Alvarus, Thomas, Liber de triplici motu, 1509

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                  <pb chead="Secunde partis." file="0026" n="26"/>
                ri differentia: aggregatum ex extremis eſt maius
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                aggregato ex mediis: et eſt maius quaꝫ medietas
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                aggregati ex illis quatnor terminis.
                  <note position="left" xlink:href="note-0026-01a" xlink:label="note-0026-01" xml:id="N12551" xml:space="preserve">calcu. de
                    <lb/>
                  10. ele. cir­
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                  ca prin.</note>
                </s>
                <s xml:id="N1251D" xml:space="preserve">vt captꝪ his
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                terminis: 12.9.7.6. dico /  aggregatum ex .12. et. 6
                  <lb/>
                eſt maius aggregato ex .9. et .7. et eſt maius quam
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                medietas illorum quatuor terminorum coniūcto­
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                rum. </s>
                <s xml:id="N12528" xml:space="preserve">Probatur / ſint quatuor termini a.b.c.d. con­
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                tinuo minores et minores continuo minori et mi­
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                nori differentia ſeſe excedentes: et dico /  aggre-
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                gatum ex a. et .d. eſt maius aggregato ex .b. et .c.</s>
              </p>
              <p xml:id="N1255B">
                <s xml:id="N1255C" xml:space="preserve">Quod ſic probatur / quia ſi c. excederet d. tãta dif-
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                ferentia quanta a. excedit .b. / tunc aggregatum ex
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                a. et d. eſſet equalis aggregato ex b.c. / vt patet ex
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                concluſione: ſed modo c. excedit d. minori exceſſu /
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                igitur d. eſt maius quam eſſet tunc et a. eſt equale:
                  <lb/>
                igitur aggregatum ex a.d. eſt maius quã eſſet tūc
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                quia componitur ex vno tanto ex quanto / tunc cõ­
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                poneretur et ex vno altero maiore quã tunc et hoc
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                adequate: igitur modo eſt maius quam tunc: ſed
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                tunc eſſet equale aggregato ex b. et c. / ergo modo ē
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                maius aggregato ex b. et c. / quod fuit probandum
                  <lb/>
                </s>
                <s xml:id="N12574" xml:space="preserve">Et ex hoc patet ſecunda pars correlarii / quoniam
                  <lb/>
                aggregatum ex omnibus illis terminis componi­
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                tur ex duobus inequalibus adequate puta ex ag-
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                gregato ex a. et d. et aggregato ex b. et c. et aggre­
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                gatum ex a. et d. eſt maius aggregato ex b. et c. / igi­
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                tur aggregatum ex a. et d. eſt maius quam medie-
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                tas totius aggreti ex illis quatuor terminis </s>
                <s xml:id="N12583" xml:space="preserve">Pa­
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                tet hec conſequētia / q2 qñcun aliquid componi-
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                tur ex duobus inequalibus adequate maius illo-
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                rum eſt magis quam medietas totius / vt facile de­
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                monſtrabitur.
                  <note position="left" xlink:href="note-0026-02a" xlink:label="note-0026-02" xml:id="N1272B" xml:space="preserve">5. correla­
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                  riū.</note>
                </s>
                <s xml:id="N12593" xml:space="preserve">¶ Sequitur quinto /  ſi ſint ſex ter­
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                mini continuo minores minori exceſſu ſeſe con-
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                tinuo excedentes aut .8. aut .10. aut in quouis nu-
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                mero pari: aggregatuꝫ ex primo et vltimo eſt ma­
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                ius quam pars aliquota denominata a numero
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                ſubduplo ad numerum illorum terminorum: et ag­
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                gregatum ex duobus terminis mediis et īmedia-
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                tis eſt minus quam talis pars aliquota totius ag­
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                gregati ex omnibus illis terminis. </s>
                <s xml:id="N125A6" xml:space="preserve">vt .19.14.10.7.
