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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21
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THEOREM. ARIT.
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n
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33
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file
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0033
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0033
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retur .20. ſcilicet et .4. certè .24. perſingulas partes diuiſo, daretur vnum proue-
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niens ſex integra, & alterum vnum & quinta pars, quorum ſumma eſſet ſeptem in-
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tegra cum quinta parte, tum altera parte per alteram diuiſa, daretur vnum proue-
<
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niens quinque integrorum & alterum vnius quinti tantum, quorum ſumma eſſet
<
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/>
quinque integra, & vna quinta pars, minor prima reliquorum duorum prouenien-
<
lb
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tium per binarium.</
s
>
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<
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<
s
xml:id
="
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"
xml:space
="
preserve
">Cuius conſiderationis cauſa, propoſitus numerus linea
<
var
>.q.p.</
var
>
ſignificetur, eius duę
<
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/>
partes lineis
<
var
>.q.x.</
var
>
et
<
var
>.x.p.</
var
>
<
reg
norm
="
tum
"
type
="
context
">tũ</
reg
>
<
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>.q.f.</
var
>
ſit proueniens ex diuiſione totius
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var
>.q.p.</
var
>
per
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var
>.x.p.</
var
>
et
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var
>.
<
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/>
q.i.</
var
>
ſit proueniens ex diuiſione eiuſdem
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>.q.p.</
var
>
per
<
var
>.q.x.</
var
>
adhæc
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var
>.h.m.</
var
>
ſit proueniens,
<
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/>
ex diuiſione
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var
>.q.x.</
var
>
per
<
var
>x.p.</
var
>
et
<
var
>.h.k.</
var
>
proue-
<
lb
/>
niensex diuiſione
<
var
>.p.x.</
var
>
per
<
var
>.q.x.</
var
>
patet igi-
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/>
<
figure
xlink:label
="
fig-0033-01
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xlink:href
="
fig-0033-01a
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number
="
44
">
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file
="
0033-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0033-01
"/>
</
figure
>
tur ex .22. theoremate huiuslibri proue-
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niés.h.m. minus eſſe proueniente
<
var
>.q.f.</
var
>
per
<
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/>
vnitaté, & proueniens
<
var
>.h.k.</
var
>
minus proue-
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/>
niente
<
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>.q.i.</
var
>
per alteram vnitatem. </
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>
<
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xml:id
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xml:space
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preserve
">Itaque
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var
>.
<
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f.q.i.</
var
>
maior erit
<
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>.m.h.k.</
var
>
per numerum binarium, quoderat propoſitum.</
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>
</
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>
</
div
>
<
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xml:id
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type
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<
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xml:id
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xml:space
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">THEOREMA.
<
num
value
="
33
">XXXIII</
num
>
.</
head
>
<
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<
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<
emph
style
="
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">QVilibet</
emph
>
numerus, medius eſt
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proportionalis inter numerum
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<
figure
xlink:label
="
fig-0033-02
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xlink:href
="
fig-0033-02a
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number
="
45
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file
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0033-02
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xlink:href
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</
figure
>
ſui quadrati & vnitatem.</
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</
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<
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<
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xml:id
="
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xml:space
="
preserve
">Detur enim numerus propoſitus,
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qui linea
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>.a.u.</
var
>
ſignificetur, cuiusqua-
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dratum ſit
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>.u.n.</
var
>
vnitas linearis ſit
<
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>.i.a.</
var
>
<
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/>
et ſuperficialis
<
var
>.o.</
var
>
patebit ex .18. ſexti
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aut 11. octaui proportionem
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>.u.n.</
var
>
ad
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var
>.
<
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/>
o.</
var
>
futuram duplam proportioni
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>.u.a.</
var
>
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/>
ad
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>.i.a.</
var
>
ſed
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>.i.a.</
var
>
e
<
unsure
/>
t.o. eadem (ſpecie)
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/>
res
<
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norm
="
sunt
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type
="
context
">sũt</
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>
, tanta ſcilicet
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>.a.i.</
var
>
quanta
<
var
>.o.</
var
>
vni
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<
figure
xlink:label
="
fig-0033-03
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xlink:href
="
fig-0033-03a
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number
="
46
">
<
image
file
="
0033-03
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0033-03
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</
figure
>
tas eſt, Itaque proportio numeri
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var
>
<
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ad
<
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>.u.a.</
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>
æqualis erit proportioni
<
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>.u.a.</
var
>
<
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/>
ad
<
var
>.i.a</
var
>
. </
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>
<
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xml:id
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xml:space
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">Quare numerus
<
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>.u.a.</
var
>
inter nu-
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merum
<
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>.u.n.</
var
>
& vnitatem, medius erit
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/>
proportionalis.</
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</
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</
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<
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<
head
xml:id
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xml:space
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">THEOREMA
<
num
value
="
34
">XXXIIII</
num
>
.</
head
>
<
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<
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xml:space
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<
emph
style
="
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">HOc</
emph
>
ipſum quod diximus & alia ratione ſpeculari licebit.</
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>
</
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<
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<
s
xml:id
="
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xml:space
="
preserve
">Propoſitus numerus, nunc etiam per
<
var
>.a.u.</
var
>
ſignificetur, eius quadratum per
<
var
>.
<
lb
/>
u.n.</
var
>
vnitas linearis per
<
var
>.a.i.</
var
>
<
reg
norm
="
productumque
"
type
="
simple
">productumq́;</
reg
>
<
var
>.a.u.</
var
>
in
<
var
>.a.i.</
var
>
terminetur,
<
reg
norm
="
ſitque
"
type
="
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">ſitq́;</
reg
>
<
var
>.n.i</
var
>
. </
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>
<
s
xml:id
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echoid-s307
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xml:space
="
preserve
">quare
<
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<
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>n.i.</
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>
conſtabit numero íuperficiali æquali numero lineari
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>.a.u.</
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>
& ex prima fexti aut .
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/>
18. vel .19. ſeptimi, eadem erit proportio
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>.u.n.</
var
>
ad
<
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>.i.n.</
var
>
quæ eſt
<
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>.a.u.</
var
>
ad
<
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>.a.i.</
var
>
ſed nu-
<
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/>
merus
<
var
>.a.u.</
var
>
cum numero
<
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>.n.i.</
var
>
idem ſpecie eſt. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Itaque medius eſt proportiona-
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lis inter
<
var
>.u.n.</
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>
& vnitatem.</
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>
</
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