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
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 347
>
Scan
Original
51
31
52
32
53
33
54
34
55
35
56
36
57
37
58
38
59
60
61
62
63
39
64
40
65
41
66
42
67
43
68
44
69
45
70
46
71
47
72
48
73
49
74
50
75
51
76
52
77
53
78
54
79
55
80
56
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 347
>
page
|<
<
(40)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div112
"
type
="
section
"
level
="
1
"
n
="
68
">
<
p
>
<
s
xml:id
="
echoid-s1412
"
xml:space
="
preserve
">
<
pb
o
="
40
"
file
="
0064
"
n
="
64
"
rhead
="
"/>
bus ſe contingunt; </
s
>
<
s
xml:id
="
echoid-s1413
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1414
"
xml:space
="
preserve
">in duobus tantùm punctis ſe mutuò ſecant. </
s
>
<
s
xml:id
="
echoid-s1415
"
xml:space
="
preserve
">Quod tan-
<
lb
/>
dem erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s1416
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div118
"
type
="
section
"
level
="
1
"
n
="
69
">
<
head
xml:id
="
echoid-head74
"
xml:space
="
preserve
">COROLL. I.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1417
"
xml:space
="
preserve
">PAtet hinc, quod ſi regulæ coni-ſectionum per vertices ſimul adſcripta-
<
lb
/>
rum ſibi ipſis congruant ſectiones quoque erunt inter ſe congruentes,
<
lb
/>
vt in primis quatuor figuris præcedentis ſchematis oſtenſum eſt; </
s
>
<
s
xml:id
="
echoid-s1418
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1419
"
xml:space
="
preserve
">ſi fuerint
<
lb
/>
inter ſe congruentes, etiam ipſarum regulæ ſimul congruent: </
s
>
<
s
xml:id
="
echoid-s1420
"
xml:space
="
preserve
">ſed cum regu-
<
lb
/>
læ ſimul congruunt, congruunt quoque, & </
s
>
<
s
xml:id
="
echoid-s1421
"
xml:space
="
preserve
">latera, & </
s
>
<
s
xml:id
="
echoid-s1422
"
xml:space
="
preserve
">è conuerſo, cum ad æ-
<
lb
/>
quales angulos inter ſe diſpoſita intelligantur, quare cum latera fuerint inter
<
lb
/>
ſe congruentia ſiue æqualia, ſectiones quoque inter ſe congruentes erunt; </
s
>
<
s
xml:id
="
echoid-s1423
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1424
"
xml:space
="
preserve
">
<
lb
/>
ſi ſectiones fuerint congruentes etiam ipſarum latera æqualia erunt.</
s
>
<
s
xml:id
="
echoid-s1425
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1426
"
xml:space
="
preserve
">Si verò regulę infra recta ſectionum latera ex vertice contingenter appli-
<
lb
/>
cata diſiunctim procedentes nunquam ſimul conueniant, nec ipſæ ſectiones
<
lb
/>
vnquam conuenient, ſed in vertice ſe mutuò contingent, & </
s
>
<
s
xml:id
="
echoid-s1427
"
xml:space
="
preserve
">ea inſcripta erit,
<
lb
/>
ſiue minor, cuius regula infra prædictam contingentem diametro ſectionum
<
lb
/>
ſit propior, ſeu cadat tota inter diametrum, & </
s
>
<
s
xml:id
="
echoid-s1428
"
xml:space
="
preserve
">regulam alterius ſectionis;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1429
"
xml:space
="
preserve
">quæ è contra circumſcripta erit, ſiue maior, vt apparet in 26. </
s
>
<
s
xml:id
="
echoid-s1430
"
xml:space
="
preserve
">figuris ſubſe-
<
lb
/>
quentibus.</
s
>
<
s
xml:id
="
echoid-s1431
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1432
"
xml:space
="
preserve
">Si tandem ipſarum regulæ infra contingentes ex vertice ſe mutuò ſecent,
<
lb
/>
ſectiones quoque, ſed in duobus tantùm punctis hinc inde à vertice (in quo
<
lb
/>
ſe tangunt) ſe mutuò ſecabunt, in illis nempe, quæ ſunt extrema eiuſdem
<
lb
/>
ordinatim applicatæ, ex regularum interſectione eductæ, ſuper qua duæ co-
<
lb
/>
ni-ſectionum portiones inerunt, quarum ea erit inſcripta, cuius regulæ ſe-
<
lb
/>
gmentum inter prædictam applicatam, & </
s
>
<
s
xml:id
="
echoid-s1433
"
xml:space
="
preserve
">contingentem interceptum, pro-
<
lb
/>
pinquius ſit diametro ſectionum, altera verò circumſcripta, ſiue maior cuius
<
lb
/>
regulæ ſegmentum à prædicta diametro magis diſtet, quod omne ſatis patet
<
lb
/>
ex reliquis eiuſdem ſchcmatis figuris.</
s
>
<
s
xml:id
="
echoid-s1434
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div119
"
type
="
section
"
level
="
1
"
n
="
70
">
<
head
xml:id
="
echoid-head75
"
xml:space
="
preserve
">COROLL. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1435
"
xml:space
="
preserve
">PAtet quoque in Parabolis, & </
s
>
<
s
xml:id
="
echoid-s1436
"
xml:space
="
preserve
">in alijs coni-ſectionibus eiuſdem nominis
<
lb
/>
per vertices ſimul adſcriptis, cum eodem tranſuerſo latere, illam, quę
<
lb
/>
minus habet rectum latus inſcriptam, ſiue minorem eſſe ea cuius rectum la-
<
lb
/>
tus maius eſt, & </
s
>
<
s
xml:id
="
echoid-s1437
"
xml:space
="
preserve
">è contra. </
s
>
<
s
xml:id
="
echoid-s1438
"
xml:space
="
preserve
">Nam in 5. </
s
>
<
s
xml:id
="
echoid-s1439
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s1440
"
xml:space
="
preserve
">ac 14. </
s
>
<
s
xml:id
="
echoid-s1441
"
xml:space
="
preserve
">figura, in quibus ſectiones
<
lb
/>
ſunt eiuſdem nominis, vti etiam in 15. </
s
>
<
s
xml:id
="
echoid-s1442
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1443
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s1444
"
xml:space
="
preserve
">(diximus enim circulum non
<
lb
/>
incongruè haberi poſſe pro Ellipſi) demonſtratum eſt ſectionem DBE, cuius
<
lb
/>
rectum BG minus eſt recto BH ſectionis ABC, totam cadere intra ABC, vn-
<
lb
/>
de erit inſcripta, ſiue minor, & </
s
>
<
s
xml:id
="
echoid-s1445
"
xml:space
="
preserve
">è contra, ſectionem ABC cuius rectum maius
<
lb
/>
eſt totam cadere extra DBE, cuius rectum eſt minus: </
s
>
<
s
xml:id
="
echoid-s1446
"
xml:space
="
preserve
">quapropter erit ei cir-
<
lb
/>
cumſcripta, ſiue maior.</
s
>
<
s
xml:id
="
echoid-s1447
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div120
"
type
="
section
"
level
="
1
"
n
="
71
">
<
head
xml:id
="
echoid-head76
"
xml:space
="
preserve
">COROLL. III.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1448
"
xml:space
="
preserve
">HInc quoque eruitur Hyperbolarum per vertices ſimul adſcriptarum
<
lb
/>
cum æqualibus rectis lateribus, illam, cuius tranſuerſum latus </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>