Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali quo ad effectū ſcḋm ſubiectū difformi.
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<
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xml:space
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">Octaua ↄ̨̨cluſio ꝓportio quadratorū
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ꝑfectoꝝ et eque ꝓfundoꝝ vniformiter eſt ꝓp̄ortio co
<
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ſtaꝝ duplicata. </
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<
s
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xml:space
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">Et voco quadratū pērfectū cuiꝰ oēs
<
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coſte ſunt eq̈les et oēs anguli recti eq̈les. </
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<
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xml:space
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gas tñ / velim dicere / oēs coſte debent eſſe eq̈les
<
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ſcḋm oēm dimēſionē: ſed ſatis eſt ſcḋm latitudinem
<
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et lõgitudinē. </
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>
<
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xml:space
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">Exēplū / vt ſi ſit vnū q̈dratū pedaliter
<
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longū, pedaliter latū et pedaliter ꝓfundū: et aliud
<
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/>
bipedaliter longū bipedaliter latū et ſolū pedali-
<
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/>
ter ꝓfundū / tūc dico / vnū eſt q̈druplū ad alteꝝ: qm̄
<
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/>
coſte ſe habēt in proportio dupla et magnitudi-
<
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nes ſe habebãt in ꝓportiõe dupla ad duplã cuiuſ-
<
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modi eſt q̈drupla ꝓportio. </
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>
<
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xml:space
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">Probat̄̄ hec cõcluſio et
<
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capio duo q̈drata ꝑfecta eq̈liter ꝓfunda vniformiṫ /
<
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q̇ꝝ minꝰ ſit a. et maiꝰ c. et habeat ſe coſta ipſius c. ad
<
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/>
coſtã ipſiꝰ a. in ꝓportione f. / tūc dico / ipſiꝰ c. ad ip
<
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ſum a. eſt ꝓportio duplicata ad ꝓportionē ipſiꝰ f.
<
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</
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<
s
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xml:space
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">Quod ꝓbo ſic et capio vnū aliud corpꝰ puta b. / ſit
<
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eque ꝓfundū et eque latū ſicut a. vniformiter et in f.
<
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/>
ꝓportiõe lõgiꝰ et manifeſtū eſt / ipſiꝰ b. ad ipſuꝫ a.
<
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/>
eſt ꝓportio f. / vt ptꝫ ex prima ſuppoſitiõe: et ipſius c.
<
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ad ipſum b. eſt etiã f. ꝓportio: vt ptꝫ ex ſcḋa ſuppo-
<
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ſitione: qm̄ cū ipſū c. (vt ponit̄̄ in caſu) ſit in f. ꝓpor-
<
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tione latiꝰ quã ipſum b. et eſt eque longū et eque ꝓ-
<
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fundū ſicut ipſum b. / igr̄ eſt in f. ꝓportiõe maiꝰ ipſo
<
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b. / vt oſtēdit p̄dicta ſcḋa ſuppoſitio: igr̄ ipſius c. ad
<
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ipſuꝫ a. eſt ꝓportio duplicata ad ꝓportionē f. </
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<
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">Ptꝫ
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hec ↄ̨ña ex cõcluſione octaua ſexti capitis ſcḋe par
<
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tis / qm̄ ibi ſunt .3. termini cõtinuo ꝓportiõales f. ꝓ-
<
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portionē / qm̄ b. ad a. eſt ꝓportio f. et c. ad b. eſt ꝓpor
<
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tio f. / igr̄ c. ad a. eſt proportio duplicata ſiue dupla
<
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ad ꝓportionē f. / vt clare oſtendit p̄dicta octaua con
<
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cluſio allegata.
<
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xml:space
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">1. correĺ.</
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>
</
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<
s
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xml:space
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">¶ Ex hac cõcluſione ſequit̄̄ tale cor-
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relariū / ꝓportio duoꝝ corpoꝝ cuboꝝ ſiue ꝑfecte
<
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/>
quadratoruꝫ ſimpliciter cuiuſmodi ſunt data ſiue
<
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/>
taxilli quoꝝ lõgitudo eſt eq̈lis latitudini et ꝓfūdi-
<
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tati: ē ꝓportio coſtaꝝ triplicata. </
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>
<
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">Exēplū / vt ſi fuerit
<
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vnū corpꝰ cubū pedaliṫ ꝓfundū et aliud corpꝰ cubū
<
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/>
bipedaliter ꝓfundū dico / illud bipedalittr ꝓfun
<
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/>
dū eſt octuplū ad illud pedaliter ꝓfundū / qm̄ coſte
<
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/>
ad coſtã ē ꝓportio dupla / igr̄ ex correlario oꝫ ꝓpor
<
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tionē magnitudīs eē triplã ad ꝓportionē duplã: et
<
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illa ē octupla / vt pꝫ ex ſcḋa ꝑte: igr̄. </
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<
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">Probat̄̄ hoc cor
<
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relariū et capio duo corꝑa cuba quoꝝ latera ſiue co
<
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ſte ſe habeãt in f. ꝓportiõe et ſit minꝰ illoꝝ a. et maiꝰ
<
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/>
illoꝝ d. / deīde capio b. corpꝰ / ſit eq̄ ꝓfnndū et eque
<
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/>
latū ſicut a. et in f. ꝓportiõe lõgiꝰ: deīde capio q̈rtū
<
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/>
corpꝰ puta c. / qḋ ſit eq̄ longū et eq̄ ꝓfundū ſicut b. et ī
<
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/>
f. ꝓportiõe latiꝰ: et arguo ſic / d. ad c. eſt f. ꝓportio / vt
<
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pꝫ ex ſcḋa ſuppõe et b. ad a. ē f. ꝓportio / vt pꝫ ex ṗma /
<
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igr̄ d. ad a. eſt triplicata ꝓportio ſiue tripla ad ꝓ-
<
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portionē f. / vt ptꝫ ex .8. ↄ̨cluſiõe ſexti capitꝪ ſcḋe ꝑtꝪ /
<
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qḋ fuit ꝓbãdū.
