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
>
241
(229)
242
(230)
243
(231)
244
(232)
245
(233)
246
(234)
247
(235)
248
(236)
249
(237)
250
(238)
<
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
|<
<
(198)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div566
"
type
="
section
"
level
="
1
"
n
="
263
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8425
"
xml:space
="
preserve
">
<
pb
o
="
198
"
file
="
210
"
n
="
210
"
rhead
="
"/>
grad. </
s
>
<
s
xml:id
="
echoid-s8426
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s8427
"
xml:space
="
preserve
">qui ſemiſsis eſt complementi dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s8428
"
xml:space
="
preserve
">60. </
s
>
<
s
xml:id
="
echoid-s8429
"
xml:space
="
preserve
">Remanebit enim numeras
<
lb
/>
20000006 pro ſecante dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s8430
"
xml:space
="
preserve
">60.</
s
>
<
s
xml:id
="
echoid-s8431
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8432
"
xml:space
="
preserve
">HAEC, quæ hoc ſcholio tradita à nobis ſunt, vera ſunt, ſi ſinus exquiſite inuen@
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-210-01
"
xlink:href
="
note-210-01a
"
xml:space
="
preserve
">Tangétes, &
<
lb
/>
Secátes ma
<
lb
/>
gis eſſe ac
<
lb
/>
curatas, per
<
lb
/>
ſinus inué
<
lb
/>
tas, q̃ per
<
lb
/>
additioné,
<
lb
/>
ſubtractio -
<
lb
/>
néue, vt in
<
lb
/>
hoc ſcholio
<
lb
/>
traditú eſt.</
note
>
ti fuerint: </
s
>
<
s
xml:id
="
echoid-s8433
"
xml:space
="
preserve
">ſed quia non omnes ſinus accurate ſunt cogniti, maxime ſinus arcus grad.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8434
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8435
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8436
"
xml:space
="
preserve
">alij ex hoc dependentes, quales ſunt ſinus arcuum per ſingula minuta extenſo-
<
lb
/>
rum; </
s
>
<
s
xml:id
="
echoid-s8437
"
xml:space
="
preserve
">fit vt neq; </
s
>
<
s
xml:id
="
echoid-s8438
"
xml:space
="
preserve
">tangentes, neq; </
s
>
<
s
xml:id
="
echoid-s8439
"
xml:space
="
preserve
">ſecantes inuẽtæ per hoſce ſinus ſint admodũ accuratæ. </
s
>
<
s
xml:id
="
echoid-s8440
"
xml:space
="
preserve
">
<
lb
/>
Quare ſi ex inuentis quibuſdam aliæ per ſolam additionem, ſubtractionem ve inqui-
<
lb
/>
rantur vt hoc ſcholio docuimus, non parum different ab eiſdem, ſi per ſinus inueſtiga
<
lb
/>
rentur. </
s
>
<
s
xml:id
="
echoid-s8441
"
xml:space
="
preserve
">Nam tangentes & </
s
>
<
s
xml:id
="
echoid-s8442
"
xml:space
="
preserve
">ſecantes per ſinus inuentæ ex vno ſolo principio non omni
<
lb
/>
ex parte vero, nempe ex ſinubus, gignuntur: </
s
>
<
s
xml:id
="
echoid-s8443
"
xml:space
="
preserve
">at eædem per ſolam additionem, ſubtra,
<
lb
/>
ctionem ve procreatæ oriuntur ex pluribus falſis principijs, nimirum ex ſinubus pr
<
lb
/>
mum, deinde vero etiá ex tangentibus, & </
s
>
<
s
xml:id
="
echoid-s8444
"
xml:space
="
preserve
">ſecátibus per ſinus inuentis, quæ accuratæ
<
lb
/>
eſſe
<
unsure
/>
non poſſunt, vt diximus. </
s
>
<
s
xml:id
="
echoid-s8445
"
xml:space
="
preserve
">Magis exquiſite ergo cognoſcentur huiuſmodi lineæ per
<
lb
/>
ſinus, vt propoſ. </
s
>
<
s
xml:id
="
echoid-s8446
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s8447
"
xml:space
="
preserve
">eiuſq́; </
s
>
<
s
xml:id
="
echoid-s8448
"
xml:space
="
preserve
">ſcholio traditum eſt. </
s
>
<
s
xml:id
="
echoid-s8449
"
xml:space
="
preserve
">Hac ratione & </
s
>
<
s
xml:id
="
echoid-s8450
"
xml:space
="
preserve
">tabulam Tangentium,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s8451
"
xml:space
="
preserve
">tabulam Secantium breui ſupputabimus. </
s
>
<
s
xml:id
="
echoid-s8452
"
xml:space
="
preserve
">Non paruos enim errores in aliorum ta-
<
lb
/>
bulis deprehendimus; </
s
>
<
s
xml:id
="
echoid-s8453
"
xml:space
="
preserve
">vt tutò illis fid ere non poſsimus; </
s
>
<
s
xml:id
="
echoid-s8454
