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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rhead
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IO. BAPT. BENED.
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n
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20
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file
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0020
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0020
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n.c.</
var
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ad
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>.a.e.</
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ſint æquales inuicem quandoqui-
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<
figure
xlink:label
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fig-0020-01
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xlink:href
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fig-0020-01a
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number
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14
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<
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file
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0020-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0020-01
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dem vnaquæque earum ex triangulorum ſimi
<
lb
/>
litudine æqualis eſt proportioni
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var
>.o.n.</
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ad
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.
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</
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<
s
xml:id
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xml:space
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">itaque
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var
>.n.t.</
var
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hoc eſt
<
var
>.a.i.</
var
>
tanto maior erit
<
var
>.a.x.</
var
>
<
lb
/>
quanto
<
var
>.n.c.</
var
>
maior eſt
<
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>.a.e.</
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>
vnde ficut
<
var
>.a.e.</
var
>
con-
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/>
ſtat octo nonis ipſius
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var
>
ita pars
<
var
>.a.x.</
var
>
ipſius
<
var
>.
<
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/>
a.e.</
var
>
octo nonis conſtabit ipſius
<
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>.a.i</
var
>
.</
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>
</
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<
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<
s
xml:id
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xml:space
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preserve
">Hinc patet ratio cur partituri numerum mino
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lb
/>
rem per maiorem collocent minorem fupra
<
lb
/>
virgulam & maiorem infra & zerum ad
<
reg
norm
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læuam
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type
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context
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.</
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</
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<
p
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<
s
xml:id
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xml:space
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preserve
">Sciendum eſt præterea diuidere numerum
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per numerum: </
s
>
<
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xml:id
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xml:space
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">eſſe inuenire
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type
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latus à quo
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lb
/>
producitur, ſuppoſito ſemper quòd numerus
<
lb
/>
diuifibilis ſuperſicialis ſit, & rectangulus.</
s
>
</
p
>
<
p
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<
s
xml:id
="
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"
xml:space
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preserve
">Exempli gratia, ſi proponantur triginta diuidenda per quinarium, nihil aliud erit
<
lb
/>
hæc diuiſio, quam inuentio alterius numeri, qui multiplicatus per quinarium produ-
<
lb
/>
cat triginta ſuperficies rectangulas, huiuſmodi verò eſt ſenarius, cuius ſingulæ vnita-
<
lb
/>
tes ſuperficiales erunt.</
s
>
</
p
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<
p
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<
s
xml:id
="
echoid-s113
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xml:space
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preserve
">Cuius rei gratia ſit ſubſcriptum rectangulum
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var
>.a.e.</
var
>
triginta vnitatum
<
reg
norm
="
ſuperſicialium
"
type
="
context
">ſuperſicialiũ</
reg
>
,
<
lb
/>
cuius latus
<
var
>.e.n.</
var
>
ſit quinque vnitatum. </
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>
<
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xml:id
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xml:space
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erit ſex vnitatum; </
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>
<
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xml:id
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xml:space
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">ita diuiden-
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tes rectangulum
<
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var
>
nihil a iud faciemus, quam vt inue-
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lb
/>
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xlink:label
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fig-0020-02
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xlink:href
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fig-0020-02a
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number
="
15
">
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file
="
0020-02
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0020-02
"/>
</
figure
>
nia mus quantum valeat latus
<
var
>.a.n.</
var
>
quod erit ſex vnitatum.
