Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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ꝑtranſit illã in ſubſexquitertio tēpore vel minori.
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<
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xml:space
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">Cõſequentia eſt nota et minor ꝓbatur: q2 ſi tran-
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ſeundo ſecundã moueretur a ſubtripla ꝓportiõe
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et ſecūda eſſet equalis prime extēſiue / tūc in triplo
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tēpore ꝑtranſiret illã ad tēpus in quo pertranſit
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primã puta in tribus horis qm̄ ꝑtranſit primã in
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hora / vt poſitū eſt: ſed modo illa ſecunda pars eſt
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ſubquadrupla ad primaꝫ / ergo in ſubquadruplo
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tēpore ꝑtranſibit eam: ſed ſubquadruplū ad tres
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horas ſunt .3. quarte: et tres quarte ſūt ſubſexqui
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tertiū ad vnã horã in qua ꝑtranſit primã partem /
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igitur ſecundã trãſit in ſubſexquitertio tēpore ad
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primã. </
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<
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xml:space
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">Et ſic ꝓbabis / tertiã in ſubſexquitertio
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tēpore ꝑtranſit ad ſecundã: et de oībus aliis con-
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ſequenter. </
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<
s
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xml:space
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">adiutorio ſecūdi correlarii quarte con
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cluſionis quarti capitis ſecunde partis.</
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<
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xml:space
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tecedens: dūmodo ille partes ꝓportiõales illius
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reſiſtentie nõ ſe habeant in ꝓportione dupla nec
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in aliqua minori: et nego cõſequentiã. </
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<
s
xml:id
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xml:space
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">Et ratio eſt /
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q2 talis reſiſtentia de qua cõceditur nõ eſt vnifor-
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miter difformis: nec talis potētia requirit tantū
<
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tēpus ad ꝑtranſeundū ſecundã partē ꝓportiõa-
<
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lem quantū ad ꝑtrãſeundū primã: vt iam ꝓbatuꝫ
<
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/>
eſt.
<
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xml:id
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xml:space
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">1. correĺ.</
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<
s
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xml:space
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">¶ Ex deductione et ſolutione huiꝰ argumenti
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ſequitur primo: ſi potentia vt quatuor cõtinuo
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moueretur per mediū vniformiter difforme a non
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gradu reſiſtentie vſ ad quartū: et perpetuo du-
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raret potentia et mediū taliter diſpoſitū: ꝑpetuo
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ipſa moueretur: et nun̄ ipſuꝫ ꝑtranſiret. </
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>
<
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hoc correlariū ex deductiõe et ſolutiõe argumenti
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<
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xml:id
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xml:space
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">2. correĺ.</
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xml:space
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">¶ Sequitur ſecūdo: reſiſtentia vniformiter dif-
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formis nõ correſpõdet gradui medio reſiſtentie:
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ita tantū reſiſtat ſicut gradus medius. </
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>
<
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">Proba
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tur hoc ex p̄cedenti correlario / q2 alias ſequeretur
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potentia vt .4. poſſet in tēpore finito ꝑtranſire
<
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reſiſtentiã vniformiter difformē a nõ gradu vel a
<
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gradu certo minori vſ ad quartū / q2 moueretur
<
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in ea a ꝓportiõe dupla vel aliqua alia certa eq̇ua
<
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lenter per totã illã reſiſtentiam. </
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>
<
s
xml:id
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xml:space
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">¶ Sed q2 aliquis
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poſſet dicere / correſpõdet gradui medio: dūmo
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do g̈dus ſūmꝰ talis teſiſtētie nõ ſit eq̈lis potentie
<
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mouēti in ea vel minor.
<
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xml:id
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xml:space
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uus de
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thebis.</
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<
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">Ideo aliter ꝓbo p̄dictum
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correlariū ratiõe Gaythani de thebis ſi memini:
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q2 ſi correſpõderet gradui medio ſeq̄ret̄̄ / poten
<
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tia vt .9. in equali tēpore adequate ꝑtranſiret re-
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ſiſtentiã vniformiter difformē a nõ gradu vſ ad
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octauū: in quo adequate ꝑtranſiret ſcḋaꝫ medie-
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tatē eiꝰ: ita ita cito ꝑtranſiret totū ſicut eiꝰ me-
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dietatē adequate: ſed ↄ̨ñs eſt manifeſte falſū: igit̄̄
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illud ex quo ſequit̄̄. </
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<
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">Sequela ꝓbatur / q2 talis po-
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tentia vt .9. haberet ad totã illã reſiſtentiã ꝓpor-
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tionē duplã ſexquiquartã: cū tota illa reſiſtentia
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ſit per te vt .4. qui eſt gradus mediꝰ. </
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<
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">Modo .9. ad
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4. eſt ꝓportio dupla ſexquiquarta: et ad ſecundaꝫ
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medietatē haberet ꝓportionē ſexquialterã: cum
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gradus eiꝰ medius ſit vt .6. </
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<
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">Modo .9. ad .6. eſt ꝓ-
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portio ſexquialtera: ſed ꝓportio ſexquialtera eſt
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ſubdupla ad duplã ſexquiquartã / vt patꝫ ex ſexto
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capite ſcḋe partis et ſpaciū trãſeundū ab illa pro
<
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portiõe puta ſcḋa medietas eſt ſubduplū ad totã
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illã reſiſtentiã: ergo ſequit̄̄ / ī equali tēpore ꝑtrã
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ſit illã ſcḋam medietatē et totã illã reſiſtentiã: qḋ
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fuit ꝓbandū.
