cõſeruantis eam in materia. <lb/>               <anchor type="note" xlink:href="note-0261-10" xlink:label="note-0261-10a"/>               </s>
              <s xml:id="N2A962" xml:space="preserve">Et hec ratio eſt Iaco. de forliuio .5. q̄. in prima ṗmi <lb/>               <anchor type="note" xlink:href="note-0261-11" xlink:label="note-0261-11a"/>               </s>
              <s xml:id="N2A96C" xml:space="preserve">¶ Ex quo ſequitur /  forme elementorū aliquando <lb/>corrūpuntur propter introductionē qualitatis cõ-<lb/>plexionalis repugnantis formis elementorū. </s>
              <s xml:id="N2A973" xml:space="preserve">Ptꝫ <lb/>hoc correlariū ex .4. concluſione p̄cedente: et ex ſcḋa <lb/>ſuppõne: videas hanc materiã de mixtione latiꝰ ꝑ <lb/>Marſiliū ī ṗmo de gene.               <anchor type="note" xlink:href="note-0261-12" xlink:label="note-0261-12a"/>               </s>
              <s xml:id="N2A981" xml:space="preserve">Et ꝑ Conci. differētia .16.</s>
            </p>
            <div xml:id="N2A984" level="5" n="25" type="float">
              <note position="right" xlink:href="note-0260-16a" xlink:label="note-0260-16" xml:id="N2A988" xml:space="preserve">p̄ma ↄ̨°.</note>
              <note position="left" xlink:href="note-0261-01a" xlink:label="note-0261-01" xml:id="N2A98E" xml:space="preserve">2. ↄ̨cluſio</note>
              <note position="left" xlink:href="note-0261-02a" xlink:label="note-0261-02" xml:id="N2A994" xml:space="preserve">Correĺ.</note>
              <note position="left" xlink:href="note-0261-03a" xlink:label="note-0261-03" xml:id="N2A99A" xml:space="preserve">3. ↄ̨cluſio</note>
              <note position="left" xlink:href="note-0261-04a" xlink:label="note-0261-04" xml:id="N2A9A0" xml:space="preserve">Dubium</note>
              <note position="left" xlink:href="note-0261-05a" xlink:label="note-0261-05" xml:id="N2A9A6" xml:space="preserve">ꝓculus</note>
              <note position="left" xlink:href="note-0261-06a" xlink:label="note-0261-06" xml:id="N2A9AC" xml:space="preserve">pḣus .12. <lb/>meth. tex <lb/>cõ. 38.</note>
              <note position="left" xlink:href="note-0261-07a" xlink:label="note-0261-07" xml:id="N2A9B6" xml:space="preserve">ma. in .2. <lb/>d. 18.</note>
              <note position="left" xlink:href="note-0261-08a" xlink:label="note-0261-08" xml:id="N2A9BE" xml:space="preserve">Galienꝰ <lb/>2. cretico­<lb/>rū .c. 2.</note>
              <note position="left" xlink:href="note-0261-09a" xlink:label="note-0261-09" xml:id="N2A9C8" xml:space="preserve">4. ↄ̨cĺo.</note>
              <note position="left" xlink:href="note-0261-10a" xlink:label="note-0261-10" xml:id="N2A9CE" xml:space="preserve">Iacobus <lb/>de for.</note>
              <note position="left" xlink:href="note-0261-11a" xlink:label="note-0261-11" xml:id="N2A9D6" xml:space="preserve">Correĺ.</note>
              <note position="left" xlink:href="note-0261-12a" xlink:label="note-0261-12" xml:id="N2A9DC" xml:space="preserve">Calcula. <lb/>diffe. 16.</note>
            </div>
            <p xml:id="N2A9E4">
              <s xml:id="N2A9E5" xml:space="preserve">Notandū eſt quatuor circa materiaꝫ <lb/>.3. argumenti /  ſcḋm dñm forluienſem .9.11. ṗma <lb/>ṗmi: duplex eſt cõplexio. </s>
              <s xml:id="N2A9EC" xml:space="preserve">quedã eſt ſcḋm formã: que­<lb/>dam o ſcḋm materiã. </s>
              <s xml:id="N2A9F1" xml:space="preserve">Cõplexio ſcḋm formam eſt <lb/>cõplexio ꝓueniens ex actione et paſſione qualitatū <lb/>prmarū etc̈. / vt iam diffinitū eſt.               <anchor type="note" xlink:href="note-0261-13" xlink:label="note-0261-13a"/>               </s>
              <s xml:id="N2A9FD" xml:space="preserve">Sed cõplexio ſcḋm <lb/>materiã eſt complexio nõ requiſita ad conſeruati-<lb/>onem forme in materia: nec reſultans ex actione ſi­<lb/>mul et paſſione qualitatum primarū: aut aliquarū <lb/>que ad has reducuntur. </s>
              <s xml:id="N2AA08" xml:space="preserve">Cauſatur autem hec com-<lb/>plexio ſecundū materiam ab influxu ſiderū: ex hac               <cb chead="De formis contrariis."/>               em̄ complexione prouenit iuuenē ſanguineū vene-<lb/>rea abhorrere .etc̈. </s>
              <s xml:id="N2AA12" xml:space="preserve">His poſitis pono duas conclu-<lb/>ſiones. </s>
              <s xml:id="N2AA17" xml:space="preserve">¶ Poſſibile eſt reperire plura īdiuidua oīo <lb/>conſimilis complexionis in ſequentis formã.               <anchor type="note" xlink:href="note-0261-14" xlink:label="note-0261-14a"/>               </s>
              <s xml:id="N2AA21" xml:space="preserve">Ptꝫ <lb/>hec concluſio ex deductione .3. argumenti.               <anchor type="note" xlink:href="note-0261-15" xlink:label="note-0261-15a"/>               </s>
              <s xml:id="N2AA2B" xml:space="preserve">¶ Secū-<lb/>da concluſio ſecundū Iacobii de forliuio poſſibile <lb/>eſt reperire plura indiuidua oīo conſimilis com-<lb/>plexionis ſecundū materiam. </s>
              <s xml:id="N2AA34" xml:space="preserve">Probatur nõ enim <lb/>principiis repugnat naturalibus ſimilia oīo agen­<lb/>tia ad generationem ſortis et platonis concurrere / <lb/>igitur poſſibile eſt ſortem et platonem oīo eodē mõ <lb/>complexionatos eſſe.                <anchor type="note" xlink:href="note-0261-16" xlink:label="note-0261-16a"/>               </s>
              <s xml:id="N2AA44" xml:space="preserve">¶ Tertia concluſio de mente <lb/>conciliatoris: nõ eſt poſſibile reperire duo indiui-<lb/>dua oīno conſimiliter complexionata complexiõe <lb/>ſecundū materiam. </s>
              <s xml:id="N2AA4D" xml:space="preserve">Probatur /  nun̄ bis eſt ea-<lb/>dem celi conſtallatio oīno: iuxta illud habraham. <lb/></s>
              <s xml:id="N2AA53" xml:space="preserve">Non poteſt / vt natiuitas vniꝰ hominis aſſimiletur <lb/>natiuitati alterius tan̄ ſibi. </s>
              <s xml:id="N2AA58" xml:space="preserve">Nec vn̄ erit ſimilis <lb/>coniūctionis proportio. </s>
              <s xml:id="N2AA5D" xml:space="preserve">Et videtur mens nicholai <lb/>horem in fine tractatus ſuarum proportionum /  <lb/>nun̄ videlicet erit bis eadeꝫ conſtellatio omnino <lb/>ſimilis. </s>
              <s xml:id="N2AA66" xml:space="preserve">Ita vt nec gemini quidem valeant eadem <lb/>oīno complexione gaudere.               <anchor type="note" xlink:href="note-0261-17" xlink:label="note-0261-17a"/>               </s>
              <s xml:id="N2AA70" xml:space="preserve">Quod proſpiciens lu­<lb/>canus inquit. </s>
              <s xml:id="N2AA75" xml:space="preserve">Stant gemini fratres fecunde glo-<lb/>ria matris. </s>
              <s xml:id="N2AA7A" xml:space="preserve">Quos eadem variis genuerūt viſcera <lb/>fatia. </s>
              <s xml:id="N2AA7F" xml:space="preserve">Hiis exactis patet reſponſio ad dubiū </s>
              <s xml:id="N2AA82" xml:space="preserve">¶ Ad <lb/>rationes dubii ante oppoſitum. </s>
              <s xml:id="N2AA87" xml:space="preserve">Ad primã reſpon­<lb/>ſum eſt ibi vſ ad vltimam replicam. </s>
              <s xml:id="N2AA8C" xml:space="preserve">ad quam re-<lb/>ſpondeo concedendo illatum. </s>
              <s xml:id="N2AA91" xml:space="preserve">¶ Ad ſecundã reſpõ­<lb/>ſum eſt vſ ad vltimam replicam. </s>
              <s xml:id="N2AA96" xml:space="preserve">Ad quam reſpõ­<lb/>deo concedendo illatū ſaltem de mixto in mediate <lb/>ex elemento generato. </s>
              <s xml:id="N2AA9D" xml:space="preserve">¶ Ad tertiam rationem ptꝫ <lb/>reſponſio ex .4. notabili. </s>
              <s xml:id="N2AAA2" xml:space="preserve">¶ Ad confirmationē. </s>
              <s xml:id="N2AAA5" xml:space="preserve">dico <lb/>primo concedēdo illatum nec illud eſt incõueniens <lb/>quicquid pḣs dicat. </s>
              <s xml:id="N2AAAC" xml:space="preserve">Dico ſecūdo negando ſequelã <lb/>et ratio eſt / q2 non quelibet varietas proportionis <lb/>inter qualitates primas agentes et pacientes ad <lb/>inuicem variat ſpeciem complexionis. </s>
              <s xml:id="N2AAB5" xml:space="preserve">¶ Sed certe <lb/>ꝓportionū diſtantie inter qualitates primas ſpe-<lb/>ciem proportionis variant. </s>
              <s xml:id="N2AABC" xml:space="preserve">Nec eſt reperire natu-<lb/>raliter infinitam latitudinem proportionis per di­<lb/>minuationeꝫ reſiſtentie:               <anchor type="note" xlink:href="note-0261-18" xlink:label="note-0261-18a"/>               q2 ſecundū philoſophū quē <lb/>hec reſponſio ſequitur datur minimū naturale ex <lb/>ſecūdo de aīa et primo phiſicorū:               <anchor type="note" xlink:href="note-0261-19" xlink:label="note-0261-19a"/>               ſecundū em̄ phi-<lb/>loſophū nõ poſſunt eſſe infinite ſpecies qualitatuꝫ <lb/>ſecundarū ex libro de ſenſu et ſen. in fine.               <anchor type="note" xlink:href="note-0261-20" xlink:label="note-0261-20a"/>               </s>
              <s xml:id="N2AADA" xml:space="preserve">Andreas <lb/>autē de nouocaſtro probat in ſecūdo ſententiarū <lb/>proceſſum in infinitum in ſpeciebus aſcendendo et <lb/>deſcēdendo. </s>
              <s xml:id="N2AAE3" xml:space="preserve">Primo / quia viſio albedinis a. que ſit <lb/>b. eſt perfectior a. et c. intuituio b. eſt perfectior b. / q2 <lb/>notitia perfectioris obiecti, et ſic in infinitum aſcē-<lb/>dendo. </s>
              <s xml:id="N2AAEC" xml:space="preserve">Deſcendendo vero arguitur infinita multi-<lb/>tudo ſpecierum ſit a. notitia intuitiua michaelis et <lb/>b. ſit notitia ipſius a, et c. ipſius b. et d. ipſius c. et ſic <lb/>in infinitū. </s>
              <s xml:id="N2AAF5" xml:space="preserve">Tūc habet̄̄ ꝓpoſitū, quelꝫ em̄ ſequēs eſt <lb/>īperfectior p̄cedēte: vt ptꝫ ex imperfectione obiecti.</s>
            </p>
            <div xml:id="N2AAFA" level="5" n="26" type="float">
              <note position="left" xlink:href="note-0261-13a" xlink:label="note-0261-13" xml:id="N2AAFE" xml:space="preserve">Iacobꝰ <lb/>cõplexio <lb/>3 formã <lb/>et maṫiaꝫ</note>
              <note position="right" xlink:href="note-0261-14a" xlink:label="note-0261-14" xml:id="N2AB0A" xml:space="preserve">ṗma ↄ̨°.</note>
              <note position="right" xlink:href="note-0261-15a" xlink:label="note-0261-15" xml:id="N2AB10" xml:space="preserve">2. ↄ̨cĺo</note>
              <note position="right" xlink:href="note-0261-16a" xlink:label="note-0261-16" xml:id="N2AB16">
                <s xml:id="N2AB1A" xml:space="preserve">3. ↄ̨cluſio <lb/></s>
                <s xml:id="N2AB1E" xml:space="preserve">ↄ̨ciliator <lb/>diffi. 23.</s>
              </note>
              <note position="right" xlink:href="note-0261-17a" xlink:label="note-0261-17" xml:id="N2AB23" xml:space="preserve">Lucanꝰ <lb/>3. pharſa­<lb/>lie.</note>
              <note position="right" xlink:href="note-0261-18a" xlink:label="note-0261-18" xml:id="N2AB2D" xml:space="preserve">pḣs .2. de <lb/>aīa ṗmo <lb/>phi.</note>
              <note position="right" xlink:href="note-0261-19a" xlink:label="note-0261-19" xml:id="N2AB37" xml:space="preserve">pḣs ḋ ſē. <lb/>et ſen.</note>
              <note position="right" xlink:href="note-0261-20a" xlink:label="note-0261-20" xml:id="N2AB3F" xml:space="preserve">andreas <lb/>de nouo­<lb/>caſtro in <lb/>2. ſen.</note>
            </div>
            <p xml:id="N2AB4B">
              <s xml:id="N2AB4C" xml:space="preserve">Ad tertiū dubiū arguit̄̄  non: q2 aīa <lb/>rationalis informat corpus complexionalum cõ-<lb/>plexione alemani vel ſclaui tali corpore exiſtente <lb/>ſano et debite excercente operatiões vitales et ani-<lb/>males: igitur propter inductionem talis qualita-<lb/>tis ſiue complexionis in corpus indi aīa ipſiꝰ indi <lb/>cum ſit eiuſdem ſpeciei non minus informabit cor-<lb/>pus ipſius indi excercendo debite omnes operati-<lb/>ones victales et animales.               <anchor type="note" xlink:href="note-0261-21" xlink:label="note-0261-21a"/>               </s>
              <s xml:id="N2AB64" xml:space="preserve">Et cõfirmatur / quia oēs <lb/>ↄ̨plexiones humane cum quibus homo ſanus per-<lb/>ſeuerat ſunt eiuſdē ſpeciei: igr̄ aīa rationalis cū q̈li­<lb/>bet illarū corpus informat: et ꝑ ↄ̨ñs nõ inductionē <lb/>ↄ̨plexiõis ſclaui vel alemani in corpꝰ indi ſequitur               <pb chead="Quarti Tractatus" file="0262" n="262"/>               infirmitas vel mors </s>
              <s xml:id="N2AB74" xml:space="preserve">¶ Coõrmatur ſecundo / quia in <lb/>ꝑmutatiõe complexionis indi in complexionē ale-<lb/>mani ſiue ſclaui generatur ſiue producitur comple­<lb/>xio temperata qualis eſt complexio hominis .4. cli­<lb/>matis aut ſecundum auicēnam habitantis lineam <lb/>equinoctialem: ergo ad inductionem talis com-<lb/>plexionis nõ debet ſequi mors īmo ſanitas inten-<lb/>ſior. </s>
              <s xml:id="N2AB85" xml:space="preserve">Probat̄̄ añs / q2 cõplexio ſclaui et indi eſt extre­<lb/>ma: ergo ex actione et paſſione eaꝝ ad īuicē generat̄̄ <lb/>media tēperãta: qñ quidē ſemꝑ ex actiõe et paſſione <lb/>qualitatū extremarum qualitas media generatur</s>
            </p>
            <div xml:id="N2AB8E" level="5" n="27" type="float">
              <note position="right" xlink:href="note-0261-21a" xlink:label="note-0261-21" xml:id="N2AB92" xml:space="preserve">ↄ̨fir̄atiuꝰ</note>
            </div>
            <p xml:id="N2AB98">
              <s xml:id="N2AB99" xml:space="preserve">In oppoſitū eſt auicēna  mediorū <lb/>primores at philoſophoꝝ eximii qui naturalem <lb/>et medicinam ſcientiam profitentur.</s>
            </p>
            <p xml:id="N2ABA0">
              <s xml:id="N2ABA1" xml:space="preserve">Pro ſolutione huiꝰ dubitationis q̄dã <lb/>ſuppoſitiones p̄mittunt̄̄ ex quibꝰ ↄ̨cluſiones dubiū <lb/>enodantes at reſoluētes inducūtur.               <anchor type="note" xlink:href="note-0262-01" xlink:label="note-0262-01a"/>               </s>
              <s xml:id="N2ABAD" xml:space="preserve">¶ Suppono <lb/>primo /  ſanitas eſt bona diſpoſitio in corpore cū <lb/>qua ipſū operat̄̄ oꝑationē quã hꝫ operari ſcḋm na­<lb/>turam, aut patitur paſſionē quaꝫ habet pati ſcḋm <lb/>naturã.               <anchor type="note" xlink:href="note-0262-02" xlink:label="note-0262-02a"/>               </s>
              <s xml:id="N2ABBD" xml:space="preserve">et hec eſt diffinitio auerro. ſcḋo colliget .pri­<lb/>mo capĺo. </s>
              <s xml:id="N2ABC2" xml:space="preserve">¶ Ex qua cū aliis infert forliuiēſis taleꝫ <lb/>diffinitionē. </s>
              <s xml:id="N2ABC7" xml:space="preserve">Sanitas eſt naturalis diſpoſitio viuē­<lb/>tis ꝑ quã viuēs põt oꝑationes ſibi debitas ↄ̨ueniē-<lb/>ter exercere.               <anchor type="note" xlink:href="note-0262-03" xlink:label="note-0262-03a"/>               </s>
              <s xml:id="N2ABD3" xml:space="preserve">¶ Egritudo vero eſt diſpoſitio nõ natu­<lb/>ralis in corpore ex qua in oꝑatiõe ꝓuenit eſſentialr̄ <lb/>nocumētū īmediate. </s>
              <s xml:id="N2ABDA" xml:space="preserve">Has diffinitiões videas apud <lb/>Iaco. de for. q̄ .3. ṗmi tegni. </s>
              <s xml:id="N2ABDF" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  oīs di-<lb/>ſpoſitio ꝑ quã oꝑationes aīalis īmediate ledūtur <lb/>eſt egritudo: dūmodo habeat eſſe ꝑmanēs in corpo­<lb/>re. </s>
              <s xml:id="N2ABE8" xml:space="preserve">qḋ dico ꝓpter illū qui nimis calefit ab igne, ex q̊ <lb/>ꝓuenit ei nocumentū, cū tñ recedit ceſſat illud nocu­<lb/>mentū.               <anchor type="note" xlink:href="note-0262-04" xlink:label="note-0262-04a"/>               </s>
              <s xml:id="N2ABF4" xml:space="preserve">¶ Scḋa ſuppoſitio ſemꝑ ex actione et paſſio­<lb/>ne ad īuicē q̈litatū ↄ̈riarū ꝓducit̄̄ q̈litas quodãmõ <lb/>media participans cū extremis. </s>
              <s xml:id="N2ABFB" xml:space="preserve">Probat̄̄ /  aliqñ <lb/>ꝓducit̄̄: et nõ eſt ratio /  aliqñ ꝓducat̄̄, et aliqñ nõ: g̊ <lb/>ſemꝑ ex tali actione ꝓducit̄̄.               <anchor type="note" xlink:href="note-0262-05" xlink:label="note-0262-05a"/>               </s>
              <s xml:id="N2AC07" xml:space="preserve">¶ Tertia ſuppoſitio. <lb/></s>
              <s xml:id="N2AC0B" xml:space="preserve">Cū due q̈litates ↄ̈rie eidē paſſo approximant̄̄: vna <lb/>īpedit actionē alteriꝰ in idē paſſū, et hoc in parte vĺ <lb/>in toto. </s>
              <s xml:id="N2AC12" xml:space="preserve">Ptꝫ / q2 alias aliqḋ paſſū eq̈uelociter mo-<lb/>ueret̄̄ motibꝰ ↄ̈riis q̇d ē īpoſſibile               <anchor type="note" xlink:href="note-0262-06" xlink:label="note-0262-06a"/>               </s>
              <s xml:id="N2AC1C" xml:space="preserve">¶ Quarta ſuppo­<lb/>ſitio: ꝑ cõplexiones oppoſitoꝝ climatū intelligo cõ­<lb/>plexiões maxīe oppoſitas in tota latitudine huma­<lb/>ne cõplexionis: vel parū ab hiis diſcedentes. </s>
              <s xml:id="N2AC25" xml:space="preserve">Per <lb/>ꝑmutationē aūt cõplexionis indi. </s>
              <s xml:id="N2AC2A" xml:space="preserve">in cõplexionē ale­<lb/>mani intelligo corruptionē cõplexionis indi. </s>
              <s xml:id="N2AC2F" xml:space="preserve">et ꝓ-<lb/>ductionē cõplexionis alemani vel quaſi ei ſimilis <lb/>vſ ad equalitatē, vel ferme, vĺ exceſſum.               <anchor type="note" xlink:href="note-0262-07" xlink:label="note-0262-07a"/>               </s>
              <s xml:id="N2AC3B" xml:space="preserve">¶ Quīta <lb/>ſuppoſitio. </s>
              <s xml:id="N2AC40" xml:space="preserve">Ad hoc /  aliqua cõplexio alicui corpo­<lb/>ri ſit ſanitas, nõ ſufficit ipſam eſſe taliter, aut talr̄ <lb/>tēperatã .etc̈. </s>
              <s xml:id="N2AC47" xml:space="preserve">Sed requirit̄̄ cū hoc /  ipſa mediante <lb/>aīa poſſit debite excercere ſuas operationes q̄ ſunt <lb/>digerere. nutrire, debitã quantitatē et qualitatem <lb/>humoꝝ et ſpirituū ꝓducere. </s>
              <s xml:id="N2AC50" xml:space="preserve">hec facile ſequit̄̄ ex diffi­<lb/>nitione ſanitatis.               <anchor type="note" xlink:href="note-0262-08" xlink:label="note-0262-08a"/>               </s>
              <s xml:id="N2AC5A" xml:space="preserve">¶ Hiis iactis ſit prima concluſio <lb/></s>
              <s xml:id="N2AC5E" xml:space="preserve">In ꝑmutatiõe cõplexionis indi in ↄ̨plexionē ſclaui <lb/>aut alemani ꝓducitur ↄ̨plexio nõ totaliter ſimilis <lb/>cõplexioni alemani: ſed quodãmodo media. </s>
              <s xml:id="N2AC65" xml:space="preserve">Patꝫ / <lb/>q2 ille cõplexiones ſunt oppoſite: ex .4. ſuppoſitiõe / <lb/>igr̄ cū agunt ad īuicē et patiūtur. </s>
              <s xml:id="N2AC6C" xml:space="preserve">quodãmodo qua-<lb/>litas media ꝓducit̄̄. </s>
              <s xml:id="N2AC71" xml:space="preserve">Ptꝫ ↄ̨ña ex ſcḋa ſuppoſitione <lb/></s>
              <s xml:id="N2AC75" xml:space="preserve">¶ Ex quo ſequit̄̄ /  cū nata inducere cõplexionē ale­<lb/>mani agūt in cõplexionē indi: ꝓducitur complexio <lb/>tēperatior cõplexionibus indi. </s>
              <s xml:id="N2AC7C" xml:space="preserve">et alemani. </s>
              <s xml:id="N2AC7F" xml:space="preserve">Proba­<lb/>tur / q2 nõ tam extrema ſicut aliqua illarū / vt ptꝫ ex <lb/>concluſione: igitur.               <anchor type="note" xlink:href="note-0262-09" xlink:label="note-0262-09a"/>               </s>
              <s xml:id="N2AC8B" xml:space="preserve">¶ Secūda cõcluſio cū in ꝑmuta­<lb/>tione cõplexionis indi in cõplexionē alemani pro-<lb/>ducitur cõplexio nimiū ſimilis cõplexioni alemani <lb/></s>
              <s xml:id="N2AC93" xml:space="preserve">Tūc due cõplexiones oppoſite ſunt in corpore indi               <cb chead="Capi. Tertium"/>               tendentes ad equalitatē in gradu. </s>
              <s xml:id="N2AC99" xml:space="preserve">Et vna illarum <lb/>impedit operationē alterius. </s>
              <s xml:id="N2AC9E" xml:space="preserve">Prima pars patꝫ ex <lb/>4. ſuppoſitione: et ſcḋa pars ptꝫ ex tertia ſuppoſi­<lb/>tione.               <anchor type="note" xlink:href="note-0262-10" xlink:label="note-0262-10a"/>               </s>
              <s xml:id="N2ACAA" xml:space="preserve">¶ Tertia concluſio. </s>
              <s xml:id="N2ACAD" xml:space="preserve">Cū in ꝑmutatione cõple­<lb/>xionis indi in cõplexionē alemani producitur com­<lb/>plexio multū ſimilis complexioni alemani tendēs <lb/>ad equalitatē. </s>
              <s xml:id="N2ACB6" xml:space="preserve">Tunc neutra illarū complexionū eſt <lb/>ſanitas ipſi indo. </s>
              <s xml:id="N2ACBB" xml:space="preserve">Probatur / quia tunc aliqua cõ-<lb/>plexio eſt ſanitas cum aīa ipſa mediante debite ex­<lb/>cercet ſuas operatiões. </s>
              <s xml:id="N2ACC2" xml:space="preserve">vt pꝫ ex prima et .5. ſuppo-<lb/>ſitionibus. </s>
              <s xml:id="N2ACC7" xml:space="preserve">Sed in tali permutatione neutra illaꝝ <lb/>cõplexionū mediante poteſt aīa debite excercere <lb/>ſuas operationes: cū vtra illarū complexionum <lb/>impediatur. </s>
              <s xml:id="N2ACD0" xml:space="preserve">vt ptꝫ ex .2. concluſione.               <anchor type="note" xlink:href="note-0262-11" xlink:label="note-0262-11a"/>               </s>
              <s xml:id="N2ACD8" xml:space="preserve">¶ Quarta cõ-<lb/>cluſio. </s>
              <s xml:id="N2ACDD" xml:space="preserve">In permutatione cõplexionis indi in cõple-<lb/>xionē alemani: cõplexiõe alemani tēdente ad equa-<lb/>litatē ipſi complexioni indi. </s>
              <s xml:id="N2ACE4" xml:space="preserve">ipſe indus efficitur in­<lb/>firmus. </s>
              <s xml:id="N2ACE9" xml:space="preserve">Probatur: q2 tunc nulla eſt in eo ſanitas: <lb/>vt ptꝫ ex precedenti: cū in eo nulla ſit diſpoſitio cū <lb/>qua ipſum operetur operationē quam debet ope-<lb/>rari ſecundū naturã: igr̄ ipſe nõ eſt ſanus: ſed eger <lb/>               <anchor type="note" xlink:href="note-0262-12" xlink:label="note-0262-12a"/>               </s>
              <s xml:id="N2ACF9" xml:space="preserve">¶ Quinta concluſio </s>
              <s xml:id="N2ACFC" xml:space="preserve">In tali permutatione nõnū̄ <lb/>accidit mors. </s>
              <s xml:id="N2AD01" xml:space="preserve">Probatur: q2 ſtat /  multo tēpore il-<lb/>le contrarie complexiones maneant prope equa-<lb/>litateꝫ: et in tali tēpore parua aut nulla ſit digeſtio <lb/>nec etiam nutritio: igr̄ oportet ꝓpter defectū dige-<lb/>ſtionis ſequi mortē. </s>
              <s xml:id="N2AD0C" xml:space="preserve">Nõ em̄ ſit cõuerſio nutrimenti <lb/>in ſubſtantiã alendi. </s>
              <s xml:id="N2AD11" xml:space="preserve">antecedēs probatur / q2 bona <lb/>complexio que eſt inſtrumentū digeſtionis impedi­<lb/>tur. </s>
              <s xml:id="N2AD18" xml:space="preserve">Nam complexio que inducitur impedit com-<lb/>plexionē que corrūpitur: et eocontra, cū vtra ni-<lb/>titur aſſimilare ſibi cibum digerendum et cõuerten­<lb/>dum in ſubſtantiã aīalis et ſic neutra illarū cõuer-<lb/>tit illud aut digerit, igr̄ tunc non ſit digeſtio.               <anchor type="note" xlink:href="note-0262-13" xlink:label="note-0262-13a"/>               </s>
              <s xml:id="N2AD28" xml:space="preserve">¶ Ex <lb/>hoc ſequitur primo ſortem continuo acquirere me­<lb/>liorem complexionē: et ipſum cõntinuo fieri magis <lb/>ac magis infirmum. </s>
              <s xml:id="N2AD31" xml:space="preserve">Probatur poſito /  ipſe ſor-<lb/>tes habeat complexionem multum recedentem a <lb/>optimo temperamento humane complexionis. </s>
              <s xml:id="N2AD38" xml:space="preserve">Et <lb/>ſit illa nichilominus ei ſanitas. </s>
              <s xml:id="N2AD3D" xml:space="preserve">Et incipiat iudici <lb/>alia complexio in corpore ſortis que ſit complexiõi <lb/>ſortis contraria: propinquior tamen optimo tem-<lb/>peramento cõplexionis humane ꝙ̄ ſortis cõplexio <lb/>et deueniant ille complexiones in corpore ſortis ad <lb/>equalitatem. </s>
              <s xml:id="N2AD4A" xml:space="preserve">Quo poſito ſortes erit infirmꝰ: quia <lb/>nõ poterit excercere debitas operationes ſani q2 <lb/>eius complexio impeditur. </s>
              <s xml:id="N2AD51" xml:space="preserve">Et quanto plus de illa <lb/>complexione inducetur: tanto plus impedietur ſor­<lb/>tis complexio a debitis ſanitatis operationibus: <lb/>igitur quanto magis inducetur de meliori ↄ̨plexi-<lb/>one: tãto ſortes magis infirmabit̄̄ </s>
              <s xml:id="N2AD5C" xml:space="preserve">¶ Ex quo ſequi-<lb/>tur /  bona complexio eſt ſorti egritudo. </s>
              <s xml:id="N2AD61" xml:space="preserve">Patet ex <lb/>precedenti, et ex diffinitione egritudinis: talis em̄ <lb/>diſpoſitio nõ eſt naturalis corpori habenti oppo-<lb/>ſitam diſpoſitionem.               <anchor type="note" xlink:href="note-0262-14" xlink:label="note-0262-14a"/>               </s>
              <s xml:id="N2AD6F" xml:space="preserve">¶ Sequitur .2. /  nõnun̄ pro­<lb/>ductio bone cõplexionis eſt ſorti infirmitas: et pro-<lb/>ductio male eſt ſorti ſanitas. </s>
              <s xml:id="N2AD76" xml:space="preserve">Ptꝫ ex dictis. </s>
              <s xml:id="N2AD79" xml:space="preserve">¶ Se-<lb/>quitur quarto /  ſi ſucceſſiue talis complexio mute­<lb/>tur per multas intermedias procedendo: nõ eſt o-<lb/>pus mortem ſequi: aut infirmitatem. </s>
              <s xml:id="N2AD82" xml:space="preserve">Probatur / q2 <lb/>tunc propter magnam cõuenientiaꝫ complexionis <lb/>que corrumpitur, et que generatur non impeditur <lb/>notabiliter operatio viuentis. </s>
              <s xml:id="N2AD8B" xml:space="preserve">et ſic ſemper manet <lb/>ſanum corpus illud cuius complexio mutatur. </s>
              <s xml:id="N2AD90" xml:space="preserve">Et <lb/>per hec patet reſponſio ad dubium. </s>
              <s xml:id="N2AD95" xml:space="preserve">¶ Ad rationē <lb/>ante oppoſitum. </s>
              <s xml:id="N2AD9A" xml:space="preserve">Patet reſponſio ex dictis.</s>
            </p>
            <div xml:id="N2AD9D" level="5" n="28" type="float">
              <note position="left" xlink:href="note-0262-01a" xlink:label="note-0262-01" xml:id="N2ADA1" xml:space="preserve">quid ſa-<lb/>nitas.</note>
              <note position="left" xlink:href="note-0262-02a" xlink:label="note-0262-02" xml:id="N2ADA9" xml:space="preserve">auerrois <lb/>.2°. colli-<lb/>get.</note>
              <note position="left" xlink:href="note-0262-03a" xlink:label="note-0262-03" xml:id="N2ADB3" xml:space="preserve">quid egri­<lb/>tudo.</note>
              <note position="left" xlink:href="note-0262-04a" xlink:label="note-0262-04" xml:id="N2ADBB" xml:space="preserve">.2. ſuppõ</note>
              <note position="left" xlink:href="note-0262-05a" xlink:label="note-0262-05" xml:id="N2ADC1" xml:space="preserve">3. ſuppõ.</note>
              <note position="left" xlink:href="note-0262-06a" xlink:label="note-0262-06" xml:id="N2ADC7" xml:space="preserve">4. ſuppõ</note>
              <note position="left" xlink:href="note-0262-07a" xlink:label="note-0262-07" xml:id="N2ADCD" xml:space="preserve">.5. ſuppõ</note>
              <note position="left" xlink:href="note-0262-08a" xlink:label="note-0262-08" xml:id="N2ADD3" xml:space="preserve">ṗma ↄ̨°.</note>
              <note position="left" xlink:href="note-0262-09a" xlink:label="note-0262-09" xml:id="N2ADD9" xml:space="preserve">2. ↄ̨cluſio</note>
              <note position="right" xlink:href="note-0262-10a" xlink:label="note-0262-10" xml:id="N2ADDF" xml:space="preserve">3. ↄ̨cluſio</note>
              <note position="right" xlink:href="note-0262-11a" xlink:label="note-0262-11" xml:id="N2ADE5" xml:space="preserve">4. ↄ̨cĺo.</note>
              <note position="right" xlink:href="note-0262-12a" xlink:label="note-0262-12" xml:id="N2ADEB" xml:space="preserve">5. ↄ̨cluſio</note>
              <note position="right" xlink:href="note-0262-13a" xlink:label="note-0262-13" xml:id="N2ADF1" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0262-14a" xlink:label="note-0262-14" xml:id="N2ADF7" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N2ADFD">
              <s xml:id="N2ADFE" xml:space="preserve">Concluſio reſponſiua: ad queſtionē <lb/></s>
              <s xml:id="N2AE02" xml:space="preserve">Et ſi probabile eſt qualitates contrarias non ſe <lb/>compati in eodem ſubiecto oppoſituꝫ tamen pro-               <pb chead="De intenſione et remiſſione formarum" file="0263" n="263"/>               babilius eſt. </s>
              <s xml:id="N2AE0C" xml:space="preserve">Prima pars ptꝫ per rationem in op-<lb/>poſitum queſtionis factam. </s>
              <s xml:id="N2AE11" xml:space="preserve">Et ſecunda probatur / <lb/>quia non tot apparentia incõuenientia ſecūtur ad <lb/>qualitates ↄ̨trarias ſe compati quot ad oppoſitū / <lb/>vt patet ex deductione queſtionis: igitur probabi­<lb/>lius eſt qualitates ↄ̨trarias ſe cõpati ꝙ̄ oppoſitū.</s>
            </p>
            <p xml:id="N2AE1C">
              <s xml:id="N2AE1D" xml:space="preserve">Ad rões ãte oppoſitū. </s>
              <s xml:id="N2AE20" xml:space="preserve">Ad primã rñſū <lb/>eſt ibi vſ ad vltimã replicã. </s>
              <s xml:id="N2AE25" xml:space="preserve">Ad quã rñdeo /  pḣs <lb/>ītelligit de mētalibꝰ actualibꝰ: et nego /  aſſumit ꝓ­<lb/>bandū: q2 nõ intēdit ꝓbare /  q̈litates actuales mē­<lb/>tales nõ ſe cõpatiunt̄̄. </s>
              <s xml:id="N2AE2E" xml:space="preserve">Sꝫ  aſſenſus ↄ̈dictorii nõ ſe <lb/>cõpatiunt̄̄. </s>
              <s xml:id="N2AE33" xml:space="preserve">¶ Ad ↄ̨firmationē rñdeo negãdo ſeq̄lã: et <lb/>rõ ē / q2 duo accidētia pñt eē ī eodē loco. </s>
              <s xml:id="N2AE38" xml:space="preserve">Sed nõ due <lb/>ſbē ↄ̨plete. </s>
              <s xml:id="N2AE3D" xml:space="preserve">qḋ fierit ſi due for̄e ſbãles ſe ↄ̨paterentt̄̄.</s>
            </p>
            <p xml:id="N2AE40">
              <s xml:id="N2AE41" xml:space="preserve">Ad ſcḋam rõnē rñdet ſcḋa concluſio. <lb/></s>
              <s xml:id="N2AE45" xml:space="preserve">¶ Ad ↄ̨firmationē dico /  dabiles ſūt maxī q̇ ſe cõ-<lb/>patiunt̄̄ q̇lꝫ em̄ q̇ ſe ↄ̨patiunt̄̄ ſūt maxī q̇ ſe ↄ̨patiūt̄̄ <lb/>copulatim. </s>
              <s xml:id="N2AE4C" xml:space="preserve">¶ Ad aliud dico /  frigiditas ſumma <lb/>eſt minima cū qua caliditas remiſſa nõ poteſt ſtare</s>
            </p>
            <p xml:id="N2AE51">
              <s xml:id="N2AE52" xml:space="preserve">Ad tertiã rõnē rñdeo negãdo ſequelã <lb/>et ad ꝓbationē nego ↄ̨ñaꝫ. </s>
              <s xml:id="N2AE57" xml:space="preserve">¶ Ad primã ↄ̨firmatiõeꝫ <lb/>nego mīorē: et ad pūctū ꝓbatiõis: dico /  et ſi ſe ↄ̨pa­<lb/>tiunt̄̄ tñ in ſuis denoīatiõibꝰ ſe īpediūt. </s>
              <s xml:id="N2AE5E" xml:space="preserve">q̇cq̇d ſit de <lb/>datis diffinitiõibꝰ. </s>
              <s xml:id="N2AE63" xml:space="preserve">¶ Ad pūctū .2. ↄ̨fir̄atiõis dico / <lb/> ̄uis ille q̈litates ſe īpediãt ne alṫa illaꝝ totaliṫ <lb/>denoīet: nõ tñ ſe īpediūt a denoīatiõe ꝑtiali gñica. <lb/></s>
              <s xml:id="N2AE6B" xml:space="preserve">¶ Ad .3. ↄ̨firmationē ↄ̨cedo ſequelã et nego falſitatē <lb/>ↄ̨ñtis et ad ꝓbationē concedo añs et nego ↄ̨ñam: q2 <lb/>̄uis in aliquo non tamen ſunt ei eque ↄ̨uenientia.</s>
            </p>
            <p xml:id="N2AE72">
              <s xml:id="N2AE73" xml:space="preserve">Ad quartã rõne rñdeo negãdo ſeq̄lã <lb/>de actualibꝰ. </s>
              <s xml:id="N2AE78" xml:space="preserve">Nã et ſi q̈litates ↄ̈rie corporales ſe cõ­<lb/>patiant̄̄: nõ tñ mētales actules: cuiꝰ rõ eſt ſola expe­<lb/>riētia. </s>
              <s xml:id="N2AE7F" xml:space="preserve">¶ Ad primã ↄ̨fir̄atiõeꝫ ↄ̨cedo ſeq̄lã de hītua-<lb/>libꝰ: et cū ꝓbat̄̄ q2 nõ dico /  nõ q̄lꝫ tꝰ denoīat qñ ē <lb/>ꝑmixta ↄ̈rio. </s>
              <s xml:id="N2AE86" xml:space="preserve">¶ Ad ſcḋaꝫ ↄ̨fir̄atiõeꝫ ↄ̨cedo ſeq̄lã ne-<lb/>gata fĺitate ↄ̨ñtis et ad ꝓbatiõeꝫ q̄ īnitit̄̄ diffinitiõi <lb/>ſanitatꝪ dico /  diffinitio d3 ſic ītelligi ſanitas eſt <lb/>diſpõ nat̄̄alis etc̈. a q̈ ꝓueniūt vĺ ꝓuenirēt oꝑatiões <lb/>ꝓportiõate ſi nõ eēt īpedimētū egritudīs. </s>
              <s xml:id="N2AE91" xml:space="preserve">Auctori-<lb/>tas aūt pḣi ītelligr̄ de his ṫmīs ſanū et egrū. </s>
              <s xml:id="N2AE96" xml:space="preserve">¶ Ad <lb/>tertiã ↄ̨fir̄atiõeꝫ dico /  auctoritas pḣi ītelligr̄ de <lb/>ṫmīs ṗmis. </s>
              <s xml:id="N2AE9D" xml:space="preserve">Nõ aūt de ṫmīs ↄ̨comitãtibꝰ.               <anchor type="note" xlink:href="note-0263-01" xlink:label="note-0263-01a"/>               </s>
              <s xml:id="N2AEA5" xml:space="preserve">Sūt aūt <lb/>ṫmī primi ṗuatio ṫmī ad quē et ṫminꝰ ad quē vt be­<lb/>ne dicit doctor ſubtilis in q̈rto d. 10. q̄ſtione ſecūda.</s>
            </p>
            <div xml:id="N2AEAC" level="5" n="29" type="float">
              <note position="left" xlink:href="note-0263-01a" xlink:label="note-0263-01" xml:id="N2AEB0" xml:space="preserve">Doctor <lb/>ſubtilis ī <lb/>4. d. 10. q̄ <lb/>.2.</note>
            </div>
            <p xml:id="N2AEBC">
              <s xml:id="N2AEBD" xml:space="preserve">Ad quintã rõne rñdeo negando ſeq̄lã <lb/>et ad ꝓbationē negat̄̄ mīor ad ꝓbatiõeꝫ negat̄̄ ↄ̨ña <lb/></s>
              <s xml:id="N2AEC3" xml:space="preserve">Et rõ eſt / q2 qñ eſt mutua actio īter q̈litates primas <lb/>nõ ſolū q̈litas ṗma īducit ī paſſū ſibi ſimilē q̈litatē <lb/>verū etiã ꝓducit q̈litatē ſcḋaꝫ ita  cū calidū agit ī <lb/>frigidū ex actiõe calididatꝪ et frigiditatꝪ ꝓducit̄̄ q̈li­<lb/>tas ſcḋa tualr̄ ↄ̨tinēs caliditatē et frigiditatē et ſi <lb/>caliditas et frigiditas ab eq̈li ꝓportiõe agãt tunc <lb/>q̈litas illa ſcḋa eq̈liṫ tualr̄ ↄ̨tinet caliditatē et fri-<lb/>giditatē et ſi caliditas agat a maiori ꝓportiõe tūc <lb/>taĺ q̈litas ſcḋa tualr̄ magis ↄ̨tinet caliditatē et a <lb/>minori minus etc. </s>
              <s xml:id="N2AED8" xml:space="preserve">Ratio in oppoſitū facile ex dictis <lb/>ſoluitur. </s>
              <s xml:id="N2AEDD" xml:space="preserve">Et hec de queſtione.</s>
            </p>
          </div>
          <div xml:id="N2AEE0" level="4" n="4" type="chapter" type-free="capitulum">
            <head xml:id="N2AEE5" xml:space="preserve">Capitulū q̈rtū / in quo principalr̄ q̄rit̄̄ penes quid <lb/>attendi intenſio qualitatis difformis debeat.</head>
            <p xml:id="N2AEEA">
              <s xml:id="N2AEEB" xml:space="preserve">AGgrediēdo vnū de precipuis <lb/>mēbris huiꝰ .4. tractatꝰ q̄ro. </s>
              <s xml:id="N2AEF0" xml:space="preserve">Utrū ītēſio <lb/>q̈litatꝪ vniformis attēdi d3 penes multi­<lb/>tudinē graduū penetratiue et vnitiue ſe habētiū. </s>
              <s xml:id="N2AEF7" xml:space="preserve">Et <lb/>vniformiter: et difformiter difformis intēſio penes <lb/>reductionem ad vniformitatem.</s>
            </p>
            <p xml:id="N2AEFE">
              <s xml:id="N2AEFF" xml:space="preserve">Et argr̄ primo ↄ̨̨tra primã partē /  nõ <lb/>q2 intēſio taĺ q̈litatꝪ d3 attendi penes diſtãtiã a nõ               <cb chead="De intenſione et remiſſione formarum"/>               g̈du: igr̄ nõ d3 attendi penes multitudinē g̈dus .etc̈. <lb/></s>
              <s xml:id="N2AF08" xml:space="preserve">Probat̄̄ añs / q2 quãto aliq̈ q̈litas eſt intēſior: tan­<lb/>to ipſa magis diſtat a non gradu qualitatis: igr̄ <lb/>ſua intenſio mētiri d3 penes diſtantiã a nõ gradu. <lb/>               <anchor type="note" xlink:href="note-0263-02" xlink:label="note-0263-02a"/>               </s>
              <s xml:id="N2AF16" xml:space="preserve">¶ Dices et bene ↄ̨cedendo añs et negando ↄ̨ñam: et <lb/>rõ eſt / q2 vtro mõ mēſurari põt q̈litatis intēſio vcꝫ <lb/>et penes mĺtitudinē g̈duū et penes diſtãtiã a nõ g̈du</s>
            </p>
            <div xml:id="N2AF1D" level="5" n="1" type="float">
              <note position="right" xlink:href="note-0263-02a" xlink:label="note-0263-02" xml:id="N2AF21" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N2AF27">
              <s xml:id="N2AF28" xml:space="preserve">Sed ↄ̨̨tra q2 tūc ſeq̄ret̄̄ /  deberet attē­<lb/>di penes ꝓpinq̇tatē ad nõ gradū. </s>
              <s xml:id="N2AF2D" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: <lb/>(q2 tūc quãto pauciores gradꝰ ↄ̨tineret tanto eſſet <lb/>intēſior) / igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N2AF34" xml:space="preserve">Seq̄la ꝓbat̄̄: q2 intē-<lb/>ſio ꝑ te attēdit̄̄ penes diſtantiã a nõ gradu. </s>
              <s xml:id="N2AF39" xml:space="preserve">Et oīs <lb/>diſtãtiã a nõ gradu eſt ꝓpinquitas ad nõ gradum <lb/>(ſuppono em̄ opinionē noīaliū nõ diſtīguentē ꝓpī­<lb/>quitatē a diſtãtia) / igr̄ intēſio attēdit̄̄ penes ꝓpin-<lb/>quitatē ad nõ gradū. </s>
              <s xml:id="N2AF44" xml:space="preserve">Ptꝫ hec ↄ̨ña in .4. figura. </s>
              <s xml:id="N2AF47" xml:space="preserve">Si-<lb/>mile argumētū põt fieri ꝓbãdo /  nõ attēdit̄̄ penes <lb/>multitudinē graduū: hoc addito /  oīs multitudo <lb/>graduū eſt paucitas.               <anchor type="note" xlink:href="note-0263-03" xlink:label="note-0263-03a"/>               </s>
              <s xml:id="N2AF55" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi attenderet̄̄ <lb/>intēſio penes diſtantiã a nõ gradu: ſequeret̄̄ gradū <lb/>ſummū eſſe remiſſum. </s>
              <s xml:id="N2AF5C" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ <lb/>ſequit̄̄. </s>
              <s xml:id="N2AF61" xml:space="preserve">Seq̄la ꝓbat̄̄: q2 in duplo plus diſtat a non <lb/>gradu ꝙ̄ gradꝰ mediꝰ vt ↄ̨ſtat: g̊ eſt in duplo magꝪ <lb/>intēſus ꝙ̄ g̈dꝰ mediꝰ et ꝑ ↄ̨ñs in duplo minꝰ remiſſus / <lb/>et ſic ſequit̄̄ /  eſt remiſſus / quod fuit ꝓbandum:</s>
            </p>
            <div xml:id="N2AF6A" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0263-03a" xlink:label="note-0263-03" xml:id="N2AF6E" xml:space="preserve">Confir.</note>
            </div>
            <p xml:id="N2AF74">
              <s xml:id="N2AF75" xml:space="preserve">Scḋo prīcipalr̄ ↄ̨̨tra ſcḋaꝫ ꝑtē q̄ſtio-<lb/>nis argr̄ ſic: q2 nulla ē q̈litas vniformiṫ difformis: <lb/>igr̄ illa pars ſupponit flm̄. </s>
              <s xml:id="N2AF7C" xml:space="preserve">Cõſequētia ptꝫ et ꝓbat̄̄ <lb/>añs. </s>
              <s xml:id="N2AF81" xml:space="preserve">q2 ſi eſſet aliqua. </s>
              <s xml:id="N2AF84" xml:space="preserve">Seq̄ret̄̄ /  quelꝫ q̈litas cuius <lb/>oēs partes īmediate ſcḋm extēſionē ſunt īmediate <lb/>ſcḋm intenſionē: q̄ vcꝫ ſic ſe hꝫ /  captis quibuſcun <lb/>duabꝰ partibꝰ īmediatis remiſſiſſimꝰ gradꝰ qui eſt <lb/>in vna eſt remiſſimꝰ qui nõ eſt in alia: eſſet vniformi­<lb/>ter difformis. </s>
