Alvarus, Thomas
,
Liber de triplici motu
,
1509
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capitulum
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Secunde partis
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0032
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32
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nalis illatio. </
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<
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xml:space
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">iſto modo arguendo ſicut ſe ha-
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bent octo ad quatuor ita duo ad vnū. </
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<
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xml:space
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">igitur ſicut
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ſe habēt vnū et duo ad duo ita quatuor et octo ad
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octo. </
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<
s
xml:id
="
N12FE8
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xml:space
="
preserve
">Et differt iſte modus arguendi a tertio / quia
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in conſequente tertii inferuntur ꝓportiones ma-
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ioris inequalitatis in iſto autem inferuntur ꝓpor
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tiones minoris inequalitatis.
<
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xlink:href
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note-0032-01a
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note-0032-01
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xml:id
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N1302D
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xml:space
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preserve
">Equa ꝓ-
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portiõa-
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litas.</
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</
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<
s
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N12FF6
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xml:space
="
preserve
">¶ Equa aūt ꝓpor-
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tionalitas eſt duabus multitudinibus quantita-
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tum aut numerorū datis numero equalibus: et ꝓ-
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portionabilibus continuo eadem proportione: ex
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cluſis mediis extremorum ꝓportionalis illatio.
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</
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<
s
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xml:space
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">Iſto modo arguendo ſicut ſe habent .1.2.4. ita .4.
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8.16. / igitur ſicut ſe habent .4. ad .16. ita .1. ad 4.</
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<
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<
s
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xml:space
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">Poteris etiã exēplificare in aliis generibus pro-
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portionū addendo in qualibet illarū duarū mul-
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titudinū quotcun terminos volueris dūmõ ſint
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continuo ꝓportionabiles: et tot in vna multitudīe
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quot in altera. </
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<
s
xml:id
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xml:space
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">¶ Et aduerte / illa particula ſicut
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ſe habent que ponitur in oībus his modis arguē-
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di: denotat ſimilitudinē ſpecificã ꝓportionum.
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xml:id
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xml:space
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">Denota-
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tio illius
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ꝑticule ſi
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cut ſe hꝫ:</
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<
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xml:space
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">Et
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intelligitur ſic ſicut ſe habēt .1.2.4. ita .3.6.12. hoc
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eſt quacun ꝓportione ꝓportionantur ſereatim
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1.2.4. / eadē ꝓportione ſpecifice ꝓportionant̄̄: 3.6.
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12. </
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xml:space
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">¶ Sed qm̄ hi ſex modi argumētandi in ꝓpor-
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tionalitatibus ſunt plurimū vſitati: et apud phi-
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loſophantes calculatores et apud primores ma-
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thematicoꝝ celebres habentur quibus magnam
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ſue doctrine partē demõſtrant: ideo nõ abs re eos
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arguendi modos in preſentiaꝝ duxi demonſtran
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dos: qm̄ hoꝝ modoꝝ arguendi demõſtrationes ex
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precedenti capite eliciūtur facile. </
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<
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">Prima concluſio. </
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">Argumentatio a
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cõuerſa ꝓportiõalitate eſt neceſſariū argumentū.
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</
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<
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xml:space
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">Hec concluſio ſuã demonſtrationē ex tertio corre-
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lario quarte cõcluſionis precedentis capitis ſorti
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tur: qm̄ illud correlariū principaliter oſtēdit hūc
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modū arguēdi ꝓportiõalitate cõuerſa eſſe validū</
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<
s
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N13092
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xml:space
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">Secunda concluſio modus ratioci-
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nandi a ꝓportionalitate permutata ſiue cõmuta-
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ta infallibilis eſt. </
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<
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xml:space
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">Probatur hec cõcluſio manife-
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ſte ex quarta precedentis capitis. </
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<
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et illa intendunt.</
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">Tertia cõcluſio </
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">Deductio illa et mo
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dus arguendi qui ꝓportionalitati cõiuncte īnitit̄̄
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omni exceptione eſt maior. </
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monſtratione euidenti ex primo correlario eiuſdē
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quarte concluſionis.</
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">Forma ratiocinã
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di a diſiūcta ꝓportiõalitate oēm exuperat inſtan-
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tiam. </
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ſio patrocinante quarto correlario quarte cõclu-
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ſionis predicte manifeſta euadet.</
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">Quinta concluſio </
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">Conſequentia il
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la que ꝓportionalitas euerſa nūcupat̄̄ omne du-
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bietatis telū euertit facile: et inconcuſſa permanet
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</
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">Equa argumenta
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tio ita equitatis mediū ſureat: vt nullo inſtantie
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vicio in eã adducto ab equitatꝪ et rectitudinis tra
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mite declinet. </
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">Huiꝰ concluſionis inconcuſſa equi-
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tas at īuiolata veritas clipeis et armis ſexti cor
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relarii eiuſdē concluſionis munitur et defenſatur
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<
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xml:space
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">Et hec ad demõſtrandos predictos arguendi mo
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dos dixiſſe ſufficiat / qm̄ illoꝝ correlarioꝝ demon-
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ſtratio harum cõcluſionum eſt euidens probatio.</
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Capitulum quartū.
