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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[Item 6.40.]
Page: 383 (371)
[Item 6.41.]
Page: 386 (374)
[Item 6.42.]
Page: 392 (380)
[Item 6.43.]
Page: 409 (397)
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Page: 417 (405)
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Page: 424 (412)
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Page: 425 (413)
[Item 6.50.]
Page: 428 (416)
[Item 6.51.]
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[Item 6.52.]
Page: 437 (425)
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351
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="
EPISTOL AE.
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n
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363
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file
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0363
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0363
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<
p
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<
s
xml:id
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xml:space
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preserve
">Volo etiam quod ad partem
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>.c.l.s.</
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>
quadrilateri conſtituta ſit alia parallela ad
<
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>.z.
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r.</
var
>
& in æquali diſtantia ab ipſa quemadmodum
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>.u.n.</
var
>
diſtat ad eademmet
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>.z.r.</
var
>
ad ean
<
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dem operationem faciendam. </
s
>
<
s
xml:id
="
echoid-s4223
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xml:space
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preserve
">Vnde in vno tantummodo itinere puncti
<
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>.s.</
var
>
ab
<
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>.r.</
var
>
<
reg
norm
="
vſque
"
type
="
simple
">vſq;</
reg
>
<
lb
/>
ad
<
var
>.c.</
var
>
deſignabimus quartam partem ſectionis, conuerſo poſtea inſtrumento, hoc eſt
<
lb
/>
poſito puncto
<
var
>.r.</
var
>
vbi prius erat
<
var
>.z.</
var
>
et
<
var
>.z.</
var
>
vbi erat
<
var
>.r.</
var
>
aliam delineabimus quartam, &
<
lb
/>
ſic ad oppoſitam partem ipſius
<
var
>.z.r.</
var
>
faciendum erit. </
s
>
<
s
xml:id
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xml:space
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preserve
">Hoc inſtrumentum poſſumus
<
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/>
etiam ita conſtruere, vt puncta
<
var
>.o.</
var
>
et
<
var
>.K.</
var
>
poſſint collocari in laterihus
<
var
>.c.e.</
var
>
et
<
var
>.e.s.</
var
>
vbi no
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lb
/>
bis magis libuerit, ita vt licebit in qualibet proportione
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type
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propoſita, oxygoniam
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deſignare. </
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<
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xml:id
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xml:space
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erit longitudo dimidij axis minoris, et
<
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>.c.e.</
var
>
dimidij maioris.</
s
>
</
p
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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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preserve
">DE CONSTITVTIONE TRIANGVLI
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orthogonij conditionati.</
head
>
<
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style
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it
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xml:space
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">Domino Ludouico de Rocchaforte.</
head
>
<
p
>
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xml:id
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xml:space
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<
emph
style
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emph
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à me poſtulas, non eſt admodum difficile, cupis enim triangulum
<
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/>
orthogonium, exempli gratia
<
var
>.o.i.e.</
var
>
in figura
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var
>.A.</
var
>
ita conſtituere, vt di-
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lb
/>
uiſum ſit à perpendiculari
<
var
>.a.i.</
var
>
& quod proportio
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var
>.o.e.</
var
>
ad
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var
>.o.i.</
var
>
ſit vt
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>.o.i.</
var
>
ad
<
lb
/>
<
var
>i.e.</
var
>
& quod quadrati
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var
>.o.i.</
var
>
ad quadratum
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var
>.o.a.</
var
>
ſit vt
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var
>.e.i.</
var
>
ad
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var
>.e.a.</
var
>
& quadra
<
lb
/>
tum
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var
>.o.i.</
var
>
ad quadratum
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var
>.e.i.</
var
>
ſit .ut
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var
>.o.a.</
var
>
ad
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var
>.e.a</
var
>
. </
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>
<
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xml:space
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">Quæ omnia in promptu veniunt, quo
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tieſcunque
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>
fuerit diameter alicuius circuli,
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type
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in puncto
<
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ſecundum pro
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portionem habentem medium
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type
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extrema, protracta deinde perpendiculari
<
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>.a.
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i.</
var
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ad
<
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>o.e.</
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>
uſque ad circunferentiam,
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<
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et
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>.i.e</
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>
: tale triangulum, omnia
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/>
ſupradicta in ſe continebit.</
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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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">Nam ex .30. tertij angulus
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var
>
rectus erit, & ex .8. ſexti
<
var
>.o.i.</
var
>
erit media proportio-
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/>
nalis inter
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var
>.o.e.</
var
>
et
<
var
>.o.a.</
var
>
et
<
var
>.e.i.</
var
>
inter
<
var
>.o.e.</
var
>
<
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<
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400
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0363-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0363-01
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figure
>
et
<
var
>.a.e.</
var
>
ſed quia ex diuiſione facta in
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>
<
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/>
cto
<
var
>.a.</
var
>
etiam
<
var
>.o.a.</
var
>
erit media proportio-
<
lb
/>
nalis inter totum & reſiduum, ideo ex
<
num
value
="
11
">.
<
lb
/>
11.</
num
>
quinti ita erit
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var
>.o.e.</
var
>
ad
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var
>.e.i.</
var
>
vt
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var
>.o.e.</
var
>
ad
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var
>.
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lb
/>
o.a.</
var
>
vnde ex .9. eiuſdem
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>.a.o.</
var
>
erit æqua-
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lb
/>
lis
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>.e.i.</
var
>
& ideo
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var
>.o.i.</
var
>
erit media proportio
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lb
/>
nalis inter
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var
>.o.e.</
var
>
et
<
var
>.e.i</
var
>
. </
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<
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xml:id
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xml:space
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tio
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ad
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<
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eſt, quę ipſius
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ad
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<
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>o.a</
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>
. </
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>
<
s
xml:id
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xml:space
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">tunc videbis ex .18. ſexti, quod pro
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portio quadrati
<
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>.o.i.</
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>
ad quadratum
<
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>.o.a.</
var
>
<
lb
/>
erit vt
<
var
>.e.i.</
var
>
ad
<
var
>.e.a.</
var
>
cum vero duo trian-
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lb
/>
guli
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>.o.i.a.</
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>
et
<
var
>.a.i.e.</
var
>
ſint inuicem ſimiles
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ex ſupradicta .8. ſexti, </
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>
<
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xml:id
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xml:space
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">tunc videbis ex
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18. et .17. eiuſdem dictos
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ean
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dem habere inter ſe proportionem, quę
<
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eſt inrer quadrata ipſius
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>.o.i.</
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>
et
<
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>.i.e.</
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>
vnde
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/>
ex prima ſexti ita ſe inuicem habebunt
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>.
<
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a.o.</
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>
et
<
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>.a.e</
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.</
s
>
</
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<
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