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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 158, page id 845634801:0164
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=164
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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 0.88
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

DE L Mt L D D A LLO NF
IE O R E H A IV.
ETA quad. - cubus = B in A Guad. quad. F B quad. in A cubum -- B cuD
Din A quad. F B quad. quact. I A, aequetur B quad. quad. in Z: CAt Bpri
mamajol in lesse les cotettilie proportionalium; difterentia vero quinque
reliquarum alterne sumpearum cstZ, _ AE A sc cunda.
Suneo proportionales conine T. 2. 4. 8. 16. 32. 10C - 32 80 + 1024
327689 + 1048576N, aquarur 11534336. fit LN 160 r et 18C= 1QQ F1C- 19 + 1H
aequatur 22, es fIt L N 2.
Ethaec lingula suam habent ex Z ere si demonstrarionem: at quxe jam se quitur collectio
sua analyrico examini subjicienda libere relinquit Fheoremat a. perrinet aucem ad aequa
licares de mulciplicibus radicibus mire explicabiles.
C A PV F ZIV.
Collectio quarta.
 H B O R E M A I
27D FD in A. A Gua, aequetuF B in D: A explicabilis est de qualibet il
E H E O R E M A TY
Si A cubus = B = D = C in A quad. = + Bin D -+ Bin C + D in C inA, aque
tur B in D in C: A explicabilis est de qualiber illarum erium B, D, vel G.
1C- 69 + LIN, aequatur 6. Fit 1N 1, 2, vel 3.
T H E O R E M A III.
Si B in Din C F Bin DinH. F Bin Gin H -+ D in C m El inA - B in D - Bin6
=Bin H =- Din C = Din HI = G in H in A quad. =F. B -+ D F C - + FI in A c1
bum =. A quad. quad, aequerur Bin D in C in L: A explicabilis est de qualibec illarum
quacuor B, D, G H.
SON- 35Q + 20C- 190. aequatur 24. fit 1N 1, 2, 3, vel 4.
E H E OR E M A IV.
Si A quadrato. cabus =B -- D - C = HI - K in A quad. quad. =F B in D F B in C
+ Bin H + BinK + Din C. F D in H -+ DinK -F C in H F G in K -+ LL in K
in A clbum = B in Din C = Bin DinH = B in D in K = Bin C in HI - Bin C inK
BiaTLInKE = D in CinHI =Din GinK = DinELInK -OinHlinK in A9uad.
F B in D in C in H + B in D in C in K. F B in D in H in K- + B in C in H in H
=FD in C in HIin K in A, aequecur B in D in C in H in K: A explicabilis es de qualiberil
larum quinque B, D, C, FI, H.
10C-1599+85C - 2259 F 274N, aquATUT12O. FIL INI, 2, 3, 4, vel 5.
Acque tixc elcgans ec perpulctua speculacionis (y llose, tractarui alioquin esu(o, Rner
aliquem e Coronida randem imponito.
Dlarum duarum B vel D.
3N - 19, aequetur 2. fit LN 1, vel 2.