Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 532
>
51
(39)
52
(40)
53
(41)
54
(42)
55
(43)
56
(44)
57
(45)
58
(46)
59
(47)
60
(48)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 532
>
page
|<
<
(39)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div161
"
type
="
section
"
level
="
1
"
n
="
86
">
<
p
>
<
s
xml:id
="
echoid-s1451
"
xml:space
="
preserve
">
<
pb
o
="
39
"
file
="
051
"
n
="
51
"
rhead
="
"/>
circunferentias vero maximorum circulorum inter parallelos, nempe A E,
<
lb
/>
B F, C G, D H, æquales eſſe. </
s
>
<
s
xml:id
="
echoid-s1452
"
xml:space
="
preserve
">Sintenim communes ſectiones circuli A I C, & </
s
>
<
s
xml:id
="
echoid-s1453
"
xml:space
="
preserve
">
<
lb
/>
parallelorum rectæ A C, E G, quæ parallelæ erunt: </
s
>
<
s
xml:id
="
echoid-s1454
"
xml:space
="
preserve
">communes vero ſectiones
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-051-01
"
xlink:href
="
note-051-01a
"
xml:space
="
preserve
">16. vndec.</
note
>
circuli B I D, & </
s
>
<
s
xml:id
="
echoid-s1455
"
xml:space
="
preserve
">parallelorum eorundem, rectæ B D, F H, quæ ſimiliter pa-
<
lb
/>
<
figure
xlink:label
="
fig-051-01
"
xlink:href
="
fig-051-01a
"
number
="
57
">
<
image
file
="
051-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/051-01
"/>
</
figure
>
rallelæ erũt. </
s
>
<
s
xml:id
="
echoid-s1456
"
xml:space
="
preserve
">Et quia circuli maximi A I C,
<
lb
/>
B I D, per polos parallelorum deſcripti ſe-
<
lb
/>
cant parallelos bifariam; </
s
>
<
s
xml:id
="
echoid-s1457
"
xml:space
="
preserve
">erunt A C, B D,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-051-02
"
xlink:href
="
note-051-02a
"
xml:space
="
preserve
">15. 1. huius.</
note
>
diametri circuli A B C D, & </
s
>
<
s
xml:id
="
echoid-s1458
"
xml:space
="
preserve
">punctum L, vbi
<
lb
/>
ſe interſecant, centrũ eiuſdem: </
s
>
<
s
xml:id
="
echoid-s1459
"
xml:space
="
preserve
">Item E G,
<
lb
/>
F H, diametri circuli E F G H, & </
s
>
<
s
xml:id
="
echoid-s1460
"
xml:space
="
preserve
">punctum
<
lb
/>
K, vbi ſe interſecant, centrum eiuſdẽ. </
s
>
<
s
xml:id
="
echoid-s1461
"
xml:space
="
preserve
">Quo
<
lb
/>
niam igitur rectæ E K, K F, rectis A L, L B,
<
lb
/>
parallelæ ſunt, ſuntq́; </
s
>
<
s
xml:id
="
echoid-s1462
"
xml:space
="
preserve
">in diuerſis planis, e-
<
lb
/>
runt anguli E K F, A L B, ad centra K, L,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-051-03
"
xlink:href
="
note-051-03a
"
xml:space
="
preserve
">10. vndeo.</
note
>
æquales. </
s
>
<
s
xml:id
="
echoid-s1463
"
xml:space
="
preserve
">Quare circunſerentiæ A B, E F,
<
lb
/>
per ea, quæ in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s1464
"
xml:space
="
preserve
">33. </
s
>
<
s
xml:id
="
echoid-s1465
"
xml:space
="
preserve
">lib 6. </
s
>
<
s
xml:id
="
echoid-s1466
"
xml:space
="
preserve
">Eu-
<
lb
/>
clid. </
s
>
<
s
xml:id
="
echoid-s1467
"
xml:space
="
preserve
">oſtendimus, ſimiles erunt. </
s
>
<
s
xml:id
="
echoid-s1468
"
xml:space
="
preserve
">Eodemq́;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1469
"
xml:space
="
preserve
">modo ſimiles erunt B C, F G, & </
s
>
<
s
xml:id
="
echoid-s1470
"
xml:space
="
preserve
">C D, G H, nec non D A, H E.</
s
>
<
s
xml:id
="
echoid-s1471
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1472
"
xml:space
="
preserve
">RVRSVS, quia rectæ ex polo I, ad puncta A, B, C, D, demiſſæ æquales
<
lb
/>
ſunt, ex defin. </
s
>
<
s
xml:id
="
echoid-s1473
"
xml:space
="
preserve
">poli, erunt quoque arcus I A, I B, I C, I D, æquales: </
s
>
<
s
xml:id
="
echoid-s1474
"
xml:space
="
preserve
">Et eo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-051-04
"
xlink:href
="
note-051-04a
"
xml:space
="
preserve
">28. tertij.</
note
>
dem modo æquales erunt arcus I E, I F, I G, I H. </
s
>
<
s
xml:id
="
echoid-s1475
"
xml:space
="
preserve
">Reliquæ igitur circunfe-
<
lb
/>
rentiæ A E, B F, C G, D H, æquales inter ſe erunt. </
s
>
<
s
xml:id
="
echoid-s1476
"
xml:space
="
preserve
">Quapropter, ſi ſint in
<
lb
/>
ſphæra paralleli circuli, &</
s
>
<
s
xml:id
="
echoid-s1477
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s1478
"
xml:space
="
preserve
">Quod erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s1479
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div164
"
type
="
section
"
level
="
1
"
n
="
87
">
<
head
xml:id
="
echoid-head99
"
xml:space
="
preserve
">THEOR. 11. PROP. 11</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">16.</
note
>
<
p
>
<
s
xml:id
="
echoid-s1480
"
xml:space
="
preserve
">SI in diametris circulorum æqualium æqua-
<
lb
/>
lia circulorum ſegmenta ad angulos rectos inſi-
<
lb
/>
ſtant, à quibus ſumantur æquales circunferentiæ,
<
lb
/>
quarum quælibet inchoata ab extremitate ſui ſe-
<
lb
/>
gmenti, ſit minor ſemiſſe circunferentiæ integri
<
lb
/>
ſegmenti, à punctis autem æquales circunferen-
<
lb
/>
tias terminantibus ducátur æquales rectæ lineę ad
<
lb
/>
circunferentias circulorum primo poſitorum; </
s
>
<
s
xml:id
="
echoid-s1481
"
xml:space
="
preserve
">ip-
<
lb
/>
ſæ circulorum primo poſitorum circunferentiæ
<
lb
/>
interceptæ inter illas rectas lineas, & </
s
>
<
s
xml:id
="
echoid-s1482
"
xml:space
="
preserve
">extremitates
<
lb
/>
diametrorum, erunt æquales.</
s
>
<
s
xml:id
="
echoid-s1483
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>