Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

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138126 indagauimus ſinum rectum grad. 12. qui dimidium eſt chordæ arcus grad. 24.
quo dicti arcus grad. 30. & 54. inter ſe differunt: ita quoque ex ſinubus rectis
11Supputatio
ſinus grad.
26. & grad.
64. arcus Min. 30. & arcus grad. 52. Min. 30. cognitis cognoſeemus ſinum rectum
grad. 26. qui dimidium eſt chordæ arcus grad. 52. quo dicti arcus Min. 30. &
grad. 52. Min. 30. inter ſe differunt, vt ſupra oſtendimus; atque ex ſinu grad. 26.
ſiet, per propof. 3. notus quoque ſinus complementi, nimirum ſinus grad. 64.

QVOD ſi arcus grad. 26. & grad. 64. & grad 89. & grad. 89. Min. 30. quo-
rum ſinus inuenti ſunt, ſecemus continue bifariam, quoad poſſumus, accipia-
22Supputatio
ſinuum ar
cuũ Miau-
tis 15. ſeſe
ſuperãuũ. musque medictatum complementa, quę rurſus continue biſariam diuidamus,
& c. adhibeamusq́ue doctrinam illam, qua ex duorum arcuum ſinubus notis
cognoſcitur ſinus medietatis differentiæ illorum arcuum, reperiemus ſin us ar
cuum numero 240. qui in ordinem redacti cum ſinubus arcuum numero 120.
prius inuentis, conſtituent ſinus arcuum numero 360. ſeſe ordine ſuperantium
Minutis 15.

VERVM quia laborioſum eſt, atque moleſtum tot ſinus ea ratione in-
33Alia ſuppu
tatio ſinuũ
arcuũ ſeſe
Minutis 15
ſuperantiũ dagare, ſatis erit, tanta difficultate inueniſſe ſinus illos arcuum ſuperiorum
numero 120. ſeſe ordine ſuperantium Minutis 45. Ex illis enim ſacile per re-
gulam proportionum reperiemus ſinus arcuum ſe ordine ſuperantium Minu-
tis 15. Deinde ex his ſinus arcuum, qui ordine ſe ſuperant Minutis 5. Acdeni-
que ex iſtis ſinus arcuum per ſingula Minuta extenſorum; neque vnquàm in
hac ſupputatione error ſenſibilis continget. Cum enim ſinum totum poſue-
rimus centies maiorem, quàm 100000. ſit vt abiectis primis duabus figuris ad
dexteram, vt ſupra dictum eſt, exquiſitiſsimi relinquantur ſinus reſpectu ſinus
totius 100000. quod totus error, qui in hac ſupputatione contingere poteſt,
conſiſtat in prima figura ad dexterá, vel ad ſummum in duabus primis. Qua-
re abiectis duabus primis figuris, remanebunt omnic ijdem ſinus, qui inuen-
ti eſſent priori illo modo Geometrico reſpectu eiuſdem ſinus totius 100000.
ſi in ſupputatione poneretur ſinus totus centies etiam maior, nempe partium
10000000. & ex inuentis ſinubus duæ figuræ reijcerentur: Id quod experien-
tia docebit. Ita autem rem exequemur. Statuátur ordine illi arcus cum ſinu-
bus, & ad dexteram cuiuſque ſinus aſcribatur differentia, qua à præcedenti ſi-
44
## Arcus # Sinus # Differentiæ
G # M
0 # 0 # 000000
0 # 45 # 130896 # 130896
1 # 30 # 261769 # 130873
2 # 15 # 392598 # 130829
3 # 0 # 523360 # 130762
3 # 45 # 654031 # 130671
nu differt; vt hic factum eſſe vides in quin
que arcubus. Deinde dic. Si Minuta 45. re-
quirunt differentiam 130896. addendam ad
ſinum Minuti. 0. vt ſiat ſinus Minutorum
45. Minuta 15. quantam poſtulant diffe-
rentiam addendam eidem ſinui Minur. 0.
vt fiat ſinus Minutorum 15? Inuenies enim
requiri differentiã 43632. quæ addita ſinui
Minuti. 0. conſtituet ſinũ Minutorum 15.
partium 43632. Rurſus dic. Poſitis ijſdem,
quantam differẽtiam exigune Minuta 30.
addendam eidem ſinui Minuti 0. vt ſiat ſi-
nus Minutorum 30? Reperies enim differentiam 87264. quæ addita ſinui Minu
tio. faciet 87264. ſinum Min 30. Item dic. Si Minuta 45. quibus arcus Min. 45.
ab arcu ſequenti grad. 1. Min. 30. differt, requirunt differentiam 130873. ad-
dendam ſinui Min. 45. vt ſiat ſinus grad. 1. Min. 30. quantam differentiam po-
ſtulant Minuta 15. addédam eidem ſinui Min. 45. vt fiat ſinus Min. 60. hoc

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116	104
117	105
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121	109
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