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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IO. BAPT. BENED.
"
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142
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file
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0142
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0142
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<
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<
s
xml:id
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xml:space
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<
var
>.b.</
var
>
eſſet in aliquo
<
lb
/>
<
figure
xlink:label
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fig-0142-01
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number
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xlink:href
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</
figure
>
laterum, puta
<
var
>.q.u.</
var
>
volo vt in rectangulo per-
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lb
/>
fecto
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var
>.q.d.a.u.</
var
>
ducta ſit vna diagonalis quam
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lb
/>
volueris puta
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var
>.q.a.</
var
>
deinde à puncto
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var
>.b.</
var
>
ad reli-
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lb
/>
quum angulum oppoſiti lateris ducta ſit recta
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var
>.
<
lb
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b.d.</
var
>
ita quod à diagonali ſecetur in puncto
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var
>.ω.</
var
>
<
lb
/>
per quod punctum demum à reliquo angulo la
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lb
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teris
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>.q.u.</
var
>
ducta ſit
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var
>.u.ω.</
var
>
vſque ad latus
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var
>.q.d.</
var
>
in
<
reg
norm
="
pum
"
type
="
context
">pũ</
reg
>
<
lb
/>
cto
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var
>.f.</
var
>
quo facto, ita faciendum erit in rectangu
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lb
/>
lo degradato, hoc eſt ducenda erit diagonalis
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var
>.
<
lb
/>
q.r.</
var
>
quę correſpondet diagonali
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var
>.q.a.</
var
>
perfecti
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lb
/>
deinde
<
var
>.f.e.</
var
>
quæ correſpondet rectæ
<
var
>.f.u.</
var
>
perfe-
<
lb
/>
cti, quæ etiam interſecabitur à diagonali
<
var
>.q.r.</
var
>
<
lb
/>
in puncto
<
var
>.o.</
var
>
correſpondens
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var
>.ω.</
var
>
perfecti, per
<
reg
norm
="
quem
"
type
="
context
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>
<
var
>.
<
lb
/>
o.</
var
>
à puncto
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var
>.d.</
var
>
cum ducta fuerit
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var
>.d.o.</
var
>
vſque ad
<
var
>.t.</
var
>
<
lb
/>
in latere
<
var
>.q.e.</
var
>
hoc
<
reg
norm
="
punctum
"
type
="
context
">punctũ</
reg
>
<
var
>.t.</
var
>
correſpondebit pun
<
lb
/>
cto
<
var
>.b.</
var
>
perfecti.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
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preserve
">Idem eueniet ſi loco diametri
<
var
>.q.a.</
var
>
ſumpta
<
lb
/>
fuerit diameter
<
var
>.u.d.</
var
>
& loco
<
var
>.b.d.</
var
>
protracta fue
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lb
/>
rit
<
var
>.b.a.</
var
>
deinde loco
<
var
>.u.ω.f.</
var
>
ducta fuerit
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var
>.q.ω.f.</
var
>
vn-
<
lb
/>
de punctum correſpondens ipſi
<
var
>.f.</
var
>
in figura de-
<
lb
/>
gradata erit in latere ſupremo
<
var
>.e.r.</
var
>
correſpon-
<
lb
/>
dens lateri
<
var
>.u.a.</
var
>
& ita ducenda erit diameter
<
var
>.d.
<
lb
/>
e.</
var
>
correſpondens diametro
<
var
>.d.u.</
var
>
et
<
var
>.q.f.</
var
>
ſurſum
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lb
/>
verſus correſpondens
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var
>.q.f.</
var
>
imum verſus deinde
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var
>.
<
lb
/>
r.o.</
var
>
reſpondens
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var
>.a.ω.</
var
>
quæ terminabicur ab
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reg
norm
="
eodem- met
"
type
="
context
">eodẽ-
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lb
/>
met</
reg
>
puncto
<
var
>.t.</
var
>
vt prius.</
s
>
</
p
>
</
div
>
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<
head
xml:id
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xml:space
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">CAP.X.</
head
>
<
p
>
<
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xml:space
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<
emph
style
="
sc
">Ex</
emph
>
mea figura
<
var
>.F.</
var
>
ſuperficiali perſpectiuæ facillimum modum locandi quoduis
<
lb
/>
punctum in perſpectiua elicui. </
s
>
<
s
xml:id
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xml:space
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preserve
">Iuſſi enim vt aptaretur tabula quædam rectan-
<
lb
/>
gula exactè plana, triplo aut quadruplo, aut quanto volueris maioris longitu-
<
lb
/>
dinis, quàm latitudinis protenſa, quæ quidem latitudo erat ad duos circiter pedes
<
lb
/>
deſignata ab
<
var
>.A.B.C.D.</
var
>
cuius duobus lateribus
<
var
>.A.B.</
var
>
et
<
var
>.B.C.</
var
>
iuſſi, vt duæ regulæ affi
<
lb
/>
gerentur, quæ ſuperficiem eiuſdem tabulæ excederent, vt
<
reg
norm
="
vnum
"
type
="
context
">vnũ</
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>
ex lateribus alicuius
<
lb
/>
anguli recti materialis, qui
<
reg
norm
="
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"
type
="
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">appellat̃</
reg
>
norma (vt inferius dicam) ei adherere poſſit, cu-
<
lb
/>
raui poſtea, ut iuxta angulum
<
var
>.D.</
var
>
in puncto
<
var
>.o.</
var
>
fixo mobilis regula
<
var
>.o.Q.</
var
>
affigeretur
<
lb
/>
tantæ longitudinis, aut paulò minoris, quantam occupabat latus
<
var
>.D.A.</
var
>
quæ circum
<
var
>.
<
lb
/>
o.</
var
>
volueretur, in rectitudine poſteà.
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var
>o.i.</
var
>
parallela ipſi
<
var
>.D.A.</
var
>
in puncto
<
var
>.i.</
var
>
duobus pedi-
<
lb
/>
bus longè à latere
<
var
>.A.B.</
var
>
aliam quoque mobilem appendere feci
<
var
>.i.M.</
var
>
in tantam ferè
<
lb
/>
longitudinem extenſam, quanta conſtat
<
var
>.A.B.</
var
>
<
reg
norm
="
conſtitui
"
type
="
context
">cõſtitui</
reg
>
etiam, vt
<
reg
norm
="
quoddam
"
type
="
context
">quoddã</
reg
>
angulum re
<
lb
/>
ctum materiale tantæ magnitudinis, quanta nobis vſui eſſe poterat ſuper eadem ta-
<
lb
/>
bula; </
s
>
<
s
xml:id
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xml:space
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preserve
">necnon regula quædam materialis neceſſariæ longitudinis
<
reg
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ſtatuerentur
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type
="
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">ſtatuerent̃</
reg
>
,
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
hæc
<
lb
/>
omnia tenuiſſima, vt fierent curaui. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">Quandam deinde lineam ad
<
var
>.o.i.</
var
>
parallelam,
<
lb
/>
ideſt
<
var
>.p.E.</
var
>
ſuper eadem tabula adeò diſtantem ab
<
var
>.o.i.</
var
>
vt inter
<
var
>.E.p.</
var
>
et
<
var
>.B.c.</
var
>
perfe-
<
lb
/>
ctæ res, quæ degradari debebant, locari poſſent, ſignaui. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Hæc autem diſtantia, quæ </
s
>
</
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