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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IO. BAPT. BENED.
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392
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file
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0392
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0392
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negotio cordarum & arcuum poſſumus geometricè demonſtrare quod valde de-
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ſideras.</
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<
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<
s
xml:id
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xml:space
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">Quapropter ſit circulus
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var
>
in quo ſit
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norm
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triangulum
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type
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reg
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æquilaterum
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var
>
& quadra
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lb
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tum
<
var
>.b.a.q.u.</
var
>
cuius periferiam probabo longiorem eſſe periferia trianguli. </
s
>
<
s
xml:id
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echoid-s4491
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xml:space
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preserve
">Sit enim
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lb
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diameter circuli
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var
>.b.q.</
var
>
qui etiam erit diameter quadrati, vt à te ſcire potes. </
s
>
<
s
xml:id
="
echoid-s4492
"
xml:space
="
preserve
">Sit etiam
<
lb
/>
<
reg
norm
="
punctum
"
type
="
context
">punctũ</
reg
>
<
var
>.b.</
var
>
commune tam anguli quadrati quam trianguli. </
s
>
<
s
xml:id
="
echoid-s4493
"
xml:space
="
preserve
">vnde ſequitur quod dictus
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lb
/>
diameter ſecabit latus
<
var
>.n.e.</
var
>
trianguli ad rectos & per æqualia in
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var
>.t</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4494
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xml:space
="
preserve
">Nam cum arcus
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var
>.b.
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lb
/>
e.</
var
>
æqualis ſit arcui
<
var
>.b.n.</
var
>
ex .27. tertij, remanet vt arcus
<
var
>.q.e.</
var
>
equalis ſit arcui
<
var
>.q.n.</
var
>
vnde
<
lb
/>
angulus
<
var
>.q.b.e.</
var
>
æqualis erit angulo
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var
>.q.b.n.</
var
>
ex .26. eiuſdem. </
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<
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xml:id
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xml:space
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preserve
">quare ex .4. primi anguli
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ad
<
var
>.t.</
var
>
erunt recti, et
<
var
>.n.t.</
var
>
æqualis erit ipſi
<
var
>.t.e.</
var
>
vt diximus.</
s
>
</
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>
<
p
>
<
s
xml:id
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xml:space
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">Deinde
<
var
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var
>
et
<
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>.q.a.</
var
>
ſeinuicem
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reg
norm
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ſecant
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type
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context
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>
in puncto
<
var
>.o.</
var
>
vt ex ſe clarum patet, ducatur po
<
lb
/>
ſtea
<
var
>.q.e.</
var
>
vnde habebimus angulum
<
var
>.b.e.q.</
var
>
rectum ex .30. tertij, </
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>
<
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xml:id
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xml:space
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">quare ex .18. primi
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var
>.q.
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lb
/>
o.</
var
>
longior erit ipſa
<
var
>.q.e.</
var
>
et
<
var
>.q.e.</
var
>
longior erit ipſa
<
var
>.e.t</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">quare
<
var
>.q.o.</
var
>
longior erit ipſa
<
var
>.t.e</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
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">Vt probemus poſtea
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var
>
longiorem eſſe ipſa
<
var
>.b.e.</
var
>
producatur
<
var
>.b.a.</
var
>
ita quod
<
var
>.a.
<
lb
/>
p.</
var
>
æqualis ſit ipſi
<
var
>.a.o.</
var
>
<
reg
norm
="
ducaturque
"
type
="
simple
">ducaturq́;</
reg
>
<
var
>o.p.</
var
>
et
<
var
>.a.e.</
var
>
cum autem ex iam dicta .30. tertij angulus
<
lb
/>
<
var
>b.a.o.</
var
>
<
reg
norm
="
rectus
"
type
="
simple
">rectꝰ</
reg
>
ſit, erit angulus
<
var
>.o.a.p.</
var
>
ſimiliter
<
reg
norm
="
rectus
"
type
="
simple
">rectꝰ</
reg
>
ex .13. primi, vnde ex .5. et .32.
