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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 262, page id 845634801:0268
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=268
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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162
PBEV DO. AEESOE A B V H
P R OP O SFFZO VTI.
Si cIAMCLUI CILCHM LCCCEIICKIPCA: etH ux differentia segmentorum
diametri ad differentiam segmentorum inleripeae, sa Maele encust a
subrensam duplo complementi anouli lectionis in (eripea e diametei.
Diamerrum enim circuli A B inscripra C D lecer in L, quam acta c cenero L.C otuat
bitariam in C. Es igieur F E. dimidia differentia segmencorum AF, E. B, d F. C. differen
tia dimidia lcomeneorum C. L
F. D. Dicoirague ur duplam P F
2d duplam P C, ica esse diame.
trum AB ad subrentam duplo
complemenci anguli FFCF. Ou0-
niam enim acta CcentrO FC, sC-
cac C D bitariam in C, ideo
norinalicer seCaL. OUare anGII=
IuS CF F. est complemeneum
anguli G F F. C OnFIMUCTUE PC
2d circumterenriam in FI, e a-
satur AI ipGF HI parallela, Ce-
canscirculum in I, e connecta.
curBI. Erie igirue circumteren-
cia BI dupla circumFerentiae BII.
de ipsa B Hlestamplicudo anouli
HIEB. Duare circum Ferencia BI
criciplus anguli FL F B amplitudo dupla. EHisicur L B Subren (a dup lo anguli G FF.
complementi anguli C. E. F. Priangulo aureM L C P. Simile criangulum est A P B. Fr8O etL
UEPL ad F. C, ira AB diameter circuli ad BL subleMam duplo complemenri anguli L. LC
_ consequenteruE F E. dupla ad F. C duplam. Ouo derar oltendendum.
PROPOSFFZO NIII.
Si Fuerint creslinex recta proportionales: composita ex omnibus 
ior exit me dix eriplo.
Suncorres proporrionales A B, B C, BD. DIcO CompolITam ex AB, BC, b
jorem este cripla B C. Facianr enim unam perperuam lineam AB, BD, e Hac AD a
meter circuli. Dux igieur excir-
cumterentia cader perpendieu
lariter ad B, erit ipla B C. conci-
nuaca autem lecer quoque circu-
Jum in E. F.C igituE C P. dupla
iplius C B. F st aurem minor dix-
etro AD, cum diamerer sicma-
jor inccripearum, alioqui AB
BC, BD estent aquales. Hlic au-
rem proponicur proporrio inx
qualicacis, non aequalicaris. Ou2-
se compolita ex AB, BD ma-
jor eAt compolita ex C B, BF..
e consequenter compolita ex
AB, BD, C B majoc est com
POlTA ex CB, C E, id estma-
jorcripla C. B. Ouod eratosten.
dendum.
n