Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 14
[out of range]
>
<
1 - 14
[out of range]
>
page
|<
<
(28)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div79
"
type
="
section
"
level
="
1
"
n
="
48
">
<
p
>
<
s
xml:id
="
echoid-s1016
"
xml:space
="
preserve
">
<
pb
o
="
28
"
file
="
0048
"
n
="
48
"
rhead
="
"/>
diametro DE deſcribatur Parabole ADG, cuius AE ſit eius ſemi-applicata:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1017
"
xml:space
="
preserve
">dico primum Parabolen ADG, etiam ſi in infinitum producatur, totam ca-
<
lb
/>
dere intra ABC, & </
s
>
<
s
xml:id
="
echoid-s1018
"
xml:space
="
preserve
">ſi ex A ducatur quæcunque ANMH, ipſam à Parabola
<
lb
/>
ADG ſecari in O, in eadem ratione, ac AC ſecatur in G, & </
s
>
<
s
xml:id
="
echoid-s1019
"
xml:space
="
preserve
">AB in D.</
s
>
<
s
xml:id
="
echoid-s1020
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1021
"
xml:space
="
preserve
">Ducta enim ex A recta AP contingente Parabolen ABC, erit FB æqualis
<
lb
/>
BP; </
s
>
<
s
xml:id
="
echoid-s1022
"
xml:space
="
preserve
">ideoque ED æqualis DR, vnde AR continget Parabolen ADG, & </
s
>
<
s
xml:id
="
echoid-s1023
"
xml:space
="
preserve
">AH
<
lb
/>
ſecabit ipſam in O.</
s
>
<
s
xml:id
="
echoid-s1024
"
xml:space
="
preserve
"/>
</
p
>
<
figure
number
="
24
">
<
image
file
="
0048-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0048-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s1025
"
xml:space
="
preserve
">Iam ductis ex H, O, ſemi - applicatis HI, OL, erit, ob Parabolen, FB ad
<
lb
/>
BI, vt quadratum AF ad HI, vel vt quadratum FM ad quadratum MI; </
s
>
<
s
xml:id
="
echoid-s1026
"
xml:space
="
preserve
">qua-
<
lb
/>
re per Lemma præcedens, erit FB ad BM, vt BM ad BI, & </
s
>
<
s
xml:id
="
echoid-s1027
"
xml:space
="
preserve
">per Coroll. </
s
>
<
s
xml:id
="
echoid-s1028
"
xml:space
="
preserve
">eiuſ-
<
lb
/>
dem, in vtraque figura, erit FM ad MI, vt FB ad BM; </
s
>
<
s
xml:id
="
echoid-s1029
"
xml:space
="
preserve
">eadem penitus ratio-
<
lb
/>
ne oſtendetur eſſe EN ad NL, vt ED ad DN, ſed eſt FB ad BM, vt ED ad
<
lb
/>
DN, quare & </
s
>
<
s
xml:id
="
echoid-s1030
"
xml:space
="
preserve
">FM ad MI erit vt EN ad NL, ſed FM ad MI, eſt vt AM ad MH,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s1031
"
xml:space
="
preserve
">EN ad NL, vt AN ad NO, quare AM ad MH erit vt AN ad NO, & </
s
>
<
s
xml:id
="
echoid-s1032
"
xml:space
="
preserve
">in pri-
<
lb
/>
ma figura conuertendo, componendo, & </
s
>
<
s
xml:id
="
echoid-s1033
"
xml:space
="
preserve
">permutando, HA ad AO, vt MA
<
lb
/>
ad AN; </
s
>
<
s
xml:id
="
echoid-s1034
"
xml:space
="
preserve
">in ſecunda verò per conuerſionem rationis, conuertendo, & </
s
>
<
s
xml:id
="
echoid-s1035
"
xml:space
="
preserve
">per-
<
lb
/>
mutando HA ad AO erit vt MA ad AN. </
s
>
<
s
xml:id
="
echoid-s1036
"
xml:space
="
preserve
">Eſt igitur in vtraque figura HA ad
<
lb
/>
AO, vt MA ad AN, vel vt BA ad AD, ſed eſt BA maior AD ex conſtru-
<
lb
/>
ctione, quare & </
s
>
<
s
xml:id
="
echoid-s1037
"
xml:space
="
preserve
">HA erit maior AO, ſed HA tota eſt intra Parabolen ABC,
<
lb
/>
vnde punctum O, quod eſt in Parabola ADG erit intra Parabolen ABC, & </
s
>
<
s
xml:id
="
echoid-s1038
"
xml:space
="
preserve
">
<
lb
/>
ſic de quocunque alio puncto Parabolæ ADG, etiam ſi ducta AH cadat in-
<
lb
/>
fra AC; </
s
>
<
s
xml:id
="
echoid-s1039
"
xml:space
="
preserve
">quare ipſa cadit tota intra ABC: </
s
>
<
s
xml:id
="
echoid-s1040
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1041
"
xml:space
="
preserve
">cum ſit HA ad AO, vt BA ad
<
lb
/>
AD, vel vt FA ad AE, vel ſumptis duplis, vt CA ad AG, erit diuidendo
<
lb
/>
HO ad OA, vt CG ad GA. </
s
>
<
s
xml:id
="
echoid-s1042
"
xml:space
="
preserve
">Quod erat, &</
s
>
<
s
xml:id
="
echoid-s1043
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s1044
"
xml:space
="
preserve
"/>
</
p
>
<
figure
number
="
25
">
<
image
file
="
0048-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0048-02
"/>
</
figure
>
</
div
>
</
text
>
</
echo
>