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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357
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EPISTOL AE.
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n
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369
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file
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0369
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0369
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gulus
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vnde ex methodo .56.
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0369-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0369-01
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primi triangulorum Monteregij,
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cognoſcemus reliqua trianguli
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<
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q.p.n</
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. </
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<
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xml:space
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lum
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æqualem angulo
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>.n.q.p.</
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propoſitum habebimus.</
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</
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<
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<
s
xml:id
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xml:space
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">Si etiam puncta
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>.q.p.</
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>
lineæ
<
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>.q.p.</
var
>
<
lb
/>
orizontali in eodem plano non exi
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ſterent cum puncto
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>.n.</
var
>
nihil refer-
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ret, dummodo in pauimento
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notem
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type
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context
">notẽ</
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>
<
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tur
<
reg
norm
="
puncta
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type
="
context
">pũcta</
reg
>
<
var
>.c.e.</
var
>
proxima
<
var
>.n.</
var
>
in ijſdem
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/>
ſuperficiebus triangulorum
<
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>.n.o.p.</
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>
<
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/>
et
<
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>.n.o.q.</
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vnde
<
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>.n.c.</
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>
et
<
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>.n.e.</
var
>
erunt
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norm
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com- munes
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type
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munes</
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ſectiones dictarum ſuperficierum cum ſuperficie pauimenti ſupra quam fit
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ſtatio.</
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xml:space
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">CONI RECTI DIVISIO A PLANO
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parallelo baſi ſecundum datam proportionem.</
head
>
<
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style
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<
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style
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emph
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volueris conum rectum diuidere à plano parallelo ba-
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ſi ſecundum vnam datam proportionem, nullius tibi erit difficultatis, con
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ceſſa
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type
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pro inuenta diuiſione cuiuſuis propoſitę proportionis per tres
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æquales partes.</
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<
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<
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xml:space
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">Sit exempli gratia conus rectus
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>
ſecandus vt dictum eſt, accipiatur latus
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ipſius, quod ſit
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>.a.c.</
var
>
<
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>
diuidatur in puncto
<
var
>.d.</
var
>
ſecundum illam proportionem
<
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/>
quam deſideras, hoc eſt ipſius
<
var
>.a.c.</
var
>
ad
<
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>.a.d.</
var
>
quo facto, inter totum
<
var
>.a.c.</
var
>
et
<
var
>.a.d.</
var
>
inuenian
<
lb
/>
tur duæ lineæ proportionales, quarum maior ſit
<
var
>.a.i.</
var
>
</
s
>
<
s
xml:id
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xml:space
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">tunc ſi conus
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>.a.b.c.</
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>
ſectus fue-
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rit à plano per punctum
<
var
>.i.</
var
>
parallelo baſi, habebimus quod quærebamus.</
s
>
</
p
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<
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>
<
s
xml:id
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xml:space
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">Cuius rei ratio, primò eſt, quia quotieſcunque conus aliquis ſectus fuerit ab ali-
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quo plano parallelo baſi ipſius, pars ſuperior ſimilis ſemper erit totali cono, quod
<
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/>
ita probo, cogitemus conum ſectum eſſe
<
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/>
à plano per axem
<
var
>.a.l.</
var
>
vnde ex .3. primi
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0369-02
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xlink:href
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Pergei, talis ſectio triangularis erit, quæ
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ſit
<
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var
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et
<
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var
>
diameter erit baſis.</
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<
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<
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xml:space
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">Imaginemur deinde
<
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>.K.i.</
var
>
communem
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eſſe ſectionem huiuſmodi trianguli cum
<
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plano parallelo ipſi baſi, </
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,
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circulare erit ex .4. primi ipſius Pergei
<
var
>.K.
<
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i.</
var
>
verò, eius diameter erit, et
<
var
>.a.m.</
var
>
<
reg
norm
="
ſuus
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type
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axis.</
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>
</
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<
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>
<
s
xml:id
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xml:space
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preserve
">Cum verò
<
var
>.a.l.</
var
>
ſit perpendicularis ipſi
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baſi conitotalis, eo quod rectus ſupponi-
<
lb
/>
tur, ideo eadem
<
var
>.a.m.l.</
var
>
erit perpendicula
<
lb
/>
ris eriam ipſi ſecundo plano circulari, ex
<
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/>
conuerſa .14. vndecimi Euclid. </
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>
<
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xml:space
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