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
>
61
(49)
62
(50)
63
(51)
64
(52)
65
(53)
66
(54)
67
(55)
68
(56)
69
(57)
70
(58)
<
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
|<
<
(57)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div206
"
type
="
section
"
level
="
1
"
n
="
102
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2200
"
xml:space
="
preserve
">
<
pb
o
="
57
"
file
="
069
"
n
="
69
"
rhead
="
"/>
Cumergo _A B, A C,_ ſe mutuo tangant in _A,_ & </
s
>
<
s
xml:id
="
echoid-s2201
"
xml:space
="
preserve
">_G H, G I,_ ſe mutue quoq; </
s
>
<
s
xml:id
="
echoid-s2202
"
xml:space
="
preserve
">tangant
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-01
"
xlink:href
="
note-069-01a
"
xml:space
="
preserve
">3. huius.</
note
>
in _G,_ conſtat propoſitum.</
s
>
<
s
xml:id
="
echoid-s2203
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div212
"
type
="
section
"
level
="
1
"
n
="
103
">
<
head
xml:id
="
echoid-head115
"
xml:space
="
preserve
">II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2204
"
xml:space
="
preserve
">CIRCVLI maximi ad maximum parallelorum æqualiter in-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-02
"
xlink:href
="
note-069-02a
"
xml:space
="
preserve
">27.</
note
>
clinati, polos habent in circunferentia eiuſdem paralleli. </
s
>
<
s
xml:id
="
echoid-s2205
"
xml:space
="
preserve
">Et circuli
<
lb
/>
maximi, qui polos habent in circunferentia eiuſdem paralleli, ad ma-
<
lb
/>
ximum parallelorum æqualiter inclinantur.</
s
>
<
s
xml:id
="
echoid-s2206
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2207
"
xml:space
="
preserve
">_CIRCVLI_ maximi _A B, C D,_ quorum poli _E, F,_ æqualiter ſint inclinati ad
<
lb
/>
<
figure
xlink:label
="
fig-069-01
"
xlink:href
="
fig-069-01a
"
number
="
79
">
<
image
file
="
069-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/069-01
"/>
</
figure
>
_D B,_ maximum parallelorum. </
s
>
<
s
xml:id
="
echoid-s2208
"
xml:space
="
preserve
">_D_ico eo-
<
lb
/>
rum polos _E, F,_ eſſe in eodem parallelo.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2209
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-069-03
"
xlink:href
="
note-069-03a
"
xml:space
="
preserve
">20. 1. huius.</
note
>
Deſcriptis enim per _G,_ polum paralle-
<
lb
/>
lorum, & </
s
>
<
s
xml:id
="
echoid-s2210
"
xml:space
="
preserve
">per _E, F,_ polos circulorum
<
lb
/>
_A B, C D,_ maximis circulis _G E, G F,_
<
lb
/>
qui recti erunt ad circulos _A B, C D;_
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2211
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-069-04
"
xlink:href
="
note-069-04a
"
xml:space
="
preserve
">15. 1. huius.</
note
>
erunt arcus _E G, F G,_ diſtantiæ polorũ
<
lb
/>
_E, F,_ à polo _G:_ </
s
>
<
s
xml:id
="
echoid-s2212
"
xml:space
="
preserve
">ſunt autem æquales,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-05
"
xlink:href
="
note-069-05a
"
xml:space
="
preserve
">Schol. 21.
