Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

ponitur ergo AE, (quæ ſinui DM, arcus grad. 54. æqualis eſt.) ex AG, me-
dietate ſinus totius, & GE, quæ æqualis eſt oſtenſa ſinui CI, arcus grad. 18. Quod eſt primum.

IAM vero, quoniam KF, ipſi EG; & EG, ipſi CI, oſtenſa eſt æqualis: erit, KF, ſinui recto CI, æqualis: Eſt autem KF, ipſi AK, æqualis. Igitur
erit quoque AK, ipſi CI, æqualis. Cum ergo AK, ſinui LN, ſit æqualis, erit
etiam ſinus LN, ſinui CI, æqualis. Eſt autem CI, ſinus arcus grad. 18. Igitur
& LN, ſinus erit arcus grad. 18. ac proinde arcus BL, cuius ſinus eſt LN,
continebit grad. 18. ideoq́ue eius complementum CL; continebit grad. 72. cuius ſinus verſus KC, cõponitur ex CG, medietate ſinus totius, & ex GK,
quæ ſinui verſo EC, arcus CD, grad. 36. oſtenſa eſt æqualis. Quod eſt ſecun-
dum. Itaque Sinus rectus arcus graduum 54. componitur, & c. Quod erat
demonſtrandum.

159.1.

34. primi.

160. COROLLARIVM.

CONSTAT cx his, triangulum ACD, cuius baſis CD, ſubtẽdit gradus 36. verticemq́; habet in centro, eſſe Iſoſceles, cuius vterque æqualium angulorum C, D, reliqui anguli ad
centrum duplus eſt. Nam angulus CAD, oſtenſus eſt continere {2/5}. vnius recti, vtrumque
vero C, & D, {4/5}.

161. THEOR. 4. PROPOS. 6.

DIFFERENTIA chordarũ duorum arcuũ
ſemicirculi, quorum alter tãto minor ſit arcu grad. 120. quanto alter maior eſt, æqualis eſt chordæ ar-
cus, quo alteruter dictorum arcuum ab arcu grad. 120. differt.

161.1.

Differentia
inter chor-
das duorũ
arcuũ, quo-
rũ alter tá
to ſit mi-
nor arcu
grad. 120.
quáto alter
maior eſt,
ęquat chot
dæ arcus,
quo alteru-
ter dictorũ
arcuũ dif-
fert ab arcu
grad. 120.

IN ſemicirculo ABC, ſit arcus BA, grad. 120. arcus vero BD, eo tan-
to minor, quanto arcus BE, maior eſt; quorum chordæ BD, BE: abſcin-
daturq́ue BF, ipſi BD, æqualis, & iungantur rectæ AD, AE, AF. Dico EF,
differentiã duarũ chor
darum BD, BE, æqua-
lem eſſe chordæ AE,
vel AD. Cõpleto enim
circulo, & inſcriptotriã
gulo æquilatero ABG,
cuius vnum latus eſt
AB, chorda arcus grad. 120. cum ſubtendat ter
tiã circunferentiæ par-
tem; erit angulus AGB,
tertia pars duorum re-
ctorum. Cum ergo ei æqualis ſit angulus AEB, in eodem cum illo exiſtens

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