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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358
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IO. BAPT. BENED.
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n
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370
"
file
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0370
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0370
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ſecunda definitione eiuſdem libr
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efficiet angulos rectos cum duabus
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et
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i.</
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in punctis
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et
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>.l.</
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et
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>.k.i.</
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parallela erit ipſi
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ex .28. primi, quod etiam poteſt con
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cludi mediante .16. vndecimi, cum
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et
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ſint communes ſectiones duorum pla
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norum cum triangulari. </
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<
s
xml:id
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xml:space
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">Deinde ex .29. primi anguli
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et
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erunt inuicem
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æquales, idem etiam dico de angulis
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et
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anguli poſtea ad
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communes
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ſunt triangulis
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et
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vt triangulis
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>.l.a.b.</
var
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et
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>.m.a.k</
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>
. </
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xml:space
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">Vnde ex .4. ſexti, eadem
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proportio erit ipſius
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ad
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& ipſius
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>.m.k.</
var
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ad
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>.l.b.</
var
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vt ipſius
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>.a.m.</
var
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ad
<
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>.a.l</
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>
. </
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<
s
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xml:space
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preserve
">Quare ex
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vndecima quinti, ita erit ipſius
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ad
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vt ipſius
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>.m.i.</
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ad
<
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>.l.c.</
var
>
& ex .13. eiuſdem, ita
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erit ipſius
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>.k.i.</
var
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ad
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>.b.c.</
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vt
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>.m.i.</
var
>
ad
<
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>.l.c.</
var
>
ſed ipſius
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>.m.i.</
var
>
ad
<
var
>.l.c.</
var
>
eſt vt ipſius
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>.a.m.</
var
>
ad
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>.a.l.</
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>
quod
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iam dictum eſt, vnde ex .11. dicta, ita erit ipſius
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ad
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var
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vt ipſius
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>.a.m.</
var
>
ad
<
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>.a.l.</
var
>
& ex
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16. dicti ita erit ipſius
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var
>.a.m.</
var
>
ad
<
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>.k.i.</
var
>
vt ipſius
<
var
>.a.l.</
var
>
ad
<
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>.b.c</
var
>
. </
s
>
<
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xml:id
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xml:space
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preserve
">Quare ex definitione ab Eu-
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cli. poſita in .11, lib. pars coni ſuperior ſimilis erit cono totali.</
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<
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xml:space
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">Deinde ſciendum eſt illud quod Euclid. ſcribit in .10. duodecimi lib. hoc eſt,
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proportio duarum pyramidum inuicem
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ſimilium, triplicata eſt ei diametrorum
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xlink:label
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fig-0370-01
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fig-0370-01a
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number
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409
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image
file
="
0370-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0370-01
"/>
</
figure
>
ſuarum baſium, hoc eſt, quod proportio
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b.c.</
var
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ad
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tertia pars erit proportionis to
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tius pyramidis
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var
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partiali pyramidi
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>.a.
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k.i.</
var
>
ſed ita eſt ipſius
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>.a.c.</
var
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ad
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>.a.i.</
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vt ipſius
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>.b.
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c.</
var
>
ad
<
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>.k.i.</
var
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ex .4. ſexti cum trianguli
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et
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ſint æquianguli, quod ex ijs, quę
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ſuperius diximus facile compręhenditur.
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</
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<
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xml:space
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ad
<
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>.a.i.</
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tertia pars erit
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proportionis totius coni
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>.a.b.c.</
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ad eius par
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tem abſciſſam
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ſed eadem proportio
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ipſius
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>.a.c.</
var
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ad
<
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>.a.i.</
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erat etiam tertia pars pro
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portionis ipſius
<
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>.a.c.</
var
>
ad
<
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>.a.d</
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>
. </
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xml:id
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xml:space
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">Quare ex com
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muni conceptu, proportio totius pyramidis, ad partem abſciſſam, æqualis erit pro-
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portioni ipſius
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>.a.c.</
var
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ad
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>.a.d</
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>
.</
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</
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</
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type
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<
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style
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xml:space
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">De differentia caloris Solis propter vaporum
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unsure
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altitudinem.</
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">AD EVNDEM.</
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">NOlo, mihi credas, ſed ex rationibus, quas tibi ſcribo conſidera, quod quo
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tieſcunque
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type
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craſſities vel
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denſitas
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type
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">dẽſitas</
reg
>
<
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norm
="
vaporum
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type
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">vaporũ</
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, ſeu altitudo, maior eſſet ea, quę nunc re-
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peritur, </
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<
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xml:space
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preserve
">tunc minor differentia eſſet inter maiorem
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minoremque
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type
="
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">minoremq́;</
reg
>
calorem Solis, quam
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nunc ſentiamus. </
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<
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xml:space
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">Pro cuius rei euidentia, imaginemur in hac ſubſcripta figura, li-
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neam
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>.o.a.</
var
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pro ſemidiametro terræ, et
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var
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pro craſſitie vaporum, vt nunc ſe
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habet, et
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>.a.d.</
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pro maiori craſſitie, imaginemurq́ue lineam
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var
>
quaſi perpen-
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dicularem ad
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>.o.a.</
var
>
quæ abſciſſa ſit in puncto u. à circunferentia
<
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>.c.u.</
var
>
inferiori prio-
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rum vaporum.</
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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">Tunc dico minorem eſſe proportionem ipſius
<
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>.a.b.</
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>
ad
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>.a.d.</
var
>
quam ipſius
<
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>.a.u.</
var
>
ad
<
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>.a.
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c.</
var
>
cogitemus ergo protractas eſſe lineas
<
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>.o.b</
var
>
:
<
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>d.b</
var
>
:
<
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>c.u.</
var
>
et
<
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>.c.n.</
var
>
quæ
<
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>.c.n.</
var
>
ſecabit
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>.a.u.</
var
>
in </
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