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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 383, page id 845634801:0389
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p CHC
lari.
recta 6i
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105 l
RESPONSORVH. LFDER VIII.
nis E BC. Angulo itaque A BF. D lunari exhibitus ett a qualiS AHSIS LCCLMIHCUS LBC.
Duoderat Faciendum.
PR OPOSLLIO IV.
A duobus xqualibus circulis lunulam describere, cujus ansulus dato
angulo existat aequalis.
Sic dacusangulus A. OpOr.
cer describere lunulam, cujus
angulus dato A angulo existar
aequalis.
In circulo (ub B centro de-
Ceripeo, Cumacur circumferen.
tia C ED aequalis amplicudini
duplae anguli A dari, d relidua
DFC secerur bitariam in F, ex
per puncta FC ducatur circu-
lus delcripro jam circulo x-
qualis. Dicotactum ese quod
oporruir. Lunulam enim esse
deleripeam, cujus angulus
EFC Ac daro A angulo e qua
lis. Recta enim FG tangaF Cir-
culum secundum in F, sCCanS
primum cum in F, cum in C
_ subrendatur FC. Circum-
Ferenria iOIr FC (CNFD CiF-
cumferentix G. C eA aequalis, urraris enim detinie amplirudinem duplam anguli rectili-
nei CFC. Ouare circumferencia C D F est circumferenLA C F D aequalis. Ip La aurEM
G F. F est amplieudo dupla anguli sectionis P. P C. continuati angulo corniculari ejuldem
circuli, vel aequalis. Angulus vero sectionis F FC comtinuacus angulo corniculari CFC, est
ipse anoulus lunaris. Lunaris ipitur anguli F. FC amplicudo dupla aequalis est circumferen-
TiX CDE, id est CFD; impla dimidia C F. D, id est ansulo A dAC0.
lraque Factum est quod oporruit.
PROPOSTTTO V.
Anguli lunulae a duobus circulis xqualibus deleripea, detititte aipi
cudinem.
Duo aequales circuli unus ABCD,
alcer BFD describane lunulam
ABED. Oportet anguLILUnaTISABFD
detinire amplicudinem.
Circulum BE D rangat recta in B.
secans primum circulum cum in B.
cum in P. Dico CirCumFerenLIAM F AB
aequalem esse duxlae amplicudini an-
Suli lunaris ABFD, Angulus enim lu-
naris componitur angulo sectionis
ABF, de angulo cornicalari F BF D;
qui quidem angulus cornicularis
FBED aequalis est angulo corniculari
quem cAticeret tangens ipsum circu-
dum ABCD: cum sinc circuli ABCD.
B E D aequales. Sed anguli sectionis
FB A, concinvari angulo corniculari
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