              <s xml:id="N2AF91" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ et añs: ſeq̄la patꝫ <lb/>mediãte loco a diffinitione. </s>
              <s xml:id="N2AF96" xml:space="preserve">Sed falſitas ↄ̨ñtis ꝓ-<lb/>batur. </s>
              <s xml:id="N2AF9B" xml:space="preserve">Et ſigno vnū bipedale cuiꝰ vna medietas ſit <lb/>vniformiter difformis a .4. vſ ad .8. </s>
              <s xml:id="N2AFA0" xml:space="preserve">Et alia medie­<lb/>tas ſit ab .8. vſ ad .16. </s>
              <s xml:id="N2AFA5" xml:space="preserve">Quo poſito ſic argumētor / <lb/>illa eſt q̈litas cuiꝰ oēs partes īmediate ſcḋm extēſi-<lb/>onē ſūt īmediate ſcḋm intēſionē etc̈. </s>
              <s xml:id="N2AFAC" xml:space="preserve">Et tñ nõ eſt vni­<lb/>formiter difformis: igr̄ illud ↄ̨ñs eſt flm̄. </s>
              <s xml:id="N2AFB1" xml:space="preserve">Probatur <lb/>mīor: q2 illa nõ correſpõdet g̈dui medio hoc eſt exi-<lb/>ſtenti in medio illiꝰ q̈ualitatis qui eſt vt .8. / igr̄ illa <lb/>nõ eſt vniformiṫ difformis. </s>
              <s xml:id="N2AFBA" xml:space="preserve">ↄ̨ña patꝫ et ꝓbat̄̄ añr: q2 <lb/>tota illa q̈litas eſt intēſa vt .9. cū vna medietas ſit <lb/>vt .12. et denoīet vt .6. et alia ſit vt .6. et denoīet vt .3. / <lb/>igr̄ tota denoīatio eſt vt .9. et nõ vt .8. / quod fuit ꝓ-<lb/>bandum. </s>
              <s xml:id="N2AFC5" xml:space="preserve">Maior ptꝫ: q2 .4. īmediate .5, īmediate, 6. <lb/>īmediate, et ſic de quibuſcū duabꝰ partibꝰ īmedia­<lb/>tis ſunt īmediate ſunt intēſionē: igr̄ oēs partes il-<lb/>liꝰ īmediate ſcḋm extēſionē ſunt īmediate ſcḋm in-<lb/>tenſionē.               <anchor type="note" xlink:href="note-0263-04" xlink:label="note-0263-04a"/>               </s>
              <s xml:id="N2AFD5" xml:space="preserve">¶ Dices et bene negando añs: et ad ꝓba-<lb/>tionē negando ſequelã. </s>
              <s xml:id="N2AFDA" xml:space="preserve">Et cū ꝓbat̄̄ negando illam <lb/>eſſe diffinitionē q̈litatis vniformiter difformis vt <lb/>bene ꝓbat argumentū.               <anchor type="note" xlink:href="note-0263-05" xlink:label="note-0263-05a"/>               </s>
              <s xml:id="N2AFE6" xml:space="preserve">¶ Et ſi querat̄̄ diffinitio: dicit̄̄ <lb/>forte cū calculatore in capĺo de inductione gradus <lb/>ſummi  q̈litas vniformiter difformis eſt illa que <lb/>ſic ſe hꝫ  cuiuſlꝫ partis eius gradꝰ medius .1. qui <lb/>eſt in medio tantū exceditur a ſumo eiuſdem par-<lb/>tis quantum excedit infimum.</s>
            </p>
            <div xml:id="N2AFF3" level="5" n="3" type="float">
              <note position="right" xlink:href="note-0263-04a" xlink:label="note-0263-04" xml:id="N2AFF7" xml:space="preserve">Dicitur.</note>
              <note position="right" xlink:href="note-0263-05a" xlink:label="note-0263-05" xml:id="N2AFFD" xml:space="preserve">Calcula.</note>
            </div>
            <p xml:id="N2B003">
              <s xml:id="N2B004" xml:space="preserve">Sed ↄ̨̨tra q2 aliqua qualitas eſt vni-<lb/>formiter difformis, et tamen non cuiuſlibet partis <lb/>eius gradus qui eſt in medio tantum exceditur etc̈ / <lb/>igitur illa diffinitio nulla: probatur antecedēs. </s>
              <s xml:id="N2B00D" xml:space="preserve">Et <lb/>capio vnam lineam giratiuam ad ymaginationē <lb/>nominaliū girantem oēs partes proportionales <lb/>vniꝰ colūne per totum vniformiter difformis ab .8. <lb/>vſ ad non gradum. </s>
              <s xml:id="N2B018" xml:space="preserve">quo poſito argr̄ ſic: illa linea <lb/>giratiua eſt pars illꝰ q̈litatis vniformiṫ difformis <lb/></s>
              <s xml:id="N2B01E" xml:space="preserve"><pb chead="Quarti tractatus." file="0264" n="264"/>               Et tamē nõ cuiuſlbet partis gradus q̇ eſt ī medio tã­<lb/>tū exceditur a ſūmo ̄tum etc̃. / igr̄ aſſumptū verum <lb/></s>
              <s xml:id="N2B028" xml:space="preserve">Probatur minor / q2 illa linea nõ hꝫ mediū cū ſit in­<lb/>finita. </s>
              <s xml:id="N2B02D" xml:space="preserve">nec tota pars eiꝰ depto prīo giro hꝫ medium <lb/>ꝓpter eãdem cãm: ergo nõ cuiuſlꝫ partis eiꝰ gradus <lb/>qui eſt in medio tm̄ excedit̄̄ etc̃.               <anchor type="note" xlink:href="note-0264-01" xlink:label="note-0264-01a"/>               </s>
              <s xml:id="N2B039" xml:space="preserve">¶ Dices forte ad pū­<lb/>ctū argumēti diſtinguendo /  in illa lignea non ſit <lb/>medium aut mediū longitudinis: et ſic ↄ̨ceditur /  ī <lb/>illa nõ ſit mediū. </s>
              <s xml:id="N2B042" xml:space="preserve">Nec de tali medio intelligit̄̄ diffi-<lb/>nitio: aut mediū magnitudines et ſic negat̄̄. </s>
              <s xml:id="N2B047" xml:space="preserve">Illa eī <lb/>linea ̄uis ſit infinite longa nõ tñ eſt corpus infini-<lb/>tū ſiue quãtitas īfinita. </s>
              <s xml:id="N2B04E" xml:space="preserve">Sed finita: et per ↄ̨ñs habet <lb/>duas medietates: illud em̄ de ratione quãti finiti-<lb/>eſt habere videlicet duas medietates: quare facile <lb/>dici põt /  ī medio magnitudinis illius eſt gradus <lb/>mediꝰ: cū tale mediū ſit dabile et de tali medio in-<lb/>telligitur dicta diffinitio.</s>
            </p>
            <div xml:id="N2B05B" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0264-01a" xlink:label="note-0264-01" xml:id="N2B05F" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2B065">
              <s xml:id="N2B066" xml:space="preserve">Sed cõtra q2 aliqua eſt qualitas vni-<lb/>formiter difformis: et tñ nõ cuiuſlꝫ partis eiꝰ gra-<lb/>dus / qui eſt in medio magnitudinis tantū exceditur <lb/>a ſūmo ̄tum excedit īfinitū / igr̄ ſolutio nulla. </s>
              <s xml:id="N2B06F" xml:space="preserve">Pro­<lb/>batur añs: et ſigno vnū quadratū vniformiṫ diffor­<lb/>miter albū ab .8. vſ ad nõ gradū: et diuido illḋ in <lb/>duas medietates triangulares ꝑ diametrū ꝓcedē-<lb/>tē ab vno angulo in relinquū: vt pꝫ in figura ī mar­<lb/>gine. </s>
              <s xml:id="N2B07C" xml:space="preserve">Et manifeſtū eſt /  altera pars ſiue medietas <lb/>triangularis illiꝰ quadrati hꝫ maiorē partē ſui ̄ <lb/>medietatē qualificatã maiori gradu ꝙ̄ vt .4. habet <lb/>enim .3. quartas incipientes a .4. et terminatas ad <lb/>nõ gradū: et vnã dūtaxat incipientē a .4. et termina­<lb/>tã ad .8. / ergo ſequit̄̄ /  gradus medius nõ eſt in me-<lb/>dio magnitudinis illius partis triangularis. </s>
              <s xml:id="N2B08B" xml:space="preserve">Sed <lb/>in fine ṗme .4. / ergo aliqua eſt qualitas vniformiter <lb/>difformis: et tamē nõ cuiuſlibet partis eius gradꝰ <lb/>qui eſt in medio talis partis tantū exceditur a ſum-<lb/>mo ̄tū excedit infiniū eiuſdē partis puta illꝰ par­<lb/>tis triangularis: quod fuit probandum.</s>
            </p>
            <p xml:id="N2B098">
              <s xml:id="N2B099" xml:space="preserve">Tertio prīcipaliter arguitur ſic. </s>
              <s xml:id="N2B09C" xml:space="preserve">Q2 <lb/>ſi qualitatis vniformiter difformis et difformiṫ dif­<lb/>formis intentio attendēda eſt penes reductionē ad <lb/>vniformitatē: ſeq̄retur /  qualitas difformis cuius <lb/>vtra medietas eſt vniofrmis correſpõderet gra-<lb/>dui medio. </s>
              <s xml:id="N2B0A9" xml:space="preserve">ſꝫ ↄ̨ñs eſt fĺm: igitur illud ex quo ſeq̇tur <lb/>ſequela pꝫ. </s>
              <s xml:id="N2B0AE" xml:space="preserve">Et ꝓbatur falſitas cõſequētis. </s>
              <s xml:id="N2B0B1" xml:space="preserve">Et ſigno <lb/>vnū bipedale cuiꝰ vna medietas ſit calida vt .8. et <lb/>alia vt .4. </s>
              <s xml:id="N2B0B8" xml:space="preserve">Et volo /  pars calida vt .8. perdat duos <lb/>gradus caliditatis: et illos acq̇rat pars calida vt <lb/>4. </s>
              <s xml:id="N2B0BF" xml:space="preserve">Et cõtinuo cū pars intēſior remittit̄̄ cõdēſetur ꝑ­<lb/>dendo ̄titatē ad ſubduplū et eque velociter pars <lb/>remiſſior rarefiat acq̇rēdo quãtitatē: ita  illḋ cor­<lb/>pus ſꝑ maneat bipedale: quo poſito ſic argumen-<lb/>tor: iſtud corpus cõtinuo intēdet̄̄: et in fine manebit <lb/>vniforme ſub gradu medio puta vt .6. / igit̄̄ modo ē <lb/>remiſſius gradu medo. </s>
              <s xml:id="N2B0CE" xml:space="preserve">Coña pꝫ et ꝓbatur maior: q2 <lb/>cõtinuo ꝑ maiorē partē illis corporis fiet intēſio ̄ <lb/>remiſſio eodē gradu: igit̄̄ cõtinuo illud corpus intē­<lb/>detur: ↄ̨ña probat̄̄ a ſimili / q2 ſi ꝑ maiorē partē ali-<lb/>cuius corporis eſſet albedo ꝙ̄ nigredo cõtinuo tale <lb/>corpus denominaret̄̄ albū: igit̄̄ aſimili ſi cõtinuo ꝑ <lb/>maiorē partē illius ſubiecti eſt intenſio ꝙ̄ remiſſio <lb/>eodē gradu: continuo illud corpus denominabitur <lb/>remitti. </s>
              <s xml:id="N2B0E1" xml:space="preserve">añs ꝓbat̄̄ videlicet /  ꝑ maiorē partē conti­<lb/>nuo fiet intēſio ꝙ̄ remiſſio et eodē gradu: q2 ↄ̨tinuo <lb/>pars q̄ intendit̄̄ erit maior parte que remittit̄̄ ꝑ to­<lb/>tū: cū modo ſit equalis: et continuo rarefiat: et alia <lb/>cõdēſetur. </s>
              <s xml:id="N2B0EC" xml:space="preserve">igr̄ cõtinuo ꝑ maiorē partem fiet intēſio <lb/>̄ remiſſio eodē gradu: qḋ fuit ꝓbandū. </s>
              <s xml:id="N2B0F1" xml:space="preserve">iam ꝓbat̄̄               <cb chead="Capitulum tertium"/>               minor videlicet /  in fine illud corpus manebit vni­<lb/>forme ſub gradu medio: quia manebit vniforme vt <lb/>ſex: q̇ ē medietas vt .8. perdet duos gradus: et me­<lb/>dietas vt .4. acq̇ret illos duos: igit̄̄ totū manebit vt <lb/>ſex: et gradus medius inter .8. et .4. cū equaliter di-<lb/>ſtet ab extremis: igit̄̄ illud corpus in fine manebit <lb/>vniforme ſub gradu medio.</s>
            </p>
            <p xml:id="N2B103">
              <s xml:id="N2B104" xml:space="preserve">Quarto principaliter arguitur ſic. </s>
              <s xml:id="N2B107" xml:space="preserve">ſi <lb/>intenſio q̈litatis vni difformis attendēda eſt penes <lb/>reductionē ad vniformitatē: ſeq̄retur /  etiam intē­<lb/>ſio corporis difformiter difformis attēdenda eſſet <lb/>penes reductionē ad vniformitatē: ſꝫ ↄ̨ñs eſt falſum / <lb/>igitur illud ex quo ſeq̄tur. </s>
              <s xml:id="N2B114" xml:space="preserve">ſequela eſt nota: et ꝓbat̄̄ <lb/>falſitas ↄ̨ñtis. </s>
              <s xml:id="N2B119" xml:space="preserve">Et capio vnū corpus finitū cuiꝰ prīa <lb/>pars ꝓportionalis ſic calida vt .4. et .2. vt .3. et ſimi­<lb/>liter quelibet ſequens ſit calida vt .3. </s>
              <s xml:id="N2B120" xml:space="preserve">Quo poſito <lb/>ſic argumētor. </s>
              <s xml:id="N2B125" xml:space="preserve">Iſtud corpus eſt difformimter cali-<lb/>dū. </s>
              <s xml:id="N2B12A" xml:space="preserve">Et tamen eius intēſio nõ debet attēdi penes re-<lb/>ductionē ad vniformitatē: igr̄ ꝓpoſitū. </s>
              <s xml:id="N2B12F" xml:space="preserve">Minor pro­<lb/>batur: q2 tunc ſeq̄retur ip̄m eſſe infinite caliduꝫ. </s>
              <s xml:id="N2B134" xml:space="preserve">Sꝫ <lb/>ↄ̨ñs eſt falſum vt cõſtat: igr̄ illḋ ex quo ſequit̄̄. </s>
              <s xml:id="N2B139" xml:space="preserve">Pro­<lb/>batur ſequela: q2 ip̄m corpus poteſt reduci ad vni-<lb/>formē caliditateꝫ infinitã: igr̄ ſeq̇tur ip̄m eē infinite <lb/>calidū ꝓbatur añs: et pono /  vnꝰ gradus q̇ eſt in .2. <lb/>parte ꝓportionali extēdat̄̄ ꝑ totū et vnꝰ q̇ eſt in .3. ex­<lb/>tendat̄̄ etiã per totū, et ſic cõſequēter et hoc penetra­<lb/>tiue et vnitiue, quo poſito illa caliditas manet infi­<lb/>nita et vniformis / igit̄̄ illud corpus poteſt reduci ad <lb/>vniformē caliditatē infinitã / quod fuit probandum <lb/></s>
              <s xml:id="N2B14D" xml:space="preserve">¶ Dices forte ad argumentū cõcedēdo ſequelam et <lb/>negando falſitatē ↄ̨ñtis et ad punctū ꝓbatiõis ne-<lb/>go /  ſequeret̄̄ illud corpus eē infinite calidū. </s>
              <s xml:id="N2B154" xml:space="preserve">Et ad <lb/>ꝓbationē diſtinguo añs videlicet /  tale corpus p̄t <lb/>reduci ad caliditatē infinitã aut debita reductione <lb/>et ſic nego, aut indebita et ſic cõcedo. </s>
              <s xml:id="N2B15D" xml:space="preserve">vnde vt dicis <lb/>ad hoc /  aliqua qualitas debite reducatur ad vni­<lb/>formitatē oportet /  nulla fiat rarefactio aut ↄ̨dē-<lb/>ſatio in qnalitate q̄ reducitur etc̃. </s>
              <s xml:id="N2B166" xml:space="preserve">Sꝫ in ꝓpoſito q̄lꝫ <lb/>caliditas exiſtens ī aliqua parte ꝓportionali alia <lb/>a prima rarefit ad ̄titatē totiꝰ corporis. </s>
              <s xml:id="N2B16D" xml:space="preserve">Non igr̄ <lb/>fit debita reductio.</s>
            </p>
            <p xml:id="N2B172">
              <s xml:id="N2B173" xml:space="preserve">Sed cõtra quia tunc ſequeretur /  ſi <lb/>eſſet vnum corpus infinitū cuius primū pedale eſſet <lb/>calidū vt .4. et quodlibet aliud: corpus eſſet infinite <lb/>calidū. </s>
              <s xml:id="N2B17C" xml:space="preserve">Sꝫ ↄ̨ñs eſt falſum (cū nõ ſit calidius corpo-<lb/>re calido vt .4. vniformiter ꝑ totū) / igr̄ illud ex quo <lb/>ſequitur. </s>
              <s xml:id="N2B183" xml:space="preserve">Probatur ſequela / q2 fine rarefactiõe et <lb/>cõdēſatiõe põt illud corpus effici infinite calidū / igr̄ <lb/>eſt infinite calidū probatur añs, et pono /  a quolꝫ <lb/>pedali ſequēte primū dematur vnus gradus et po-<lb/>natur in prīo et hoc ſiue aliqua rarefactione aut cõ­<lb/>dēſatione. </s>
              <s xml:id="N2B190" xml:space="preserve">Et manifeſtum eſt /  in fine ī primo peda­<lb/>li ſunt īfiniti gradus caliditatis, et ꝑ ↄ̨ñs infinities <lb/>infiniti volo igr̄ /  capiantur infiniti ex illis et po-<lb/>nantur in .2. pedali: et iterū alii infiniti et ponãtur <lb/>in .3. </s>
              <s xml:id="N2B19B" xml:space="preserve">Et ſic cõſequēter fine rarefactione et cõdēpſa-<lb/>tione. </s>
              <s xml:id="N2B1A0" xml:space="preserve">quo poſito in fine totū illud corpus manebit <lb/>vniformiter infinite calidū: igitur iam modo eſt in­<lb/>finite calidū patet hec conſequētia / q2 per te eius in­<lb/>tenſio debet attendi penes reductionē ad vniformi­<lb/>tatē debite factam, quēadmodū ſit in propoſito.</s>
            </p>
            <p xml:id="N2B1AB">
              <s xml:id="N2B1AC" xml:space="preserve">Quinto principaĺr arguitur ſic </s>
              <s xml:id="N2B1AF" xml:space="preserve">Si <lb/>corporis difformis intenſio deberet cognoſci pe-<lb/>pes reductionem ad vniformitatē ſeq̄retur /  ſi vnū <lb/>pedale diuidatur ꝑ partes ꝓportionales ꝓportio­<lb/>ne quadrupla et prima ſit aliqualiter alba et .2. in               <pb chead="De difformium intenſione" file="0265" n="265"/>               duplo plus: et 3. in duplo plus ꝙ̄ .2. </s>
              <s xml:id="N2B1BF" xml:space="preserve">Et .4. in duplo <lb/>pluſ̄ .3. </s>
              <s xml:id="N2B1C4" xml:space="preserve">Et ſic ↄ̨ñter. </s>
              <s xml:id="N2B1C7" xml:space="preserve">Tale corpus eſſet īfinite albuꝫ / <lb/>ſed ↄ̨ñs eſt falſum: igit̄̄ illud ex quo ſeq̇tur </s>
              <s xml:id="N2B1CC" xml:space="preserve">Falſitas <lb/>ↄ̨ſequētis pꝫ / qr illud corpꝰ eſt finite albū: igit̄̄ </s>
              <s xml:id="N2B1D1" xml:space="preserve">Pro­<lb/>batur añs. </s>
              <s xml:id="N2B1D6" xml:space="preserve">Et pono gratia argumēti /  albedo pri­<lb/>me partis ꝓportionalis ſit vt .4. / et manifeſtum eſt / <lb/> ip̄a denominat totū vt .3. / igr̄ tota illa denominat <lb/>illud corpus vt .6. / et per ↄ̨ñs finite totū denoīat: et ex <lb/>cõſequēti illud corpus ē finite albū / qḋ fuit ꝓbãdum <lb/></s>
              <s xml:id="N2B1E2" xml:space="preserve">Probatur tñ ↄ̨ña: qr ſi albedo exiſtens in prīa par­<lb/>te ꝓportionali denoīat totū vt .3. </s>
              <s xml:id="N2B1E7" xml:space="preserve">Et albedo exiſtēs <lb/>in .2. eſt in duplo intēſior: et eſt in ſubquadruplo ſub­<lb/>iecto: igr̄ denoīat in duplo minus ptꝫ ↄ̨ña: qr ſi eēt <lb/>abedo .2. partis equalis intēſiõis albedine prīe de­<lb/>noīaret in ſubquadruplo: ſꝫ mõ denoīat in duplo <lb/>plus cum ſit in duplo intēſior: ergo denoīat in du-<lb/>plo minus ꝙ̄ albedo prīe qr dupluꝫ ſubq̈drupli eſt <lb/>ſubduplū quadrupli. </s>
              <s xml:id="N2B1F8" xml:space="preserve">Et eadē rõne albedo exiſtens <lb/>in .3. denoīat in ſubduplo minꝰ ꝙ̄ albedo exiſtens ī <lb/>2. </s>
              <s xml:id="N2B1FF" xml:space="preserve">Et ſic cuiuſlibet ꝑtis ſequētis albedo denoīat in <lb/>duplo minus illud ſubiectū ꝙ̄ albedo īmediate p̄ce­<lb/>dentis ip̄am: igitur denoīato illiꝰ albedinis ↄ̨po-<lb/>nitur ex infinitis ↄ̨tinuo ſe habētibꝰ in ꝓportiõe du­<lb/>pla: et primū illoꝝ eſt vt .3. / ergo totū eſt vt ſex: pꝫ hec <lb/>ↄ̨ña ex ṗma parte huiꝰ libri. </s>
              <s xml:id="N2B20C" xml:space="preserve">Sꝫ iam ꝓbo ſeq̄laꝫ: qr <lb/>ſi in prīa parte ꝓportionali alicuius corꝑis ꝓpor-<lb/>tiõe dupla diuiſi ponat̄̄ aliq̈ albedo: et in .2. duplo ī­<lb/>tenſior ꝑ totū ſiue mixtione ↄ̈rii in .3. in duplo intē-<lb/>ſior  in .2. et in .4. in duplo ītēſior ꝙ̄ in .3. / et ſic ↄ̨ſe-<lb/>quēter: tale corpus eēt infinite albū: igit̄̄ pari rõne <lb/>ſi diuidat̄̄ ꝓportione quadrupla: et in prima parte <lb/>ponatur aliqua albedo: et in .2. ī duplo intēſior etc. <lb/>tale corpus erit infinite albū. </s>
              <s xml:id="N2B21F" xml:space="preserve">Patꝫ ↄ̨ña / qr nõ vide­<lb/>tur maior ratio de vno ꝙ̄ de altero. </s>
              <s xml:id="N2B224" xml:space="preserve">Probat̄̄ añs: <lb/>et pono gr̄a argumenti /  albedo prime partis ſit <lb/>vt .2. deīde volo /  in prīa parte ꝓportionabili vniꝰ <lb/>hore capiãtur .4. gradus exiſtētes ī .2. parte ꝓpor-<lb/>tionali illiꝰ corporis q̄ eſt vna quarta: et ponatur <lb/>quilibet illoꝝ in diuerſa quarta. </s>
              <s xml:id="N2B231" xml:space="preserve">Et in .2. ꝑte hore <lb/>ponatur q̇lꝫ .8. graduū exiſtentiū in .3. parte corpo-<lb/>ris que eſt vna octaua in diuerſa octaua illius cor­<lb/>ris. </s>
              <s xml:id="N2B23A" xml:space="preserve">Et in .3. parte hore capiat̄̄ q̇lꝫ ſexdecim graduū <lb/>exiſtentiū in quarta ꝑte corꝑis et ponat̄̄ in diuerſa <lb/>decimaſexta: et ſic ↄ̨ñter: quo poſito in fine hore illḋ <lb/>corpus habebit ꝑ totū infinitã albedinē / vt cõſtat: et <lb/>erit reductū ad vniformitatē: igitur illud corpꝰ mõ <lb/>ante reductionē ad vniformitatē eſt infinite album /1 <lb/>quod fuit ꝓbandum.</s>
            </p>
            <p xml:id="N2B249">
              <s xml:id="N2B24A" xml:space="preserve">In oppoſitum arguitur ſic </s>
              <s xml:id="N2B24D" xml:space="preserve">Sit a. dif­<lb/>forme: et pono /  reducatur ad vniformitatem nul-<lb/>la facta rarefactiõe aut condēſatione qualitatis in <lb/>parte aut in tota: nulla qualitate poſita in maiori <lb/>aut minori parte ꝙ̄ erat antea etc. </s>
              <s xml:id="N2B258" xml:space="preserve">Et tūc manifeſtū <lb/>eſt /  tale corpus eſt vniforme. </s>
              <s xml:id="N2B25D" xml:space="preserve">Sit igitur vniforme <lb/>c. gradu. </s>
              <s xml:id="N2B262" xml:space="preserve">Et arguo ſic / a. eſt intenſum c. gradu: et eſt <lb/>ita intenſuꝫ ſicut erat ante reductionē ad vniformi-<lb/>tatē: igit̄̄ ante reductionē ad vniformitatē erat a. in­<lb/>tenſum c. gradu. </s>
              <s xml:id="N2B26B" xml:space="preserve">Et ꝑ ↄ̨ñs eius intēſio et pari ratio-<lb/>ne cuiuſcū difformis mēſuranda eſt penes redu-<lb/>ctionē ad vniformitatē. </s>
              <s xml:id="N2B272" xml:space="preserve">Minor ꝓbatur / qr a. nullaꝫ <lb/>intenſionē acq̇ſiuit aut ꝑdidit / qr quantã ꝑdidit vna <lb/>eiꝰ pars tantã acquiſiuit ſibi equalis: g̊ a. eſt ita in­<lb/>tenſum ſicut erat añ reductionē ad vniformitatē.</s>
            </p>
            <p xml:id="N2B27B">
              <s xml:id="N2B27C" xml:space="preserve">Quatuor articuli hãc queſtionē abſol­<lb/>uent: primꝰ notabit: ſcḋs cõcluſiões inducet: tertius <lb/>dubitabit: quartꝰ vero ratiões añ oppoſitū ſoluet. </s>
            </p>
            <p xml:id="N2B283">
              <s xml:id="N2B284" xml:space="preserve">Notandum eſt primo tangendo ma-               <cb chead="De difformium intenſione"/>               teriam primi argumēti: iſti termini paruitas et ma­<lb/>gnitudo ſunt termini ſe habentes ꝑ modū priuati-<lb/>ui et poſitiui: et ſimiĺr iſti intenſio et remiſſio: et iſti <lb/>multitudo et paucitas. </s>
              <s xml:id="N2B290" xml:space="preserve">Et ꝓ eadē reverificant̄̄: omīs <lb/>eī magnitudo ē paruitas et oīs paruitas eſt magni­<lb/>tudo. </s>
              <s xml:id="N2B297" xml:space="preserve">Quãuis tamē idē ſit magnitudo et paruitas <lb/>nichilominus nõ ſequit̄̄ hec magnitudo efficit̄̄ ma-<lb/>ior: et hec magnitudo eſt paruitas: g̊ paruitas effi­<lb/>citur maior. </s>
              <s xml:id="N2B2A0" xml:space="preserve">Sed debet cõcludi: ergo paruitas effi-<lb/>citur maior magnitudo. </s>
              <s xml:id="N2B2A5" xml:space="preserve">Et qm̄ iſti termini diſtan-<lb/>tia et propinq̇tas etiã eodē mõ ſe habent ſicut ma-<lb/>gnitudo et paruitas: dico /  oīs diſtantia eſt ꝓpin­<lb/>quitas: et oīs ꝓpinquitas eſt diſtantia. </s>
              <s xml:id="N2B2AE" xml:space="preserve">Tñ iſtã ↄ̨ña <lb/>nõ valet iſta ꝓpinq̇tas efficitur maior. </s>
              <s xml:id="N2B2B3" xml:space="preserve">Et iſta ꝓpī-<lb/>quitas eſt iſta diſtãtia: g̊ iſta diſtãtia efficit̄̄ maior. <lb/></s>
              <s xml:id="N2B2B9" xml:space="preserve">Sꝫ debet cõcludi: g̊ iſta diſtãtia efficit̄̄ maior ꝓprin-<lb/>quitas.               <anchor type="note" xlink:href="note-0265-01" xlink:label="note-0265-01a"/>               </s>
              <s xml:id="N2B2C3" xml:space="preserve">Aduerte vlteriꝰ /  intēſionem attēdi penes <lb/>maiorē diſtãtia a nõ gradu nichil aliud eſt ꝙ̄ maio­<lb/>ritatē intenſiõis cognoſci mediãte veritate huiꝰ ꝓ-<lb/>poſitionis. </s>
              <s xml:id="N2B2CC" xml:space="preserve">Quanta diſtãtia qualitatis a nõ gra-<lb/>du eſt maior tanto intēſio qualitatis eſt maior. </s>
              <s xml:id="N2B2D1" xml:space="preserve">ma­<lb/>gnitudo aūt diſtantie attēditur penes multitudinē <lb/>graduū eiuſdē intenſionis ipſius qualitatis.               <anchor type="note" xlink:href="note-0265-02" xlink:label="note-0265-02a"/>               </s>
              <s xml:id="N2B2DD" xml:space="preserve">¶ Ex <lb/>quo ſequit̄̄ primo /  meliꝰ cognoſcit̄̄ intenſiõis ma­<lb/>ioritas penes multitudinē graduū: ꝙ̄ penes diſtan­<lb/>tiã a nõ gradu: qñ quidē ipſius diſtantie maioritas <lb/>penes multitudinē graduū tandē cognoſcit̄̄ de hoc <lb/>plura in expoſitiõe ṗmi capitis calculatoris.               <anchor type="note" xlink:href="note-0265-03" xlink:label="note-0265-03a"/>               </s>
              <s xml:id="N2B2EF" xml:space="preserve">¶ Se­<lb/>quitur ſcḋo / hanc ↄ̨ñam nõ valere iutēſio attēditur <lb/>penes maiorē diſtantiã a nõ gradu: et oīs diſtãtia <lb/>eſt ꝓpinq̇tas: igitur intenſio attēdit̄̄ penes ꝓpīqui­<lb/>tatē ad nõ gradū. </s>
              <s xml:id="N2B2FA" xml:space="preserve">Probat̄̄ / q2 cõuertit̄̄ cū iſta mala <lb/>ↄ̨ña intenſio mēſuratur mediãte veritate huiꝰ ꝓpo­<lb/>ſitiõis: quãto diſtãtia a nõ gradu eſt maior tanto ī-<lb/>tenſio eſt maior: et oīs diſtãtia eſt ꝓpinq̇tas: igit̄̄ in­<lb/>tenſio mēſuratur mediante itate huiꝰ ꝓpoſitiõis <lb/></s>
              <s xml:id="N2B306" xml:space="preserve">Quanto ꝓpinq̇tas ad nõ gradū eſt maior tanto in­<lb/>tenſio eſt maior. </s>
              <s xml:id="N2B30B" xml:space="preserve">Et ꝑ hoc ſoluirur prmū argumen-<lb/>tū ante oppoſitū               <anchor type="note" xlink:href="note-0265-04" xlink:label="note-0265-04a"/>               ¶ Seq̇tur .3. gradum ſummū eē re­<lb/>miſſum. </s>
              <s xml:id="N2B317" xml:space="preserve">Patꝫ hoc correlariū ex confirmatione pri­<lb/>mi argumenti.</s>
            </p>
            <div xml:id="N2B31C" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0265-01a" xlink:label="note-0265-01" xml:id="N2B320" xml:space="preserve">Aduerte.</note>
              <note position="right" xlink:href="note-0265-02a" xlink:label="note-0265-02" xml:id="N2B326" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0265-03a" xlink:label="note-0265-03" xml:id="N2B32C" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0265-04a" xlink:label="note-0265-04" xml:id="N2B332" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N2B338">
              <s xml:id="N2B339" xml:space="preserve">Notandum eſt ſecundo / circa materiã <lb/>ſecundi argumēti inq̇rendo diffinitionē qualitatis <lb/>vniformiṫ difformis /  duplex eſt qualitas quedaꝫ <lb/>eſt vniformis: q̄dã eſt difformis. </s>
              <s xml:id="N2B342" xml:space="preserve">Qualitas vnifor-<lb/>mis eſt illa cuius oēs partes ̄titatiue ſunt eque in­<lb/>tenſe. </s>
              <s xml:id="N2B349" xml:space="preserve">Sed qualitas difformis eſt qualitas cuiꝰ nõ <lb/>om̄s partes equales quãtitatiue ſunt eque intenſe <lb/></s>
              <s xml:id="N2B34F" xml:space="preserve">Hec aūt eſt duplex: quia q̄dã eſt vniformiter diffor-<lb/>mis: quedã vero vniformiter difformis. </s>
              <s xml:id="N2B354" xml:space="preserve">Sꝫ q2 qua­<lb/>litas vniformiter difformis diuerſi mode a diuer-<lb/>ſis diffinitur: ideo ad inq̇rendã diffinitionē eiꝰ po-<lb/>no aliquas ꝓpoſitiones.               <anchor type="note" xlink:href="note-0265-05" xlink:label="note-0265-05a"/>               </s>
              <s xml:id="N2B362" xml:space="preserve">¶ Prima ꝓpõ. </s>
              <s xml:id="N2B365" xml:space="preserve">Qualitas <lb/>vnifor. diffor. non bene ſic diffinit̄̄. </s>
              <s xml:id="N2B36A" xml:space="preserve">Qualitas vni-<lb/>for. diffor. eſt qualitas difformis cuiꝰ om̄s partes <lb/>immediate ſcḋm extenſionē ſunt īmediate ſecundū <lb/>intēſionē: vt declaratū eſt in .2. argumēto. </s>
              <s xml:id="N2B373" xml:space="preserve">Ptꝫ hec <lb/>ꝓpoſitio ex eodē .2. argumēto añ oppoſitū.               <anchor type="note" xlink:href="note-0265-06" xlink:label="note-0265-06a"/>               </s>
              <s xml:id="N2B37D" xml:space="preserve">¶ Secū­<lb/>da ꝓpõ. </s>
              <s xml:id="N2B382" xml:space="preserve">Qualitas vnifor. diffor. non bene diffinit̄̄ <lb/>ſic. </s>
              <s xml:id="N2B387" xml:space="preserve">Qualitas vnifo. diffor. ē illa que ſic ſe habet  <lb/>cuiuſlibet partis eius gradus medius .i. qui eſt ī me­<lb/>dio tanto exceditur a ſummo quanto excedit infini­<lb/>um.               <anchor type="note" xlink:href="note-0265-07" xlink:label="note-0265-07a"/>               </s>
              <s xml:id="N2B395" xml:space="preserve">Et hoc eſt cõtra calcula in c. de inductiõe gradꝰ <lb/>ſummi. </s>
              <s xml:id="N2B39A" xml:space="preserve">pꝫ hoc ꝓpõ ex deductiõe prime replice di-<lb/>cti .2 argu. ante oppoſitum.               <anchor type="note" xlink:href="note-0265-08" xlink:label="note-0265-08a"/>               </s>
              <s xml:id="N2B3A4" xml:space="preserve">¶ Tertia ꝓpõ. </s>
              <s xml:id="N2B3A7" xml:space="preserve">Quali-<lb/>tas vnifor. diffor. nõ bene diffinitur ſic. </s>
              <s xml:id="N2B3AC" xml:space="preserve">Qualitas <lb/>vnifor. diffor eſt illa que ſic ſe habet  cuiuſlꝫ part-<lb/>tis eius gradus medius .i. qui eſt in medio ſecundū <lb/>magnitudinem tanto exceditur a ſūmo quantum etc. <lb/></s>
              <s xml:id="N2B3B6" xml:space="preserve"><pb chead="Quarti tractatus." file="0266" n="266"/>               Patet hec ꝓpõ ex .2. replica dicti ſecūdi argumēti. <lb/>               <anchor type="note" xlink:href="note-0266-01" xlink:label="note-0266-01a"/>               </s>
              <s xml:id="N2B3C4" xml:space="preserve">¶ Ex hac ꝓpõne ſequit̄̄ /  aliqua eſt qualitas vni. <lb/>diffor. cuiꝰ ſcḋm aliquã diuiſiõeꝫ q̄lꝫ pars ꝓportio­<lb/>nalis eſt difformiter difformis. </s>
              <s xml:id="N2B3CB" xml:space="preserve">pꝫ diuidēdo vnum <lb/>quadratū vniformiter difformē ꝑ lineas tranſuer-<lb/>ſales ſiue diametrales.               <anchor type="note" xlink:href="note-0266-02" xlink:label="note-0266-02a"/>               </s>
              <s xml:id="N2B3D7" xml:space="preserve">¶ Quarta ꝓpõ. </s>
              <s xml:id="N2B3DA" xml:space="preserve">Qualitas <lb/>vnifor. diffor. nõ bñ diffinitur ſic. </s>
              <s xml:id="N2B3DF" xml:space="preserve">Qualitas vnifor. <lb/>diffor. eſt illa q̄ ſic ſe hꝫ  ſecūdū aliquã eiꝰ diuiſio­<lb/>nē cuiuſlꝫ partis gradus medius .i. q̇ eſt ī medio .etc̃. <lb/></s>
              <s xml:id="N2B3E7" xml:space="preserve">Probat̄̄ / qr illa diffinitio ſic intellecta conuenit illi <lb/>qualitati q̄ nõ eſt vniformiter difformis de qua fit <lb/>mētio in .2. argumēto añ oppoſitū, eſto  illa diui-<lb/>datur ꝑ partes ꝓportionales ꝓportione dupla. vt <lb/>cõſtat intelligēti caſum.               <anchor type="note" xlink:href="note-0266-03" xlink:label="note-0266-03a"/>               </s>
              <s xml:id="N2B3F7" xml:space="preserve">¶ Quinta ꝓpõ. </s>
              <s xml:id="N2B3FA" xml:space="preserve">Qualitas <lb/>vnifor. diffor. nõ bene diffinit̄̄ ſic. </s>
              <s xml:id="N2B3FF" xml:space="preserve">Qualitas vnifor. <lb/>diffor. eſt illa q̄ ſic ſe hꝫ  ſcḋm aliquã diuiſionē di­<lb/>uidendo ſecundū ṫuã dimēſionē cuiuſlibet partꝪ eiꝰ <lb/>gradus q̇ eſt in medio ſcḋm magnitudinē tantū ex-<lb/>ceditur a ſūmo: quãto etc̃. </s>
              <s xml:id="N2B40A" xml:space="preserve">Probatur. </s>
              <s xml:id="N2B40D" xml:space="preserve">q2 capto qua­<lb/>drato ꝑfecto cuiꝰ vna .3. in medio ꝓcedēs ab vno la-<lb/>tere in reliquū ſit vniformiter difformis ab .8. vſ <lb/>ad .4. </s>
              <s xml:id="N2B416" xml:space="preserve">Et vna alia .3. ex trãſuerſo ꝓcedēs vſ ad alte­<lb/>ram ex vtro latere ꝑ modū crucis ſit etiã vnifor-<lb/>miter difformis ab .8. vſ ad .4. </s>
              <s xml:id="N2B41D" xml:space="preserve">Et reſidue partes <lb/>ſint vniformis. </s>
              <s xml:id="N2B422" xml:space="preserve">Tunc manifeſtū eſt illã qualitatem <lb/>non eſſe vniformiter difformē: et tñ illa diffinitio ei <lb/>cõuenit / vt patꝫ intelligēti caſum. </s>
              <s xml:id="N2B429" xml:space="preserve">igr̄ illa diffinitio <lb/>nulla. </s>
              <s xml:id="N2B42E" xml:space="preserve">Hoc videas clariꝰ in expõne .2. capi. Calcu. in <lb/>prīcipio.               <anchor type="note" xlink:href="note-0266-04" xlink:label="note-0266-04a"/>               </s>
              <s xml:id="N2B438" xml:space="preserve">¶ Sexta ꝓpõ. </s>
              <s xml:id="N2B43B" xml:space="preserve">Qualitas vnifor. diffor. bñ <lb/>diffinit̄̄ ſic.               <anchor type="note" xlink:href="note-0266-05" xlink:label="note-0266-05a"/>               </s>
              <s xml:id="N2B445" xml:space="preserve">Qualitas vniformiter diffor. eſt quali-<lb/>tas ita ſe hñs  in ea ꝓportõe in qua queuis om̄ia <lb/>puncta eiꝰ intrīſeca equalis intēſiõis magis diſtãt <lb/>quãtitatiue a gradu euius ſūmo in ea ꝑ maiorē la-<lb/>titudinē diſtãt intēſiue ab eodē gradu ſūmo: ita  <lb/>in quacū ꝓportiõe vna pars eius eſt maior alte-<lb/>ra ̄titatiue (inequalis tñ intēſiõis) in ea extremū <lb/>eius intēſiꝰ ꝑ maiorē latitudinē excedit extremū re­<lb/>miſſiꝰ eiuſdem. </s>
              <s xml:id="N2B458" xml:space="preserve">exēplū / vt capta latitudine vniformi­<lb/>ter difformi. </s>
              <s xml:id="N2B45D" xml:space="preserve">ab .8. vſ ad nõ gradū manifeſtuꝫ eſt / <lb/> punctus vt .4. iu duplo plꝰ diſtat ̄titatiue ꝙ̄ pū­<lb/>ctus vt .6. a gradu .8. et etiã ꝑ in duplo maiorem la­<lb/>titudinē gradus octauus excedit .4. ꝙ̄ .6. / vt ſatis cõ­<lb/>ſtat. </s>
              <s xml:id="N2B468" xml:space="preserve">et ſic de aliis gradibꝰ et punctis poteris facile <lb/>exēplificare. </s>
              <s xml:id="N2B46D" xml:space="preserve">Itē capta medietate intēſiori que ē ab <lb/>octauo vſ ad .4. et prīa quarta alteriꝰ medietatꝪ <lb/>q̄ eſt a .4. vſ ad .2. manifeſtū eſt  in ea ꝓportione <lb/>puta dupla q̈ in medietas ē maior illa quarta ī ea <lb/>ꝑ maiorē latitudinē extremū intēſius eiꝰ excedit eiꝰ <lb/>extremū remiſſius ꝙ̄ extremū intēſius ipſius quar­<lb/>te excedat eius extremū remiſſius. </s>
              <s xml:id="N2B47C" xml:space="preserve">Hanc diffinitio­<lb/>nē nõ aliter ſufficiētē ꝓbo niſi q2 nõ video defectuꝫ <lb/>in ea.               <anchor type="note" xlink:href="note-0266-06" xlink:label="note-0266-06a"/>               </s>
              <s xml:id="N2B488" xml:space="preserve">difficile em̄ eſt cõſtruere diffinitionē vt inquit <lb/>phūs .6. thopi.               <anchor type="note" xlink:href="note-0266-07" xlink:label="note-0266-07a"/>               </s>
              <s xml:id="N2B492" xml:space="preserve">Si q̇s aūt defectū inuenerit: aut eo <lb/>affectu excuſet Aulus geliꝰ .i. nocti. atti. varro­<lb/>nē in cõplete inducias diffiniētē excuſat: aut corri-<lb/>gat.               <anchor type="note" xlink:href="note-0266-08" xlink:label="note-0266-08a"/>               </s>
              <s xml:id="N2B4A0" xml:space="preserve">Nõ em̄ (vt cū Auguſto .i. de trini. loquar) pude­<lb/>bit me ſicubi heſito querere aut ſicubi erro diſcere. <lb/></s>
              <s xml:id="N2B4A6" xml:space="preserve">Nõ eī eſt hõ q̇ nõ peccet .3. regū .8.               <anchor type="note" xlink:href="note-0266-09" xlink:label="note-0266-09a"/>               </s>
              <s xml:id="N2B4AE" xml:space="preserve">Oēs eī errauimꝰ <lb/>Eſaie .53. qḋ et de volūtatis et etiã intellectꝰ errore <lb/>ſatis cõmode intelligi põt. </s>
              <s xml:id="N2B4B5" xml:space="preserve">¶ Qualitas aūt vnifor­<lb/>miter difformis eſt duplex: q̄dã eī terminat̄̄ ad gra­<lb/>dū. </s>
              <s xml:id="N2B4BC" xml:space="preserve">q̄dã vero ad nõ gradū. </s>
              <s xml:id="N2B4BF" xml:space="preserve">Qualitas vnifor. diffor. <lb/>terminata ad nõ gradū eſt qualitas vnifor. diffor. <lb/>cuiꝰ oīa puncta ↄ̨ſimilis intēſionis in ea ꝓportiõe <lb/>plus diſtant quãtitatiue a nõ gradu in q̈ ſunt inten­<lb/>ſiora: et econtra. </s>
              <s xml:id="N2B4CA" xml:space="preserve">vt qualitas vniformiter diffor. ab <lb/>octauo vſ ad nõ gradū.               <anchor type="note" xlink:href="note-0266-10" xlink:label="note-0266-10a"/>               </s>
              <s xml:id="N2B4D4" xml:space="preserve">¶ Ex hac diffinitione ſeq̇­<lb/>tur  in omni qualitate vnifor. diffor. termīata ad               <cb chead="Capitulum quartum"/>               non gradū et vniformiū dimēſionū in ea ꝓportio-<lb/>ne in qua puncta magis diſtant a nõ gradu ſecūdū <lb/>longitudinē: in ea ſunt maioris intenſiõis.               <anchor type="note" xlink:href="note-0266-11" xlink:label="note-0266-11a"/>               </s>
              <s xml:id="N2B4E5" xml:space="preserve">¶ Seq̇-<lb/>tur ſcḋo / quedaꝫ ꝓprietas qualitatis vnifor. diffor. <lb/>ad gradū termīate que et diffinitio eſt v3 qualitas <lb/>vnifor. diffor. ad gradū termīate ē q̈litas vniformi­<lb/>ter diffor. inter cuiꝰ gradus maior eſt ꝓpõ intēſionū <lb/>̄ diſtentiaꝝ ab extremo eius remiſſiori: hoc facile <lb/>ꝓbatur ex diffinitiõe qualitatis vni. diffor. ad non <lb/>gradū terminate. </s>
              <s xml:id="N2B4F6" xml:space="preserve">hoc addito /  quelꝫ qualitas vni. <lb/>diffor. põt eſſe in potētia ꝓpinqua pars vni: diffor. <lb/>ad nõ gradū terminate. </s>
              <s xml:id="N2B4FD" xml:space="preserve">Et  vtro termino ꝓpor­<lb/>tionis maioris inequalitatis equaliter decreſcēte <lb/>ꝓportio augetur               <anchor type="note" xlink:href="note-0266-12" xlink:label="note-0266-12a"/>               </s>
              <s xml:id="N2B509" xml:space="preserve">¶ Seq̇tur .3. /  ſi q̈litas vniformis <lb/>addatur q̈litati vnifor. dif. oīno eq̈lium dimēſionū: <lb/>reſultabit qualitas vniformiter difformis. </s>
              <s xml:id="N2B510" xml:space="preserve">Proba­<lb/>tur. </s>
              <s xml:id="N2B515" xml:space="preserve">q2 facta tali vnione adhuc puncta oīo eodē mo­<lb/>do ſe excedēt ſicut añ ſe excedebãt in illa q̈litate vni­<lb/>formiter diffor. </s>
              <s xml:id="N2B51C" xml:space="preserve">Sꝫ in illa qualitate vniformi. dif. <lb/>puncta eo mõ ſe excedūt ſicut ſufficit ad qualitateꝫ <lb/>vni. dif. / igit̄̄ facta tali vniõe illa qualitas manet vni­<lb/>for. dif. </s>
              <s xml:id="N2B525" xml:space="preserve">Minor pꝫ. </s>
              <s xml:id="N2B528" xml:space="preserve">et maior ꝓbat̄̄ ꝑ hoc /  qñcun <lb/>aliqua ſe excedūt: et equalē latitudinē oīo acquirūt <lb/>cõtinuo equali exceſſu ſe excedūt. </s>
              <s xml:id="N2B52F" xml:space="preserve">vt facile eſt demõ­<lb/>ſtrare.               <anchor type="note" xlink:href="note-0266-13" xlink:label="note-0266-13a"/>               </s>
              <s xml:id="N2B539" xml:space="preserve">¶ Sequit̄̄ .4. </s>
              <s xml:id="N2B53C" xml:space="preserve">Si due q̈litates vnifor. dif. ad <lb/>non gradū terminate: et ↄ̨ſimiliū oīno dimēſionum <lb/>nõ gradibus ſimul vnitis: et extremis aliis etiã ad <lb/>inuicem vnitis: reſultabit qualitas totalis vni. dif. <lb/></s>
              <s xml:id="N2B546" xml:space="preserve">Probatur / q2 puncta correſpõdētia in vna illaruꝫ <lb/>ſe habēt oīo in eadē ꝓportiõe quo ad intēſionē et <lb/>diſtantiã a nõ gradu: ſicut ſe habēt correſpõdentia <lb/>in altera: ergo ipſa ſimul vnita manebūt in eadem <lb/>ꝓportiõe: et ꝑ ↄ̨ñs illa totalis q̈litas manebit vni. <lb/>dif. </s>
              <s xml:id="N2B553" xml:space="preserve">Patet hec ↄ̨ña auxilio huius / qḋ in .2. parte de­<lb/>monſtratū eſt /  v3 talis eſt ꝓportio cõiunctorū qua­<lb/>lis eſt diuiſorū.               <anchor type="note" xlink:href="note-0266-14" xlink:label="note-0266-14a"/>               </s>
              <s xml:id="N2B55F" xml:space="preserve">¶ Seq̇t̄̄ .5. /  ſi q̈litati vni. dif. oīno <lb/>equaliū dimēſionū extremis ītēſioribꝰ ad inuiceꝫ <lb/>iūctꝪ: et remiſſoribꝰ ad īuicē ſiĺr iūctꝪ addat̄̄ q̈li. vni. <lb/>dif. reſultabit q̈litas vni. dif. (ſꝑ abigo muſcas). </s>
              <s xml:id="N2B568" xml:space="preserve">ꝓ­<lb/>bat̄̄ / q2 vel vtra illaꝝ termīat̄̄ ad nõ g̈dū. </s>
              <s xml:id="N2B56D" xml:space="preserve">et ſic ex .4. <lb/>corre. manebit vni. dif. aut vna terminat̄̄ ad nõ gra­<lb/>dum: et alia nõ: et tūc dematur ab illa termīata ad <lb/>gradū maximꝰ gradus vniformis ꝑ totū: et tunc vt <lb/>conſtat manebit totū reſiduū qualitas vni. diffor. <lb/>ad nõ gradū terminata: vniat̄̄ igit̄̄ alteri termina­<lb/>te ad nõ gradū: et ex .4. corre. manebit qualitas vni. <lb/>diffor. addatur / ergo illa qualitas vni. diffor. gra-<lb/>dui vniformi dēpto a q̈litate terminata ad graduꝫ <lb/>et ex .3. corre. manebit qualitas vni. dif. / igit̄̄ ſi quali­<lb/>tati vni. diffor. addat̄̄ etc. reſultabit quali. vni dif. <lb/></s>
