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
61 - 90
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241 - 270
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361 - 390
391 - 420
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<
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384
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rhead
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IO. BAPT. BENED.
"
n
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396
"
file
="
0396
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0396
"/>
eiuſdem erit vt
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ad
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>.d.b</
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. </
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<
s
xml:id
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xml:space
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preserve
">Idem etiam dico in ſecunda parabola, ſed ipſius
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ad
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<
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>o.r.</
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eſt vt
<
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>.a.b.</
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ad
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>.b.d.</
var
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ex .6. ſexti Eucli. </
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<
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xml:space
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">vnde ex .11. quinti
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ad
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>.f.x.</
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erit vt
<
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>.ω.y.</
var
>
<
lb
/>
ad
<
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>.y.g</
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>
. </
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>
<
s
xml:id
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xml:space
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preserve
">Sed in precedenti iam tibi dixi
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mediam proportionalem eſſe inter
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>.h.</
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>
<
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et
<
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>.b.d</
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. </
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>
<
s
xml:id
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xml:space
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">Sit nunc
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>.z.</
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>
pro ſecunda parabola, ita ut
<
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>.h.</
var
>
eſt pro prima, vnde
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>.o.x.</
var
>
crit media
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lb
/>
proportionalis inter
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>.z.</
var
>
et
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>.o.r.</
var
>
& ex .11. quinti ita erit
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var
>.h.</
var
>
ad
<
var
>.a.b.</
var
>
vt
<
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>.z.</
var
>
ad
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>.x.o.</
var
>
& ex .22.
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h. ad
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>.a.x.</
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>
ut z. ad
<
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>.x.g.</
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>
& quia ex .16. ſexti
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>.a.x.</
var
>
media proportionalis eſt inter
<
var
>.h.</
var
>
et
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var
>.f.
<
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/>
x.</
var
>
cum ſupponatur productum
<
var
>.h.</
var
>
in
<
var
>.f.x.</
var
>
æquale eſſe quadrato
<
var
>.a.x</
var
>
. </
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>
<
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xml:id
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xml:space
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">Idem dico
<
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>.x.g.</
var
>
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mediam eſſe proportionalem inter
<
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>.z.</
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>
et
<
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>.g.y.</
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>
</
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<
s
xml:id
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xml:space
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preserve
">quare ex .11. iam dicta, ita erit
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ad
<
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>.f.
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x.</
var
>
vt
<
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>.y.g.</
var
>
ad
<
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>.x.o.</
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>
& ex eadem, ita erit ipſius
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var
>.f.n.</
var
>
ad
<
var
>.a.b.</
var
>
ut
<
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>.y.ω.</
var
>
ad
<
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>.x.o.</
var
>
& ſic
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>.f.n.</
var
>
ad
<
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>.d.a.</
var
>
<
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/>
vt
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>.y.ω.</
var
>
ad
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>.x.r.</
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>
ſed
<
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>.f.m.</
var
>
ad
<
var
>f.n.</
var
>
eſt vt
<
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>.y.t.</
var
>
ad
<
var
>.y.ω.</
var
>
ex .18. quinti vnde
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>.f.m.</
var
>
ad
<
var
>.a.d.</
var
>
erit vt
<
lb
/>
<
var
>y.t.</
var
>
ad
<
var
>.x.r</
var
>
. </
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>
<
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xml:id
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xml:space
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">Idem dico de eorum duplis.</
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>
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<
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<
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xml:space
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preserve
">Ex ijſdem rationibus dico ita eſſe
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>
ad
<
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>.b.m.</
var
>
vt
<
var
>.o.r.</
var
>
ad
<
var
>.o.t.</
var
>
& ex .17. quinti
<
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>.d.m.</
var
>
<
lb
/>
ad
<
var
>.b.m.</
var
>
vt
<
var
>.r.t.</
var
>
ad
<
var
>.t.o</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Reliqua tibi conſideranda relinquo.</
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<
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position
="
here
"
number
="
437
">
<
image
file
="
0396-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0396-01
"/>
</
figure
>
<
p
>
<
s
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xml:space
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preserve
">In reliquis verò propoſitionibus illius lib. nullo pacto poteris dubitare: </
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<
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xml:space
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">Verum ne
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in .4. aliquid tibi noui exurgat, te ſcire volo
<
ref
id
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ref-0025
">corollarium .20. in libr. de quadratu
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ra parabolę</
ref
>
docere poſſibile eſſe inſcriptionem rectilineæ, ea tamen conditione
<
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type
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>
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dicit Archimedes.</
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<
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xml:space
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">In quinta poſtea animaduertendum eſt, quod prima pars, probat tantummodo de
<
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centro trianguli, et .2. pars probat de centro pentagoni, à te ipſo deinde potes pro-
<
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bare de centro nonanguli: </
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>
<
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xml:space
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">& ſic de cæteris: </
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<
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xml:space
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">eo quod cum probatum fuerit de centro
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figuræ in medio locatæ ſi conſtitutæ poſtea fuerint ſimiles figuræ in portionibus la-
<
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teralibus habebitur propoſitum in infinitum.</
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>
</
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<
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xml:space
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">Idem intelligendum eſt in .3. propoſitione quamuis exemplum vlterius non ex-
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tendatur quam ad pentagonos.</
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</
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<
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<
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xml:space
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">Sexta verò
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tibi ſacilis erit, quæ nihilominus
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type
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<
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type
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hoc
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mon
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type
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ſcili
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cet. </
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<
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">Sint .4.
