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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93
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THEOREM. ARIT.
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105
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file
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0105
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xlink:href
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tum eſt, ideo cognoſcemus
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ſed
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cum
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minor ſit
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>.a.u.</
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>
ex .18. & penultima primi,
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ſi
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fuerit quadratum
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>.e.u.</
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ex quadrato
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>.a.u.</
var
>
remanebit nobis
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norm
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cognitum
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type
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<
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quadra- tum
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type
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">quadra-
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tũ</
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<
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>.a.e.</
var
>
& ſic nota erit nobis perpendicularis
<
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>.a.e.</
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>
ex penultima primi, quæ quidem
<
var
>.
<
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a.e.</
var
>
ſi multiplicata fuerit in dimidium
<
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>.o.u.</
var
>
dabit nobis
<
reg
norm
="
ſuperficiem
"
type
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">ſuperficiẽ</
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trianguli
<
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>.a.o.u.</
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ex
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41. dicti libri. </
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<
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xml:id
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xml:space
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">Et quia proportio trianguli
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var
>
ad triangulum
<
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>.u.i.n.</
var
>
(propter ſimi
<
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/>
litudinem) eſt vt quadrati
<
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>.o.u.</
var
>
ad quadratum
<
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>.n.i.</
var
>
ex communi ſcientia cum vna-
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/>
quæque iſtarum proportionum dupla ſit proportioni
<
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>.o.u.</
var
>
ad
<
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>.n.i.</
var
>
ex .17. et .18. ſexti,
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deinde cum nobis cognitæ ſint tres iſtarum quatuor quantitatum hoc eſt ſuperficies
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trianguli
<
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>.a.o.u.</
var
>
ſuperficies trianguli
<
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>.u.n.i.</
var
>
& quadrati
<
var
>.o.u.</
var
>
</
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>
<
s
xml:id
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xml:space
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">quare ex regula de tribus
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cognoſcemus etiam quadratum
<
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>.n.i.</
var
>
& ſic
<
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>.n.i.</
var
>
latus primi trianguli, vnde reliqua la
<
lb
/>
tera illicò nobis innoteſcent exipſa regula de tribus, cum dixerimus, ſi
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>.o.u.</
var
>
dat nobis
<
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/>
<
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>u.a</
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>
. </
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>
<
s
xml:id
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xml:space
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">tunc
<
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>.i.n.</
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dabit
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var
>
quòd etiam infero de
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>.u.i</
var
>
.</
s
>
</
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<
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<
s
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xml:space
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">Poſſemus etiam ita hoc perficere,
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ſcilicet inuenire
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quantitatem me-
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diam proportionalem inter duas ſu-
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perficies triangulorum, vnde ſuper-
<
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/>
ficies trianguli
<
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>.i.a.u.o.</
var
>
ad
<
var
>.x.</
var
>
ſe ha-
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/>
beret ut
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var
>.o.u.</
var
>
ad
<
var
>.i.n.</
var
>
& ita ex regula
<
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/>
detribus cognoſcemus
<
var
>.i.n</
var
>
. </
s
>
<
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xml:id
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xml:space
="
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">Multo
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type
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/>
pore poſtquàm hoc theorema conſtruxi, ipſum conſcriptum inueni in decimo
<
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ſecundi libri Ioannis de monte Regio, ſatis tamen obſcurè expreſſum.</
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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">THEOREMA
<
num
value
="
139
">CXXXIX</
num
>
.</
head
>
<
p
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<
s
xml:id
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xml:space
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">IN eodem primo libro vltimæ partis numerorum, Tartalea probat, via algebrę
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quòd quælibet duo latera trianguli orthogonij, angulumrectum continentia,
<
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/>
ſint tertio longiora per diame-
<
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<
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xlink:label
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xlink:href
="
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number
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<
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file
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0105-02
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xlink:href
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trum circuli inſcriptibilis in ip-
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ſo triangulo. </
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>
<
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xml:space
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geometricè poteſt
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,
<
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quemadmodum in ſubſcripta
<
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hic figura videre eſt, proptereà
<
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quòd cum anguli
<
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>.A.o.u.</
var
>
et
<
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>.n.</
var
>
<
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/>
omnes ſint recti et
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>.A.u.</
var
>
æqualis
<
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/>
<
var
>o.n.</
var
>
et
<
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>.A.n.</
var
>
ęqualis
<
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var
>
ipſæ
<
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>.A.
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u.</
var
>
et
<
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>.A.n.</
var
>
æquales erunt diame-
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tro ipſius circuli. </
s
>
<
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xml:space
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">Sed eædem
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A.u.</
var
>
et
<
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>.A.n.</
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ſunt ſuperfluum, quo
<
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>.A.B.</
var
>
et
<
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>.A.C.</
var
>
ſunt maiores
<
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>.B.C.</
var
>
cum
<
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>.B.u.</
var
>
et
<
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>.C.n.</
var
>
<
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/>
ſint æquales
<
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>.B.C.</
var
>
ex penultima tertij Eucli.</
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>
</
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<
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xml:space
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">THEO. SEQVENS THEO. CXXXIX.</
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>
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xml:space
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">SImiliter in nono capite ſecundi libri nouæ ſcientiæ poterat ipſe Tartalea breuio
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ri methodo abſque vlla operatione ipſius Algebræ inuenire
<
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>.A.H.</
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>
reſpectu
<
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>.A.
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E.</
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>
eſſe vt .4.
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vno ſeptimo ad
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. </
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ipſe ſupponit
<
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>.A.E.</
var
>
<
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decimam
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type
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">decimã</
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>
<
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eſſe ipſius </
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