              <s xml:id="N2B585" xml:space="preserve">Patꝫ igit̄̄ corre.               <anchor type="note" xlink:href="note-0266-15" xlink:label="note-0266-15a"/>               </s>
              <s xml:id="N2B58D" xml:space="preserve">Et hec eſt .4. cal. in .c. de inductione <lb/>gradus ſū. </s>
              <s xml:id="N2B592" xml:space="preserve">quã longis ambagibus ꝓbat.               <anchor type="note" xlink:href="note-0266-16" xlink:label="note-0266-16a"/>               </s>
              <s xml:id="N2B59A" xml:space="preserve">¶ Sequi­<lb/>tur .6. /  ſemꝑ ex vnione duarū qualitū vni. diffor-<lb/>miū oīno equaliū et ↄ̨ſimiliū dimēſionū reſultat q̈-<lb/>litas vniformis vel vniformiter dif. hanc facile eſt <lb/>ex predictis demõſtrare. </s>
              <s xml:id="N2B5A5" xml:space="preserve">¶ Sequit̄̄ .7. </s>
              <s xml:id="N2B5A8" xml:space="preserve">Qñcū eadē <lb/>latitudo vel oīno ↄ̨ſimilis vni. dif. extendit̄̄ ꝑ duo <lb/>ſubiecta inequalia: in ꝓportione qua vnū ſubiectū <lb/>eſt maius alio in ea puncta ↄ̨ſimilia ī maiori plꝰ <lb/>diſtaut ̄titatiue a gradu ſūmo q̈ eis ſimilia ī mi­<lb/>nori. </s>
              <s xml:id="N2B5B5" xml:space="preserve">exemplū / vt ſi latitudo ab .8. vſ ad .4. exten-<lb/>datur in pedali et in ſemipedali punctus vt .6. in du­<lb/>plo plus diſtat a ſūmo in pedali ꝙ̄ in ſemipedali <lb/></s>
              <s xml:id="N2B5BD" xml:space="preserve">Probatur / ſit a. lati. vni. diffor. extenſa ꝑ aliqḋ ſub­<lb/>iectū. </s>
              <s xml:id="N2B5C2" xml:space="preserve">et b. oīo cõſimilis lati. extenſa ꝑ ſubiectum in <lb/>f. ꝓportiõe minus: et ſit .c. punctꝰ in a. et d. cõſimilis <lb/>in b. et excedat gradus ſummꝰ in g. ꝓportione ma-<lb/>iori exceſſu extrema illaꝝ latitu. ꝙ̄ ipſa puncta c.d: <lb/></s>
              <s xml:id="N2B5CC" xml:space="preserve"><pb chead="De difformium intenſione" file="0267" n="267"/>               Et manifeſtū eſt ex diffinitiõe q̈litatis vni. diffor. /  <lb/>diſtãtia extremi remiſſioris ip̄us a. vel non gradꝰ a <lb/>ſuo gradu ſūmo eſt in g. proportiõe maior diſtãtia <lb/>ipſius c. ab eodē gradu ſūmo: et eadē rõne diſtantie <lb/>extremi remiſſioris vel nõ gradus ipſius b. a gradu <lb/>ſūmo ad diſtãtiã ipſius .d. ab eodē gradu ſūmo eſt <lb/>g. proportio. </s>
              <s xml:id="N2B5DF" xml:space="preserve">Tunc dico /  diſtãtia ipſiꝰ c. a gradu <lb/>ſummo eſt in f. ꝓportione maior diſtantia ipſiꝰ d. <lb/>a gradu ſummo. </s>
              <s xml:id="N2B5E6" xml:space="preserve">Quod ſic ꝓbat̄̄ / q2 ex hypotheſi ſi­<lb/>cut ſe hꝫ diſtãtia extremi remiſſiorꝪ in a. ab ſuo gra­<lb/>du ſummo ad diſtantiã ipſiꝰ c. ab eodē gradu ſūmo <lb/>ita ſe hꝫ diſtãtia extremi remiſſioris in b. a ſuo gra-<lb/>du ſummo ad diſtãtiã ipſius d. ab eodē gradu ſum­<lb/>mo: ergo auxilio loci a ꝑmutata ꝓportione. </s>
              <s xml:id="N2B5F3" xml:space="preserve">ſeq̇tur <lb/>manifeſte probandum. </s>
              <s xml:id="N2B5F8" xml:space="preserve">pꝫ ergo corre.</s>
            </p>
            <div xml:id="N2B5FB" level="5" n="6" type="float">
              <note position="right" xlink:href="note-0265-05a" xlink:label="note-0265-05" xml:id="N2B5FF" xml:space="preserve">1. propõ.</note>
              <note position="right" xlink:href="note-0265-06a" xlink:label="note-0265-06" xml:id="N2B605" xml:space="preserve">2. propõ.</note>
              <note position="right" xlink:href="note-0265-07a" xlink:label="note-0265-07" xml:id="N2B60B" xml:space="preserve">ↄ̨tra cal.</note>
              <note position="right" xlink:href="note-0265-08a" xlink:label="note-0265-08" xml:id="N2B611" xml:space="preserve">3. propõ.</note>
              <note position="left" xlink:href="note-0266-01a" xlink:label="note-0266-01" xml:id="N2B617" xml:space="preserve">Correla.</note>
              <note position="left" xlink:href="note-0266-02a" xlink:label="note-0266-02" xml:id="N2B61D" xml:space="preserve">4. ꝓpõ.</note>
              <note position="left" xlink:href="note-0266-03a" xlink:label="note-0266-03" xml:id="N2B623" xml:space="preserve">5. propõ.</note>
              <note position="left" xlink:href="note-0266-04a" xlink:label="note-0266-04" xml:id="N2B629" xml:space="preserve">6. ꝓpõ.</note>
              <note position="left" xlink:href="note-0266-05a" xlink:label="note-0266-05" xml:id="N2B62F" xml:space="preserve">q̇d quali­<lb/>tas vni. <lb/>diffor.</note>
              <note position="left" xlink:href="note-0266-06a" xlink:label="note-0266-06" xml:id="N2B639" xml:space="preserve">phūs .6. <lb/>thopi.</note>
              <note position="left" xlink:href="note-0266-07a" xlink:label="note-0266-07" xml:id="N2B641" xml:space="preserve">Aulꝰ ge. <lb/>i. nocttuꝫ <lb/>atti. c. 25.</note>
              <note position="left" xlink:href="note-0266-08a" xlink:label="note-0266-08" xml:id="N2B64B" xml:space="preserve">Augu. i. <lb/>de trini. <lb/>3. reg. 8.</note>
              <note position="left" xlink:href="note-0266-09a" xlink:label="note-0266-09" xml:id="N2B655" xml:space="preserve">eſaie .53.</note>
              <note position="left" xlink:href="note-0266-10a" xlink:label="note-0266-10" xml:id="N2B65B" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0266-11a" xlink:label="note-0266-11" xml:id="N2B661" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0266-12a" xlink:label="note-0266-12" xml:id="N2B667" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0266-13a" xlink:label="note-0266-13" xml:id="N2B66D" xml:space="preserve">4. correĺ.</note>
              <note position="right" xlink:href="note-0266-14a" xlink:label="note-0266-14" xml:id="N2B673" xml:space="preserve">5. correĺ.</note>
              <note position="right" xlink:href="note-0266-15a" xlink:label="note-0266-15" xml:id="N2B679" xml:space="preserve">Calcula.</note>
              <note position="right" xlink:href="note-0266-16a" xlink:label="note-0266-16" xml:id="N2B67F" xml:space="preserve">6. correĺ</note>
            </div>
            <note position="left" xml:id="N2B685" xml:space="preserve">Calcula.</note>
            <p xml:id="N2B689">
              <s xml:id="N2B68A" xml:space="preserve">Notandū eſt tertio circa materiam .3. <lb/>argumēti /  due ſunt opiniões circa difformiū q̈li-<lb/>tatū denoīatiões quas Cal. recitati .2. capi. prima <lb/>eſt  intēſio q̈litatis difformis et eiꝰ denoīatio me-<lb/>tiri d3 penes reductionē ad vniformitatē: quomo-<lb/>do autē debeat fieri talis reductio ſequēs notabi-<lb/>le declarabit. </s>
              <s xml:id="N2B699" xml:space="preserve">Alia vero eſt opinio  intēſio diffor­<lb/>miū mēſurãda eſt gradu ſūmo. </s>
              <s xml:id="N2B69E" xml:space="preserve">v3  ſi in pedali ſit <lb/>qualitas difformis ab .8. vſ ad nõ g̈dū: ſubiectuꝫ <lb/>eius denoīabit̄̄ intenſum vt .8. etiã ſi ꝑ .4. partē ſub­<lb/>iecti vel ̄tūcun paruã extendat̄̄. </s>
              <s xml:id="N2B6A7" xml:space="preserve">Sꝫ cal. volēs im­<lb/>pugnare primã opinionē facit talē ↄ̨ñam. </s>
              <s xml:id="N2B6AC" xml:space="preserve">Per ma­<lb/>iorem partē alicuius ſubiecti cõtinuo fit intenſio ̄ <lb/>remiſſio eodē gradu: ergo ↄ̨tinuo totū ītēdit̄̄. </s>
              <s xml:id="N2B6B3" xml:space="preserve">Ideo <lb/>ad inquirēdū an in tali reductiõe ſubiectū ſꝑ inten­<lb/>datur, aut ſꝑ remittat̄̄, aut aliqñ intēdatur, aliquã­<lb/>do vero remittat̄̄, aut maneat eque intenſum pono <lb/>aliq̈s ꝓpoſitiões. </s>
              <s xml:id="N2B6BE" xml:space="preserve">¶ Prima ꝓpõ. </s>
              <s xml:id="N2B6C1" xml:space="preserve">Iſta ↄ̨ña nichil va­<lb/>let ꝑ maiorē partē huiꝰ ſubiecti ↄ̨tinuo fit intenſio <lb/>̄ remiſſio eodē gradu: g̊ totuꝫ ſubiectū intenditur. <lb/></s>
              <s xml:id="N2B6C9" xml:space="preserve">Probat̄̄ et ſigno vnū pedale difformiter albuꝫ cuiꝰ <lb/>vna medietas ſit vniformis .8. et alia vt vnū vnifor-<lb/>mis: et volo /  ꝑ totã horã futurã remittat̄̄ pars in-<lb/>tēſior et ꝑdat duos gradus adeq̈te: et totidē acq̇rat <lb/>pars remiſſior: et cū hoc cõdēſetur pars intēſior ad <lb/>ſubduplū pars vero remiſſior rarefiat: ita  quãtã <lb/>̄titatē deꝑdit pars intēſior tantã acq̇rat adequa-<lb/>te pars remiſſior. </s>
              <s xml:id="N2B6DA" xml:space="preserve">Quo poſito in fine hore illḋ ſub­<lb/>iectum erit remiſſius ꝙ̄ modo ſit. </s>
              <s xml:id="N2B6DF" xml:space="preserve">Et tñ intēſio con-<lb/>tinuo fit ꝑ maiorē partē ꝙ̄ remiſſio eodē gradu: igr̄ <lb/>in illo caſu añs illiꝰ ↄ̨ñe eſt verū / et ↄ̨ñs falſum. </s>
              <s xml:id="N2B6E6" xml:space="preserve">Et ꝑ <lb/>ↄ̨ñs ↄ̨ña nõ valet / qḋ fuit ꝓbandū. </s>
              <s xml:id="N2B6EB" xml:space="preserve">Minor ē declarat <lb/>coſus: et maior ꝓbat̄̄ / q2 in ṗncipio talis alteratio-<lb/>nis totū illud pedale eſt album vt .4. cum dimidio. <lb/></s>
              <s xml:id="N2B6F3" xml:space="preserve">Prīa em̄ medietas illius albedinis denoīat vt .4. <lb/>quia eſt vt .8. et alia vt dimidiū q2 eſt vt vnū. </s>
              <s xml:id="N2B6F8" xml:space="preserve">Et in fi­<lb/>ne totum illud pedale eſt albuꝫ vt .3. cum .3. quartis: <lb/>igr̄ in fine hore illud pedale eſt remiſſius ꝙ̄ in prīci­<lb/>pio. </s>
              <s xml:id="N2B701" xml:space="preserve">Mīor ꝓbat̄̄ / q2 in fine hore .3. quarte illiꝰ peda-<lb/>lis erunt albe vt .3. </s>
              <s xml:id="N2B706" xml:space="preserve">Et ſic denoīabunt totuꝫ albuꝫ vt <lb/>duo cum vna quarta. reliq̈ o quarta intēſior cū ſit <lb/>vt .6. denīat vt vnū cum dimidio. </s>
              <s xml:id="N2B70D" xml:space="preserve">Modo duo cū vna <lb/>quarta: et vnū cum dimidio faciunt .3. cum .3. quartꝪ: <lb/>igit̄̄ totuꝫ illud pedale ī fine eſt albū vt .3. cuꝫ .3. quar­<lb/>tis. </s>
              <s xml:id="N2B716" xml:space="preserve">¶ Scḋa ꝓpõ </s>
              <s xml:id="N2B719" xml:space="preserve">Iſta ↄ̨ña nõ valet ꝑ maiorē partem <lb/>huiꝰ ſubiecti ↄ̨tinuo fit remiſſio ꝙ̄ intēſio eodē gra-<lb/>du: g̊ hoc ſubiectū remittit̄̄. </s>
              <s xml:id="N2B720" xml:space="preserve">Probat̄̄ et ſigno vnum <lb/>pedale cuius vna medietas ſit alba vniformiter vt <lb/>8. et alia vt duo: et ꝑ horã futurã ꝑdat ſucceſſiue ꝑs <lb/>intenſior duos gradus albedinis: pars o remiſſi­<lb/>or acq̇rat illos duos adequate: et cū hoc pars intē-<lb/>ſior rarefiat ad ſexq̇alteruꝫ acq̇rendo .4. pedalis: et               <cb chead="De difformium intenſione"/>               tantum deꝑdat medietas remiſſior. </s>
              <s xml:id="N2B730" xml:space="preserve">Quo poſito in <lb/>fine hore illud pedale erit albiꝰ ꝙ̄ mõ ſit: et tñ ma-<lb/>iorem partē ↄ̨tinuo fiet remiſſio ꝙ̄ intēſio eodē gra­<lb/>du: igr̄ illa ↄ̨ña nulla. </s>
              <s xml:id="N2B739" xml:space="preserve">Maior ꝓbatur / q2 in ṗncipio <lb/>alteratiõis illud pedale ē album vt .5. / vt conſtat: et ī <lb/>fine eſt album vt .5. cū dimidio: igr̄ in fine hore ē al-<lb/>bius ꝙ̄ modo ſit. </s>
              <s xml:id="N2B742" xml:space="preserve">minor ꝓbatur / q2 ī fine .3. quarte al­<lb/>be vt .6. denoīant illud pedale vt .4. cum dimidio / vt <lb/>patet calculãti: et alia q̈rta vt .4. denoīat totum vt <lb/>vnum: igit̄̄ totum vnū pedale eſt albū vt .5. cū dimi-<lb/>dio: quod fuit ꝓbandū. </s>
              <s xml:id="N2B74D" xml:space="preserve">¶ Et q̊ ſeq̇tur /  nõnū̄ in-<lb/>tenſio fit ꝑ maiorē partē ꝙ̄ remiſſio eodē gradu: et <lb/>tamē totum remittit̄̄: et aliqñ etiã intendit̄̄. </s>
              <s xml:id="N2B754" xml:space="preserve">Et ple-<lb/>rū ꝑ aliqḋ tēpus intēdit̄̄: et ꝑ aliqḋ remittit̄̄. </s>
              <s xml:id="N2B759" xml:space="preserve">Pa­<lb/>tent oīa iſta cum multis aliis hãc materiã tangēti-<lb/>bus in expoſitiõe ſupra .2. capitulū Calculatoris vi­<lb/>deas ea ibi. </s>
              <s xml:id="N2B762" xml:space="preserve">Et ꝑ hoc pꝫ ſolutio .3. argumēti.</s>
            </p>
            <p xml:id="N2B765">
              <s xml:id="N2B766" xml:space="preserve">Notandum eſt quarto pro declaratio­<lb/>ne materie quinti argumēti:  calculator aliter mē­<lb/>ſurat q̈litatis et ſiĺr q̈lificati difformis intēſionem <lb/>quã ꝑ reductionē ad vniformitatē: metit̄̄ em̄ diffor-<lb/>mis corꝑis intēſionē penes denoīationē ꝑtiū ipſiꝰ <lb/>qualitatis difformis: ita  vĺr cuiuſlꝫ difformis in­<lb/>tēſio mēſurari hꝫ penes gradū denoīatiõis q̊ talis <lb/>q̈litas nata eſt ſuū totale ſubiectū denoīare ſecluſa <lb/>ↄ̈rii ꝑmixtiõe. </s>
              <s xml:id="N2B779" xml:space="preserve">procuiꝰ ītellectu faciliori ponit̄̄ talis <lb/>ſuppõ q̄ in hac mã ꝓ baſi et fundamēto hētur q̄ ta-<lb/>lis eſt. </s>
              <s xml:id="N2B780" xml:space="preserve">minꝰ facit q̈litas extēſa ꝑ ꝑtē ſubiecti ad de-<lb/>noīationē ſui ſubiecti ꝙ̄ ſi eadē ꝑ totū extendat̄̄ ma­<lb/>nēte eq̈li intēſione. </s>
              <s xml:id="N2B787" xml:space="preserve">Et ī quacū ꝓportiõe pars in <lb/>qua eſt talis qualitas eſt minor ſuo toto in eadē ta­<lb/>lis qualitas minus ſuū ſubiectū denoīant. </s>
              <s xml:id="N2B78E" xml:space="preserve">ita  in <lb/>quadruplo minꝰ denoīat qualitas totū qñ eſt p̄ciſe <lb/>extenſa ꝑ vnam quartã ꝙ̄ qñ eſt extenſa ꝑ totū et per <lb/>tertiã in triplo minꝰ, et ꝑ medietatē in dupla minꝰ. <lb/></s>
              <s xml:id="N2B798" xml:space="preserve">Exemplū / vt albedo vt .4. extēſa p̄ciſe ꝑ quartã ꝑtem <lb/>ſubiecti denoīat totū ſubiectū albū vt vnū: q2 ſi eēt <lb/>extenſa ꝑ totū denoīaret totū ſubiectuꝫ vt .4. ſꝫ mo­<lb/>do eſt in ꝑte ī quadruplo mīori ſuo toto: g̊ in qua-<lb/>druplo minꝰ denoīat ſuum ſubiectū </s>
              <s xml:id="N2B7A3" xml:space="preserve">Huiꝰ maior de­<lb/>claratio ponit̄̄ in expoſitiõe ſcḋi capitis calculato­<lb/>ris. </s>
              <s xml:id="N2B7AA" xml:space="preserve">Ad menſurãdã aūt intēſionē alicuiꝰ difformis <lb/>cuiꝰ difformitas eſt īfinita aūt in īfinitū ꝓcedēs: vt <lb/>ſi ponat̄̄ /  prīa pars ꝓportionalis alicuiꝰ corpo-<lb/>ris ſit aliqualr̄ alba: et ſcḋa in ſexq̇altero magis: et <lb/>tertia in ſexq̇altero magis ꝙ̄ ſcḋa: et ſic ↄ̨ñter diui-<lb/>ſione corꝑis fctã ꝓportiõe ſexq̇tertia aut ̄uis alia <lb/>etc. </s>
              <s xml:id="N2B7B9" xml:space="preserve">Aduertēda eſt q̄dã diuiſio qualitatū inherētiū <lb/>ꝑtibꝰ alicuiꝰ ſubiecti q̄ huic inq̇ſitiõi plurimū ē ac-<lb/>comoda et neceſſaria </s>
              <s xml:id="N2B7C0" xml:space="preserve">Illã tñ abſoluã: qm̄ iam ip̄a ex­<lb/>poſita eſt in ſcḋo tractatu huiꝰ partis capite .6. </s>
              <s xml:id="N2B7C5" xml:space="preserve">Di­<lb/>uiſio aūt eſt hec. </s>
              <s xml:id="N2B7CA" xml:space="preserve">qualitates ꝑ diuerſas ꝑtes ſubie-<lb/>cti extēſe qñ ſunt equales nõnun̄ o inequales <lb/>intenſiue facile eſt exēpla dare. </s>
              <s xml:id="N2B7D1" xml:space="preserve">Et ſi ſunt equales <lb/>aut extendunt̄̄ ſiue īherēt ꝑtibꝰ equalibꝰ aut īequa­<lb/>libꝰ exēpla ſunt ī prõptu. </s>
              <s xml:id="N2B7D8" xml:space="preserve">Et ſi ſint īequales ītenſiue <lb/>ſiĺr valent extēdi ꝑ partes equales ſubiecti aut per <lb/>partes īequales. </s>
              <s xml:id="N2B7DF" xml:space="preserve">Si qualitates īequales ī equalibꝰ <lb/>ptibꝰ ſubiecti īhereãt: hoc cõtīgit dupĺr / q2 aut ma­<lb/>ior qualitas maiori parti īheret aut mīori exēpluꝫ <lb/>ṗmi vt ſi albedo vt octo īhereat mediati pedalis et <lb/>albedo vt .4. vni tertie eiuſdē pedalis exēplū ſecū-<lb/>di vt ſi fiat conuerſo. </s>
              <s xml:id="N2B7EC" xml:space="preserve">Si aūt ītenſior qualitas īhe­<lb/>ret parti ſubiecti mīori remiſſior qualitas maiori <lb/>parti ſubiecti. </s>
              <s xml:id="N2B7F3" xml:space="preserve">hoc contīgit tripĺr: q2 aut ꝓportio <lb/>illarū partiū ſubiecti excedit ꝓportõem illaꝝ qua-<lb/>litatū: aut ꝓportio qualitatū excedit ꝓportõem il-               <pb chead="Quarti trctatus." file="0268" n="268"/>               larū partiū ſubiecti: aut proportio illarū partiū ē <lb/>equalis ꝓportioni qusalitatū exemplū primi: vt ſi <lb/>in vna medietate pedalis ponat̄̄ albedo vt .4. et in <lb/>vna quarta albedo vt .5. / tunc ꝓportio partiū eſt ma­<lb/>ior ꝓportiõe q̈litatū. </s>
              <s xml:id="N2B807" xml:space="preserve">Nam hec ē ſexq̇quīta illa <lb/>vero dupla. / exēmplū ſcḋi: vt ſi in vna medietate ſubie­<lb/>cti ponat̄̄ albedo vt .2. et in quarta ponat̄̄ albedo vt <lb/>6. tunc ꝓportio q̈litatū excedit ꝓportionē ꝑtiū ſub­<lb/>iecti. </s>
              <s xml:id="N2B812" xml:space="preserve">nã hec dupla illa vero tripla. </s>
              <s xml:id="N2B815" xml:space="preserve">exēmplū tertii / vt ſi <lb/>in vna medietate ponat̄̄ albedo vt .8. et in vna quar­<lb/>ta albedo vt ſexdecim tunc eadē eſt ꝓportio illaruꝫ <lb/>partiū et etiã qualitatū: et tot modis poſſunt quali­<lb/>tates variari ſi intenſior qualitas maiori ꝑti ſubie­<lb/>cti inhereat remiſſior vero minori. </s>
              <s xml:id="N2B822" xml:space="preserve">adhibeas exem-<lb/>pla. Cõſummata diuiſione ponende ſunt aliq̄ pro-<lb/>poſitiões.               <anchor type="note" xlink:href="note-0268-01" xlink:label="note-0268-01a"/>               </s>
              <s xml:id="N2B82E" xml:space="preserve">¶ Prima propõ. </s>
              <s xml:id="N2B831" xml:space="preserve">Si qualitates eq̄ inten­<lb/>ſe partibꝰ extendant̄̄ equalibꝰ: ip̄e equaliter totuꝫ <lb/>ſubiectum denoīant: ſi vero ꝑtibus ſubiecti ineq̈li-<lb/>bus inhereãt: tūc illa qualitas q̄ ꝑ maiorē ꝑtē extē-<lb/>ditur plus denoīat totū (deducto impedimēto) ī ea <lb/>ꝓportiõe in q̈ ſe habēt ille ꝑtes ſubiecti ad inuicem. <lb/>               <anchor type="note" xlink:href="note-0268-02" xlink:label="note-0268-02a"/>               </s>
              <s xml:id="N2B845" xml:space="preserve">¶ Scḋa propõ. </s>
              <s xml:id="N2B848" xml:space="preserve">Qñ inequales qualitates equalibꝰ <lb/>ꝑtibus ſubiecti inherent: tūc intēſior in ea ꝓportio­<lb/>ne plus denoīat ſubiectū in qua eſt intēſior.               <anchor type="note" xlink:href="note-0268-03" xlink:label="note-0268-03a"/>               </s>
              <s xml:id="N2B854" xml:space="preserve">¶ Ter-<lb/>tia propõ. </s>
              <s xml:id="N2B859" xml:space="preserve">Si inequales qualitates intēſiue exten-<lb/>dant̄̄ ꝑ inequales partes vnius ſubiecti: et intenſior <lb/>maiori parti inhereat remiſſior vero minori: tunc <lb/>intenſior plꝰ denoīat totale ſubiectū ꝙ̄ remiſſior in <lb/>ꝓportiõe ↄ̨poſita ex ꝓportioni partis maioris ad <lb/>partem minorem: et qualitatis intenſioris ad qua-<lb/>litatem remiſſiorem. </s>
              <s xml:id="N2B868" xml:space="preserve">Exemplū / vt ſi in vna medieta­<lb/>te pedalis ponatur albedo vt .4. et in 4. eiuſdē po-<lb/>natur albedo vt .2. </s>
              <s xml:id="N2B86F" xml:space="preserve">Dico /  albedo exiſtēs īmediate <lb/>in quadruplo plus denoīat illud pedale ꝙ̄ albedo <lb/>exiſtēs in quarta eiuſdē pedalis: q2 proportio illa-<lb/>rum qualitatū, et etiaꝫ partiū eſt dupla compoſita <lb/>vero ex duabus duplis quadrupla.               <anchor type="note" xlink:href="note-0268-04" xlink:label="note-0268-04a"/>               </s>
              <s xml:id="N2B87F" xml:space="preserve">¶ Quarta pro­<lb/>poſitio. </s>
              <s xml:id="N2B884" xml:space="preserve">Si intēſior qualitas parti extēdatur mīo-<lb/>ri: et remiſſior maiori: ſit equalis ꝓportio ꝑtium <lb/>ad inuicē et etiã intenſionū: tunc ille qualitates eq̈li­<lb/>ter ad totius denoīationē faciūt. </s>
              <s xml:id="N2B88D" xml:space="preserve">Exemplum / vt ſi ī <lb/>vna medietate ponat̄̄ qualitas vt .4. et in vna quar-<lb/>ta vt .8. q2 tunc inter partes et etiã qualitates ē pro­<lb/>portio dupla tantū facit ad denoīationē totiꝰ qua­<lb/>litas vt .8. in vna quarta: ̄tum qualitas vt .4. ī me­<lb/>dietate: q2 vtra. </s>
              <s xml:id="N2B89A" xml:space="preserve">vt .2. / vt pꝫ.               <anchor type="note" xlink:href="note-0268-05" xlink:label="note-0268-05a"/>               </s>
              <s xml:id="N2B8A2" xml:space="preserve">¶ Quinta propõ. </s>
              <s xml:id="N2B8A5" xml:space="preserve">Si ī­<lb/>tenſior qualitas parti coextēdat̄̄ mīori: et remiſſior <lb/>maiori: ꝓportio intenſionū illarū qualitatū par­<lb/>tiū proportionē exuperat: tunc qualitas exiſtens in <lb/>minori parte ſubiecti totale ſubiectum intēſius de­<lb/>noīabit ꝙ̄ qualitas exiſtēs in minori parte: in ea ꝓ­<lb/>portiõe ꝑ quam ꝓportio intenſionū illarū qualita­<lb/>tū ꝑtium ꝓportionē excedit. </s>
              <s xml:id="N2B8B6" xml:space="preserve">Exēplū / vt ſi in vna me-<lb/>dietate pedalis ponatur albedo vt .2. et in quarta <lb/>eiuſdē albedo vt .8. q2 ꝓportio ꝑtium dupla excedit̄̄ <lb/>a ꝓportione intenſionū illarū qualitatū quadru-<lb/>pla: et quadrupla excedit duplã ꝑ duplã: ideo in du-<lb/>plo plus denoīat qualitas vt .8. ꝙ̄ vt .2. illud totale <lb/>ſubiectum. </s>
              <s xml:id="N2B8C5" xml:space="preserve">quia illa vt .2. denoīat vt vnū alia o vt <lb/>8. denoīat vt .2. / vt patēt.               <anchor type="note" xlink:href="note-0268-06" xlink:label="note-0268-06a"/>               </s>
              <s xml:id="N2B8CF" xml:space="preserve">¶ Sexta ꝓpõ. </s>
              <s xml:id="N2B8D2" xml:space="preserve">Ubicū in-<lb/>tenſior qualitas parti ſubiecti minori inheret: et re­<lb/>miſſior maiori: eſt inter partes maior ꝓportio ̄ <lb/>inter illarū qualitatū intēſiones: et tūc qualitas re­<lb/>miſſior plus facit ad totius denominationē ꝙ̄ intē­<lb/>ſior in ea ꝓportione per quã proportio partium ꝓ­<lb/>portionē intenſionum antecedit. </s>
              <s xml:id="N2B8E1" xml:space="preserve">Exemplum / vt ſi in <lb/>vna medietate ſit qualitas vt .4. et in vna quarta <lb/>ſit qualitas vt .6. quia qualitas intenſior minori               <cb chead="Capitulum quartum"/>               parti inheret: et proportio partium dupla excedit ꝓ­<lb/>portionē intenſionū ſexq̇alterã per ſexquitertiam: <lb/>ideo qualitas vt .6. exiſtens in quarta in ſexq̇tertio <lb/>minus denominat totale ſubiectū ꝙ̄ qualitas vt .4. <lb/>exiſtens in mediate. </s>
              <s xml:id="N2B8F3" xml:space="preserve">Harum .6. ꝓpoſitionū demon-<lb/>ſtrationes inuenies in expõne ſcḋi capitis calcula-<lb/>toris: et facile ex his que dicta ſunt capite tertio ſe-<lb/>cundi tractatus: et primo capite tertii tractatus ꝓ-<lb/>bari valent mutatis mutandis. </s>
              <s xml:id="N2B8FE" xml:space="preserve">Quibus premiſſis <lb/>ponūtur concluſiones.</s>
            </p>
            <div xml:id="N2B903" level="5" n="7" type="float">
              <note position="left" xlink:href="note-0268-01a" xlink:label="note-0268-01" xml:id="N2B907" xml:space="preserve">porpõ.</note>
              <note position="left" xlink:href="note-0268-02a" xlink:label="note-0268-02" xml:id="N2B90D" xml:space="preserve">.propõ.</note>
              <note position="left" xlink:href="note-0268-03a" xlink:label="note-0268-03" xml:id="N2B913" xml:space="preserve">propõ.</note>
              <note position="left" xlink:href="note-0268-04a" xlink:label="note-0268-04" xml:id="N2B919" xml:space="preserve">.propõ</note>
              <note position="left" xlink:href="note-0268-05a" xlink:label="note-0268-05" xml:id="N2B91F" xml:space="preserve">.propõ.</note>
              <note position="left" xlink:href="note-0268-06a" xlink:label="note-0268-06" xml:id="N2B925" xml:space="preserve">6. propõ.</note>
            </div>
            <p xml:id="N2B92B">
              <s xml:id="N2B92C" xml:space="preserve">Prima concluſio </s>
              <s xml:id="N2B92F" xml:space="preserve">Diuiſo corpore qua­<lb/>libuerit ꝓportione et prima pars ꝓportionalis eiꝰ <lb/>ſit aliqualiter intenſa et ſecunda in duplo plus et <lb/>tertia in triplo ꝙ̄ prima et quarta in quadruplo ̄ <lb/>prima: et ſic ī infinitū. </s>
              <s xml:id="N2B93A" xml:space="preserve">et hoc eadē qualitate ſiue ad­<lb/>mixtione ↄ̈rii: tunc totū corpus eſt intenſius prima <lb/>prima parte ꝓportionali in ea ꝓportiõe qua ſe hꝫ <lb/>totū ſic diuiſuꝫ ad ṗmã ꝑtē eius ꝓportionalē. </s>
              <s xml:id="N2B943" xml:space="preserve">Pro­<lb/>batur cõcluſio vĺr. </s>
              <s xml:id="N2B948" xml:space="preserve">et ſuppono /  diuiſo aliquo cor-<lb/>pore ꝑ partes ꝓportionales aliqua ꝓportõe: et pri­<lb/>mo ꝑ totū illud corpus extendat̄̄ aliqua qualitas: <lb/>et ꝑ totū reſiduū a ṗma parte ꝓportionali ſuꝑ illaꝫ <lb/>extendatur tanta: et ꝑ reſiduū a ṗma et a ſecūda ite­<lb/>rum tanta extendat̄̄ ſupra p̄exñteꝫ: et deinde ſupra <lb/>reſiduū a prima ſcḋa et tertia extendatur iterū tan­<lb/>ta ſupra preexñteꝫ: et ſic ↄ̨ñter: tunc in fine illud cor­<lb/>pus ita ſe habebit  prima ꝑs eius ꝓportionalis <lb/>erit aliqualiter intenſa: ſecūda in duplo plus: et ter­<lb/>tia in triplo plus ꝙ̄ prima: et quarta ī quadruplo / <lb/>et ſic conſequenter vt ponitur in caſu concluſionis. <lb/></s>
              <s xml:id="N2B962" xml:space="preserve">Patet hec ſuppoſitio: qm̄ ſi in prīa eſt aliquis gra­<lb/>dus puta c. per ſcḋam et totū erūt reſiduū duo gra­<lb/>dus puta c. per ſcḋam et totū erūt reſiduū duo gra­<lb/>dus c. et per tertiam et totum tres tales gradus c. et <lb/>per quartam et totum reſiduū .4. tales: et ſic ↄ̨ñter: <lb/>igitur prima eſt aliqualiter intenſa: et ſecūda ī du­<lb/>plo plus: et tertia in triplo plus ꝙ̄ ṗma: et ſic ↄ̨ñter <lb/></s>
              <s xml:id="N2B972" xml:space="preserve">Quo poſito ꝓbatur concluſio. </s>
              <s xml:id="N2B975" xml:space="preserve">et ſit aliqḋ corpꝰ di­<lb/>uiſum ꝑ partes ꝓportionales ꝓportione f. et ſit g. <lb/>ꝓportio totiꝰ diuiſi ꝑ partes ꝓportionales ꝓpor-<lb/>tione f. ad primã eius partē ꝓportiõalē: et ṗma ꝑs <lb/>ꝓportionalis illius ſit aliquaĺr intēſa: et ſecūda in <lb/>duplo plus: et tertia in triplo plus ꝙ̄ ṗma: et ſic cõ-<lb/>ſequenter. </s>
              <s xml:id="N2B984" xml:space="preserve">Tūc dico /  totum eſt intenſius ṗma ꝑte <lb/>ꝓportionali in ꝓportione g. q̄ eſt ꝓportio totiꝰ ad <lb/>primã partē ꝓportionalē. </s>
              <s xml:id="N2B98B" xml:space="preserve">Quod ſic ꝓbatur: quia <lb/>per totuꝫ illud corpus extenditur aliqua qualitas <lb/>puta illa q̄ eſt in prima parte ꝓportionali: et per to­<lb/>tum reſiduum a prima parte ꝓportionali iterum <lb/>tanta ſupra illam: et per totum reſidnum a prima <lb/>et ſecunda iterum tanta: et ſic conſequenter. </s>
              <s xml:id="N2B998" xml:space="preserve">vt patꝫ <lb/>ex ſuppoſitione: et illa qualitas que extenditur per <lb/>totum denominat aliqualiter tale corpus: et que ex­<lb/>tenditur ꝑ totum reſiduum a prima parte ꝓportio­<lb/>nali denominat in f. ꝓportione minus: et que exten­<lb/>ditur per totum reſiduum a ṗma parte ꝓportiona-<lb/>li et ſecunda iterum denoīat in f. ꝓportiõe minus ̄ <lb/>illa que extenditur per totum reſiduum a prima: et <lb/>ex iſtis denominationibus totius corporis denoīa­<lb/>tio conſurgit: igit̄̄ illa denoīatio intēſiõis totiꝰ cor­<lb/>poris cõponitur ex infinitis ꝑtialibꝰ denoīatiõibꝰ <lb/>ↄ̨tinuo ſe habētibus in ꝓportiõe f. / igit̄̄ tota illa de­<lb/>noīatio cõpoſita ex illis infinitis ſe habet ad ṗmã <lb/>illarū in ꝓportiõe qua ſe habet aliquod totum di-<lb/>uiſum ꝑ partes ꝓportionales ꝓportione f. ad pri-<lb/>mã eius ꝑtem ꝓportionalem: qm̄ illa totalis deno­<lb/>minatio in tales partes proportionales ſecatur: et <lb/>illa eſt g. ex hypotheſi: ergo in ꝓportione g. totum <lb/>eſt intenſius ṗma ꝑte ꝓportionali / qḋ fuit ꝓbanduꝫ <lb/></s>
              <s xml:id="N2B9C0" xml:space="preserve"><pb chead="De intenſione difformium" file="0269" n="269"/>               Sed iã probo /  illa qualitas que extendit̄̄ pro to-<lb/>tum prīo denoīat aliq̈liter et q̄ ꝑ totū reſiduū a pri­<lb/>ma in f. ꝓportione minꝰ ꝙ̄ illa q̄ extēditur ꝑ totum: <lb/>et ſic ↄ̨ñten. </s>
              <s xml:id="N2B9CD" xml:space="preserve">Qm̄ oēs ille qualitates ſunt equalis <lb/>intēſionis: et q̄libet ſequēs ꝑ minꝰ in f. ꝓportiõe ex-<lb/>extēdit̄̄ ꝙ̄ precedēs: qm̄ totū illud corpus eſt in f. ꝓ­<lb/>portiõe maius ꝙ̄ totū aggregatū ex oībus ꝑtibus <lb/>ꝓportionalibꝰ eius ſequētibus primã: et totū reſi-<lb/>duū a prima eſt in f. ꝓportiõe maius toto reſiduo a <lb/>prīa et ſcḋa: et ſic ↄ̨ñter: vt pꝫ ex prīa cõcluſione quin­<lb/>ti capitis prime partis: hoc addito /  quacū pro­<lb/>portiõe diuidit̄̄ totū eadē proportõe diuidit̄̄ aggre­<lb/>gatū ex oībus ꝑtibus ꝓportionalibꝰ ſequētibꝰ pri­<lb/>mã: et etiã ſequētibꝰ ſcḋam: et tertiã: et q̈rtã: et ſic ↄ̨ſe­<lb/>quenter: igr̄ illa qualitas q̄ ꝑ totū extenditur deno­<lb/>minãt aliquãtulū: et q̄ ꝑ totuꝫ reſiduū a prīa in f. ꝓ­<lb/>portiõe minꝰ: et q̄ per totū reſiduū a ṗma et ſecūda <lb/>in f. ꝓportiõe minꝰ ꝙ̄ illa q̄ per totū reſiduū a prīa / <lb/>et ſic ↄ̨ñter / qḋ erat ꝓbandū </s>
              <s xml:id="N2B9EE" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ ſecundã <lb/>partē prīe ꝓpõnis vltimi notabilis.               <anchor type="note" xlink:href="note-0269-01" xlink:label="note-0269-01a"/>               </s>
              <s xml:id="N2B9F8" xml:space="preserve"><gap/>Ex hac ↄ̨clu-<lb/>ſione ſeq̇tur prīo /  ſi aliqḋ corpus diuidatur ꝑ par­<lb/>tes ꝓportionales ꝓportiõe tripla: et ṗma pars ꝓ-<lb/>portionalis eiꝰ ſit aliquaĺr intenſa: et ſcḋa ī duplo <lb/>et tertia in triplo plus ꝙ̄ ṗma cõtinuo eadē qualita­<lb/>te: et ſic ↄ̨ñter: ſine aliqua ↄ̈rii admixtione: totū ē in <lb/>ſexquialtero intenſius ṗma parte ꝓportionali. </s>
              <s xml:id="N2BA08" xml:space="preserve">Et <lb/>ſi diuidat̄̄ corpꝰ ꝓportiõe quadrupla totū erit intē­<lb/>ſius prima parte ꝓportionali in ſexq̇tertio. </s>
              <s xml:id="N2BA0F" xml:space="preserve">Et ſi ꝓ-<lb/>portiõe quītupla: erit intēſius prīa parte ꝓportio-<lb/>nali in ſexq̇quarto. </s>
              <s xml:id="N2BA16" xml:space="preserve">Et ſi ſextupla in ſexq̇quīto. </s>
              <s xml:id="N2BA19" xml:space="preserve">Et ſi <lb/>ſeptupla in ſexq̇ſextor / et ſic ↄ̨ñter ꝓcedēdo ꝑ ſpecies <lb/>ꝓportõis multiplicis et ſuꝑparticularis. </s>
              <s xml:id="N2BA20" xml:space="preserve">Probat̄̄ / <lb/>hoc correlariū: q2 corpus diuiſum ꝓportiõe tripla <lb/>ſe hꝫ ad primã ꝑtē ꝓportionalē eius in ꝓportiõe ſex­<lb/>quialtera: et diuiſum quadrupla ſe hꝫ ad p̄mã par-<lb/>tē proportionalē in ꝓportiõe ſexq̇tertia: et diuiſum <lb/>quintupla ſe hꝫ ad primã partē ꝓportionalē in ꝓ-<lb/>portione ſexq̇quarta: et ſic ↄ̨ñter: vt pꝫ ex primo cor­<lb/>relario tertie ↄ̨°nis quīti capitis prime partis: igr̄ <lb/>in caſu correlarii ſequit̄̄ ſi diuidat̄̄ corpus ꝓportio­<lb/>ne tripla  ip̄m erit intēſius prima parte ꝓportio­<lb/>nali in ſexq̇altero: et ſi quadrupla ī ſexq̇tertio: et ſi <lb/>quintupla in ſexq̇quinto: et ſic ↄ̨ñter. </s>
              <s xml:id="N2BA39" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ <lb/>cõcluſioneꝫ.               <anchor type="note" xlink:href="note-0269-02" xlink:label="note-0269-02a"/>               </s>
              <s xml:id="N2BA43" xml:space="preserve">¶ Seq̇tur ſcḋo /  ſi diuidat̄̄ corpus per <lb/>partes ꝓportiõales proportõe dupla et diſtribuat̄̄ <lb/>aliqua intēſio ꝑ illas partes ꝓportionales / vt po-<lb/>nitur in p̄cedēti correlario: tūc totū eſt in duplo in-<lb/>tenſius prīa ſui ꝑte ꝓportionali. </s>
              <s xml:id="N2BA4E" xml:space="preserve">Probat̄̄ / q2 totuꝫ <lb/>diuiſum per partes ꝓportionales ꝓportiõe dupla <lb/>eſt duplū ad primã partē ꝓportionalē eiꝰ / vt ptꝫ ex <lb/>primo correlario tertie ↄ̨cluſionis prime partis p̄-<lb/>allegato: igr̄ ꝑ cõcluſionē illud eſt intēſius ſuã prīa <lb/>parte ꝓportionali in ꝓportiõe dupla.               <anchor type="note" xlink:href="note-0269-03" xlink:label="note-0269-03a"/>               </s>
              <s xml:id="N2BA60" xml:space="preserve">¶ Sequitur <lb/>tertio /  diuiſo corpore ſic ꝑ partes ꝓportionales <lb/>ꝓportione dupla etc. / vt ponit̄̄ in añti correlario to-<lb/>tū eſt ita intenſum ſicut ſcḋa ꝑs ꝓportionalis eius. <lb/></s>
              <s xml:id="N2BA6A" xml:space="preserve">ꝓbat̄̄ / q2 in duplo intēſiꝰ prīa vt p̄cedēs correlariū <lb/>oſtēdit: et ſcḋa ꝑs ꝓportionalis ē eēt in duplo ītēſior <lb/>prima: g̊ totum eſt ita intenſum ſicut ſcña pars pro­<lb/>portionalis / quod fuit probandum. </s>
              <s xml:id="N2BA73" xml:space="preserve">Patet cõſequē­<lb/>tia per hanc maximam habentia equalem propor­<lb/>tionem ad vnum tertium ſunt equalia. </s>
              <s xml:id="N2BA7A" xml:space="preserve">Et hec eſt pri­<lb/>ma concluſio calculatoris in capite de difformibꝰ. <lb/>               <anchor type="note" xlink:href="note-0269-04" xlink:label="note-0269-04a"/>               </s>
              <s xml:id="N2BA86" xml:space="preserve">¶ Sequitur quarto /  ſi aliquod corpus diuidatur <lb/>proportione ſexquialtera: et prima pars propor-<lb/>tionalis ſit aliqualiter intenſa: et ſecunda in duplo <lb/>plus: et tertia in triplo ꝙ̄ prima: et ſic conſequenter / <lb/>vt <gap/>̀ concluſionis: tunc totum eſt in               <cb chead="De intenſione difformium"/>               triplo intenſius prima parte proportionali. </s>
              <s xml:id="N2BA96" xml:space="preserve">Et ſi <lb/>diuidatur ꝓportiõe ſexquitertia: totum erit inten-<lb/>ſius prima parte proportionali in quadruplo. </s>
              <s xml:id="N2BA9D" xml:space="preserve">Et <lb/>ſi diuidatur ꝓportione ſexquiquarta totum erit in­<lb/>tenſius prima parte ꝓportionali in quintuplo. </s>
              <s xml:id="N2BAA4" xml:space="preserve">Et <lb/>ſi ſexquiquinta totum erit intenſius prima parte ꝓ­<lb/>portionali in ſextuplo. </s>
              <s xml:id="N2BAAB" xml:space="preserve">Et ſi ſexq̇ſexta in ſeptuplor / <lb/>et ſic cõſequēter ꝓcedendo cõtinuo ꝑ ſpecies propor­<lb/>tionis ſuperparticularis in diuiſione corporis: et <lb/>per ſpecies ꝓportionis multiplicis ex parte inten-<lb/>ſionis. </s>
              <s xml:id="N2BAB6" xml:space="preserve">Probatur hoc correlariū: quia totum diui­<lb/>ſum proportione ſexquialtera eſt triplum ad pri-<lb/>mam partem ꝓportionalē eius et diuiſum ſexq̇ter-<lb/>tium eſt quadruplū: et ſexquiquarta eſt quintupluꝫ <lb/>et ſexq̇quinta ſextuplū ad primã eius partē ꝓpor-<lb/>tionalē: vt pꝫ ex quarta cõcluſiõe quinti capitis pri­<lb/>me partis: g̊ in eiſdē ꝓportionibus ſe habēt inten-<lb/>ſiones totius ad intenſionē prime partis ꝓportio­<lb/>ntialis / vt patet ex cõcluſione: igr̄ correlariū verum <lb/></s>
              <s xml:id="N2BACA" xml:space="preserve">¶ Sequitur quīto /  ſi diuidatur corpus / vt dicitur <lb/>in precedēti correlario: vt puta ꝓportiõe ſexq̇alte-<lb/>ra et prima pars ſit aliqualiter intēſa: et ſecūda in <lb/>duplo plus: et tertia ī triplo plus ꝙ̄ prima etc. / vt ibi <lb/>dicitur: totū eſt ita intenſū ſicut tertia pars ꝓpor-<lb/>tionalis. </s>
              <s xml:id="N2BAD7" xml:space="preserve">Et ſi ꝓportione ſexquitertia: ſicut quarta <lb/>ꝑs ꝓportionalis. </s>
              <s xml:id="N2BADC" xml:space="preserve">Et ſi ſexq̇quarta ſicut quinta ꝑs <lb/>ꝓportionalis. </s>
              <s xml:id="N2BAE1" xml:space="preserve">Et ſi ſexquiq̇nta ſicut ſexta pars ꝓ-<lb/>portionalis: et ſic ↄ̨ñter deſcendendo per partes ꝓ-<lb/>portionales et ꝑ ſpecies proportionis ſuperparti­<lb/>ticularis in infinitum. </s>
              <s xml:id="N2BAEA" xml:space="preserve">Probatur / quoniam ſi cor-<lb/>pus ſit diuiſum proportione ſexquialtera ipſuꝫ eſt <lb/>in triplo intenſius prima parte eius ꝓportionali / <lb/>vt patet ex precedenti correlario: et tertia pars pro­<lb/>portionalis eſt etiam in triplo intenſior prima / vt <lb/>patet ex caſu: ergo ita intenſum eſt tale corpus ſi-<lb/>cut tertia pars proportionalis. </s>
              <s xml:id="N2BAF9" xml:space="preserve">Item ſi diuidatur <lb/>proportione ſexquitertia ipſum eſt in quadruplo <lb/>intenſius prima eius parte proportionali ex pre-<lb/>cedēti correlario. </s>
              <s xml:id="N2BB02" xml:space="preserve">et etiã quarta pars proportiona­<lb/>lis eius ē in quadruplo intenſior prima ex caſu: igi­<lb/>tur illud corpus ita diuiſuꝫ proportione ſexquiter­<lb/>tia eſt ita intenſum ſicut quarta pars proportiona­<lb/>lis eius. </s>
              <s xml:id="N2BB0D" xml:space="preserve">Et iſto modo ꝓbabis ceteras ꝑticulas cor­<lb/>relarii. </s>
              <s xml:id="N2BB12" xml:space="preserve">¶ Sequitur ſexto /  ſi aliquod corpus diui­<lb/>datur ꝑ partes ꝓportionales ꝓportione ſuprabi-<lb/>partiente tertias et ꝑtes eiꝰ ſint intēſe vt ſepiꝰ dcim̄ <lb/>eſt totū erit intēſiꝰ prīa ꝑte ꝓportionali ī ꝓportiõe <lb/>dupla ſexq̇altera: ita  ſi prima ſit calida vt .2. to-<lb/>tum eſt calidum vt .5. </s>
              <s xml:id="N2BB1F" xml:space="preserve">Probat̄̄ correlariū / qm̄ totū <lb/>eſt intenſiꝰ prīa ꝑte ꝓportionali in tali caſu in pro­<lb/>portione qua ſe habet aliqḋ totū diuiſum ꝑ ꝑtes ꝓ­<lb/>portionales ꝓportiõe ſuprabiꝑtiēte tertias ad ſuã <lb/>primã ꝑtē ꝓportionalē / vt pꝫ ex ↄ̨°ne: ſꝫ talis ē ꝓpor­<lb/>tio dupla ſexq̇altera / vt pꝫ intelligēti .5. cõcluſioneꝫ <lb/>quinti capitis ṗme partis: igit̄̄ correlariū verum.</s>
            </p>
            <div xml:id="N2BB2E" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0269-01a" xlink:label="note-0269-01" xml:id="N2BB32" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0269-02a" xlink:label="note-0269-02" xml:id="N2BB38" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0269-03a" xlink:label="note-0269-03" xml:id="N2BB3E" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0269-04a" xlink:label="note-0269-04" xml:id="N2BB44" xml:space="preserve">4. correĺ</note>
            </div>
            <p xml:id="N2BB4A">
              <s xml:id="N2BB4B" xml:space="preserve">Secūda cõcluſio. </s>
              <s xml:id="N2BB4E" xml:space="preserve">diuiſo corpore qua <lb/>volueris ꝓportiõe: et in q̈cū ꝓportiõe ſe habuerīt <lb/>ꝑtes aliq̄ proportiõalis ī eadē vel maiori ſe habue­<lb/>rit intēſio mīoris ad intēſionē maioris: totū illud <lb/>corpꝰ eſt īfinite intēſuꝫ. </s>
              <s xml:id="N2BB59" xml:space="preserve">Exēplum / vt ſi diuiſo corꝑe <lb/>ꝓportõe dupla: et prīa ꝑs ꝓportionalis ſit aliq̈liṫ <lb/>alba: et ſcḋa ī duplo plꝰ: et tertia ī duplo plꝰ ꝙ̄ .2. et <lb/>4. in duplo plꝰ ꝙ̄ .3. / et ſic ↄ̨ñter: totū illḋ corpꝰ ē infi-<lb/>nire albū q2 q̄lꝫ ꝑs tm̄ denoīat ſicut prima: et ſunt <lb/>infinite </s>
              <s xml:id="N2BB66" xml:space="preserve">(Sꝑ aūt ītelligo ſine ↄ̈rii ꝑmixtiõe) </s>
