# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 102, page id 845634801:0118
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=118
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.87
# 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.

DE R E COCNFFFOH
De iildem aliter,
P H E O R E M a VII.
EF A quad. =+ BM A aeguETuF Splano = D plano: A quad. quad. =De
no2 - B ead. LI A quad. - F B in Splanum 2 in A, aequabitur S plano. plano
Ouoniam enim A quad. = B in A, aquatur S plano =D planO: ipirr per anriche
Sin, A quad. F D plano, aequabirur S plano - B in A. Veraque igituE parS duCaEur qua
dratice: ergo A quad. quad. + D plano in A quad. 2 F D plano plano, aequabitur Spla
n0. plano =B in S planum in A 2 = B quad. in A quod. Ex omnibusrire ordinalti
A quad. quad. -T D plono. = B quas in A quad. F B in S planum 2 in A, Xquabirur Splane
plano- Dplano. plano. ur elt enunciacum.
Si FC + 8 N aquerur 20. differentiae inter 40 ex 60. 20 0 + 16Q + 960 N, aqu
bitur 2000.
T E E O R E M A VITT.
CF A quadr. = B in A aquetur S plano = D plano: A quadr. quadt.
D=D plno 2 - B quad. in A quad. = B in S planum 2 in A, requabitur S plano
Plano =D plano- plano.
Nec dissimilis est ab ea quae anrecedenre Theoremare expolica est demonstrario.
Sir B = 8 N aquetur 20. differentiae inver 40 8 60. 1Q e + 16 9 = 96O N, aqua
bitur 2000.
T H E O R E M A 1Z.
SFB in A = A quad. aquetur S plano =D plano: B in D planum 2 in A
FB quad. = Splano 2 in A quad. - A quad. - quad, aequabicur S plano plano
Dplano- plano.
Nec dissimilis est ab ea quae in seprimo hujus Theoremaris capite exposira est de
monstratio.
Si 12N - 1 9 aequetur 20. differenia inter 40 87 60. 960 N + 24 0 - 1 e 9, agu
bitur 2000.
De quadrato quadratis affectis sub cubo.
E H E O R E M A X.
SF A quad. F B in A RquCtuE Z planO: A quad. quad. = v in Z nun
in AcubUME, a GcaDIEIE Z ptano piauo vlano
lano
B guac.
Z PlanO X B quad
Ouoniam enim A quad. +. B in A aquatur Z plano, igitur per antichetin, A quac
aequabicu Z plano = B in A. Omnia ducantur in A, erBo A cubus aquAtuTZ plano
A = B in A quad. Ceu alicer ex designato A quadrari valore, A cubuS RquatuE Z planOL
A - B in Z planum F B quad. in A. FFurraque parre hujus aequarionis divila pes
Planum = B 9u24. 25uBus + Z plano
Zolano  B quas. XquabitUr A. Ouod igirur dicieur, A quad. Xquas
Z plano =B in A, idiplum Ex desIBNaEO A valore ita exprimitur. A quad. XquVaTUIE
dirootnoo+ i
cuvum. Rursus venio ad primam propolicam aequarionem: A quad. F B1a
A, aquAEI Z planO. Veraque pars ducitor quadrarice: igitur A quad quad L B in A c
bum 2 L B quad. in A quad, xe quabicur Z plano. plano. lam afectio B quadrari in A gu
dratum, incerprecationem accipiro ex poltremum designato a quadrari valore, ip(a et
3cae
d. in Z. 1
A quad. quad. +v 171
cubum Dua incerprerarione adscira, de omnibus rice ordinacis
uni rocuvo in A cubum, aequabicur = oono stne vino, uE CAt Or ditacum
5118 + 14N aquatur 147. 189 + 20 C, aequabitur 9261.
6qu
-D Plano plano.
TH PO