Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15216" level="3" n="8" type="chapter" type-free="capitulum">
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                  <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.
                  <note position="left" xlink:href="note-0051-01a" xlink:label="note-0051-01" xml:id="N14FB8" xml:space="preserve">1. correl.</note>
                </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>
              <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.
                  <note position="left" xlink:href="note-0051-02a" xlink:label="note-0051-02" xml:id="N15109" xml:space="preserve">1. correl.</note>
                </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.
                  <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>
                </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.
                  <note position="right" xlink:href="note-0051-04a" xlink:label="note-0051-04" xml:id="N15119" xml:space="preserve">3. correl.</note>
                </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
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                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
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                bare /  .hd. eſt maius quam .cd. quia h. eſt maius
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                ipſo c. cum a. maiorem ꝓportionem habeat ad c.
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                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"/>
              </p>
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