              <s xml:id="N2BB69" xml:space="preserve">Proba­<lb/>tur ↄ̨° facile: qm̄ ex caſu ↄ̨°nis cõtinuo talis eſt pro-<lb/>portio ꝑtiū ſubiecti q̈lis eſt proportio intenſionis               <pb chead="Quarti tractatus." file="0270" n="270"/>               minoris partis ad intēſionē maioris: g̊ cõtinuo tã-<lb/>tum denoīat vna ſicut altera. </s>
              <s xml:id="N2BB77" xml:space="preserve">Ptꝫ ↄ̨ña ex q̈rta ꝓpõe <lb/>et cū ſint infinite totū denoīant infinite. </s>
              <s xml:id="N2BB7C" xml:space="preserve">Et ꝑ locū a <lb/>maiori ꝓbat̄̄ alia pars vcꝫ  ſi cõtinuo īter partes <lb/>eſſet mīor ꝓportio ꝙ̄ inter intenſiones mīoris par­<lb/>tis et maioris: intenſio totiꝰ corꝑis eſt infinita. </s>
              <s xml:id="N2BB85" xml:space="preserve">qm̄ <lb/>data vna denoīatione q̈ pars aliqua totū denoīat <lb/>q̄libet ſequēs plus denoīabit: et ſunt infinite: igitur <lb/>ꝓpoſitū.               <anchor type="note" xlink:href="note-0270-01" xlink:label="note-0270-01a"/>               </s>
              <s xml:id="N2BB93" xml:space="preserve">¶ Ex hac cõcluſione ſeq̇tur primo /  ꝑtito <lb/>aliquo corpore ꝓportiõe ſexq̇altera: et prima ſit ali­<lb/>qualiter alba: et ſcḋa in duplo plus: et tertia in du-<lb/>plo pluſ̄ ſcḋa: et q̈rta ꝙ̄ tertia etc. totū corpꝰ eſt in­<lb/>finite album. </s>
              <s xml:id="N2BB9E" xml:space="preserve">¶ Sequit̄̄ ſcḋo /  diuiſo corꝑe ꝓpor-<lb/>tione ſexq̇tertia et prīa pars ſit aliquaĺr alba: et ſe­<lb/>cūda in ſexq̇altero plus: et tertia in ſexq̇altero plus <lb/>̄ ſcḋa: et ſic ↄ̨ñter: totū corpus ē infinite albū. </s>
              <s xml:id="N2BBA7" xml:space="preserve">Pa­<lb/>tent correlaria ex concluſione.</s>
            </p>
            <div xml:id="N2BBAC" level="5" n="9" type="float">
              <note position="left" xlink:href="note-0270-01a" xlink:label="note-0270-01" xml:id="N2BBB0" xml:space="preserve">1. correĺ.</note>
            </div>
            <p xml:id="N2BBB6">
              <s xml:id="N2BBB7" xml:space="preserve">Tertia concluſio. </s>
              <s xml:id="N2BBBA" xml:space="preserve">Diuiſo aliquo cor-<lb/>pore qua volueris ꝓportiõe et in certa ꝓportione q̈-<lb/>libet pars p̄cedens ſit intenſior īmediate ſequenti: <lb/>totius intēſionis ad ītēſionē ſiue denoīationē qua <lb/>totū denoīabitur a qualitate ṗme partis ꝓportio-<lb/>nalis eſt illa ꝓportio qua ſe hꝫ totū diuiſuꝫ in pro­<lb/>portione ↄ̨poſita ex ꝓportione partis ꝓportiona-<lb/>lis p̄cedētis ad īmediate ſequētē: et intēſiõis p̄cedē-<lb/>tis ad intēſionē īmediate ſequentis ad ṗmã eiꝰ par­<lb/>tem ꝓportionalē. </s>
              <s xml:id="N2BBCF" xml:space="preserve">Ut ſi aliqḋ corpus diuidat̄̄ ꝑ par­<lb/>tes ꝓportionales ꝓportiõe dupla: et ↄ̨tinuo intēſio­<lb/>nis partis p̄cedentis ad intēſionē partis īmediate <lb/>ſequentis ſit proportio ſexq̇altera. </s>
              <s xml:id="N2BBD8" xml:space="preserve">et ex dupla et ſex­<lb/>quialtera cõiunctis cõſurgit tripla: ſi denomīatio <lb/>qua prima pars denoīat totum ſit vt .2. totū erit vt <lb/>3. intenſum: qm̄ totum diuiſuꝫ ꝓportiõe tripla ē ſex­<lb/>quialterū ad primã partē ꝓportionalē / vt pꝫ ex pri­<lb/>mo correlario ſcḋe ↄ̨°nis q̇nti capitis prīe partis. <lb/></s>
              <s xml:id="N2BBE6" xml:space="preserve">Hec concluſio cū multis ſiĺibus facile ꝓbat̄̄ ex his / <lb/>que dicta ſunt tertio capite ſcḋi tractatus mutatis <lb/>mutãdis.               <anchor type="note" xlink:href="note-0270-02" xlink:label="note-0270-02a"/>               </s>
              <s xml:id="N2BBF2" xml:space="preserve">¶ Ex quo ſequit̄̄ primo /  diuiſo corpore <lb/>per partes ꝓportionales ꝓportione dupla: et prīa <lb/>pars ꝓportionalis ꝑ ſui medietatē habet vnū gra­<lb/>dū albedinis: reliqua medietate priuata albedine <lb/>et nigredine: et ſcḋa pars ꝓportionalis habeat per <lb/>ſui quartã mediū gradū albedinis reliqua nec al-<lb/>ba exiſtente ne nigra: et tertia pars ꝓportionalis <lb/>per ſui octauã habeat vnã q̈rtã vniꝰ gradus albe-<lb/>dinis etc̃. / et ſic in īfinitū: totiꝰ intēſiõis ad denoīatio­<lb/>nē qua totū denoīat̄̄ a q̈litate prime partis ꝓpor-<lb/>tionalis ē ꝓportio qua ſe hꝫ totū diuiſum ꝓportio­<lb/>ne quadrupla ad primã ſui partē ꝓportionalē q̄ eſt <lb/>ſexquitertia: et totum erit intenſum vt vna tertia.</s>
            </p>
            <div xml:id="N2BC0D" level="5" n="10" type="float">
              <note position="left" xlink:href="note-0270-02a" xlink:label="note-0270-02" xml:id="N2BC11" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="left" xml:id="N2BC17" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N2BC1B">
              <s xml:id="N2BC1C" xml:space="preserve">¶ Seq̇tur ſcḋo /  diuiſo corpore per partes ꝓpor-<lb/>tionales proportiõe quadrupla: et ꝑ vnã quartam <lb/>prime partis proportionalis extēdat̄̄ aliqua albe-<lb/>do: reſiduo eiuſdē prime partis nec albedo exñte nec <lb/>nigro: et per vnã ſextaꝫ ſecūde partis ꝓportionalis <lb/>extendat̄̄ albedo in quadruplo mīor reliquis ſextꝪ <lb/>nõ exñtibus albis vel nigris: et per vnã nonã tertie <lb/>partis ꝓportionalis ponat̄̄ iterū albedo in q̈dru-<lb/>plo minor quã in ſexta partis precedentis reſiduo <lb/>nec albo nec nigro et per vnã decimã octauã q̈rte ꝑtꝪ <lb/>ꝓportionalis extēdat̄̄ iterū albedo ī q̈druplo mīor <lb/>̄ ī nona ꝑtꝪ īmediate p̄cedētꝪ, et ſic ↄ̨ñter / ita  cõti­<lb/>nuo ꝑtes ꝑ q̈s extēdit̄̄ albedo ſe hēant ī ꝓportõe ſex­<lb/>tupla: tūc totiꝰ intēſiõis ad denoīationē q̈ totū de-<lb/>noīat̄̄ ab q̈litate exñte ī q̈rta prīe partꝪ ꝓportiona-<lb/>lis eſt ꝓportio ſexq̇viceſima ṫtia q̈lis eſt .24. ad .23. <lb/></s>
              <s xml:id="N2BC3E" xml:space="preserve">Patēt hec correlaria ex ↄ̨°ne iuuãtibꝰ his q̄ dcã ſūt <lb/>in prima et ſcḋa partibꝰ huius operis. </s>
              <s xml:id="N2BC43" xml:space="preserve">¶ Infinita               <cb chead="Capitulum quartum"/>               talia correlaria poteris inferre.</s>
            </p>
            <p xml:id="N2BC49">
              <s xml:id="N2BC4A" xml:space="preserve">Quarta cõcluſio. </s>
              <s xml:id="N2BC4D" xml:space="preserve">diuiſo corpore ꝑ par­<lb/>tes ꝓportionales aliqua ꝓportiõe multiplici: aut <lb/>aliqua maiori ſuꝑparticulari ꝓportiõe: et ī prīa ꝑ-<lb/>te ꝓportionali ſit aliquãtula albedo ꝑ totū: et in ſe­<lb/>cūda ī ſexq̇altero intēſior: et in ṫtia ī ſexq̇tertio intē-<lb/>ſior ꝙ̄ in prīa: et in q̈rta in ſexq̇quarto intēſior ꝙ̄ in <lb/>prīa: et ſic ↄ̨ñter ꝓcedēdo ꝑ ſpēs ꝓportiõis ſuꝑpar­<lb/>ticularis: totiꝰ corporis intēſio cēſenda eſt incõmē-<lb/>ſurabilis intēſiõi prīe partis ꝓportionalis et deno­<lb/>minatiõi qua ip̄a qualitas exñs ī prīa ꝑte ꝓportio­<lb/>nali totū denoīat: vel ſaltē ſi incõmēſurabilis eſt a <lb/>nobis ꝓ flatu iſto finitã capacitatē hñtibꝰ nequa̄ <lb/>cõmēſurari p̄t. </s>
              <s xml:id="N2BC68" xml:space="preserve">Probat̄̄ / qm̄ ille intēſiones cõtinuo <lb/>ſe hñt in alia et alia ꝓportiõe: et nõ eſt poſſibile oēs <lb/>tales ꝓportiões mēſurari ab ītelectu finito nec in-<lb/>ter illas intēſiones põt cõtinuo eadē et eadē propor­<lb/>tio inueniri: igr̄ in tali caſu intenſio totiꝰ corꝑis cē­<lb/>ſenda eſt incõmēſurabilis intēſioni prime partis ꝓ­<lb/>portionalis etc. </s>
              <s xml:id="N2BC77" xml:space="preserve">¶ Ex hac ↄ̨cluſiõe ſeq̇tur /  ſi aliqḋ <lb/>corpus diuidat̄̄ per partes ꝓportionales propor-<lb/>tione dupla, et prīa ſit aliqualiter alba: et ſcḋa ī ſex­<lb/>q̇tertio plꝰ: et tertia ī ſexq̇quīto plus ꝙ̄ prīa: et q̈rta <lb/>in ſexquiſeptimo plus ꝙ̄ prīa: et ſic ↄ̨ñter ꝓcedendo <lb/>ꝑ ſpēs ꝓportõis ſuꝑparticularis denoīatas a nūe­<lb/>ris īparibꝰ: totiꝰ intēſio cēſenda ē irrõnalis ad in­<lb/>tenſionē prime partis. </s>
              <s xml:id="N2BC88" xml:space="preserve">Siĺr ſi diuiſo corpore ꝓpor­<lb/>tiõe quadrupla: et prīa ꝑs ꝓportiõalis ſit aliq̈liter <lb/>alba: et ſcḋa ī ſupratriꝑtiēte q̈rtas plꝰ: et ṫtia in ſu­<lb/>pratriꝑtiēte octauas ītēſior ꝙ̄ prīa, et q̈rta ī ſupra­<lb/>triꝑtiēte decīas ſextas intēſior ꝙ̄ prīa: et ſic ↄ̨ñter ꝓ-<lb/>cedēdo ꝑ ſpēs proportiõis ſupratriꝑtiētis denoīa­<lb/>tas a nūeris pari<gap/> ꝑibꝰ: totiꝰ intēſio incõmēſurabi­<lb/>lis eſt intēſioni prime partis ꝓportionalis. </s>
              <s xml:id="N2BC9B" xml:space="preserve">Et iſto <lb/>modo multa ſimilia inferes prima et ſecunda par-<lb/>tibus intellectis.</s>
            </p>
            <p xml:id="N2BCA2">
              <s xml:id="N2BCA3" xml:space="preserve">Quinta cõcluſio. </s>
              <s xml:id="N2BCA6" xml:space="preserve">Diuiſo corpore per <lb/>partes proportionales ꝓportiõe irrationali et pri­<lb/>ma pars proportiõalis ſit aliquaĺr calida: et ſcḋa <lb/>in duplo plꝰ, et ṫtia in triplo ꝙ̄ prīa: et ſic ↄ̨ñter / vt <lb/>ponit̄̄ in prīa ↄ̨°ne: totiꝰ intēſio ē incõmēſurabilis <lb/>intēſioni prīe partis ꝓportionalis. </s>
              <s xml:id="N2BCB3" xml:space="preserve">Probat̄̄ / q̊niaꝫ <lb/>tota intēſio ſe hꝫ ad intēſionē prīe partis ꝓportio­<lb/>nalis in ea ꝓportiõe qua ſe hꝫ totū diuiſuꝫ illa pro­<lb/>portiõe irrõnali ad primã eiꝰ partē ꝓportionalē / vt <lb/>pꝫ ex prīa ↄ̨°ne: ſꝫ talis eſt irrõnalis: igr̄ ↄ̨cluſio a <lb/>               <anchor type="note" xlink:href="note-0270-03" xlink:label="note-0270-03a"/>               </s>
              <s xml:id="N2BCC5" xml:space="preserve">¶ Ex quo ſequitur primo:  diuiſo corpore ꝑ par-<lb/>tes proportionales ꝓportiõe irrõnali diametri ad <lb/>coſtã que eſt medietas duple: et ī prima ꝑte propor­<lb/>tionali ponatur aliqua albedo: et in ſcḋa ī ſexq̇ter-<lb/>tio maior: et in ṫtia in ſeq̇tertio maior ꝙ̄ ī ſcḋa: et ſic <lb/>ↄ̨ñter: totius intēſiõis ad denoīationē qua totū de­<lb/>noīabit̄̄ ab albedine prīe et ſcḋe partis proportio-<lb/>nalis eſt illa proportio: qua ſe hꝫ totum diuiſum <lb/>in proportione ſexq̇octaua qualis eſt .18. ad .16 ad <lb/>primã ſui ꝑtē ꝓportiõalē. </s>
              <s xml:id="N2BCDA" xml:space="preserve">pꝫ hoc correlariū ex mõ <lb/>probãdi ↄ̨°nē. </s>
              <s xml:id="N2BCDF" xml:space="preserve">hoc addito:  cū corpus diuidit̄̄ pro­<lb/>portione irrationali q̄ eſt medietas duple: partes ī­<lb/>pares et ſiĺr pares ↄ̨tinuo ſe hñt in proportiõe du-<lb/>pla. </s>
              <s xml:id="N2BCE8" xml:space="preserve">qḋ pꝫ ex ſcḋo correlario ſcḋe ↄ̨°nis ſexti capitꝪ <lb/>prīe ꝑtꝪ: et  in cãu correlarii ītēſiões ꝑtiū pariū et <lb/>ſiĺr īpariū ↄ̨tinuo ſe hñt ī ꝓportiõe ſupraſeptiꝑtiē­<lb/>te nonas qḋ claret: cū ītēſiõis partꝪ parꝪ ad ītēſiõeꝫ <lb/>īparis īmediate p̄cedētꝪ ſit ꝓportio ſexq̇tertia ex ca­<lb/>ſu.               <anchor type="note" xlink:href="note-0270-04" xlink:label="note-0270-04a"/>               </s>
              <s xml:id="N2BCFA" xml:space="preserve">¶ Seq̇t̄̄ .2. /  diuiſo corpore per partes propor-<lb/>tionales proportiõe irrationali  eſt medietas tri-<lb/>ple: et in prīa parte proportionali ponatur aliqua <lb/>albedo: et in ſecunda in duplo minor: et in tertia in               <pb chead="De intenſione difformium" file="0271" n="271"/>               duplo minor ꝙ̄ in ſecūda: et ſic cõſequenter: totius <lb/>intēſionis ad intēſionē ſiue denoīationē qua totuꝫ <lb/>denoīabit̄̄ ab albedine prīe et ſcḋe partis ꝓportio­<lb/>nalis eſt illa ꝓportio qua ſe hꝫ totum diuiſuꝫ in ꝓ-<lb/>portiõe duodecupla ad primã cuiꝰ partē ꝓportio-<lb/>nalē. </s>
              <s xml:id="N2BD12" xml:space="preserve">Ptꝫ hoc correlariū habito /  diuidēdo corpꝰ <lb/>ꝓportiõe irrõnali que eſt medietas triple: oēs ꝑtes <lb/>pares et oēs impares immediate ſe habent in ꝓpor­<lb/>tione tripla: quod pꝫ ex .4. correlario ſcḋe ↄ̨cluſio-<lb/>nis ſextis capitis ſcḋe partis. </s>
              <s xml:id="N2BD1D" xml:space="preserve">et  in caſu correlarii <lb/>continuo intenſiõis partis paris ad intētionē pa-<lb/>ris īmediate ſequētis eſt ꝓportio quadrupla et ſiĺr <lb/>intenſionis partis īparis ad ītēſionem īparis īme­<lb/>diate ſequētis. </s>
              <s xml:id="N2BD28" xml:space="preserve">Quod pꝫ intuēti caſum. </s>
              <s xml:id="N2BD2B" xml:space="preserve">¶ Inferas <lb/>ꝓpria induſtria quot volueris correlaria.</s>
            </p>
            <div xml:id="N2BD30" level="5" n="11" type="float">
              <note position="right" xlink:href="note-0270-03a" xlink:label="note-0270-03" xml:id="N2BD34" xml:space="preserve">1. correĺ.</note>
              <note position="right" xlink:href="note-0270-04a" xlink:label="note-0270-04" xml:id="N2BD3A" xml:space="preserve">2. correĺ.</note>
            </div>
            <p xml:id="N2BD40">
              <s xml:id="N2BD41" xml:space="preserve">Sexta concluſio </s>
              <s xml:id="N2BD44" xml:space="preserve">A. nunc eſt ſolum fi­<lb/>nite intēſum: et ꝑ rarefactionē finitã ſolū fiet ſubito <lb/>infinite intenſum. </s>
              <s xml:id="N2BD4B" xml:space="preserve">Probat̄̄ / ſit a. tale corpus quale <lb/>eſt illud de quo fit mentio in caſu ṗme concluſionis <lb/>cuiꝰ vcꝫ prima pars ꝓportionalis eſt eq̈liter intēſa <lb/>ſcḋa in duplo intēſior et .3. in triplo intēſior ꝙ̄ prīa <lb/>etc. incipiat a. rarefieri iſto mõ vcꝫ  prīa pars ꝓ­<lb/>portionalis acq̇rat vniformiter in hora ̄titatē pe­<lb/>dalē: et in quocū tꝑe ipſa acq̇rit aliquã ̄titatem <lb/>pars ꝓportionalis duple ītenſionis ad illam acq̇-<lb/>rat ſubduplã ̄titatē ad acq̇ſitam ipſi prime parti <lb/>et pars quadruple ītenſionis ad primã acq̇rat ī eo-<lb/>dem tempore ſubquadruplã ̄titatē ad acq̇ſitã pri­<lb/>me: et ꝑs octuple intēſionis ad primã acq̇rat in eo-<lb/>dē tēpore ſuboctuplã ̄titatē ad acquiſitam prime / <lb/>et ſic ↄ̨ñter ꝓcedēdo ꝑ partes ꝓportionales ↄ̨tinuo <lb/>ſe hñtes in ꝓportiõe dupla quo ad intēſionē: ita  <lb/>q̄libet ſequēs in duplo minꝰ acq̇rat ↄ̨tinuo de quã-<lb/>titate ꝙ̄ īmediate p̄cedēs. </s>
              <s xml:id="N2BD6E" xml:space="preserve">Quo poſito argr̄ ſic / īme­<lb/>diate poſt inſtãs īitiatiuū talis rarefactiõis illud <lb/>corpus erit infinite intenſum: et hoc ꝑ rarefactionē <lb/>finitã ſolū: et in illo inſtanti eſt ſolū finite intenſum: <lb/>igitur ꝓpoſitum. </s>
              <s xml:id="N2BD79" xml:space="preserve">Coña patet: et argr̄ maior / q2 īme­<lb/>diate poſt illud inſtãs erūt ibi īfinite partes quarū <lb/>q̄lꝫ denoīabit tm̄ ſicut prima illaꝝ: g̊ īmediate poſt <lb/>illud inſtãs totū erit īfinite ītenſum. </s>
              <s xml:id="N2BD82" xml:space="preserve">pꝫ ↄ̨ña et ꝓba­<lb/>tur añs / qm̄ īmediate poſt illud inſtãs illud qḋ acq̇-<lb/>ſitū erit prīe parti ꝓportionali aliquãtulū denoīa­<lb/>bit: et illḋ qḋ tunc acq̇ſitū erit parti duple ītēſiõis <lb/>ad primã tm̄: q2 eſt ſubduple ̄titatꝪ et in duplo ītēſi­<lb/>us: et ſiĺr tm̄ denoīabit illḋ qḋ tūc acq̄ſitū erit par­<lb/>ti quadruple intēſiõis ad ṗmã: et ſic ↄ̨ñter: igr̄ īme-<lb/>diate poſt illḋ inſtãs erūt ibi īfinite ꝑtes quaꝝ que-<lb/>libet denoīabit totum tm̄ ſicut ṗma illarū / qḋ erat <lb/>ꝓbandū. </s>
              <s xml:id="N2BD97" xml:space="preserve">QꝪ vero illa rarefactio ſit finita pꝫ: q2 in <lb/>tꝑe finito finitã quãtitatē adequate a. acq̇rit puta <lb/>bipedalem / vt pꝫ. </s>
              <s xml:id="N2BD9E" xml:space="preserve">Nã acq̇rit infinita ↄ̨tinuo ſe habē­<lb/>tia in ꝓportiõe dupla et primū illorū eſt pedale ex <lb/>hypotheſi. </s>
              <s xml:id="N2BDA5" xml:space="preserve">Et ſic ptꝫ cõcluſio.               <anchor type="note" xlink:href="note-0271-01" xlink:label="note-0271-01a"/>               </s>
              <s xml:id="N2BDAD" xml:space="preserve">¶ Ex quo ſeq̇tur prīo / <lb/> aliqḋ corpus eſt nūc infinite albū et ꝑ ſolã ↄ̨dēſa­<lb/>tionē finitã efficiet̄̄ remiſſe albū hoc eſt ſine deperdi­<lb/>tione aut acq̇ſitiõe alicuiꝰ qualitatis.               <anchor type="note" xlink:href="note-0271-02" xlink:label="note-0271-02a"/>               </s>
              <s xml:id="N2BDBB" xml:space="preserve">¶ Seq̇t̄̄ ſcḋo / <lb/> aliquid ē mõ īfinite albū: et ꝑ ſolã rarefactionem <lb/>finitã efficiet̄̄ nõ albū nulla qualitate acquiſita aut <lb/>deꝑdita.               <anchor type="note" xlink:href="note-0271-03" xlink:label="note-0271-03a"/>               </s>
              <s xml:id="N2BDC9" xml:space="preserve">¶ Seq̇tur tertio /  aliqḋ corpus ē nõ albuꝫ <lb/>et per ſolã finitã condēſationē efficiet̄̄ infinite albū <lb/>nõ acq̇rēdo aut deperdēdo aliquã qualitatē.               <anchor type="note" xlink:href="note-0271-04" xlink:label="note-0271-04a"/>               </s>
              <s xml:id="N2BDD5" xml:space="preserve">¶ Se­<lb/>quit̄̄ .4. /  aliqḋ corpus eſt p̄ciſe albū vt .4. et nõ eſt <lb/>in eo aliqua impediētis qualitatis aut cõtrarie ad­<lb/>mixtio: et illḋ nõ acq̇ret aliquã qualitatē nec deper­<lb/>det nec m ſe nec m aliq̇d eiꝰ: nec rarefiet aut cõdē­<lb/>ſabitur et tamen ſubito efficietur infinite album.</s>
            </p>
            <div xml:id="N2BDE2" level="5" n="12" type="float">
              <note position="left" xlink:href="note-0271-01a" xlink:label="note-0271-01" xml:id="N2BDE6" xml:space="preserve">1. correĺ.</note>
              <note position="left" xlink:href="note-0271-02a" xlink:label="note-0271-02" xml:id="N2BDEC" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0271-03a" xlink:label="note-0271-03" xml:id="N2BDF2" xml:space="preserve">3. correĺ.</note>
              <note position="left" xlink:href="note-0271-04a" xlink:label="note-0271-04" xml:id="N2BDF8" xml:space="preserve">4. correĺ</note>
            </div>
            <cb chead="De intenſione difformium"/>
            <note position="right" xml:id="N2BE00" xml:space="preserve">5. correĺ.</note>
            <p xml:id="N2BE04">
              <s xml:id="N2BE05" xml:space="preserve">¶ Seq̇tur .5. /  infinite album nec rarefiet: nec cõdē-<lb/>ſabitur: nec aliquã qualitatē acq̇ret aut deperdet, <lb/>qualitatibꝰ cõtrariis aut ſe impediētibus excluſis <lb/>et tamē efficietur finite albū.               <anchor type="note" xlink:href="note-0271-05" xlink:label="note-0271-05a"/>               </s>
              <s xml:id="N2BE13" xml:space="preserve">Patēt oīa iſta corre-<lb/>laria ex expoſitiõe ſcḋe cõcluſiouis calculatoris in <lb/>capitulo de difformibus.</s>
            </p>
            <div xml:id="N2BE1A" level="5" n="13" type="float">
              <note position="right" xlink:href="note-0271-05a" xlink:label="note-0271-05" xml:id="N2BE1E" xml:space="preserve">Calcula. <lb/>de diffor.</note>
            </div>
            <note position="right" xml:id="N2BE26" xml:space="preserve">Decīa cõ­<lb/>cluſio cal­<lb/>cu. in c. de <lb/>diffor.</note>
            <p xml:id="N2BE30">
              <s xml:id="N2BE31" xml:space="preserve">Septima concluſio </s>
              <s xml:id="N2BE34" xml:space="preserve">A. eſt infinite in-<lb/>tenſum et b. ſolū finite intenſuꝫ et a. cõtinuo tm̄ deꝑ-<lb/>dit preciſe ſicut b. et per tantū ſubiectū et a. remitte­<lb/>tur ad nõ gradū et nõ b. </s>
              <s xml:id="N2BE3D" xml:space="preserve">Probat̄̄ / ſit a. vnū infinituꝫ <lb/>quãtitatiue cuiꝰ primū pedale habeat infinitas calidi­<lb/>tates vt .4. et ſcḋm infinitas in duplo mīores et ter-<lb/>tium infinitas in quadruplo minores, et quartū in­<lb/>fiuitas in octuplo mīores: et ſic in īfinitū: ita  qḋ­<lb/>libet pedale ſequens ſit infinite intēſum hñs īfini-<lb/>tas caliditates quarū quelꝫ ſit ſubdupla ad quãlꝫ <lb/>infinitarū pedalis īmediate p̄cedētꝪ .b. vero habeat <lb/>duas per totū equalis intēſionis cū duabꝰ ṗmi pe­<lb/>dalis ipſiꝰ a. puta duas vt .4. et inſuꝑ vnã vt .4. ita <lb/> ſit vniforme vt .12. et in qualꝫ parte ꝓportionali <lb/>vnius hore primū pedale ipſius a. ꝑdat vnã illaruꝫ <lb/>infinitaꝝ qualitatū ↄ̨tinuo ꝑ ordinē nullã omitten-<lb/>do et in qualꝫ parte ꝓportionali dempta prīa m <lb/>pedale ipſius a. perdat vnã illarū ſuarū infinitaꝝ <lb/>qualitatū per ordinē ↄ̨ñter nullã omittēdo et ī qua­<lb/>libet parte ꝓportionali dēpta ṗma et ſcḋa: m peda­<lb/>le ipſiꝰ a. ꝑdat vnã ſuaꝝ īfinitaꝝ qualitatū: et ī qua-<lb/>libet ſequēte tertiã quartū pedale perdat vnã ſuaꝝ / <lb/>et ſic ↄ̨ñter: ita  ṗmū perdat per oēs, m per oēs <lb/>excepta prīa ṫtiū per oēs excepta .1. et .2. et ſic ī īfini-<lb/>tū: ita  ī fine nichil maneat in ip̄o a. nec ī eiꝰ aliq̄ <lb/>pedali. </s>
              <s xml:id="N2BE6C" xml:space="preserve">Et ī ṗma parte ꝓportionali ṗmū pedale ip­<lb/>ſius b. perdat vnã illaꝝ qualitatū vt .4. quas hꝫ, et <lb/>in ſcḋa qñ primū pedale ipſiꝰ a. perdit vnã qualita­<lb/>tē vt .4. et m perdit vnã vt .2. m pedale ipſiꝰ b. per-<lb/>dat vnã vt .4. et ṗmū eiuſdē perdat vnã vt .2. et in ṫtia <lb/>parte ꝓportionali qñ primū pedale ipſiꝰ a. perdit <lb/>4. gradus: et m duos: et tertiū vnū: ṗmū ipſiꝰ b. per­<lb/>dat vnū: et m .2. et ṫtiū .4. et ſic in īfinitū ita  qua-<lb/>cun parte hore ꝓportionali data in illa perdat <lb/>ṗmū pedale ipſiꝰ a. vnã ſuarū qualitatū corrñdētē <lb/>in nūero tali parti ꝓportionali: et ī quacū parte <lb/>ꝓportionali dēpta ṗma m pedale perdat vnã ſua­<lb/>rū corrñdētē ī nūero parti ꝓportionali īmediate p̄-<lb/>cedēti / et ſic ↄ̨ñter: et ī eadē parte ꝓportiõali pedale <lb/>ipſius b. corrñdēs in nūero tali parti proportiona­<lb/>li deperdat tantã qualitatē ſicut primū ipſius a. et <lb/>pedale immediate precedens in b. perdat tãtum ſi-<lb/>cut ſecundum pedale ipſius a. / et ſic conſequenter.</s>
            </p>
            <p xml:id="N2BE91">
              <s xml:id="N2BE92" xml:space="preserve">Exemplū / vt data ſexta parte proportionali hore: <lb/>tunc primū pedale ipſius a. deperdit ſextã illarum <lb/>ſuarū qualitatū vt .4. et ſecūdum quintã que eſt vt <lb/>2. et tertiū quartã q̄ eſt vt vnū: et quartū tertiã q̄ eſt <lb/>vt dimidiū et q̇ntū ſcḋaꝫ vt vna quarta: et ſextū prīaꝫ <lb/>vt vna octaua: et in eadē parte ſextū ipſiꝰ b. perdit <lb/>4. gradus et q̇ntū .2. et quartū vnū: et ṫtiū dimidiuꝫ, <lb/>et m vnã quartã: et primū vnã octauã. </s>
              <s xml:id="N2BEA3" xml:space="preserve">Quo poſito <lb/>pꝫ /  ipſum a. in fine erit nõ intēſum: et b. per totum <lb/>erit intēſum vt .4. / igr̄ ↄ̨° vera. </s>
              <s xml:id="N2BEAA" xml:space="preserve">Probationē huiꝰ vi-<lb/>deas latiꝰ in expõe calculatoris cuius hec ↄ̨° eſt de­<lb/>cima.               <anchor type="note" xlink:href="note-0271-06" xlink:label="note-0271-06a"/>               </s>
              <s xml:id="N2BEB6" xml:space="preserve">¶ Expedito primo articulo et ſecundo iam re­<lb/>ſtat dubia mouere.</s>
            </p>
            <div xml:id="N2BEBB" level="5" n="14" type="float">
              <note position="right" xlink:href="note-0271-06a" xlink:label="note-0271-06" xml:id="N2BEBF" xml:space="preserve">3. articu.</note>
            </div>
            <p xml:id="N2BEC5">
              <s xml:id="N2BEC6" xml:space="preserve">Dubitat̄̄ primo vtrū cuiuſlibet quali­<lb/>tatis difformis ſiue qualificati intenſio correſpon­<lb/>deat qualitati vniformi ad cuius intenſionem po-<lb/>teſt reduci.</s>
            </p>
            <pb chead="Quarti tractatus" file="0272" n="272"/>
            <p xml:id="N2BED3">
              <s xml:id="N2BED4" xml:space="preserve">Dubitat̄̄ ſcḋo. </s>
              <s xml:id="N2BED7" xml:space="preserve">Utrum intenſio mixti <lb/>habentis qualitates contrarias coextenſas per to­<lb/>tum attenditur penes exceſſum qualitatis cxceden­<lb/>tis ſuper exceſſam.</s>
            </p>
            <p xml:id="N2BEE0">
              <s xml:id="N2BEE1" xml:space="preserve">Dubitatur tertio. </s>
              <s xml:id="N2BEE4" xml:space="preserve">Utrum dabilis ſit <lb/>qualitas nullius intenſionis ſecundum ſe et quãli-<lb/>bet eius partem.</s>
            </p>
            <p xml:id="N2BEEB">
              <s xml:id="N2BEEC" xml:space="preserve">Ad primū dubiū arguit̄̄ primo /  non <lb/></s>
              <s xml:id="N2BEF0" xml:space="preserve">Et ſigno vnū pedale diuiſum ꝑ partes ꝓportioua­<lb/>les ꝓportione q̄ eſt medietas triple, et in prima ꝑte <lb/>ꝓportiõali eiꝰ ſit albedo vt duo et in ſcḋa in duplo <lb/>minꝰ et in .3. in duplo minꝰ ꝙ̄ in .2. et in .4. in duplo <lb/>minus ꝙ̄ in .3. / et ſic ↄ̨ñter. </s>
              <s xml:id="N2BEFB" xml:space="preserve">Quo poſito argr̄ ſic / illud <lb/>pedale eſt difforme: et tñ eiꝰ albedo nõ corrñdet al-<lb/>bedi vniformi ad quã poſſit reduci: igr̄ ꝑs negati-<lb/>ua dubit a. </s>
              <s xml:id="N2BF04" xml:space="preserve">Probat̄̄ añs / q2 totiꝰ intēſionis illius <lb/>albedīs ad intēſionē albedinis prime ꝑtis eſt pro-<lb/>portio irratiõalis vt facile ex dictis ꝑcipi põt: igit̄̄ <lb/>nõ videt̄̄ modꝰ eã reducēdi ad vniformitatē:  ſi ne­<lb/>gas des illū.               <anchor type="note" xlink:href="note-0272-01" xlink:label="note-0272-01a"/>               </s>
              <s xml:id="N2BF14" xml:space="preserve">¶ Et ↄ̨firmat̄̄ et ſigno vnū pedale diui­<lb/>ſum ꝑ partes ꝓportiõales ꝓportiõe dupla: et ṗma <lb/>ſit aliq̈liter alba vniformiṫ, et .2. in ſexq̇altero plus <lb/>̄ ṗma, et .3. in ſexq̇tertio plus ꝙ̄ prima, et .4. in ſexq̇­<lb/>q̈rto pluſ̄ ṗma. </s>
              <s xml:id="N2BF1F" xml:space="preserve">et ſic ↄ̨ñter ꝓcedendo ꝑ oēs ſpecies <lb/>ꝓportiõis ſupraparticularis. </s>
              <s xml:id="N2BF24" xml:space="preserve">Quo poſito argr̄ ſic <lb/>illud corpꝰ eſt difforme: et tñ nõ põt reduci ad vnifor­<lb/>mitatē: igr̄ nõ qḋlꝫ difforme põt ad vniformitatē re­<lb/>duci: añs ꝓbat̄̄ / q2 nullꝰ eſt modꝰ ſue reductionis: qḋ <lb/>ſi negas des illū.               <anchor type="note" xlink:href="note-0272-02" xlink:label="note-0272-02a"/>               </s>
              <s xml:id="N2BF34" xml:space="preserve">¶ Et ↄ̨firmat̄̄ ſcḋo. </s>
              <s xml:id="N2BF37" xml:space="preserve">Et ſigno vnum <lb/>infinitū cuiꝰ primū pedale ſit albū vt .6, ſcḋm vt .7. <lb/>3. vt .7. cū dimidio, 4. vt .7. cū tribꝰ q̈rtis: et ſic ↄ̨ñter <lb/>ita  primo pedali deficiat prima ꝑs ꝓportiõalis <lb/>4. gradū proportiõe dupla ad hoc vt ſit vt .8, et .2, <lb/>ſcḋa, et .3. tertia, et .4. q̈rta, et ſic ↄ̨ñter. </s>
              <s xml:id="N2BF44" xml:space="preserve">Quo poſito <lb/>ſic argumētor / illud corpꝰ eſt difforme vt .8, et tñ eiꝰ <lb/>q̈litas nõ põt ad vniformitatē reduci: igr̄ pars ne-<lb/>gatiua a. </s>
              <s xml:id="N2BF4D" xml:space="preserve"> autē illud corpꝰ ſit albū vt .8. ꝓbat̄̄: q2 <lb/>addēdo illi corpori vnã q̈litatē cuiꝰ primū pedale ē <lb/>vt .2. m vt vnū, tertiū vt dimidiū .4. vt vna q̈rta, et <lb/>ſic ↄ̨ñter: illḋ corpꝰ manebit albū vt .8. ꝑ totū et nul-<lb/>la intēſio addit̄̄ ei: q2 illa q̈litas adddita nulliꝰ eſt in­<lb/>tēſionis: igr̄ iã ãtea illud corpꝰ erat ītenſū vt .8. </s>
              <s xml:id="N2BF5A" xml:space="preserve">Q, <lb/>autē nõ poſſit riduci ad vniformitatē. </s>
              <s xml:id="N2BF5F" xml:space="preserve">Ptꝫ: q2 nõ vr̄ <lb/>modꝰ debitꝰ talis reductiõis: qḋ ſi negas des illū.</s>
            </p>
            <div xml:id="N2BF64" level="5" n="15" type="float">
              <note position="left" xlink:href="note-0272-01a" xlink:label="note-0272-01" xml:id="N2BF68" xml:space="preserve">.1. ↄ̨fir̄a°.</note>
              <note position="left" xlink:href="note-0272-02a" xlink:label="note-0272-02" xml:id="N2BF6E" xml:space="preserve">2. ↄ̨fir̄a°.</note>
            </div>
            <p xml:id="N2BF74">
              <s xml:id="N2BF75" xml:space="preserve">In oppoſitū arguit̄̄ ſic / ſit a. difforme <lb/>inteſum c. gradu. </s>
              <s xml:id="N2BF7A" xml:space="preserve">Et argr̄ ſic / q̈litate ipſiꝰ a. diffor-<lb/>mi reducta ad vniformitatē c. gradꝰ et extēſa ꝑ totū <lb/>a. ipſum a. manebit ita intēſum ſicut antea mediã-<lb/>te eadē q̈litate vniformiter: igr̄ cuiuſlꝫ difformis in­<lb/>tenſio corrñdet q̈litati vniformi. </s>
              <s xml:id="N2BF85" xml:space="preserve">Tota rõ eſt clara: <lb/>hoc addito /  q̄lꝫ q̈litas quãtūcū intenſa aut re-<lb/>miſſa põt fieri cuiuſuis intēſiõis aut remiſſiõis / vt <lb/>ptꝫ ex primo capite huius .4. tractatus in notabi-<lb/>li vbi agitur de potentia rei.</s>
            </p>
            <p xml:id="N2BF90">
              <s xml:id="N2BF91" xml:space="preserve">Pro declaratione huiꝰ dubitationis. <lb/></s>
              <s xml:id="N2BF95" xml:space="preserve">¶ Notandū eſt et ſupponendū /  q̈litas exiſtens in <lb/>parte ſubiecti nõ admixta ↄ̈rio in ea ꝓportiõe mi-<lb/>nus denoīat totū ꝙ̄ denoīaret ſi eſſet ꝑ totū in qua <lb/>totū eſt maiꝰ illa ꝑte: hec ſupponit̄̄ / q2 eſt huiꝰ poſi-<lb/>tionis fundamentū / vt ſupra dictū eſt. </s>
              <s xml:id="N2BFA0" xml:space="preserve">Scḋo ſuppo­<lb/>nendū eſt in oī bona reductione difformis finiti ad <lb/>vniformitatē in ea ꝓportiõe qua q̈litas exiſtens in <lb/>parte ponit̄̄ ꝑ maiꝰ ſubiectū in ea d3 effici remiſſior <lb/>̄ ipſa ſit: et ꝙ̄ ipſa denomīat partē ſubiecti in qua <lb/>ponit̄̄ et ſi ponat̄̄ ꝑ minꝰ in ea ꝓportiõe efficiat̄̄ intē­<lb/>ſior in q̈ ꝑ minꝰ ſubiectū ponit̄̄. </s>
              <s xml:id="N2BFAF" xml:space="preserve">Ptꝫ / q2 alias plus <lb/><gap/>̀ denoīaret ꝙ̄ antea et ꝑ ↄ̨ñs reductio nõ va-               <cb chead="Capitulū quarū"/>               leret fundat̄̄ em̄ modꝰ reducēde q̈litatis difformis <lb/>ad vniformitatē in hoc  tantū denominat quali-<lb/>tas vniformis ſicut difformis ſibi correſpondes. <lb/></s>
              <s xml:id="N2BFBD" xml:space="preserve">Hiis ſuppoſitis pono aliquas concluſiones.</s>
            </p>
            <p xml:id="N2BFC0">
              <s xml:id="N2BFC1" xml:space="preserve">Prima cõcluſio. </s>
              <s xml:id="N2BFC4" xml:space="preserve">Ad reducendū aliqḋ <lb/>difforme finitū ad vniformitatē diuidenda eſt q̈li-<lb/>tas in aliq̈s partes quãtitatiuas adeq̈te: et tūc cõ-<lb/>ſideranda eſt intēſio quã hꝫ aliq̈ talis pars: et in q̈ <lb/>ꝓportione pars ſubiecti in qua ponit̄̄ talis pars <lb/>q̈litatis eſt mīor ſuo toto. </s>
              <s xml:id="N2BFD1" xml:space="preserve">Et tūc in ea ꝓportione in <lb/>qua pars in qua ponit̄̄ eſt mīor ſuo toto in ea talis <lb/>pars q̈litatis fiet remiſſior et vniformis nõ quidē ꝑ <lb/>deꝑditionē q̈litatis: ſed ꝑ ↄ̨tinuationē partiū ſcḋm <lb/>intēſionē partibꝰ ſcḋm extēſionē). </s>
              <s xml:id="N2BFDC" xml:space="preserve">Et ſic remiſſa ex-<lb/>tēdat̄̄ ꝑ totū ſubiectū: et ſic fiat de qualibet alia ꝑte <lb/>q̈litatis. </s>
              <s xml:id="N2BFE3" xml:space="preserve">Et in fine habebit̄̄ debita qualitatis redu­<lb/>ctio ad vniformitatē. </s>
              <s xml:id="N2BFE8" xml:space="preserve">Probatur / q2 in fine tota illa <lb/>q̈litas manet vniformrs ꝑ totū / vt ptꝫ: et tm̄ denoīat <lb/>quantū ante reductionē: cū q̄lꝫ eiꝰ pars tm̄ denoīet <lb/>ſubiectū quantū ante reductio oē: g̊ in fine habebit̄̄ <lb/>debita qualitatis reductio ad vniformitatem.</s>
            </p>
            <p xml:id="N2BFF3">
              <s xml:id="N2BFF4" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
              <s xml:id="N2BFF7" xml:space="preserve">Ad reducēdū difforme <lb/>ad vniformitatē in caſu prime ↄ̨cluſiõis q̄ſtiõis hu­<lb/>ius opꝫ capere totū gradū quo ſcḋa ꝑs ꝓportiõa-<lb/>lis excedit primã extēſum ꝑ totū reſiduū a prima: et <lb/>facere illū rēiſſiorē ī ꝓportiõe diuiſiõis: et extēdere <lb/>ꝑ totū: deinde capere totū gradū quo .3. pars pro-<lb/>portiõalis excedit .2. et facere illū remiſſiorē ꝙ̄ p̄ce-<lb/>dens in ꝓportiõe diuiſiõis: ita  quilꝫ ſequēs fiat <lb/>remiſſior p̄cedēte in ꝓportiõe diuiſiõis. </s>
              <s xml:id="N2C00A" xml:space="preserve">De quibus <lb/>aūt ſequētibꝰ g̈dibꝰ loquor declarat ſuppõ ṗme cõ­<lb/>cluſiõis huiꝰ q̄ſtiõis. </s>
              <s xml:id="N2C011" xml:space="preserve">Exemplū / vt diuiſo corꝑe ꝓpor-<lb/>tione dupla, et ṗma pars ſit aliq̈liṫ alba: et .2. in du­<lb/>plo plꝰ, et .3. in triplo vt in caſu prime ↄ̨cluſiõis q̄ſti­<lb/>onis: et ſit albedo ṗme partis vt vnū / tūc capiã vnū <lb/>gradū extēſum ꝑ totū reſiduū a prima. / q̊ .2. pars ex­<lb/>cedit primã: et volo /  fiat in duplo remiſſior: et extē­<lb/>dat̄̄ ꝑ totū: et deīde capiat̄̄ vnꝰ gradꝰ extēſus ꝑ totū <lb/>reſiduū a ṗma et a .2. et fiat in duplo remiſſior ꝙ̄ fue­<lb/>rit factꝰ p̄cedēs et extēdat̄̄ ꝑ totū. </s>
              <s xml:id="N2C024" xml:space="preserve">Et vnꝰ extēſus per <lb/>totū reſiduū a ṗma .2. et .3, et fiat in duplo remiſſior <lb/>̄ fuerit factꝰ in mediate p̄cedēs, et extēdat̄̄ ꝑ totum <lb/>vniformiṫ, et ſic ↄ̨ñter: et habebit̄̄ debita reductio: <lb/>et ſic exēplificabis in oībꝰ. </s>
              <s xml:id="N2C02F" xml:space="preserve">Ptꝫ hec ↄ̨cĺo: qm̄ in fine <lb/>tota illa q̈litas manebit vniformis / vt conſtat: et tm̄ <lb/>denoīabit ſicut antea: cū q̄lꝫ eiꝰ pars tm̄ denoīat ſi­<lb/>cut ãtea: vt pꝫ: igr̄ ſic oꝑãdo habet̄̄ debita reductio</s>
            </p>
            <p xml:id="N2C038">
              <s xml:id="N2C039" xml:space="preserve">Tertia ↄ̨̨cluſio. </s>
              <s xml:id="N2C03C" xml:space="preserve">Ad reducendū diffor-<lb/>me ad vniformitatē in caſu .4. ↄ̨cĺonis q̄ſtiõis huiꝰ <lb/>opꝫ facere q̈litatē exiſtentē in ṗma ꝑte ꝓportionali <lb/>in ea ꝓportiõe remiſſiorē qua illa ꝑs eſt minor ſuo <lb/>toto: hoc eſt in illa ꝓportiõe qua ſe hꝫ totū diuiſuꝫ <lb/>ꝓportiõe qua diuidit̄̄ illud difforme ad ſuã primã <lb/>partē ꝓportionalē: et extēdat̄̄ ſic vniformiṫ ꝑ totū: et <lb/>q̈litas exiſtēs in ſcḋa ꝑte ꝓportiõali fiat etiã remiſ-<lb/>ſior ꝙ̄ iã eſt in ꝓportiõe qua ſe hꝫ totū ad primã eiꝰ <lb/>partē ꝓportionalē et ex vna ꝓportiõe diuiſiõis: et ex-<lb/>tēdat̄̄ ꝑ totū. </s>
              <s xml:id="N2C053" xml:space="preserve">Et q̈litas exiſtēs in .3. fiat remiſſior in <lb/>ꝓportiõe cõpoſita ex ꝓportiõe qua ſe hꝫ totū ad pri­<lb/>mã eiꝰ partē ꝓportiõalē et ex duabꝰ ꝓportiõibꝰ di-<lb/>uiſiõis: et ſic ↄ̨ñter: ita  cuiuſlꝫ partis ꝓportiõalis <lb/>qualitas ponat̄̄ ꝑ totū vniformiṫ. </s>
              <s xml:id="N2C05E" xml:space="preserve">Et in ea ꝓporti-<lb/>one fiat remiſſior. </s>
              <s xml:id="N2C063" xml:space="preserve">Huiꝰ ↄ̨cĺonis exēplū ptꝫ ex prima <lb/>et ſcḋa partibus huius libri: et probatio ex prima <lb/>concluſione huius dubii.</s>
            </p>
            <p xml:id="N2C06A">
              <s xml:id="N2C06B" xml:space="preserve">Quarta ↄ̨̨cluſio. </s>
              <s xml:id="N2C06E" xml:space="preserve">Ubicun denoīatio <lb/>alicuiꝰ difformis eſt incõmenſurabilis denoīatiõi               <pb chead="De difformium intenſione" file="0273" n="273"/>               prime ꝑtis ꝓportiõalis qua totū denoīat: ibi tota <lb/>q̈litas reducta ad vniformitatē eſt incõmēſurabi-<lb/>lis intēſioni ṗme ꝑtis ꝓportiõalis poſt̄ ꝑ totū ex-<lb/>tendit̄̄. </s>
              <s xml:id="N2C07E" xml:space="preserve">Probat̄̄ / q2 ſemꝑ totalis intēſio difformis <lb/>q̈litatis poſt̄ reducit̄̄ ad vniformitatē corrñdet in <lb/>g̈du totali denoīatiõi ipſiꝰ: et denoīatio qua prima <lb/>pars ꝓportiõalis totū denoīat: et q̈litas eiꝰ iã re-<lb/>miſſa et extenſa ꝑ totū ſiĺr corrñdent in gradu: g̊ cõ­<lb/>cluſio vera. </s>
              <s xml:id="N2C08B" xml:space="preserve">Sed ad cognoſcendã intenſionē diffor-<lb/>mis infiniti quãtitatiue: pono aliquas ↄ̨cluſiones.</s>
            </p>
            <p xml:id="N2C090">
              <s xml:id="N2C091" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
              <s xml:id="N2C094" xml:space="preserve">Cuiuſlꝫ īfiniti diffor-<lb/>mis in quo nõ ſunt q̈litates ſe īpediētes intenſio d3 <lb/>attendi penes maximū gradū vniformē ꝑ īfinita eiꝰ <lb/>pedalia extēſum: aut penes gradū qui nõ extēdit̄̄ <lb/>ꝑ infinita eiꝰ pedalia. </s>
              <s xml:id="N2C09F" xml:space="preserve">ſed quilꝫ quē ille gradꝰ exce-<lb/>dit extēdit̄̄ ꝑ īfinita eiꝰ pedalia vniformiṫ. </s>
              <s xml:id="N2C0A4" xml:space="preserve">Nõ dico / <lb/>aut penes minimū gradū qui nõ extēdit̄̄ ꝑ infinita <lb/>eiꝰ pedalia ꝓpter gradū īfinitū qui nõ eſt paruus. <lb/>               <anchor type="note" xlink:href="note-0273-01" xlink:label="note-0273-01a"/>               </s>
              <s xml:id="N2C0B2" xml:space="preserve">¶ Ex hac ↄ̨cĺone ſequit̄̄ primo /  corpꝰ infinitū cuiꝰ <lb/>primū pedale eſt vt .4. et .2. vt .5. et .3. vt quin cū di-<lb/>midio, et .4. vt .5. cū duabꝰ primis partibꝰ ꝓportio-<lb/>nabilibꝰ vniꝰ, et .5. vt quī cū .3. primis ꝑtibꝰ ꝓpor-<lb/>tionabilibꝰ vniꝰ (intelligo ꝓportione dupla) </s>
              <s xml:id="N2C0BD" xml:space="preserve">Et .6. <lb/>vt quī cū .4, primis partibꝰ ꝓportionalibꝰ vniꝰ / et <lb/>ſic ↄ̨ñter eſt intenſum vt .6. </s>
              <s xml:id="N2C0C4" xml:space="preserve">Probat̄̄ / q2 ille vt .6. eſt <lb/>gradꝰ qui nõ extēdit̄̄ ꝑ īfinita eiꝰ pedalia: ſed quilꝫ <lb/>quē ſex excedūt extēdit̄̄ vniformiṫ ꝑ īfinita eiꝰ peda-<lb/>lia: vt ↄ̨ſtat: igr̄ ex .5. ↄ̨cĺone tale corpꝰ infinitū eſt vt <lb/>6.               <anchor type="note" xlink:href="note-0273-02" xlink:label="note-0273-02a"/>               </s>
              <s xml:id="N2C0D4" xml:space="preserve">¶ Sequit̄̄ .2°. /  corpꝰ infinitū cuiꝰ primū pedale <lb/>eſt vt .6. et .2. vt .5. et .3. vt .5. cū dimidio, et .4. vt .5. cum <lb/>vna quarta, et .6. vt .5. cū vua octaua, et .7. vt .5. cum <lb/>vna decimaſexta: et ſic ↄ̨ñter eſt intēſum vt .5. </s>
              <s xml:id="N2C0DD" xml:space="preserve">Pro-<lb/>bat̄̄ / q2 gradꝰ quītꝰ maximꝰ gradꝰ vniformis qui <lb/>extēdit̄̄ ꝑ infinita eiꝰ pedalia / vt ptꝫ. </s>
              <s xml:id="N2C0E4" xml:space="preserve">igr̄ ex ↄ̨cĺone <lb/>illud infinitū eſt intēſum vt .5.               <anchor type="note" xlink:href="note-0273-03" xlink:label="note-0273-03a"/>               </s>
              <s xml:id="N2C0EE" xml:space="preserve">¶ Sequit̄̄ .3. /  corpꝰ <lb/>īfinitū cuiꝰ primū pedale eſt vt vnū, et .2. vt duo, et .3. <lb/>vt tria, et .4. et quatuor: et ſic in infinitū aſcendendo <lb/>ꝑ oēs nūeros eſt īfinite intēſuꝫ ſemꝑ excludo ↄ̈rias <lb/>q̈litates. </s>
              <s xml:id="N2C0F9" xml:space="preserve">Probat̄̄ / q2 īfinitꝰ gradꝰ nõ extēdit̄̄ ꝑ infi­<lb/>nita eiꝰ pedalia: et quilꝫ quē gradꝰ īfinitꝰ excedit ex-<lb/>tēdit̄̄ ꝑ infinita eiꝰ pedalia / vt ↄ̨ſtat: g̊ ex .5. ↄ̨cluſione <lb/>illud corpꝰ eſt infinite intēſum.               <anchor type="note" xlink:href="note-0273-04" xlink:label="note-0273-04a"/>               </s>
              <s xml:id="N2C107" xml:space="preserve">¶ Sequit̄̄ .4. /  infi-<lb/>tū cuiꝰ primū pedale vel queuis pars finita eſt īfini­<lb/>te alba et totū reſiduū eſt vt .4. eſt albū vt .4. </s>
              <s xml:id="N2C10E" xml:space="preserve">Pro-<lb/>bat̄̄ / q2 gradꝰ vt quatuor eſt maximꝰ extēſus ꝑ īfini­<lb/>ta eius pedalia: igr̄.               <anchor type="note" xlink:href="note-0273-05" xlink:label="note-0273-05a"/>               </s>
              <s xml:id="N2C11A" xml:space="preserve">Et hoc correlariū eſt de mente <lb/>Calculatoris in .2. capĺo. </s>