<
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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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<
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xml:space
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">¶ Ex q̊ ſequit̄̄ / datꝪ duobꝰ q̈drãgu
<
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lis cubis quoꝝ coſte ſe hñt in ꝓportiõe ſexq̇altera:
<
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maiorꝪ q̈drãguli ad mīorē ē ꝓportio tripla ſuꝑtri
<
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partiēs octauas q̈lis .27. ad .8. </
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<
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xml:space
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">Probat̄̄ qm̄ / vt ptꝫ
<
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ex p̄cedēti correlario ꝓportio duoꝝ cuboꝝ ſiue q̈dra
<
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toꝝ perfectorū ē ꝓportio coſtaꝝ triplata: ſꝫ ꝓpor-
<
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tio tripla ſuꝑtriꝑtiēs .8. eſt tripla ad ꝓportionē ſex
<
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q̇alterã / q̄ ē īter coſtas datoꝝ q̈dratoꝝ: igr̄ talia q̄-
<
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drata cuba ſe hñt ī ꝓportiõe tripla ſuꝑtriꝑtiēte .8.
<
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</
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<
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xml:space
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">Maior ptꝫ cū ↄ̨ña: et ꝓbat̄̄ minor / qm̄ ꝓportior .27.
<
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ad .8. ↄ̨ponit̄̄ ex tribꝰ ſexq̇alterꝪ. </
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>
<
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">Sint em̄ īter illos
<
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nūeros .4. termini cõtinuo ꝓportiõales ꝓportione
<
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ſexq̇altera. </
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>
<
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xml:space
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">Nã .27. ad .18. eſt ꝓportio ſexq̇altera et
<
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18. ad .12. eſt ꝓportio ſexq̇altera et .12. ad .8. ſexq̇alte
<
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ra.
<
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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:space
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">¶ Seq̇tur vlteriꝰ / datis duobꝰ q̈dratis cubicis
<
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quoꝝ latera ſe hñt in ꝓportiõe tripla: īter maius et
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De motu locali quo ad effectū ſcḋm ſubiectū difformi.
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minꝰ reperit̄̄ ꝓportio vicecupla ſeptupla: qualis eſt
<
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ꝓportio .27. ad vnū. </
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>
<
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">Ptꝫ hoc correlariū ex primo
<
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correlario hoc addito / proportio vicecupla ſe-
<
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ptupla ex tribꝰ triplis cõponit̄̄ / qḋ facile eſt ꝓſpice
<
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re. </
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>
<
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">Nã .27. ad .9. eſt ꝓportio tripla: et .9. ad .3. eſt pro
<
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portio tripla: et .3. ad vnū ſimiliter tripla ꝓportio
<
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</
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<
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">Iſto modo ꝓcedēdo aliquãtula primeditatiõe et cõ
<
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ſideratione cõpoſitionis ꝓportionū: īfinita corre-
<
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laria ex p̄dicto primo correlario īferri valent et ſi-
<
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militer ex cõcluſione. </
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<
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">ſed differantur vſ ad mate-
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riam de augmentatione.</
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</
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brauarḋ</
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<
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<
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">Scḋm opinionē q̄ po
<
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nit velocitatē motus difformiter difformis quo ad
<
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ſubiectū attendi debere penes gradū ſummū: ꝓpor
<
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tio motus duaꝝ ſperaꝝ ſiue duoꝝ orbiū: pariter
<
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duoꝝ circuloꝝ in equali tēpore ceteris paribꝰ circū
<
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giratoꝝ eſt ſicut ꝓportio ſuoꝝ diametroꝝ. </
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>
<
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<
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tur hec cõcluſio / qm̄ ꝓportio perimetroꝝ circulorū
<
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eſt ſicut ꝓportio diametroꝝ: et quãto vna diameter
<
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/>
eſt maior altera tanto maiorē lineã deſcribit eius
<
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punctꝰ maxime a centro diſtans: igr̄ cõcluſio vera.
