Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secunde partis.
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0046
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46
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quia aggregatum ex aliquo et medietate eiꝰ ē ſex
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quialterum ad illud / vt conſtat ex diffinitione ſex-
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quialteri. </
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<
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N14764
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xml:space
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preserve
">Et iſto modo inuenitur octuplam eē ſex
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quialteram ad quadruplam. </
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<
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xml:id
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N14769
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xml:space
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preserve
">Si vero inueſtigare
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et ſcire velis an q̈drupla habeat ſexquiquartam
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ſcias primo ꝑ doctrinam ſecundi correlarii: an ip
<
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ſa proportio quadrupla habeat ſubquadruplaꝫ
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rationalem: et ſi ſic concludas / habet ſexquiq̈r-
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tam rationalem: quoniam reperta quarta ipſius
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quadruple ad dandam ſexquiquartam ad ipſam
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quadruplam nihil aliud oportet quaꝫ addere ipſi
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quadruple ſuam quartam: et tunc aggregatuꝫ ex
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ipſa quadrupla et ſua quarta rationali ſe habet
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ad ipſaꝫ quadrumplam in proportiõe ſexquiquar
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ta. </
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<
s
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xml:space
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">Continet enim illud aggregatum ipſam qua-
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druplam et vnam quartam eius adequate. </
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<
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N14787
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xml:space
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">Et iſto
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modo inuenitur trigecuplam ſecūdam eſſe ſexqui
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quartam ad ſexdecuplam. </
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<
s
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N1478E
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xml:space
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preserve
">Et iſto modo in quali-
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bet proportione rationali īueſtigare poteris: an
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habeat ſexquioctauam, ſexquiſexdecimam, et ſic
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conſequēter rationales. </
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<
s
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N14797
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xml:space
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preserve
">Et ſic patet correlarium
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<
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xml:space
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xml:space
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">¶ Ex quo ſequitur quarto / ſi aliqua ꝓportio ra
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tionalis non habet ſubduplam rationalem: ipſa
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non habet ſexquialteram rationalem, nec ſexqui
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q̈rtã: nec ſexquioctauam: nec ſexquiſexdecimam: et
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ſic conſequenter. </
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">Probatur / quia ſi talis ꝓportio
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non habeat ſubduplam rationaleꝫ: ſequitur / nõ
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habet numerum qui ſit medium ꝓportionale īter
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ſua extrema: et ſi nõ hꝫ numerū mediū etc. / ſequit̄̄
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non habet ſubquadruplam, nec ſuboctuplam,
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nec ſubſexdecuplam rationalem / et ſic in infinituꝫ
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aſcendendo per numeros pariter pares / vt patet
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ex nona concluſione huius: et ſi non habet ſubdu-
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plam, nec ſubquadruplam: nec ſuboctuplam ra-
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tionales: et ſic conſequenter: iam manifeſtum eſt /
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non habet ſexquialteram rationalem: nec ſex-
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quiquartam: nec ſexquioctauam: et ſic ſine fine / vt
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patet ex probatione precedentis correlarii. </
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ſi data proportio rationalis nõ habet ſubduplaꝫ
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rationalem: ipſa non habet ſexquialteram ratio
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nalem: nec ſexquiquartaꝫ: nec ſexquioctauã etc. / qḋ
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fuit probandum. </
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">¶ Se-
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quitur quinto / ſi aliqua proportio ꝓpoſita non
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habuerit ſubduplam rationalem: ipſa non habe
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bit duplam ſexquialteram rationalem nec duplã
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ſexquiquartam nec ſuprapartienteꝫ quartas, nec
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aliquam ſuprapartientem denominatam ab vni
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tate et partibus aliquotis denominatis a nume-
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ro pariter pari: nec aliquam multiplicē ſuperpar
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ticularem, aut multiplicē ſuprapartientem deno
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minatã a numero et a parte vel partibus aliquo-
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tis que denominantur a numeris pariter paribꝰ
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</
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<
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">Patet hoc correlarium facile: quia ſi data ꝓpor
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tio non habuerit ſubduplam rationalem: iam nõ
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habet illas partes aliquotas rationales deno-
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minatas a numeris pariter paribus: vt patet ex
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quarto correlario: et ſi non habet illas partes ali
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quotas que ſunt ꝓportiones rationales: iam non
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habet illas proportiones rationales denomina-
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tas ab illis partibus / vt conſtat.