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<
head
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xml:space
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">Capitulum quartum / in quo agitur de ex-
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ceſſu cõpoſitione et diuiſione ꝓportionū.</
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<
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<
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quibus ꝓportionibus ꝓportio aliqua
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cõponitur: in quas reſoluitur: et qua vĺ
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quibus minorē excedit: pono aliquas ſuppoſitio-
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nes quarum alique ſunt diffinitiones: et petitio-
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nes: alie vero demonſtrabuntur.</
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<
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<
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">Prima ſuppoſitio. </
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<
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">Primi termini a-
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licuius ꝓportionis ſunt illi qui in ſua ꝓportione
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ſunt minimi.
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right
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xlink:href
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xml:id
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xml:space
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">Minimi
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termini.</
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<
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">Minimi autē termini alicuiꝰ ꝓporti-
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onis (et loquor tam in quantitate continua quam
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diſcreta) ſunt quorū minor denominatur ab vni-
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tate: maior vero a numero vel numero cū fractiõe
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vel vnitate cū fractione. </
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<
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tio eſt ſed exēplo explicatur binarius em̄ et vnitas
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ſunt primi termini ꝓportionis duple: ternarius et
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vnitas triple: quaternarius et vnitas quadruple:
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et ſic cõſequenter. </
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<
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">Unitas et vnitas cū medietate: et
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vnitas cū vnitate et tertia. </
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<
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">Itē vnitas cū quarta et
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vnitas / et ſic cõſequenter ſunt primi termini ſuper-
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particulariū proportionum. </
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<
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">Unitatis .n. cum me-
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dietate ad vnitatem eſt ſexquialtera: et vnitatis
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cum tertia ad vnitatem ſexquitertia: vnitatis cum
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quarta ſexquiquarta: et ſic conſequēter. </
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<
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xml:space
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">Et iſto mo
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do exēplificabis in aliis generibus proportionis.</
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<
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">Secunda ſuppoſitio. </
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<
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">Denominatio
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alicuius ꝓportionis eſt illa que ſumitur a maiori
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primoꝝ terminoꝝ talis ꝓportionis. </
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<
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">vt denomina
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tio duple ſumitur a binario qui eſt maior termi-
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norū primoꝝ proportionis duple: et denominatio
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ſexquialtere ab vnitate cū dimidio.
<
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xlink:href
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xml:space
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">1. correla
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rium.</
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</
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<
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">¶ Ex quo ſe-
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quitur / ſpecies ꝓportionis multiplicis denomi
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nãtur cõſequenter a naturali ſerie numeroꝝ. </
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<
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">Ptꝫ /
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q2 maior terminus primoꝝ terminoꝝ ꝓportionis
<
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duple eſt binariꝰ, triple, ternariꝰ, quadruple qua
<
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ternarius: et ſic conſequēter ꝓcedendo per natura
<
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lē ſeriē numeroꝝ referendo numeros ad vnitatem /
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igitur ex ſecūda ſuppoſitione tales ſpecies deno-
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minantur a naturali ſerie.
<
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xml:id
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xml:space
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">2. correĺ.</
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<
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xml:space
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">¶ Sequitur ſecundo /
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ſpecies ꝓportionis ſuperparticularis denominã
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tur ab vnitate cū aliqua parte aliquota. </
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<
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xml:space
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">Probat̄̄ /
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q2 maior terminus primoꝝ numeroꝝ ꝓportionis
<
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ſexquialtere eſt vnitas cū dimidio: et ſexquitertie
<
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vnitas cū tertia: et ſexquiquarta cū quarta / et ſex-
<
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quiquinta cū quinta: et ſic conſequenter deſcendē-
<
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do per partes aliquotas denominatas continuo
<
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a naturali ſerie numeroꝝ: igitur ſpecies ꝓportio-
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nis ſuperparticularis denominantur ab vnitate
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cū parte aliquota.
<
note
position
="
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xlink:href
="
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xlink:label
="
note-0032-06
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xml:id
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xml:space
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">3. correĺ.</
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</
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<
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xml:id
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xml:space
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">¶ Sequitur tertio / oēs ſpeci-
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es ꝓportionis ſuprapartientis denominantur ab
<
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vnitate cū aliquot partibus aliquotis nõ facien-
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tibus vnã. </
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>
<
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="
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xml:space
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">Probatur / q2 maior primoꝝ terminoꝝ
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ꝓportionis ſuprabipartientis tertias eſt vnitas
<
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cū duabus tertiis: et ſuprapartiētis quītas vni-
<
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tas cū duabus quintis: et ſuprabipartientis ſepti
<
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mas vnitas cū duabus ſeptimis: et ſic conſequen-
<
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ter: diſcurrēdo per duas partes aliquotas nume-
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ri imparis. </
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>
<
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N131C6
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xml:space
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">Item diſcurrendo per tres partes ali
<
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quotas nõ facientes vnã. / per quatuor. / per quin /
<
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et ſic conſequenter: igitur ſpecies ꝓportionis ſu-
<
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prapartiētis denominãtur ab vnitate cū aliquot
<
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partibus aliquotis nõ facientibus vnã
<
note
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xlink:href
="
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note-0032-07
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xml:id
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xml:space
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">4. correĺ.</
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>
</
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<
s
xml:id
="
N131D6
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xml:space
="
preserve
">¶ Sequit̄̄
<
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quarto / ꝓportiones cõpoſite denominãtur a nu
<
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/>
mero cū fractione partis aliquote vel partiū ali-
<
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quotarū nõ facientiū vnã. </
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>
<
s
xml:id
="
N131DF
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xml:space
="
preserve
">Oſtendas hoc correla-
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riū ſicut precedentia.</
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