# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 397, page id 845634801:0403
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=403
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.90
# 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.

Ecuum dia.
10
lium
RESPONSORYM. LIBER VITI.
O Puncto. Frit aurem O ali-
quanco elarius, sed ea differentia
erie admodum exigua. EC CUErA-
vis DHI, DF. Foret quadcaselima
PaES, auE OEtOgCSIMA, aUEPEORE-
bicrio minurula Cemiperimetri,
ED vero vel D Crancula lemidia-
merri, tanco proxius punctum P
ad O punctum accedet. Sane A
Per puncta FDK describatur cir-
culus, quem recta tangat in D
puncto incercipiens BO in C, crit
BO minor ip (a B P nedum minOr
ipla BO, ita uE B P inter B Q 8
BO consistac, ue numeris quoque
Porest demonstrari. Trianoulum
isicur ODB sen ODB, hetrrian-
Sulo PDBhoc est arex circulicam
prope aequale quam placuerit.
Frianoulo aurem rectilineo BDO
aequale guadratum Con(LICLLALHE
RSTV. Circulo isituE ABCD
quadrarum R S Y V inventum est
tam proxime quam placuir ae qua-
C. Ouod erar taciendum.
C APV F XVII.
Proeressio Geomeirica.
PRosressionis Gcometri-
Cae doctrina uno ferc ab-
Solritur Theoremate, didu-
ctis videliceE Cx CO QUAHIOF
dedouevors.
Y H E O R E M A.
Si Fuerine magnicudines continue proporrionales: crit ut terinuS Fa-
tionis major ad terminum rationis minorem, ita disterentia compollEX Cx
omnibus e minima ad differentiam compoliex ex omnibus s maxime.
Sine maonicudines continue proportionales, quarum maxima sic D, minim a X, et
Compolica ex omnibus F, ee scratio majorisad minorem sicur D ad B. Dico este uc D
AdB, ita F minus X ad F MinUSD.
Redourvor I.
Quaque davis D, B, X, dabitur F. Fnim vero ~ omd. = v n Z aequabitur F.
Contra datis D, B, F, dabitur X. Enimvero iunt B gua. = v 0 2 aequabitur R.
Et datis D, P, X. dabitur B. Enimvero in: - D  aequabitur B.
Et datis B, F, Z, dabitur D. Enim vero D in F. =D quad. aequabitur B int
=B in Z
Elehaec in Analycicis abunde demonsorara, et exempliticara lune.
CCC2