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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305
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rhead
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EPISTOLAE.
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n
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317
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file
="
0317
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0317
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eo quod tam proportio producti
<
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>.n.o.</
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in
<
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>.o.u.</
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ad productum
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>.m.o.</
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in
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quam pro-
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portio trianguli
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ad triangulum
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componitur ex proportione
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>.u.o.</
var
>
ad
<
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>.o.
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x.</
var
>
& ex proportion
<
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>e.n.o.</
var
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ad
<
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>.m.o.</
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>
vnde proportio dictorum productorum nobis co-
<
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/>
gnita erit, eo quod cum nobis cognita ſit proportio
<
var
>.A.</
var
>
ad
<
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>.B.</
var
>
vt data, cognita etiam
<
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/>
nobis erit coniuncta, hoceſt
<
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>.A.B.</
var
>
ad
<
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>.B</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">& propterea ea quæ trianguli
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>.n.o.u.</
var
>
ad
<
reg
norm
="
trian- gulum
"
type
="
context
">triã-
<
lb
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gulum</
reg
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<
var
>.m.o.x.</
var
>
& ſimiliter productorum. </
s
>
<
s
xml:id
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xml:space
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preserve
">Quæſiui poſtea modum inueniendi duas
<
lb
/>
dictas lineas
<
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>.m.o.</
var
>
et
<
var
>.o.x.</
var
>
& cognoui quod ſi producta fuerit
<
var
>.p.i.</
var
>
æquidiſtans li-
<
lb
/>
neæ
<
var
>.o.x.</
var
>
<
reg
norm
="
producendoque
"
type
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simple
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<
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>.o.n.</
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>
quouſque cum
<
var
>.p.i.</
var
>
ſe interſecarent in puncto
<
var
>.i.</
var
>
inuenien
<
lb
/>
do poſtea lineam quandam, quæ ducta cum
<
var
>.p.i.</
var
>
efficeret rectangulum æquale rectan
<
lb
/>
gulo cognito quod ex
<
var
>.m.o.</
var
>
in
<
var
>.o.x.</
var
>
poteſt fieri, quod cognitum dico, eo quod nobis
<
lb
/>
cognita eſt proportio data, & rectangulum etiam
<
var
>.n.o.</
var
>
in
<
var
>.o.u.</
var
>
deinde ſecando ab
<
var
>.o.
<
lb
/>
n.</
var
>
partem æqualem lineæ iam inuentæ, quæ ſit
<
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>.o.t</
var
>
. </
s
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<
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xml:id
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xml:space
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preserve
">Inueniendo poſtea, ex .28. ſexti
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lineam
<
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>.o.m.</
var
>
cuius productum in
<
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>.m.t.</
var
>
æquale ſit producto
<
var
>.t.o.</
var
>
in
<
var
>.o.i.</
var
>
vnde ex .15. eiuſ
<
lb
/>
dem proportio
<
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>.o.i.</
var
>
ad
<
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>.m.o.</
var
>
eadem eſſet, quæ
<
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>.m.t.</
var
>
ad
<
var
>.o.t.</
var
>
& componendo, ita ſe ha-
<
lb
/>
beret
<
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>.m.i.</
var
>
ad
<
var
>.m.o.</
var
>
vt
<
var
>.m.o.</
var
>
ad
<
var
>.o.t.</
var
>
ſed ex .4. ſexti, ita eſſet
<
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>.p.i.</
var
>
ad
<
var
>.o.x.</
var
>
vt
<
var
>.m.i.</
var
>
ad
<
var
>.m.o</
var
>
.
<
lb
/>
</
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<
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xml:id
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xml:space
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">quare ex .11. quinti, ita eſſet
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>
ad
<
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>.o.x.</
var
>
vt
<
var
>.m.o.</
var
>
ad
<
var
>.o.t.</
var
>
vnde ex .15. ſexti productum
<
var
>.