"
xml:space
="
preserve
">propterea quòd multas tangen-
<
lb
/>
tes, & </
s
>
<
s
xml:id
="
echoid-s8455
"
xml:space
="
preserve
">ſecátes vel per partem proportionalem, vel per ſolam additionem aut ſubtra-
<
lb
/>
ctionem inueſtigarunt, non autem omnes per ſinus. </
s
>
<
s
xml:id
="
echoid-s8456
"
xml:space
="
preserve
">Subiungemus tamen paulo infra
<
lb
/>
aliorum tabulas, donec per tempus nouas conſtruere licebit.</
s
>
<
s
xml:id
="
echoid-s8457
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div571
"
type
="
section
"
level
="
1
"
n
="
264
">
<
head
xml:id
="
echoid-head291
"
xml:space
="
preserve
">THEOR. 13. PROPOS. 21.</
head
>
<
p
>
<
s
xml:id
="
echoid-s8458
"
xml:space
="
preserve
">TANGENS cuiuſuis arcus eſt ad tangen-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-210-02
"
xlink:href
="
note-210-02a
"
xml:space
="
preserve
">Tangentes
<
lb
/>
duorum at
<
lb
/>
cuú quotú-
<
lb
/>
libet sút re
<
lb
/>
ciprocè {pro}-
<
lb
/>
portionales
<
lb
/>
cũ tangen-
<
lb
/>
tibꝰ comple
<
lb
/>
métorú ar-
<
lb
/>
cuú eoiun-
<
lb
/>
dem.</
note
>
tem alterius arcus cuiuſlibet, vt tangens comple-
<
lb
/>
menti poſterioris arcus ad tangétem complemen-
<
lb
/>
ti prioris.</
s
>
<
s
xml:id
="
echoid-s8459
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8460
"
xml:space
="
preserve
">IN quadrante ABC, arcus CD, tangens ſit CE, & </
s
>
<
s
xml:id
="
echoid-s8461
"
xml:space
="
preserve
">ſecans AE: </
s
>
<
s
xml:id
="
echoid-s8462
"
xml:space
="
preserve
">Item ar-
<
lb
/>
cus CF, tangens ſit CG, & </
s
>
<
s
xml:id
="
echoid-s8463
"
xml:space
="
preserve
">ſecans AG: </
s
>
<
s
xml:id
="
echoid-s8464
"
xml:space
="
preserve
">Ducta autem recta BH, circulum tan
<
lb
/>
gente, & </
s
>
<
s
xml:id
="
echoid-s8465
"
xml:space
="
preserve
">vtrique ſecanti AE, AG, occurrente in I, H; </
s
>
<
s
xml:id
="
echoid-s8466
"
xml:space
="
preserve
">erit BI, tangens com-
<
lb
/>
plementi arcus CD; </
s
>
<
s
xml:id
="
echoid-s8467
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8468
"
xml:space
="
preserve
">BH, tangens comple-
<
lb
/>
<
figure
xlink:label
="
fig-210-01
"
xlink:href
="
fig-210-01a
"
number
="
154
">
<
image
file
="
210-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/210-01
"/>
</
figure
>
menti arcus CF. </
s
>
<
s
xml:id
="
echoid-s8469
"
xml:space
="
preserve
">Dico ita eſſe CE, tangentem
<
lb
/>
arcus CD, ad CG, tangentem arcus CF, vt eſt
<
lb
/>
BH, tangens complementi poſterioris arcus
<
lb
/>
CF, ad BI, tangentem complementi arcus prio
<
lb
/>
ris CD. </
s
>
<
s
xml:id
="
echoid-s8470
"
xml:space
="
preserve
">Cum enim ſinus totus ſit medius pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-210-03
"
xlink:href
="
note-210-03a
"
xml:space
="
preserve
">18. huius</
note
>
portionalis tam inter CE, tangenté arcus CD,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s8471
"
xml:space
="
preserve
">BI, tangentem complementi arcus eiuſdem
<
lb
/>
CD, quàm inter CG, tangentem arcus CF, & </
s
>
<
s
xml:id
="
echoid-s8472
"
xml:space
="
preserve
">
<
lb
/>
BH, tangentem complementi arcus eiuſdem
<
lb
/>
CF; </
s
>
<
s
xml:id
="
echoid-s8473
"
xml:space
="
preserve
">erit tam rectangulum ſub CE, BI, quam re-
<
lb
/>
ctangulum ſub CG, BH, quadrato ſinus totius æquale: </
s
>
<
s
xml:id
="
echoid-s8474
"
xml:space
="
preserve
">ac proinde rectangu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-210-04
"
xlink:href
="
note-210-04a
"
xml:space
="
preserve
">17. ſexti.</
note
>
lum ſub CE, BI, rectangulo ſub CG, BH, æquale erit. </
s
>
<
s
xml:id
="
echoid-s8475
"
xml:space
="
preserve
">Quare erit, vt CE,
<
lb
/>
prima ad CG, ſecundam, ita BH, tertia ad BI, quartam; </
s
>
<
s
xml:id
="
echoid-s8476
"
xml:space
="
preserve
">nempe vt CE, tan-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-210-05
"
xlink:href
="
note-210-05a
"
xml:space
="
preserve
">16. ſexti.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>