<
reg
norm
="
eiuſdem
"
type
="
context
">eiuſdẽ</
reg
>
<
lb
/>
angulus
<
var
>.a.p.o.</
var
>
erit dimidium recti, & ſimiliter, exijſdem, angulus
<
var
>.b.q.a.</
var
>
eſt dimidium
<
lb
/>
recti </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">quare angulus
<
var
>.a.p.o.</
var
>
æqualis erit angulo
<
var
>.a.q.b.</
var
>
ſed angulus
<
var
>.a.e.b.</
var
>
æqualis eſt an
<
lb
/>
gulo
<
var
>.a.q.b.</
var
>
ex .20. tertij, ergo angulus
<
var
>.b.p.o.</
var
>
æqualis erit angulo .b,
<
var
>e.a.</
var
>
angulus vero
<
lb
/>
<
var
>a.b.e.</
var
>
communis eſt ambobus triangulis
<
var
>.a.b.e.</
var
>
et
<
var
>.o.b.p</
var
>
. </
s
>
<
s
xml:id
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xml:space
="
preserve
">quare ex .32. primi anguli
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var
>.
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b.a.e.</
var
>
et
<
var
>.b.o.p.</
var
>
reliqui ex duobus rectis æqua
<
lb
/>
<
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0392-01
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xlink:href
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les inuicem erunt. </
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xml:space
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et .18. quinti proportio
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var
>
ad
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var
>.b.p.</
var
>
erit, vt
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/>
<
var
>b.a.</
var
>
ad
<
var
>.b.e.</
var
>
ſed ex .18. primi
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>.b.o.</
var
>
maior eſt
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ipſa
<
var
>.b.a</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">quare ex .14. quinti
<
var
>.b.p.</
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>
maior erit
<
lb
/>
ipſa
<
var
>.b.e.</
var
>
ſed
<
var
>.b.p.</
var
>
æquatur ipſis
<
var
>.b.a.</
var
>
cum
<
var
>.a.</
var
>
o
<
lb
/>
ex hypoteſi, ergo
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var
>.b.a.</
var
>
cum
<
var
>.a.o.</
var
>
maior erit
<
lb
/>
ipſa
<
var
>.b.e.</
var
>
ſed
<
var
>.q.o.</
var
>
maior erat ipſa
<
var
>.t.e.</
var
>
vt ſupe
<
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/>
rius vidimus, </
s
>
<
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xml:id
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xml:space
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">quare
<
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>.b.a.</
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>
cum
<
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>.a.o.</
var
>
et
<
var
>.o.q.</
var
>
ma
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lb
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ior eſt ipſa
<
var
>.b.e.</
var
>
cum
<
var
>.e.t.</
var
>
hoc eſt dimidium
<
lb
/>
periferię ipſius quadrati,
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reg
norm
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maius
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type
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">maiꝰ</
reg
>
erit dimidio
<
lb
/>
periferię
<
reg
norm
="
ipſius
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type
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">ipſiꝰ</
reg
>
<
reg
norm
="
trianguli
"
type
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">triãguli</
reg
>
propoſiti, </
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>
<
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xml:id
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xml:space
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">quare ex 14.
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dicta tota periferia dicti trianguli, ſimiliter
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probarem de omnibus alijs figuris regulari
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bus eodem circulo inſcriptis.</
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">CONSIDERATIONES NONNVLLÆ IN
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Archimedem.</
head
>
<
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style
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">Doct ßimo atque Reuerendo Domino Vincentio
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Mercato.</
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>
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<
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>
tibi aliàs dixi verum eſt, intellectum ſcilicet non omninò quieſcere cir
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/>
ca illas duas Archimedis propoſitiones, quæ in translatione Tartaleæ ſunt
<
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/>
ſub numeris .4. et .5. & in impreſſione Baſileæ ſub numeris .6. et .7. vbi
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tractat </
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