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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 86, page id 845634801:0102
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=102
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.90
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# After the first blank line: the recognised lines in reading order, one per line.

DE R E COCN LFFON E
Data media trium proportionalium es differentia inter extremas, invenire
majorem extremam.
EAto illa A. minor igitur eric A = B. ducarur major in minorem; sE A quad. -
in A, aequale Z quad. Id aurem ipsum cA quod ordinatur.
FO - 10 Naequacur F4 4. est V 14 4 media inter extremas differentes per 10. Cx fit L N Major E
trema ex serierrium proporiionalium 8. 12. 18.
PH E OR E M A TTT.
A N PTBOAOT.
SF B in A = A quad. XquetUE Z. quad: SUNEEeS propOrtionales, quarum
media estZ, aGBTETALUII EXCTCIAEUI B; _CAE A MIHOF, MinOErC Cx.
tema.
Ex Zeterico:
Data mediarrium proportionatium ex aegrezato extremarum; invenire al
terutram extremam.
Sic enim data Z. Media, AGOTEGATUM VETO ExErEMarUM B: OpOrTeE invenire mino
reM exTremam. F. so illa A. major isitur erir B = A. quare B in A, = A quad. a qua
Dieur Z quadeaco.
SEdAE A MajOE EXTTCAEUI; CriE B = A; MInOE ExTREAEUM. IEaquE FUTUS B in
A, = A quad. aquabitur Z quad. Vndc A sive de MInOTC exTTEMarUM, Cve de Ma
jore poresteminciari.
26N - 1 O aequerur r + 4. est a L4 4 media inter extremas quarum agereearum est 26. ex fit 1H.
minor, majorve extrema ex serieerium proporrionalium 8. 12. 18.
A
RUTCUS ex Z ecericis.
C A P V Y IV
Constitura equationum cubicarum: ac primum earum in
quibus affectiones existunt sub latere.
Suationum quo que cubicarum aftectionibus sub latere obrolurarum
constirurio ex L erericis, sciru diena est. quo pertinent tria quxe le quun
tur Theoremata.
T H B OR E M A I.
RAT A BA YTRHS.
xA cubus t. B quad. HL A, XquCtUE B quad. in Z: CuNEquatuOF Concin
ProPOraleS, GlatuI prima maiorminorre inter exEremas eA B, 20
oregatum vero secundae ex quartae est Z, _ sic A sccunda.
Lx Lecerico.
Data prima, es aggrecato secunda es quarta in serie quatuor cont u oyo
tionalium, invenire secundam.
Eso secunda A, quarra  L.=a. Sollao autem lub primae quadrato
quarta, aequatur cubus c secunda: quum sicur quadrarum primae ad quadearum secu
da. ira lecunda ad quarram. leaque A cubus, aequabitur B quad. in Z, = B quad.
A; ee per ancichesin, A cubus F B quad. in A, aequabitur B quad. in Z. WE ett o
dinacuIH.
ter extremat est V 64. id est 8. axgreearum vero secunda es quarta =   8 id est 39. ex fis L N. secti
da ex serieproporcionalium 8. 12. 18. 27.
eoa LCtCCCO:
Si + C. + 64 N. aquetur 2496. Sune quaruor continue proporcionales, quarum prima minor i