Alvarus, Thomas, Liber de triplici motu, 1509

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                  <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>
              <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
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                d: eſt etiam proportio f. </s>
                <s xml:id="N15609" xml:space="preserve">Quod ſic probatur facile
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                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-
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                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
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                portio f. / quod fuit probandum. </s>
                <s xml:id="N1561C" xml:space="preserve">Patet igitur cor-
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                relarium.
                  <note position="left" xlink:href="note-0055-01a" xlink:label="note-0055-01" xml:id="N15653" xml:space="preserve">8. correl.</note>
                </s>
                <s xml:id="N15626" xml:space="preserve">¶ Sequitur octauo /  quando inter ali­
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                quos terminos eſt aliqua proportio et vtro illo­
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                rum decreſcente manet inter eos continuo eadem
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                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
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                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 /
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                quia inter a. et b. continuo terminos decreſcentes
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                continuo manet proportio f. / igitur continuo a. et
                  <lb/>
                b. eque velociter proportionabiliter decreſcunt / vt
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                patet ex primo correlario quarte concluſionis hu­
                  <lb/>
                ius ſed infinitam proportioneꝫ deperdit b. / igit̄̄ a.
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                in eodem tempore adequate infinitam deperdit et
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                ſic in eodem tempore deuenit vſ ad non graduꝫ /
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                quod fuit probandum.</s>
              </p>
              <p xml:id="N15659">
                <s xml:id="N1565A" xml:space="preserve">Quinta concluſio. </s>
                <s xml:id="N1565D" xml:space="preserve">Quando aliqua
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                proportio maioris inequalitatis maioratur per
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                maioris extremi crementum ſtante minori: tūc da­
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                ta ꝓportio efficitur maior per illam proportionē
                  <lb/>
                per quam maior terminus augmentatur. </s>
                <s xml:id="N15668" xml:space="preserve">Et quã-
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                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
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                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 /
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                 proportio f. per h. proportionem maioratur ꝑ
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                quam etiam maioratur ipſum b. maior terminus
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                </s>
                <s xml:id="N15685" xml:space="preserve">Quod probatur ſic / q2 facto tali cremento: ꝓpor-
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                tio .ab. ad c. componitur ex proportiõe .ab. ad b.
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                et b. ad c. / ergo proportioni f.b. ad c. fuit addita ꝓ­
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                portio h. que eſt .ab. ad b. / vt patet rx hypoteſi: igi-
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                tur ex conſequenti proportio f.b. ad c. fuit augmē­
                  <lb/>
                tata per h. proportionem / per quaꝫ augmentatur
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                b. terminus maior / quod fuit probandum. </s>
                <s xml:id="N15694" xml:space="preserve">Patet
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                conſequentia ex ſecunda ſuppoſitione: et ex conſe­
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                quenti prima pars. </s>
                <s xml:id="N1569B" xml:space="preserve">Eodem modo demonſtrabis
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                ſecundam partem concluſionis </s>
                <s xml:id="N156A0" xml:space="preserve">Et ſic manifeſta ē
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                concluſio.
                  <note position="left" xlink:href="note-0055-02a" xlink:label="note-0055-02" xml:id="N158C2" xml:space="preserve">1. correl.</note>
                </s>
                <s xml:id="N156AA" xml:space="preserve">¶ Ex hoc ſequitur primo /  quando ali­
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                qua proportio maioris inequalitatis augetur ꝑ
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                maiorationem maioris termini. </s>
                <s xml:id="N156B1" xml:space="preserve">et minorationē
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                minoris: tunc data ꝓportio augetur et efficit̄̄ ma­
                  <lb/>
                ior per proportionem compoſitam ex proportio-
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                ne per quam maior terminus efficitur maior ſiue
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                quam ſupra ſe acquirit terminus maior, et ex pro­
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                portione per quam minor terminus efficitur mi-
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                nor, ſiue quam minor terminus deperdit / qḋ idem
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                eſt. </s>
                <s xml:id="N156C2" xml:space="preserve">Patet hec correlarium ex concluſione: quoni-
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                aꝫ ſi ſtante minore termino in prima parte tempo­
                  <cb chead="Capitulum octauum"/>
                ris in quo fit talis maioratio ꝓportionis: maior
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                terminus acquireret totam illam ꝓportionē quã
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                debet acquirere in toto tēpore: et in ſecunda par-
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                te eiuſdem temporis ſtante iam maiore: minor de­
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                perderet illam ꝓportionem quam debet deperde­
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                re in toto tempore: tunc ꝓportio īter illos termi-
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                nos in prima parte temporis efficietur maior per
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                proportionem per quam maior terminus effici-
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                tur maior / vt patet ex prima parte concluſionis: et
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                in ſecunda parte eiuſdem temporis efficiet̄̄ adhuc
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                maior ceteris manentibus paribus per proportio­
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                nem per quam minor terminus efficitur minor / vt
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                patet ex ſecunda parte huius concluſionis: igitur
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                in toto illo tempore cathegorematice efficitur il-
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                la proportio maior per ꝓportionem compoſitaꝫ
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                ex proportione per quam maior terminus effici-
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                tur maior et ex proportione per quam minor ter-
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                minus efficitur minor: vt patet, et in caſu correla-
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                rii data ꝓportio in fine talis crementi manet ade­
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                quate tanta quanta modo in caſu dato: igitur in
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                caſu correlarii per tantam ꝓportionem efficit̄̄ ma­
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                ior per quam iam in caſu dato: et in caſu dato effi­
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                citur maior per proportionem compoſitam ex ꝓ-
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                portione per quam maior terminus efficitur ma-
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                ior et ex proportione per quam minor efficitur mi­
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                nor: igitur per illam compoſitam ex illis duabus
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                data ꝓportio efficitur maior ī caſu correlarii / qḋ
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                fuit probandum.
