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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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0224
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diametri ſint
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et
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quæ ſe inuicem interſecent in puncto
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vnde cum anguli
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contra ſe poſiti circa
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æquales inuicem ſint ex .15. primi Eucli. </
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">& angulus
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æ-
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qualis angulo
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& angulus
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æqualis angulo
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et
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angulo
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ex .20. tertij tunc triangulus
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ſimilis erit triangulo
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et
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ſimilis trian-
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gulo
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ex definitione. </
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<
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xml:space
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">Vnde eadem proportio erit ipſius
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ad
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quæ ipſius
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ad
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& ipſius
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eadem quæ
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ad
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& ipſius
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eadem
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quæ
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ad
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proportio igitur
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ad
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cognita nobis erit, vt compoſita ex
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ea quæ eſt
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ad
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ex
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var
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ad
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quæ nobis cognitę ſunt, mediante
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proportione ipſius
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ad
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& ipſius
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ad
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proportio ſimiliter ipſius
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ad
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nobis cognita erit, vt compoſita ex proportione ipſius
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ad
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>
&
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ipſius
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ad
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cognitis, mediante proportione ipſius
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ad
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& ipſius
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ad
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<
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cum
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type
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proportio ipſius
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ad
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>
nobis cognita ſit, </
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>
<
s
xml:id
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xml:space
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">tunc nobis cognita erit
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proportio ipſius
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var
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ad
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>.a.b</
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. </
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>
<
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xml:id
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xml:space
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ad
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>
eſt vt
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ad
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ex ſimilitudine,
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</
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>
<
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xml:space
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">quare proportio compoſiti ex primo, & quarto terminorum ad compoſitum ex .2. &
<
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tertio, cognita erit. </
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>
<
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xml:id
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xml:space
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">ſed quod fit ex
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var
>
in
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var
>
cognitum nobis eſt, vt æquale duobus
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productis, hoc eſt ex
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var
>
in
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var
>
& ex
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var
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in
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var
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var
>
ex ſecunda primi Almageſti. </
s
>
<
s
xml:id
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xml:space
="
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">quæ
<
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producta nobis cognita ſunt, cum nobis data ſint eorum latera. </
s
>
<
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xml:space
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">Quapropter facta
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cum fuerit figura quadrilatera rectangula ſimilis alicui alterirectangulæ figuræ pro
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ductæ à duobus lateribus inuicem ita proportionatis, vt ſe habet
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var
>
ad
<
var
>.a.b.</
var
>
æqua-
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lis tamen duobus productis, hoc eſt producto ex
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in
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var
>
& ex
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var
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in
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>
ex
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doctrina, 25. ſexti Eucli quæ quidem figura, exempli gratia, ſit
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>
eius verò latera
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ſint
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var
>
et
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var
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var
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Hæc enim dico æqualia eſſe
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et
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hoc eſt
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var
>
maius maio-
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ri
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>
et
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var
>
minus minori
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var
>
. </
s
>
<
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">Quod ita probabo. </
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<
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xml:space
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">cogitemus rectangulum
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var
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productum eſſe ex duobus lateribus
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var
>
et
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var
>
ſed,
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var
>
æqualis ſit
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var
>
et
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var
>
æqua-
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lis
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var
>
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norm
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ſintque
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type
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reg
>
duæ lineæ
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var
>
et
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var
>
inuicem directè coniunctæ, vnde
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var
>
directè
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coniuncta etiam erit cum
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var
>
ex quo rectangulum
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var
>
æquale erit rectangulo
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var
>
ex
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communi conceptu,
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type
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proportio erit
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ad
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quę
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var
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ad
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eo
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ita fa-
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ctum fuit, cum autem ita ſit
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ad
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vt
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var
>
ad
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var
>
</
s
>
<
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xml:id
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xml:space
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">tunc permutando ita erit
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var
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ad
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<
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var
>
vt
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var
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ad
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var
>
ſed quia ita eſt
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var
>
ad
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var
>
vt
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var
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ad
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var
>
ex 15. ſexti, </
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<
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xml:space
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">tunc permutan
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do ita erit
<
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>.n.r.</
var
>
ad
<
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var
>
vt
<
var
>.n.u.</
var
>
ad
<
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>.n.s.</
var
>
</
s
>
<
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xml:space
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">quare ex 11. quinti ita erit
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var
>
ad
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var
>
vt
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var
>
ad
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var
>.n.
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t.</
var
>
quapropter ex neceſſitate ſequitur
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var
>
et
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var
>
inuicem æquales eſſe, et
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var
>
ſimiliter
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cum
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>.n.s</
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>
.</
s
>
</
p
>
<
p
>
<
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xml:id
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xml:space
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">Inuentæ nunc cum fuerint duæ diametri
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var
>
et
<
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>.a.b.</
var
>
ipſius quadrilateri, difficile
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non erit eius angulos inuenire, eo
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reg
norm
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quod
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type
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>
mediante
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>
cognita, ſimul cum
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var
>
et
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var
>
da
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tis, faciemus triangulum
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var
>
vel
<
reg
norm
="
mediante
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type
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context
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reg
>
<
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>.q.d.</
var
>
et
<
var
>.q.a.</
var
>
et
<
var
>.a.d.</
var
>
cognitis faciemus
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norm
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triam
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type
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context
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>
<
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gulum
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>.a.q.d.</
var
>
ex .22. primi. </
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>
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xml:space
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">Vnde cum centrum circuli circunſcriptibilis cuiuſuis di-
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ctorum triangulorum ex quinta quarti inuentum fuerit, triangulum reliquum, ab eo
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dem circulo circunſcriptum erit, ex communi ſcientia.</
s
>
</
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<
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<
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xml:space
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">SEd vt ipſa operatio facilior fiat, Sint eędem lineæ
<
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>.b.d</
var
>
:
<
var
>b.q</
var
>
:
<
var
>a.q.</
var
>
et
<
var
>.a.d.</
var
>
ex quibus
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poſſit
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type
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effici. </
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<
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xml:space
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">Videatur deinde primò quas volumus oppoſitas ſibi
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inuicem eſſe, ponatur ergò ut
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var
>
et
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var
>
velimus oppoſitas inuicem facere, et
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>
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cum
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>
ſimiliter, accipiemus nunc
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var
>
cuiuſuis magnitudinis, cui comparetur
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var
>
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ita proportionata, vt
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var
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var
>
eſt ipſi
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>
ex doctrina .10. ſexti Eucli. vel accipiatur
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var
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var
>
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/>
vice
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var
>.K.</
var
>
et
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var
>.q.b.</
var
>
vice
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var
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>
quod idem erit, & expeditius, inuenietur ſimiliter
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>
ita pro-
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portionata ad
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>
et
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>
ad
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vt
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>
eſt ad
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>
vel
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>
ad
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var
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>
vt
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ipſi
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>
quod
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type
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>
erit.</
s
>
</
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>
<
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>
<
s
xml:id
="
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xml:space
="
preserve
">Hoc facto coniungantur inuicem directè
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>.g.</
var
>
et
<
var
>.e.</
var
>
quarum compoſitum ſit
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var
>.g.e.</
var
>
&
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lb
/>
ita duæ
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var
>.K.</
var
>
et
<
var
>.h.</
var
>
ex quibus ſit
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>.K.h</
var
>
. </
s
>
<
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xml:id
="
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xml:space
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preserve
">Nunc ex iſtis duabus lineis
<
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>.e.g.</
var
>
et
<
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>K.h.</
var
>
fiat paral- </
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>
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