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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 147, page id 845634801:0153
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=153
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.79
# 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.

Xqua
F. pla
Epla
10di
ilI
FuIV
AeL
etI
esse
4000
ICFI
+6P
+4Q + 72ON - 1 B, aequatur 160
A OY A F FO N V M.
plano. a = Z placio plano + IH E quadr. aguetI B Colido-(OLIdO. FEE INHOTCICaL
CACD. D in A - A quad ae quabitur D quad. = - C plan0 =
3. sit L+1OML. 1C. d8O= 4464 1, aqua
Tur 528400. sit 2_ L44. Gunatum ab512. 12N - 1 9, aequatur 20. fit L N 10 vel 2.
L A EOR E M A VI.
plano- plano;  F quad. cubus = G plano + in P quad.  quad. +2 plano plano+
Cplano. plano + In P quad., aequetur B Colido. Polido. FF Finnorelcac eNCD. D in
A - A quad, xequabitur D quad. : = C plano = do
11 4 B - 12ON =9 C, aequatur 200. es sit LN 2 vel 10. 2C -228 0 + 12196N,
aequacur 14400. fit 2 N 144. quad. abs 12. 12. -= 2 8, aquarur 20. fic L. N 10 vel 2.
T E E O R F M A VTI.
SFB Colidum in A = G plavo 2 in A quad. = A quad. - quad., Xquetu Z
Plario. plano, e F quad. cubus + G plano + in F quad. - guad. = Z plano. plano 4
+ C plano ptano + II P quad, ae quetur Bsolido. solido. FF P innotelcat esse D. D in
A - A quad, xquabitur D quad. = - + C p lanO =B Sonae
144ON = 16 9 - + 0O, aequatur 2800, e fit + N 10 vet 2. TC- 32 9 - 10944 N,
aequatur 2073600. 87 fit 2 N. 144 quadratum abs 12. 22. N - + 9, aequatur 20. 8 fit L N
10 vel 2.
Ad poleriorem aurem Formulam perrinent quae sequuneur.
T H E O R E M A T.
Secundum posteriorem Formulam.
A quad. = quad. - + G pLanO in A quad. - + BColido in A, XquCtuIE Z pla.
nO-planO, _ F planI-CubUS -Gplano in F plani quad. t Z plano 4 in
Eplanum, requetur B Lolo- (olido-F Z. plano= plano 4 in C planLM. FF
ItHOTCICaEE planum eAC F planu. A quad. + V Eptani = Cplano iM A, Xqu a-
bicur
c
F plaMO :.
200.7 60 + 88ON, aequatur 1800. fit LN 2.
2C-- 60 + 720ON, aequatur
817600. fit LN70. 70- 6 est quadratum abs8. 19 F 8 N, aequabitur 20. fit L N 2.
T H E OR E M A TI.
Et A quad. quad. - F C plano in A quad. = B Colido in A, aquetur Z. pla-
Dno plano, dx P plani cubus = G plano in P plani. quad. - L Z plano- pl2-
no + in E planum, aequetur B solido- Colido-i Z plano- plano + in C pla-
NUM. EEinNOTCSCaE F planum eNC F planuM. A quad. = Y xplani - C plano iM A,
aequabitur
SELIIS
=FplanO =.
109 + 60 - 8BON, aquarur 1800. fIt FN10, 1C -69 + 720ON, aqu a1uT 81760O.
sit LN70. 70 - 6 est quadracum abs 8. 1O - 8 N, aequabitur 20. fit L N 1O.
T H E OR E M A III.
2T A quad. - quad. = G planO I A quad. t BColido in A, Xguetur Z pta
Ono. planio, s P. plani- cubuts. C plano in P plani quad. t Z plano- pla-
no+ in Eplanum, aequetur Drort Tolido - Z. plano. plano 4 in C planum.
LMnOTCICAEAULCM EPTaHUm CNC F pLaMUM. A quad. - F N F ptani = C plano in A,
=F plano .
equabiE colido
F Plani a