              <s xml:id="N2C11F" xml:space="preserve">Nã ſcḋm eū q̈litas īfinita <lb/>extenſa ꝑ partē finitã p̄ciſe alicuiꝰ corporis infiniti <lb/>nõ confert aliq̇d ad denoīationē corporis infiniti.</s>
            </p>
            <div xml:id="N2C126" level="5" n="16" type="float">
              <note position="left" xlink:href="note-0273-01a" xlink:label="note-0273-01" xml:id="N2C12A" xml:space="preserve">correĺ.</note>
              <note position="left" xlink:href="note-0273-02a" xlink:label="note-0273-02" xml:id="N2C130" xml:space="preserve">2. correĺ.</note>
              <note position="left" xlink:href="note-0273-03a" xlink:label="note-0273-03" xml:id="N2C136" xml:space="preserve">.3. correĺ.</note>
              <note position="left" xlink:href="note-0273-04a" xlink:label="note-0273-04" xml:id="N2C13C" xml:space="preserve">4. correĺ.</note>
              <note position="left" xlink:href="note-0273-05a" xlink:label="note-0273-05" xml:id="N2C142" xml:space="preserve">Calcula.</note>
            </div>
            <p xml:id="N2C148">
              <s xml:id="N2C149" xml:space="preserve">Sexta ↄ̨̨cĺo. </s>
              <s xml:id="N2C14C" xml:space="preserve">Quã <gap/> īfiniti difformis <lb/>intēſio nõ ſit penes reductionē ad vniformitatē at-<lb/>tendenda et cognoſcēda: ſed mõ dicto in .5. ↄ̨cĺone: <lb/>nichilominꝰ põt ad vniformitatē ſue denoīationis <lb/>reduci. </s>
              <s xml:id="N2C159" xml:space="preserve">Prima ꝑs ꝓbat̄̄: q2 tota reductio ad vnifor­<lb/>mitatē fundat̄̄ in hoc  tm̄ põt qualitas extenſa ꝑ <lb/>partē denoīare totū ſicut extēſa ſub mīori intēſiõe <lb/>ꝑ totū. </s>
              <s xml:id="N2C162" xml:space="preserve">Sed hoc nõ hꝫ locū in corꝑe īfinito: vt ptꝫ ex <lb/>4. correlario .5. ↄ̨cĺonis: igr̄ nõ d3 ↄ̨mēſurari ītēſio <lb/>īfiniti difformis penes reductionē ad vniformitatē <lb/></s>
              <s xml:id="N2C16A" xml:space="preserve">¶ Scḋa pars ꝓbat̄̄: q2 q̄lꝫ q̈litas põt ad quãcū in­<lb/>tenſionē reduci: vt ptꝫ ex p̄mo capĺo huiꝰ tractatus <lb/>vbi agit̄̄ ḋ poña rei: igr̄. </s>
              <s xml:id="N2C171" xml:space="preserve">Cõcĺo reſpõſiua ad dubiū <lb/>ptꝫ ex dictis ↄ̨cluſionibus. </s>
              <s xml:id="N2C176" xml:space="preserve">¶ Ad rationem ante op-<lb/>poſitum reſpondent ↄ̨cluſiones et correlaria.</s>
            </p>
            <p xml:id="N2C17B">
              <s xml:id="N2C17C" xml:space="preserve">Ad ſcḋm dubiū argr̄ pars negatiua: <lb/>q2 ſi pars affirmatiua eēt a: ſeq̄ret̄̄ /  pedale hñs <lb/>ꝑ totū caliditatē et .6. et frigiditatē vt .8. eēt frigidū <lb/>et .2. / ſed ↄ̨ñs eſt fim̄: igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N2C185" xml:space="preserve">Seq̄la ptꝫ / <lb/>q2 .8. excedūt .6. per .2. et falſitas ↄ̨ñtis. </s>
              <s xml:id="N2C18A" xml:space="preserve">Probat̄̄. </s>
              <s xml:id="N2C18D" xml:space="preserve">q2               <cb chead="De difformium intenſione"/>               illud eſt frigidū vt .8. igr̄. </s>
              <s xml:id="N2C193" xml:space="preserve">Añs ꝓbat̄̄ / q2 aliq̇ .2. gra­<lb/>dus frigiditatꝪ denominãt illud pedale frigidū vt <lb/>2. vt ↄ̨ſtat: et nõ eſt maior rõ de aliq̇bꝰ ꝙ̄ de q̇buſcū-<lb/> aliis .2. / igr̄ q̇lꝫ duo denominãt vt .2. / et ꝑ ↄ̨ñs oēs <lb/>8. collectiue denoīant vt .8. </s>
              <s xml:id="N2C19E" xml:space="preserve">Maior eſt nõ, et minor <lb/>ꝓbat̄̄: q2 nõ eſt maior rõ  īpediãt̄̄ ſeptimꝰ et octa-<lb/>uus, ꝙ̄ primꝰ et ſcḋs: ſcḋs et tertiꝰ .etc̃.               <anchor type="note" xlink:href="note-0273-06" xlink:label="note-0273-06a"/>               </s>
              <s xml:id="N2C1AA" xml:space="preserve">¶ Dices et bñ <lb/>ↄ̨cedēdo qḋ infert̄̄: et negãdo falſitatē ↄ̨ñtis et ad cū <lb/>ꝓbat̄̄ negat̄̄ añs: et cū ꝓbat̄̄: nego maiorē. </s>
              <s xml:id="N2C1B1" xml:space="preserve">Dico em̄ / <lb/> nulli 2. gradꝰ denoīant illḋ pedale frigidū vt .2. <lb/>ſed oēs .8. collectiue. </s>
              <s xml:id="N2C1B8" xml:space="preserve">Nã quãuis .6. gradꝰ īpediant̄̄ <lb/>a q̈litate ↄ̈ria nõ tñ totaliṫ: ſed q̄lꝫ dualitas illiꝰ fri­<lb/>giditatꝪ aliq̇ mõ denoīat puta vt vna medietas: et <lb/>qualibet gradus vt vna quarta vbi ſine contrarii <lb/>permixtione denominaret vt vnum.</s>
            </p>
            <div xml:id="N2C1C3" level="5" n="17" type="float">
              <note position="right" xlink:href="note-0273-06a" xlink:label="note-0273-06" xml:id="N2C1C7" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N2C1CD">
              <s xml:id="N2C1CE" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N2C1D1" xml:space="preserve">Q2 ſi hoc eſſet verū ſeq̄ret̄̄ <lb/>aliquã frigiditatē extēſam ꝑ aliqḋ corpꝰ ↄ̨tinuo re­<lb/>mitti: et corpꝰ ↄ̨tinuo eſſe frigidꝰ: ſed ↄ̨ñs videt̄̄ im-<lb/>poſſibile: igr̄ illud ex q̊ ſeqnit̄̄. </s>
              <s xml:id="N2C1DA" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono / <lb/> ſucceſſiue ꝑ vnã horã remittat̄̄ frigiditas et cali-<lb/>ditas illiꝰ pedalis: ita tñ  qñ frigiditas ꝑdit ali-<lb/>quē gradū caliditas ꝑdat duplū ad illū. </s>
              <s xml:id="N2C1E3" xml:space="preserve">Quo po-<lb/>ſito illud pedale ꝑ illã horã erit frigidiꝰ et frigidiꝰ: <lb/>et tñ ↄ̨tinuo frigiditas eiꝰ ꝑ totū remittit̄̄: igr̄ pro-<lb/>poſitū. </s>
              <s xml:id="N2C1EC" xml:space="preserve">Coña ptꝫ cū mīore: et argr̄ maior / q2 ↄ̨tinuo <lb/>exceſſus frigiditatis ſupra caliditatem erit maior <lb/></s>
              <s xml:id="N2C1F2" xml:space="preserve">Nã qñ remittet̄̄ vnꝰ gradꝰ frigiditatꝪ remittentur <lb/>duo caliditatꝪ: et ſic qñ frigiditas erit vt .7. calidi-<lb/>tas erit vt .4. / igr̄ frigiditas excedit, tūc caliditateꝫ <lb/>ꝑ .3. gradꝰ: et aña p̄ciſe excedebat ꝑ duos. </s>
              <s xml:id="N2C1FB" xml:space="preserve">Itē qñ fri­<lb/>giditas ꝑdiderit duos gradꝰ: caliditas ꝑdidit .4. <lb/>ex caſu: igr̄ cū frigiditas erit vt .6. caliditas erit vt <lb/>2, et ſic exceſſus erit .4. gradus: igitur continuo ex-<lb/>ceſſus augetur / quod fuit probandum.               <anchor type="note" xlink:href="note-0273-07" xlink:label="note-0273-07a"/>               </s>
              <s xml:id="N2C20B" xml:space="preserve">¶ Dices et be­<lb/>ne ↄ̨cedendo quod infert̄̄ tan̄ correlariū ſequēs.</s>
            </p>
            <div xml:id="N2C210" level="5" n="18" type="float">
              <note position="right" xlink:href="note-0273-07a" xlink:label="note-0273-07" xml:id="N2C214" xml:space="preserve">Dicitur</note>
            </div>
            <p xml:id="N2C21A">
              <s xml:id="N2C21B" xml:space="preserve">Sed ↄ̨̨tra. </s>
              <s xml:id="N2C21E" xml:space="preserve">Q2 ꝑ idē ſeq̄ret̄̄ /  a.  b. pe­<lb/>dalia ſunt mõ equalr̄ frigida: et ↄ̨tinuo ꝑ horã futu­<lb/>rã a. erit frigidiꝰ b. et tñ frigiditas ipſiꝰ a. ↄ̨tinuo ꝑ <lb/>horã remittet̄̄: frigiditas o ipſiꝰ b. ↄ̨tinuo intēdet̄̄ <lb/>ꝑ horã: ſed hoc eſt īpoſſibile: igr̄. </s>
              <s xml:id="N2C229" xml:space="preserve">Probat̄̄ tñ ſeq̄la: <lb/>et volo /  a. et b. pedalia habeãt ꝑ totū caliditatē vt <lb/>6. et frigiditatē vt .8. et a. vniformiṫ in iſta hora ꝑ-<lb/>dat duos gradꝰ frigiditatis et .4. caliditatꝪ .b. vero <lb/>vniformiṫ in eadē hora acq̇rat duos frigiditatꝪ et <lb/>4. caliditatis. </s>
              <s xml:id="N2C236" xml:space="preserve">Quo poſito a. et b. pedalia ſūt eq̈liṫ <lb/>frigida: et cõtinuo ꝑ horã futurã a. erit frigidꝰ b. et <lb/>ↄ̨tinuo ꝑ eandē horã remittet̄̄ frigiditas ipſiꝰ a. et <lb/>intēdit̄̄ frigiditas ipſiꝰ b. / igr̄ ꝓpoſitū. </s>
              <s xml:id="N2C23F" xml:space="preserve">Cõſequētia <lb/>ptꝫ cū maiore: et argr̄ mīor: q2 a ↄ̨tinuo intendet̄̄ in <lb/>frigiditate: et b. ↄ̨tinuo remittet̄̄ / vt pꝫ intuenti, et in <lb/>principio ſunt eq̄ frigida: igr̄ ↄ̨tinuo a. erit frigidꝰ <lb/>b. / qḋ fuit ꝓbandū. </s>
              <s xml:id="N2C24A" xml:space="preserve">¶ Itē ſeq̄ret̄̄ /  in aliq̊ frigido cõ­<lb/>tinuo intēderet̄̄ frigiditas: et tñ ipſū in infinitū re-<lb/>mitteret̄̄: qḋ eſt īpoſſibile. </s>
              <s xml:id="N2C251" xml:space="preserve">Seq̄la ꝓbat̄̄ et volo /  a. <lb/>hñs frigiditatē vt .6. et caliditatē vt .4. vniformiter <lb/>in iſta hora acq̇rat duos gradꝰ frigiditatꝪ, et .4. ca­<lb/>liditatis. </s>
              <s xml:id="N2C25A" xml:space="preserve">Quo poſito in īfinitū remittet̄̄ ipſū a: cū <lb/>in īfinitū paruus erit exceſſus frigiditatꝪ ſupra ca-<lb/>liditatē: igr̄.               <anchor type="note" xlink:href="note-0273-08" xlink:label="note-0273-08a"/>               </s>
              <s xml:id="N2C266" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 tūc ſeq̄ret̄̄ /  aliquod <lb/>corpꝰ calidū efficeret̄̄ nec calidū nec frigidū ſine de­<lb/>ꝑditione aut acq̇ſitiõe caliditatis aut frigiditatis / <lb/>qḋ īplicat. </s>
              <s xml:id="N2C26F" xml:space="preserve">Seq̄la ꝓbat̄̄ / et ſit a. corpꝰ diuiſū ꝑ par-<lb/>tes ꝓportionales ꝓportiõe dupla, et in ṗma eiꝰ ꝑte <lb/>ꝓportiõali ſit caliditas vt .2. et frigiditas vt vnū, et <lb/>in ſcḋa ꝑte ꝓportiõali ſit caliditas et frigiditas in <lb/>duplo maior ꝙ̄ in ṗma, et in tertia ſit caliditas et <lb/>frigiditas in triplo maior ꝙ̄ in prima / et ſic ↄ̨ñter. <lb/></s>
              <s xml:id="N2C27D" xml:space="preserve">Quo poſito manifeſtū eſt expõne et ṗma ↄ̨cluſione <lb/>q̄ſtiõs /  a. corpꝰ eſt calidū vt duo cū tota ſua cali-               <pb chead="Quarti tractatus" file="0274" n="274"/>               ditas ſit vt .4. et tota frigiditas vt .2. q̄ ſunt in ſcḋa <lb/>ꝑte ꝓportionali a. corꝑis. </s>
              <s xml:id="N2C289" xml:space="preserve">Uolo igr̄ /  prima pars <lb/>ꝓportiõalĺ a. corꝑis acq̇rat in hõ aliquã quãtitatē <lb/>ꝑ rarefactiõeꝫ acq̇rēdo et ꝑs hñs duplã caliditatē <lb/>ad caliditatē ṗme partꝪ in eadē hora acq̇rat ſubdu­<lb/>pla quãtitatē, et pars hñs q̈druplã caliditatem ad <lb/>caliditatē ṗme ꝑtis in eadē hora acq̇rat ſubq̈dru-<lb/>plã quãtitatē etc̈. </s>
              <s xml:id="N2C298" xml:space="preserve">Quo poſito argr̄ ſic / a. in fine ra-<lb/>refactiõis nec eſt calidū nec frigidū: et aña erat ca-<lb/>lidū: et nullã caliditatē aut frigiditatē deperdidit <lb/>aut acq̇ſiuit etc̈. / igr̄ ꝓpoſitū. </s>
              <s xml:id="N2C2A1" xml:space="preserve">Q, in fine nec eſt cali-<lb/>dū nec frigidū ꝓbat̄̄: q2 in fine hꝫ caliditatē ſuffici-<lb/>entē ip̄m denoīare īfinite calidū, et frigiditatē ſuffi­<lb/>entē ipſuꝫ denoīare īfinite frigidū puta illã quã hꝫ <lb/>in quãtitate acq̇ſita ꝑ rarefactionē: igr̄ caliditas et <lb/>frigiditas totalr̄ et adeq̈te ſe īpediūt: et ꝑ ↄ̨ñs illud <lb/>nec eſt calidū nec frigidū / qḋ fuit ꝓbandū. </s>
              <s xml:id="N2C2B0" xml:space="preserve">Q, autē <lb/>caliditas exñs in quãtitate acq̇ſita ꝑ rarefactionē <lb/>et ſiĺr frigiditas exñs in eadē quãtitatē ſufficiat de­<lb/>noīare a. infinite ſatis / ptꝫ ex his que dicta ſunt cir­<lb/>ca ſextam concluſionem queſtionis.</s>
            </p>
            <div xml:id="N2C2BB" level="5" n="19" type="float">
              <note position="right" xlink:href="note-0273-08a" xlink:label="note-0273-08" xml:id="N2C2BF" xml:space="preserve">ↄ̨fir̄atio.</note>
            </div>
            <p xml:id="N2C2C5">
              <s xml:id="N2C2C6" xml:space="preserve">Scḋo ad idē argr̄ ſic. </s>
              <s xml:id="N2C2C9" xml:space="preserve">Si ꝑs affirma­<lb/>tiua dubii eēt a: ſeq̄ret̄̄ alicuiꝰ corꝑis certa diuiſi­<lb/>one quãlꝫ partē ꝓportiõalē ꝓportiõe dupla eē ca-<lb/>lidã: et tñ totū nõ eē calidū: ↄ̨ñs videt̄̄ īpoſſibile: igr̄ <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N2C2D4" xml:space="preserve">Seq̄la ꝓbat̄̄, et ſit a. diuiſū per <lb/>ꝑtes ꝓportiõales ꝓportiõe dupla, et in ṗma ꝑte ſit <lb/>caliditas vt .2. et frigiditas vt vnū, et in ſcḋa parte <lb/>ſit in duplo maior caliditas et ſiĺr frigiditas ꝙ̄ in <lb/>ṗma, et in tertia in duplo maior caliditas et frigi-<lb/>ditas ꝙ̄ in ſcḋa, et ſic deinceps ita  in qualꝫ parte <lb/>proportionali caliditas ſit dupla ad frigiditatē. <lb/></s>
              <s xml:id="N2C2E4" xml:space="preserve">Quo poſito manifeſtū eſt quãlꝫ partē ꝓportiõalē <lb/>ſcḋm illã diuiſionē eſſe calidã: </s>
              <s xml:id="N2C2E9" xml:space="preserve">Sed  totū nõ ſit ca­<lb/>lidū ꝓbat̄̄ / q2 caliditas īpedit totalr̄ frigiditatē: et <lb/>eocõtra: igr̄ neutra illaꝝ denoīat. </s>
              <s xml:id="N2C2F0" xml:space="preserve">Añs ꝓbat̄̄ / quia <lb/>vtra illaꝝ ſufficit denoīare īfinite vt ſatis ptꝫ ex <lb/>ſcḋa ↄ̨cluſiõe q̄ſtiõis: igr̄ ſe totalr̄ īpediūt. </s>
              <s xml:id="N2C2F7" xml:space="preserve">¶ Itē ſe-<lb/>queret̄̄ alicuiꝰ corꝑis certa diuiſiõe ̄lꝫ partē ꝓpor­<lb/>tionalē ꝓportiõe dupla eſſe īfinite calidã: et tñ totū <lb/>nõ eſſe calidū / qḋ īplicat. </s>
              <s xml:id="N2C300" xml:space="preserve">Seq̄la ꝓbat̄̄ retēto caſu ſu­<lb/>periori: hoc addito /  ꝑ totū a. ſit caliditas vnifor-<lb/>mis īfinite intenſiõis. </s>
              <s xml:id="N2C307" xml:space="preserve">Sed  hoc ſit flm̄ ꝓbat̄̄ / q2 bñ <lb/>ſequit̄̄ ſcḋm hãc diuiſionē q̄lꝫ pars ꝓportiõalis <lb/>eiꝰ eſt calida: igr̄ ſcḋm hãc diuiſionē oēs ſunt calide <lb/>et oēs ſunt ip̄m totū: igr̄ totū eſt calidū / qḋ eſt nega­<lb/>tū.               <anchor type="note" xlink:href="note-0274-01" xlink:label="note-0274-01a"/>               </s>
              <s xml:id="N2C317" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi intenſio mixti hñtis q̈litates <lb/>ↄ̈rias coextēſas ꝑ totū attendit̄̄ penes exceſſū q̈lita­<lb/>tis excedētis ſupra exceſſam: ſequit̄̄ /  intēſio mixti <lb/>hñtis q̈litates ↄ̈rias nõ coextēſas: ſed extēſas in di­<lb/>uerſis partibꝰ ſubiecti itidē attendit̄̄ penes exceſſū <lb/>q̈litatis excedētis ſupra exceſſã: ſed hoc eſt flm̄: igr̄ <lb/>illud ex quo ſequit̄̄. </s>
              <s xml:id="N2C326" xml:space="preserve">Seq̄la videt̄̄ nota: ſed falſitas <lb/>ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄ret̄̄ /  frigiditas nullo pacto <lb/>īpediret caliditatē / qḋ eſt ↄ̈ fundamentū opinionis. <lb/></s>
              <s xml:id="N2C32E" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono /  ſit a. pedale in cuiꝰ vna me-<lb/>dietate ſic caliditas vt .8. et in alia frigiditas vt .4. <lb/>et b. in cuiꝰ vna medietate ſit caliditas vt .8. et alia <lb/>nec habeat caliditatē nec frigiditatē. </s>
              <s xml:id="N2C337" xml:space="preserve">Quo poſito <lb/>a. per te eſt calidū vt .4. cū .8. excedãt .4. per .4. et b. <lb/>ſimiltr eſt calidum vt .4. / igr̄ frigiditas in a. nullo <lb/>pacto īpedit caliditatem cum oīno habeãt eandem <lb/>caliditatem per eandem partem.</s>
            </p>
            <div xml:id="N2C342" level="5" n="20" type="float">
              <note position="left" xlink:href="note-0274-01a" xlink:label="note-0274-01" xml:id="N2C346" xml:space="preserve">ↄ̨fir̄tio.</note>
            </div>
            <p xml:id="N2C34C">
              <s xml:id="N2C34D" xml:space="preserve">In oppoſitū tñ argit̄̄ ſic / q2 intenſio <lb/>mixti hñtis q̈litates ↄ̈rias coextēſas ꝑ totū nõ attē­<lb/>dit̄̄ penes intēſionē q̈litatis intenſioris: cū tūc ↄ̈rie <lb/>q̈litates nullo mõ ſe īpedirēt in denoīationibꝰ ſuis <lb/>nec penes ꝓportionē q̈litatis excedētis ad q̈litatē <lb/>exceſſū: igr̄ d3 attendi penes exceſſū q̈litatis excedē­               <cb chead="Capitulū quartū."/>               tis ſupra exceſſū cū nõ ſit aliꝰ modꝰ quo talis inten-<lb/>ſio poſſet mēſurari. </s>
              <s xml:id="N2C35F" xml:space="preserve">Coña ptꝫ cū maiore: et ꝓbatur <lb/>mīor / q2 alias ſeq̄ret̄̄ albedinē vt .4. denoīare īfini-<lb/>te. </s>
              <s xml:id="N2C366" xml:space="preserve">Seq̄la ꝓbat̄̄ / et ſit in a. pedali albedo vt .4. ꝑ totū <lb/>coextēſa nigredini vt .2. et remittat̄̄ vniformiṫ ni-<lb/>gredo vſ ad nõ gradū in hora ſtãte albedīe. </s>
              <s xml:id="N2C36D" xml:space="preserve">Quo <lb/>poſito argr̄ ſic / in infinitū augebit̄̄ ꝓportio albedi­<lb/>nis ſupra nigredinē: igr̄ ꝑ te in īfinitū intēdet̄̄ deno­<lb/>minatio albedinis: et per conſequens in infinitum <lb/>denominabit illa albedo / quod fuit probandum.</s>
            </p>
            <p xml:id="N2C378">
              <s xml:id="N2C379" xml:space="preserve">Pro ſolutione huiꝰ dubii. </s>
              <s xml:id="N2C37C" xml:space="preserve">Notandum <lb/>eſt /  q̈litates ↄ̈rie exiſtētes in eodē ſubiecto ſe īpe-<lb/>diūt in ſuis denoīationibꝰ. </s>
              <s xml:id="N2C383" xml:space="preserve">Nõ em̄ eq̄ albū et cor-<lb/>pus in quo ſunt ꝑ totū .6. gradꝰ albedīs cū .2. gra-<lb/>dibus nigredīs ſicut corpꝰ in q̊ ſūt .6. gradꝰ albedīs <lb/>ſine admixtiõe ↄ̈rie q̈litatis. </s>
              <s xml:id="N2C38C" xml:space="preserve">Et nõ ſolū qualitates <lb/>ↄ̈rie ſe īpediūt qñ coextēdunt̄̄: verū etiã qñ in diuer-<lb/>ſis partibꝰ ſubiecti ponunt̄̄. </s>
              <s xml:id="N2C393" xml:space="preserve">Nõ em̄ tm̄ denoīat al-<lb/>bedo vt .4. exñs in vna medietate corꝑis in cuiꝰ alia <lb/>medietate eſt vnꝰ gradꝰ nigredīs quantū denoīaret <lb/>ſi in ſubiecto nõ eſſet aliq̈ nigredo. </s>
              <s xml:id="N2C39C" xml:space="preserve">Hoc ſuppoſito <lb/>aduertendū eſt /  quadruplex eſt opinio penes qḋ <lb/>debeat attendi inteſio mixti hñtis ↄ̈rias q̈litates <lb/>coextēſas: q̈s recitat calcu. in capĺo de ītēſio mixto-<lb/>rū. </s>
              <s xml:id="N2C3A7" xml:space="preserve">¶ Prima eſt /  intēſio mixti d3 attēdi penes ꝓ-<lb/>portionē q̈litatis excedētis ad q̈litatē exceſſã. </s>
              <s xml:id="N2C3AC" xml:space="preserve">Scḋa <lb/>dicit /  d3 attēdi penes q̈litatē excedentē. </s>
              <s xml:id="N2C3B1" xml:space="preserve">Tertia di­<lb/>cit /  penes medietatē exceſſus q̈litatis excedentis. <lb/></s>
              <s xml:id="N2C3B7" xml:space="preserve">Quarta dicit /  penes exceſſū. </s>
              <s xml:id="N2C3BA" xml:space="preserve">Sed ꝓ īpugnatiõe <lb/>3. ṗmaꝝ opinionū pono tres ꝓpõnes. </s>
              <s xml:id="N2C3BF" xml:space="preserve">¶ Prima ꝓ-<lb/>poſitio </s>
              <s xml:id="N2C3C4" xml:space="preserve">Intēſio mixti nõ attendit̄̄ penes ꝓportionē <lb/>q̈litatis excedētis ad exceſſam. </s>
              <s xml:id="N2C3C9" xml:space="preserve">Probat̄̄ / q2 tūc ſeq̄-<lb/>ret̄̄ /  albedo vt duo īfinite poſſet denoīare ſubie-<lb/>ctū albū ipſa ↄ̨tinuo manēte vt duo: ſed hoc eſt flm̄: <lb/>igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N2C3D2" xml:space="preserve">Seq̄la probat̄̄: et pono /  in a. <lb/>pedali ſit albedo vt duo: et nigredo vt vnū coextēſe <lb/>et remittat̄̄ nigredo vſ ad nõ gradū: ipſa albedīe <lb/>ↄ̨tinuo manēte vt duo. </s>
              <s xml:id="N2C3DB" xml:space="preserve">Quo poſita manifeſtū eſt /  <lb/>īfinita erit ꝓportio albedīs vt duo ad nigredinem / <lb/>igr̄ īfinite illa albedo ſubiectū ſuū denoīabit. </s>
              <s xml:id="N2C3E2" xml:space="preserve">¶ Se­<lb/>cūda ꝓpõ intēſio mixti nõ attendit̄̄ penes q̈litateꝫ <lb/>excedentē. </s>
              <s xml:id="N2C3E9" xml:space="preserve">Probat̄̄ / q2 tūc ſeq̄ret̄̄ /  vna q̈litas ↄ̈ria <lb/>nõ īpediret alterã in ſua denoīatiõe: qḋ eſt ↄ̈ notatū <lb/>ptꝫ ſeq̄la: q2 albedo vt .6. ſcḋm iſtã poſitionē ad mi-<lb/>xta nigredini vt .2. denoīat vt .6: et tm̄ denoīaret nõ <lb/>admixta ↄ̈rio: igr̄. </s>
              <s xml:id="N2C3F4" xml:space="preserve">¶ Tertia ꝓpõ. </s>
              <s xml:id="N2C3F7" xml:space="preserve">Intēſio mixti nõ <lb/>attendit̄̄ penes medietatē exceſſus q̈litatis excedē-<lb/>tis. </s>
              <s xml:id="N2C3FE" xml:space="preserve">Probat̄̄: q2 tūc ſeq̄ret̄̄ /  albedo vt duo īpedi-<lb/>ret totalr̄ .4. g̈dus nigredīs ſecū extenſe: ſed ↄ̨ñs eſt <lb/>flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
              <s xml:id="N2C405" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄: et po­<lb/>no /  .6 g̈dus nigredīs coextēdant̄̄ duobꝰ albedīs: <lb/></s>
              <s xml:id="N2C40B" xml:space="preserve">Tūc ſcḋm iſtã poſitionē illa nigredo denoīat vt .2. <lb/>q2 g̈dus vt duo eſt medietas exceſſus quo .6. exce-<lb/>dūt .2. / igr̄ .4. g̈dus illiꝰ nigredīs vt .6. īpediūtur ab <lb/>illis .2. g̈dibꝰ albedīs: et ſic albedo vt .2. īpedit tota­<lb/>liter .4. g̈dus nigredīs: qḋ fuit ꝓbãdū. </s>
              <s xml:id="N2C416" xml:space="preserve">Hiis p̄miſſis</s>
            </p>
            <p xml:id="N2C419">
              <s xml:id="N2C41A" xml:space="preserve">Sit prima ↄ̨̨cluſio. </s>
              <s xml:id="N2C41D" xml:space="preserve">Intenſio mixti in <lb/>quo ſunt qualitates ↄ̈rie ſiue coextēſe ſiue nõ: men-<lb/>ſurãda eſt penes exceſſū denoīatiõis qua vna illaꝝ <lb/>q̈litatū admixta ↄ̈rio nata eſt magis denoīare ſub­<lb/>iectū ꝙ̄ alia: ceretis paribꝰ. </s>
              <s xml:id="N2C428" xml:space="preserve">Exēplū / vt coextēſa al-<lb/>bedini vt .6. nigredīe vt .2. per totū ſubiectū: qm̄ albe­<lb/>do vt .6. toti coextēſa ſubiecto valet ſine ↄ̈rii admix­<lb/>tione denoīare vt .6. et nigredo vt duo coextēſa etiã <lb/>ꝑ totū ſubiectū deducto īpedimēto denoīaret vt .2. <lb/></s>
              <s xml:id="N2C434" xml:space="preserve">Et .6. excedūt duo ꝑ .4. / ↄ̨ñs eſt illud ſubiectū eſſe al-<lb/>bū vt .4. </s>
              <s xml:id="N2C439" xml:space="preserve">Siĺr accõmoda exēplū ↄ̈riis q̈litatibꝰ non <lb/>coextēſis: ſemꝑ ad denoīatiões, et nõ ad q̈litatū in-<lb/>tenſiões aſpiciēdo. </s>
              <s xml:id="N2C440" xml:space="preserve">Probat̄̄ / q2 totū reſiduū deno-               <pb chead="De difformium intenſione" file="0275" n="275"/>               minatiõis ab cxceſſu a ↄ̈ria denoīatiõe ſibi equali <lb/>īpedit̄̄: igr̄ ille exceſſus īmunis ab īpedimento ma-<lb/>nēs illud ſubiectū denoīat. </s>
              <s xml:id="N2C44C" xml:space="preserve">Et ꝑ ↄ̨ñs penes illū ex-<lb/>ceſſum denominationis eſt mixti intenſio metien-<lb/>da: quod fuit probaudum.</s>
            </p>
            <note position="left" xml:id="N2C453" xml:space="preserve">8. ↄ̨cl° de <lb/>diffo. q̈m <lb/>calcula. <lb/>negat.</note>
            <p xml:id="N2C45D">
              <s xml:id="N2C45E" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
              <s xml:id="N2C461" xml:space="preserve">Aliqḋ eſt calidū īfinite <lb/>intenſum: et vna medietas eſt vniformis ſub certo <lb/>gradu et alia, nec calida, nec frigida. </s>
              <s xml:id="N2C468" xml:space="preserve">Probatur: ſit <lb/>f. vnum quadratum diuiſum in .4. quadrata equa­<lb/>lia                <anchor type="figure" xlink:href="fig-0275-01" xlink:label="fig-0275-01a"/>               a.b.c.d. / vt patet in figura: <lb/>et ſit quadratum b. infinite ca-<lb/>lidū, et a. frigidum vt .4. et c. et <lb/>d. vniformiṫ calida vt .4. </s>
              <s xml:id="N2C47A" xml:space="preserve">Quo <lb/>poſito arguit̄̄ ſic / f. eſt īfinite ca-<lb/>lidum: cū vna quarta eius ſit in­<lb/>finite calida et nulla ſit in corpo­<lb/>re f. frigiditas īfinita: et vna eiꝰ <lb/>medietas eſt vniformiter calida <lb/>certo gradu puta vt .4. et alia nec calida nec frigi-<lb/>da / igr̄ ↄ̨cluſio vera. </s>
              <s xml:id="N2C48B" xml:space="preserve">Cõſequētia pꝫ cū maiore, et mi­<lb/>nor ꝓbat̄̄ / q2 medietas cõpoſita ex c. et d. eſt vnifor-<lb/>miter calida vt .4. / vt pꝫ ex caſu: igr̄. </s>
              <s xml:id="N2C492" xml:space="preserve">Sed  alia me­<lb/>dietas ſit nec calida nec frigida ꝓbat̄̄ / q2 medietas <lb/>ↄ̨poſita ex a. et c. nec eſt calida nec frigida: quia vna <lb/>medietas eiꝰ puta a. eſt frigida vt .4. et alia puta <lb/>c. calida et .4. / ergo medietas a.c. nec eſt calida nec <lb/>frigida: quod fuit probandum. </s>
              <s xml:id="N2C49F" xml:space="preserve">Et ſic ptꝫ concluſio <lb/>               <anchor type="note" xlink:href="note-0275-01" xlink:label="note-0275-01a"/>               </s>
              <s xml:id="N2C4A9" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  a. et b. ſūt ineq̄ intēſa: ita ꝙ̄ a. eſt in­<lb/>finite intenſū et b. īfinite remiſſū et q̄lꝫ pars finita ip­<lb/>ſius a. eſt eq̄ intēſa cū ꝑte corrñdente ipſiꝰ b. </s>
              <s xml:id="N2C4B0" xml:space="preserve">Probr̄ / <lb/>ſit b. īfinitū in cuiꝰ ṗmo pedali ſint duo g̈dus calidi­<lb/>tatis et vnꝰ frigiditatis, et in ſecūdo pedali in duplo <lb/>plꝰ de caliditate et frigiditate ꝙ̄ in ṗmo, et in tertio <lb/>in duplo plus de caliditate et frigiditate ꝙ̄ in ſcḋo <lb/>et ſic deinceps: ſed a. ſit īfinitū in cuiꝰ ṗmo pedali ſit <lb/>vnꝰ g̈dus caliditatꝪ ꝑ totū, in ſcḋo duo, in tertio .4. / <lb/>et ſic ↄ̨ñter ſine admixtiõe ↄ̈rii / tūc a. eſt īfinite intēſū / <lb/>vt pꝫ ex p̄cedēti dubio, et b. īfinite rēiſſū, cū ī eo cali-<lb/>ditas et frigiditas īfinite ſe adeq̈te īpediãt: et q̄lꝫ ꝑs <lb/>finita ipſiꝰ a. eſt eque intēſa cū parte correſpõdēte <lb/>ipſiꝰ b. / vt pꝫ diligenter intuēti: igr̄ correlariū verū.</s>
            </p>
            <div xml:id="N2C4C9" level="5" n="21" type="float">
              <figure xlink:href="fig-0275-01a" xlink:label="fig-0275-01" xml:id="N2C4CD">
                <image file="0275-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0275-01"/>
              </figure>
              <note position="left" xlink:href="note-0275-01a" xlink:label="note-0275-01" xml:id="N2C4D3" xml:space="preserve">9. ↄ̨° quã <lb/>calcula. <lb/>negat.</note>
            </div>
            <p xml:id="N2C4DD">
              <s xml:id="N2C4DE" xml:space="preserve">Tertia ↄ̨̨cĺo. </s>
              <s xml:id="N2C4E1" xml:space="preserve">A nūc eſt calidū qḋ non <lb/>ītēdet̄̄: nec remittet̄̄.               <anchor type="note" xlink:href="note-0275-02" xlink:label="note-0275-02a"/>               </s>
              <s xml:id="N2C4EB" xml:space="preserve">Et tñ in fine manebit nõ calidū <lb/>hanc ↄ̨cĺonē negat Calcu. in capĺo de mixtoꝝ intē-<lb/>ſiõe. </s>
              <s xml:id="N2C4F2" xml:space="preserve">Quã tñ ꝓbo ſic. </s>
              <s xml:id="N2C4F5" xml:space="preserve">Sit a. diuiſū ꝑ partes ꝓporti-<lb/>onales ꝓportiõe dupla: et in ṗma ſit aliq̈ albedo: et <lb/>ī ſcḋa in duplo ītēſior: et in .3. in q̈druplo intēſior: et <lb/>in .4. in octuplo intēſior: et ſic in īfinitū ꝓcedēdo per <lb/>nūeros pariter pares. </s>
              <s xml:id="N2C500" xml:space="preserve">Et deinde inducat̄̄ in quãlꝫ <lb/>partē ſubdupla frigiditas ſucceſſiue in hora īcipi-<lb/>piēdo a ṗma. </s>
              <s xml:id="N2C507" xml:space="preserve">Tūc ex p̄dictis ptꝫ ↄ̨cĺo hoc addito /  <lb/>intēdi et remitti dicūt motū: et ſucceſſionē. </s>
              <s xml:id="N2C50C" xml:space="preserve">¶ Ex hac <lb/>ſequit̄̄ /  a. nūc eſt nõ calidū: et nõ intēdet̄̄ nec remit­<lb/>tet̄̄: et tñ in fine manebit infinite calidū. </s>
              <s xml:id="N2C513" xml:space="preserve">Ptꝫ in caſu <lb/>ↄ̨cĺonis poſito /  in hora ſequēti remittat̄̄ ſucceſſi-<lb/>ue frigiditas ad nõ gradū eo ordine quo ante indu­<lb/>cebatur: quo poſito ptꝫ correlariū pro fine tēporis</s>
            </p>
            <div xml:id="N2C51C" level="5" n="22" type="float">
              <note position="left" xlink:href="note-0275-02a" xlink:label="note-0275-02" xml:id="N2C520" xml:space="preserve">hanc ne-<lb/>gat cal.</note>
            </div>
            <p xml:id="N2C528">
              <s xml:id="N2C529" xml:space="preserve">Quarta ↄ̨̨cĺo. </s>
              <s xml:id="N2C52C" xml:space="preserve">A. nõ eſt calidum. </s>
              <s xml:id="N2C52F" xml:space="preserve">Et tñ <lb/>eiꝰ ſcḋm certã diuiſionē q̄lꝫ pars eſt infinite calida. <lb/></s>
              <s xml:id="N2C535" xml:space="preserve">Sit a. corpꝰ finitū diuiſū in duas medietates ſcḋm <lb/>latitudinē: et ſit vna illaꝝ medietatū īfinite calida ꝑ <lb/>totū vniformiter ſiue ↄ̈rii coextēſione. </s>
              <s xml:id="N2C53C" xml:space="preserve">Et alteriꝰ me­<lb/>dietatis ṗma pars ſit aliqualr̄ frigida, et .2. in du­<lb/>plo plus, et .3. in q̈druplo) et .4. in octuplo, et ſic in <lb/>īfinitū ꝓcedēdo ſus extremū ipſiꝰ a. </s>
              <s xml:id="N2C545" xml:space="preserve">Et deīde diui­<lb/>datur totū a. ex tranſuerſo ꝑ partes proportiona­<lb/>les quauis proportione. </s>
              <s xml:id="N2C54C" xml:space="preserve">Et patet concluſio.</s>
            </p>
            <p xml:id="N2C54F">
              <s xml:id="N2C550" xml:space="preserve">Quīta ↄ̨̨cĺo. </s>
              <s xml:id="N2C553" xml:space="preserve">Diuiſo a. ꝑ partes ꝓpor­               <cb chead="De difformium intenſione"/>               tionales ꝓportiõe dupla: et in p̄ma pari ponant̄̄ .4. <lb/>g̊dus albedīs. </s>
              <s xml:id="N2C55B" xml:space="preserve">Et in .2. pari .8. </s>
              <s xml:id="N2C55E" xml:space="preserve">Et in .3. pari .16. / et ſic <lb/>ↄ̨ñter aſcēdendo ꝑ nūeros pariṫ pares </s>
              <s xml:id="N2C563" xml:space="preserve">Et in prima <lb/>in pari ponant̄̄ .4. nigredīs, et in .2.8. </s>
              <s xml:id="N2C568" xml:space="preserve">Et in .3.16. / et <lb/>ſic ↄ̨ñter: vt fit in paribꝰ. </s>
              <s xml:id="N2C56D" xml:space="preserve">Totū a. eſt nigrū vt duo. <lb/></s>
              <s xml:id="N2C571" xml:space="preserve">Ptꝫ / q2 tota deneīatio nata ꝓuenire ab illa albe-<lb/>dine non ꝑmixta ↄ̈rio eſt vt duo. </s>
              <s xml:id="N2C576" xml:space="preserve">Et tota denoīatio <lb/>nata ꝓuedire ab illa nigredīe eſt vt .4. ceteris pari-<lb/>bus remoto īpedimento: g̊ ex prima ↄ̨cĺone totū a. <lb/>eſt nigrū vt duo. </s>
              <s xml:id="N2C57F" xml:space="preserve">Añs pꝫ calculãti facile: ex p̄dictis <lb/>               <anchor type="note" xlink:href="note-0275-03" xlink:label="note-0275-03a"/>               </s>
              <s xml:id="N2C589" xml:space="preserve">¶ Ex hac ↄ̨cĺone ſequit̄̄ /  ſi in caſu eiꝰ ṗma ꝑs par <lb/>rarefiat acq̇rēdo aliquã ̄titatē </s>
              <s xml:id="N2C58E" xml:space="preserve">Et .2. par ſubduplã <lb/></s>
              <s xml:id="N2C592" xml:space="preserve">Et .3. par ſubq̈druplã, et ſic ↄ̨ñter: ita  q̄lꝫ ſequens <lb/>acq̇rat in duplo mīorē quãtitatē ꝙ̄ p̄cedes. </s>
              <s xml:id="N2C597" xml:space="preserve">Tūc in <lb/>fine illud manebit infinite album. </s>
              <s xml:id="N2C59C" xml:space="preserve">Ptꝫ ex modo ꝓ-<lb/>bande .6. ↄ̨cĺonis q̄ſtiõis. </s>
              <s xml:id="N2C5A1" xml:space="preserve">Et iſto mõ poteris īfinita <lb/>talia īferre: q̄ oīa ex p̄dictis facilē ſortiunt̄̄ ꝓbatio­<lb/>nē. </s>
              <s xml:id="N2C5A8" xml:space="preserve">Et ſic pꝫ rñſio ad dubiū. </s>
              <s xml:id="N2C5AB" xml:space="preserve">¶ Ad rõnes dubii. </s>
              <s xml:id="N2C5AE" xml:space="preserve">Ad <lb/>primã rñſum eſt ibi vſ ad replicã: ad quam rñdeo <lb/>cõcedendo qḋ īfert̄̄. </s>
              <s xml:id="N2C5B5" xml:space="preserve">¶ Et ſiĺr ad ↄ̨firmationē rñdeo <lb/>ↄ̨cedēdo illatū nec illud eſt incõueniēs. </s>
              <s xml:id="N2C5BA" xml:space="preserve">¶ Ad ſcḋam <lb/>rõnē rñdeo ↄ̨cedendo illatū et nego illud eſſe incõue-<lb/>niēs. </s>
              <s xml:id="N2C5C1" xml:space="preserve">¶ Ad ↄ̨firmationē nego ſequelã: nec eſt ſimile: <lb/>īmo dico /  iutenſio talis mixti debet attēdi penes <lb/>exceſſum vnius denominationis ſuper alteram / vt <lb/>patet ex prima concluſione huius dubii.</s>
            </p>
            <div xml:id="N2C5CA" level="5" n="23" type="float">
              <note position="right" xlink:href="note-0275-03a" xlink:label="note-0275-03" xml:id="N2C5CE" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N2C5D4">
              <s xml:id="N2C5D5" xml:space="preserve">Ad tertiū dubiū. </s>
              <s xml:id="N2C5D8" xml:space="preserve">Argr̄ /  nõ ſit dabi-<lb/>lis q̈litas nulliꝰ intēſionis etc̈. </s>
              <s xml:id="N2C5DD" xml:space="preserve">Q2 tūc ſeq̄ret̄̄ illam <lb/>nõ eſſe q̈litatē. </s>
              <s xml:id="N2C5E2" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. <lb/></s>
              <s xml:id="N2C5E6" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 oīs q̈litas eſt intenſa cū illud ſit ei <lb/>ꝓpriū. </s>
              <s xml:id="N2C5EB" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 tū ſeq̄ret̄̄ illã eſſe qualitatē <lb/>nõ intenſibilē. </s>
              <s xml:id="N2C5F0" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. <lb/></s>
              <s xml:id="N2C5F4" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 illa q̈litas eſſet intēſibilis cū q̄lꝫ <lb/>eiꝰ pars ſit nõ ītenſa: tūc ex nõ ītenſis cõponeret̄̄ in­<lb/>tēſū: qḋ eſt manifeſte flm̄. </s>
              <s xml:id="N2C5FB" xml:space="preserve">¶ In oppoſitū argr̄ / q2 p̄t <lb/>dari quãtitas nulliꝰ extenſiõis: igr̄ põt dari q̈litas <lb/>nulliꝰ intēſionis. </s>
              <s xml:id="N2C602" xml:space="preserve">pꝫ ↄ̨ña / a ſiĺi et añs cõiter cõcedit̄̄ <lb/>de benedicto corpore chriſti in ſacramēto altaris. <lb/></s>
              <s xml:id="N2C608" xml:space="preserve">Item hoc non implicat: igitur. </s>
              <s xml:id="N2C60B" xml:space="preserve">¶ Pro ſolutione <lb/>huiꝰ dubitationis. </s>
              <s xml:id="N2C610" xml:space="preserve">Pono aliquas coucluſiones.</s>
            </p>
            <p xml:id="N2C613">
              <s xml:id="N2C614" xml:space="preserve">Prima ↄ̨̨cĺo. </s>
              <s xml:id="N2C617" xml:space="preserve">Nõ eſt poſſibĺe naturalr̄ <lb/>dare q̈litatē nulliꝰ intēſiõis. </s>
              <s xml:id="N2C61C" xml:space="preserve">hãc paſſim oēs admit-<lb/>tūt. </s>
              <s xml:id="N2C621" xml:space="preserve">Et ei experiētia ſuffragat̄̄.               <anchor type="note" xlink:href="note-0275-04" xlink:label="note-0275-04a"/>               </s>
              <s xml:id="N2C629" xml:space="preserve">Qḋ aūt ab oībꝰ dr̄ <lb/>p̄ſtat fidē de itate ex libro de ſomno et vigi. (ab oī­<lb/>bus ) q2 qḋ parū deeſt ꝓ nichilo reputat̄̄ ex .2. <lb/>phiſicoꝝ: hac ſuaſione hec ↄ̨° ſuã ſūmat apparētiã</s>
            </p>
            <div xml:id="N2C632" level="5" n="24" type="float">
              <note position="right" xlink:href="note-0275-04a" xlink:label="note-0275-04" xml:id="N2C636" xml:space="preserve">pḣus de <lb/>ſomno et <lb/>vigi.</note>
            </div>
            <p xml:id="N2C640">
              <s xml:id="N2C641" xml:space="preserve">Scḋa ↄ̨̨cĺo. </s>
              <s xml:id="N2C644" xml:space="preserve">Poſſibile eſt ſimpĺr dare <lb/>q̈litatē nulliꝰ ītēſiõis. </s>
              <s xml:id="N2C649" xml:space="preserve">Probat̄̄: et ſigno vnã q̈lita­<lb/>tē īfinitã extēſiue diuiſam ꝑ partes ꝓportiõales ꝓ­<lb/>portiõe q̈drupla aſcēdendo. </s>
              <s xml:id="N2C650" xml:space="preserve">Et ṗma eiꝰ pars puta <lb/>primū pedale ſit ītenſū vt vnū: et ſcḋa puta .4. ſeq̄n­<lb/>tia pedalia vt dimidiū, et .3. puta .16. pedalia vt vna <lb/>q̈rta: </s>
              <s xml:id="N2C659" xml:space="preserve">Et .4. puta .64. vt vna octaua: et ſic ↄ̨ñter ſub-<lb/>duplando intēſionē. </s>
              <s xml:id="N2C65E" xml:space="preserve">Quo poſito manifeſtū eſt illã <lb/>qualitatē nulliꝰ eſſe intenſionis q2 nullꝰ gradꝰ certe <lb/>intenſionis eſt ꝑ infinita eiꝰ pedalia extēſus: igitur <lb/>ex .5. ↄ̨cluſiõe p̄cedētis dubii illa nõ eſt alicuiꝰ inten­<lb/>ſionis.               <anchor type="note" xlink:href="note-0275-05" xlink:label="note-0275-05a"/>               </s>
              <s xml:id="N2C66E" xml:space="preserve">¶ Ex hac ↄ̨cluſiõe ſeqnit̄̄ /  a. eſt nõ intenſuꝫ. <lb/></s>
              <s xml:id="N2C672" xml:space="preserve">Et ꝓportionabilr̄ ſicut ſua q̈litas partialis exten­<lb/>det̄̄ ꝑ mīores ꝑtes ita ꝓportiõabilr̄ fiet intēſior: et <lb/>in fine erit īfinite intenſum. </s>
              <s xml:id="N2C679" xml:space="preserve">Probat̄̄ poſito /  a. ſit <lb/>corpꝰ de quo fit mentio in caſu ↄ̨cluſions īmediate <lb/>p̄cedentis. </s>
              <s xml:id="N2C680" xml:space="preserve">Et cuiuſlꝫ illaꝝ partiū ſe habentiū in ꝓ-<lb/>portione quadrupla totalis qualitas ponatur in <lb/>primo eiꝰ pedali: et ꝓportionãbiliter ſicut ponitur <lb/>in minori parte ꝓportiõabiliter fiat intēſior. </s>
              <s xml:id="N2C689" xml:space="preserve">Quo <lb/>poſito a. in fine manebit infinite intenſum: et modo <lb/>eſt nõ intenſum: et ꝓportionabiliter ſicut ſua quali­<lb/>tas partialis etc̈. / igr̄ correlariū verum. </s>
              <s xml:id="N2C692" xml:space="preserve">Sed ꝓbatur /               <pb chead="Quarti tractatus" file="0276" n="276"/>                in fine manebit infinite intenſum. </s>
              <s xml:id="N2C69A" xml:space="preserve">q2 primū eius <lb/>pedale erit intenſum vt vnū: et .2. vt duo: q2 habebit <lb/>.4. medietates vniꝰ gradus que antea erant extenſe <lb/>per .4. pedalia: </s>
              <s xml:id="N2C6A3" xml:space="preserve">Et .3. eiꝰ pedale erit vt .4. q2 habebit <lb/>16. quartas gradus que ante extendebant̄̄ per .16. <lb/>pedalia: modo: 16. quarte ſunt .4. gradus. </s>
              <s xml:id="N2C6AA" xml:space="preserve">Et .4. <lb/>pedale habebit .8. gradus: quia habebit .64. octa-<lb/>uas que faciunt .8. gradus. </s>
              <s xml:id="N2C6B1" xml:space="preserve">Nam ille ante extende-<lb/>batur per .64. pedalia. </s>
              <s xml:id="N2C6B6" xml:space="preserve">Et ſic conſequenter ſemper <lb/>īuenies quodlibet ſequens pedale in duplo inten-<lb/>ſius precedente. </s>
              <s xml:id="N2C6BD" xml:space="preserve">igitur ex .3. correlario .5. concluſio-<lb/>nis primi dubii huiꝰ capitis a. eſt infinite intenſum <lb/></s>
              <s xml:id="N2C6C3" xml:space="preserve">Iunto loco a. maiori. </s>
              <s xml:id="N2C6C6" xml:space="preserve">Et hec eſt .11. Calcula. in ſcḋo <lb/>capĺo videas eam amplius in expoſitione eius.</s>
            </p>
            <div xml:id="N2C6CB" level="5" n="25" type="float">
              <note position="right" xlink:href="note-0275-05a" xlink:label="note-0275-05" xml:id="N2C6CF" xml:space="preserve">Correĺ.</note>
            </div>
            <p xml:id="N2C6D5">
              <s xml:id="N2C6D6" xml:space="preserve">Tertia ↄ̨̨cĺo. </s>
              <s xml:id="N2C6D9" xml:space="preserve">Corpus infinite longū <lb/>cuiꝰ primū pedale eſt pedaliter longū latum et pro-<lb/>fundū et aliqualiter album. </s>
              <s xml:id="N2C6E0" xml:space="preserve">Et .2. pedale equaliter <lb/>longū et in duplo minoris magnitudinis et etiã in <lb/>duplo minꝰ album. </s>
