# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 320, page id 845634801:0326
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=326
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
# Lines: 78 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

3L
AD ADR. ROM A NE PR OBE E A A
Rurtus in circulo cujus Acenrrum, diamerer BC, sumantur circum ferenrix aequales
CD, DE, EF, FG, GHI, FL, IK, et
Subrendanta CD, BF, CF5D3
21
CH, Bl, CK. C
CF, e religua. ut elt ordinatum
in secundo ad resoluriones Theore.
MaTe.
Sit AC sert Lrea
allcti
concinue ploporcionales ca lecta,
quarum pruna sic spu sensretatselio
AC aequalis, secunda ips CD. FxIE
prima bis Cohrinue proporctolsau
minus celcta aequalis ipl BL.
Secunda cer minus guarra aequalis
100,000,000
20,000,000.
Ci seu secunda
Terria
806,600.
160,000.
32,000.
6, 400.
13 280.
ipsa (CD Y.
(BF 196,000,000. vero ICF XI.
59, 200,000. Circn - CF XVII.
XILI
Iiaque erit) BG 184, 260, 000. feren. LCG ZZIT. LVII.
recta VL 96,032, 000. HR CH ZXXVIIT. XLT.
BI 164, 953, 600. semis-CI XXXIY. XXVI.
CK 129, 022, 720. Ses. (CK XL.
COROLLARErM II.
2.
Ouoniam aurem eadem recta circulo inseripea non diameter duabus circum,e
rentiis subtenditur, quarum una minor est semicircumferentia circuli, altera ma-
jor. Aqualitas inter subrensam minori majorive, ex subtensam sermentomino
rispertinebit ad subtensam quoque simili sermento majoris, es ad subtensas dent
que reliquis circum ferentiis quae aeque mulsiplices majorem minorem- ve in circh
bationibus component.
Aeque hine TheoremariahXeC.
Staruitor Xsinus rorus. B vero sinus duplus anculi subsecandi. Z5 esto F. sinuo
duplus sermenti.
TE EOR EM A TFON L
X quadra L LCudo aquatt aguaatato En B. F.  pt L anpick. i sin
duplus anguli subrripli. ii sinus duplus differentia inter anculum subtriptume
trientem duorum rectorum.
innoris ZN = +C, aequetur a 2. Ouoniam posito L sinu torO, fit V 2 sinus duplus aneuli par
sium X EP, ideo L N est sinus duplus angulipartium XY, vel eriam est sinus duplus anguli pareium. I LH
Erit isitur L Nradix binomia 2 = V 2. Vel etiam N 2.
3N = 2C, aequetur 1. Ononiam posito L sinu roco, fol 2 sinus duptus anguli pareium X X X, ide
aN est sinus duplusanguli parcium X, vel etiam est sinus duplus anpuliparcium L.
XLIV.
P A RF. SCRVD. SBC.
XL.
CL.
X
Ouaria
e Duinta
Sexta
depolicao
Octava
C
XZVXTI.
4,000,000.
ad
qua
t
113
er
Vel
10
qua
dis
d