Alvarus, Thomas, Liber de triplici motu, 1509

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              <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.
                  <note position="left" xlink:href="note-0053-01a" xlink:label="note-0053-01" xml:id="N1537E" xml:space="preserve">1. correĺ.</note>
                </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
                  <note position="left" xlink:href="note-0053-02a" xlink:label="note-0053-02" xml:id="N15384" xml:space="preserve">2. correĺ.</note>
                </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>
              <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.
                  <note position="right" xlink:href="note-0053-03a" xlink:label="note-0053-03" xml:id="N155DF" xml:space="preserve">1. correĺ.</note>
                </s>
                <s xml:id="N153CE" xml:space="preserve"/>
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