                  <note position="right" xlink:href="note-0055-03a" xlink:label="note-0055-03" xml:id="N158C8" xml:space="preserve">2. correl.</note>
                </s>
                <s xml:id="N15705" xml:space="preserve">¶ Sequitur ſecundo /  quando
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                aliqua proportio maioris inequalitatis augetur
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                vtro eius termino creſcente: tunc ipſa efficietur
                  <lb/>
                maior per proportionem per quam proportio ac­
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                quiſita maiori termino excedit ꝓportionem acq̇ſi­
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                tam minori termino. </s>
                <s xml:id="N15712" xml:space="preserve">Probatur / et ſit f. proportio
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                inter b. maiorem et d. minorem: et acquirat b. ter-
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                minus ꝓportionem g. acquirendo ſupra ſe a. lati­
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                tudinem: et d. acquirat h. ꝓportionem acquirēdo
                  <lb/>
                ſupra ſe c. latitudinem / ita  in fine maneat ꝓpor-
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                tio ipſius .ab. ad: cd. excedat tamen proportio g.
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                proportionem h. per e. proportionem: et tunc di-
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                co /  data proportio f. efficitur maior per e. ꝓpor­
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                tionem. </s>
                <s xml:id="N15725" xml:space="preserve">Quod ſic probatur / quoniam ſi quando
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                minor terminus acquirit h. proportionem: maior
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                terminus acquireret tantaꝫ adequate: inter illos
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                termīos adhuc maneret proportio f. / adequate vt
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                patet ex correlario decime ſuppoſitionis ſecundi
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                capitis huius: ſed modo vltra h. proportionē ma-
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                ior terminus acquirit adhuc e. proportionem: mi­
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                nore vltra nichil acquirente: igitur illa ꝓportio f.
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                per e. proportionem efficitur maior / quod fuit pro­
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                bandum. </s>
                <s xml:id="N1573A" xml:space="preserve">Patet conſequentia ex concluſione </s>
                <s xml:id="N1573D" xml:space="preserve">Ma­
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                nifeſtum igitur correlarium.
                  <note position="right" xlink:href="note-0055-04a" xlink:label="note-0055-04" xml:id="N158CE" xml:space="preserve">3. correl.</note>
                </s>
                <s xml:id="N15747" xml:space="preserve">¶ Sequitur tertio / 
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                quando aliqua proportio maioris inequalitatis
                  <lb/>
                augetur vtro eius termino decreſcente: tnnc ip̄a
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                proportio efficitur maior per illam proportiõem
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                per quam proportio deperdita a termino minori
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                excedit proportionem deperditam a termino ma­
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                iori. </s>
                <s xml:id="N15756" xml:space="preserve">Probatur: et ſit .ab. terminus maior: et .cde.
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                minor inter quos ſit ꝓportio f. et perdat terminꝰ
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                maior proportionem que eſt .ab. ad b. et minor ꝓ­
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                portionem .cde. ad e. que excedat proportionē de­
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                perditam a maiori termino per proportionē .de.
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                ad .e. que vocetur g: et tunc dico /  proportio f. effi­
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                citur maior per proportionem g. </s>
                <s xml:id="N15765" xml:space="preserve">Quod ſic ꝓba-
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                tur / quoniam ſi quando maior terminus .ab. per-
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                dit proportionem .ab. ad b. minor perderet adeq̈­
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                te ꝓportionem .cde. ad .de. / tunc inter b. et .de. ma­
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                neret adhuc proportio f. / vt patet ex ſecunda par-
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                te decime ſuppoſitionis ſecundi capitis huiꝰ par­
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                tis: et mõ minor terminus, nichil deperdente aut </s>
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