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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 364, page id 845634801:0370
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=370
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000370.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.88
# 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.

364
V ARZORrM DE REDVS MIA Z H EM A LICF
rentia BMTin L, _e iph circumferenrix BL LumaTuFXqualISCIFCUTLCLLHEIA BF, dE jungan
EUERECtA FB, FM, Z. L. IpCaque FM abscindac diamerrum LBIH L, Z L vero in O.
Ouoniam ixicur sire anguli BZ. M sive anguli MFB det cuplam amplirudinem cit
cumterentia BL.MI, erun aequales anguli MZ B, MFB, ac linguli duarum seprimarum re
Eti. Iphus aurem circum ferenrix BL. M dimidia est circumterema r B, detiniens ampl
cudinem anguli FZB. FFest triangulum Z. FBrectangulum. Mare angulus F.Z Bcrir le
prima pars recti, angulus vero FDZ. reliquus e recto contmmbir lex leprimas. Cum itaqu
in criangulo F.BNIangulus ad P sic duarum seprimarum recll, angulus vero ad B (ex lepe
marum, reliquus FN
erie quoque lex lepri
marum, uc complean.
eur duo recti. Ouare
CTUTAFNT, FB erUnEX
qualia. Friangulo au
TeM FNTB AE Smile EEL
angulum Z N NI. IIE
que in eo CruS ZN crU
ri quoque ZM erit 2
quale, acque adeo 2.
secabie M N in O 2
angulos rectos, cum (e
Cet e BaLIM _E aNGU
lum verricis bitariam
Ec ideo erunt similia
erianoula ZON set
TOM _ZBF
Ec quoniam angu.
BZMI duplus est ans
luSBAM, e consequo
TEF QuATHOE Seprima
rum: cum hICCCeNEE
ille (IF e cirCUmFeTCM
ca; angulus vero FNB constiruus est lex seprimarum: idco ineriangulo ANM religua
angulus AMN erir quoque quaruor seprimarum ad complendum duos ansulos rectos,
henc rectae AN, MH aequales.
Er vero oblimilicudinem criangulorum L. OIH, LBF, Cu L B2d FIV, ira L. a
ON. leaque quod her subZ. N, F Nid cABF, xequalc eric ei quod Ac sub ON, Z B,-
eAt subMH, AB.
Et quonam lubtenta L.B, FM lele incertecant h N, estuc Z. N adtMN, ica F. N 1d C
EBadHB. Exper consequens ur Z. N ad MIN, ica quod Ec sub FB, ZN, id est sub M
AB ad id quod Er hub NB, Z. N. Scd MN scu A N differenia est inter Z N seu Z. M. 
ZA(cu AB. EF NB disterentia estincer Z B seu AB bis eC ZMI. Ouare per interprecalt
nem, exic uL Z. M ad Z M minus AB, ita quod sic sub Z. M, AB, minus quadrato ex AB 
id quod Eic sub Z. M, ABbis, minusquadrato ex ZM. EF sub ducendo eric, uc Z M ad A
ica quod Er sub Z.M, AB, minus quadraco ex AB ad quadrarum ex Z. M, minus quadiaa
ex AB, et insupet eo quod Frsub ZM, AB. Fx cum guae hiunc solida sub excremis anat
sixe illius cerminis comparabuncur iis gux sunc sub extremis. de urrobique ad dacur ton
dum sub AB et quadraco ex ZM. Cubus ex Z. M, minus Colido sub AB de quadraco ex L.
aquabicur solido duplo sub ZM e quadraro ex AB, minus cubo ex AB. uod exal
Rendendum.
Sit Z. M 200,000,000, fit Z. M 180, 293, 774. Leaque recta BM seu FL. fit 86, 6713
latus tepraseni circulo inseripri cujus Z. M est diamet.
Sit ABL. ZMFN. LC -- +O, aequabitur ZN - 1.
de