              <s xml:id="N2C6E7" xml:space="preserve">Et .3. in duplo minoris magni-<lb/>tudinis ꝙ̄ .2. et etiam in duplo minꝰ albū: et ſic cõſe-<lb/>quenter: ita  quodlibet ſequens ſit in duplo minꝰ <lb/>albū et mīoris magnitudinis ꝙ̄ īmediate precedēs <lb/></s>
              <s xml:id="N2C6F1" xml:space="preserve">Tota illa albedo denoīat illud corpus in ſexqui-<lb/>tertio albius ꝙ̄ ipſum denominet albedo primi pe­<lb/>dalis eius: ita  ſi primū pedale eſt vt .4. totū eſt in­<lb/>tenſū vt .2. cū duabus tertiis. </s>
              <s xml:id="N2C6FA" xml:space="preserve">Probatur: quia totū <lb/>illud corpus eſt bipedale. </s>
              <s xml:id="N2C6FF" xml:space="preserve">Cū cõponatur ex infinitꝪ <lb/>cõtinuo ſe habentibꝰ in ꝓportioue dupla ex caſu: et <lb/>primū illoꝝ eſt pedale. </s>
              <s xml:id="N2C706" xml:space="preserve">et primū pedale illiꝰ eſt albū <lb/>vt .4. vt ſuppono gratia argumenti: igit̄̄ tota illa <lb/>albedo primi pedalis denoīat illud corpus infinite <lb/>longū vt duo album: et albedo exiſtens in .2. pedali <lb/>denominat in quadruplo minꝰ: quia eſt in ſubdu-<lb/>pla parte, et eſt ſubduple intenſionis. </s>
              <s xml:id="N2C713" xml:space="preserve">Et eadē rati-<lb/>one quelibet ſequens albedo alicuiꝰ pedalis deno-<lb/>minat in quadruplo minꝰ albedine pedalis īmedia­<lb/>te precedētis: igitur ibi ſunt infinite denoīationes <lb/>cõtinuo ſe habentes in ꝓportione quadrupla de-<lb/>ſcendendo. </s>
              <s xml:id="N2C720" xml:space="preserve">et prima eſt vt duo: igitur aggregatū ex <lb/>oībus ſimul eſt vt duo cū duabꝰ tertiis. </s>
              <s xml:id="N2C725" xml:space="preserve">Ptꝫ hec cõ­<lb/>ſequentia ex prima parte: quãdo quidē totū diuiſū <lb/>ꝓportione quadrupla ſe habet ad primã ſui partē <lb/>in ꝓportione ſexquitetia. </s>
              <s xml:id="N2C72E" xml:space="preserve">Et ex cõſequenti ſequitur / <lb/> tota illa albedo denoīat illud corpus in ſexqui-<lb/>tertio albius ꝙ̄ ipſum denoīet albedo primi peda-<lb/>lis eius: cū duoꝝ cū duabus tertiis ad duo ſit pro-<lb/>portio ſexquitertia .etc̈.               <anchor type="note" xlink:href="note-0276-01" xlink:label="note-0276-01a"/>               </s>
              <s xml:id="N2C73E" xml:space="preserve">¶ Ex quo ſequit̄̄ lineã gira-<lb/>tiuã girantē oēs partes ꝓportionales vniꝰ colūne <lb/>vniformiter difformiter albe a nõ gradu vſ ad .8. <lb/>eſſe alicuiꝰ tīenſiõis: et nõ iufinite remiſſionis. </s>
              <s xml:id="N2C747" xml:space="preserve">Pro-<lb/>batur / q2 talis linea eſt finitū corpus cuiꝰ primū gi-<lb/>rum eſt certe intenſionis: et eſt minus ſuo toto in cer­<lb/>ta proportione: igitur .etc̈.</s>
            </p>
            <div xml:id="N2C750" level="5" n="26" type="float">
              <note position="left" xlink:href="note-0276-01a" xlink:label="note-0276-01" xml:id="N2C754" xml:space="preserve">ↄ̨fir̄atio.</note>
            </div>
            <p xml:id="N2C75A">
              <s xml:id="N2C75B" xml:space="preserve">Quarta concluſio. </s>
              <s xml:id="N2C75E" xml:space="preserve">Eſt poſſibile ſuper­<lb/>naturaliter dare qualitatē cuiꝰ nulla pars ſit alicu­<lb/>ius intenſionis. </s>
              <s xml:id="N2C765" xml:space="preserve">Probatnr ſit / vnū pedale albedi-<lb/>nis vniforme vt .4. et in prima parte proportionali <lb/>hore fuure diuidatur in duas medietates ſecnndū <lb/>intenſionē et ponãtur ille medietates vnitiue ſecun­<lb/>dū extenſionem, et condenſetur totū quoad efficia-<lb/>tur pedalis magnitudinis adequate, et manifeſtuꝫ <lb/>eſt /  manebit tota albedo intenſa vt .2. preciſe. </s>
              <s xml:id="N2C774" xml:space="preserve">De­<lb/>inde in ſecunda parte proportiõali diuidatur rur-<lb/>ſus illa albedo in duas medietates intenſiuas et <lb/>vniantur ſecundū extenſionē, et iterum condenſetur <lb/>totū ad quantitatem pedalē. </s>
              <s xml:id="N2C77F" xml:space="preserve">Et ſic fiat in qualibet <lb/>parte proportionali ſequente: ita  in qualibet ſe-<lb/>quēte fiat ſubduple intenſionis ad intenſionē quaꝫ               <cb chead="Capitulū quartū."/>               habebat in parte īmediate precedente, et maneat <lb/>in fine hore non reſtituta alicui priſtine intenſioui <lb/>aut maiori. </s>
              <s xml:id="N2C78D" xml:space="preserve">Quo poſito albedo illa in inſtanti ter­<lb/>minatiuo hore non eſt alicuius intenſionis nec ali-<lb/>qua eiꝰ pars / vt pꝫ intelligēti caſum / igr̄ ↄ̨cluſio a <lb/></s>
              <s xml:id="N2C795" xml:space="preserve">Nec valet non amittē caſum: quia ille caſus nõ plꝰ <lb/>repugnat quã caſus qui ponitur  tam forma la-<lb/>pidis quam materia reducantur ad non quantum <lb/>               <anchor type="note" xlink:href="note-0276-02" xlink:label="note-0276-02a"/>               </s>
              <s xml:id="N2C7A3" xml:space="preserve">¶ Ex hac cõcluſione ſequit̄̄ /  poſſibile eſt qualita-<lb/>tem mentalem non quantã q̄ v3 non eſt quanta effici <lb/>quantã et extenſam. </s>
              <s xml:id="N2C7AA" xml:space="preserve">Probatur / q2 ad illud nullum <lb/>ſequitur incõueniens: igitur illud eſt poſſibile. </s>
              <s xml:id="N2C7AF" xml:space="preserve">Añs <lb/>probatur: q2 nullum aliud videtur ſequi incõueni-<lb/>ens niſi  illa qualitas ſi reducētur ad mētē poſt̄ <lb/>erat extenſa eſſet infinite intenſionis cū haberet in­<lb/>finitas partes equales non cõicantes in eodē ſitu <lb/>penetratiue: quia prīa pars ꝓportionalis illius qñ <lb/>ipſa erat extenſa erat aliquãte intenſionis: et queli­<lb/>bet pars ſequens cū eſſet extenſa erat tante inten-<lb/>ſionis: et ſunt in mente omnes ſimul penetratiue et <lb/>vnitiue: igitur illa qualitas eſt infinite intenſionis <lb/></s>
              <s xml:id="N2C7C5" xml:space="preserve">Sꝫ illud incõueniens nõ ſequitur: q2 illa qualitas <lb/>cū extenditur nõ eſt intenſa nec aliqua eius pars.</s>
            </p>
            <div xml:id="N2C7CA" level="5" n="27" type="float">
              <note position="right" xlink:href="note-0276-02a" xlink:label="note-0276-02" xml:id="N2C7CE" xml:space="preserve">1. correĺ.</note>
            </div>
            <note position="right" xml:id="N2C7D4" xml:space="preserve">2. correĺ.</note>
            <p xml:id="N2C7D8">
              <s xml:id="N2C7D9" xml:space="preserve">¶ Sequitur ſcḋo /  qualitas mētalis vt .4. id eſt in­<lb/>tenſionis vt .4. non poteſt eſſe maioris aut mino-<lb/>ris. </s>
              <s xml:id="N2C7E0" xml:space="preserve">Probatur / q2 alias cum effecitur nõ intenſa: et <lb/>deinde reducitur ad mentem poſſet effici infinite in­<lb/>tenſionis. </s>
              <s xml:id="N2C7E7" xml:space="preserve">quod eſt falſum: quia alias quelibet qua­<lb/>litas mentalis poſſet effici cuiuſcū intenſionis: et <lb/>etiam remiſſionis. </s>
              <s xml:id="N2C7EE" xml:space="preserve">quod eſt falſum. </s>
              <s xml:id="N2C7F1" xml:space="preserve">Et ſi illud velis <lb/>concedere: tunc ego concedo tibi /  poteſt qualitas <lb/>mētalis extendi intenſiue in lapide.               <anchor type="note" xlink:href="note-0276-03" xlink:label="note-0276-03a"/>               </s>
              <s xml:id="N2C7FD" xml:space="preserve">¶ Sequitur ter­<lb/>tio /  albedo .4. graduū poteſt reduci ad punctū ſꝑ <lb/>manens p̄ciſe intenſa vt .4. </s>
              <s xml:id="N2C804" xml:space="preserve">Probatur poſito  </s>
              <s xml:id="N2C807" xml:space="preserve"> de­<lb/>us ponat albdineꝫ vt .4. penetratiue in puncto: et <lb/> non vniantur partes alio modo ꝙ̄ ante vnieban­<lb/>tur: ſicut ſuperius dictū eſt in corpore dñi noſtri in <lb/>ſacramento altaris. </s>
              <s xml:id="N2C812" xml:space="preserve">quo poſito iam patet correla­<lb/>rium. </s>
              <s xml:id="N2C817" xml:space="preserve">Non enim ſufficit ad maiorem intenſionē pe­<lb/>netratio plurimū gradum. </s>
              <s xml:id="N2C81C" xml:space="preserve">Sed cū hoc requiritur / <lb/> vniantur illi gradus ſecundum penetrationem. <lb/>               <anchor type="note" xlink:href="note-0276-04" xlink:label="note-0276-04a"/>               </s>
              <s xml:id="N2C828" xml:space="preserve">¶ Seq̇tur .4. /  non eſt propriuum qualitati inten-<lb/>ſio aut remiſſio: ſed proprium eſt illi  intenſibi-<lb/>lis ſit et remiſſibilis. </s>
              <s xml:id="N2C82F" xml:space="preserve">Prima pars patet ex .3. cõclu-<lb/>ſione huius dubii. </s>
              <s xml:id="N2C834" xml:space="preserve">Et .2. cõmuniter om̄s depto bur­<lb/>leo admittūt.               <anchor type="note" xlink:href="note-0276-05" xlink:label="note-0276-05a"/>               </s>
              <s xml:id="N2C83E" xml:space="preserve">¶ Sequitur .5. /  ̄uis ex hiis que nõ <lb/>ſunt intenſa poteſt fieri qualitas intēſa adequate. <lb/></s>
              <s xml:id="N2C844" xml:space="preserve">Tñ nun̄ ex non intenſis adequate cõponitur qua­<lb/>itas intēſa. </s>
              <s xml:id="N2C849" xml:space="preserve">Probatur hoc ex dictis: et aſimili: qm̄ <lb/>quēadmodū ex hiis que non ſunt extenſa poteſt ef­<lb/>fici extenſum / vt patet reducēdo aſinum ad non ̄tū <lb/>per dei potentiam: et deinde reſtituendo eum pri-<lb/>ſtine ̄titati. </s>
              <s xml:id="N2C854" xml:space="preserve">Tamen nun̄ poteſt adequate ↄ̨poni <lb/>extenſum. </s>
              <s xml:id="N2C859" xml:space="preserve">ex non extenſis igitur aſimili dicendū eſt <lb/>de qualitate ſuaſum eſt / igitur correlarium. </s>
              <s xml:id="N2C85E" xml:space="preserve">Et per <lb/>hoc patet reſponſio ad dubium. </s>
              <s xml:id="N2C863" xml:space="preserve">Et ad rationes an­<lb/>te oppoſitum.</s>
            </p>
            <div xml:id="N2C868" level="5" n="28" type="float">
              <note position="right" xlink:href="note-0276-03a" xlink:label="note-0276-03" xml:id="N2C86C" xml:space="preserve">3. correĺ.</note>
              <note position="right" xlink:href="note-0276-04a" xlink:label="note-0276-04" xml:id="N2C872" xml:space="preserve">4. correĺ.</note>
              <note position="right" xlink:href="note-0276-05a" xlink:label="note-0276-05" xml:id="N2C878" xml:space="preserve">5. correĺ.</note>
            </div>
            <p xml:id="N2C87E">
              <s xml:id="N2C87F" xml:space="preserve">Concluſio reſponſiua patet ex dictis <lb/>in concluſionibus queſtionis et in primo dubio.</s>
            </p>
            <p xml:id="N2C884">
              <s xml:id="N2C885" xml:space="preserve">Ad rationes ante oppoſitnm queſtio­<lb/>nis. </s>
              <s xml:id="N2C88A" xml:space="preserve">¶ Ad primã pꝫ rñſio ex prīo notabili q̄ſtionis.</s>
            </p>
            <p xml:id="N2C88D">
              <s xml:id="N2C88E" xml:space="preserve">Ad .2. rationē ſufficienter reſpondet <lb/>2. notabile queſtionis.</s>
            </p>
            <p xml:id="N2C893">
              <s xml:id="N2C894" xml:space="preserve">Ad tertiam rationem reſpondet ter-<lb/>tium notabile.</s>
            </p>
            <p xml:id="N2C899">
              <s xml:id="N2C89A" xml:space="preserve">Ad quartam rationem reſpondet pri­<lb/>mum dubium huius queſtionis.</s>
            </p>
            <pb chead="Inductionis gradꝰ ſūmi ↄ̨̨ſideratio." file="0277" n="277"/>
            <p xml:id="N2C8A3">
              <s xml:id="N2C8A4" xml:space="preserve">Ad quintam rationem reſpõdent con­<lb/>cluſiones queſtionis. </s>
              <s xml:id="N2C8A9" xml:space="preserve">Et ſignanter ſecunda et tertia <lb/>et hec de queſtione.</s>
            </p>
          </div>
          <div xml:id="N2C8AE" level="4" n="5" type="chapter" type-free="capitulum">
            <head xml:id="N2C8B3" xml:space="preserve">Capitulum quintum inquirens penes quid <lb/>gradus ſummi inductio ſit attendenda.</head>
            <p xml:id="N2C8B8">
              <s xml:id="N2C8B9" xml:space="preserve">QUeritur quinto. </s>
              <s xml:id="N2C8BC" xml:space="preserve">Utrum indu­<lb/>ctio gradus ſummi per aliquod ſubiecti <lb/>ſucceſſiue attendi habeat penes velocita­<lb/>tem progreſſionis ſiue partialis acquiſitionis: ita <lb/> quãto talis acquiſitio gradus ſummi fuerit per <lb/>maiorem partem in eodem tempore tanto motus <lb/>inductiõis ſiue ipſa inductio gradus ſummi (quod <lb/>idem eſt) eſt velocior.</s>
            </p>
            <p xml:id="N2C8CD">
              <s xml:id="N2C8CE" xml:space="preserve">Et arguitur primo  non. </s>
              <s xml:id="N2C8D1" xml:space="preserve">Quia tunc <lb/>ſequeretur /  velocitas inductiõis gradus ſummi <lb/>attenderetur penes maioritateꝫ ſubiecti per quod <lb/>in eodē tempore inducitur. </s>
              <s xml:id="N2C8DA" xml:space="preserve">Sed cõſequens eſt falſū / <lb/>igitur illud ex quo ſequitur. </s>
              <s xml:id="N2C8DF" xml:space="preserve">Sequela patꝫ quoniã <lb/>quanto ſubiectū eſt maius per quod in eodem tem-<lb/>pore inducitur gradus ſummns, tanto progreſſio <lb/>ſiue partialis acq̇ſitio ipſiꝰ gradꝰ ſūmi partibꝰ ſub­<lb/>iecti eſt maior. </s>
              <s xml:id="N2C8EA" xml:space="preserve">Sꝫ falſitas ↄ̨ñtꝪ ꝓbr̄: q2 tūc ſeq̄ret̄̄ qḋ <lb/>in omne vniformiṫ difforme, ad ſummū terminatū, <lb/>vniformi latitudine alteratiõis per totū alteratuꝫ <lb/>vniformiter induceretur gradꝰ ſūmꝰ. </s>
              <s xml:id="N2C8F3" xml:space="preserve">Sed cõſequēs <lb/>eſt falſū: igitur illud ex quo ſequitur. </s>
              <s xml:id="N2C8F8" xml:space="preserve">Sequela pro-<lb/>batur / q2 in ea proportione qua aliquis punctꝰ eſt <lb/>propinquior ſūmo in ea per minorem latitudinem <lb/>diſtat a ſūmo. </s>
              <s xml:id="N2C901" xml:space="preserve">vt pꝫ ex diffinitione qualitatꝪ vnifor­<lb/>miter difformis. </s>
              <s xml:id="N2C906" xml:space="preserve">et oīa pūcta eq̄uelociter alterãtur <lb/>ↄ̨tinuo: igitur in ea proportione qua aliquis pun-<lb/>ctus eſt propinquior ſūmo. </s>
              <s xml:id="N2C90D" xml:space="preserve">in ea citius ad eum ve-<lb/>niet gradus ſummus: et ſic vniformiter inducetur: <lb/>vt patet / quod fuit ꝓbãdū. </s>
              <s xml:id="N2C914" xml:space="preserve">Sed falſitas conſequen-<lb/>tis probat̄̄: quia tunc ſequeretur /  ſi duo inequa-<lb/>lia quantitatiue vniformiter difformia eadem la-<lb/>titudine omnino ad ſummū terminata eadem lati-<lb/>tudine alterationis vniformi per totum alterentur <lb/>quouſ per totum ſint ſumma: in ea proportione <lb/>qua vnum eſt minus alio quantitatiue in ea tardiꝰ <lb/>in eum inducitur gradus ſummus. </s>
              <s xml:id="N2C925" xml:space="preserve">Sed conſequēs <lb/>eſt falſu: igitur illud ex quo ſequitur. </s>
              <s xml:id="N2C92A" xml:space="preserve">Sequela pro­<lb/>batur: et ſit proportio quantitatis maioris ad quã­<lb/>titatē minoreꝫ f. </s>
              <s xml:id="N2C931" xml:space="preserve">Et arguitur ſic: eque cito illa erūt <lb/>ſumma per totum: quia extrema remiſſiora eque ci­<lb/>to erunt ſumma, cum equaliter diſtent a ſummo, et <lb/>equeuelociter continuo alterentur. </s>
              <s xml:id="N2C93A" xml:space="preserve">Et nõ citius de-<lb/>ueniet in aliquo illorū gradus ſummꝰ ad extremuꝫ <lb/>remiſſius ꝙ̄ ad oīa puncta intrinſeca: quia vnifor-<lb/>miter inducetur in vtro illorum / vt arguitum eſt: <lb/>igr̄ in f. proportiõe tardius in eodem tempore pro­<lb/>greditur per minus ſubiectū ꝙ̄ per maius: et ꝑ con­<lb/>ſeq̄ns in f. ꝓportiõe tardius inducit̄̄ gradꝰ ſūmꝰ in <lb/>minus ꝙ̄ in maius / quod fuit probandū. </s>
              <s xml:id="N2C94B" xml:space="preserve">Iã proba­<lb/>tur falſitas ↄ̨ñtis: quia tunc ſequeretur /  ſi ſint <lb/>duo vni. diffor. inequalia quantitatiue ad ſummū <lb/>terminata: et in ea proportione qua vnū eſt minus <lb/>reliquo in eadem extremū eius remiſſius ſit minus <lb/>intenſum: et alterentur per totū equali alteratione <lb/>vniformi. </s>
              <s xml:id="N2C95A" xml:space="preserve">Tunc gradus ſūmus inducetur in minus <lb/>tardius ꝙ̄ in maius in proportione compoſita ex <lb/>proportione quantitatis maioris ad quãtitatem <lb/>minoris: et intenſionis extremi remiſſioris maioris <lb/>ad intenſionē extremi remiſſioris minoris. </s>
              <s xml:id="N2C965" xml:space="preserve">ſꝫ conſe­<lb/>quens eſt falſum: igr̄ illud ex quo ſequitur. </s>
              <s xml:id="N2C96A" xml:space="preserve">Seque-<lb/>la probatur et ſit a. maius et b. minus et proportio <lb/>quãtitatis a. ad quãtitatē b. ſit f. et ſimiliter extremi <lb/>remiſſioris etc̈. </s>
              <s xml:id="N2C973" xml:space="preserve">Et arguitur ſic / eque cito erit vtrū               <cb chead="Inductionis gradꝰ ſūmi ↄ̨̨ſideratio."/>               illorū ſummū cū extremo ſuo remiſſiori / vt argutū <lb/>eſt. </s>
              <s xml:id="N2C97B" xml:space="preserve">Et ſi vtriuſ illorum extrema remiſſiora eſſent <lb/>eque intenſa in f. proportione tardius induceretur <lb/>gradus ſummꝰ in b. ꝙ̄ in a. / vt iam argutuꝫ eſt. </s>
              <s xml:id="N2C982" xml:space="preserve">Sed <lb/>modo inducetur in b. adhuc in f. proportiõe tardiꝰ <lb/>̄ tūc qm̄ extremū remiſſiꝰ in f. proportione magis <lb/>diſtat ꝙ̄ a ſūmo tunc ex caſu: igr̄ mõ in f. ꝓportione <lb/>tardius inducitur gradus ſummꝰ in b. ꝙ̄ tunc. </s>
              <s xml:id="N2C98D" xml:space="preserve">Et iã <lb/>tunc inducebatur in b. in f. proportione tardius ̄ <lb/>in a. </s>
              <s xml:id="N2C994" xml:space="preserve">Ergo modo in duplici proportione f. tardius <lb/>inducitur gradus ſūmꝰ in b. ꝙ̄ in a. </s>
              <s xml:id="N2C999" xml:space="preserve">Sed falſitas cõ­<lb/>ſequentis. </s>
              <s xml:id="N2C99E" xml:space="preserve">Patet / quia cõtinuo equales partes in-<lb/>tenſiue ipſius gradus ſummꝰ inducuntur per totū <lb/>b. ſicut per totum a. / vt patet ex caſu: igitur equeue-<lb/>lociter inducitur gra. ſū. in a. ſicut in b. et nõ tardiꝰ. <lb/></s>
              <s xml:id="N2C9A8" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi queſtio eſſet vera ſequeret̄̄ /  ſint <lb/>duo inequalia quãtitatīe vni. diffor. ad ſum. termi. <lb/></s>
              <s xml:id="N2C9AE" xml:space="preserve">Et qualis eſt proportio quãtitatis vnius ad quan-<lb/>titatē alterius: talis eſt inter exceſſum quo gra. ſū. <lb/>excedit extremū remiſſius maioris ad exceſſuꝫ quo <lb/>excedit extremū remiſſius minorꝪ: alterētur equali <lb/>altera. vniformi per totū. </s>
              <s xml:id="N2C9B9" xml:space="preserve">In vtrū illorū eque ve-<lb/>lociter inducetur gradus ſūmus. </s>
              <s xml:id="N2C9BE" xml:space="preserve">quod eſt falſum. <lb/></s>
              <s xml:id="N2C9C2" xml:space="preserve">Probatur. </s>
              <s xml:id="N2C9C5" xml:space="preserve">Et ſit a. maius et b. minus in f. ꝓportio­<lb/>ne: in eadem ꝓportione ꝑ minꝰ diſtet a ſum. </s>
              <s xml:id="N2C9CA" xml:space="preserve">Et ar­<lb/>guitur ſic. </s>
              <s xml:id="N2C9CF" xml:space="preserve">Eque cito in vtrun illorū inducetur gra­<lb/>dus ſicut in extrema eorum remiſſiora et etiam vni-<lb/>formiter / vt argutū eſt: ſꝫ in f. ꝓportione citiꝰ īducet̄̄ <lb/>ī extremū remiſſi. ipſius b. ꝙ̄ ipſiꝰ a. quia equaliter <lb/>alterantur: et in f. proportione per minus diſtat a <lb/>ſum. extremū b. ꝙ̄ a. / igitur in f. proportione citius <lb/>inducetur gra. ſum. in b. ꝙ̄ a. et b. eſt in f. ꝓportione <lb/>minus ꝙ̄ a: ergo eque velociter īduci. gra. ſum. in b. <lb/>ſicut in a. / qḋ fuit probanduꝫ. </s>
              <s xml:id="N2C9E2" xml:space="preserve">Sed falſitas cõſequē­<lb/>tis probatur / quia alteratio ad gra. ſū. nõ eſt alud <lb/>̄ inductio gra. ſum. </s>
              <s xml:id="N2C9E9" xml:space="preserve">Sed alteratio a. non eſt equa-<lb/>lis alterationi ipſius b. / vt patet ex primo capite <lb/>huius tractatꝰ. </s>
              <s xml:id="N2C9F0" xml:space="preserve">igit̄̄ inductio gra. ſum. in b. non eſt <lb/>equalis indnctioni gra. ſū. in a. / qḋ eſt oppoſi. ↄ̨ñtis</s>
            </p>
            <p xml:id="N2C9F5">
              <s xml:id="N2C9F6" xml:space="preserve">Secundo principaliter arguitur ſic. <lb/></s>
              <s xml:id="N2C9FA" xml:space="preserve">Si queſtio eſſet vera ſeq̄ret̄̄ /  aliqḋ vni. dif. ad ſū. <lb/>termina. alteretur latitudine vni. dif. extremo intē­<lb/>ſiori ſus extremū intenſius ſubiecti. </s>
              <s xml:id="N2CA01" xml:space="preserve">Nõ tardius <lb/>incipit induci gradus ſū. ꝙ̄ ſi extremo intenſiori il-<lb/>lius latitudinis vniformiter per totum alteraretur / <lb/>ſꝫ ↄ̨ſequens eſt falſum: igitur illud ex quo ſequitur. <lb/></s>
              <s xml:id="N2CA0B" xml:space="preserve">ſeq̄la ꝓbatur. </s>
              <s xml:id="N2CA0E" xml:space="preserve">Et ſit extremū intenſius alteratiõis <lb/>a. </s>
              <s xml:id="N2CA13" xml:space="preserve">Et arguit̄̄ ſic / gra. ſū. mediante illa alteratiõe inci­<lb/>pit velocius induci ꝙ̄ ſi quouis alio remiſſiori inci-<lb/>peret induci / igitur non tardius incipit induci ꝙ̄ ſi <lb/>gradu intenſiori illius altera. vnifor. ꝑ totū incipe­<lb/>peret īduci. </s>
              <s xml:id="N2CA1E" xml:space="preserve">Probat̄̄ añs: quia nullus eſt remiſſior <lb/>gradus ipſo a. quī aliqua pars illius altera. termi­<lb/>nata minor ad ipſum a. ſit illo vt conſtat: igitur me­<lb/>diante illa parte incipit gra. ſum. velociꝰ induci ̄ <lb/>ſi quouis gradu remiſſiori ipſo a. inciperet induci. <lb/></s>
              <s xml:id="N2CA2A" xml:space="preserve">quod fuit ꝓbandum. </s>
              <s xml:id="N2CA2D" xml:space="preserve">Sed iam ꝓbat̄̄ falſitas ↄ̨ñtis / <lb/>q2 tūc ſequeretur /  tardius induceretur gra. ſum. <lb/>mediante lati. illa vni. difformi in tale corpus vni. <lb/>diffor. ꝙ̄ ſi induceretur mediante extremo illius re­<lb/>miſſiori vnifor. per totū extenſo. </s>
              <s xml:id="N2CA38" xml:space="preserve">Sed ↄ̨ñs eſt falſuꝫ / <lb/>quia continuo tale corpus alteratur per totaꝫ par­<lb/>tem remiſſam intenſiori latitudine ꝙ̄ ſi remiſſiori <lb/>gradu illius latitudinis ꝑ totum alteraretur: igit̄̄ <lb/>velo. continuo inducetur gra. ſum. mediante illa la­<lb/>ti. ꝙ̄ mediante extremo eius remiſſiori. </s>
              <s xml:id="N2CA45" xml:space="preserve">quod eſt op­<lb/>poſitum ↄ̨ſequentis. </s>
              <s xml:id="N2CA4A" xml:space="preserve">Iam ꝓbatur ſequela / quia ſit <lb/>a. tale vni. diffor. alteratū lati. c. vni. diffor. / vt poni­<lb/>tur in caſu argumenti: et ſit b. oīno et cõſimile ꝑ to-               <pb chead="Inductionis gradus ſūmi ↄ̨̨ſideratio." file="0278" n="278"/>               tū alteratū extrēo rēiſſiori taĺ latitudīs vni. dif. tūc <lb/>dico /  ī a. tardiꝰ īducet̄̄ g̈dꝰ ſū: ꝙ̄ in b. / qḋ ſic ꝓbr̄ / q2 <lb/>eq̄ cito erit g̈. ſū. īductꝰ ꝑ totū a. ſic ꝑ totū b. / q2 eq̄ ci­<lb/>to erit īductꝰ ad vtriuſ extrēa rēiſſiora q̄ a prīci­<lb/>pio ſū eq̈lia: et eq̄uelociṫ ↄ̨tinuo alterãt̄̄. </s>
              <s xml:id="N2CA5E" xml:space="preserve">Et gra. ſū <lb/>ↄ̨tinuo citiꝰ deueīet ad qḋlꝫ pūctū a. ꝙ̄ ad ↄ̨ſimile <lb/>ī b. q2 qḋlꝫ tale pūctū eſt eq̄ īteſū ī a: ſic in b. et in a <lb/>ↄ̨tinuo velo. altera. / vt ↄ̨ſtat. </s>
              <s xml:id="N2CA67" xml:space="preserve">igr̄ ↄ̨tinuo mīor pars <lb/>ipſiꝰ a. reſtabit ꝑtrãſeūda ab ipſo g̈. ſū. in a ꝙ̄ in b <lb/></s>
              <s xml:id="N2CA6D" xml:space="preserve">Et eq̄ cito veīet ad finē g̈. ſū. ī vtro. </s>
              <s xml:id="N2CA70" xml:space="preserve">igr̄ tardiꝰ in­<lb/>ducet̄̄ g̈. ſū. ī a. ꝙ̄ in b. / qḋ fuit ꝓbãdū.               <anchor type="note" xlink:href="note-0278-01" xlink:label="note-0278-01a"/>               </s>
              <s xml:id="N2CA7A" xml:space="preserve">¶ Dices et bñ <lb/>ↄ̨cedēdo ſeq̄lã vt bñ ꝓbat argu. </s>
              <s xml:id="N2CA7F" xml:space="preserve">Et negãdo falſitatē <lb/>ↄ̨ñtis. </s>
              <s xml:id="N2CA84" xml:space="preserve">Et ad ꝓbationē negãdo ſequelã. </s>
              <s xml:id="N2CA87" xml:space="preserve">īmo q2 per <lb/>totū ꝑ qḋ altera. </s>
              <s xml:id="N2CA8C" xml:space="preserve">dēto pūcto extrīſeco. </s>
              <s xml:id="N2CA8F" xml:space="preserve">altera a. <lb/>velociꝰ ꝙ̄ b. / iõ tardiꝰ inducet̄̄ in eo gra ſū. ̄. in b.</s>
            </p>
            <div xml:id="N2CA94" level="5" n="1" type="float">
              <note position="left" xlink:href="note-0278-01a" xlink:label="note-0278-01" xml:id="N2CA98" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2CA9E">
              <s xml:id="N2CA9F" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
              <s xml:id="N2CAA2" xml:space="preserve">Q2 tūc ſe­<lb/>q̄ret̄̄ /  ſi a. alteret̄̄ <lb/>lati. vni. di. ab .8. vſ ad .4. tardiꝰ in q̊lꝫ totali tꝑe <lb/>terīto ad finē tꝑis īduceret̄̄ ī a. g̈. ſū. ꝙ̄ īduceret̄̄ ī ta­<lb/>li tꝑe ſi a. alṫaret̄̄ lati. vni. di. ab: 6. vſ ad .4. </s>
              <s xml:id="N2CAAD" xml:space="preserve">Sed <lb/>ↄ̨ñs ē flm̄ / igr̄ illḋ ex q̊ ſeq̇t̄̄ </s>
              <s xml:id="N2CAB2" xml:space="preserve">Seq̄la. </s>
              <s xml:id="N2CAB5" xml:space="preserve">ſatꝪ ptꝫ ex deducti­<lb/>one argumēti. </s>
              <s xml:id="N2CABA" xml:space="preserve">Sꝫ fĺitas ↄ̨ñtis ar̄. </s>
              <s xml:id="N2CABD" xml:space="preserve">q2 tūc ſeq̄ret̄̄ /  ſi <lb/>eſſēt īfinita oīo ↄ̨ſiĺr diſpoſita ſiċ a. </s>
              <s xml:id="N2CAC2" xml:space="preserve">Et ṗmū īciꝑet <lb/>alṫari lati. vni. di. ab 8. vſ ad .4. </s>
              <s xml:id="N2CAC7" xml:space="preserve">Et .2. lati. ab: 16 <lb/>vſ ad 4. </s>
              <s xml:id="N2CACC" xml:space="preserve">Et .3. lati. ab .32. vſ ad 4. / et ſic ↄ̨ñr dupli­<lb/>cãdo ſꝑ extremū ītēſiꝰ manēte ſꝑ eodē extrēo rēiſſi­<lb/>ore ſꝰ extremū rēiſſiꝰ ſubiecti. </s>
              <s xml:id="N2CAD3" xml:space="preserve">Infinitū tarde īdu­<lb/>cet̄̄ g̈. ſū. ī aliqḋ iſtoꝝ </s>
              <s xml:id="N2CAD8" xml:space="preserve">Sꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄ <lb/></s>
              <s xml:id="N2CADC" xml:space="preserve">Seq̈la ꝓbr̄ / q2 īmediate pꝰ h° īfinitū mīor erit ꝑs <lb/>rēiſſa alicuiꝰ illoꝝ ꝙ̄ ipſiꝰ b. ꝑ qḋ vni. īducit̄̄ g̈. ſū: <lb/></s>
              <s xml:id="N2CAE2" xml:space="preserve">Et nõ citiꝰ deueniet g̈. ſū. ad finē alicuꝰ illaꝝ ꝙ̄ ad fi­<lb/>nē ipſiꝰ b. / g̊ infinitū tarde īducet̄̄ g̈. ſū. ī aliqḋ illoꝝ <lb/>̄ ī b. / et ꝑ ↄ̨ñs īfinitū tarde īducet̄̄ ī aliqḋ illoꝝ </s>
              <s xml:id="N2CAE9" xml:space="preserve">(Cū ī <lb/>b. īducat̄̄ vīfor̄ṫ) / qḋ fuit ꝓbãdū </s>
              <s xml:id="N2CAEE" xml:space="preserve">Sꝫ fĺitas ↄ̨ñtꝪ ꝓba­<lb/>tur / q2 tūc ſeq̄ret̄̄ /  ītēſio alṫatiõis ꝑ partē remiſſã <lb/>per quam debet induci gra. ſum. eſſet impedimēto <lb/>inductioni gra. ſū. / quod apparet manifeſte falſuꝫ</s>
            </p>
            <p xml:id="N2CAF7">
              <s xml:id="N2CAF8" xml:space="preserve">Tertio prīcipalr̄ ar̄ ſic </s>
              <s xml:id="N2CAFB" xml:space="preserve">Si q̄ſtio eſſet <lb/>a ſeq̄ret̄̄ /  mediãte īfinita lati. alṫa niſi diffor̄e <lb/>ſubiectū finitū terīatū ad ſū. vni. ↄ̨tinuo īduceret̄̄ g̈ <lb/>ſū </s>
              <s xml:id="N2CB04" xml:space="preserve">Sꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄ </s>
              <s xml:id="N2CB07" xml:space="preserve">Seq̄la ꝓbr̄: ſigno <lb/>a pedale diuiſū ꝑ ꝑtas ꝓportõales ꝓportõe dupla <lb/>et ṗma ſit vni. di. a ſū. vſ ad 4. </s>
              <s xml:id="N2CB0E" xml:space="preserve">Et ita intēſa et oīo <lb/>diſpoſita ſit q̄lꝫ ſeq̄ns </s>
              <s xml:id="N2CB13" xml:space="preserve">Et ī ṗma ꝑte ꝓportõali vniꝰ <lb/>hore alṫret̄̄ ṗma ꝑs ꝓportiõalĺ a alṫa vni. q̈ vni. īdu­<lb/>cat̄̄ g̈. ſū. ꝑ illã adeq̈te et ī .2. ꝑte tꝑis alṫet̄̄ 2. ꝑs ꝓpor­<lb/>tiõaĺ ipſiꝰ a. ꝑ totū adeq̈te alṫa vni. ī duplo maiori <lb/>et ī .3. ꝑte tꝑis alṫre. 3. ꝑs ipſiꝰ a. alṫa: ī duplo maiori <lb/>̄ .2. ſꝑ vni. et totã ꝑtē extēſã: et ſic ↄ̨ñr, ſꝑ duplãdo <lb/>alṫa°nē </s>
              <s xml:id="N2CB22" xml:space="preserve">Quo poſito ar̄ ſic / ī ṗma ꝑte ꝓpor°ali tꝑis <lb/>ꝓportiõe dupla, ṗma ꝑs ꝓpor°aĺ ipſiꝰ a. edē pro-<lb/>portõe vni. efficiet̄̄ ſūma </s>
              <s xml:id="N2CB29" xml:space="preserve">Et ī .2. tꝑis .2. ipſiꝰ a ēt effi­<lb/>ciet̄̄ ſūma vni </s>
              <s xml:id="N2CB2E" xml:space="preserve">Et ī 3. tꝑis .3. ip̄iꝰ a. / et ſic ↄ̨des;ñr / igr̄ ꝑ ip̄m <lb/>a. ↄ̨tinuo īducet̄̄ g̈. ſū ↄ̨ña pꝫ et ꝓbr̄ añs. </s>
              <s xml:id="N2CB33" xml:space="preserve">Nã ī ṗmaꝫ <lb/>īducit̄̄ g̈. ſū. ī ṗma ꝑte tꝑis vt poīt caſꝰ et q2 ī 2. ꝑte <lb/>tꝑis 2. ꝑs ꝓpor°aĺ ip̄iꝰ a. alṫat̄̄ alṫa°ne ī du. maio­<lb/>re ꝑ totū vni. iõ ip̄a ī .2. ꝑte tꝑis fiet ſū. vni </s>
              <s xml:id="N2CB3C" xml:space="preserve">Nã ſi p̄-<lb/>ciſe alṫet̄̄ g̈du q̊ ṗma ip̄a ī tãto tꝑe ī quãto ṗma effi­<lb/>ceret̄̄ ſū. / ſꝫ mõ alṫat̄̄ ī duplo maiori alṫa°ne. </s>
              <s xml:id="N2CB43" xml:space="preserve">iõ ī du­<lb/>plo mīori tꝑe efficiet̄̄ ſū. / et ꝑ ↄ̨ñs ī .2. ꝑte ꝓportiõali <lb/>tꝑis. </s>
              <s xml:id="N2CB4A" xml:space="preserve">Et ſic argu. ē de .3. et ḋ q̈uis alia: igr̄. </s>
              <s xml:id="N2CB4D" xml:space="preserve">Sꝫ iã ꝓbo <lb/>fĺitatē ↄ̨ñtꝪ / q2 tūc ſeq̄ret̄̄ /  b. ē oīo ↄ̨ſiĺr dipoſitū et <lb/>ēt eq̈le ip̄i a. et a. īfinita alṫa°ne alṫabr̄ / vt iã dictū ē <lb/></s>
              <s xml:id="N2CB55" xml:space="preserve">Et ēt deductꝪ aliis motibꝰ. </s>
              <s xml:id="N2CB58" xml:space="preserve">et tñ ī b. in īfinitū tarde <lb/>īducet̄̄ g̈. ſū. et ī a. vni. / vt dictū &amp;etilde; </s>
              <s xml:id="N2CB5D" xml:space="preserve">Sꝫ ↄ̨ñs ē flm̄ / q2 vtra­<lb/> alṫa°ē īfinita / g̊ ꝑ nullã illaꝝ d3 g̈. ſū. ī īfinitū tarḋ <lb/>īduci </s>
              <s xml:id="N2CB64" xml:space="preserve">Sꝫ ꝓbo ſeq̄lã et ſi a tale q̈le iã poſitū ē et eo° ī <lb/>illḋ īducat̄̄ g̈. ſū. / vt iã dictū ē: et ſit b. oīo eq̈le ↄ̨ſiĺ. </s>
              <s xml:id="N2CB69" xml:space="preserve">di­               <cb chead="Inductionis gradus ſūmi ↄ̨̨ſideratio."/>               ſpoſitū ſiċ a. et qñ ṗma ꝑs ꝓportõaĺ a. ꝓpor°ne du­<lb/>pla effict̄̄ ſūma. </s>
              <s xml:id="N2CB71" xml:space="preserve">efficiãt̄̄. </s>
              <s xml:id="N2CB74" xml:space="preserve">et ṗme ip̄iꝰ b. puta ṗma et .2 <lb/>ſõme et qñ .2. ip̄iꝰ a. due ſeq̄ntes īmediate .2. ip̄iꝰ b. / et <lb/>ſic ↄ̨ñr ꝓcedēdo ↄ̨tīuo ī b. ꝑ ꝑtes ꝓpor°ales ꝓpor°ne <lb/>q̈drupla ſꝑ em̄ .2. ꝑtes īmediate ꝓportõe dupla ſūt <lb/>vna ꝑs ꝓportõe q̈drupla / vt pꝫ ex .2 ꝑte </s>
              <s xml:id="N2CB7F" xml:space="preserve">Quo poſito <lb/>auxilio eoꝝ q̄ dicta ſṫ .3.c.2. tractatꝰ ſeq̇t̄̄ qḋ īferre ī­<lb/>tēdebã. </s>
              <s xml:id="N2CB86" xml:space="preserve">Dices et bñ ↄ̨cedēdõ /  īfert̄̄: et negãdo fĺita­<lb/>tē ↄ̨ñtꝪ et cū ꝓbr̄ ↄ̨cedo qḋ īfert̄̄ nec illḋ ē īcõueniēs ſꝫ <lb/>veꝝ. </s>
              <s xml:id="N2CB8D" xml:space="preserve">Et cū ꝓbr̄ /  nõ: q2 vtra illaꝝ alṫa°nū ē īfīta <lb/>dico īſeq̄do Cal. ↄ̨cedo añs: et negãdo ↄ̨ñaꝫ q2 coex­<lb/>tēſio ꝑtibꝰ tꝑis variat effectū motꝰ / vt pꝫ ex 3.c p̄alle</s>
            </p>
            <p xml:id="N2CB94">
              <s xml:id="N2CB95" xml:space="preserve">Sꝫ ↄ̨̨tra. </s>
              <s xml:id="N2CB98" xml:space="preserve">Q2 tūc ſeq̄ret̄̄ /  in a. pedale <lb/>vni. dif. terīatū ad ſū. īduceret̄̄ g̈. ſū. vni. mediãte īfini­<lb/>ta lati. alṫatõs ꝑ totū extēſa extrēo īfini° ſꝰ extre­<lb/>mū ip̄iꝰ a. terīto </s>
              <s xml:id="N2CBA1" xml:space="preserve">Sꝫ ↄ̨ñs vr̄ flm̄ / igr̄ illḋ ex q̊ ſeq̇t̄̄ </s>
              <s xml:id="N2CBA4" xml:space="preserve">Se­<lb/>q̄la ꝓbr̄ / et ſit ī a. vni. dif. ad ſū. terīatū et capio lati. <lb/>q̈ q̇lꝫ pūctꝰ nõ ſūmꝰ excedit̄̄ a ſūmo et diuido q̈lꝫ il­<lb/>laꝝ ꝑ ſuas ꝑtes ꝓpor°ales ꝓportõe dupla / et pono /  <lb/>ī ea ꝓportõe q̇lꝫ pūctꝰ nõ ſūmꝰ acq̇rat lati. ꝑ quã di­<lb/>ſtat a ſūmo ī mīori tꝑe īq̈ taĺ pūctꝰ magꝪ duīuta ſū <lb/></s>
              <s xml:id="N2CBB2" xml:space="preserve">Sꝫ tēpꝰ illḋ diuidat̄̄ ꝑ ꝑtes ꝓpor°nales ꝓportõe q̈­<lb/>drupla et ī q̈lꝫ tali ꝑte acq̇rat pūctꝰ de illi lati. vnã <lb/>ꝑtē corrñdētē. </s>
              <s xml:id="N2CBB9" xml:space="preserve">Quo poſito ſeq̇t̄̄ facile illḋ / qḋ fuit ī­<lb/>ferēdū auxilio 3.c. p̄allegati. </s>
              <s xml:id="N2CBBE" xml:space="preserve">ↄ̨tīuo em̄ / vt pꝫ ex caſu <lb/>vniformiter inducet̄̄ gru. ſū. </s>
              <s xml:id="N2CBC3" xml:space="preserve">Et tñ ↄ̨tīuo alteratio <lb/>terminabr̄ ad extremū infinitū ꝓpo. gra. ſū. / igitur</s>
            </p>
            <p xml:id="N2CBC8">
              <s xml:id="N2CBC9" xml:space="preserve">Quarto prīcipaliṫ ar̄ ſic </s>
              <s xml:id="N2CBCC" xml:space="preserve">Seq̄ret̄̄ / vt iã <lb/>dictū ē īductõeꝫ g̈ ſū. debē attēdi penes ſubcm̄ ꝑ qḋ <lb/>īducit̄̄ g̈: ſū. / ſꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄ ſeq̄la pꝫ et <lb/>fĺitas ↄ̨ñtꝪ ꝓbr̄ et pono / ꝙ̄ ꝑ .a pedale vni. di. terīatū <lb/>ad ſū. īducat̄̄ lati. alṫatiõs vni. ꝑ totū: et cū h° rarefi­<lb/>at a ad duplū ī gö ſꝰ g̈. ſū. q̇eſcēte extrēo eiꝰ rēiſſio­<lb/>ri / qḋ fiat ſū. ī hõ. </s>
              <s xml:id="N2CBDB" xml:space="preserve">Quo poſito ar̄ ſic: ſi vĺocitas īdu­<lb/>ctiõs g̈. ſū. dēret attēdi penes ſubiectū ī qḋ īducit̄̄ g̈. <lb/>ſū. / tūc ſeq̄ret̄̄ /  ī a ī caſu poſito ī duplo vĺociꝰ īdu­<lb/>ceret̄̄ g̈. ſū: ꝙ̄ ſi ñ rarefiēt / ſꝫ ↄ̨ña ē flm / igr̄ illḋ ex q̊ ſe­<lb/>q̇t̄̄ ſeq̄la ꝓbr̄ / q2 a ī fine erit ꝑ totū ſū. / vt pꝫ ex caſu et <lb/>erit ī duplo maiꝰ ꝙ̄ ſi ñ fuiſſꝫ rarefa° ex caſu / igr̄ ꝑ ī <lb/>duplo maiꝰ ſbcm̄ ꝓgrediebat̄̄ g̈. ſū. ꝙ̄ ſi ñ fuiſſꝫ fctã <lb/>rarefa° et ꝑ ↄ̨ñs ī duplo vĺociꝰ īducit̄̄ g̈. ſū. ꝙ̄ ſi ñ ra­<lb/>refiēt / qḋ fuit ꝓbãdū. </s>
              <s xml:id="N2CBEE" xml:space="preserve">iã ꝓbr̄ fĺitas ↄ̨ñtꝪ / q2 ſi h° eſſet <lb/>veꝝ ſeq̄ret̄̄ /  ī caſu mõeret̄̄ g̈. ſū. ſiue eiꝰ ī dn° p̄ciſe ꝑ <lb/>pedale et tñ ī īfinitū vĺociṫ īduceret̄̄: ſꝫ ↄ̨ñs ē fĺ3. </s>
              <s xml:id="N2CBF5" xml:space="preserve">igr̄ <lb/>illḋ q̊ ſeq̇t̄̄ </s>
              <s xml:id="N2CBFA" xml:space="preserve">Seq̄la ꝓbr̄: et pono /  ī a. pedale vni. di. <lb/>terīato ad ſū. īducat̄̄ g̈. ſū. et nū̄ rarefiat ꝑs aliq̈ q̊­<lb/>uſ fuerit ſū. ſꝫ. cū fuerit ſū. ī īfinitū rarefiat </s>
              <s xml:id="N2CC01" xml:space="preserve">Quo <lb/>põito mãifeſtū ē  g̈. ſū. ñ mouet̄̄ niſi ad pedalē di-<lb/>ſtãtiã et tñ ī īfinitū velĺr īducit̄̄: qm̄ ī fine ſbm̄ eiꝰ qḋ <lb/>ē īductꝰ īfinitū vĺ ſaltē ī īfinitū magnū fuit ī hõ / igr̄ <lb/>ī illa hõ ī īfinitū velĺr īducit̄̄ g̈. ſū </s>
              <s xml:id="N2CC0C" xml:space="preserve">Et tñ pedalē diſtã­<lb/>tiã p̄ciſe ꝑtrãſit.               <anchor type="note" xlink:href="note-0278-02" xlink:label="note-0278-02a"/>               </s>
              <s xml:id="N2CC16" xml:space="preserve">¶ Dices et bñ ↄ̨cedēdo ſeq̄lã. </s>
              <s xml:id="N2CC19" xml:space="preserve">et ne-<lb/>gãdo falcitatē ↄ̨ñtꝪ: et ad ꝓbationē adīſſo caſu ne­<lb/>gãdo ſeq̄lã et rõ ē: q2 velocitas īductiõis gra. ſum. <lb/>in ſubiecto q̇eſcēte motu rarefactionis et ↄ̨dēſatio­<lb/>nis deb3 attēdi penes ſubiecttuꝫ ī quod īducit̄̄ ita <lb/> in ea ꝓportione in qua eſt maius ceteris paribꝰ <lb/>in ea in illud velociꝰ gra. ſum. īducit̄̄. </s>
              <s xml:id="N2CC28" xml:space="preserve">Sꝫ occurren­<lb/>te aliq̊ motu deb3 attēdi penes ſpaciuꝫ fixus quod <lb/>deſcribit talis g̈. ſum. cū īducit̄̄ / vt dictū eſt ſuperiꝰ <lb/>2. tractatu. c.4. de velocitate motus mixti vide ibi.</s>
            </p>
            <div xml:id="N2CC31" level="5" n="2" type="float">
              <note position="right" xlink:href="note-0278-02a" xlink:label="note-0278-02" xml:id="N2CC35" xml:space="preserve">Dicitur.</note>
            </div>
            <p xml:id="N2CC3B">
              <s xml:id="N2CC3C" xml:space="preserve">Sed cõtra </s>
              <s xml:id="N2CC3F" xml:space="preserve">Q2 ſi illa ſolutio eſſet bo-<lb/>na ſequeret̄̄ ꝙ̄ quãdocū ſubiectum rarefit ſus <lb/>gradum ſū. cõtinuo gradꝰ ſūmꝰ tardiꝰ inducitur <lb/>̄ ſi nõ rarefieret ſubiectū: ſed cõſequens eſt falſuꝫ / <lb/>igitur illud ex quo ſequit̄̄: ſequela probatur et po-<lb/>no /  a. pedale vnifor. diffor. terminū ad ſūmū               <pb chead="Inductionis gradus ſūmi ↄ̨̨ſideratio." file="0279" n="279"/>               per quod in horas inducetur gradꝰ ſūmꝰ rarefiat <lb/>ſus gradū ſūmū tardiꝰ tñ rarefiat m oēm eius <lb/>pūctū ꝙ̄ g̈dꝰ ſūmꝰ īducat̄̄ q̇eſcēte rēiſſiori extremo. <lb/></s>
              <s xml:id="N2CC56" xml:space="preserve">Tūc manifeſtū ē /  ↄ̨tinuo pūcta in q̇bꝰ erit grg̈dꝰ <lb/>ſūmꝰ magꝪ diſtabūt ab extremo q̇eſcēte ꝙ̄ ſi nõ eēt <lb/>rarefactio: g̊ continuo inter ipſa et punctum a quo <lb/>incipit induci gradus ſummꝰ erit minꝰ de ſpacio <lb/>fixo ꝙ̄ ſi nõ rareficeret: et penes tale ſpacium cõmē­<lb/>ſuranda eſt inductionis gradꝰ ſūmi velocitas / vt <lb/>dicit ſolutio: ergo quãdocun ſubiectū rarefit -<lb/>ſus gradus ſūmū continuo gradus ſummus tar-<lb/>dius inducitur ꝙ̄ ſi nõ rarefieret. </s>
              <s xml:id="N2CC69" xml:space="preserve">Iã ꝓbatur falſi-<lb/>tas ↄ̨ſequētis: et pono /  a. alteret̄̄ per totã partē <lb/>nõ ſummã alteratione vniformi: et arguo ſic: eque <lb/>cito erit gra. ſū. ad punctuꝫ ſiue extremuꝫ remiſſiꝰ <lb/>quieſcens ſiċ ſi nõ rarefieret ſubiectum / vt conſtat: <lb/>et nõ citius deueniet ad extremū remiſſiꝰ ꝙ̄ ad oīa <lb/>puncta intrinſeca ſimul: igitur eque cito a. erit ſū-<lb/>mū ac ſi nõ rarefieret: et per cõſequens nõ tradius <lb/>inducetur gradꝰ ſummꝰ ꝙ̄ ſi nõ rarefieret / quod eſt <lb/>opppſitum illati.               <anchor type="note" xlink:href="note-0279-01" xlink:label="note-0279-01a"/>               </s>
              <s xml:id="N2CC83" xml:space="preserve">¶ Et cõfiirmatur / q2 ſi velocitas <lb/>inductionis gradꝰ ſummꝰ deberet attendi penes <lb/>ſubiectū per quod adequate inducitur in eodem tē­<lb/>pore deductis aliis motibus: ſequeretur /  a. et b. <lb/>nūc ſunt oīno cõſimilia quãtitatiue et qualitatiue <lb/>vnifor. diffor. termīata ad ſum: et incipiūt alterari <lb/>cõſimili latitudine vniformi. </s>
              <s xml:id="N2CC92" xml:space="preserve">Et tamē ī duplo aut <lb/>in maiori proportione inducetur gradꝰ ſummus <lb/>velociꝰ in a. ꝙ̄ in b. ceteris aliis motibus deductis <lb/></s>
              <s xml:id="N2CC9A" xml:space="preserve">Sed cõſequens videt̄̄ impoſſibile: igit̄̄ illud ex quo <lb/>ſequitur </s>