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</
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<
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xml:id
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xml:space
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">¶ Hic tñ aduerte / ad inducendã hanc concluſionē
<
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proceſſu mathematico oportet maiori apparatu
<
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vti quã p̄ſens exigat opus: ſatis eſt em̄ in iſtis. </
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<
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<
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clidi et mathematicoꝝ ṗmoribꝰ fidē exhibere. </
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<
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xml:space
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">In
<
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hac em̄ cõſideratione phiſica mathematice ſcien
<
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tie ſubalternari nõ dedignatur: quēadmodū in ſci
<
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entia de iride ſubalternata perſpectiue dinoſcitur
<
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teſte philoſopho primo poſteriorum.</
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>
</
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xml:space
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mo po-
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ſteriorū.</
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>
<
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<
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<
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">Proportio motuū
<
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duaꝝ ſpheraꝝ ſolidaꝝ eſt ſicut ꝓportio diametro-
<
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rum. </
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>
<
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xml:space
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">Et hoc ſcḋm oēm opinionē. </
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>
<
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xml:id
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xml:space
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">Probat̄̄ ex priori
<
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̄tum ad opinionē / q̄ dicit velocitatē attendi debe-
<
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/>
re penes punctū velociſſime motū. </
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>
<
s
xml:id
="
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xml:space
="
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">Sed ̄tū ad aliã
<
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opinionē ptꝫ / qm̄ ſcḋm aliã velocitas ſpere ſolide
<
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/>
debet attendi ſcḋm lineã deſcriptã a pūcto medio
<
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/>
ſemidiametri īter centrū et circūferentiã: et ꝑ ↄ̨ñs a
<
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/>
puncto deſcripto ab vna quarta ſemidiametri: ſed
<
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/>
in quacū ꝓportione vna diameter eſt maior alte
<
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/>
ra in eadē vna quarta eſt maior vna quarta alteriꝰ /
<
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/>
ergo ſcḋm hãc opinionē in quacū ꝓportionē dia
<
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/>
meter vniꝰ ſpere ſolide erit maior diametro alteriꝰ
<
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/>
in eadē ꝓportiõe maiorē lineã deſcribet punctꝰ me
<
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/>
dius ſemidiametri: et per ↄ̨ñs ꝓportio motus erit
<
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ſicut ꝓportio diametrorum / quod fuit probandū.</
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>
</
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>
<
p
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<
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xml:space
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">Undecima ↄ̨̨cluſio </
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>
<
s
xml:id
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xml:space
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">Proportio motuū
<
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duaꝝ ſperaꝝ īequaliū in eode tēpore circūgirataꝝ
<
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dūmodo ſint ſolide eſt ſubtripla ad ꝓportionē ſpe
<
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raꝝ īter ſe. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Probat̄̄ hec cõcluſio / qm̄ ꝓportio mo-
<
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/>
tuū duaꝝ ſperaꝝ eſt ꝓportio diametroꝝ taliū ſpe
<
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/>
raꝝ / vt ptꝫ ex priori: ſꝫ ꝓportio ſperaꝝ īequaliū eſt
<
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/>
ꝓportio diametroꝝ triplata ſiue eſt tripla ad pro
<
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portionē diametroꝝ / qḋ idē eſt / vt patꝫ ex vltīa decī
<
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elemētoꝝ. </
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>
<
s
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">Euclidis
<
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g̊ ꝓportio diametroꝝ eſt ſubtri
<
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pla ad ꝓportionē ſperaꝝ et talis ē ꝓportio motuū /
<
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/>
igr̄ ꝓportio motuuū duaꝝ ſperaꝝ ineq̈liū etc. ē ſub
<
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tripla ꝓportio ad proportionem ſperarū inter ſe.
<
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/>
<
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xml:id
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xml:space
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preserve
">1. correĺ.</
note
>
</
s
>
<
s
xml:id
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"
xml:space
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">¶ Ex quo ſequit̄̄ / ſi vna ſpera eſt in octuplo maior
<
lb
/>
altera / mouet̄̄ preciſe in duplo velociꝰ altera: et ſi
<
lb
/>
vna ſpera fuerit in triplo ſupertripartiēti octauas
<
lb
/>
maior altera ipſa mouet̄̄ in ſexq̇altero velociꝰ alte
<
lb
/>
ra. </
s
>
<
s
xml:id
="
N1DBF4
"
xml:space
="
preserve
">Ptꝫ hoc correlariū / q̊ ad primã ꝑtē qm̄ ꝓportio
<
lb
/>
octupla eſt tripla ad duplã: g̊ ſi ſpere ſe habēt ī octu
<
lb
/>
pla ꝓportione motꝰ earū ſe habebūt in dupla q̄ eſt
<
lb
/>
ſubtripla ad octuplã: ptꝫ ↄ̨ña ex immediate prece-
<
lb
/>
dēte ↄ̨cluſione. </
s
>
<
s
xml:id
="
N1DBFF
"
xml:space
="
preserve
">Eodē mõ ptꝫ / q̄ ad ſcḋaꝫ partē qm̄ ſi
<
lb
/>
ſpere ſe habent in ꝓportione tripla ſuꝑtripartiēti </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>