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
|<
<
(74)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div237
"
type
="
section
"
level
="
1
"
n
="
107
">
<
p
>
<
s
xml:id
="
echoid-s2536
"
xml:space
="
preserve
">
<
pb
o
="
74
"
file
="
0098
"
n
="
98
"
rhead
="
"/>
interceptæ applicatarum portiones à contingente AE magis remouentur eò
<
lb
/>
ſunt minores, vnde tales ſectiones ad ſe propiùs accedunt. </
s
>
<
s
xml:id
="
echoid-s2537
"
xml:space
="
preserve
">Sed quod de
<
lb
/>
congruentibus, ſiue æqualibus parabolis hactenus expoſuimus, & </
s
>
<
s
xml:id
="
echoid-s2538
"
xml:space
="
preserve
">iam olim
<
lb
/>
demonſtrauimus (dum Aſymptoton doctrina promoueri poſſe animaduer-
<
lb
/>
timus) maximos poſtea Geometras, Torricellium nempe, ac Gregorium à
<
lb
/>
S. </
s
>
<
s
xml:id
="
echoid-s2539
"
xml:space
="
preserve
">Vincentio aliter quoque oſtendiſſe reperimus, quorum edita opera ad
<
lb
/>
vberiorem de hac re eruditionem conſulere ſuademus.</
s
>
<
s
xml:id
="
echoid-s2540
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2541
"
xml:space
="
preserve
">Dico tandem has con-
<
lb
/>
<
figure
xlink:label
="
fig-0098-01
"
xlink:href
="
fig-0098-01a
"
number
="
67
">
<
image
file
="
0098-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0098-01
"/>
</
figure
>
gruentes Parabolas ad in-
<
lb
/>
teruallum ſimul peruenire
<
lb
/>
minus quocunque dato in-
<
lb
/>
teruallo 1 2. </
s
>
<
s
xml:id
="
echoid-s2542
"
xml:space
="
preserve
">Fiat enim vt
<
lb
/>
1 2 ad AE, ita AE ad 2 3
<
lb
/>
quæ ipſi 1 2 indirectum po-
<
lb
/>
natur, & </
s
>
<
s
xml:id
="
echoid-s2543
"
xml:space
="
preserve
">tota 1 3 bifariam
<
lb
/>
ſecetur in 4, & </
s
>
<
s
xml:id
="
echoid-s2544
"
xml:space
="
preserve
">per B appli-
<
lb
/>
cetur BK ęqualis 1 4; </
s
>
<
s
xml:id
="
echoid-s2545
"
xml:space
="
preserve
">aga-
<
lb
/>
turque KI parallela ad BX,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2546
"
xml:space
="
preserve
">per I recta IDS contingẽti
<
lb
/>
BK æquidiſtans, erit ergo
<
lb
/>
IX æqualis KB, ſiue 4 1;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2547
"
xml:space
="
preserve
">eſtque IX dimidium IS, & </
s
>
<
s
xml:id
="
echoid-s2548
"
xml:space
="
preserve
">
<
lb
/>
4 1 dimidium 1 3; </
s
>
<
s
xml:id
="
echoid-s2549
"
xml:space
="
preserve
">quare
<
lb
/>
IS, 1 3 ſunt æquales; </
s
>
<
s
xml:id
="
echoid-s2550
"
xml:space
="
preserve
">ſed
<
lb
/>
factum eſt rectangulum 1 2 3 æquale quadrato AE, & </
s
>
<
s
xml:id
="
echoid-s2551
"
xml:space
="
preserve
">rectangulum IDS
<
lb
/>
oſtenſum eſt æquale eidem quadrato AE, ergo rectangula IDS, 1 2 3 in-
<
lb
/>
ter ſe ſunt æqualia; </
s
>
<
s
xml:id
="
echoid-s2552
"
xml:space
="
preserve
">ſed rectæ IS, 1 3, ſunt æquales, quare ſegmentum ID
<
lb
/>
æquatur dato interuallo 1 2; </
s
>
<
s
xml:id
="
echoid-s2553
"
xml:space
="
preserve
">interceptæ verò infra ID ſunt minores ipſa
<
lb
/>
intercepta ID, quapropter huiuſmodi congruentes Parabolę ad interuallum
<
lb
/>
perueniunt minus dato interuallo 1 2. </
s
>
<
s
xml:id
="
echoid-s2554
"
xml:space
="
preserve
">Quod erat vltimò demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s2555
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div240
"
type
="
section
"
level
="
1
"
n
="
108
">
<
head
xml:id
="
echoid-head113
"
xml:space
="
preserve
">COROLL. I.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2556
"
xml:space
="
preserve
">EXhac patet, in congruentibus Parabolis per diuerſos vertices ſimul ad-
<
lb
/>
ſcriptis, omnes, inter eas, interceptas lineas communi diametro ęqui-
<
lb
/>
diſtanter ductas, eſſe inter ſe æquales, quales ſunt EB, DN, &</
s
>
<
s
xml:id
="
echoid-s2557
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s2558
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div241
"
type
="
section
"
level
="
1
"
n
="
109
">
<
head
xml:id
="
echoid-head114
"
xml:space
="
preserve
">COROLL. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2559
"
xml:space
="
preserve
">PAtet quoque, ex penultima parte huius, rectangula ſegmentorum ap-
<
lb
/>
plicatarum vtranque Parabolen ſecantium omnia inter ſe æqualia eſſe,
<
lb
/>
qualia ſunt rectangula LMY, IDS, &</
s
>
<
s
xml:id
="
echoid-s2560
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s2561
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>