<
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/>
</
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>
<
s
xml:id
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xml:space
="
preserve
">Sin verò diuiſerimus per latus
<
var
>.a.n.</
var
>
quæremus latus
<
var
>.e.n.</
var
>
<
lb
/>
quinque vnitatum. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ex quo, proportio totius numeri diuifi-
<
lb
/>
bilis ad numerum qui oritur, erit ſicut diuidentis ad vnita-
<
lb
/>
tem, ex prima ſexti, aut .18. vel .19. ſeptimi, & permutatim
<
lb
/>
ita ſe habebit diuiſibile ad diuidentem, ſicut numerus qui
<
lb
/>
oritur ad vnitatem.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Partiri igitur nihil aliud eſt, quam inuenire latus rectanguli, quod productum in
<
lb
/>
diuidente, numerum diuiſibilem compl at, ex quo numerus diuiſibilis ſuperficialis
<
lb
/>
eſt, diuidens autem, & qui oritur, numeri lineares & latera producentia huiuſcemodi
<
lb
/>
numerum diuiſibilem. </
s
>
<
s
xml:id
="
echoid-s119
"
xml:space
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preserve
">nam multiplicare & diuidere opponuntur inuicem, cum au-
<
lb
/>
tem ex multiplicatione laterum ſiue linearum generatur ſuperficies, ex diuiſione po-
<
lb
/>
ſtea ipſius ſuperficiei inuenitur alterum latus. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">quare mirum non eſt, ſi proueniens ex
<
lb
/>
vna diuiſione (via fractorum) ſit ſemper maius numero diuiſibili.</
s
>
</
p
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<
p
>
<
s
xml:id
="
echoid-s121
"
xml:space
="
preserve
">Exempli gratia, diuidendo dimidium per tertiam partem, reſultat vnus integer nu
<
lb
/>
merus cum dimidio pro numero qui oritur. </
s
>
<
s
xml:id
="
echoid-s122
"
xml:space
="
preserve
">Sit itaque dimidium ſuperſiciale diuiſi-
<
lb
/>
bile
<
var
>.b.c.</
var
>
cuius totum ſit
<
var
>.b.p.</
var
>
quadratum. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">tertium verò lineare diuidens,
<
var
>b.n.</
var
>
cuius to-
<
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/>
tum lineare ſit
<
var
>.b.d.</
var
>
quærendum nobis eſt latus
<
var
>.b.s.</
var
>
quod cum latere
<
var
>.b.n.</
var
>
producat re
<
lb
/>
ctangulum
<
var
>.n.s.</
var
>
æquale dimidio ſuperſiciali propoſito
<
var
>.b.c.</
var
>
quod ſi ſiat, ex .15. ſexti,
<
lb
/>
aut .20. ſeptimi. erit eadem proportio
<
var
>.b.n.</
var
>
ad
<
var
>.b.q.</
var
>
quæ eſt
<
var
>.q.c.</
var
>
ad
<
var
>.b.s.</
var
>
dicemus itaque
<
lb
/>
ſi
<
var
>.n.b.</
var
>
dat
<
var
>.b.q.</
var
>
quid dabit
<
var
>.q.c</
var
>
? </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">certè
<
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>.b.s.</
var
>
ſed
<
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>.n.b.</
var
>
eſt tertium lineare et
<
var
>.b.q.</
var
>
lineare
<
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norm
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in- tegrum
"
type
="
context
">in-
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tegrũ</
reg
>
, &
<
var
>b.s.</
var
>
proueniens lineare. </
s
>
<
s
xml:id
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"
xml:space
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">& quia
<
var
>.b.c.</
var
>
dimidium ſuperficiale, producitur à
<
var
>.q.c.</
var
>
<
lb
/>
dimidio lineari in
<
var
>.q.b.</
var
>
integro lineari. </
s
>
<
s
xml:id
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"
xml:space
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preserve
">quare cum
<
var
>.n.s.</
var
>
ſit ęqualis
<
var
>.b.c.</
var
>
& productum ex
<
var
>.
<
lb
/>
b.n.</
var
>
minori
<
var
>.q.c.</
var
>
neceſſe eſt, vt producatur in
<
var
>.b.s.</
var
>
maiore
<
var
>.q.b.</
var
>
quod
<
var
>.q.b.</
var
>
maius eſt
<
var
>.q.c.</
var
>
<
lb
/>
quod quidem
<
var
>.q.c.</
var
>
ita appellatur ſicut
<
var
>.b.c</
var
>
. </
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>
<
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xml:id
="
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"
xml:space
="
preserve
">quare mirum non eſt ſi proueniens per fra-
<
lb
/>
ctos numeros ex diuiſione, maior ſit numero diuiſibili.</
s
>
</
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