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
Table of Notes
<
1 - 3
[out of range]
>
[Note]
Page: 31
[Note]
Page: 31
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 32
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 34
<
1 - 3
[out of range]
>
page
|<
<
(89)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div282
"
type
="
section
"
level
="
1
"
n
="
130
">
<
pb
o
="
89
"
file
="
101
"
n
="
101
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s3440
"
xml:space
="
preserve
">IN circunferentia maximi circuli AB, ſit parallelorum polus A, eumque
<
lb
/>
duo alij circuli maximi BC, DE, ad angulos rectos ſecent, quorum BC, ſit
<
lb
/>
maximus parallelorum, & </
s
>
<
s
xml:id
="
echoid-s3441
"
xml:space
="
preserve
">DE, ad parallelos obliquus tãgens parallelum DF.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3442
"
xml:space
="
preserve
">Per polum quoq; </
s
>
<
s
xml:id
="
echoid-s3443
"
xml:space
="
preserve
">A, alius
<
lb
/>
<
figure
xlink:label
="
fig-101-01
"
xlink:href
="
fig-101-01a
"
number
="
105
">
<
image
file
="
101-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/101-01
"/>
</
figure
>
circulus maximus deſcri-
<
lb
/>
batur AE, ſecans obliquũ
<
lb
/>
DE, in puncto E, inter ma
<
lb
/>
ximũ parallelorum BC, & </
s
>
<
s
xml:id
="
echoid-s3444
"
xml:space
="
preserve
">
<
lb
/>
parallelum DF, quem ob-
<
lb
/>
liquus tangit, poſito. </
s
>
<
s
xml:id
="
echoid-s3445
"
xml:space
="
preserve
">Di-
<
lb
/>
co diametrum ſphæræ ad
<
lb
/>
diametrum paralleli DF,
<
lb
/>
maiorem habere rationé,
<
lb
/>
quàm circunferétiam BC,
<
lb
/>
ad circunferentiam DE.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3446
"
xml:space
="
preserve
">Sit AG, recta communis
<
lb
/>
ſectio circulorũ AB, AE; </
s
>
<
s
xml:id
="
echoid-s3447
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3448
"
xml:space
="
preserve
">BG, communis ſectio
<
lb
/>
circulorũ AB, BC; </
s
>
<
s
xml:id
="
echoid-s3449
"
xml:space
="
preserve
">eruntq; </
s
>
<
s
xml:id
="
echoid-s3450
"
xml:space
="
preserve
">
<
lb
/>
AG, BG, ſemidiametri
<
lb
/>
ipſorum, (cum ſe mutuo
<
lb
/>
ſecent bifariã circuli ma-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-01
"
xlink:href
="
note-101-01a
"
xml:space
="
preserve
">11.1.huius.</
note
>
ximi in ſphæra) atque adeo & </
s
>
<
s
xml:id
="
echoid-s3451
"
xml:space
="
preserve
">ſphæræ, ſecantes ſe ſe in G, centro ſphæræ, & </
s
>
<
s
xml:id
="
echoid-s3452
"
xml:space
="
preserve
">
<
lb
/>
circulorum maximorum. </
s
>
<
s
xml:id
="
echoid-s3453
"
xml:space
="
preserve
">Sit quoque DL, communis ſectio circulorum AB,
<
lb
/>
DE, quæ quoque diameter ſphæræ erit tranſiens per centrum G. </
s
>
<
s
xml:id
="
echoid-s3454
"
xml:space
="
preserve
">Rurſus
<
lb
/>
DM, ſit communis ſectio circulorum AB, DF; </
s
>
<
s
xml:id
="
echoid-s3455
"
xml:space
="
preserve
">eritque DM, diameter cir-
<
lb
/>
culi DF, propterea quòd circulus AB, parallelum DF, ſecet bifariam per
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-02
"
xlink:href
="
note-101-02a
"
xml:space
="
preserve
">15. 1. huius.</
note
>
polos. </
s
>
<
s
xml:id
="
echoid-s3456
"
xml:space
="
preserve
">Item FN, CG, ſint communes ſectiones circulorum DF, BC,
<
lb
/>
cum circulo AE. </
s
>
<
s
xml:id
="
echoid-s3457
"
xml:space
="
preserve
">Ex polo A, interuallo vero AE, parallelus deſcribatur
<
lb
/>
OE, fintq́ue OH, EH, communes eius ſectiones cum circulis AB, AE;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3458
"
xml:space
="
preserve
">Eruntq́ue & </
s
>
<
s
xml:id
="
echoid-s3459
"
xml:space
="
preserve
">FN, EH, CG, ſemidiametri circulorum DF, OE, BC, quòd
<
lb
/>
ipſos bifariam ſecet circulus maximus AE, per polos; </
s
>
<
s
xml:id
="
echoid-s3460
"
xml:space
="
preserve
