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 handwritten notes
<
1 - 3
[out of range]
>
<
1 - 3
[out of range]
>
page
|<
<
(127)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div379
"
type
="
section
"
level
="
1
"
n
="
166
">
<
p
>
<
s
xml:id
="
echoid-s5271
"
xml:space
="
preserve
">
<
pb
o
="
127
"
file
="
139
"
n
="
139
"
rhead
="
"/>
ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5272
"
xml:space
="
preserve
">1? </
s
>
<
s
xml:id
="
echoid-s5273
"
xml:space
="
preserve
">Inuenies enim differentiã 43624. </
s
>
<
s
xml:id
="
echoid-s5274
"
xml:space
="
preserve
">quæ addita ad 130896. </
s
>
<
s
xml:id
="
echoid-s5275
"
xml:space
="
preserve
">ſinũ Min.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5276
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5277
"
xml:space
="
preserve
">faciat 174520. </
s
>
<
s
xml:id
="
echoid-s5278
"
xml:space
="
preserve
">ſinũ grad. </
s
>
<
s
xml:id
="
echoid-s5279
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5280
"
xml:space
="
preserve
">qui licet minor aliquanto ſit illo, quem alio mo
<
lb
/>
do inuenimus, abiectis tamẽ duabus primis ſiguris 20. </
s
>
<
s
xml:id
="
echoid-s5281
"
xml:space
="
preserve
">relinquetur ſinus 1745. </
s
>
<
s
xml:id
="
echoid-s5282
"
xml:space
="
preserve
">
<
lb
/>
exquiſitiſsimus grad. </
s
>
<
s
xml:id
="
echoid-s5283
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5284
"
xml:space
="
preserve
">reſpectu ſinus totius 100000. </
s
>
<
s
xml:id
="
echoid-s5285
"
xml:space
="
preserve
">Dic pręterea. </
s
>
<
s
xml:id
="
echoid-s5286
"
xml:space
="
preserve
">Iiſdẽ poſi-
<
lb
/>
tis, quantam differentiam poſcunt Minuta 30. </
s
>
<
s
xml:id
="
echoid-s5287
"
xml:space
="
preserve
">addendam eidẽ ſinui Min. </
s
>
<
s
xml:id
="
echoid-s5288
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5289
"
xml:space
="
preserve
">
<
lb
/>
vt ſiat ſinus Min. </
s
>
<
s
xml:id
="
echoid-s5290
"
xml:space
="
preserve
">75. </
s
>
<
s
xml:id
="
echoid-s5291
"
xml:space
="
preserve
">hoc eſt, ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5292
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5293
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5294
"
xml:space
="
preserve
">15? </
s
>
<
s
xml:id
="
echoid-s5295
"
xml:space
="
preserve
">Inuenies enim differentiam
<
lb
/>
87249. </
s
>
<
s
xml:id
="
echoid-s5296
"
xml:space
="
preserve
">quæ addita ad 130896. </
s
>
<
s
xml:id
="
echoid-s5297
"
xml:space
="
preserve
">ſinum Min. </
s
>
<
s
xml:id
="
echoid-s5298
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5299
"
xml:space
="
preserve
">faciet 218145. </
s
>
<
s
xml:id
="
echoid-s5300
"
xml:space
="
preserve
">ſinum grad. </
s
>
<
s
xml:id
="
echoid-s5301
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5302
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5303
"
xml:space
="
preserve
">
<
lb
/>
15. </
s
>
<
s
xml:id
="
echoid-s5304
"
xml:space
="
preserve
">qui licet ſit aliquanto minor illo, quem prior ille modus exhibet, tamen
<
lb
/>
abiectis duabus primis figuris 45. </
s
>
<
s
xml:id
="
echoid-s5305
"
xml:space
="
preserve
">remanebit ſinus 2181. </
s
>
<
s
xml:id
="
echoid-s5306
"
xml:space
="
preserve
">ex quiſitiſsimus grad. </
s
>
<
s
xml:id
="
echoid-s5307
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5308
"
xml:space
="
preserve
">
<
lb
/>
Min. </
s
>
<
s
xml:id
="
echoid-s5309
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s5310
"
xml:space
="
preserve
">reſpectu ſinus totius 100000. </
s
>
<
s
xml:id
="
echoid-s5311
"
xml:space
="
preserve
">Item dic. </
s
>
<
s
xml:id
="
echoid-s5312
"
xml:space
="
preserve
">Si Minuta 45. </
s
>
<
s
xml:id
="
echoid-s5313
"
xml:space
="
preserve
">quibus arcus
<
lb
/>
grad. </
s
>
<
s
xml:id
="
echoid-s5314
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5315
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5316
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5317
"
xml:space
="
preserve
">differt ab arcu ſequentigrad 2. </
s
>
<
s
xml:id
="
echoid-s5318
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5319
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s5320
"
xml:space
="
preserve
">requirunt differẽtiam
<
lb
/>
130829. </
