Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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IO. BAPT. BENED.
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390
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0390
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xml:space
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laris trianguli æquilateri cum eiuſdem latere.</
head
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<
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xml:space
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head
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<
s
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xml:space
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">ID quod à me poſtulas eſt omnino impoſſibile, velles enim duos numeros inueni
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re inter ſe ita ſe habentes, vt ſe habent perpendicularis in triangulo æquilatero
<
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cum vno eius laterum, quod vero hoc fieri non poſſit, conſidera in figura præcedenti
<
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triangulum æquilaterum
<
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>.d.l.q.</
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cuius perpendicularis ſit
<
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>.d.o.</
var
>
quæ diuidit
<
var
>.l.q.</
var
>
per
<
lb
/>
æqualia in
<
var
>.o.</
var
>
vnde ex .4. ſecundi Euclidis, quadratum
<
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>.l.q.</
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>
(ideſt
<
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>.d.q.</
var
>
) quadruplum
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erit quadrato
<
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& ex penultima primi ęquale quadratis
<
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et
<
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>
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<
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xml:space
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quitertium quadrato ipſius
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>
& ita quadratum
<
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>.d.o.</
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>
erit triplum quadrato ipſius
<
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>.
<
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o.q.</
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hæe autem proportiones non ſunt vt numeri quadrati ad numerum quadratum
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quod ſi ita fuiſſent, ſequeretur ternarium numerum eſſe quadratum ex .22. octaui.
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ma decimi
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var
>
eſſe incommenſurabilem ipſi
<
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>.l.q.</
var
>
ſeu
<
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>.d.q.</
var
>
in longitudine.</
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<
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<
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xml:space
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ad quadratum ipſius
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>
eſt in ge
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nere ſuperparticulari, cum ſit ſeſquitertia, vnde quadratum ipſius
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numeris da-
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ri non poteſt, eo quod ſi dabilis fuiſſet, ſequeretur, quod inter quadratum ipſius. l
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>.
<
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q.</
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& ipſius
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eſſet aliquis numerus medius proportionalis ex .16. octaui, vnde ex
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octaua eiuſdem vnitas diuiſibilis eſſet, quod fieri non poteſt.</
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xml:space
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<
s
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xml:space
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">MOdum quem conſideraui circa triangulum æquilaterum & pentagonum, vt
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tibi ſignificaui ita ſe habet.</
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<
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xml:space
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ad .3.</
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<
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cuius periferia diſtenta ſit
<
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var
>
baſis autem
<
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>.m.
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g.</
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>
bifariam diuiſa ſit in puncto
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<
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:
<
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>b.g.</
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et
<
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clarum erit
<
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>
perdicu-
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larem eſſe ad
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ex .8. primi Eucli. cum
<
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et
<
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>
(baſes triangulorum
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