DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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<
chap
id
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N10019
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<
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077/01/149.jpg
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pagenum
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145
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<
emph
type
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italics
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OR.
<
expan
abbr
="
iungãturq́
">iungantur〈que〉</
expan
>
; E
<
emph.end
type
="
italics
"/>
k
<
emph
type
="
italics
"/>
FI GH.
<
emph.end
type
="
italics
"/>
quæ inter ſe, & ipſi AC
<
expan
abbr
="
çquidiſtãtes
">çquidiſtantes</
expan
>
<
arrow.to.target
n
="
marg247
"/>
<
lb
/>
erunt; bifariam què à diametro BD in punctis LMN diuiſæ e
<
lb
/>
runt. </
s
>
<
s
id
="
N1565C
">Iungantur ſimiliter
<
emph
type
="
italics
"/>
& ST YV QZ
<
emph.end
type
="
italics
"/>
, quas bifariam dia
<
lb
/>
meter OR in punctis 9
<
foreign
lang
="
grc
">αβ</
foreign
>
diuidet. </
s
>
<
s
id
="
N1566A
">eruntquè ductæ lineæ ipſi
<
lb
/>
XP, & inter ſe æquidiſtantes.
<
emph
type
="
italics
"/>
Quoniam igitur BD diuiditur à lineis
<
lb
/>
æquidiſtantibus
<
emph.end
type
="
italics
"/>
GH FI EK
<
emph
type
="
italics
"/>
in proportionibus numeris deinceps impa
<
lb
/>
ribus;
<
emph.end
type
="
italics
"/>
poſito enim vno BN, eſt quidem NM tria, ML quin〈que〉,
<
lb
/>
& LD ſeptem. </
s
>
<
s
id
="
N15680
">ſed
<
emph
type
="
italics
"/>
& RO ſimiliter
<
emph.end
type
="
italics
"/>
à lineis QZ YV ST in pro
<
lb
/>
portionibus diuiditur numeris deinceps imparibus,
<
expan
abbr
="
eadẽ
">eadem</
expan
>
.
<
expan
abbr
="
n.
">enim</
expan
>
<
lb
/>
ratione ſi ponatur O
<
foreign
lang
="
grc
">β</
foreign
>
vnum, erit
<
foreign
lang
="
grc
">βα</
foreign
>
tria,
<
foreign
lang
="
grc
">α</
foreign
>
9
<
expan
abbr
="
quinq́
">quin〈que〉</
expan
>
;, & 9R
<
lb
/>
ſeptem.
<
emph
type
="
italics
"/>
& portiones ipſorum
<
emph.end
type
="
italics
"/>
diametrorum BD OR
<
emph
type
="
italics
"/>
ſunt numero æ
<
lb
/>
quales.
<
emph.end
type
="
italics
"/>
quot.n ſunt BN NM ML LD, tot ſunt O
<
foreign
lang
="
grc
">β βα α</
foreign
>
9 9R.
<
emph
type
="
italics
"/>
pa
<
lb
/>
tet diametrorum portiones in eadem eſſe proportione
<
emph.end
type
="
italics
"/>
, vt 〈que〉m
<
expan
abbr
="
admodũ
">admodum</
expan
>
<
lb
/>
eſt BN ad NM, & NM ad ML, & ML ad LD, ita eſſe O
<
foreign
lang
="
grc
">β</
foreign
>
ad
<
lb
/>
<
foreign
lang
="
grc
">βα</
foreign
>
, &
<
foreign
lang
="
grc
">βα</
foreign
>
ad
<
foreign
lang
="
grc
">α</
foreign
>
9, &
<
foreign
lang
="
grc
">α</
foreign
>
9 ad 9R. Atverò quoniam ita eſt DB ad BL,
<
lb
/>
vt RO ad O9; (ſunt.n.ut ſexdecim ad nouem) & ut DB ad
<
arrow.to.target
n
="
marg248
"/>
<
lb
/>
ita eſt quadratum ex AD ad
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
ex EL; & vt RO ad O9,
<
lb
/>
ita eſt
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
ex XR ad quadratum ex S
<
emph
type
="
italics
"/>
9
<
emph.end
type
="
italics
"/>
; erit
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
ex
<
lb
/>
AD ad
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
ex EL, vt
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
ex XR ad ex S9
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
.