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">¶ Ex quo ſequi-
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tur ſexto / nec tripla, nec dupla, habent ꝓportio
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nē ſexquialterã: ſexquiquartam: ſexquioctauam:
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duplã ſupratripartientē quartas rationalem: et
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ſic de multis aliis. </
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bet ſubduplam rationalem: vt patet ex primo cor
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relario: igitur neutra illarum habet ſexquialterã
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ſexquiquartam etc. / vt patet ex īmediate preceden-
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ti. </
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dictis.</
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Capitulum ſextum
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<
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">Nulla propor-
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tio rõnalis ſe habet ī aliqua proportiõe multipli
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ci ad aliquam rationalem niſi inter primos nūe-
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ros eius reperiantur tot numeri cõtinuo ꝓportio
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nabiles computatis etiam extremis vno plꝰ ade-
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quate: quotus eſt numerus a quo denomīatur da
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ta ꝓportio multiplex. </
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<
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">vt ſi velis inue-
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ſtigare et ſcire vtrum ꝓportio quadrupla ſe habe
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at in ꝓportione dupla ad aliquam ꝓportioneꝫ
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rationalem: conſidera primum a quo numero de
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nominatur proportio dupla: et īuenies / a bina
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rio iuxta doctrinam primi correlarii ſecunde ſup
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poſitionis quarti capitis huius: tunc capias pri
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mos numeros eius qui ſunt .4. et .1: et vide ſi inue-
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nias ibi tres numeros continuo ꝓportionabiles
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eadem ꝓportione cõputatis extremis: et ſi ſic dico /
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ꝓportio quadrupla ſe habet in ꝓportione du-
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pla ad aliquaꝫ rationalem. </
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numeri continuo ꝓportionabiles computatis ex
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tremis: iam illa ꝓportio quadrupla que eſt extre-
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mi ad extremum eſt dupla ad vtrã interdiarum:
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vt patet ex octaua concluſione: et ſi velis ſcire an
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quadrupla ſit tripla ad aliquam ꝓportionem ra
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tionalem: quia tripla denominatur a numero ter
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nario. </
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<
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">videas vtrum inter primos numeros ꝓpor
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tionis quadruple reperiantur tres nūeri vno plꝰ
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puta quatuor continuo ꝓportionabiles aliqua ꝓ
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portione: et ſi ſic: tunc quadrupla ſe habet in pro-
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portione tripla ad aliquam ꝓportionē rationalē
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puta ad quãlibet illarum conſtitutarum inter ali
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quos ex illis numeris continuo ꝓportionabilibꝰ
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et īmediatis: et quia tu non inuenies inter primos
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numeros ꝓportionis quadruple quatuor nume-
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ros continuo ꝓportionabiles computatis extre-
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mis: concludas / quadrupla nõ habet ſubtriplã
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rationalem. </
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">q2 ſi data ꝓ
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portio rationalis que ſit a. ſe habeat in aliqua ꝓ
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portione multiplici ad aliquam proportioneꝫ ra
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tionalem que ſit b. / ſequitur / a. aliquoties conti-
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net b. adequate / et ſic b. erit pars aliquota ipſius
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a denominata a numero a quo denominatur pro
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portio multiplex in qua a. ſe habet ad b. / vt puta ſi
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a. ſe habet ad b: in proportione quadrupla erit b.
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vna quarta ipſius a. et ſic erit b. pars aliquota de
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nominata a numero quaternario a quo denomi-
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natur ꝓportio illa multiplex puta quadrupla in
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qua a. ſe habet ad b: et ſi ſic iam neceſſe eſt b. re-
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periatur inter aliquos numeros ipſius a. toties
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quoties eſt numerus a quo denominatur talis ꝓ-
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portio multiplex in qua a. ſe habet ad b. et ſi ſic iã
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inter terminos ipſius a. computatis extremis re-
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perientur tot nūeri quotus eſt ille numerus a quo
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denominatur data ꝓportio multiplex in qua a. ſe
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habet ad b. vno plus: quoniam ſemper termini ſi
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ue numeri continuo ꝓportionabiles ſunt vno plu
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res proportionibus inter ipſos ad inuentis / vt ptꝫ
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ex octaua concluſione huius: et ex conſequēti ſi nõ
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fuerint reperti tot numeri continuo ꝓportionabi-
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les inter aliquos numeros ipſius proportionis a.
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quotus eſt numerus a quo denominatur propor-
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tio multiplex in qua ponitur a. ſe habere ad b. / di-
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co / tūc b. non eſt ꝓportio rationalis nec a. ſe ha
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bet in tali ꝓportione multiplici ad aliquam pro-
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portionem rationalem. </
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tia / quia ſi ſe haberet ad b. proportioneꝫ rationa
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lem in tali ꝓportione multiplici: iam aliquoties
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componeretur ex ipſa b. ꝓportione rationali et ꝑ
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conſequens aliquoties reperiretur b. inter nume-
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ros eius: puta toties quotus ē numerus a quo de- </
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