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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rhead
="
EPISTOL AE.
"
n
="
371
"
file
="
0371
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0371
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puncto
<
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>.i.</
var
>
ex communi conceptu, &
<
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fig-0371-01
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xlink:href
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number
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410
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="
0371-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0371-01
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</
figure
>
parallcla erit ipſi
<
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>.d.b.</
var
>
ex. ſecunda par-
<
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/>
te ſecundæ ſexti, vnde ex prima parte
<
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ciuſdem, ita eritipſius
<
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>.b.i.</
var
>
ad
<
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>.i.a.</
var
>
vt
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var
>.d.
<
lb
/>
c.</
var
>
ad
<
var
>.c.a.</
var
>
& coniunctim ita erit ipſius
<
var
>.b.
<
lb
/>
a.</
var
>
ad
<
var
>.a.i.</
var
>
vt ipſius
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var
>.d.a.</
var
>
ad
<
var
>.a.c.</
var
>
& permu
<
lb
/>
tatim ipſius
<
var
>.a.b.</
var
>
ad
<
var
>.a.d.</
var
>
erit, vt
<
var
>.a.i.</
var
>
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lb
/>
ad
<
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>.a.c.</
var
>
ſed cum
<
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>.a.u.</
var
>
maior ſit ipſa
<
var
>.a.i.</
var
>
<
lb
/>
vt omne totum maius eſt ſua parte.
<
lb
/>
</
s
>
<
s
xml:id
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xml:space
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preserve
">maior proportio erit ipſius
<
var
>.a.u.</
var
>
ad
<
var
>.a.
<
lb
/>
c.</
var
>
quam ipſius
<
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>.a.i.</
var
>
ad
<
var
>.a.c.</
var
>
hoc eſt quam
<
lb
/>
ipſius
<
var
>.a.b.</
var
>
ad
<
var
>.a.d</
var
>
. </
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>
<
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xml:id
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xml:space
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">Verum igitur eſt
<
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propoſitum.</
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>
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type
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<
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xml:id
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style
="
it
"
xml:space
="
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">De differentia caloris Solis reſpectu altitudinis ipſius.</
head
>
<
head
xml:id
="
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"
xml:space
="
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">AD EVNDEM.</
head
>
<
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>
<
s
xml:id
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xml:space
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">QVodà me poſtulas deinde, ita ſe habet. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Inquis enim, quod cum differentia
<
lb
/>
inter maiorem,
<
reg
norm
="
minoremque
"
type
="
simple
">minoremq́;</
reg
>
calorem, oriatur etiam ex differentia maioris
<
lb
/>
quantitatis vaporum ad minorem, per quam quantitatem vaporum rranſit lumen
<
lb
/>
Solis (vt alias etiam tibi dixi) velles nunc ſcire quantitatem ipſius differentię, quæ
<
lb
/>
inter duas Solis datas altitudines ſupra orizontem reperitur.</
s
>
</
p
>
<
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>
<
s
xml:id
="
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xml:space
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preserve
">Quapropter imaginemur circulum
<
var
>.a.e.</
var
>
pro magno terræ, et
<
var
>.z.b.d.</
var
>
pro magno
<
lb
/>
vaporum, ſupponatur etiam quod angulus
<
var
>.z.o.d.</
var
>
vel
<
var
>.z.a.b.</
var
>
qui ſunt inuicem fe-
<
lb
/>
rè æquales, ſit angulus diſtantiæ Solis à zenit,
<
var
>z.a.</
var
>
verò ſit ſpiſſitudo vaporum, et
<
var
>.a.
<
lb
/>
b.</
var
>
radius tranſiens per vapores dictos. </
s
>
<
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xml:id
="
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"
xml:space
="
preserve
">nunc
<
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/>
<
figure
xlink:label
="
fig-0371-02
"
xlink:href
="
fig-0371-02a
"
number
="
411
">
<
image
file
="
0371-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0371-02
"/>
</
figure
>
quæratur proportio, quæ eſt inter
<
var
>.a.b.</
var
>
et
<
var
>.a.
<
lb
/>
z.</
var
>
qua inuenta, angulo
<
var
>.z.a.b.</
var
>
mediante,
<
lb
/>
quæremus eandem mediante angulo
<
var
>.z.a.b.</
var
>
<
lb
/>
maiore priori, velipſo minore, vnde cogno
<
lb
/>
ſcemus differentiam duarum
<
var
>.a.b.</
var
>
quæ qui-
<
lb
/>
dem inæquales inuicem erunt, eo quod ſup
<
lb
/>
ponatur
<
var
>.a.z.</
var
>
immutabilis, & hoc ita facie-
<
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/>
mus. </
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>
<
s
xml:id
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xml:space
="
preserve
">Imaginabimur
<
var
>.o.b.</
var
>
quæ claudat trian
<
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/>
gulum
<
var
>.a.b.o.</
var
>
& quia
<
var
>.a.z.</
var
>
cognita eſt quam
<
lb
/>
Alhazem docetinuenire, cognoſcimus
<
reg
norm
="
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type
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>
<
lb
/>
<
var
>o.a.</
var
>
vt ſemidiametrum terræ, vnde
<
var
>.o.b.</
var
>
et
<
var
>.
<
lb
/>
o.a.</
var
>
duo latera trianguli
<
var
>.a.o.b.</
var
>
cognita
<
reg
norm
="
erunt
"
type
="
context
">erũt</
reg
>
<
lb
/>
ſimul cum angulo
<
var
>.o.a.b.</
var
>
reſiduo duorum re
<
lb
/>
ctorum, eo quod reliquus
<
var
>.z.a.b.</
var
>
datus eſt.
<
lb
/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Quare
<
var
>.a.b.</
var
>
cognita erit reſpectu
<
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>.o.a.</
var
>
et
<
var
>.o.
<
lb
/>
b.</
var
>
et
<
var
>.a.z.</
var
>
quæ eſt eorum differentia. </
s
>
<
s
xml:id
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xml:space
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preserve
">Nunc
<
lb
/>
ſi idem faciemus cum alia
<
var
>.a.b.</
var
>
ſub diuerſo
<
lb
/>
angulo, habebimus propoſitum.</
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>
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