              <s xml:id="N2CC9F" xml:space="preserve">Seq̄la probatur et pono /  ſint a. et b. oī­<lb/>no ſimilia / vt ponitur: et inducat̄̄ pertibiliṫ latitu-<lb/>do equalis alterationis vniformis per a. et per b. <lb/>eo mõ quo inducitur reſiſtētia in mediū nõ reſiſtēs <lb/>et ī vtro progrediatur vniformiter cõtinuo quo <lb/>ad partes ſubiecti in duplo tamē velociꝰ cõtinuo <lb/>progrediatur per a. ꝙ̄ per b. </s>
              <s xml:id="N2CCAE" xml:space="preserve">Quo poſito manife-<lb/>ſtū eſt ꝙ̄ in duplo citius quilibet pūctus a. efficiet̄̄ <lb/>ſummus ꝙ̄ correſpõdens punctꝰ in b. cum ad illū <lb/>in duplo citius deueniat alteratio et illa puncta <lb/>ſint cõſimilia in a. et b. / igitur in duplo velocius <lb/>inducetur gradus ſummus in a. ꝙ̄ in b. </s>
              <s xml:id="N2CCBB" xml:space="preserve">Et tamen <lb/>a. et b. ſunt equalia oīo etc̈. / et alterantur conſimili <lb/>latitudine vniformi etc̈. / quod fuit inferendum.</s>
            </p>
            <div xml:id="N2CCC2" level="5" n="3" type="float">
              <note position="left" xlink:href="note-0279-01a" xlink:label="note-0279-01" xml:id="N2CCC6" xml:space="preserve">ↄ̨firma°.</note>
            </div>
            <p xml:id="N2CCCC">
              <s xml:id="N2CCCD" xml:space="preserve">In appoſitum ar̄ ſic. </s>
              <s xml:id="N2CCD0" xml:space="preserve">Quia inductio <lb/>gradus ſummi nõ eſt niſi quedã particĺis progreſ­<lb/>ſio per partes ſubiecti: ergo ſequitur /  quãto pro­<lb/>greſſio eſt maior tanto inductio gradus ſummi eſt <lb/>velocior: tanto autem progreſſio eſt maior quãto <lb/>fit per maiorem partem ſubiecti vel per maiꝰ ſub-<lb/>iectum. </s>
              <s xml:id="N2CCDF" xml:space="preserve">igitur tanto inductio gradꝰ ſummi eſt ve-<lb/>locior quanto fit per maius ſubiectum.</s>
            </p>
            <p xml:id="N2CCE4">
              <s xml:id="N2CCE5" xml:space="preserve">Huius queſtiõis talis eſt ordo primo <lb/>ponuntur notabilia. </s>
              <s xml:id="N2CCEA" xml:space="preserve">Secundo concluſiones. </s>
              <s xml:id="N2CCED" xml:space="preserve">Ter-<lb/>tio ſoluentur rationes ante oppoſitum.</s>
            </p>
            <p xml:id="N2CCF2">
              <s xml:id="N2CCF3" xml:space="preserve">Notandū eſt.               <anchor type="note" xlink:href="note-0279-02" xlink:label="note-0279-02a"/>               </s>
              <s xml:id="N2CCFB" xml:space="preserve">Primo / quid eſt gradus <lb/>ſūmꝰ et q̇d eiꝰ īductio. </s>
              <s xml:id="N2CD00" xml:space="preserve">Uñ ꝓprie gradꝰ ſūmꝰ eſt in­<lb/>tenſiſſima q̈litas naturalr̄ in ſua ſp̄e poſſibilis q̈ <lb/>ꝓduct̄̄ a. agēs ceſſat agere ad pūctū ad quē ipſa ē <lb/>ꝓducta </s>
              <s xml:id="N2CD09" xml:space="preserve">Utrū aūt ſit dabilis gradꝰ ſūmꝰ ſimpĺr di­<lb/>co /  illḋ eſt mihi dubiū. </s>
              <s xml:id="N2CD0E" xml:space="preserve">dicit tñ doctor ſubtilis in <lb/>3.  ſic. </s>
              <s xml:id="N2CD13" xml:space="preserve">Inductio aūt gra. ſū. diffinit̄̄ a. Calcuĺ: iſto <lb/>mõ.               <anchor type="note" xlink:href="note-0279-03" xlink:label="note-0279-03a"/>               </s>
              <s xml:id="N2CD1D" xml:space="preserve">Inductio gradꝰ ſūmꝰ eſt ꝓgreſſio illiꝰ gradꝰ <lb/>ſūmi ſiue ꝑtialis acq̇ſitio eiꝰ q̊ ad ꝑtes ſubiecti. </s>
              <s xml:id="N2CD22" xml:space="preserve">vt <lb/>ſi g̈dꝰ octauꝰ q̇ ſignet̄̄ ſūmus ꝓgrediat̄̄ ſiue īducat̄̄ <lb/>ꝑtibilr̄ quo ad ꝑtes ſubiecti: ita  ad omnē pūctū <lb/>ꝓpinquiꝰ extremo a q̊ īcipit induci citiꝰ ꝓducat̄̄ ̄ <lb/>ad remotiꝰ ac ſi eſſet vnꝰ punctꝰ mouēs ſupra idē <lb/>ſubiectū illud ſubiectū ꝑtialr̄ ꝑtrãſiens. </s>
              <s xml:id="N2CD2F" xml:space="preserve">Talis pro­<lb/>greſſio ſiue a ſiue ymagīaris dr̄ īductio gra. ſū.               <cb chead="Inductionis gradus ſūmi ↄ̨̨ſideratio."/>               </s>
              <s xml:id="N2CD37" xml:space="preserve">Hoc mõ declarat hãc diffinitionē calculator ī prī-<lb/>cipio c. huiꝰ materie.               <anchor type="note" xlink:href="note-0279-04" xlink:label="note-0279-04a"/>               </s>
              <s xml:id="N2CD41" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  q̈uis ī aīam <lb/>poſſit ꝓduci gra. ſūmꝰ </s>
              <s xml:id="N2CD46" xml:space="preserve">nõ tñ põt ꝓduci ī aīaꝫ gra. <lb/>ſūmꝰ. </s>
              <s xml:id="N2CD4B" xml:space="preserve">pꝫ / q2 ibi nõ põt eē ꝑtibilꝪ acq̇ſitio q̊ od ſub­<lb/>iectū               <anchor type="note" xlink:href="note-0279-05" xlink:label="note-0279-05a"/>               </s>
              <s xml:id="N2CD55" xml:space="preserve">¶ Sequit̄̄ .2. /  ſi aliqḋ vniforme alteret̄̄ lati-<lb/>tudīe vni. ꝑ totū ita  eq̄ cito ſit ꝑ totū gradꝰ ſū. <lb/>talis alteratio ad gra. ſū: ſiue acq̇ſitio gra. ſū. nõ <lb/>eſt īductio gra. ſūmi. </s>
              <s xml:id="N2CD5E" xml:space="preserve">pꝫ ex diffinitiõe               <anchor type="note" xlink:href="note-0279-06" xlink:label="note-0279-06a"/>               </s>
              <s xml:id="N2CD66" xml:space="preserve">¶ Sequit̄̄ .3 / <lb/> ꝑ nullã alteratione vn. vniformiṫ extēſã ꝑ ali-<lb/>qḋ vniforme ꝑ totū: v3 aliquo° īduci gra. ſū. ad <lb/>vnū pūctū ꝙ̄ ad alteꝝ / qḋ eſt ↄ̈ rõnē īductiõis. </s>
              <s xml:id="N2CD6F" xml:space="preserve">Hoc <lb/>tñ nõ obſtãte põt ꝑ alṫationē vniformē īduci gra. <lb/>ſū. ſubiectū vni. dū mõ alṫatio ꝓgrediat̄̄ ꝑtibiĺr q̊ <lb/>ad ſubiectū: ſꝫ tūc illq̈ totale ſubiectū īcipit eē dif-<lb/>for̄e / vt ↄ̨ſtat </s>
              <s xml:id="N2CD7A" xml:space="preserve">Et ī ꝓpoſito iſto terīo vtimur ꝑ ītē°ne</s>
            </p>
            <div xml:id="N2CD7D" level="5" n="4" type="float">
              <note position="left" xlink:href="note-0279-02a" xlink:label="note-0279-02" xml:id="N2CD81" xml:space="preserve">q̈d g̈. ſū.</note>
              <note position="left" xlink:href="note-0279-03a" xlink:label="note-0279-03" xml:id="N2CD87" xml:space="preserve">q̇d īduc° <lb/>g̈dꝰ ſūmꝰ</note>
              <note position="right" xlink:href="note-0279-04a" xlink:label="note-0279-04" xml:id="N2CD8F" xml:space="preserve">Correĺ.</note>
              <note position="right" xlink:href="note-0279-05a" xlink:label="note-0279-05" xml:id="N2CD95" xml:space="preserve">2. correĺ.</note>
              <note position="right" xlink:href="note-0279-06a" xlink:label="note-0279-06" xml:id="N2CD9B" xml:space="preserve">3. correĺ.</note>
            </div>
            <p xml:id="N2CDA1">
              <s xml:id="N2CDA2" xml:space="preserve">Notãdū eſt. </s>
              <s xml:id="N2CDA5" xml:space="preserve">Scḋo /  gradꝰ ſummꝰ <lb/>aliqñ īducit̄̄ in ſubiectū ab aliis motibꝰ alienū: ali­<lb/>qñ o īducit̄̄ in ſubectū qḋ localr̄ mouet̄̄ vt viſū eſt <lb/>in argumētꝪ. </s>
              <s xml:id="N2CDAE" xml:space="preserve">aliqñ aūt ī ſubiectū qḋ rarefit aut cõ­<lb/>dēſat̄̄. </s>
              <s xml:id="N2CDB3" xml:space="preserve">Et hoc duplr̄ aut extremo remiſſiori, aut nõ <lb/>g̈. q̇eſcēte a rarefactiõe, aut extrēo ītēſiori. </s>
              <s xml:id="N2CDB8" xml:space="preserve">Itē qñ <lb/>q̇eſcit extremū rēiſſiꝰ aut ītēſiꝰ mouēt̄̄ velociꝰ ꝑ ra­<lb/>refactionē ꝙ̄ gra. ſū. īcipiat īduci: aut eq̄uelociter <lb/>aut tardiꝰ. </s>
              <s xml:id="N2CDC1" xml:space="preserve">Itē cū extremū remiſſiꝰ mouet̄̄: et ītēſiꝰ <lb/>q̇eſcit, aut rarefit ſcḋm ſe totū: aut rarefit p̄ciſe m <lb/>partē remiſſã. </s>
              <s xml:id="N2CDC8" xml:space="preserve">multꝪ aliis modis põt ymagīari g̈. <lb/>ſūmꝰ īduci ī ſubiectū aliis motibꝰ mutatū. </s>
              <s xml:id="N2CDCD" xml:space="preserve">Et ſiĺr <lb/>dicas de ↄ̨dēſatiõe. </s>
              <s xml:id="N2CDD2" xml:space="preserve">Ad hñdã aūt vĺr notitiã veloci­<lb/>tatis īductiõis gra. ſūmi. </s>
              <s xml:id="N2CDD7" xml:space="preserve">Pono aliq̈s ꝓportiões <lb/>               <anchor type="note" xlink:href="note-0279-07" xlink:label="note-0279-07a"/>               </s>
              <s xml:id="N2CDE1" xml:space="preserve">¶ Prīa ꝓpõ velocitas īductiõis gra. ſū nõ d3 vĺr <lb/>attēdi penes manitudinē ſubiecti per qḋ īducitur <lb/></s>
              <s xml:id="N2CDE7" xml:space="preserve">Probat̄̄ / q2 obſtat rarefactio et ↄ̨dēſatio / vt ptꝫ ex <lb/>4. argumēto ãte oppoſitū               <anchor type="note" xlink:href="note-0279-08" xlink:label="note-0279-08a"/>               </s>
              <s xml:id="N2CDF1" xml:space="preserve">¶ Scḋa ꝓpõ. </s>
              <s xml:id="N2CDF4" xml:space="preserve">Uelocitas <lb/>īductiõis gra. ſū. nõ eſt vĺr attēdēda penes ſpaciū <lb/>fixū īterceptū in fine īductiõis īter pūctū a q̊ incipit <lb/>īduci g̈. ſū. et pūctū ad quē terīat̄̄ īductio gra. ſū. / pꝫ <lb/>hec clare ex deductiõe argumēti 4. obſtat em̄ motꝰ <lb/>localis               <anchor type="note" xlink:href="note-0279-09" xlink:label="note-0279-09a"/>               </s>
              <s xml:id="N2CE06" xml:space="preserve">¶ Tertia ꝓpõ. </s>
              <s xml:id="N2CE09" xml:space="preserve">Uelocitas īductiõis gra. ſū. <lb/>nõ d3 vĺr attēdi penes motū imagīariū pūcti exi-<lb/>ſtētis ↄ̨tinuo cū gra. ſū. </s>
              <s xml:id="N2CE10" xml:space="preserve">Ptꝫ etiã hec ꝓpõ ex p̄alle-<lb/>grato argumēto               <anchor type="note" xlink:href="note-0279-10" xlink:label="note-0279-10a"/>               </s>
              <s xml:id="N2CE1A" xml:space="preserve">¶ Quarta ꝓpõ. </s>
              <s xml:id="N2CE1D" xml:space="preserve">Uelocitas īducti­<lb/>onis g̈. ſū. ī ſubiectū: nec rarefactū nec ↄ̨dēſatū ſiue <lb/>moueat̄̄ localr̄ ſiue nõ: ſꝑ attēdenda eſt penes ma-<lb/>gnitudinē ſubiecti. </s>
              <s xml:id="N2CE26" xml:space="preserve">pꝫ / q2 nõ apparet alter modꝰ <lb/>cognoſcēde velocitatꝪ. </s>
              <s xml:id="N2CE2B" xml:space="preserve">īductiõis gra. ſū. ī tali caſu <lb/>               <anchor type="note" xlink:href="note-0279-11" xlink:label="note-0279-11a"/>               </s>
              <s xml:id="N2CE35" xml:space="preserve">¶ Quīta ꝓpõ </s>
              <s xml:id="N2CE38" xml:space="preserve">Uelocitas īductiõis g̈. ſū. cū ſubiectū <lb/>rarefit aut ↄ̨dēſat̄̄ gra. ſū. ↄ̨tīuo manēte ī eodē pū­<lb/>cto ſpacii fixi d3 attēdi penes ſpaciū īterceptū īter <lb/>tale pūctū ſpacii fixi ī q̊ ↄ̨tinuo eſt gra. ſū. et pūctū <lb/>fixū in q̊ erat pūctꝰ ſubiecti in quē mõ ṗmo inducit̄̄ <lb/>exēplū / vt poſito /  a. in qḋ īducit̄̄ g̈. ſū. in prīcipio <lb/>fit bipedale: et rarefiat ſus gra. ſū. et īductio g̈. ſū. <lb/>maneat in eodē pūcto fixo: tūc dico /  cū g̈. ſū. ṗmo <lb/>fuerit īductꝰ ꝑ totū ṗmū pedale qḋ tã tūc erit maiꝰ <lb/>tã velociṫ fuit īductꝰ g̈. cū. ac ſi pedale q̇euiſſet a mo <lb/>in rarefactiõis.               <anchor type="note" xlink:href="note-0279-12" xlink:label="note-0279-12a"/>               </s>
              <s xml:id="N2CE54" xml:space="preserve">¶ Sexta ꝓpõ. </s>
              <s xml:id="N2CE57" xml:space="preserve">Uelocitas īductiõis <lb/>g̈. ſū. cū. g̈. ſū. mouet̄̄ in ordine ad ſpaciū fixū motu <lb/>o vĺ imagīario et ſubiectū rarefit vĺ ↄ̨dēſat̄̄ d3 at­<lb/>tēdi penes ſpaciū fixū qḋ deſcribit. </s>
              <s xml:id="N2CE60" xml:space="preserve">exemplū habes <lb/>in argumēto .4.               <anchor type="note" xlink:href="note-0279-13" xlink:label="note-0279-13a"/>               </s>
              <s xml:id="N2CE6A" xml:space="preserve">¶ Ex hoc ſeq̇t̄̄ /  in caſu p̄cedēti cõ­<lb/>cĺonis in toto tꝑe q̊ gra. ſū. īducit̄̄ ꝑ totū gra. ſū. eq̄­<lb/>uelociṫ īducit̄̄ ac ſi q̇eſceret a rarefactiõe. </s>
              <s xml:id="N2CE71" xml:space="preserve">et ī q̈lꝫ ꝑte <lb/>illiꝰ tꝑis terīata ad prīcipiū totiꝰ tꝑis īducit̄̄ tar-<lb/>diꝰ et ī q̈lꝫ terīata ad finē īducit̄̄ velociꝰ </s>
              <s xml:id="N2CE78" xml:space="preserve">Hoc correĺ. <lb/>pꝫ bñ ↄ̨ſiderati vltimã replicã .4. argumēti ãte op­<lb/>poſitū. </s>
              <s xml:id="N2CE7F" xml:space="preserve">Et hec ſūt dicta cõforīter ad opinionē quã <lb/>recitat et īpugnare nititur calcu. quaſi ī principio <lb/>2. c. de inducti. g̈. ſ. </s>
              <s xml:id="N2CE86" xml:space="preserve">Sed tenēdo modum dicendi cal­<lb/>cu. pono .7. ꝓpoſitionem               <anchor type="note" xlink:href="note-0279-14" xlink:label="note-0279-14a"/>               </s>
              <s xml:id="N2CE90" xml:space="preserve">¶ Septīa propoſitio. </s>
              <s xml:id="N2CE93" xml:space="preserve">Ue-               <pb chead="Inductionis gradus ſūmi cõſideratio." file="0280" n="280"/>               locitas inducti. g. ſ. cum ſubiectum rarefit aut condē-<lb/>ſatur debet attendi penes totam quantitatem ſubie­<lb/>cti dempta illa quam acquirunt aut deperdunt par­<lb/>tes poſt̄ ſunt ſūme. </s>
              <s xml:id="N2CEA1" xml:space="preserve">vt ſi totū erat pedale in princi-<lb/>pio: et in fine manet tripedale: et partes poſt̄ erant <lb/>ſumme acquiſiuerunt pedale preciſe tūc velocitas in­<lb/>ductionis debet attendi penes bipedale preciſe. </s>
              <s xml:id="N2CEAA" xml:space="preserve">Ui-<lb/>deas cal. in .2. ca. de inductione grad. ſum. </s>
              <s xml:id="N2CEAF" xml:space="preserve">Et hic mo­<lb/>dus cal. michi placat: quãuis alter poſſit ſuſtineri</s>
            </p>
            <div xml:id="N2CEB4" level="5" n="5" type="float">
              <note position="right" xlink:href="note-0279-07a" xlink:label="note-0279-07" xml:id="N2CEB8" xml:space="preserve">ṗma ꝓpõ</note>
              <note position="right" xlink:href="note-0279-08a" xlink:label="note-0279-08" xml:id="N2CEBE" xml:space="preserve">2. porpõ.</note>
              <note position="right" xlink:href="note-0279-09a" xlink:label="note-0279-09" xml:id="N2CEC4" xml:space="preserve">3. propõ.</note>
              <note position="right" xlink:href="note-0279-10a" xlink:label="note-0279-10" xml:id="N2CECA" xml:space="preserve">4. propõ</note>
              <note position="right" xlink:href="note-0279-11a" xlink:label="note-0279-11" xml:id="N2CED0" xml:space="preserve">5. propõ.</note>
              <note position="right" xlink:href="note-0279-12a" xlink:label="note-0279-12" xml:id="N2CED6" xml:space="preserve">6. propõ.</note>
              <note position="right" xlink:href="note-0279-13a" xlink:label="note-0279-13" xml:id="N2CEDC" xml:space="preserve">Correĺ.</note>
              <note position="right" xlink:href="note-0279-14a" xlink:label="note-0279-14" xml:id="N2CEE2" xml:space="preserve">7. propõ</note>
            </div>
            <p xml:id="N2CEE8">
              <s xml:id="N2CEE9" xml:space="preserve">Notandum eſt tertio /  cum gradus <lb/>ſummus inducitur per duo vnifor. difformia ter-<lb/>minata ad ſum. mediante alteratione vniformi per <lb/>totum extenſa illa poſſunt multipliciter ſe habere. <lb/></s>
              <s xml:id="N2CEF3" xml:space="preserve">quia aut illa ſunt equalia in quantitate et quali-<lb/>tate omnino, aūt in quantitate tãtum, aut inequa­<lb/>lia in qualitate et quãtitate ſiĺ. </s>
              <s xml:id="N2CEFA" xml:space="preserve">¶ Si ſunt inequa-<lb/>lia in quantitate et qualitate ſimul: hoc contingit <lb/>dupliciter quia aut maius excedit in quantitate et <lb/>qualitate, aut in quantitate ſolum. </s>
              <s xml:id="N2CF03" xml:space="preserve">Et hic exceſſus <lb/>venit ſumendus extremo remiſſiori / vt conſtat. </s>
              <s xml:id="N2CF08" xml:space="preserve">¶ Si <lb/>autem illa ſunt equalia in quanti. et quali. aut al-<lb/>terantur per totum equali alteratione aut non. <lb/></s>
              <s xml:id="N2CF10" xml:space="preserve">¶ Si autem ſunt equalia quantitatiue tantum aut <lb/>alterantur alteratione equali. </s>
              <s xml:id="N2CF15" xml:space="preserve">aut inequali. </s>
              <s xml:id="N2CF18" xml:space="preserve">¶ Si <lb/>inequali aut intenſius alteratur maiori, aut mino-<lb/>ri. </s>
              <s xml:id="N2CF1F" xml:space="preserve">Si minori aut minori in ea proportione qua ſe <lb/>habent exceſſus quibꝰ gra. ſum. excedit extrema re-<lb/>miſſiora. </s>
              <s xml:id="N2CF26" xml:space="preserve">aut in maiori, aut in minori. </s>
              <s xml:id="N2CF29" xml:space="preserve">¶ Si vero <lb/>ſunt equalia in qualitantum. </s>
              <s xml:id="N2CF2E" xml:space="preserve">aut alterantur equa­<lb/>li alteratione, aut non. </s>
              <s xml:id="N2CF33" xml:space="preserve">¶ Sed ſi ſint inequalia in <lb/>quãti. et quali. et maiꝰ vtro modo excedit aut al­<lb/>terantur equali alteratione, aut non. </s>
              <s xml:id="N2CF3A" xml:space="preserve">Si non, aut <lb/>maius alteratur maiori aut minori. </s>
              <s xml:id="N2CF3F" xml:space="preserve">Si minori aut <lb/>in ea proportiõe minori qua ſe habet exceſſus quo <lb/>gra. ſum. excedit extremum remiſſioris ad exceſſum <lb/>quo excedit extremum remiſſius intenſioris aut in <lb/>maiori, aut in minori. </s>
              <s xml:id="N2CF4A" xml:space="preserve">¶ Si autem ſunt inequalia <lb/>vtro modo et minus excedit in qualitate tunc aut <lb/>equali alteratione alterantur aut non. </s>
              <s xml:id="N2CF51" xml:space="preserve">Si non aut <lb/>minus alteratur maiori, aut minori: </s>
              <s xml:id="N2CF56" xml:space="preserve">Si minori aut <lb/>in ea proportione minori qua ſe habet exceſſus q̊ <lb/>gradus ſum. excedit extremum remiſſioris ad exceſ­<lb/>ſum quo excedit extremū remiſſius intenſioris aut <lb/>in maiori aut in minori. </s>
              <s xml:id="N2CF61" xml:space="preserve">Exempla nõ poſui gratia <lb/>breuitatis. </s>
              <s xml:id="N2CF66" xml:space="preserve">Hac diuiſione conſummata pono ali­<lb/>quas concluſiones.</s>
            </p>
            <note position="left" xml:id="N2CF6B" xml:space="preserve">2. pars q̄­<lb/>ſtionis.</note>
            <p xml:id="N2CF71">
              <s xml:id="N2CF72" xml:space="preserve">Prima concluſio. </s>
              <s xml:id="N2CF75" xml:space="preserve">Si aliquod vni. dif­<lb/>for. terminatum ad ſummum alteretur latitudine <lb/>alterationis vniformi per totum in ipſum vnifor-<lb/>miter continuo inducitur gradus ſummus. </s>
              <s xml:id="N2CF7E" xml:space="preserve">hec con­<lb/>cluſio patet ex primo argumento ante oppoſitum</s>
            </p>
            <p xml:id="N2CF83">
              <s xml:id="N2CF84" xml:space="preserve">Secunda concluſio. </s>
              <s xml:id="N2CF87" xml:space="preserve">Si duo vni. dif­<lb/>for. terminata ad ſum. equalia omnino in quanti. et <lb/>quali. alterentur eadem latitu. alterationis vnifor­<lb/>mi per totum in ipſa equeuelociter continuo indu-<lb/>citur gradus ſumus. </s>
              <s xml:id="N2CF92" xml:space="preserve">Probatur / quia equeuelociter <lb/>continuo gradus ſum. deueniet ad punctum vnius <lb/>ſicut ad punctum correſpondens alterius et pūcta <lb/>correſpondentia equaliter diſtant a puncto initia­<lb/>tiuo motus / vt conſtat / quia ſūt equalia / igitur eque­<lb/>uelociter gradus ſummus in ipſa inducetur.</s>
            </p>
            <p xml:id="N2CF9F">
              <s xml:id="N2CFA0" xml:space="preserve">Tertia concluſio. </s>
              <s xml:id="N2CFA3" xml:space="preserve">Si in caſu prioris <lb/>concluſionis vnū illorum alteretur alteratione vni. <lb/>per totum minori ſiue remiſſiori ꝙ̄ aliud: in ea pro­<lb/>portione qua alteratio vnius excedit olterationem <lb/>alterius in ea velocius continuo inducitur in ipſū <lb/>gradus ſūmus. </s>
              <s xml:id="N2CFB0" xml:space="preserve">Probatur / et ſit proportio altera-<lb/>tiouum f. et a. alteratū velocius et b. tardius. </s>
              <s xml:id="N2CFB5" xml:space="preserve">Et ar­               <cb chead="Inductionis gradus ſūmi cõſideratio."/>               guo ſic / ad punctum extremum ipſius a. in f. propor­<lb/>tione citius deueniet gra. ſum. ꝙ̄ ad correſpondēs <lb/>in b. quia illa puncta extrema equaliter diſtant a <lb/>ſummo, et illa diſtantia in .f. proportione citius a-<lb/>quiritur in extremo ipſius a. ꝙ̄ ipſius b. cum altera­<lb/>tio continuo ſit in f. proportione maior in extremo <lb/>ipſius a. ꝙ̄ ipſius b. ex caſu. </s>
              <s xml:id="N2CFC7" xml:space="preserve">igitur cõtinuo in f. pro-<lb/>portiõe velociꝰ inducitur gradus ſūmus in a. ꝙ̄ in <lb/>b. / quod fuit probandū </s>
              <s xml:id="N2CFCE" xml:space="preserve">Patet conſequentia / quia in <lb/>vtrū illoꝝ vniformiter continuo inducit̄̄ gra. ſū. <lb/>ex prima concluſione.</s>
            </p>
            <p xml:id="N2CFD5">
              <s xml:id="N2CFD6" xml:space="preserve">Quarta cõcluſio. </s>
              <s xml:id="N2CFD9" xml:space="preserve">Si equalia in quã-<lb/>titate tm̄ vni, diff. termi. ad ſū. alterētur equali al-<lb/>ratiõe vniformi ꝑ totū per intenſius illoꝝ ↄ̨tinuo <lb/>velocius inducit̄̄ gra. ſū in ea ꝓportiõe qua ſe hñt <lb/>exceſſus q̇bus gradus ſū. excedit extrema remiſſio-<lb/>ra illoꝝ. </s>
              <s xml:id="N2CFE6" xml:space="preserve">Probat̄̄ / ſit a. intēſius et b. remiſſius: et ſit f. <lb/>ꝓportio exceſſus quo gra. ſū. excedit extremū remiſ­<lb/>ſius b. ad exceſſū quo excedit extremū remiſſiꝰ ip̄iꝰ <lb/>a. </s>
              <s xml:id="N2CFEF" xml:space="preserve">Et arguit̄̄ ſic / in .f. ꝓportiõe gra. ſū. citius erit ad <lb/>extremū ip̄iꝰ a. ꝙ̄ ip̄ius b. cū alteratlo ad illa extre­<lb/>ma ſit equalis: et in .f. ꝓportione minꝰ diſtat extre-<lb/>mū .a. a ſū. ꝙ̄ extremū ipſiꝰ b. / ergo in .f. ꝓportiõe ve­<lb/>locius ↄ̨tinuo inducitur gra. ſū. in a. ꝙ̄ in b. / qḋ fuit <lb/>ꝓbãdū. </s>
              <s xml:id="N2CFFC" xml:space="preserve">pꝫ ↄ̨ña / q2 ex prima concluſio gradus ſū. in <lb/>vtrum illorum continuo vnifor. inducitur.</s>
            </p>
            <p xml:id="N2D001">
              <s xml:id="N2D002" xml:space="preserve">Quinta concluſio. </s>
              <s xml:id="N2D005" xml:space="preserve">Si in caſu quar. <lb/>conclu. intenſius alteretur maiori alteratione ꝙ̄ re-<lb/>miſſius. </s>
              <s xml:id="N2D00C" xml:space="preserve">Tunc in ipſum velocius inducitur gra. ſum. <lb/>̄ in aliud in proportione compoſita ex proportione <lb/>exceſſum quibus gra. ſum. excedit extrema remiſſio-<lb/>ra i lorum: et proportione alterationum. </s>
              <s xml:id="N2D015" xml:space="preserve">Ponatur <lb/>prior hypoteſis. </s>
              <s xml:id="N2D01A" xml:space="preserve">et ſit g. proportio alterationum: et al­<lb/>teretur a maiori altera. </s>
              <s xml:id="N2D01F" xml:space="preserve">Et arguitur ſic / ſi alteraren-<lb/>tur equali alteratione in f. proportione gra. ſum. in­<lb/>duceretur velocius in a. ꝙ̄ in b. ex priori conclu. </s>
              <s xml:id="N2D026" xml:space="preserve">Sed <lb/>adhuc modo in a. in g. proportione velocius īducitur <lb/>gradus ſummꝰ ꝙ̄ tunc: igitur modo in a. inducit̄̄ gra­<lb/>dus ſummi velociuſ in b. in proportione compoſi-<lb/>ta ex f. et g. / quod fuit probandum. </s>
              <s xml:id="N2D031" xml:space="preserve">Probatur minor / <lb/>quia in g. proportione quilꝫ punctus velocius altera­<lb/>tur ꝙ̄ tunc: et equaliter a principio alteratiõis diſtat <lb/>a ſūma ſicut tunc: et vniformi. continuo in a. inducitur <lb/>gradus ſummꝰ et ſimiliter in b. ex prima conſiõe / igi-<lb/>tur modo in g. proportione velocius inducitur gra-<lb/>dus ſummꝰ.</s>
            </p>
            <p xml:id="N2D040">
              <s xml:id="N2D041" xml:space="preserve">Sexta concluſio. </s>
              <s xml:id="N2D044" xml:space="preserve">Si predicta a.b. al­<lb/>terentur vniformi alteratione per totum. </s>
              <s xml:id="N2D049" xml:space="preserve">et b. in f. <lb/>proportione maiori alteratione alteretur: equeuelo-<lb/>citer in ipſa inducitur gradus ſummꝰ. </s>
              <s xml:id="N2D050" xml:space="preserve">Probatur q̇a <lb/>ſi a. et b. equali alteratione alterarentur in b.f. ꝓpor­<lb/>tione tardius induceretur gradus ſummꝰ ꝙ̄ in a. ex <lb/>quarta concluſione. </s>
              <s xml:id="N2D059" xml:space="preserve">Sed modo in f. proportione ve-<lb/>locius inducitur in b. ꝙ̄ tunc: ergo modo equeueloci­<lb/>ter inducitur gradus ſummꝰ in b. ſicut in a. </s>
              <s xml:id="N2D060" xml:space="preserve">Similis <lb/>minor in precedenti concluſione arguta eſt.</s>
            </p>
            <p xml:id="N2D065">
              <s xml:id="N2D066" xml:space="preserve">Septima concluſio. </s>
              <s xml:id="N2D069" xml:space="preserve">Si predicta a.b. <lb/>alterentur alte. vni. per totum et b. alteretur in maio­<lb/>ri proportione ꝙ̄ f. maiori alteratione ꝙ̄ a. tunc in b. <lb/>inducitur velocius gradus ſummꝰ in ea proportione <lb/>per quam proportio alterationum excedit f. propor­<lb/>tionem. </s>
              <s xml:id="N2D076" xml:space="preserve">Et ſi b. alteretur maiori alteratione que ta-<lb/>men ſit in minori proportione maior ꝙ̄ ſit f. propor-<lb/>tio: tunc in b. tardius inducitur gradus ſummꝰ ꝙ̄ in <lb/>a. in proportione per quã proportio f. excedit ꝓpor­<lb/>tionem illarum alterationum. </s>
              <s xml:id="N2D081" xml:space="preserve">Hoc ex iam dictis au-<lb/>xiliantibus hiis que dicta ſunt in tertia concluſiõe .2. <lb/>tractatus ſuam ſortitur oſtenſionem.</s>
            </p>
            <pb chead="Inductio gradus ſūmi cõſideratio." file="0281" n="281"/>
            <p xml:id="N2D08C">
              <s xml:id="N2D08D" xml:space="preserve">Octaua concluſio. </s>
              <s xml:id="N2D090" xml:space="preserve">Si duo equalia. <lb/></s>
              <s xml:id="N2D094" xml:space="preserve">in quali. tantū termi. ad ſū. alterentur equali lati-<lb/>tu. alterationis vniformi per totū: velocius conti-<lb/>nuo inducitur gra. ſū. in maiori in ea proportione <lb/>qua eſt maius. </s>
              <s xml:id="N2D09D" xml:space="preserve">Sit a. maius b. in f. proportione cuꝫ <lb/>ceteris poſitis in concluſione. </s>
              <s xml:id="N2D0A2" xml:space="preserve">Et arguitur ſic / eque <lb/>cito a. et b. erunt ſumma. </s>
              <s xml:id="N2D0A7" xml:space="preserve">et a. eſt in f. proportione <lb/>maius ipſo b. ex hypotheſi: et vniformiter gradus <lb/>ſū. inducitur continuo in a. et in b. / ergo in f. propor­<lb/>tiõe velocius inducitur in a. ꝙ̄ in b. </s>
              <s xml:id="N2D0B0" xml:space="preserve">Patet conſequē­<lb/>tia ex .4. ꝓpõe. </s>
              <s xml:id="N2D0B5" xml:space="preserve">et ↄ̨tinuo notabilis huius c. et tn f. <lb/>proportionc a. eſt maius b. / igitur conclu. vera. </s>
              <s xml:id="N2D0BA" xml:space="preserve">Sed <lb/> eque cito erūt ſūma a. et b. probatur / a quia eque <lb/>cito inducitur in extrema ipſorum a.b. gra. ſū. cum <lb/>equaliter diſtent a ſū. et equaliter continuo per idē <lb/>tempus alterentur. </s>
              <s xml:id="N2D0C5" xml:space="preserve">igitur eque cito / a. et b. erunt ſū­<lb/>ma patet conſequentia. </s>
              <s xml:id="N2D0CA" xml:space="preserve">quia eque cito / erunt ſū. cuꝫ <lb/>ſuis extremis remiſſioribus et non ante: vt conſtat <lb/>nec poſt cum continuo inducatur vniformiter par-<lb/>tibiliter ex prima conclu.               <anchor type="note" xlink:href="note-0281-01" xlink:label="note-0281-01a"/>               </s>
              <s xml:id="N2D0D8" xml:space="preserve">¶ Ex hac conclu. ſequitur <lb/>primo /  ſi a. in caſu conclu. alteretur maiori alte-<lb/>ratione ꝙ̄ b. in ipſum velocius inducitur gra. ſum. <lb/>̄ in b. in proportione compoſita ex proportione <lb/>quantitatis a. ad quantitatē b. et alterationis ip̄iꝰ <lb/>a. ad alterationem ipſius b. </s>
              <s xml:id="N2D0E5" xml:space="preserve">Probatur et ſit g. pro­<lb/>portio alterationum et h. compoſita ex f. et g. / et ar-<lb/>guo ſic / ſi a. alteraretur equeuelociter cum b. in f. ꝓ­<lb/>portione velocius inducetur gra. ſum. in a. ꝙ̄ in b. / <lb/>vt patet ex hac .8. conclu. </s>
              <s xml:id="N2D0F0" xml:space="preserve">Sed modo in g. propor-<lb/>tione velocius adhuc inducitur gra. ſum. in a. ꝙ̄ tūc / <lb/>vt patet ex .3. conclu. / ergo modo in duabus propor­<lb/>tionibus v3 g. et f. velocius inducitur gradus ſum. <lb/>in a. ꝙ̄ in b. </s>
              <s xml:id="N2D0FB" xml:space="preserve">Et g. et f. ſunt h. / igitur in h. proportione <lb/>velocius inducitur gra. ſum. in a. ꝙ̄ in b. </s>
              <s xml:id="N2D100" xml:space="preserve">Et ſic patꝫ <lb/>corre.               <anchor type="note" xlink:href="note-0281-02" xlink:label="note-0281-02a"/>               </s>
              <s xml:id="N2D10A" xml:space="preserve">¶ Sequitur .2. / ſi  in caſu predicte conclu. b. al­<lb/>teratur alteratione maiori ꝙ̄ illa qua alteratur ī ea <lb/>proportione qua a. eſt maius b. </s>
              <s xml:id="N2D111" xml:space="preserve">Tunc equeuelociter <lb/>continuo inducitur gra. ſum. in b. ſicut in a. </s>
              <s xml:id="N2D116" xml:space="preserve">Probat̄̄ / <lb/>quia ſi a. et b. equali alteratione alterarentur: in b. ī <lb/>f. ꝓportione continuo tardius induceretur gra. ſum. <lb/>̄ in a. ex hac octaua conclu. </s>
              <s xml:id="N2D11F" xml:space="preserve">Sed modo in f. propor-<lb/>tione inducitur gra. ſum. velocius in b. ꝙ̄ tunc ex .3. cõ­<lb/>clu. / ergo equeuelociter modo inducitur in b. ſicut in <lb/>a. / quod fuit probandum.               <anchor type="note" xlink:href="note-0281-03" xlink:label="note-0281-03a"/>               </s>
              <s xml:id="N2D12D" xml:space="preserve">¶ Sequitur .3. /  ſi in caſu cõ­<lb/>cluſionis b. alteretur velocius a. in maiori ꝓportiõe <lb/>̄ f. </s>
              <s xml:id="N2D134" xml:space="preserve">Tunc gra. ſum. velius inducitur in b. ꝙ̄ in a. in <lb/>ea proportione per quam ꝓportio alterationum ex-<lb/>cedit ꝓportionē f. quantitatum. </s>
              <s xml:id="N2D13B" xml:space="preserve">Et ſi b. maiori altera­<lb/>tione alteretur ꝙ̄ a. que alteratio ipſius b. ſit maior <lb/>altera. ipſius a. in mīori ꝓportione ꝙ̄ ſit f. </s>
              <s xml:id="N2D142" xml:space="preserve">Tūc gra. <lb/>ſum. tardius inducitur in b. ꝙ̄ in a. in ꝓportione per <lb/>quam proportio quantitatum f. excedit proportionē <lb/>alterationum. </s>
              <s xml:id="N2D14B" xml:space="preserve">Hoc corre. facile ex priori auxiliante .3. <lb/>conclu. demonſtrationem admittit.</s>
            </p>
            <div xml:id="N2D150" level="5" n="6" type="float">
              <note position="left" xlink:href="note-0281-01a" xlink:label="note-0281-01" xml:id="N2D154" xml:space="preserve">1. corre.</note>
              <note position="left" xlink:href="note-0281-02a" xlink:label="note-0281-02" xml:id="N2D15A" xml:space="preserve">1. Corre.</note>
              <note position="left" xlink:href="note-0281-03a" xlink:label="note-0281-03" xml:id="N2D160" xml:space="preserve">3. Corre.</note>
            </div>
            <p xml:id="N2D166">
              <s xml:id="N2D167" xml:space="preserve">Nona concluſio. </s>
              <s xml:id="N2D16A" xml:space="preserve">Si duo vni. diff. ad <lb/>ſum. termi. in equalia in quãti. et qualitate et maius <lb/>vtro modo excedit minꝰ: et equali alteratiõe ꝑ totū <lb/>alterant̄̄ </s>
              <s xml:id="N2D173" xml:space="preserve">Tūc in maius velocius īducitur ↄ̨tinuo gra. <lb/>ſum. ꝙ̄ in minus in ꝓportione cõpoſita ex ꝓportione <lb/>exceſſuū quibus gradus ſum. excedit extrema illorū <lb/>remiſſa et ex ꝓportione quanti. maioris ad quanti. <lb/>minoris. </s>
              <s xml:id="N2D17E" xml:space="preserve">probatur. </s>
              <s xml:id="N2D181" xml:space="preserve">Sit a. maius in f. proportione ip­<lb/>ſo b. </s>
              <s xml:id="N2D186" xml:space="preserve">Et exceſſus quo gra. ſum. excedit extremuꝫ b. ad <lb/>exceſſum quo excedit extremū ipſius a. ſit g. propor-<lb/>tio. </s>
              <s xml:id="N2D18D" xml:space="preserve">Et cõpoſita ex hiis ſit h. </s>
              <s xml:id="N2D190" xml:space="preserve">Tūc dico /  gradus ſū. ī <lb/>h. proportione velocius inducitur continuo in a. ꝙ̄ in <lb/>b. </s>
              <s xml:id="N2D197" xml:space="preserve">Probatur / quia ſi a. eſſet equale ī qualitate ip̄i .b.               <cb chead="Inductio gradus ſūmi cõſideratio."/>               in f. proportione in ipſum velocius induceretur gra-<lb/>dus ſum. ꝙ̄ in b. ex .8. conclu. </s>
              <s xml:id="N2D19F" xml:space="preserve">Sed modo in g. ꝓporti-<lb/>one exceſſuū inducitur adhuc velocius in ipſum a. ̄ <lb/>tunc ex .4. conclu. / ergo modo in ꝓportionibus f. et g. <lb/>ſimul velocius inducitur gra. ſum. in a. ꝙ̄ in b. </s>
              <s xml:id="N2D1A8" xml:space="preserve">Et f. et <lb/>g. ſunt h. proportio ex hypoteſi: igitur in h. proporti­<lb/>one gradus ſum. velocius inducitur cõtinuo in a. ꝙ̄ ī <lb/>b. / quod fuit probandum.               <anchor type="note" xlink:href="note-0281-04" xlink:label="note-0281-04a"/>               </s>
              <s xml:id="N2D1B6" xml:space="preserve">¶ Sequitur .1. /  ſi a. cum to­<lb/>to reſiduo caſus .9. conclu: alteretur ītenſiori altera-<lb/>tione vni. per totum ꝙ̄ b. </s>
              <s xml:id="N2D1BD" xml:space="preserve">Tunc in ipſum a. velocius <lb/>continuo inducitur gradus ſūmus in proportione cõ­<lb/>poſita ex ꝓportione quantitatum, et proportione ex­<lb/>ceſſum quibus gradus ſum. excedit extrema illorum <lb/>remiſſa: et ex proportione alterationum. </s>
              <s xml:id="N2D1C8" xml:space="preserve">Probatur <lb/></s>
              <s xml:id="N2D1CC" xml:space="preserve">Sit proportio alterationum e. cum reſiduo hypote-<lb/>ſis conclu. 9. et compoſita ex e. et f. et g. ſit h. </s>
              <s xml:id="N2D1D1" xml:space="preserve">Tunc di­<lb/>co /  gradus ſummus cõtinuo inducitur velocius in <lb/>a. ꝙ̄ in b. in h. proportione. </s>
              <s xml:id="N2D1D8" xml:space="preserve">Quod ſic oſtenditur / quia <lb/>ſi a alteretur equali alteratiõe cum ipſo b. in ipſum <lb/>a. velocius inducerētur continuo gradus ſummus ̄ <lb/>in b. in ꝓportione cõpoſita ex f. et g. ex 9. conclu. </s>
              <s xml:id="N2D1E1" xml:space="preserve">Sed <lb/>modo adhuc velocius iuducitur ꝙ̄ tunc in e. propor-<lb/>tione alterationum ex .3. conclu. / ergo modo velocius <lb/>inducitur gra. ſum. in a. ꝙ̄ in b. ꝓportionibus e.f.g. <lb/></s>
              <s xml:id="N2D1EB" xml:space="preserve">Et proportione e.f.g. ſunt h. ꝓportio: igitur modo <lb/>gra. ſum. velocius continuo inducitur non a. ꝙ̄ in b. in <lb/>h. proportione. </s>
              <s xml:id="N2D1F2" xml:space="preserve">quod fuit probãdum.               <anchor type="note" xlink:href="note-0281-05" xlink:label="note-0281-05a"/>               </s>
              <s xml:id="N2D1FA" xml:space="preserve">¶ Sequitur .2. / <lb/> ſi cum toto reſiduo caſus conclu. 9 .b. alteretur al-<lb/>teratiõe vni. per totum maiori ꝙ̄ alteratio ipſius a. <lb/>in proportione compoſita ex ꝓportione quanti. et ex­<lb/>ceſſum quibus gra. ſum. excedit etc̈. </s>
              <s xml:id="N2D205" xml:space="preserve">Tunc in b. equeue­<lb/>lociter continuo inducitur gra. ſum. ſicut in ipſum a. <lb/></s>
              <s xml:id="N2D20B" xml:space="preserve">Probatur / quia ſi a. et b. equali alteratione alterarē­<lb/>tur: gra. ſum. induceretur tardius in b. ꝙ̄ in a. in pro-<lb/>portione h. compoſita ex proportione quanti. et exceſ­<lb/>ſuū. </s>
              <s xml:id="N2D214" xml:space="preserve">vt patet ex .9. conclu. </s>
              <s xml:id="N2D217" xml:space="preserve">Sed modo in h. proportio­<lb/>ne intenſiori alteratione alteratur per totum ipſum <lb/>b. ꝙ̄ tunc: ergo modo in h. proportione velocius indu­<lb/>citur gra. ſum. in b. ꝙ̄ tunc / vt pꝫ ex .3. conclu. </s>
              <s xml:id="N2D220" xml:space="preserve">Et tam <lb/>velociter inducitur in ipſum a. / ergo in b. eque velociṫ <lb/>continuo inducitur gradus ſum. ſicuit in ipſum a. / qḋ <lb/>fuit probandum               <anchor type="note" xlink:href="note-0281-06" xlink:label="note-0281-06a"/>               </s>
              <s xml:id="N2D22E" xml:space="preserve">¶ Sequitur .3. /  ſi cum toto reſiduo <lb/>caſus b. alteretur alteratione vni. maiori alteratione <lb/>̄ a. in maiore proportione ꝙ̄ ſit ꝓportio compoſita <lb/>ex ꝓportione exceſſuū et quantitatum que eſt g. </s>
              <s xml:id="N2D237" xml:space="preserve">Tūc <lb/>in b. velocius continuo inducitur gra. ſum. ꝙ̄ in a. ī ea <lb/>proportione per quam ꝓportio alterationum exce-<lb/>dit ꝓportionem h. </s>
              <s xml:id="N2D240" xml:space="preserve">Et ſi talis ꝓportio qua alteratio <lb/>b. excedit alterationem ipſius a. ſit minor ꝙ̄ ꝓpor-<lb/>tio h. </s>
              <s xml:id="N2D247" xml:space="preserve">Tunc tardius inducetur gra ſum. in b. ꝙ̄ in a. <lb/>in ꝓportione per quam ꝓportio h excedit proportio­<lb/>nem alterationum. </s>
              <s xml:id="N2D24E" xml:space="preserve">Hoc facile patet ex priori auxi-<lb/>lio .3. conclu.</s>
            </p>
            <div xml:id="N2D253" level="5" n="7" type="float">
              <note position="right" xlink:href="note-0281-04a" xlink:label="note-0281-04" xml:id="N2D257" xml:space="preserve">1. Corre.</note>
              <note position="right" xlink:href="note-0281-05a" xlink:label="note-0281-05" xml:id="N2D25D" xml:space="preserve">2. Corre.</note>
              <note position="right" xlink:href="note-0281-06a" xlink:label="note-0281-06" xml:id="N2D263" xml:space="preserve">3. Corre.</note>
            </div>
            <p xml:id="N2D269">
              <s xml:id="N2D26A" xml:space="preserve">Decima cõcluſio. </s>
              <s xml:id="N2D26D" xml:space="preserve">Si ſint duo īequa-<lb/>lia vtro modo vni diff. termi. ad ſū. </s>
              <s xml:id="N2D272" xml:space="preserve">Et minus exce­<lb/>dit ī qualitate ipſuꝫ maius: </s>
              <s xml:id="N2D277" xml:space="preserve">Et equali alteratione in <lb/>qua vnum eſt maius in ea extremum remiſſius illius <lb/>per maiorem latitudinem diſtat a ſū. ꝙ̄ extremum re­<lb/>miſſius ipſius minoris. </s>
              <s xml:id="N2D280" xml:space="preserve">Tunc per illa continuo eque­<lb/>uelociter inducitur gra. ſū. </s>
              <s xml:id="N2D285" xml:space="preserve">Probatur. </s>
              <s xml:id="N2D288" xml:space="preserve">Sit propor-<lb/>tio exceſſuum .f. que etiam eſt proportio quantitatuꝫ <lb/>a. maioris ad .b. minus. </s>
              <s xml:id="N2D28F" xml:space="preserve">Et arguo ſic / in .f. proportio­<lb/>ne citius gra. ſū. veniet ad extremum remiſſius ipſius <lb/>b. ꝙ̄ ipſius .a. cum illa extrema equeuelociter cõtinuo <lb/>alterentur: et extremum remiſſius ipſius .b. per mino­<lb/>rem latitudinem in .f. proportione diſtat a ſū. ex caſu <lb/>̄ extremum remiſſius ipſius .a. </s>
