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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126
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IO. BAPT. BENED.
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138
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file
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0138
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0138
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æqualis ſit ipſi
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)
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0138-01
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<
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etiam
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: et
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k.</
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vt in figura
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cla
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riſſimè patet. </
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xml:space
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type
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multas lineas in
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alijs figuris non
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ob
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type
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duxi,
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quam
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type
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">quã</
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ad
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facilius
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eruendas
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type
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è te-
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nebris ignorantiæ, &
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in cognitionis lucem
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proferendas horum
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effectuum cauſas, vt
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dixi.</
s
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<
head
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xml:space
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">CAP. VI.</
head
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<
emph
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vtlocum altitudinis, in noſtro plano perpendiculari orizonti, & ita
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<
unsure
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,
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vt poſtremo diximus, inueniamus; </
s
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<
s
xml:id
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xml:space
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preserve
">duas hîc ſubſcriptas figuras conſiderabimus
<
var
>.
<
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/>
G.</
var
>
corpoream, & G. ſuperficialem, ſimiles duabus
<
var
>.E.E.</
var
>
proximè præcedentibus,
<
lb
/>
in quarum corporea ſit linea
<
var
>.b.M.</
var
>
altitudinis perpendicularis orizonti. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Quare ſi
<
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deſiderabis inuenire in noſtro plano ſitum puncti
<
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>.M.</
var
>
ideſt punctum radij
<
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>.o.M.</
var
>
vi-
<
lb
/>
ſualis in quo ipſe radius à plano eſt diuiſus, quod ſit
<
var
>.R.</
var
>
quamuis extra
<
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norm
="
triangulum
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type
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">triangulũ</
reg
>
<
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/>
<
var
>i.q.d.</
var
>
tibi imaginatione confige ductam eſſe lineam
<
var
>.p.b.</
var
>
quæ erit ſectio commu-
<
lb
/>
nis orizontis cum ſuperficie
<
var
>.o.p.b.M.</
var
>
quæ ſuperficies erit perpendicularis ipſi ori-
<
lb
/>
zonti ex .18. lib 11. </
s
>
<
s
xml:id
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xml:space
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preserve
">Quòd autemnon minus
<
var
>.o.p.</
var
>
quàm.M.b. ſit in vna eademq́ue
<
lb
/>
ſuperficie dubitandum non eſt, quia ſi imaginabimur ductam eſſe lineam
<
var
>.p.M.</
var
>
ha
<
lb
/>
bebimus triangulum
<
var
>.o.p.b.</
var
>
cum triangulo
<
var
>.M.b.p.</
var
>
communibus partibus in vna ea-
<
lb
/>
demq́ue ſuperficie conſtantem, vt triangulum quoque
<
var
>.o.p.M.</
var
>
cum triangulo
<
var
>M.b.</
var
>
<
lb
/>
o & triangulum
<
var
>.o.p.b.</
var
>
cum triangulo
<
var
>.o.p.M.</
var
>
& triangulum
<
var
>.M.b.p.</
var
>
cum triangulo
<
var
>.
<
lb
/>
M.b.o</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Vnde cum quilibet triangulus in vnica tantum ſuperficie ſit ex .2. lib. 11. ſe-
<
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quetur ſuperficiem
<
var
>.o.p.b.M.</
var
>
planam eſſe, & vnicam, cuius communis ſectio cum no-
<
lb
/>
ſtro plano ſit. θ.K.R. quæ perpendicularis orizonti exiſtet ex .19. lib. 11. eritq́ue pa-
<
lb
/>
rallela ipſi
<
var
>.i.x.</
var
>
ex .6. eiuſdem. </
s
>
<
s
xml:id
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xml:space
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">Imaginare nunc erectam eſſe
<
var
>.m.T.</
var
>
æqualem ipſi
<
var
>.
<
lb
/>
b.M.</
var
>
orizonti perpendicularem, quæ extenſa erit in ſuperficie
<
var
>.p.t.</
var
>
quod ex ſe ad
<
lb
/>
conſiderandum admodum facilè, clarumq́ue exiſtit, reducendo ad impoſſibilia
<
lb
/>
quemlibet hæc negare volentem. </
s
>
<
s
xml:id
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xml:space
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preserve
">Imaginemur quoque ductam eſſe lineam
<
var
>.M.
<
lb
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T.</
var
>
quæ
<
var
>.b.m.</
var
>
ex .33. primi erit parallela, quia
<
var
>.m.T.</
var
>
ęqualis
<
var
>.b.M.</
var
>
parallela eſt
<
lb
/>
ipſi
<
var
>.b.M.</
var
>
ex .6. lib. 11. præter hæc
<
var
>.b.m.</
var
>
parallela eſt ipſi
<
var
>.q.d.</
var
>
quia ſic fuit ducta
<
lb
/>
ſuperius, vnde
<
var
>.M.T.</
var
>
parallela erit ipſi
<
var
>.q.d.</
var
>
ex .9. vndecimi, & obid perpendi-
<
lb
/>
cularis erit ſuperficiei
<
var
>.b.t.</
var
>
ex .8. eiuſdem. </
s
>
<
s
xml:id
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xml:space
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preserve
">Nunc ſit
<
var
>.R.V.</
var
>
communis ſectio trian-
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guli
<
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>.o.M.T.</
var
>
cum noſtro plano, vnde
<
var
>.R.V.</
var
>
perpendicularis erit ſuperficiei
<
var
>.p.t.</
var
>
<
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/>
ex .19. lib. 11. quam ob cauſam parallela erit ipſi
<
var
>.q.d.</
var
>
ex .6. aut ex .9. eiuſdem
<
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/>
quia ex .6. dicta, parallela eſt ipſi
<
var
>.M.T</
var
>
. </
s
>
<
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xml:space
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">Atſi
<
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>.R.V.</
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parallela eſt ipſi
<
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>.q.d.</
var
>
<
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/>
etiam
<
var
>.f.K.</
var
>
probatum iam fuit parallelam eſſe eidem, ergo
<
var
>.R.V.</
var
>
parallela erit
<
lb
/>
ipſi
<
var
>.K.f.</
var
>
ex .30. primi, </
s
>
<
s
xml:id
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xml:space
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">Vnde ex .34. æqualis erit ipſi
<
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>.K.f</
var
>
. </
s
>
<
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xml:space
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">Accedamus nunc
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ad
<
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">figurã</
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<
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>.G.</
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>
<
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type
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">extructã</
reg
>
ſupra figuram
<
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>.E.</
var
>
ſuperficialem, & erigamus
<
var
>.m.T.</
var
>
perpendi-
<
lb
/>
cularem ipſi
<
var
>.m.p.</
var
>
ſed æqualem perfectæ altitudini, & ducamus
<
var
>.T.o.</
var
>
vt ſecet li-
<
lb
/>
neam
<
var
>.i.x.</
var
>
in puncto
<
var
>.V.</
var
>
ab ipſo ducentes
<
var
>.V.R.</
var
>
parallelam ipſi
<
var
>.q.d.</
var
>
ducendo de- </
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>
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