Alvarus, Thomas, Liber de triplici motu, 1509

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                  <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.
                  <note position="left" xlink:href="note-0056-01a" xlink:label="note-0056-01" xml:id="N158D4" xml:space="preserve">4. correĺ.</note>
                </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
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                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-
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                ma, que ſcilicet eſt inter duas quantitates mino-
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                res, per maiorem proportionem excedit tertiam
                  <lb/>
                que eſt illarum trium proportionū minima: vt ca-
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                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
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                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
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                ex quarta concluſione quarti capitis huiꝰ partis
                  <lb/>
                </s>
                <s xml:id="N157C7" xml:space="preserve">Modo ſexquioctaua ſexquiquindecima maior eſt /
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                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-
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                ſum a. / ita
                  <gap/>
                ta b. quantitas excedat a. quanti-
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                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. /
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                tunc dico /  in fine et poſt iſtorum quatuor diuerſa­
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                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
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                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
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                ua ſuppoſitione quarti capitis huius. </s>
                <s xml:id="N15846" xml:space="preserve">Et maior
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                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
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                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. /
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                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
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                tione: vt patet ex caſu: igitur inter exceſſum quo
                  <lb/>
                maxima puta h. excedit mediam puta c. et exceſſuꝫ
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                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
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                rior pars maioris et per conſequens totum corre-
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                larium.</s>
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