# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 246, page id 845634801:0252
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=252
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 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.

P L E N E N F Y X
Cenrro B incerrallo quocumque describatur circulus, et agarur diameter C BD
emcircumferentia D E, definiens amplicudinem anguli daci: productaque
sinice, educatur recta F. F C secans diamerrum continuatam in fi, circumte
rentia vero in G, ita uEF G xqualis SEB C vel BD semidiamerro circuli. Dico ane
lum P F C eserrienrem anguli F BD, id est anguli A dari; e iplum arcum CC elle
clenris illius amplicudinem.
sungatur enim C B. Friangulum igitur xequicrurum estF CB, a cujus balis cermt
BoB ducta cAt BF. ipLI B C cruri aqualis. O uare angulusF. BD criplus est anguli CB
246
SUmaLA
DBC iI
(en G F B. Iphius aurem anguli G B F. amplicudinem detinic arcus C. ocHet 2b al
Cu D F. ab ScindAnEUE arCUS D HI, HI I ipSI arcui C C aequales, de avanrur rectx BH, B
Ergo angulus F BD, id est A datus, sectus est critariam a rectis BHI, BI. Quod eracta
ciendum.
LROPOSFETO Z.
Si fuerine eres linex recta proporrionales: est uc prima ad cerriam, i
adoregacum quadratorum primxe e secundae ad aderegatum quadratoruns
secundx e Terrix.
Est enim ue prima ad sccundam, ira sccunda ad certiam: et consequenterur quadea
tum e prima ad quadrarum e secunda, ira quadrarum c secunda ad quadratu C FCrHa
ex per synaerelin ue quadrarum e prima ad quadratum e secunda, ita adgregatum qua
dracorum secundae deprimae ad adoregarum quadratorum secunda d terrix. Sed l
quadracum e prima ad quadearum e sccunda, ica est prima ad cerriam. FrBO est uE pruum
ad cerciam. ita aderegarum quadratorum primae ee secunda ad adercxarum quadeaco
rum secunda ee cerriae. Ouod crac ostendendum.
P R O POSFFTO XI.
Si tuerineeres linex rectxe proportionales: est urprima ad adgrCslu
Primae ec terrix, ita quadratum secundxe ad ader egacum quadracorum le
cundae a Tertix.
Es enim urprima ad certiam, ita quadrarum e seccunda ad quadrarum e cercia, et pe
synaereEn uc prima ad aderegarum primae ecterria, ita quadrarum (ecunda ad adere8
cum quadearorum lecundae d terrix.
Consectarium.
leaque li tuerine tres linex rectae proporrionales, cria Colida ab iis eHellu
xqualia (UInE.
Primum.
dec