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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THEOR. ARITH.
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25
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0025
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xlink:href
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tum ipſius
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talem eſſe partem quadrati ipſius
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qualis quadratum ipſius
<
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>
<
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eſt quadrati ipſius
<
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>.f.g</
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>
. </
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<
s
xml:id
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xml:space
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">Scimus pręterea ex .19. ſexti, aut vndecima octaui, propor-
<
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tioné quadrati ipſius
<
var
>.b.q.</
var
>
ad
<
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norm
="
quadratum
"
type
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">quadratũ</
reg
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ipſius
<
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>.d.q.</
var
>
duplam eſſe proportioni
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var
>.b.q.</
var
>
ad
<
var
>.
<
lb
/>
d.q.</
var
>
ſuarum radicum (cuborum enim tripla eſſet & cenſuum cenſuum, quadrupla,
<
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<
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atque
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ita deinceps ex præcedenti theoremate) Id ipſum dico de dignitatibus ipſius
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var
>.
<
lb
/>
f.g.</
var
>
et
<
var
>.i.g.</
var
>
reſpectu radicum
<
var
>.f.g.</
var
>
et
<
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>.i.g</
var
>
. </
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>
<
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xml:id
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xml:space
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">Vnde
<
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cum proportio dignitatis ipſius
<
var
>.b.q.</
var
>
ad il-
<
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lam
<
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>.d.q.</
var
>
ęqualis ſit proportioni dignitatis
<
lb
/>
<
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0025-01
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ipſius
<
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>.f.g.</
var
>
ad illam
<
var
>.g.i.</
var
>
ex communi ſcien-
<
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tia apertè cognoſcemus ſimplices propor-
<
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/>
tiones eſſe interſe æquales, nempe eam quę
<
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/>
eſt
<
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>.b.q.</
var
>
ad
<
var
>.d.q.</
var
>
æqualem eſſe ei, quæ eſt
<
var
>.f.
<
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/>
g.</
var
>
ad
<
var
>.i.g.</
var
>
<
reg
norm
="
itaque
"
type
="
simple
">itaq;</
reg
>
ſequitur ex definitione diuiſionis
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>.d.q.</
var
>
eſſe proueniens ex diuiſione
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>.
<
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b.q.</
var
>
per
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>.f.g</
var
>
.</
s
>
</
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</
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<
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<
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xml:space
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<
num
value
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19
">XVIIII</
num
>
.</
head
>
<
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<
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xml:space
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">CVR productum ex duabus radicibus quadratis, eſt quadrata radix, producti
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ſuorum quadratorum ſimul?</
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</
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<
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<
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xml:space
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">In cuius rei gratiam, ſint duo quadrata
<
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>.d.a.</
var
>
et
<
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>n.o.</
var
>
coniuncta ſimul, prout in ſub-
<
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ſcripta figura apparet, ita tamen vtangulus
<
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>.a.n.u.</
var
>
ſitre
<
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ctus, </
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>
<
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xml:id
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xml:space
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">quare ex quartadecima primi, duo latera
<
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>.n.c.</
var
>
et
<
var
>.
<
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/>
<
figure
xlink:label
="
fig-0025-02
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xlink:href
="
fig-0025-02a
"
number
="
26
">
<
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file
="
0025-02
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xlink:href
="
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</
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n.a.</
var
>
directe
<
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adinuicem, prout etiam reli-
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qua duo latera
<
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>.n.u.</
var
>
et
<
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>.n.d</
var
>
. </
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<
s
xml:id
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xml:space
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">Cogitato deinde
<
var
>.a.u.</
var
>
pro
<
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/>
ducto ipſius
<
var
>.a.n.</
var
>
in
<
var
>.n.u.</
var
>
duarum videlicet radicum
<
lb
/>
quadratarum ſimul, dabitur ex prima ſexti, aut de-
<
lb
/>
cimaottaua ſeptimi, productum
<
var
>.a.u.</
var
>
medium propor
<
lb
/>
tionale inter quadratum
<
var
>.a.d.</
var
>
et
<
var
>.u.c.</
var
>
quod ſi cogi-
<
lb
/>
temus has tres ſuperficies, tres numeros eſſe, pate-
<
lb
/>
bit ex vigeſimaprima ſeptimi productum
<
var
>.a.u.</
var
>
in ſe-
<
lb
/>
ipſum, quadratum ſcilicet
<
var
>.a.u.</
var
>
æquale eſſe producto
<
var
>.
<
lb
/>
a.d.</
var
>
in
<
var
>.u.c.</
var
>
ex quo propoſiti euidentia conſequetur.</
s
>
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<
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xml:space
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<
num
value
="
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">XX</
num
>
.</
head
>
<
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<
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xml:space
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">QVA ratione id ipſum in cubis cognoſci poterit.
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</
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<
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xml:space
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">Sit cubus
<
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>.l.b.</
var
>
& cubus
<
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>.o.p.</
var
>
quorum productum ſit
<
var
>.u.g.</
var
>
quod aſſero eſle
<
lb
/>
<
figure
xlink:label
="
fig-0025-03
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xlink:href
="
fig-0025-03a
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number
="
27
">
<
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file
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0025-03
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xlink:href
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>
cubum, quamuis Eucli. idem probet
<
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in
<
ref
id
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ref-0008
">.4. noni.</
ref
>
cuius radicem demonſtra-
<
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bo eſſe numeri æqualis numero
<
var
>.m.q.</
var
>
<
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/>
qui
<
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>.m.q.</
var
>
productum eſt ipſius
<
var
>.m.e.</
var
>
in
<
var
>.e.
<
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/>
q.</
var
>
radicum propoſitorum cuborum. </
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>
<
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xml:id
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xml:space
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">Pa-
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tet enim ex præcedenti theoremate
<
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>.m.
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<
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xlink:label
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fig-0025-04
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xlink:href
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fig-0025-04a
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number
="
28
">
<
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0025-04
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