">atque adeo communes
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-03
"
xlink:href
="
note-101-03a
"
xml:space
="
preserve
">15. 1. huius.</
note
>
ſectiones diametri ſint occurrentes diametris DM, OH, BG, in centris N,
<
lb
/>
H, G. </
s
>
<
s
xml:id
="
echoid-s3461
"
xml:space
="
preserve
">Eſt enim & </
s
>
<
s
xml:id
="
echoid-s3462
"
xml:space
="
preserve
">OH, diameter circuli OE, cum eum circulus AB, per po-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-04
"
xlink:href
="
note-101-04a
"
xml:space
="
preserve
">15. 1. huius.</
note
>
lum A, bifariam ſecet. </
s
>
<
s
xml:id
="
echoid-s3463
"
xml:space
="
preserve
">Sit rurſum EG, communis ſectio circulorum maximo-
<
lb
/>
rum AE, DE, quæ etiam diameter erit tran ſiens per G, centrum ſphæræ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3464
"
xml:space
="
preserve
">Denique EI, communis ſit ſectio circulorum DE, OE. </
s
>
<
s
xml:id
="
echoid-s3465
"
xml:space
="
preserve
">Et quoniam re-
<
lb
/>
cta AG, ducta per polos paralleli OE, recta eſt ad planum paralleli, ca-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-05
"
xlink:href
="
note-101-05a
"
xml:space
="
preserve
">10. 1. huius.</
note
>
ditq́ue in eius centrum H; </
s
>
<
s
xml:id
="
echoid-s3466
"
xml:space
="
preserve
">erit angulus OHG, ex defin. </
s
>
<
s
xml:id
="
echoid-s3467
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s3468
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3469
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s3470
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s3471
"
xml:space
="
preserve
">in
<
lb
/>
triangulo GHI, rectus; </
s
>
<
s
xml:id
="
echoid-s3472
"
xml:space
="
preserve
">atque adeo angulus HGI, acutus. </
s
>
<
s
xml:id
="
echoid-s3473
"
xml:space
="
preserve
">Latus igitur GI,
<
lb
/>
maius erit latere HI. </
s
>
<
s
xml:id
="
echoid-s3474
"
xml:space
="
preserve
">Auferatur recta IK, rectæ IH, æqualis, iungaturq́ue
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-06
"
xlink:href
="
note-101-06a
"
xml:space
="
preserve
">19. primi.</
note
>
recta EK. </
s
>
<
s
xml:id
="
echoid-s3475
"
xml:space
="
preserve
">Rurſus quia vterq; </
s
>
<
s
xml:id
="
echoid-s3476
"
xml:space
="
preserve
">circulus DE, OE, rectus eſt ad circulum AB;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3477
"
xml:space
="
preserve
">erit & </
s
>
<
s
xml:id
="
echoid-s3478
"
xml:space
="
preserve
">EI, communis eorum ſectio ad eundem perpendicularis: </
s
>
<
s
xml:id
="
echoid-s3479
"
xml:space
="
preserve
">ac proinde,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-07
"
xlink:href
="
note-101-07a
"
xml:space
="
preserve
">19. vndec.</
note
>
ex defin. </
s
>
<
s
xml:id
="
echoid-s3480
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s3481
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3482
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s3483
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s3484
"
xml:space
="
preserve
">vterque angulus EIH, EIK, rectus. </
s
>
<
s
xml:id
="
echoid-s3485
"
xml:space
="
preserve
">Quoniam igi-
<
lb
/>
tur duo latera EI, IH, trianguli EIH, duobus lateribus EI, IK, trianguli
<
lb
/>
EIK, ęqualia ſunt, angulosq́; </
s
>
<
s
xml:id
="
echoid-s3486
"
xml:space
="
preserve
">continent æquales, népe rectos, vt oſtendimus,
<
lb
/>
crunt anguli quoq; </
s
>
<
s
xml:id
="
echoid-s3487
"
xml:space
="
preserve
">IHE, IKE, æquales. </
s
>
<
s
xml:id
="
echoid-s3488
"
xml:space
="
preserve
">Quia verò maior eſt proportio re-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-101-08
"
xlink:href
="
note-101-08a
"
xml:space
="
preserve
">4. primi.</
note
>
ctæ GI, ad rectam I k, quàm anguli I k E, hoc eſt anguli OHE, ſibi </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>