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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xml:space
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">De incommenſur abilitate, in longitudine perpendicu-
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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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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
<
lb
/>
cum vno eius laterum, quod vero hoc fieri non poſſit, conſidera in figura præcedenti
<
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triangulum æquilaterum
<
var
>.d.l.q.</
var
>
cuius perpendicularis ſit
<
var
>.d.o.</
var
>
quæ diuidit
<
var
>.l.q.</
var
>
per
<
lb
/>
æqualia in
<
var
>.o.</
var
>
vnde ex .4. ſecundi Euclidis, quadratum
<
var
>.l.q.</
var
>
(ideſt
<
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>.d.q.</
var
>
) quadruplum
<
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erit quadrato
<
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var
>
& ex penultima primi ęquale quadratis
<
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>.d.o.</
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et
<
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>.o.q.</
var
>
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<
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xml:space
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">quare erit ſeſ-
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quitertium quadrato ipſius
<
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>.d.o.</
var
>
& ita quadratum
<
var
>.d.o.</
var
>
erit triplum quadrato ipſius
<
var
>.
<
lb
/>
o.q.</
var
>
hæe autem proportiones non ſunt vt numeri quadrati ad numerum quadratum
<
lb
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quod ſi ita fuiſſent, ſequeretur ternarium numerum eſſe quadratum ex .22. octaui.
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xml:space
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">Cum igitur non ſint vt numeri quadrati ad numerum quadratum, ſequitur ex ſepti-
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ma decimi
<
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>.d.o.</
var
>
eſſe incommenſurabilem ipſi
<
var
>.l.q.</
var
>
ſeu
<
var
>.d.q.</
var
>
in longitudine.</
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<
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<
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xml:space
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">Vel dicamus ita, proportio quadrati ipſius
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>
ad quadratum ipſius
<
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>.o.d.</
var
>
eſt in ge
<
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nere ſuperparticulari, cum ſit ſeſquitertia, vnde quadratum ipſius
<
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>.d.o.</
var
>
numeris da-
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ri non poteſt, eo quod ſi dabilis fuiſſet, ſequeretur, quod inter quadratum ipſius. l
<
unsure
/>
<
var
>.
<
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q.</
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>
& ipſius
<
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>.d.o.</
var
>
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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<
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xml:space
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">Iam tibi notam puto proportionem lateris trianguli ad latus pentagoni eſſe vt .5.
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ad .3.</
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>
cuius periferia diſtenta ſit
<
var
>.K.z.</
var
>
baſis autem
<
var
>.m.
<
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/>
g.</
var
>
bifariam diuiſa ſit in puncto
<
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var
>
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type
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>
<
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var
>
:
<
var
>b.g.</
var
>
et
<
var
>.b.m.</
var
>
clarum erit
<
var
>.a.b.</
var
>
perdicu-
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/>
larem eſſe ad
<
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>.m.g.</
var
>
ex .8. primi Eucli. cum
<
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var
>
et
<
var
>.b.g.</
var
>
(baſes triangulorum
<
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var
>
</
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