              <s xml:id="N2D29C" xml:space="preserve">Et vniformiṫ in vtrū­               <pb chead="Quarti tractatus" file="0282" n="282"/>                illorum inducitur gra. ſū. et b. eſt in .f. proportione <lb/>minus ip̄o .a. / ergo equeuelociter continuo per .a. et .b. <lb/>inducitur gradus ſnm. </s>
              <s xml:id="N2D2A8" xml:space="preserve">Patet conſequentia ex .4. <lb/>propoſitione .2. notabilis (ſemper deduco rarefactio­<lb/>nem et condenſationem).               <anchor type="note" xlink:href="note-0282-01" xlink:label="note-0282-01a"/>               </s>
              <s xml:id="N2D2B4" xml:space="preserve">¶ Ex hac concluſione ſequit̄̄ / <lb/> ſi excedente minore in quali. ꝓportio exceſſus quo <lb/>gra. ſū. etc̃. fuerit maior proportione quãtitatis. </s>
              <s xml:id="N2D2BB" xml:space="preserve">Tūc <lb/>velocius inducitur gra. ſū. per minꝰ ī ea ꝓportione ꝑ <lb/>quam ꝓportio exceſſum excedit proportionem quã­<lb/>titatum: ipſius equali alteratione continuo alteratis <lb/></s>
              <s xml:id="N2D2C5" xml:space="preserve">Et ſi proportio quantitatum fuerit minor proportio­<lb/>ne exceſſum alteratione continuo equali: </s>
              <s xml:id="N2D2CA" xml:space="preserve">Tunc gra. <lb/>ſū. velocius inducitur in maius ꝙ̄ in minus in ea pro­<lb/>portione per quam proportio quantitatum excedit <lb/>proportionem exceſſuum. </s>
              <s xml:id="N2D2D3" xml:space="preserve">Hoc facile patet ex conclu-<lb/>ſione. </s>
              <s xml:id="N2D2D8" xml:space="preserve">hoc addito:  quanto diſtantia eſt minor a ſū. <lb/>tanto mediante cõſimili alteratione citius inducitur <lb/>gra. ſum.</s>
            </p>
            <div xml:id="N2D2DF" level="5" n="8" type="float">
              <note position="left" xlink:href="note-0282-01a" xlink:label="note-0282-01" xml:id="N2D2E3" xml:space="preserve">Corre.</note>
            </div>
            <p xml:id="N2D2E9">
              <s xml:id="N2D2EA" xml:space="preserve">Undecima cõcluſio. </s>
              <s xml:id="N2D2ED" xml:space="preserve">Si ſint duo vni <lb/>diff. ad ſū. terminata vtro modo inequalia. </s>
              <s xml:id="N2D2F2" xml:space="preserve">Et ma­<lb/>ius alteratur maiori alteratione ꝙ̄ minus: et propor­<lb/>tio compoſita ex proportione quantitatum et pro-<lb/>portione alterationum excedit proportionē exceſſuū <lb/></s>
              <s xml:id="N2D2FC" xml:space="preserve">Tunc in maius velocius inducitur gra ſū. in ea pro-<lb/>portione per quam proportio compoſita ex propor-<lb/>tione quantita. et alterationum excedit proportionē <lb/>exceſſuum. </s>
              <s xml:id="N2D305" xml:space="preserve">Et ſi eocontra. </s>
              <s xml:id="N2D308" xml:space="preserve">velocius inducitur gradus <lb/>ſum. in minus ꝙ̄ in maius in proportione per quam <lb/>proportio exceſſuum excedit proportionem compoſi­<lb/>tam ex proportione quantitatum et alterationum.</s>
            </p>
            <p xml:id="N2D311">
              <s xml:id="N2D312" xml:space="preserve">Hec cum multis aliis que poſſunt conformiter ad pre­<lb/>dicta induci facile oſtendi poteſt ex dictis.</s>
            </p>
            <note position="left" xml:id="N2D317" xml:space="preserve">13. cal.</note>
            <p xml:id="N2D31B">
              <s xml:id="N2D31C" xml:space="preserve">Duodecima cõcluſio. </s>
              <s xml:id="N2D31F" xml:space="preserve">Si aliquid ſit <lb/>vni. diffor. termina. ad ſū. alteratum latitudine vni. <lb/>diff. extenſa per totum: in nulla proporcione velocius <lb/>aut tardius incipit induci gra. ſū. ꝙ̄ ſi per totum al-<lb/>teraretur tali gradu vniformi quod verſus extremuꝫ <lb/>intenſius ſubiecti procedit et hec eſt .13. cal. </s>
              <s xml:id="N2D32C" xml:space="preserve">Et hec pa­<lb/>tet ex .2. argumento ante oppo.               <anchor type="note" xlink:href="note-0282-02" xlink:label="note-0282-02a"/>               </s>
              <s xml:id="N2D336" xml:space="preserve">¶ Ex quo ſequitur /  <lb/>ſi vni diff. terminatum ad ſū. alteretur latitudine vni. <lb/>diff. extremo intenſiori verſus extremuꝫ intenſius ſub­<lb/>iecti:               <anchor type="note" xlink:href="note-0282-03" xlink:label="note-0282-03a"/>               gra. ſū. continuo tardius et tardius inducetur et <lb/>hoc corre. patet ex deductione .2. argumenti ante op-<lb/>po. et eſt .14. cal.</s>
            </p>
            <div xml:id="N2D348" level="5" n="9" type="float">
              <note position="left" xlink:href="note-0282-02a" xlink:label="note-0282-02" xml:id="N2D34C" xml:space="preserve">Corre.</note>
              <note position="left" xlink:href="note-0282-03a" xlink:label="note-0282-03" xml:id="N2D352" xml:space="preserve">14. cal.</note>
            </div>
            <p xml:id="N2D358">
              <s xml:id="N2D359" xml:space="preserve">Tridecima concluſio. </s>
              <s xml:id="N2D35C" xml:space="preserve">a. et .b. ſunt vni <lb/>diffor. ad ſūmum terminata omnino conſimilia: et a. <lb/>alteratur latitudine vni. diffor. terminata in extremo <lb/>remiſſiori ad duo continuo extremo remiſſiori verſꝰ <lb/>extremum remiſſius ſubiecti: </s>
              <s xml:id="N2D367" xml:space="preserve">Et in qualibet parte ꝓ­<lb/>portionali temporis certa diuiſione data extremum <lb/>intenſius illius alterationis augebitur ad duplum <lb/>deductis aliis motibus. </s>
              <s xml:id="N2D370" xml:space="preserve">Et .b. continuo alterato per <lb/>totum vt duo. </s>
              <s xml:id="N2D375" xml:space="preserve">Et tamen .a. et .b. mediantibus illis al-<lb/>terationibus eque cito fient ſumma. </s>
              <s xml:id="N2D37A" xml:space="preserve">Patet facile / q2 <lb/>ſua extrema que continuo ſunt equalia: eque cito fient <lb/>ſumma. </s>
              <s xml:id="N2D381" xml:space="preserve">Et .a. et .b. non citius fient ſumma ꝙ̄ ſua extre­<lb/>ma remiſſiora nec tardius / igitur propoſitum.</s>
            </p>
            <p xml:id="N2D386">
              <s xml:id="N2D387" xml:space="preserve">Quartadecima concluſio tangendo <lb/>4. argu. ante oppoſitum. </s>
              <s xml:id="N2D38C" xml:space="preserve">Si aliquod vnifor. diffor. <lb/>terminatum ad ſummum alteretur per totum vni <lb/>alteratione et continuo rarefiat vniformiter quo <lb/>ad tempus et ſubiectum: inductio gradus ſummi <lb/>continuo vniformiter intenditur. </s>
              <s xml:id="N2D397" xml:space="preserve">Probatur et ſup­<lb/>pono /  cum aliquid in quod inducitur gra. ſum. <lb/>mediante vniformi alteratione per totum extenſa <lb/>rarefit. </s>
              <s xml:id="N2D3A0" xml:space="preserve">Tunc in quolibet inſtanti ita velox eſt indu­<lb/>ctio gra. ſum. ſicut eſſet ſi immediate poſt illud in-               <cb chead="Capitulū quintū."/>               ſtans ceſſaret rarefactio. </s>
              <s xml:id="N2D3A8" xml:space="preserve">Quo ſuppoſito arguitur <lb/>ſic / cõtinuo pars remiſſa vniformiter acquirit quã-<lb/>titatem et efficitur maior vniformiter ex caſu con-<lb/>clu. cū totū rarefiat vniformiter quo ad tēpꝰ et ſub-<lb/>iectum: et ſicut pars remiſſa eſt maior et maior in <lb/>quovis inſtanti: ita inductio gra. ſum. eſt velocior: <lb/>vt facile elicitur ex ſuppoſito. </s>
              <s xml:id="N2D3B7" xml:space="preserve">Sed ex caſu queuis <lb/>pars continuo vniformiter maioratur: igitur con-<lb/>tinuo inductio gra. ſū vniformiter augetur. </s>
              <s xml:id="N2D3BE" xml:space="preserve">qnod <lb/>fuit probandum.</s>
            </p>
            <p xml:id="N2D3C3">
              <s xml:id="N2D3C4" xml:space="preserve">Quintadecima concluſio. </s>
              <s xml:id="N2D3C7" xml:space="preserve">a. et .b. ſunt <lb/>omnino equalia in quantitate et vniformia eodeꝫ <lb/>gradu omnino per totum. </s>
              <s xml:id="N2D3CE" xml:space="preserve">Et adequate per equale <lb/>tempus alterantur omnino conſimili latitudine al­<lb/>terationis continuo per equales partes ipſorum. <lb/>a.b. adequate extenſe. </s>
              <s xml:id="N2D3D7" xml:space="preserve">Et tamen citius inducet̄̄ gra. <lb/>ſum. in .a. vel aliquam eius partem ꝙ̄ in b. vel ali-<lb/>quam eius partem. </s>
              <s xml:id="N2D3DE" xml:space="preserve">Probatur / ſint a.b calida vt .4. <lb/>per totum vniformiter et inducatur latitudo alte-<lb/>rationis vniformiter difformiter ab .8. vſ ad .4. ī <lb/>a. et in b. partibiliter quo ad ſubiectum et ſit ſemꝑ <lb/>illa latitudo extenſa per equales partes omnino <lb/>ipſorum a.b. quieſcat tamen in ea in vno extremo <lb/>a quo incipit induci illa latitudo punctus vt .8. et <lb/>moueat̄̄ punctus vt .4. econtra vero fiat in .b. </s>
              <s xml:id="N2D3EF" xml:space="preserve">Quo <lb/>poſito manifeſtum eſt /  ad punctum in quo quieſ-<lb/>cit gra. vt .8. in a. citius deueniet gradus ſum. ̄ <lb/>ad aliquod punctum .b. cum nullum punctum ipſiꝰ <lb/>b. continuo alteretur tanto gradu ſicut extremum <lb/>ipſius a. / vt patet ex caſu. </s>
              <s xml:id="N2D3FC" xml:space="preserve">Nam per nullum tempus <lb/>manet gradus .8. in aliquo puncto ipſius b. quan-<lb/>diu illa alteratio progreditur: ergo citius inducet̄̄ <lb/>gra. ſum. in a. vel aliquã partem eius ꝙ̄ in b. vel ali­<lb/>quam partem eius. </s>
              <s xml:id="N2D407" xml:space="preserve">patet igitur cõcluſio </s>
              <s xml:id="N2D40A" xml:space="preserve">Plura in <lb/>hac materia ſcriberem niſi vrgeret bibliopola.</s>
            </p>
            <p xml:id="N2D40F">
              <s xml:id="N2D410" xml:space="preserve">Concluſio reſponſiua ad queſtionem <lb/>patet ex ſecundo notabili</s>
            </p>
            <p xml:id="N2D415">
              <s xml:id="N2D416" xml:space="preserve">Ad rationem ante oppo. </s>
              <s xml:id="N2D419" xml:space="preserve">Ad primam <lb/>patet reſponſio ex concluſionibus queſtionis: </s>
              <s xml:id="N2D41E" xml:space="preserve">Et ſi­<lb/>militer ad confirmationem.</s>
            </p>
            <p xml:id="N2D423">
              <s xml:id="N2D424" xml:space="preserve">Ad ſecundã rationem reſponſum eſt <lb/>ibi vſ ad replicam ad quam reſpondeno con-<lb/>cedo quod infertur: et nego  illud ſit falſum.</s>
            </p>
            <p xml:id="N2D42B">
              <s xml:id="N2D42C" xml:space="preserve">Ad tertiam rationem reſponſum eſt <lb/>ibi vſ ad replicam. </s>
              <s xml:id="N2D431" xml:space="preserve">ad quam reſpõdeo cõcedēdo <lb/>illatum nec illud eſt inconueniens.</s>
            </p>
            <p xml:id="N2D436">
              <s xml:id="N2D437" xml:space="preserve">Ad quartã rationem ſufficienter re-<lb/>ſpondet .2. notabile. </s>
              <s xml:id="N2D43C" xml:space="preserve">Ad confirmationem reſpon-<lb/>deo concedendo illatum et ratio eſt quia talis al-<lb/>teratio non extenditur per equalem partem ſubie­<lb/>cti </s>
              <s xml:id="N2D445" xml:space="preserve">De qua partibili progreſſione alteratiõis vide­<lb/>as cal. in ſcḋo capitulo de inductione gra. ſum. cir­<lb/>ca finem. </s>
              <s xml:id="N2D44C" xml:space="preserve">Et hec breuiter de inductione gradus ſū-<lb/>mi ad laudem et gloriam dei ſummi </s>
              <s xml:id="N2D451" xml:space="preserve">Poſt hac aūt <lb/>reliquū erit dicere de alteratione anime ad quali­<lb/>tates ſpirituales quibus ipſa anima intelligit et <lb/>diligit. </s>
              <s xml:id="N2D45A" xml:space="preserve">demeretur penam et meretur gloriam il-<lb/>lam immarceſſibilem quã nec oculus vidit nec au-<lb/>ris audiuit </s>
              <s xml:id="N2D461" xml:space="preserve">Ad quam nos perducat ille qui cū pa­<lb/>tre et ſpritu ſancto viuit et regnat per omnia ſecu­<lb/>la ſeculorum </s>
              <s xml:id="N2D468" xml:space="preserve">Amen.</s>
            </p>
            <p xml:id="N2D46B">
              <s xml:id="N2D46C" xml:space="preserve">¶ Explicit liber de triplici motu cõpoſitꝰ per Ma­<lb/>giſtrū Aluarū Thomam vlix bonenſem Regentem <lb/>Parrhiſius in Collegio Coquereti. </s>
              <s xml:id="N2D473" xml:space="preserve">Anno domi-<lb/>ni. 1509. Die Februarii .11.</s>
            </p>
          </div>
        </div>
      </div>
    </div>
    <div xml:id="N2D478" level="1" n="1" type="back">
      <div xml:id="N2D47C" level="2" n="1" type="errata">
        <pb chead="Recognita ex libro de triplici motu." file="0283" n="283"/>
        <head xml:id="N2D484" xml:space="preserve">Recognita ex ſecunda parte <lb/>huius operis.</head>
        <p xml:id="N2D489">
          <s xml:id="N2D48A" xml:space="preserve">¶ Secundo capite columna .11. linea .48. poteris in-<lb/>ferre quibuſcū terminis in pari numero. </s>
          <s xml:id="N2D48F" xml:space="preserve">lengdum <lb/>in impari. </s>
          <s xml:id="N2D494" xml:space="preserve">¶ Capite octauo colūna octaua linea .35. <lb/>et acquiſitum minori eſt proportio. </s>
          <s xml:id="N2D499" xml:space="preserve">legendum eſt ma-<lb/>ior proportio.</s>
        </p>
      </div>
      <div xml:id="N2D49E" level="2" n="2" type="errata">
        <div xml:id="N2D4A2" level="3" n="1" type="errata">
          <head xml:id="N2D4A6" xml:space="preserve">Recognita ex primo tractatu.</head>
          <p xml:id="N2D4A9">
            <s xml:id="N2D4AA" xml:space="preserve">¶ Tertio capite columna ſecunda linea .38. magnes <lb/>a que velocite.r </s>
            <s xml:id="N2D4AF" xml:space="preserve">legendum eque velociter. </s>
            <s xml:id="N2D4B2" xml:space="preserve">¶ Capite et <lb/>colūna eiſdeꝫ linea .51. q2 ſi in horolohio ſolari .etc̈. la­<lb/>ri ponatur magnes. </s>
            <s xml:id="N2D4B9" xml:space="preserve">legendū ſi in horologio ſola-<lb/>ri ponatur magnes. </s>
            <s xml:id="N2D4BE" xml:space="preserve">Capite et columna eiſdem liuea <lb/>66. gnete in ipſo ferro. </s>
            <s xml:id="N2D4C3" xml:space="preserve">legenduꝫ magnete in ipſo fer-<lb/>ro. </s>
            <s xml:id="N2D4C8" xml:space="preserve">¶ Capite .6. co. 3. li. 35. velociter continuo et vnifor­<lb/>miter cum deperdatur. </s>
            <s xml:id="N2D4CD" xml:space="preserve">legendum cum alia deperda­<lb/>tur. </s>
            <s xml:id="N2D4D2" xml:space="preserve">¶ Capite eodem co. 9. linea .21. proportionem du­<lb/>plam et ad tertiam ſexquialteram. / legendum et ad ſe­<lb/>cundam ſexquialteram. </s>
            <s xml:id="N2D4D9" xml:space="preserve">¶ Capite et columna eiſdem <lb/>linea .28. et in minori quam ſit equalis ſufficit. </s>
            <s xml:id="N2D4DE" xml:space="preserve">legen-<lb/>dum ꝙ̄ ſit tale ſufficit. </s>
            <s xml:id="N2D4E3" xml:space="preserve">¶ Capite ſeptimo co. 9. li. 26. <lb/>motum ſuum vſ ad non gradum. </s>
            <s xml:id="N2D4E8" xml:space="preserve">legendum motum <lb/>ſuū a nõ gradu. </s>
            <s xml:id="N2D4ED" xml:space="preserve">¶ Capite et co. eiſdē li. 45. motū ſuuꝫ <lb/>ad nõ gradū. </s>
            <s xml:id="N2D4F2" xml:space="preserve">legēdū a nõ gradu. </s>
            <s xml:id="N2D4F5" xml:space="preserve">Capite .8. co. 4. li. <lb/>63. c. partem cū equali reſiſtentia. </s>
            <s xml:id="N2D4FA" xml:space="preserve">legendū .e. partem <lb/>cum equali reſiſtentia. </s>
            <s xml:id="N2D4FF" xml:space="preserve">Eodem capite co. 5. li. 21. ade-<lb/>quate pertrãſit̄̄ .d. pars. </s>
            <s xml:id="N2D504" xml:space="preserve">legendum adequate pertrã-<lb/>ſitur et pars ad tempus in quo pertranſitur .d. pars. <lb/></s>
            <s xml:id="N2D50A" xml:space="preserve">Eodem capite colum. 9. li. 39. tranſeundo ſtat aut re­<lb/>mittit potentiam ſuam. </s>
            <s xml:id="N2D50F" xml:space="preserve">legendum aut intendit potē­<lb/>tiam ſuaꝫ. </s>
            <s xml:id="N2D514" xml:space="preserve">Eodem capite co. 15. li. 42. inuariata .c. me­<lb/>dium inuariatum. </s>
            <s xml:id="N2D519" xml:space="preserve">legendum inuariata tranſiens .c. <lb/>medium inuariatum. </s>
            <s xml:id="N2D51E" xml:space="preserve">Eodem capite co. 16. li. 35. totuꝫ <lb/>hoc ſupereſt. </s>
            <s xml:id="N2D523" xml:space="preserve">intendo motum ſuum .etc̃. </s>
            <s xml:id="N2D526" xml:space="preserve">Eodem capite <lb/>co. 20. li. 61. cū maiori reſiſtentia legendum cum mi-<lb/>nori reſiſtentia.</s>
          </p>
          <p xml:id="N2D52D">
            <s xml:id="N2D52E" xml:space="preserve">¶ Nono capite co. 3. li. 28. alterius mobilis quod mo­<lb/>uetur in ſecundo medio. </s>
            <s xml:id="N2D533" xml:space="preserve">legendum in primo medio.</s>
          </p>
          <p xml:id="N2D536">
            <s xml:id="N2D537" xml:space="preserve">Eodem capite columna octaua li. 21. cum in infinituꝫ <lb/>velociṫ antea ītēdebat motū ſuū. </s>
            <s xml:id="N2D53C" xml:space="preserve">legēdū remittebat. <lb/></s>
            <s xml:id="N2D540" xml:space="preserve">Eodem capite co. 12. li. 10. patet cum maiore. </s>
            <s xml:id="N2D543" xml:space="preserve">legendū <lb/>cum minore. </s>
            <s xml:id="N2D548" xml:space="preserve">Capite eodem co. 14. li. 33. </s>
            <s xml:id="N2D54B" xml:space="preserve">Sed cõtra quī­<lb/>tam concluſionem. </s>
            <s xml:id="N2D550" xml:space="preserve">legendum quartam. </s>
            <s xml:id="N2D553" xml:space="preserve">¶ Undecimo <lb/>capite co. 4. li. 35. ſexquialtera ad duplam. </s>
            <s xml:id="N2D558" xml:space="preserve">legendum <lb/>ſexquialtera ad ſexquialteram. </s>
            <s xml:id="N2D55D" xml:space="preserve">¶ Duodecimo capite <lb/>co. 5 lī. 50. mouetur illa potētia quam aliqua aliaruꝫ <lb/>potentiarum. </s>
            <s xml:id="N2D564" xml:space="preserve">legendum antea ꝙ̄ aliqua aliarum po-<lb/>tentiarum. </s>
            <s xml:id="N2D569" xml:space="preserve">¶ Capite tridecimo co. 2. li. 35. quieſcente <lb/>extremo remiſſiori. </s>
            <s xml:id="N2D56E" xml:space="preserve">legendum intenſiori. </s>
            <s xml:id="N2D571" xml:space="preserve">Eodem capi­<lb/>te co. 3. li. 17. cum illo puncto mouere velocius  ille <lb/>punctus. </s>
            <s xml:id="N2D578" xml:space="preserve">legendum ꝙ̄ ille pūctus. </s>
            <s xml:id="N2D57B" xml:space="preserve">Eodem capite co. 7. <lb/>li. 42. et alia puncta intenſiora. </s>
            <s xml:id="N2D580" xml:space="preserve">legendum remiſſiora. <lb/></s>
            <s xml:id="N2D584" xml:space="preserve">¶ Capite quartodecimo co. 2. linea .46. ſit .b. pun-<lb/>ctus extrinſecus. </s>
            <s xml:id="N2D589" xml:space="preserve">legendum intrinſecus. </s>
            <s xml:id="N2D58C" xml:space="preserve">Eodem capi-<lb/>te co. 3. linea prima / ergo .k. proportio eſt maior quaꝫ <lb/>f. proportio et .k. eſt proportio. </s>
            <s xml:id="N2D593" xml:space="preserve">legendum / ergo .h. pro­<lb/>portio eſt maior ꝙ̄ .f. proportio et .h. ē proportio. </s>
            <s xml:id="N2D598" xml:space="preserve">Eo-<lb/>dem capite co. 6. linea .30. patet ex immediate prece-<lb/>dente. </s>
            <s xml:id="N2D59F" xml:space="preserve">legēdum ex ſecunda. </s>
            <s xml:id="N2D5A2" xml:space="preserve">Eodem capite co. 10. linea <lb/>63. que eſt in latitudine minus intenſa legendum ex-<lb/>tenſa. </s>
            <s xml:id="N2D5A9" xml:space="preserve">¶ Quindecimo capite co. 5. linea .54. in prima <lb/>ſuppoſitione. </s>
            <s xml:id="N2D5AE" xml:space="preserve">legendum in tertia. </s>
            <s xml:id="N2D5B1" xml:space="preserve">Capite eodeꝫ co. 7. <lb/>linea .7. tamen punctat .4. </s>
            <s xml:id="N2D5B6" xml:space="preserve">legendum punctus vt .4. <lb/></s>
            <s xml:id="N2D5BA" xml:space="preserve">Eodem capite co. 9. linea .29. potentia et omni pun-<lb/>cto verſus intenſius extremum. </s>
            <s xml:id="N2D5BF" xml:space="preserve">legenduꝫ remiſſius ex­<lb/>tremum</s>
          </p>
        </div>
        <div xml:id="N2D5C4" level="3" n="2" type="errata">
          <head xml:id="N2D5C8" xml:space="preserve">Recognita ex ſecundo tractatu.</head>
          <p xml:id="N2D5CB">
            <s xml:id="N2D5CC" xml:space="preserve">¶ Primo capite co. 7. linea .65. dico /  neuter illorū             <cb chead="Recognita ex libro de triplici motu."/>             mediorum requiritur. </s>
            <s xml:id="N2D5D2" xml:space="preserve">legendum modorum. </s>
            <s xml:id="N2D5D5" xml:space="preserve">¶ Secun-<lb/>do capite co. 2. poſt quartam lineam hoc eſt tota ro-<lb/>ta tantam lineam deſcribit et tam velociter moue= in <lb/>peripheria talis rote.tur quã velociter mouetur vnꝰ <lb/>puctus qui eſſet. </s>
            <s xml:id="N2D5E0" xml:space="preserve">legendum hoc eſt tota rota tãtam li­<lb/>neam deſcribit et tam velociter mouetur ꝙ̄ velociter <lb/>mouetur vnus punctus qui eſſet in peripheria talis <lb/>rote. </s>
            <s xml:id="N2D5E9" xml:space="preserve">Capite et co. eiſdem li. 65. verſus medietatem in­<lb/>tenſiorem. </s>
            <s xml:id="N2D5EE" xml:space="preserve">legendum inferiorem. </s>
            <s xml:id="N2D5F1" xml:space="preserve">¶ Tertio capite co. <lb/>30. linea .5. ſe habet in proportione .f. ad ꝓportionem. <lb/></s>
            <s xml:id="N2D5F7" xml:space="preserve">legēdū. </s>
            <s xml:id="N2D5FA" xml:space="preserve">ad velocitatē. </s>
            <s xml:id="N2D5FD" xml:space="preserve">Eodē capite co. 33. li. 8. ſpaciū ꝑ­<lb/>tranſitū in ꝑte ꝓportionali legēdū ī ṗma ꝑte ꝓpor-<lb/>tionali. </s>
            <s xml:id="N2D604" xml:space="preserve">Capite eodem co. 35. linea .9. ſi vero propor-<lb/>tio ē ſexq̇tertia legendū ſi vero ꝓportione ſexq̇tertia. <lb/></s>
            <s xml:id="N2D60A" xml:space="preserve">Eodem capite co. 38. linea .14. excedit proportionem <lb/>ſexquialteram per .4. ꝓportionem ſexquiſextam. </s>
            <s xml:id="N2D60F" xml:space="preserve">le-<lb/>gendum per .1. proportionem ſexquiſextaꝫ. </s>
            <s xml:id="N2D614" xml:space="preserve">Edeom ca­<lb/>pite co. 41. linea .63. vſ ad gradum partis paris le-<lb/>gendum partis imparis.</s>
          </p>
        </div>
        <div xml:id="N2D61B" level="3" n="3" type="errata">
          <head xml:id="N2D61F" xml:space="preserve">Recognitum ex tertio tractatu.</head>
          <p xml:id="N2D622">
            <s xml:id="N2D623" xml:space="preserve">¶ In quarto dubio primi capitis columna ſexta linea <lb/>13. iuadet ne precipitetur editio: nonū̄  prematur <lb/>in annum. </s>
            <s xml:id="N2D62A" xml:space="preserve">legendum nonun prematur in annum. <lb/></s>
            <s xml:id="N2D62E" xml:space="preserve">¶ Hi ſunt errores candide lector quos forte recogno­<lb/>uimus. </s>
            <s xml:id="N2D633" xml:space="preserve">Si qui alii inueniantur errorculi nõ te turba-<lb/>bunt. </s>
            <s xml:id="N2D638" xml:space="preserve">Semidoctus (credo) eos facile caſtigabit.</s>
          </p>
        </div>
      </div>
      <div xml:id="N2D63B" level="2" n="1" type="postface" type-free="poem">
        <head xml:id="N2D640" xml:space="preserve">Iohannes de haya ad hermanū lethmate <lb/>de gouda germane nationis procuratioriuꝫ.</head>
        <p xml:id="N2D645">
          <s xml:id="N2D646" xml:space="preserve">Bruta torturis agioſmata vafra patebunt.</s>
        </p>
        <p xml:id="N2D649">
          <s xml:id="N2D64A" xml:space="preserve">Colliſis queque callida turba tulit.</s>
        </p>
        <p xml:id="N2D64D">
          <s xml:id="N2D64E" xml:space="preserve">Tuta caracteribus ſpeculabitur atria athene</s>
        </p>
        <p xml:id="N2D651">
          <s xml:id="N2D652" xml:space="preserve">Nunc hermane tuo munere docta cohors.</s>
        </p>
        <p xml:id="N2D655">
          <s xml:id="N2D656" xml:space="preserve">Excutis glumis latitantia grana petitis</s>
        </p>
        <p xml:id="N2D659">
          <s xml:id="N2D65A" xml:space="preserve">Quis potes indigeti tollere docte famem.</s>
        </p>
        <p xml:id="N2D65D">
          <s xml:id="N2D65E" xml:space="preserve">Hinc te poſteritas donabit fixa triſeclis</s>
        </p>
        <p xml:id="N2D661">
          <s xml:id="N2D662" xml:space="preserve">Curriculis: et qui hoc nobile preſſit opus.</s>
        </p>
      </div>
      <div xml:id="N2D665" level="2" n="2" type="postface" type-free="poem">
        <head xml:id="N2D66A" xml:space="preserve">Idem ad lectores.</head>
        <p xml:id="N2D66D">
          <s xml:id="N2D66E" xml:space="preserve">Aurea te decorat ſupreme virga caballe</s>
        </p>
        <p xml:id="N2D671">
          <s xml:id="N2D672" xml:space="preserve">Turba dee cecronis: ſuſcipe poſco lubens.</s>
        </p>
        <p xml:id="N2D675">
          <s xml:id="N2D676" xml:space="preserve">Ingenii cultum et doctrine callidioris</s>
        </p>
        <p xml:id="N2D679">
          <s xml:id="N2D67A" xml:space="preserve">Senſa feret ceſmi ſollicitata vafre.</s>
        </p>
        <p xml:id="N2D67D">
          <s xml:id="N2D67E" xml:space="preserve">Sepius attentus viuaces ambitus ortus</s>
        </p>
        <p xml:id="N2D681">
          <s xml:id="N2D682" xml:space="preserve">Suggeret ad queq̄ mentis amica rate.</s>
        </p>
        <p xml:id="N2D685">
          <s xml:id="N2D686" xml:space="preserve">Importuna ſophi ſenſus acidoſ reſoluet.</s>
        </p>
        <p xml:id="N2D689">
          <s xml:id="N2D68A" xml:space="preserve">Que tritis pluteis hiſpida turba tulit.</s>
        </p>
        <p xml:id="N2D68D">
          <s xml:id="N2D68E" xml:space="preserve">Carneade, aut ſuiſeth, torquebere nõ laberinthi.</s>
        </p>
        <p xml:id="N2D691">
          <s xml:id="N2D692" xml:space="preserve">Nexibus amibiguis: fila ſecunda tibi.</s>
        </p>
        <p xml:id="N2D695">
          <s xml:id="N2D696" xml:space="preserve">Fila ſecunda tibi cartharea munera prebent</s>
        </p>
        <p xml:id="N2D699">
          <s xml:id="N2D69A" xml:space="preserve">Aluari thome terſa lepore pio.</s>
        </p>
        <p xml:id="N2D69D">
          <s xml:id="N2D69E" xml:space="preserve">Cecula non fies greſſus rege naue ſecunda.</s>
        </p>
        <p xml:id="N2D6A1">
          <s xml:id="N2D6A2" xml:space="preserve">Thracia conſpicies ſaxa togata ſinu.</s>
        </p>
      </div>
      <div xml:id="N2D6A5" level="2" n="3" type="postface" type-free="poem">
        <head xml:id="N2D6AA" xml:space="preserve">Ad librum phaleution carmen.</head>
        <p xml:id="N2D6AD">
          <s xml:id="N2D6AE" xml:space="preserve">Salebris rudibus timen libelle.</s>
        </p>
        <p xml:id="N2D6B1">
          <s xml:id="N2D6B2" xml:space="preserve">Sub ſannarioneris ſacri cybelles:</s>
        </p>
        <p xml:id="N2D6B5">
          <s xml:id="N2D6B6" xml:space="preserve">Obtrectare daphanitas loquaces.</s>
        </p>
        <p xml:id="N2D6B9">
          <s xml:id="N2D6BA" xml:space="preserve">Et te ſedigitas manus minaces.</s>
        </p>
        <p xml:id="N2D6BD">
          <s xml:id="N2D6BE" xml:space="preserve">Signare hermaphroditi hiantis audax.</s>
        </p>
        <p xml:id="N2D6C1">
          <s xml:id="N2D6C2" xml:space="preserve">Credin<gap/> rite notandus aſſeriſco.</s>
        </p>
        <p xml:id="N2D6C7">
          <s xml:id="N2D6C8" xml:space="preserve">Ibis. zoileos caduce morſus.</s>
        </p>
        <p xml:id="N2D6CB">
          <s xml:id="N2D6CC" xml:space="preserve">Rimaris. </s>
          <s xml:id="N2D6CF" xml:space="preserve">ne ſiniſter amibitus te</s>
        </p>
        <p xml:id="N2D6D2">
          <s xml:id="N2D6D3" xml:space="preserve">Torquet. </s>
          <s xml:id="N2D6D6" xml:space="preserve">degener aut libido fame<gap/></s>
        </p>
      </div>
      <div xml:id="N2D6DA" level="2" n="4" type="postface" type-free="poem">
        <head xml:id="N2D6DF" xml:space="preserve">Liber</head>
        <p xml:id="N2D6E2">
          <s xml:id="N2D6E3" xml:space="preserve">Spero preſidio viris futurum.</s>
        </p>
        <p xml:id="N2D6E6">
          <s xml:id="N2D6E7" xml:space="preserve">Meme: et ſtentoreas abeſſe nuſ̄</s>
        </p>
        <p xml:id="N2D6EA">
          <s xml:id="N2D6EB" xml:space="preserve">Uoces: quis ſatago: fauor popelli</s>
        </p>
        <p xml:id="N2D6EE">
          <s xml:id="N2D6EF" xml:space="preserve">Fex. </s>
          <s xml:id="N2D6F2" xml:space="preserve">olim ſtatuet decus minerue</s>
        </p>
        <p xml:id="N2D6F5">
          <s xml:id="N2D6F6" xml:space="preserve">Fetus. </s>
          <s xml:id="N2D6F9" xml:space="preserve">nec monumenta plebs valebit</s>
        </p>
        <p xml:id="N2D6FC">
          <s xml:id="N2D6FD" xml:space="preserve">Un̄ ſternere. </s>
          <s xml:id="N2D700" xml:space="preserve">diligent cathones.</s>
        </p>
        <pb file="0284" n="284"/>
      </div>
      <div xml:id="N2D706" level="2" n="5" type="postface" type-free="letter">
        <head xml:id="N2D70B" xml:space="preserve">Georgius bruniau vindocineſis <lb/>ſno aluaro thome. Salutem.</head>
        <p xml:id="N2D710">
          <s xml:id="N2D711" xml:space="preserve">Fabii quintiliani preceptum eſt (doctiſſime aluare) cuiuis ſeſe in eruditio­<lb/>rū albo inſcriptū efflagitãti ad amuſſim obſeruandū / vt efficiatur orbis ille doctrinarum quē greci <lb/>encyclopediam id eſt (tullio interprete) concentū doctinarū oīm at cõſenſum appellitant. </s>
          <s xml:id="N2D718" xml:space="preserve">Qua q̇ <lb/>aſſequuntur vt ꝓperariores phenice ſunt ita reliquis hoībus eo preſtabiliores quo phenix auibꝰ nec <lb/>ab re. </s>
          <s xml:id="N2D71F" xml:space="preserve">Si em̄ ꝓ merito nun̄ ſatis cõmendet̄̄ qui vel vnius diſcipline apicem ꝑtingere meruit que tã-<lb/>dem equa merces quis honos, q̄ gloria his rependdi poterit quos labores indefeſſi iugeſ vigilie oī <lb/>genis lr̄arū floſculis, pigmētis, diuitiis excultos, mõſtrabiles, ſuffarcinoſ reddidere: </s>
          <s xml:id="N2D726" xml:space="preserve">Sꝫ quorſuꝫ <lb/>iſtec (mi aluare) vt ip̄e ꝓfecto qui inter litteratos ne imo quidē dignus ſubſellio litteratorū ſim ama­<lb/>tor pene zelotipus officioſiſſimiſ buccinator, quid de te cū pleriſ oībꝰ ſentirē, oblata imprimis <lb/>occaſione pñtiſſima expectatiſſima ſignaficarem. </s>
          <s xml:id="N2D72F" xml:space="preserve">In goc nēpe parriſienſi gymnaſio bonarum litte­<lb/>rarū emporio percelebri cū non parū multos. </s>
          <s xml:id="N2D734" xml:space="preserve">Et eos q̇dē eruditiſſimos liberaliū artium profeſſio-<lb/>res videre ſit, tu michi ſemꝑ viſus es ſi non oīm cõſūmatiſſimꝰ (ne verbū aut adulationis ſuſpitionē <lb/>aut inuidiã pariat) ſaltem inter ↄ̨ſummatiſſimos nõ infimus. </s>
          <s xml:id="N2D73B" xml:space="preserve">Sunt (fateor) te cõpluſculi audatiores <lb/>ſui oſtendatores magis ſoliciti quibꝰ tamē vt tua cedat modeſtia tm̄ abeſt vt eos (me iudice) lõge <lb/>poſt reliquas trãſcendas ſuperes. </s>
          <s xml:id="N2D742" xml:space="preserve">Quãdoquidem vnus ſis qui michi videaris orbiculatã illa diſci-<lb/>plinarū ſeriem abſolutiſſime conſecutus, a quibuſdē diſciplinarū cultiorū nõ modo ignaris ſꝫ et cõ­<lb/>temporibus multo alieniſſimꝰ: qui cū ſermocinales ſe naturaleſ philoſophos iacta cundi p̄dicent <lb/>ac glorientur ego philodicos potius vocitandos cenſuerim id eſt maniat exſucco verboruꝫ ſonitu <lb/>gaudētes hoīes profecto ruſticos īuenuſtos et) vt greco vtar verbo) niſi ſodales ideſt omnē litterarū <lb/>elegantiã nitorē peroſos: </s>
          <s xml:id="N2D74F" xml:space="preserve">Tu vero maiori nun̄ leticia ꝓfunderit ꝙ̄ cū vel ciceronianū aliquid vel <lb/>liuianū depromis. </s>
          <s xml:id="N2D754" xml:space="preserve">Si de ſacꝪ lr̄is diſertare q̇c̄ ceꝑis theologie tū theorice tū parctice oē3 operã to-<lb/>toſ dies īpendiſſe iudicabere. </s>
          <s xml:id="N2D759" xml:space="preserve">Si īter iuris vtriſ peritos forte ↄ̨grediaris ceſareis te põtificuſ <lb/>dūtaxat libris vacaſſe cõſtantiſſime antinuabunt. </s>
          <s xml:id="N2D75E" xml:space="preserve">Taceo ꝙ̄ familiaris tibi ſit et moralis et naturalis <lb/>philoſophia vt in tanta philoſophantiū corona, philoſophia nomen tibi peculiariter vēdicaberis <lb/>vt preceptorē tuum petrū de alliaco inter philoſophie ꝓfeſſores dum viueret doctiſſimū aut equa­<lb/>ueris aut (qḋ potius crediderim) ſuperaueris quem ſi fata virum ſeruaſſent huic parrſiorum achade­<lb/>mie oībuſ philoſophie ſtudioſis fructis non parū (quod ſperabant omnes procul dubio attuliſſet <lb/></s>
          <s xml:id="N2D76A" xml:space="preserve">Quid vero quadrinii certiſſimã peritiã refere opus eſt) cū vel minimo cui hic tuus de triplici mo-<lb/>tu liber monſtret aꝑtius: quē ſex menſibꝰ ſecundum in coqueretico ſtadio curriculū expectans ſedu­<lb/>liſſime nec minꝰ affabre excudiſti ocii potius vitandi ꝙ̄ oſtentationis gr̄a non ignorans nichil illoꝝ <lb/>ingenio at animis deteſtabiliꝰ qui de genere ocio obliteſcunt oſcitanteſ victitant aut patius vi­<lb/>tam trahunt. </s>
          <s xml:id="N2D775" xml:space="preserve">Hoc aūt libro quid ad theoreticam illam phiſicē (que id etatis apud parriſios non me-<lb/>diocri in precio eſt) conducibilius ſit non video. </s>
          <s xml:id="N2D77A" xml:space="preserve">Sed cum vino vendibili hedera (quod aiunt) ſuſpen­<lb/>ſa non opus ſit receptui cecinero. </s>
          <s xml:id="N2D77F" xml:space="preserve">¶ Uale ex edibus noſtris coq̄reticis ſeptimo Idus Februarri</s>
        </p>
      </div>
      <div xml:id="N2D782" level="2" n="6" type="postface" type-free="letter">
        <head xml:id="N2D787" xml:space="preserve">Ioannes de haya dūm hermanū lethmate de guoda germa-<lb/>ne nationis procuratiorum ſalute plurima iubet impartire.</head>
        <p xml:id="N2D78C">
          <s xml:id="N2D78D" xml:space="preserve">Qui pro ſimilitudine lucis dominice culmina abſolute magie anhelãtes <lb/>perueſtigarunt: ſpiritalē imaginem pleriſ affectibus diſſultantē ꝓfeſſi ſunt. </s>
          <s xml:id="N2D792" xml:space="preserve">Hinc ab eo ad qḋ nuꝑ <lb/>hac llucinabatur ſtatim abhorebit: que ſublimioris claritate rumoris ad imū (vt aiunt) ſpm̄: et adu-<lb/>ratiſſima optimi cuiuſ imitatiõe: et implorato cõgruēte ſilētio: peculiariter veīt demulcēda. </s>
          <s xml:id="N2D799" xml:space="preserve">quod <lb/>quo dicerpta parte ſenſili animi ꝓpenſione obires: locupletiſſimã parētū tuorū ſupellectilē pili feci­<lb/>ſti. </s>
          <s xml:id="N2D7A0" xml:space="preserve">Et litterarū emporiū (qui parriſiꝰ apellat̄̄) ad ingenti cultum ꝓfectus es. </s>
          <s xml:id="N2D7A3" xml:space="preserve">In quo decurſa ꝓpoſi-<lb/>te methodi inter capedine (taceo tue aduleſentie flagrãtiſſimū ſtudiū quo te totū lr̄is mancipabas: <lb/>ad faſtigiū aſpirans nominis precipui (quo merito potitꝰ es) et accepta in gr̄ali ꝓuīcia: belle ſigna­<lb/>tus es oculis mille. quo degenere ambitu ſeq̄ſtrato: in oēs cõmunicabas. </s>
          <s xml:id="N2D7AC" xml:space="preserve">hinc eorū ad quos res per­<lb/>tinebat amica adminiſtratiõe (licet ex ephebis vix diceſſiſſeces) in te cõceſſuꝫ eſt om̄e ius ꝓcuratoriuꝫ <lb/>germane nationis. </s>
          <s xml:id="N2D7B3" xml:space="preserve">Uidebaris em̄ (faceſſat adulatio, cõgruã mūri auxeſim allaturꝰ: quos ſpes neu­<lb/>tiſper fefellit. </s>
          <s xml:id="N2D7B8" xml:space="preserve">patuit em̄ tante nationis alea ꝑfectiſſima. </s>
          <s xml:id="N2D7BB" xml:space="preserve">Demõ diſtorſos ſuggilãs affectꝰ quo mēs <lb/>defecatis q̇buſcū futilibꝰ celebrioribꝰ ſaginaretur artibus (quo ſemꝑ pedotrine vſus es) aluaro <lb/>thome (quē merito alterū gorgiã liõtinū appelaueri3: cuiuſcū em̄ rõnē imp̄mediate affert) addictus <lb/>es: maturioribꝰ cū eo diſſultans aſſidue rõnibus: ſubacidiora attrectans: eliminãs funditus euellēs <lb/>nec his cõtentus (qḋ tua intermiſſio eſt) eloquētie informas tete ſupellectile, tã greca, ꝙ̄ latina, in te <lb/>(quo breuis loquar) ꝑfecta eſt nature ingenuitas, affabilitas et ardore charitatis coruſcans gra-<lb/>tia: qua poſteritati conſulens et omniū vtilitati (quod tīeis forte carie aut turpi ſitu apocopãdū erat <lb/>totius philoſophie lenociniū aluari thome: oībꝰ et origenes: et: baces: perſcrutantibus peculiare: vt <lb/>palam et oībus ſeſe offeret ꝑ ꝙ̄ ſolicite egiſti: in quo nõ minus laboris ꝙ̄ diligētie ceſim rimãdo tra­<lb/>ctando: et ad methodum vſ dirigēdo cum petentem et ingenti viribus: et acrimonia impendiſti: quo <lb/>(tan̄ elogio: aut monumento) </s>
          <s xml:id="N2D7D2" xml:space="preserve">Ille īmortalitē adipiſcetur tu vero (ſi eo munere p̄ueris) laudeꝫ glo­<lb/>riam et argutorū virorū rumorē. </s>
          <s xml:id="N2D7D7" xml:space="preserve">Uale. </s>
          <s xml:id="N2D7DA" xml:space="preserve">Ex edibus coquereticis q̇nto idus februarii.</s>
        </p>
      </div>
      <div xml:id="N2D7DD" level="2" n="7" type="postface" type-free="poem">
        <p xml:id="N2D7E2">
          <s xml:id="N2D7E3" xml:space="preserve">Anabat hex ſtruxit fulgente volumina nixu</s>
        </p>
        <p xml:id="N2D7E6">
          <s xml:id="N2D7E7" xml:space="preserve">Quilibet ambroſias hauriat ore dapes</s>
        </p>
        <p xml:id="N2D7EA">
          <s xml:id="N2D7EB" xml:space="preserve">Huc mons quillermum gaudet genuiſſe relaxus</s>
        </p>
        <p xml:id="N2D7EE">
          <s xml:id="N2D7EF" xml:space="preserve">Quo preluſtraris clare britanne ſolum</s>
        </p>
        <p xml:id="N2D7F2">
          <s xml:id="N2D7F3" xml:space="preserve">Diui martini ſubcelſis edibus ortus</s>
        </p>
        <p xml:id="N2D7F6">
          <s xml:id="N2D7F7" xml:space="preserve">Nūc decorat miro nomine pariſius</s>
        </p>
        <p xml:id="N2D7FA">
          <s xml:id="N2D7FB" xml:space="preserve">Qui cauſas ideo librorum noſcere queris</s>
        </p>
        <p xml:id="N2D7FE">
          <s xml:id="N2D7FF" xml:space="preserve">Per pauco viſeas munere lectior eum</s>
        </p>
        <pb file="0285" n="285"/>
      </div>
      <figure xml:id="N2D805">
        <image file="0285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0285-01"/>
      </figure>
    </div>
  </text>
</echo>