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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41
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IO. BABPT. BENED.
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388
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0388
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0388
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<
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<
s
xml:id
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xml:space
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">Poſſumus etiam probare quod periferia quadrati æqualis triangulo æquilatero
<
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minor ſit periferia ipſius trianguli æquilateri. </
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<
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xml:id
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xml:space
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">Cogita triangulum æquilaterum hic
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ſubſcriptum
<
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>.d.l.q.</
var
>
cuius baſis
<
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>.l.q.</
var
>
diuiſa ſit per æqualia à perpendiculari
<
var
>.d.o.</
var
>
<
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deſcri- ptumque
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type
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ptũq́;</
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ſit rectangulum
<
var
>.o.g.</
var
>
quod æquale erit triangulo
<
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>.d.l.q.</
var
>
ſed periferia trianguli
<
lb
/>
maior eſt periferia rectanguli, nam
<
var
>.l.q.</
var
>
æqualis eſt
<
var
>.o.q.</
var
>
cum
<
var
>.d.g.</
var
>
ſed
<
var
>.q.d.</
var
>
maior eſt
<
var
>.o.
<
lb
/>
d.</
var
>
ex .18. primi, vnde
<
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>.l.d.</
var
>
maior etiam
<
var
>.q.g.</
var
>
cum ex .34. dicti latera oppoſita ipſius re
<
lb
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ctanguli ſint inuicem æqualia, accipiamus poſtea
<
var
>.e.c.</
var
>
æqualem
<
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>.o.d.</
var
>
et
<
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>.c.h.</
var
>
indire-
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ctum æqualem
<
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>.o.q.</
var
>
circa quem diametrum
<
var
>.e.h.</
var
>
intelligatur circulus
<
var
>.e.i.h.k.</
var
>
et. à pun
<
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/>
cto
<
var
>.c.</
var
>
dirigatur perpendicularis
<
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>.k.i.</
var
>
ad
<
var
>.e.h.</
var
>
vnde ex .3. tertij
<
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>.c.i.</
var
>
æqualis erit
<
var
>.c.k.</
var
>
& ex
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34. quod fit ex
<
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>.c.i.</
var
>
in
<
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>.c.k.</
var
>
hoc eſt quadratum ipſius
<
var
>.c.i.</
var
>
æquale erit ei quod fit .ex
<
var
>.e.c.</
var
>
<
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/>
in
<
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>.c.h.</
var
>
hoc eſt rectangulo
<
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>.g.o.</
var
>
hoc eſt triangulo
<
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>.d.l.q.</
var
>
ſed
<
var
>.e.h.</
var
>
eſt dimidium perife-
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lb
/>
rię ipſius rectanguli
<
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>.g.o.</
var
>
quæ minor eſt di midio periferiæ trianguli
<
var
>.d.l.q.</
var
>
vt vidimus
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/>
et
<
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>.i.k.</
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>
eſt dimidium periferię quadrati ipſius
<
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>.i.c.</
var
>
& minor etiam ipſa
<
var
>.e.h.</
var
>
ex .14. tertij
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</
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>
<
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xml:id
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xml:space
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">quare verum eſt propoſitum.</
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0388-01
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xlink:href
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<
p
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<
s
xml:id
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xml:space
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">Sed quando periferiæ ſunt inuicem æquales, poſſumus etiam breuiter videre id
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quod ſupradiximus, hoc eſt, quod quadratum, maius ſit triangulo æquilatero. </
s
>
<
s
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xml:space
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">Nam
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cum
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>.b.g.</
var
>
ſeſquitertia ſit ad
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>.b.a.</
var
>
ergo
<
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>.b.g.</
var
>
erit vt .4. et
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>.b.a.</
var
>
ut .3. vnde
<
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>.b.q.</
var
>
erit vt .16
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et
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>.b.l.</
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>
vt .9. et
<
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>.c.q.</
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>
vt .8. </
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>
<
s
xml:id
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xml:space
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">quare
<
var
>.b.l.</
var
>
maius erit ipſo
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type
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>
<
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>.c.q.</
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>
ſed
<
var
>.c.q.</
var
>
maius eſt
<
reg
norm
="
triam
"
type
="
context
">triã</
reg
>
<
lb
/>
gulo
<
var
>.b.o.g.</
var
>
cum
<
var
>.q.g.</
var
>
quæ æqualis eſt
<
var
>.o.g.</
var
>
maior ſit
<
var
>.o.c.</
var
>
ex .18. vel penultima primi,
<
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/>
nam ſi
<
var
>.q.g.</
var
>
æqualis eſſet
<
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>.o.c.</
var
>
</
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>
<
s
xml:id
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xml:space
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preserve
">tunc
<
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>
æqualis eſſet triangulo
<
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>.b.o.g.</
var
>
ex .41. primi.</
s
>
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<
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>
<
s
xml:id
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xml:space
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preserve
">Alia etiam via maiores noſtri vſi ſunt quæ generalis eſt vt in Theone ſupra Al-
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mageſtum videre eſt, medijs perpendicularibus à centris ad latera figurarum, ſed
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/>
quia
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longitudinum ipſarum perpendicularium alio medio inueniri poteſt,
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/>
eo quo ipſi vſi ſunt, prætermittere nolo quin tibi ſcribam.</
s
>
</
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<
p
>
<
s
xml:id
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xml:space
="
preserve
">Ego enim ita diſcurro.</
s
>
</
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>
<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Sint duæ figuræ iſoperimetrę æquilaterę & æquiangulæ, puta primò trian-
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gulum & quadratum quorum centra ſint
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>.e.</
var
>
et
<
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>.o.</
var
>
à quibus centris ad latera ſint per-
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pendiculares
<
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>.e.n.</
var
>
et
<
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>.o.u.</
var
>
vnde
<
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>.n.</
var
>
et
<
var
>.u.</
var
>
diuident latera per æqualia vt ſcis, ducantur
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poſtea
<
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>.e.t.</
var
>
et
<
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>.o.a.</
var
>
ad angulos dictorum laterum, vnde habebimus angulum
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>
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norm
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"
type
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midiũ</
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recti, et
<
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>.e.t.n.</
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>
tertia pars vnius recti, vt ex te ipſo videre potes, </
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>
<
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