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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1 - 30
31 - 60
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352
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I O. BAPT. BENED.
"
n
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364
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file
="
0364
"
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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var
>.u.o.</
var
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ad quadratum
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>.o.n.</
var
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vt lineæ
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>.o.a.</
var
>
ad lineam
<
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>.o.e.</
var
>
partes diametri
<
var
>.o.i.</
var
>
ipſius
<
lb
/>
circuli, terminatæ à perpendicularibus
<
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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echoid-s4233
"
xml:space
="
preserve
">Hoc neceſſario contingit, propterea quod cum fuerint protractæ
<
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>.u.i.</
var
>
et
<
var
>.n.i.</
var
>
<
reg
norm
="
tunc
"
type
="
context
">tũc</
reg
>
<
lb
/>
habebimus ad partem
<
var
>.o.u.i.</
var
>
triangulum
<
var
>.o.u.i.</
var
>
diuiſum in duo triangula ſimilia ipſi
<
lb
/>
totali triangulo. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Idem etiam dico ad partem
<
var
>.o.n.i.</
var
>
vnde ex tali ſimilitudine habe-
<
lb
/>
bimus
<
var
>.o.u.</
var
>
mediam proportionalem inter
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var
>.o.i.</
var
>
et
<
var
>.o.a.</
var
>
et ſic
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var
>.o.n.</
var
>
erit media proportio
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lb
/>
nalis inter
<
var
>.o.i.</
var
>
et
<
var
>.o.e.</
var
>
</
s
>
<
s
xml:id
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xml:space
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">quare ex .16. ſexti, quadratum
<
var
>.o.u.</
var
>
æquale erit producto ipſius
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/>
<
var
>o.i.</
var
>
in
<
var
>.o.a.</
var
>
& quadratum
<
var
>.o.n.</
var
>
æquale producto
<
var
>.o.i.</
var
>
in
<
var
>.o.e.</
var
>
ſed ex prima eiuſdem, ea
<
lb
/>
dem proportio eſt ipſius
<
var
>.o.a.</
var
>
ad
<
var
>.o.e.</
var
>
quæ producti ipſius
<
var
>.o.i.</
var
>
in
<
var
>o.a.</
var
>
ad productum
<
var
>.o.
<
lb
/>
i.</
var
>
in
<
var
>.o.e.</
var
>
</
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>
<
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xml:id
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xml:space
="
preserve
">quare, ex
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norm
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type
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conceptu, ita erit quadrati
<
var
>.o.u.</
var
>
ad quadratúm.o.n. </
s
>
<
s
xml:id
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xml:space
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preserve
">Et hęc
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eſt alia circuli paſſio.</
s
>
</
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<
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>
<
s
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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/>
<
var
>a.u.</
var
>
et
<
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>.b.s.i.</
var
>
ſint inuicem ęquales, diuiſæ verò non æquali modo, ſed tali, quod
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var
>.a.</
var
>
<
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/>
maior ſit quam
<
var
>.u.</
var
>
et
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>.b.s.</
var
>
maior quam
<
var
>.i.</
var
>
quomodo poteſt fieri, quod ſi
<
var
>.u.</
var
>
maior fue-
<
lb
/>
rit
<
var
>.i.</
var
>
proportio
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var
>.a.</
var
>
ad
<
var
>.i.</
var
>
maior ſit quam ipſius
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var
>.b.s.</
var
>
ad
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var
>.u</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Hoc etiam ex neceſſitate cuenit, eo
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lb
/>
quod ſi accepta fuerit
<
var
>.t.n.</
var
>
æqualis
<
var
>.u.</
var
>
ab
<
lb
/>
<
figure
xlink:label
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fig-0364-01
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xlink:href
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fig-0364-01a
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number
="
401
">
<
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file
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0364-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0364-01
"/>
</
figure
>
<
reg
norm
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ipſaque
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type
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simple
">ipſaq́;</
reg
>
abſciſa fuerit
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var
>.t.</
var
>
æqualis
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var
>.i.</
var
>
& ab
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>.
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b.s.</
var
>
abſciſa
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>.s.</
var
>
æqualis
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>.n.</
var
>
habebimus
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>
et
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lb
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b. inuicem æ quales, vnde habebis ma-
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lb
/>
iorem propor tionem ipſius
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>.b.</
var
>
ad
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>.t.</
var
>
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
lb
/>
s. ad
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var
>.n.</
var
>
quod cum clarum per ſe ſit, tibi
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/>
relinquo. </
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>
<
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xml:id
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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.</
var
>
ad
<
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>.n.</
var
>
& ex
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/>
28.
<
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type
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>
<
reg
norm
="
proportio
"
type
="
simple
">ꝓportio</
reg
>
<
var
>.b.s.</
var
>
ad
<
var
>.s.</
var
>
maior erit,
<
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/>
quam
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>.t.n.</
var
>
ad
<
var
>.n.</
var
>
& ex .27. maior propor
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/>
tio erit ipſius
<
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>.b.s.</
var
>
ad
<
var
>.n.t.</
var
>
quam
<
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>.s.</
var
>
ad
<
var
>.n.</
var
>
<
lb
/>
ergo ex .33. maior erit ipſius
<
var
>.b.</
var
>
ad
<
var
>.t.</
var
>
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
lb
/>
<
var
>b.s.</
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>
ad
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>.n.t.</
var
>
hoc eſt maior ipſius
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var
>.a.</
var
>
ad
<
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/>
i. quam
<
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>.b.s.</
var
>
ad
<
var
>.u.</
var
>
quod eſt propo-
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ſitum.</
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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">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. </
s
>
<
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xml:id
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xml:space
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preserve
">Nam cum putauerint philo-
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ſophi ipſas moueri, ſemper eandem
<
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ſeruando
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type
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>
inuicem diſtantiam, non ſine ratione
<
lb
/>
crediderunt eas fixas eſſe eodem in orbe, idem etiam poſtea de planetis opinaue-
<
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/>
runt. </
s
>
<
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xml:id
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xml:space
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">Hoc eſt, vnumquemque, aliquo in orbe, fixo exiſtere.</
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