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                5.4. captis aggregatum ex .19. et .4. eſt maius quã
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                vna tertia aggregati ex omnibus illis ſex termīs
                  <lb/>
                et aggregatum ex .10. et .7. eſt minus / vt patet cal-
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                culanti </s>
                <s xml:id="N125B1" xml:space="preserve">Probatur correlarium / ſint ſex termini a
                  <lb/>
                b.c.d.e.f. continuo minori et minori differentia ſe­
                  <lb/>
                ſe excedentes. </s>
                <s xml:id="N125B8" xml:space="preserve">et dico /  aggregatuꝫ ex a. et f. ē ma­
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                ius quam tertia aggregati ex omnibus illis ter-
                  <lb/>
                minis et aggregatum ex c.d. terminis mediis et ī-
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                mediatis eſt minus quam tertia totius aggrega-
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                ti ex omnibus ſex. </s>
                <s xml:id="N125C3" xml:space="preserve">Probatur / quia totum illud ag­
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                gregatum ex omnibus illis ſex componixur ex tri­
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                bus inequalibus adequate quorum primum ē ma­
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                ius ſecundo et ſecundum maius tertio / igitur pri-
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                mum eſt maius quam tertia totius: et tertium mi-
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                nus quam tertia: </s>
                <s xml:id="N125D0" xml:space="preserve">Patet hec conſequentia quoni-
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                am ſi primuꝫ eſſet vna tertia oporteret /  alia duo
                  <lb/>
                eſſent due tertie / et ſic non eēt vtrū alioꝝ duorum
                  <lb/>
                minus primo: et ſi primum eſſet minus qnaꝫ tertia
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                oporteret /  aliquod aliorū eſſet maius primo: q2
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                alias illa tria non facerent tres tertias illius to-
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                tius: et ſic nõ adequate componerēt totū. </s>
                <s xml:id="N125DF" xml:space="preserve">Et eodē
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                modo patet /  tertium eſt minus quam tertia to-
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                tius quia ſi eſſet tertia vel maius tertia oporteret /
                  <lb/>
                 vel reliqua duo eſſent due tertie vel aliquod illo­
                  <lb/>
                rum minus eo quod tameu eſt falſum. </s>
                <s xml:id="N125EA" xml:space="preserve">Et ex conſe­
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                quenti arguitur: primum illorum eſt maius quam
                  <cb chead="Capitulum ſecundū."/>
                tertia totius et tertium minus quam tertia ſed pri­
                  <lb/>
                mum illormm eſt aggregatum ex a. et f. et tertium
                  <lb/>
                eſt aggregatum ex c.d. / igitur aggregatum ex a.f:
                  <lb/>
                eſt maius quam tertia illius totius et aggregatū
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                ex c.d. minus. </s>
                <s xml:id="N125FA" xml:space="preserve">Couſequentia patet ex ſe </s>
                <s xml:id="N125FD" xml:space="preserve">Sed reſtat
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                ſimul probare aggregatum ex omnibus illis ſex
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                terminis cõponi ex tribus inequalibus quoruꝫ pri­
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                mum eſt maius ſecundo 2. ſecundū maius tertio et
                  <lb/>
                 primum illorum eſt aggregatū ex a. et f. et ſccun­
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                dū aggregatū ex b. et e. etc̈. quia aggregatum ex il­
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                lis ſex terminis cõponitur adequate ex aggregato
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                ex a. et f. et aggregato ex b. et e. et aggregato ex c. et
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                d. / que ſunt tria aggregata partialia / vt conſtat: et
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                aggregatum ex a. et .f. eſt maius aggregato ex b. et
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                e. etc̈. / igitur propoſitū. </s>
                <s xml:id="N12614" xml:space="preserve">Arguitur minor / quia ſi per
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                tantã dnr̄aꝫ ſiue tantū exceſſū e. excederet f. ſicut a.
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                excedit b. / tunc aggregatum ex a. et f. eēt equale ag­
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                gregato ex b. et e. / vt patet ex ſecunda concluſione:
                  <lb/>
                ſed modo aggregatum ex a. et f. eſt maius / quã tūc
                  <lb/>
                quia vna pars eius v3 f. eſt maior / quam tunc et re-
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                liqua equalis puta a. quia per minus exceditur f.
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                ab vno tertio / quam tunc ab eodem / igitur aggre-
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                gatum ex a. et f. eſt maius aggregato ex b. et e. / et ea­
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                dem ratione probabitur /  aggregatum ex b. et e
                  <lb/>
                eſt maius aggregato ex c.d. / quod fuit ꝓbandum.
