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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253
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rhead
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EPISTOLAE.
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265
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file
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0265
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0265
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angulo
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vnde ex .4. ſexti eadem proportio erit ipſius
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ad
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quæ
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ad
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. </
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<
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xml:space
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">quare ex .16. eiuſdem patebit propoſitum.</
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<
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xml:space
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">Secundus autem modus ita ſe habet, ducta
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habebimus duo triangula ortho-
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gonia ſimilia inuicem
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et
<
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eo quod angulus
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>.b.</
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communis ambobus exi-
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ſtit, </
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<
s
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xml:space
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">quare ex .4. ſexti ita ſe habebit
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ad
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>.b.o.</
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>
vt
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>.q.b.</
var
>
ad
<
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>.b.n.</
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>
vnde ex .15. eiuſdem
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quod fit ex
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>.u.b.</
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in
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>.b.n.</
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æquale erit ei, quod fit ex
<
var
>.q.b.</
var
>
in
<
var
>.b.o</
var
>
. </
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<
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xml:space
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">Sed ex .16. eiuſdem,
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fit ex
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in
<
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ęquatur quadrato
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quia
<
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media proportionalis eſt inter dia
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metrum & ſemidiametrum eiuſdem circuli. ex .4. eiuſdem, </
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">quare quod fit ex
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in
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<
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var
>
æquale erit quadrato ipſius
<
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>.b.e</
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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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">Tertius modus adiungitur, & eſt quod cum quadratum
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exiſtente
<
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>.u.</
var
>
extra cir-
<
lb
/>
culum æquale ſit ei, quod ſit ex
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>.u.b.</
var
>
in
<
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>.b.n.</
var
>
ſimul ſumpto cum eo,
<
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norm
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type
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fit ex
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in
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>
<
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/>
ex ſecunda ſecundi, & idem quadratum
<
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>.u.b.</
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>
æquale duobus quadratis
<
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>.u.o.</
var
>
et
<
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>.o.b.</
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>
ex
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penultima primi, ideo duo dicta producta æqualia erunt dictis duobus quadratis
<
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>.o.</
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>
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number
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0265-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0265-01
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</
figure
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u. ſcilicet et
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>.o.b.</
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>
ſed quadratum
<
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o u. æquatur ei, quod fit ex
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>.a.u.</
var
>
<
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/>
in
<
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>.e.u.</
var
>
& ei quod fit. ex
<
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>.o.e.</
var
>
in ſe
<
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/>
ipſam ex .6. ſecundi, </
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xml:space
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">quare duo
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<
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norm
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iam
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type
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">iã</
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>
dicta producta æqualia erunt
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duobus dictis quadratis,
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>o.b.</
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>
ſci
<
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licet. et
<
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>.o.e.</
var
>
& ei quod fit ex
<
var
>.a.
<
lb
/>
u.</
var
>
in
<
var
>.u.e.</
var
>
ſed quod fit ex
<
var
>b.u.</
var
>
in
<
var
>.u
<
lb
/>
n.</
var
>
æquale eſt ei quod fit ex
<
var
>.a.u.</
var
>
<
lb
/>
in
<
var
>.u.e.</
var
>
ex .35. 3.
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type
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ergo
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/>
vt id
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norm
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quod
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type
="
wordlist
">qđ</
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fit ex
<
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>.u.b.</
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in
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>
æqua-
<
lb
/>
le ſit
<
reg
norm
="
duobus
"
type
="
simple
">duobꝰ</
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>
quadratis
<
var
>.o.b.</
var
>
et
<
var
>.o.
<
lb
/>
e</
var
>
. </
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>
<
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xml:space
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">quare & quadrato ipſius
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>.b.e.</
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<
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/>
ex Pitagorica.</
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</
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<
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">Siautem
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reg
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>.u.</
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fuiſſet intra
<
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circulum idem eueniret. </
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>
<
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xml:space
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">Nam
<
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quadrato
<
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<
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æquantur
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type
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reg
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duo qua
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drata
<
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>.o.b.</
var
>
et
<
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>.o.e.</
var
>
ſed vice qua-
<
lb
/>
drati
<
var
>.o.e.</
var
>
dicemus
<
reg
norm
="
quadratum
"
type
="
context
">quadratũ</
reg
>
<
var
>.o.
<
lb
/>
u.</
var
>
cum eo quod fit ex
<
var
>.a.u.</
var
>
in
<
var
>.u.e.</
var
>
<
lb
/>
ex .5. ſecundi, id eſt quadratum
<
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>.
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o.u.</
var
>
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
eo quod fit ex
<
var
>.b.u.</
var
>
in
<
var
>.u.
<
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/>
n.</
var
>
ex .34. tertij, vnde quadratum
<
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<
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>b.e.</
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>
æquale erit quadrato
<
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>.o.b.</
var
>
<
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& quadrato
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>.o.u.</
var
>
ideſt quadrato
<
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/>
<
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>b.u.</
var
>
ex Pitagorica ſimul
<
reg
norm
="
cum
"
type
="
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">cũ</
reg
>
pro-
<
lb
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ducto
<
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>.b.u.</
var
>
in
<
var
>.u.n.</
var
>
ideſt producto
<
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/>
<
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>n.b.</
var
>
in
<
var
>.b.u.</
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>
quod æquale eſt qua
<
lb
/>
drat
<
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>o.b.u.</
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>
cum producto
<
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>.b.u.</
var
>
in
<
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<
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>u.n.</
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>
ex .3. ſecundi.</
s
>
</
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<
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<
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xml:id
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xml:space
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">Circa tres paſſiones commu-
<
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nes poſtea circulo hyperboli, &
<
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defectioni notandum eſt
<
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norm
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primam
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type
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">primã</
reg
>
<
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patere ex .36: primi Pergei, ſe- </
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