# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0274
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0274?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 268, page id 845634801:0274
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=274
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000274.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.89
# 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.

68
PSEV DO- MIESOL AB VH.
PROPOSEETO XIV.
Si FICTINE QULAEHOF IIMCX rectX Continue proportionales: differentia et
cremarum major exit rriplo differentixe mediarum.
Id aurem est manifeltum, cum difterentia extremarum ad differentiam mediarum
obtensa est se habere, sicur composira eprima, secunda, e cerria ad secundam, vel exle
cunda, cerria ee quarta ad certiam. Pres aurem continue proporrionales majores lunt
medixcriplo.
Si fHICFIHEGIIaEHIOF MCA LecLA COHMIC prOPOEtionales: Cricut differen
tia extremarum minus dupla disferentia mediarum ad differentiam media-
rum, ita adoregatum exrremarum ad adgregatum mediarum.
Omentum enim est eNeur differentia extremarum ad differentiam mediarum, ica ad
Gregarum exrremarum plus duplo adoregari mediarum ad adgresarum mediarum.
Ouare subducendo eric ur differentia excremarum minus duplo differentia mediarun
ad difterenciam mediarum, ita aderegacum excremarum ad adsregacum me diarum.
PROBOSTETO ZVI
SITuCFINEQUAEIOF PCCCX ICX PLOPOtiOnales: quadratum adgresari et
tremarum, minus quadrato adgresati mediarum, erie xe quale quadrato dil
Fexencix excremarum, minus quadraco differentix mediarum.
Exponatur circulus ACBL
cujus diamerer AB secot in(er
PEalm qUaMCUMquE CD in F: IIa
QuE SIE VE AE ad FC, IEa F D aC
FB. Cum igitur C. D secabitur iI
El ad rectos angulos ab ea quxe ell
ex C CentrO, dt connectetuIr CC
erir CC dimidia compolica ex ex
tremis, _ CII dimidia compol
ex mediis. Sed e C. F dimidia el
differencia exrremarum, d
dimidia disferentia mediarum
Dico igitur quadracum ex dup.
OE, minusquadraro ex dupla L
aequari quadraco duplae C 6, 1
nus quadraro dupla CF. Id au
cem est manitectum cum erians
Ia CHO, GFTI, quorum GH b a
sis est communis, sInE rectanBu
Ieaque quadratcum ex CG. minus
Cb ex EFL. FIt auensCace uo actlorum quae dimidii ad dimidium.
PROPOSTTTO XVIL
PXOFO5FF+O LV.
quadraro ex C FI, aquarur quact AI CK C FI. HCHEetam GUaoTatUM Cx C. F, minus quadl
Daco adoresao Cat Ladoresaro mediarum in et Ropolil
quatuor rectarum continue proportionalium, distinguere continue pro
porcionales.
Propo
192
POrr