# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 300, page id 845634801:0306
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=306
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.85
# 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.

HI F O R F M A Z s
Aeque ita deinceps; inverso ordine Theorematis sexei, prouc illie detot oaum est, nisi quod bini.
300
alternatim locis affecoio s atentur.
Si Rcetur (emicircum Fereneia circuli in parces quole que aquales, et
insuper cujus Guadeatum adjunele minimae quadrato efticie quadratur
diametri ad componca ex omnibus eductis duplam.
ab A diametri cermino, rc Cx ad lCClOMCS L CUCAHEUT AB. AC, AD, AE, AF, AC, divica
FMX. HaTUI GUE ExTTEMA alterNa, COMHCCtanEEran (VCTLX C RN, DSO, ETP, FVO. C.
Fririgitur BN aequalis ipsCA.
CN ipA AD, _ CO ipAAF, d D
ip(IAF. codemquemodo, de rectu
EP, EQ, FO, FX iildem sigillacim
sumpris aquales osendentur. de 
CX ipsi BA aequalis, cruncicaque ic
x AB, BN, CH, CO, DO, DI
FP, EO. FO, FX, OX, aquales du
Pla iplarum AB, A C, AD, AF,
eE Prarerea ipH diametrO D
vel
AC. ad datur verisque AC diametet
crune oirnes dictxe cum diamett
AG, duplae omnium AB, AC, A
AE, A F, AC. est aureM UE AH aC
HIB, id es AB vel CF ad F A.
HLR ad HN, _e R LadIC, ec 15
1O, _ SH ad KD, de H F ad RP,
YN
TLadLF, de VL ad L. C, 8
AdMF, _ CM ad M X: ur ixicUE ABAd AF, ita A C ad omnes simul pespendicolata
in diamerrum AC. ec permurando AB ad AC. ue A F ad omnes limul perpendicula
irerum, eAt AH ad AB, id eA FC vel AB adt AC, uE HI R ad R N. et R lad R C, dt l
SO, et SK adSD, et R T ad TP, _ T L. ad TE, ee L V ad VQ, de V M ad V F, a
C
ad CX, ergo uc AB ad AG, ita omnes AHL, R L, ecc. id est A C ad omnes tran lverlat
mul: exat aurem uc  DAet AC, Id AF adt Outes perpendiculares, exie isitur ue AB
AC ira COmpOlITA ex AP, A C. ad omnes rransversas ex perpendiculares, e componeua
uE AB ad A C ita compolica ex eribus AF, AC, AB ad compolicam ex omnibus)
pendicularibus, omnibus eran (verlis, ec recta A C, id est (ut demonstratum est) 2d
plam OnIu AB, AC, AD, AF, AF, AC. Ouod erar demonstrandum.
Freoanemine prius aenica Mysteria, tam in Arithmeticis quam Ceont
rricis, pandis Analytice sectionum Angularium.
P R OB E E N A Y
Datanumero ratione angulorum, dareratIOnEM LAFEFUM.
Hloc abunde docuir Theorema z.
P R O B L E M A L1
Facere uenumerus ad numerum, ica angulum ad angulum:
a termino diameeri educantur rectxe ad quaelibet sectionum puncta, estu
minima educta ad diametrum, ita compolica ex diametro e minima, ee c.
tur quoque de lemicirculus reliquus incoltoem segmenra prioribus aequalia AN, N
OP, PO, CX, ZC, cum puncta xequaliter a diametri terminis LCOta COnReCtanEuL
Sic lemicirculus in punctis A, B, C, D, E, F, C sectus in partes quorcunque aequales,
ctis. quxe diametrum secabunc ad angulos rectos, sineque ex BHN, CIO, DKP, L L. C
li
deine
re
DrCI
ca
coxiu