s
>
<
s
xml:id
="
echoid-s5321
"
xml:space
="
preserve
">addendã ſinuigrad. </
s
>
<
s
xml:id
="
echoid-s5322
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5323
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5324
"
xml:space
="
preserve
">30 vt ſiat ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5325
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s5326
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5327
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s5328
"
xml:space
="
preserve
">quantã diffe
<
lb
/>
rentiam poſcunt Minuta 15. </
s
>
<
s
xml:id
="
echoid-s5329
"
xml:space
="
preserve
">addendam eidẽ ſinui grad. </
s
>
<
s
xml:id
="
echoid-s5330
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5331
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5332
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5333
"
xml:space
="
preserve
">vt ſiat ſinus
<
lb
/>
grad. </
s
>
<
s
xml:id
="
echoid-s5334
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5335
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5336
"
xml:space
="
preserve
">45? </
s
>
<
s
xml:id
="
echoid-s5337
"
xml:space
="
preserve
">quantam præterea differentiã ſlagitant Minuta 30. </
s
>
<
s
xml:id
="
echoid-s5338
"
xml:space
="
preserve
">addendam
<
lb
/>
eidem ſinui grad. </
s
>
<
s
xml:id
="
echoid-s5339
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5340
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5341
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5342
"
xml:space
="
preserve
">vt fiat ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5343
"
xml:space
="
preserve
">2? </
s
>
<
s
xml:id
="
echoid-s5344
"
xml:space
="
preserve
">Reperies enim priorem diffe-
<
lb
/>
rentiã eſſe 43610. </
s
>
<
s
xml:id
="
echoid-s5345
"
xml:space
="
preserve
">quę addita ad 261769. </
s
>
<
s
xml:id
="
echoid-s5346
"
xml:space
="
preserve
">ſinum grad. </
s
>
<
s
xml:id
="
echoid-s5347
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5348
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5349
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5350
"
xml:space
="
preserve
">efficiet 305379. </
s
>
<
s
xml:id
="
echoid-s5351
"
xml:space
="
preserve
">
<
lb
/>
ſinum grad. </
s
>
<
s
xml:id
="
echoid-s5352
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5353
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5354
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5355
"
xml:space
="
preserve
">Poſteriorem vero differentiam inuenies eſſe 87219. </
s
>
<
s
xml:id
="
echoid-s5356
"
xml:space
="
preserve
">quæ
<
lb
/>
addita ad 261769. </
s
>
<
s
xml:id
="
echoid-s5357
"
xml:space
="
preserve
">ſinum eundem grad. </
s
>
<
s
xml:id
="
echoid-s5358
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5359
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5360
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5361
"
xml:space
="
preserve
">componet 348988. </
s
>
<
s
xml:id
="
echoid-s5362
"
xml:space
="
preserve
">ſinũ grad. </
s
>
<
s
xml:id
="
echoid-s5363
"
xml:space
="
preserve
">
<
lb
/>
2. </
s
>
<
s
xml:id
="
echoid-s5364
"
xml:space
="
preserve
">qui duo ſinus quamuis minores ſint, quàm illi, quos prior ille modus exhi-
<
lb
/>
bet, reiectis tamen duabus figuris primis ex vtroque, reliquierunt ſinus 3053. </
s
>
<
s
xml:id
="
echoid-s5365
"
xml:space
="
preserve
">
<
lb
/>
3489. </
s
>
<
s
xml:id
="
echoid-s5366
"
xml:space
="
preserve
">exquiſitiſsimi reſpectu ſinus totius 100000. </
s
>
<
s
xml:id
="
echoid-s5367
"
xml:space
="
preserve
">Hac eadem arte progredien
<
lb
/>
dum erit in cæteris, donec inuenti ſint ſinus omnium arcuum per 15. </
s
>
<
s
xml:id
="
echoid-s5368
"
xml:space
="
preserve
">Minuta
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-139-01
"
xlink:href
="
note-139-01a
"
xml:space
="
preserve
">Sinus eut
<
lb
/>
magis ex-
<
lb
/>
quiſite per
<
lb
/>
regulã pro-
<
lb
/>
portionum
<
lb
/>
inueniátur
<
lb
/>
prope qua-
<
lb
/>
drantis ini
<
lb
/>
tiũ quàm
<
lb
/>
prope finé.</
note
>
extenſorum vſque ad arcum grad. </
s
>
<
s
xml:id
="
echoid-s5369
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5370
"
xml:space
="
preserve
">Vltra hunc etenim progredi hac via nõ
<
lb
/>