<
lb
/>
huius.</
note
>
quòd circuli _A B, C D,_ ponantur æqua
<
lb
/>
liter inclinati ad circulum _D B._ </
s
>
<
s
xml:id
="
echoid-s2213
"
xml:space
="
preserve
">Igitur
<
lb
/>
circulus _E F,_ ex polo _G,_ & </
s
>
<
s
xml:id
="
echoid-s2214
"
xml:space
="
preserve
">interuallo
<
lb
/>
_G E,_ vel _G F,_ deſcriptus, parallelus
<
lb
/>
eſt circulo _DB;_ </
s
>
<
s
xml:id
="
echoid-s2215
"
xml:space
="
preserve
">in quo quidem paralle-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-06
"
xlink:href
="
note-069-06a
"
xml:space
="
preserve
">2. huius.</
note
>
lo _E F,_ circuli _A B, C D,_ polos _E, F_
<
lb
/>
habent. </
s
>
<
s
xml:id
="
echoid-s2216
"
xml:space
="
preserve
">Quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s2217
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2218
"
xml:space
="
preserve
">_SED_ iam circuli maximi _A B, C D,_
<
lb
/>
habeant polos _E, F,_ in parallelo, _E F._
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2219
"
xml:space
="
preserve
">Dico eos æqualiter inclinari ad _D B,_ ma
<
lb
/>
ximum parallelorum. </
s
>
<
s
xml:id
="
echoid-s2220
"
xml:space
="
preserve
">Erunt enim ex defin. </
s
>
<
s
xml:id
="
echoid-s2221
"
xml:space
="
preserve
">poli, rectæ _G E, G F,_ æquales, atque obid
<
lb
/>
arcus _E G, F G,_ æquales quoque erunt. </
s
>
<
s
xml:id
="
echoid-s2222
"
xml:space
="
preserve
">Cum ergo ijdem arcus ſint diſtantiæpolorum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-07
"
xlink:href
="
note-069-07a
"
xml:space
="
preserve
">28. tertij.
<
lb
/>
Schol. 21.
<
lb
/>
huius.</
note
>
_E, F,_ à _G,_ polo parallelorum; </
s
>
<
s
xml:id
="
echoid-s2223
"
xml:space
="
preserve
">æqualiter inclinati erunt circuli _A B, C D,_ ad _D B,_
<
lb
/>
parallelorum maximum.</
s
>
<
s
xml:id
="
echoid-s2224
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2225
"
xml:space
="
preserve
">_SEQVITVR_ iam in codice græco prepoſitio 22. </
s
>
<
s
xml:id
="
echoid-s2226
"
xml:space
="
preserve
">cuius demon ſtratio longiſsi-
<
lb
/>
ma eſt. </
s
>
<
s
xml:id
="
echoid-s2227
"
xml:space
="
preserve
">Vnde quoniam in alia verſione multo breuius, dilucidiusque eadem demon-
<
lb
/>
ſtratur, viſum eſt hoc loco inſerere alia tria theoremata a lterius verſionis, vt faci-
<
lb
/>
lius deinde propoſitionem 22. </
s
>
<
s
xml:id
="
echoid-s2228
"
xml:space
="
preserve
">huius libri demonſtremus. </
s
>
<
s
xml:id
="
echoid-s2229
"
xml:space
="
preserve
">Eſt autem primum Theorema
<
lb
/>
ſecunda pars propoſ. </
s
>
<
s
xml:id
="
echoid-s2230
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s2231
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s2232
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s2233
"
xml:space
="
preserve
">Theodoſii, quamuis magis vniuerſale ſit, vt hic proponi-
<
lb
/>
tur. </
s
>
<
s
xml:id
="
echoid-s2234
"
xml:space
="
preserve
">Primum ergo Theorema, quod ordine tertium eſt in hoc ſcholio, ita ſe habet.</
s
>
<
s
xml:id
="
echoid-s2235
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div216
"
type
="
section
"
level
="
1
"
n
="
104
">
<
head
xml:id
="
echoid-head116
"
xml:space
="
preserve
">III.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2236
"
xml:space
="
preserve
">SI ſuper diametro circuli conſtituatur rectum circuli ſegmen-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-069-08
"
xlink:href
="
note-069-08a
"
xml:space
="
preserve
">28.</
note
>
tum, diuidatur autem ſegmenti inſiſtẽtis circunferentia in duas inæ-
<
lb
/>
quales partes, & </
s
>
<
s
xml:id
="
echoid-s2237
"
xml:space
="
preserve
">à puncto ſectionis ad circunferentiam circuli primi
<
lb
/>
plurimæ rectæ lineæ cadant; </
s
>
<
s
xml:id
="
echoid-s2238
"
xml:space
="
preserve
">erit recta ſubtendens minorem partem
<
lb
/>
inſiſtentis ſegmenti omnium minima: </
s
>
<
s
xml:id
="
echoid-s2239
"
xml:space
="
preserve
">quæ autem maiorem ſubten-
<
lb
/>
dit, omnium maxima. </
s
>
<
s
xml:id
="
echoid-s2240
"
xml:space
="
preserve
">Reliquarum vero propinquior maximæ remo
<
lb
/>
tiore ſem per maior eſt: </
s
>
<
s
xml:id
="
echoid-s2241
"
xml:space
="
preserve
">At propinquior minimæ remotiore </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>