<
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xml:id
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">3. correĺ.</
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<
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">¶ Sequit̄̄ tertio / quãuis potentia
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vt .4. nõ ſufficit ꝑtrãſire reſiſtentiam vniformiter
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difformē a ſcḋo g̈du vſ ad quartū: cuiꝰ videlicet
<
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prima pars ꝓportiõalis ꝓportiõe dupla incipit
<
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a ſcḋo vſ ad tertiū et ſcḋa īcipit a tertio vſ ad
<
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tertiū cū dimidio / et ſic cõſequēter: nichilominꝰ tñ
<
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Capitulū ſextū.
"/>
talis potētia vt .4. ſufficit ꝑtrãſire tantã reſiſten-
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tiã extenſiue: cuiꝰ videlicet prima pars ꝓportiõa-
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lis ꝓportione quadrupla eſt oīno cõſimilis reſi-
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ſtētie cū prima parte ꝓportiõali ꝓportiõe dupla
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alterius reſiſtentie vniformiter difformis, et ſcḋa
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cū ſecūda, et tertia cū tertia, et ſic cõſequēter. </
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<
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ma pars ptꝫ ex deductione et ſolutione argumēti
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et ſecūda ex deductione et ſolutione replice.
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xml:id
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<
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">¶ Se-
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quitur quarto / quãuis potētia vt .4. nõ ſufficit
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ꝑtranſire in aliquo tēpore finito reſiſtentiã peda
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lem vniformiter difformē terminatã ad quartū:
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cuiꝰ videlicet prima pars ꝓportiõalis ꝓportione
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dupla incipiat a ſcḋo et terminet̄̄ ad tertiū .etc̈. vt
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poſitū eſt in priori ꝑte p̄cedētꝪ correlarii: nichilo
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minus vbi talis reſiſtētia pedalis efficeretur qua
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drupedalis per rarefactionē aut augmentationē
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(nõ eſt cura) ita tamen ille partes reſiſtētie que
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cõtinuo ſe habebant in ꝓportione dupla cõtinuo
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ſe habeant in ꝓportione quadrupla quo ad extē-
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ſionē: ipſis tamē manētibꝰ ſemꝑ in eodē ſtatu quo
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ad ītēſionē: potētia vt .4. ſufficit tūc illã reſiſtentiã
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in tꝑe finito ꝑtrãſire. </
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<
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ex ṗori correlaro et ſcḋa ex deductiõe replice.
<
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xml:id
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xml:space
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<
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">¶ Ex
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q̊ correlario ſequitur facile quītū / quãuis talis
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reſiſtentia ſic ad quadruplū augeat̄̄ extenſiue: ni
<
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chilominus tamē infinite partes eiꝰ ꝓportiõales
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diminuūtur, et efficiūtur minores extenſiue. </
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<
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ma pars ponit̄̄ / et ſcḋa ꝓbatur / q2 ſi infinite mane
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rent tante quãte erant antea: cū maneãt eque in-
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tenſe et eque reſiſtētes: eo modo reſiſterēt quo reſi
<
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ſtebant antea quãdo cõtinuo ſe habebãt in ꝓpor
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tione dupla: ſed antea requirebat̄̄ tēpus infinitū
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ad ꝑtranſeundū illas a tali potentia: cū tantū tē
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pus requirebat̄̄ ad ꝑtranſeundū aliquã partē vel
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maiꝰ quantū ad quãlibet p̄cedentē: vt ptꝫ ex dedu
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ctione argumēti: igitur modo etiã requireret̄̄ tē-
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pus infinitū: ſed hoc eſt falſum / vt patꝫ ex p̄cedenti
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correlario / igitur illud ex quo ſequitur: et ꝑ conſe
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quēs dicendū eſt / īfinite efficiūtur minores extē-
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ſiue: cū nec etiã dicendū ſit / efficiant̄̄ maiores vt
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facile eſſet ꝓbare ꝑ locū a maiori. </
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<
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">Et hoc etiã faci
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le ptꝫ experimēto: nã capto tali pedali ſic diuiſo
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ꝑ partes ꝓportiõales ꝓportiõe dupla vt poſituꝫ
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eſt: et augeatur prima pars ꝓportiõalis eius ad
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quadruplū: ita efficiat̄̄ bipedalis: tūc ad hoc /
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ſecūda efficiatur ſubquadrupla ad ipſaꝫ oportet
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ipſam ſimiliter augeri ad duplū: ita efficiatur
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ſemipedalis: et oportet tertiam manere nec auctã
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nec diminutã: q2 eſt vna octaua: ſed oportet iam
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quartam minui ad ſubduplū: q2 erat vna decima
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ſexta et oportet efficiatur vna triceſimaſecūda:
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vt ſit ſubquadrupla ad octauã que eſt tertia pars /
<
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et tunc manebit equalis cū quīta parte et ſic opor-
<
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tebit quintã ad ſubquadruplum minui: et ſextam
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ad ſuboctuplum: et ſic in infinitū / vt patet intuenti
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igitur.
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xml:id
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xml:space
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">Calcu. in
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capite de
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augmen.</
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<
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xml:space
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">Et ferme hoc modo intendit calculator ꝓ-
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bare in capitulo de augmentatione concluſione
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quindecima probatione ſecunda: quantūcun
<
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modicum ſit aliquod ſubiectum diuiſum per par
<
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tes proportionales certa proportione: et ſit aliud
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quantūcun magnum diuiſum in partes propor
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tionales proportione maiori: aliqua erit pars
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proportionalis minoris, maior parte proporti-
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onali correſpondente maioris.
<
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xml:id
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">6. correĺ</
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<
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xml:space
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">¶ Sequitur ſexto /
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quãuis talis reſiſtentia aucta in quantitate ad
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quadruplum vel octuplum quocun modo pla-
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cuerit: dummodo partes reſiſtentie que antea ſe
<
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habebant in proportione dupla quo ad extenſio
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nem ſe habeãt quo ad extenſionē in proportione </
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