Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <div xml:id="N1194D" level="2" n="2" type="other" type-free="pars">
            <div xml:id="N15216" level="3" n="8" type="chapter" type-free="capitulum">
              <p xml:id="N14FD2">
                <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.
                  <note position="left" xlink:href="note-0054-01a" xlink:label="note-0054-01" xml:id="N155E5" xml:space="preserve">4. correl.</note>
                </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.
                  <note position="left" xlink:href="note-0054-02a" xlink:label="note-0054-02" xml:id="N155EB" xml:space="preserve">5. correl.</note>
                </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/>
                  <note position="right" xlink:href="note-0054-03a" xlink:label="note-0054-03" xml:id="N155F1" xml:space="preserve">6. correĺ.</note>
                </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.
                  <note position="right" xlink:href="note-0054-04a" xlink:label="note-0054-04" xml:id="N155F7" xml:space="preserve">7. correl.</note>
                </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 </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum