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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151 - 163
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363
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rhead
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EPISTOL AE.
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n
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375
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file
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0375
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0375
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& qua drato
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ex
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eadem
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. </
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<
s
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xml:space
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<
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norm
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duplum
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type
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context
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reg
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quadrati
<
var
>.a.e.</
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<
reg
norm
="
cum
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type
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duplo qua
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drati
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var
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reg
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cum
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type
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duplo quadrati
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ſit æquale duplo quadrati
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quadrato
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&
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cum quadrato
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>.a.c</
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. </
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>
<
s
xml:id
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xml:space
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preserve
">Sed quia tam ex vna parte quàm ex alia habemus duplum qua-
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drati
<
var
>.a.e</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Videndum igitur erit vtrum duplum quadrati
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>.a.b.</
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>
ſimul cum duplo qua-
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drati
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ęquale ſit quadrato
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cum quadrato
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>
ſed hoc manifeſtum eſt .ex .10.
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lb
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ſecundi Euclidis, dato quod
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type
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ſit inter
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et
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ſed ſi fuerit inter
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et
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hoc
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manifeſtum erit ex .9. ſecundi dicti, nihilominus accipe hunc alium modum.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Sit hic ſubſcriptum quadratum
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var
>.D.</
var
>
ex
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var
>.a.c.</
var
>
in ſeipſa producta, cuius diameter ſit
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<
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reg
norm
="
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type
="
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parallelę
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:
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et
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type
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addatur
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>.c.p.</
var
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ad
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æqua-
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lis tamen
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type
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protracta
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vſque ad
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vnde habebimus
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>
pro totali
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quadrato, et
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>
pro partiali, & æquali quadrato lineæ
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var
>.a.d</
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. </
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>
<
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xml:id
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xml:space
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">Videndum nunc eſt,
<
reg
norm
="
vtrum
"
type
="
context
">vtrũ</
reg
>
<
lb
/>
hęc duo quadrata æqualia ſint duobus quadratis lineæ
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>.a.b.</
var
>
& duobus lineæ
<
var
>.b.c.</
var
>
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reg
norm
="
Nam
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type
="
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reg
>
<
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duo quadrata lineæ
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var
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>
ſint
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var
>
et
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videndum nunc eſt utrum reſiduum ęquale
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ſit duobus quadratis lineę
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quorum vnum ſit
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alterum verò
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>
quod ſupe-
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rat
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>
et
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figuræ
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per ſupplementum
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cui æquale eſt parallelogrammum
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m.</
var
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figuræ
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>.D.</
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ſed ſi punctus
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poſitus fuerit inter
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et
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conſtituto quadrato
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type
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omnibus parallelis, vtin figura
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>
viderelicet, in qua figura videbimus quadrata
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n.</
var
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et
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>
ęquari duplo quadratorum
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>.l.n.</
var
>
et
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>.r.l.</
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>
nam in quadrato
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>.r.n.</
var
>
ipſa duo quadra-
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lb
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ta
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>.l.n.</
var
>
et
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>.r.l.</
var
>
capiuntur, reliquum eſt igitur vt videamus an duo ſupplementa
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>.l.t.</
var
>
et
<
var
>.l.
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lb
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s.</
var
>
cum quadrato
<
var
>.d.r.</
var
>
ſint æqualia dictis
<
reg
norm
="
quadratis
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type
="
typo
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>
<
var
>.l.n.</
var
>
et
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var
>.r.l.</
var
>
ſed quadratum
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var
>.d.l.</
var
>
æ qua-
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lb
/>
tur quadrato
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var
>.l.n.</
var
>
videndum igitur eſt,
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lb
/>
an duo ſupplementa
<
var
>.l.t.</
var
>
et
<
var
>.l.s.</
var
>
cum qua
<
lb
/>
<
figure
xlink:label
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fig-0375-01
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xlink:href
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fig-0375-01a
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number
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<
image
file
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0375-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0375-01
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</
figure
>
drato
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var
>.d.r.</
var
>
ſint æqualia duobus quadra
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lb
/>
tis
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var
>.d.l.</
var
>
et
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var
>.r.l.</
var
>
ſed quadratum
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var
>.d.l.</
var
>
æqua-
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lb
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tur quadrato
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var
>.d.r.</
var
>
& ſupplemento
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var
>.l.t.</
var
>
<
lb
/>
mediante
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var
>.q.l.</
var
>
& ſupplemento
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var
>.r.b.</
var
>
ſup-
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lb
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plementum verò
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var
>.l.s.</
var
>
ſuperat
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norm
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>
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tum
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var
>.r.b.</
var
>
per quantitatem
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norm
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qua-
<
lb
/>
drato
<
var
>.r.l.</
var
>
</
s
>
<
s
xml:id
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xml:space
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preserve
">quare duo ſupplementa
<
var
>.l.t.</
var
>
<
lb
/>
et
<
var
>.l.s.</
var
>
cum quadrato
<
var
>.d.r.</
var
>
æquantur qua
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lb
/>
drato
<
var
>.d.l.</
var
>
<
reg
norm
="
cum
"
type
="
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">cũ</
reg
>
quadrato
<
var
>.l.r.</
var
>
verum igitur eſt duas
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var
>.d.e.e.c.</
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>
figuræ
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var
>.A.</
var
>
æquales eſſe in
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/>
potentia duabus
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var
>d.e.e.c.</
var
>
figurę
<
var
>.D.</
var
>
quæ quidem affectio circuli, à nemine fuit adhuc
<
lb
/>
(quod ſciam) detecta.</
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>
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