<
lb
/>
ergo ut AD ad EL, ita XR ad S9. & horum dupla
<
expan
abbr
="
nẽpè
">nempè</
expan
>
AC ad
<
lb
/>
EK, vt XP ad ST:
<
expan
abbr
="
eademq́
">eadem〈que〉</
expan
>
; prorſus
<
expan
abbr
="
rõne
">ronne</
expan
>
, quoniam ita eſt
<
arrow.to.target
n
="
marg249
"/>
<
lb
/>
ad BM, vt 9O ad O
<
foreign
lang
="
grc
">α</
foreign
>
(ſunt.n.ut nouem ad quatuor) oſtendetur
<
lb
/>
EL ad FM ita eſſeut S9 ad Y
<
foreign
lang
="
grc
">α</
foreign
>
, & horum dupla, ſcilicet EK ad FI
<
lb
/>
ita eſſe, ut ST ad YV.
<
expan
abbr
="
Cùmq́
">Cùm〈que〉</
expan
>
; ſit MB ad BN, vt
<
foreign
lang
="
grc
">α</
foreign
>
O ad O
<
foreign
lang
="
grc
">β</
foreign
>
, ut ſci
<
lb
/>
licet quatuor ad vnum; ſimiliter oſtendetur FM ad GN ita eſſe
<
lb
/>
vt Y
<
foreign
lang
="
grc
">α</
foreign
>
ad Q
<
foreign
lang
="
grc
">β</
foreign
>
; FI uerò ad GH, vt YV ad QZ. vnde colligitur
<
expan
abbr
="
nõ
">non</
expan
>
<
lb
/>
ſolùm portiones diametrorum (ut dixim us) in eadem eſſe pro
<
lb
/>
portione, ſed
<
emph
type
="
italics
"/>
& parallelas
<
emph.end
type
="
italics
"/>
AC EK FI GH, & XP ST YV QZ
<
emph
type
="
italics
"/>
in
<
lb
/>
<
expan
abbr
="
eadē
">eadem</
expan
>
eſſe proportione. </
s
>
<
s
id
="
N15753
">& T rapeziorum ipſius quidem AE
<
emph.end
type
="
italics
"/>
k
<
emph
type
="
italics
"/>
C, & ipſius
<
emph.end
type
="
italics
"/>
<
arrow.to.target
n
="
marg250
"/>
<
lb
/>
<
emph
type
="
italics
"/>
XSTP centra grauitatum eſſe in lineis LD 9R ſimiliter poſita, cùm
<
lb
/>
eandem habeant proportionem AC EK, quam XP ST.
<
emph.end
type
="
italics
"/>
lineæquè
<
lb
/>
LD 9R bifariam diuidant ſuas æquidiſtantes AC EK.
<
lb
/>
& XP ST. etenim ſi ponatur trapezij AK centrum graui
<
lb
/>
tatis
<
foreign
lang
="
grc
">γ</
foreign
>
, ipſius vcrò XT centrum grauitatis
<
foreign
lang
="
grc
">δ</
foreign
>
, erit L
<
foreign
lang
="
grc
">γ</
foreign
>
ad
<
foreign
lang
="
grc
">γ</
foreign
>
D,
<
lb
/>
vt dupla ipſius AC cum EK ad duplam ipſius
<
arrow.to.target
n
="
marg251
"/>
<
lb
/>
cum AC. & 9
<
foreign
lang
="
grc
">δ</
foreign
>
ad
<
foreign
lang
="
grc
">δ</
foreign
>
R erit, vt dupla ipſius XP cum
<
lb
/>
ST ad duplam ST cum XP. quoniam autem ita eſt AC ad EK, </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>