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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 101, page id 845634801:0117
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=117
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.81
# 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.

NON
uad.
210.
dum
C etit
1.
Ae2.
Sico
raio
EHM
C0
18
duI
la BO1
1aded
12B0
quo
ed
A, QV A F YO N V M.
10L
quad. =F. B cabo -r. Bin Z planum 2 in A x quabitur Z. plano plano f B quad. in Z. planuMI. UE CAt
enunciacum.
Si +O = 8N. aquetur 20. +89. + 832 N. aequabitur 1680.
Y H E OR E M A II.
I A quad. =BIn A XQUCTUE Z planO: A quad. quad. = Bcabo = B in Z planum =
in A, aquabitur Z. plano. plano = t Bguad. in Z planum.
Nec distimilis est ab ca quae in ancecedence Theoremate exposira est demon-
Aracio.
Si + O - 8N. aequetur 20. +C C - 832 N. aequabitur 1680.
T H EOR FM A TII.
SF B in A = A quad. XGuETuF Z planO: Bcabus = Bin Zplanum L In A - A quad.
quad, aequabicur B quad. in Z planum - Z plano- plano.
Nec dissimilis est ab ca qua in primo hujus capicis Theoremare expolica cA de-
monstratio.
Si 12 N. = 1 9. aquetur 20. 1248N. = 1O O. aequabitur 2480.
Dequadrato quadraris affectis sub latere; ex quadrato.
T N EOR EM A IV.
SF A quad. - +. B in A aquetuE S plano =+. D plano: A quad. quad.
=Oplano 2 - B quact. In A quact. - + B in S planU 2 in A, aquabiEIF S plano-
Plano = D plano- Plano.
Duoniam enim A quad. F B in A, aquatur Splano = D plano, igirur per ancithe.
SIn A quad = D plano, aequabitur SplanO -B in A. VETAGUC PAES IEA ETaN(POTIEX X-
quacionis, ducarur quadratiec. Ergo A quad. quad, = D plano in A quad. 2 + D plano-
plano, aequabicur S plano- plano = B in A in S planum 2 + B quad in A quad. EC om-
nibusrice ordinaris, A quad. quad. = D piano 2 - B quad. in A quad. + B in S planum 2 in A,
aequabicur Splano. plano, - D plano. plano. uc est enunciacum.
Si 1Q F 8N. aequetur 2O. composito ex 1585. 1Q= 74 8. + 240 N. aequabitur
200.
P H BOR E M A V.
EF A quad. = B in A aquCtuE S planO + D planO: A quad. quad.
Dpiano = B guac. in A quad. = B iI S plANUM ZIN A, XquabItT S planO-
plano =D plano. plano.
Nec distimilis est ab ea qua in ancecedente Theoremate exposica eAt demon-
Rracio.
Si 1 9 = 8 N. aquatur 20. composito ex 15 835. 18 2 = 74 P = 240 N aquabitur 200.
T H E OR EM A VI.
SFBIn A = A quad. Xquetur S planO -+ D plaHO: B guad. -- 5 plano= in A qu2d.
Bim D planum 2 in A = A quad. quad, aquabicur S plano. p laHO -
D plano plano.
Nec distimilis est ab ea quae in quarro hujus capiris Theoremace expolica est demon-
Aracio.
Si 12 N. = 1 9. aguetur 20. composito ex 15 8 5. 124 D- 12ON = 1 Q e. aequabitur 200.