# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0273
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0273?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 267, page id 845634801:0273
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=273
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000273.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.85
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Cad Cd,
CAadC
AeTMUI
sectaet
plicet, d
it
Eeros
E Y D O - HIE S OL A BY M.
aequalis e parallela secans FC in O. Fric ioirur MIC differentia dimidia seemeneorum
AC, CB. Er quoniam criangula rectan gula E AC, CBL suneSimilia, pFOPFeF LA, IL P2
rallelas. ideo est CA ad F C, liCuE C B adCP, ex Sicur differentia inter C A, C B Ad MIHeren-
tiam InEeC FC, CL. Sed differentia inter CA, CB est dupla CMI, e est C A Ad L. C, licur
Mtad CO ob similicudinem eriangulorum COM, C F A. Ouare CO erie dimidia quo-
que differentia inEeE FC, CL. atque adeo F. L. secta est bitariam in O. Compolica aurem
CALL ExFC, C.A, CB. _ eAt uE AC ad CB, ita compot CnLC, CA, CDad composi-
TAM eRCA, CB, CG. Itaque CL erir eadem quxe compoa ex C A, CB, C6. proinde
GL, EF CTUnEIPE AB COIPOSIX ex CA, CB equales. AB d GIANDUS itaquICLO, OL
aequales GL, E. F subducendo, sc FO aequalis ip(i OC. Intcribatur per O recta PO, ip(i5
AB, HI Parallela secans HIA, IB in R, S. Fririgicur KS Gat  vel HII, d CeA 2
BIFALLALIM O HCHE AB, FIL InNI, NI, RE CTUNERP, S aGualeS. Dux igicur inscripex cir-
culo FO, P Secancur bitariam in circulo. Ouare urr sue est diameter. Fsigirur dia-
Metex FC. Daraisiturrecta AB, _ in ea puncto C, AVentus est circulus AFB cui dat2
AB intetBITGE, _ cum diameter FC eam ableMe Mcato C puncto, existune segmenra
AC, CB in concinua propostoneet LO, Cmurua legmenta diametri FC. Ouod
PRDPOSTEIO XIII.
SI FHICTINE GIALIOTFECtX CONFINLIC DEOPOLCOMAICS: CHILDEWIHCTENEA eX
cribus pilus aalccundam: e ita compolitac tribus poltremis ad tertiam.
Exponacur circulus ACBBC ametet AB lecec inscripeam quamcum que C.D ul
E, ITAUEAE, F.C, ED, EB ine in concinua proporcione. Id enim heri posse lecundum
quamcum que rarionem datam expolicum est. Cum igirur CD secabitur in C_ D per
Pendicularirer a rectis CF, DO, occurrencibus ip(EE A in F, O. FFIMEFA, BO ipsi CD
aquales. Sic AureM FLCenErUM, per quod secetuF CD ad rectosanguloSin I. F. sigituE
AI dimidia compolita ex exrremis. C I dimidia composica exmediis, HIE dimidia diffe-
reneia extremarum, F. L dimidia differencia mediarum, F. A rel BC compolica exmediis,
cremarum ad difterenciam mediarum, ita adgresatum extremarum, plus
duplo adoresati mediarum ad adoregatum mediarum: _ ita COMPOIIEa C
FE compotira etribus primis, EC exrribus postremis. Eadem aurem est ratio torius ad
lorum quae parris ad parrem. Dicoisicur eNeur HE. ad EI, ita FFL ad LC, _L ita FF ad LC.
al ira FC ad F.D. Id aurem est mae P aSOIH ILLL.
E. C, GF. D.