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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[Figure 431]
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[Figure 443]
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[Figure 444]
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[Figure 445]
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<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 445
>
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352
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I O. BAPT. BENED.
"
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364
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file
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0364
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0364
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habes in circulo .ω vbi fateris te non videre qua ratione eadem proportio ſit qua-
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lb
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drati
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ad quadratum
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var
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vt lineæ
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var
>
ad lineam
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var
>
partes diametri
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var
>
ipſius
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lb
/>
circuli, terminatæ à perpendicularibus
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var
>.u.a.</
var
>
et
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>.n.e</
var
>
.</
s
>
</
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>
<
p
>
<
s
xml:id
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xml:space
="
preserve
">Hoc neceſſario contingit, propterea quod cum fuerint protractæ
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>.u.i.</
var
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et
<
var
>.n.i.</
var
>
<
reg
norm
="
tunc
"
type
="
context
">tũc</
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>
<
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/>
habebimus ad partem
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var
>.o.u.i.</
var
>
triangulum
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var
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var
>
diuiſum in duo triangula ſimilia ipſi
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/>
totali triangulo. </
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<
s
xml:id
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xml:space
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preserve
">Idem etiam dico ad partem
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var
>.o.n.i.</
var
>
vnde ex tali ſimilitudine habe-
<
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/>
bimus
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var
>.o.u.</
var
>
mediam proportionalem inter
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>.o.i.</
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>
et
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>
et ſic
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erit media proportio
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nalis inter
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var
>
et
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>.o.e.</
var
>
</
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>
<
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xml:id
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xml:space
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">quare ex .16. ſexti, quadratum
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>.o.u.</
var
>
æquale erit producto ipſius
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/>
<
var
>o.i.</
var
>
in
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var
>
& quadratum
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var
>
æquale producto
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var
>
in
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var
>
ſed ex prima eiuſdem, ea
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dem proportio eſt ipſius
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var
>
ad
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>.o.e.</
var
>
quæ producti ipſius
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var
>
in
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>o.a.</
var
>
ad productum
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lb
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i.</
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in
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var
>
</
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>
<
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xml:id
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xml:space
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">quare, ex
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type
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conceptu, ita erit quadrati
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>
ad quadratúm.o.n. </
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<
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xml:id
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xml:space
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eſt alia circuli paſſio.</
s
>
</
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<
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<
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xml:id
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xml:space
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preserve
">Reliqua verò difficultas quam te habere ſcribis, eſt, quare cum duæ lineę
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>a.u.</
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>
et
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ſint inuicem ęquales, diuiſæ verò non æquali modo, ſed tali, quod
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maior ſit quam
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et
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maior quam
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>
quomodo poteſt fieri, quod ſi
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>
maior fue-
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rit
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proportio
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ad
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maior ſit quam ipſius
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ad
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.</
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>
</
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>
<
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>
<
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xml:id
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xml:space
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preserve
">Hoc etiam ex neceſſitate cuenit, eo
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quod ſi accepta fuerit
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>.t.n.</
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>
æqualis
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ab
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fig-0364-01
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401
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xlink:href
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</
figure
>
<
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abſciſa fuerit
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æqualis
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& ab
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b.s.</
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abſciſa
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æqualis
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habebimus
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et
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b. inuicem æ quales, vnde habebis ma-
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iorem propor tionem ipſius
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ad
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norm
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type
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s. ad
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>
quod cum clarum per ſe ſit, tibi
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relinquo. </
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<
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xml:space
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">ſed ex .27. quinti, proportio
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b. ad. s, maior erit quam
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>.t.</
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>
ad
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>.n.</
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>
& ex
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28.
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<
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proportio
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type
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">ꝓportio</
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>.b.s.</
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>
ad
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>
maior erit,
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quam
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>.t.n.</
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>
ad
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>
& ex .27. maior propor
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tio erit ipſius
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>
ad
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>.n.t.</
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>
quam
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>
ad
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/>
ergo ex .33. maior erit ipſius
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>.b.</
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>
ad
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>.t.</
var
>
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reg
norm
="
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>
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hoc eſt maior ipſius
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>
ad
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i. quam
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>.b.s.</
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>
ad
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>.u.</
var
>
quod eſt propo-
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ſitum.</
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>
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<
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xml:space
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">Id verò de quo me interrogas
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de
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diſtinctione orbium cęleſtium, ortum
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habet à communi opinione motuum
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fixarum. </
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>
<
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xml:id
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xml:space
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">Nam cum putauerint philo-
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ſophi ipſas moueri, ſemper eandem
<
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ſeruando
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>
inuicem diſtantiam, non ſine ratione
<
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/>
crediderunt eas fixas eſſe eodem in orbe, idem etiam poſtea de planetis opinaue-
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runt. </
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>
<
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xml:space
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">Hoc eſt, vnumquemque, aliquo in orbe, fixo exiſtere.</
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