<
lb
/>
o.x.</
var
>
in
<
var
>.m.o.</
var
>
æquale eſſet producto. p, i. in
<
var
>.o.t.</
var
>
& ſic haberemus intentum.</
s
>
</
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<
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<
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xml:space
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<
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>.m.</
var
>
caderet in punctum
<
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>.n.</
var
>
idem eſſet, ſi vorò punctum
<
var
>.m.</
var
>
tranſiret
<
lb
/>
n. oporteret nos facere hoc in latere
<
var
>.n.u.</
var
>
ipſum quærendo in linea
<
var
>.n.u.</
var
>
ducendo pri
<
lb
/>
mum lineam
<
var
>.p.i.</
var
>
<
reg
norm
="
æquidiſtantem
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type
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<
var
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>
& producendo
<
var
>.u.n.</
var
>
ad partem
<
var
>.u.</
var
>
proſequendo,
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<
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ſuperius iam dictum eſt.</
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style
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head
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<
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xml:space
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">AD EVNDEM.</
head
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<
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<
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xml:space
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">DAtum parallelogrammum in duas partes diuidere, ſecundum aliquam datam
<
lb
/>
proportionem à linea tranſeunte per punctum propoſitum.</
s
>
</
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<
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<
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xml:space
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">Sit exempli gratia, datum parallelogrammum
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>.b.u.</
var
>
datum verò punctum
<
var
>.o.</
var
>
extra
<
lb
/>
figuram, proportio autem ea ſit, quæ
<
var
>.A.</
var
>
ad
<
var
>.B.</
var
>
vt ſupra. </
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>
<
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xml:id
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xml:space
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">Nunc diuidatur primò re-
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lb
/>
ctangulum datum per æqualia, mediante linea
<
var
>.r.c.</
var
>
parallela ambobus lateribus
<
var
>.b.x.</
var
>
<
lb
/>
et
<
var
>.s.u.</
var
>
quæ quidem linea diuidatur in puncto
<
var
>.i.</
var
>
ita quod eadem proportio ſit
<
var
>.r.i.</
var
>
ad
<
var
>.
<
lb
/>
i.c.</
var
>
vt
<
var
>.A.</
var
>
ad
<
var
>.B.</
var
>
protrahatur deinde à puncto
<
var
>.o.</
var
>
linea
<
var
>.o.i.q.</
var
>
quæ ſecabit ambo duo la-
<
lb
/>
tera
<
var
>.b.x.</
var
>
vel
<
var
>.s.u.</
var
>
intra terminos eorum, vel tantum
<
var
>.b.x.</
var
>
reliquum verò extra termi-
<
lb
/>
nos
<
var
>.s.u</
var
>
.</
s
>
</
p
>
<
p
>
<
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xml:space
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">Nunc autem ſi intra dictos terminos tranſibit, vt in prima figura videre potes,
<
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/>
problema ſolutum erit, eo quod
<
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/>
<
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fig-0317-01a
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number
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339
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0317-01
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xlink:href
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ſi à puncto
<
var
>.i.</
var
>
protracta fuerit
<
var
>.p.
<
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/>
d.</
var
>
pa rallela ad
<
var
>.u.x.</
var
>
habebimus
<
lb
/>
ex prima ſexti eandem propor-
<
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/>
tionem
<
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>.s.d.</
var
>
ad
<
var
>.p.x.</
var
>
ut
<
var
>.r.i.</
var
>
ad
<
var
>.i.c.</
var
>
<
lb
/>
hoc eſt vt
<
var
>.A.</
var
>
ad
<
var
>.B.</
var
>
ſed
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>
<
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<
var
>i.e.d.</
var
>
æqualis eſt triangulo
<
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>.i.q.p.</
var
>
<
lb
/>
vt tibi facilè patebit, vnde qua-
<
lb
/>
drilaterum
<
var
>.e.q.u.x.</
var
>
æquale erit
<
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/>
quadrilatero
<
var
>.d.u.</
var
>
ex communi </
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