                  <lb/>
                </s>
                <s xml:id="N1262C" xml:space="preserve">Et equali ratione probabis /  cuꝫ dantur octo ter­
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                mini continuo per minus et minus ſe excedentes:
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                et continuo minores et minores:  tunc aggrega­
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                tum ex primo et vltimo eſt maius ꝙ̄ quarta aggre­
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                gati ex omnibus: et aggregatum ex quarto et quī­
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                to eſt minus quam quarta. </s>
                <s xml:id="N12639" xml:space="preserve">Et ſi ſint decem aggre­
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                gatum ex primo et vltimo eſt maius quaꝫ vna quī­
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                ta totius: et aggregatum ex quinto et ſexto eſt mi­
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                nus quam quinta totius: et ſic conſequenter: quia
                  <lb/>
                tale aggregatum ex octo talibus terminis cõpo-
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                nitur ex quatuor quorum quodlibet eſt cuilibet al­
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                teri inequale. </s>
                <s xml:id="N12648" xml:space="preserve">puta primū maius ſecundo et ſecun­
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                dū maius tertio / et ſic ↄ̨ſequenter: et primū illoꝝ eſt
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                aggregatū ex primo et vltimo et ſecundū ex ſecun­
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                do et ſeptimo. </s>
                <s xml:id="N12651" xml:space="preserve">et tertiū ex tertio et ſexto et quartum
                  <lb/>
                ex quarto et quinto. </s>
                <s xml:id="N12656" xml:space="preserve">igitur maximū illorum puta
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                aggregatū ex primo et vltimo eſt maius quã q̈r-
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                ta et minimū puta aggregatū eſt quarto et quinto
                  <lb/>
                eſt minus quã quarta: </s>
                <s xml:id="N1265F" xml:space="preserve">Et ſic in omnibus aliis oꝑa­
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                beris. </s>
                <s xml:id="N12664" xml:space="preserve">Patet ergo correlariū.
                  <note position="right" xlink:href="note-0026-03a" xlink:label="note-0026-03" xml:id="N12733" xml:space="preserve">6. corre-
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                  lariū</note>
                </s>
                <s xml:id="N1266C" xml:space="preserve">¶ Sexto ſequitur / 
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                ſi ſint plures termini in numero pari conſtituti cõ­
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                tinuo maiores et maiores continuo maiori et ma­
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                iori exceſſu ſe excedentes: aggregatum ex primo et
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                vltimo eſt maius quã pars aliquota denoīata a
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                numero ſubduplo ad numerū in quo illi termini
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                conſtituuntur et aggregatū ex duobus mediis ī-
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                mediatis equaliter diſtantibus ab extremis: mi-
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                nus quam pars aliquota denoīata ab eodem nu­
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                mero ſubduplo. vt .4.5.7.10.14.19. captis: aggre-
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                gatum ex extremis puta ex .4. et .19. eſt maius quã
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                tertia totius aggregati ex omnibus illis: et aggre­
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                gatum ex .7. et .10. eſt minus quã tertia totius. </s>
                <s xml:id="N12687" xml:space="preserve">Hoc
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                correlariuꝫ ex p̄cedenti ſuã ſortitur demonſtratio­
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                nē et quidē euidenter quoniã in eiſdē terminis de­
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                monſtratur ordine prepoſtero ſe habentibus: pu-
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                ta in iſto incipiendo a minoribus in precedenti ve­
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                ro a maioribus.
                  <note position="right" xlink:href="note-0026-04a" xlink:label="note-0026-04" xml:id="N1273B" xml:space="preserve">7. corre-
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                  lariū</note>
                </s>
                <s xml:id="N12699" xml:space="preserve">¶ Sequitur ſeptimo /  ſi ſint plu­
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                res termini numero pari conſtituti continuo mi-
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                nores et minores maiori et maiori exceſſu ſeſe cõ-
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                tinuo excedenter: aggregatuꝫ ex primo et vltimo
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                erit minor pars aliquota totius aggregati ex oī- </s>
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