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<
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var
>
ipſius Archimedis
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ſupponendo
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type
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<
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>.a.</
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>
pro figura rectilinea
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inſcripta in parabola, et
<
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pro reſiduo ipſius parabolę et
<
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>.c.</
var
>
pro triangulo
<
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>.a.b.c.</
var
>
in me
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/>
dio ipſius parabolę et
<
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>.d.</
var
>
pro triangulo
<
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>.r</
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>
. </
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<
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xml:space
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">Nunc cum
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>.a.</
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maior ſit
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>.c.</
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>
prout totum ma-
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ius eſt ſua parte, ideo ex .8. quinti maior proportio habebit
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>.a.</
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>
ad
<
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>.b.</
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>
quam
<
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>.c.</
var
>
ad
<
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>.b.</
var
>
<
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/>
Cum autem
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>.b.</
var
>
minor ſit
<
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>.d.</
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>
ex ſuppoſito, ideo ex eadem dicta, maior proportio habe
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/>
bit
<
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>.a.</
var
>
ad
<
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>.b.</
var
>
quam
<
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>.c.</
var
>
ad
<
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>.d.</
var
>
cum verò centrum cuiuſuis figuræ plenæ neceſſariò ſit intra
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ipſam figuram, idcirco centrum reſidui ipſius parabolę intra ipſam reperietur. </
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<
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ita
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<
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type
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">ꝑ</
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ſe eſt,
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type
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quoduis aliud axioma, & quia
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type
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>
<
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type
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">centrũ</
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>
ex .8. primi
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de centris, neceſſariò eſt in linea
<
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>.b.h.</
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>
inter
<
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>.b.</
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>
et
<
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>.h</
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>
. </
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>
<
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xml:id
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xml:space
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">Sit igitur
<
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>.g.</
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>
vnde ex eadem .8. ita
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erit
<
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>.g.h.</
var
>
ad
<
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>.h.e.</
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>
vt
<
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>.a.</
var
>
ad
<
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>.b.</
var
>
ergo
<
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>.g.h.</
var
>
ad
<
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>.h.e.</
var
>
maior proportio erit
<
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norm
="
quam
"
type
="
context
">quã</
reg
>
<
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>.c.</
var
>
ad
<
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>.d.</
var
>
hoc eſt
<
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/>
quam
<
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>.b.h.</
var
>
ad
<
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>.f.</
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>
ex .12. quinti. </
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>
<
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<
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cum
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type
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>
<
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>.h.b.</
var
>
maior ſit ipſa
<
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>.h.g.</
var
>
prout omne totum ma-
<
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/>
ius eſt ſua parte, ideo maior proportio habebit
<
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>.h.b.</
var
>
ad
<
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>.h.e.</
var
>
quam
<
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>.h.g.</
var
>
ad
<
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>.h.e.</
var
>
vnde
<
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/>
multo
<
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="
maiorem
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type
="
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">maiorẽ</
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>
<
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norm
="
quam
"
type
="
context
">quã</
reg
>
<
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>.h.b.</
var
>
ad
<
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>.f.</
var
>
ex
<
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coni
"
type
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">cõi</
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>
<
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conceptu
"
type
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">cõceptu</
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>
, </
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>
<
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xml:space
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">quare
<
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>.h.e.</
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>
erit minor ipſa
<
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>.f.</
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>
ex .10.
<
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="
quinti
"
type
="
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">quĩti</
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>
.</
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>
</
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<
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>
<
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xml:space
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">Septima verò et .8. propoſitio nullius tibi erit difficultatis.</
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