Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secunde partis.
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26
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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.
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">calcu. de
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10. ele. cir
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ca prin.</
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<
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">vt captꝪ his
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terminis: 12.9.7.6. dico / aggregatum ex .12. et. 6
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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. </
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<
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xml:space
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">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.</
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<
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">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:
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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
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<
s
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">Et ex hoc patet ſecunda pars correlarii / quoniam
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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 </
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<
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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.
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">5. correla
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riū.</
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<
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">¶ 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. </
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<
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">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
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et aggregatum ex .10. et .7. eſt minus / vt patet cal-
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culanti </
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">Probatur correlarium / ſint ſex termini a
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b.c.d.e.f. continuo minori et minori differentia ſe
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ſe excedentes. </
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<
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xml:space
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">et dico / aggregatuꝫ ex a. et f. ē ma
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ius quam tertia aggregati ex omnibus illis ter-
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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. </
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">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: </
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xml:space
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">Patet hec conſequentia quoni-
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am ſi primuꝫ eſſet vna tertia oporteret / alia duo
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eſſent due tertie / et ſic non eēt vtrū alioꝝ duorum
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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. </
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">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 /
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vel reliqua duo eſſent due tertie vel aliquod illo
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rum minus eo quod tameu eſt falſum. </
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">Et ex conſe
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quenti arguitur: primum illorum eſt maius quam
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Capitulum ſecundū.
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tertia totius et tertium minus quam tertia ſed pri
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mum illormm eſt aggregatum ex a. et f. et tertium
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eſt aggregatum ex c.d. / igitur aggregatum ex a.f:
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eſt maius quam tertia illius totius et aggregatū
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ex c.d. minus. </
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">Couſequentia patet ex ſe </
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">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
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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. </
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">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:
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ſed modo aggregatum ex a. et f. eſt maius / quã tūc
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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
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eſt maius aggregato ex c.d. / quod fuit ꝓbandum.
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</
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<
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">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. </
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<
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">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
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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. </
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<
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">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. </
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<
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">et tertiū ex tertio et ſexto et quartum
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ex quarto et quinto. </
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<
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">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
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eſt minus quã quarta: </
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<
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">Et ſic in omnibus aliis oꝑa
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beris. </
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<
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">Patet ergo correlariū.
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lariū</
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<
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">¶ 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. </
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<
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">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.
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lariū</
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<
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">¶ 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- </
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