expedit, cum magis exquiſite ſinus complementorum arcuũ illorum, per pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s5371
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s5372
"
xml:space
="
preserve
">inueſtigari poſsint, reſpectu ſinus totius 10000000. </
s
>
<
s
xml:id
="
echoid-s5373
"
xml:space
="
preserve
">quàm per regulam
<
lb
/>
proportionum; </
s
>
<
s
xml:id
="
echoid-s5374
"
xml:space
="
preserve
">propterea quòd, vt ſupra oſtendimus in coroll. </
s
>
<
s
xml:id
="
echoid-s5375
"
xml:space
="
preserve
">propof. </
s
>
<
s
xml:id
="
echoid-s5376
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5377
"
xml:space
="
preserve
">dif-
<
lb
/>
ferentiæ ſinuum verſus ſinem quadrantis minores ſunt, quàm prope initium
<
lb
/>
quadrantis; </
s
>
<
s
xml:id
="
echoid-s5378
"
xml:space
="
preserve
">ac proinde fæpius differentiæ ſinuum mutantur prope ſinem qua-
<
lb
/>
drantis, quàm iuxta principium. </
s
>
<
s
xml:id
="
echoid-s5379
"
xml:space
="
preserve
">Ex quo ſit rectius prope quadrantis initium
<
lb
/>
reperiri ſinus per regulam proportionum, quàm prope ſinem: </
s
>
<
s
xml:id
="
echoid-s5380
"
xml:space
="
preserve
">quandoquidem
<
lb
/>
ibi vna eademq́ue differentia pluribus ſinubus deſeruit, quàm hic, vt dictũ eſt.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5381
"
xml:space
="
preserve
">Id quod experientia a pertiſsime quoque demonſtrat.</
s
>
<
s
xml:id
="
echoid-s5382
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5383
"
xml:space
="
preserve
">QVOD ſi omnes ſinus arcuum per 15. </
s
>
<
s
xml:id
="
echoid-s5384
"
xml:space
="
preserve
">Minuta progredientium, initio fa-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-139-02
"
xlink:href
="
note-139-02a
"
xml:space
="
preserve
">Supputatio
<
lb
/>
ſinuum ar-
<
lb
/>
cuum per
<
lb
/>
5. Minuta,
<
lb
/>
& perſingu
<
lb
/>
la Minura
<
lb
/>
extenſorũ.</
note
>
cto ab arcu Min. </
s
>
<
s
xml:id
="
echoid-s5385
"
xml:space
="
preserve
">0. </
s
>
<
s
xml:id
="
echoid-s5386
"
xml:space
="
preserve
">in ordinem redigantur, vna cum eorum differentijs; </
s
>
<
s
xml:id
="
echoid-s5387
"
xml:space
="
preserve
">repe-
<
lb
/>
riemus eodem artificio ſinus omnium arcuum per 5. </
s
>
<
s
xml:id
="
echoid-s5388
"
xml:space
="
preserve
">minuta extenſorum: </
s
>
<
s
xml:id
="
echoid-s5389
"
xml:space
="
preserve
">Ex
<
lb
/>
quibus demum eadem ratione ſinus omnium arcuum per ſingula minuta pro-
<
lb
/>
gredientium explorabimus; </
s
>
<
s
xml:id
="
echoid-s5390
"
xml:space
="
preserve
">ac proinde tabulam ſinuum conficiem us vſque ad
<
lb
/>
arcum gra. </
s
>
<
s
xml:id
="
echoid-s5391
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s5392
"
xml:space
="
preserve
">Per ſinus autem horũ arcuũ eliciemus, per propof. </
s
>
<
s
xml:id
="
echoid-s5393
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s5394
"
xml:space
="
preserve
">ſinus com-
<
lb
/>
plementorum arcuum eorundem. </
s
>
<
s
xml:id
="
echoid-s5395
"
xml:space
="
preserve
">Quare tota ſinuum tabula conſecta erit: </
s
>
<
s
xml:id
="
echoid-s5396
"
xml:space
="
preserve
">ac
<
lb
/>
proinde ſinus rectos omnium arcuum Quadrantis ſeſe ordine ſuperantium
<
lb
/>
vno Minuto, in partibus Sinus totius in quotcunque particulas diſtributi,
<
lb
/>
ſupputauimus. </
s
>
<
s
xml:id
="
echoid-s5397
"
xml:space
="
preserve
">Quod faciendum erat.</
s
>
<
s
xml:id
="
echoid-s5398
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div397
"
type
="
section
"
level
="
1
"
n
="
167
">
<
head
xml:id
="
echoid-head193
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">Demonſtr@
<
lb
/>
tio ſupputa
<
lb
/>
tiõis ſinuũ
<
lb
/>
per regulã
<
lb
/>
proportio-
<
lb
/>
num.</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s5399
"
xml:space
="
preserve
">_CAETERVM_ vt rationem ſupputationis ſinuum per proportionum regulam
<
lb
/>
videas, ſint in Quadrante _ABC_, arcuum _BD_, _BE_, ſinus _DF_, _EG_, noti, ex quibus
<
lb
/>
propoſitum ſit elicere ſinum _HI_, arcus _BH_, inter duos illos arcus poſiti Ducta recta
<
lb
/>
_DK_, perpendiculari ad _EG_; </
s
>
<
s
xml:id
="
echoid-s5400
"
xml:space
="
preserve
">erunt rectæ _LI_, _KG_, ſinui _DF_, æquales s atque </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>