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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130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
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<
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128
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IO. BAPT. BENED.
"
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140
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file
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0140
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0140
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<
head
xml:id
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xml:space
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preserve
">CAP. VII.</
head
>
<
p
>
<
s
xml:id
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"
xml:space
="
preserve
">ALiarn tamen inueni viam breuiorem vt in figura
<
var
>.H.H.</
var
>
in qua ſit punctus
<
var
>.
<
lb
/>
b.</
var
>
perfecti, &
<
var
>.k.</
var
>
degradati plani. </
s
>
<
s
xml:id
="
echoid-s1565
"
xml:space
="
preserve
">Nunc ducatur
<
var
>.b.c.s.</
var
>
ad rectos cum
<
var
>.
<
lb
/>
p.m.</
var
>
indefinitè, quæ quidem abſcindatur in puncto
<
var
>.s.</
var
>
ita quòd
<
var
>.c.s.</
var
>
æqualis ſit alti
<
lb
/>
tudini perfectæ, deinde coniungatur rectà. s. cum
<
var
>.i</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1566
"
xml:space
="
preserve
">Tunc ſi ab
<
var
>.k.</
var
>
vſque ad
<
reg
norm
="
protractam
"
type
="
context
">protractã</
reg
>
<
lb
/>
<
var
>i.s.</
var
>
ducta fuerit
<
var
>.k.R.</
var
>
parallela li-
<
lb
/>
<
figure
xlink:label
="
fig-0140-01
"
xlink:href
="
fig-0140-01a
"
number
="
194
">
<
image
file
="
0140-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0140-01
"/>
</
figure
>
neę
<
var
>.c.s.</
var
>
hæc
<
var
>.R.k.</
var
>
erit altitudo
<
lb
/>
quæſita ſeu degradata.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1567
"
xml:space
="
preserve
">Quod ita probo. </
s
>
<
s
xml:id
="
echoid-s1568
"
xml:space
="
preserve
">Iam nulli du
<
lb
/>
bium eſt quin
<
var
>.f.V.</
var
>
ſit æqualis alti-
<
lb
/>
tudini quęſitæ ſeu degradatę, quo
<
lb
/>
<
reg
norm
="
tieſcunque
"
type
="
simple
">tieſcunq;</
reg
>
ergo
<
reg
norm
="
probauerimus
"
type
="
simple
">ꝓbauerimus</
reg
>
<
var
>.k.R.</
var
>
<
lb
/>
æqualem eſſe lineæ
<
var
>.f.V.</
var
>
habebi-
<
lb
/>
mus propoſitum. </
s
>
<
s
xml:id
="
echoid-s1569
"
xml:space
="
preserve
">Quare certum
<
lb
/>
nobis erit eandem proportionem
<
lb
/>
eſſe lineæ
<
var
>.c.s.</
var
>
ad
<
var
>.k.R.</
var
>
quam
<
var
>.c.i.</
var
>
ad
<
lb
/>
<
var
>k.i.</
var
>
et
<
var
>.c.i.</
var
>
ad
<
var
>.k.i.</
var
>
vt
<
var
>.x.i.</
var
>
ad
<
var
>.f.i.</
var
>
et
<
var
>.x.
<
lb
/>
i.</
var
>
ad
<
var
>.f.i.</
var
>
vt
<
var
>.m.o.</
var
>
ad
<
var
>.f.o.</
var
>
et
<
var
>.m.o.</
var
>
ad
<
var
>.
<
lb
/>
f.o.</
var
>
vt
<
var
>.m.T.</
var
>
ad
<
var
>.f.V.</
var
>
ex ſimilitudine
<
lb
/>
triangulorum. </
s
>
<
s
xml:id
="
echoid-s1570
"
xml:space
="
preserve
">Ergo
<
var
>.m.T.</
var
>
ad
<
var
>.f.V.</
var
>
<
lb
/>
erit vt
<
var
>.c.s.</
var
>
ad
<
var
>.k.R.</
var
>
ex .11. quinti,
<
lb
/>
ſed
<
var
>.c.s.</
var
>
ſumpta fuit æqualis
<
var
>.m.T</
var
>
.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1571
"
xml:space
="
preserve
">quare
<
var
>.c.s.</
var
>
ad
<
var
>.f.V.</
var
>
erit, vt
<
var
>.m.T.</
var
>
ad
<
lb
/>
<
reg
norm
="
eandem
"
type
="
context context
">eãdẽ</
reg
>
<
var
>.f.V.</
var
>
ex .7.
<
reg
norm
="
quinti
"
type
="
simple
">ꝗnti</
reg
>
, & ex .11. eiuſ-
<
lb
/>
dem
<
var
>.c.s.</
var
>
ad
<
var
>.f.V.</
var
>
erit vt
<
var
>.c.s.</
var
>
ad
<
var
>.k.R.</
var
>
<
lb
/>
quapropter ex .9. eiuſdem
<
var
>.k.R.</
var
>
æqualis erit
<
var
>.f.V</
var
>
.</
s
>
</
p
>
</
div
>
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type
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<
head
xml:id
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"
xml:space
="
preserve
">CAP. VIII.</
head
>
<
p
>
<
s
xml:id
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"
xml:space
="
preserve
">MOdus ab antiquis philoſophis obſeruatus, eſt etiam vtilis,
<
reg
norm
="
compendioſaque
"
type
="
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">compendioſaq́;</
reg
>
via
<
lb
/>
progreditur, cuius ſpeculationem, in ſubſcripta figura, quadam ex parte
<
reg
norm
="
ſecun- dum
"
type
="
context
">ſecũ-
<
lb
/>
dum</
reg
>
morem antiquum, quadam etiam ex parte ſecundum ingenij mei vires
<
reg
norm
="
conſtru- cta
"
type
="
context
">cõſtru-
<
lb
/>
cta</
reg
>
, cognoſcemus. </
s
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">In qua ego diuiſi
<
var
>.x.i.</
var
>
in puncto
<
var
>.s.</
var
>
ab
<
var
>.x.</
var
>
ita eleuato, quanta eſt
<
lb
/>
<
figure
xlink:label
="
fig-0140-02
"
xlink:href
="
fig-0140-02a
"
number
="
195
">
<
image
file
="
0140-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0140-02
"/>
</
figure
>
</
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</
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