# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0270
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0270?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 264, page id 845634801:0270
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=270
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000270.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.92
# 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.

264
S EV DO- H E S OE A BV M.
CB, rurus erit DBmajoF ip (a CB. In Continuata itaque AC SumaTuE BE ipE DB aequalis,
_C pet A agatuT recta AF ip A BF parallela, secanS BC continuatam in F. FE CeNETOA, M
cervallo AF delcribatur circulus, quem AB urrinque continuara secer in G, TI, BC vel
secetu, I. DCBleomenta CB, BF, BI, BI elle in conrinua proporrione. Excitetur
enim perpinteuit recta FK, iph FL perpendicularis, occurrens diametro OFL cou
FinvBEX in R. Ericisime BC ad AB, SICUE CF ad AH; pataseLA aMICI CONAruCta CuI
BF AF. quare est BC ad BF, SICULC F ad AF. EF per lynehelin BC a AD qua COMP
sira est ex BE e dupla BC. ita C F ad compolicam ex AF L FL, qua Guidem F I dup l2
iDtuS CF. OuarE CompOlITa ex AF ex FI est eadem quX LA. VIINquE aetmaEuT AF L
AG, HEK O ipH FL aequaliS. F. A auTeM R C continvario aIAMCHTAA PWHCLLIOCCULLUISC)
rectae qua secuir in (eripram ad angulos rectos per ipliuIS CxErCia. L.IGDMMHEIM COnFIIS
propoctione legmenta, CB, BF, BI, BII. Ad dacum itague Al Sc ABC ci aquale
quitum sectione inscriprae e diamerri, cundem que reliquum crecto eujulvis erians
rectanculi dummodo illius hyporenula major sictriplo petpendiculi, exhibica (unE
segmetira in continua proporrione. Quod crar Facienduu.
Ex his licet anculorum qui fiunt in sectione inseripta ex diametri cum musta
earum feementa sunt in concinua proxorsib semata expendere.
Sit circuli diameter AB. Et quo
niam ratio diamerri ad subtensat
duplo complementi ejus anguli qui s
ab inscripea es diametro, cum se
ementa earum sunt in continua pro
portione, est ut differentia excrema
rum ad differentiam mediarum, o
porcet autem differentiam extremd
rum majorem esse criplo differentt
mediarum. Subcendatur BC triens
diamerri AB. erit isitur angulu
CBA systema extremum omniuus
angulorum quos oportebis eo esse ma
jores.
Placeat autem cum continue pro
portionales sune in ratione dupla s
stema adnotare. Ouonam ratio est
Ut 2 ad F, numerus aurem proxim
postbinarium est cernarius, ducatu.
3 in 2, funt 6, quibus addaturuni
de