# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 297, page id 845634801:0303
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=303
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000303.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
# Lines: 78 recognised, mean confidence 0.83
# 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.

ue X 
entiacu
Im COnt
secun
recdt.
CiCId.
leprI
quatet
arta V
adtect
5 ild
p.
netOS.
TuuI
Sed
poit
3. 5. desib
EUI
AD ANGVEARES SECFFOHES.
AE
(Terria.
enaria.
Ouinta.
Sexta
Seprima
Octava
Decima
In nocis sie minima educta r. secunda LN. Erit
e
F 1
102 +
QCC = 7CC
acque itannicarem radicem cum sibi proximo juneendo, m sicumque cum proxime deinceps se-
enci componendo, creabuncur reliqur adficientium mulciplicrum numer  insinitum. quos stubet 
avella ob oculosponere; id quidem factu facile fueric, quemadmodum à nobis prasticum est pracedenet
proposiione.
T H E OR FM A VTI.
Si a rermino diamerri liumantur in peripheria CirCHs Patles uCuu
aquales, _ ab ejusdem diametri extremis educantur rectae ad lingula le-
ationum puncta: exicuc semidiameter ad subrenlam parcium aequalium uni.
Careliquarum quae libet ab alcerurro diametri termino educta, praeter dia-
Metrum, aur diametro proximam quum in iplassectionesincidune ad diffe-
eneram duarum a reliquo ejuldem cermino eductarum ad sectiones libi
rinque PFOximaS: ac ita diameter ipla quum in sectionem aequalem inci-
ac, vel quum non incidic, eiproxima in sectionem incidens ad summam
alarum ab alcero diametri cermino, ad proximas utrinque sectiones edu-
ctarum.
Circa diamerrum AB, centro C, describarur circulus cujus peripheria secetur in par-
ao quOrCUnque aquales AD, DE, EF, FG, OFL, HIB, BI, educancurque rectae à punctis
R ad Cingulas sectiones, suIacUT aUCEM _ AK ip (I AD quoque aqualis, e duCanEUE
Ect HL, GL, OH, PK, FK, DK, AK, lrque semidiamerer C H, de Secerrecta C. L diame-
crum in L puncto.
Duoniam isicur recta Hlangulum
BIL bitariam dividens, bas perpendi-
cularis eH, cric criangulum BIL. ilolce-
Cs, et limile triangulo HCB: est au-
cem criangulum BLI simile criangulo
BAL, est icaque G A L. criangulum
ilolceles, _ latera GA, AL aequalia.
VEAuTeM C HL ad FIB, ita HIB vel BI ad
BL differentiam lacerum AC, AB. Si
milirer quoniam anguliGBF, F. KC
aequales luncangulo HCB, (illi siqui-
dem duplae peripheria in circumte-
renria, hic simplae in cenero insictir.)
angulique KEB, BOK aequales angulo
CBH, aequalibus insistences circunte-
cenriis. SCCenE sC reCtA CK, EBin M,
erunr criangula FKM, CBM Similia
ManeulO HCB, _C UEHC aAHB, ica CB ad CM disterenciam iplarum C K id cAt FL A
equalibus nam que lubrenduntur circumferenciis) et E K id CA AF (quae xquales quoque
abrendum circum terentias.) Fodemquemodo. Secent serectae FKL, DB inpuncto N,
Alnerriang ula FBN, DKN, aequicrura ec limilia crianoulo H CB, _ WT HC ad HB, ica
bad FN d. Herenciam subrentarum FK, DK, id estuc supra C. A. P. A. Similicer secentse
ACLAEK, AB in puncto O, exiique HC ad HIB, ira FB ad FO diftereniam rectarum
, AKid CstFA, DA. Fodemque modo, demonstrabitur ese ur HIC ad HIB, ita C A
2
1CCC - 890C., 21QC = 20C +58