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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EPISTOL AE.
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n
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305
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file
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0305
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0305
"/>
ideo vnaquæque eius pars
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et
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ſimiliter nobis cognita erit ex quinta ſecundi
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Eucl. </
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<
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xml:space
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">vnde ex penultima primi habebimus propoſitum.</
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<
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<
s
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xml:space
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">Poſſumus item circulum mente concipere cuius
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ſit diameter, & ab eius cen-
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tro
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>.e.</
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protracta cum fuerit
<
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>.e.b.</
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>
quæ nobis cognita erit, vt medietas ipſius
<
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>.a.g.</
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de cu
<
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/>
ius potentia, dempta
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cum
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type
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">cũ</
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fuerit potentia
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ipſius
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type
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<
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>b.o.</
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remanebit nobis potentia ipſius
<
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>.d.
<
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e.</
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& ita eius longitudo, quæ addita medietati
<
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>.e.g.</
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& detracta à dimidio
<
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>.e.d.</
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>
erunt
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nobis cognitæ
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>.a.d.</
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et
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>.d.g.</
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vnde
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>.b.g.</
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et
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>.b.d.</
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remanebunt nobis cognitæ ex dicta pe-
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nultima primi Eucli. </
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">huiuſmodi figuram videbis in dicto .25. problemate .2. li. Mon-
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tisregij.</
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<
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xml:space
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">Aliter etiam poſſumus hoc idem efficere.</
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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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">Sit rectangulus hic ſubſcriptus
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>.a.b.c.u.</
var
>
ſuperficiei cognitę ſimul cum diametro
<
var
>.a.
<
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/>
c.</
var
>
extendatur imaginatione
<
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>.b.c.</
var
>
vſque ad, f. ita quod
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>.c.f.</
var
>
æqualis ſit
<
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>.c.u.</
var
>
intelligan-
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/>
<
reg
norm
="
turque
"
type
="
simple
">turq́;</
reg
>
quadrata
<
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>.g.f</
var
>
:
<
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>g.u.</
var
>
ct
<
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>.u.f.</
var
>
vnde
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summa
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type
="
context
">sũma</
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>
<
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norm
="
quadratorum
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type
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">quadratorũ</
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<
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>.g.u</
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>
:u.f. cognita nobis erit ex
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penultima primi. </
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>
<
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xml:space
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">nam
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data nobis fuit, quare
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>.g.u</
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:u.b: et
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>.u.f.</
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>
cognoſce-
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/>
mus, cui
<
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norm
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summæ
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type
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">sũmæ</
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addito ſuplemento
<
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>.d.e.</
var
>
æ quali
<
var
>.u.
<
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/>
b.</
var
>
dabit nobis
<
reg
norm
="
cognitum
"
type
="
context
">cognitũ</
reg
>
quadrarum
<
var
>.g.f.</
var
>
totale, qua
<
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/>
<
figure
xlink:label
="
fig-0305-01
"
xlink:href
="
fig-0305-01a
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number
="
327
">
<
image
file
="
0305-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0305-01
"/>
</
figure
>
re cognoſcetur eius radix
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>.b.f.</
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>
cognita igitur
<
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>.b.f.</
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>
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cum pro ducto
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>
illico ex .5. ſecundi cognoſce-
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tur
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>.b.c.</
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>
et
<
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>.c.f.</
var
>
forte cognita
<
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>.b.f.</
var
>
diuiſa
<
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norm
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per
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type
="
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">ꝑ</
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>
æqualia
<
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/>
in puncto
<
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>.t.</
var
>
& per inæqualiz in
<
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norm
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puncto
"
type
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">pũcto</
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>
<
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>.c</
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>
. </
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>
<
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xml:space
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">Nam qua
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type
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ipſius
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>.t.f.</
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>
cognitum, ęquatur
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reg
norm
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rectangulo
"
type
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">rectãgulo</
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>
<
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>.b.u.</
var
>
<
lb
/>
<
reg
norm
="
cum
"
type
="
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">cũ</
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>
quadrato ipſius
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>.t.c.</
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>
<
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type
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igitur rectangulo,
<
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>b.
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u.</
var
>
ex quadrato ipſius
<
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>.t.f.</
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>
relinquetur quadratum
<
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/>
<
reg
norm
="
ipſius
"
type
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>
<
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>.t.c.</
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>
cognitum & eius radix
<
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>.t.c.</
var
>
qua addita ipſi
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/>
medietati
<
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>.b.t.</
var
>
&
<
reg
norm
="
dempta
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type
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">dẽpta</
reg
>
ex medietate
<
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>.f.t.</
var
>
relinque-
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/>
tur propoſitum.</
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>
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<
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<
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xml:space
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">Similiter de tertio exemplo eiuſdem Stifelij
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infero.</
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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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">Sit rectangulus
<
var
>.a.b.c.u.</
var
>
cuius diametri
<
var
>.a.c.</
var
>
quantitas, ſimul cum proportione late
<
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/>
rum
<
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>.b.c.</
var
>
et
<
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>.b.a.</
var
>
nobis data ſit. </
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>
<
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xml:id
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xml:space
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">cum autem ſcire voluerimus eius ſuperficiem
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>.b.u.</
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>
cla-
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rum eſt, quod cum nobis data ſit proportio
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>.b.c.</
var
>
ad
<
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>.b.a.</
var
>
illico cognoſcemus
<
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norm
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etiam
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type
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">etiã</
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pro-
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portionem quadrati ipſius
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>.b.c.</
var
>
ad quadratum ip-
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/>
<
figure
xlink:label
="
fig-0305-02
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xlink:href
="
fig-0305-02a
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number
="
328
">
<
image
file
="
0305-02
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0305-02
"/>
</
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>
ſius
<
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>
cum dupla ſit ei quæ
<
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ad
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>.b.a.</
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>
ita etiam
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& aggregati dictorum quadratorum ad quadra-
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tum ipſius
<
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>.b.a.</
var
>
hoc eſt nota erit nobis proportio
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quadrati ipſius
<
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>.a.c.</
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>
diagonalis ad quadratum ip-
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ſius
<
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>.a.b.</
var
>
idem dico de quadrato
<
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>.b.c.</
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>
ideſt quod
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proportio quadrati ipſius
<
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>.a.c.</
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>
ad quadratum
<
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>.b.c.</
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>
<
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/>
cognita nobis erit, ſed
<
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>.a.c.</
var
>
data nobis fuit, qua-
<
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/>
re cognoſcemus etiam omnia dicta quadrata eo-
<
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<
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norm
="
rumque
"
type
="
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">rumq́;</
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radices
<
var
>.a.b.</
var
>
et
<
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>.b.c.</
var
>
</
s
>
<
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xml:id
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xml:space
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">quare & ſuperficiem re-
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ctanguli quæſitam.</
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>
</
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<
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<
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xml:space
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">Quartum exemplum etiam faciliori via poteſt
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ſolui, propterea, quod cum nobis cognita ſit ba-
<
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/>
ſis trianguli cum ſumma reliquorum laterum, &
<
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/>
<
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cum
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">cũ</
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>
angulo oppoſito baſi ipſius reliqua cognita no
<
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bis emergunt ex .15. problemate ſecundi lib. de Triangulis ipſius Monteregii.</
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