# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 155, page id 845634801:0161
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=161
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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 0.83
# 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.

rOpO.
plariu
videm
3et
5
A
it
nA2
eAB
ist
onib
B4
LL OV A Z EO N V M.
1C. - 309 + 236N, aquetur 360. BituT ZON = + 9, aquatuT 36, ex fit L N Z vel 18.
Tildem posiris, ipla AHc quoque B, sire B criplum quadratum praestec, sive cedat D
plano. Duoniam enim proponieur Acubus = B in A quadr. 3 F D planoin A, aequari
Dplano in B =B cubo 2. Ip la aurem LL I quoque B, isicur B cubus = B cubo3 + D pl 2-
+C = 309. + 236 N, aequatur 360. es osten sa est + N 2 vel 18. eadem quoque est 10. ZC. -3
2 = 264 N, aequarur 640. fic 2 N 4 Vl 16. Nam 2ON - 1 9, aequacur 64. es fit 1 N 4 vel 16.
IE OR E M A. IV.
F DI A quadr. 3 - + D pldno in A = A cubo, aequecur B cubo 2- + D
PlaoinB, A quad. = B _ A2, aquabitur B quad. 2 + D planO.
Ouoniam enim A quad. = B in A L, aequarur B quad. 2 F D plano. Ductis omnibus
in B = A. B in A quad. - B quadr.  A2 = A cubo F B in A quad. 2, a quabIEEB CU-
Er aequalicare ordinata, B in A quad. 3. + D plano in A = A cubo, aequabirue B cubO2
30B -+ 24N - + C, aequatur 2240. TgiturY O = 2O N, aquaTur 224. e fILL N28.
TiEdem expolitis, Ac A quoque D. Ouoniam enim proponitmr B in A quad. 3- F D pla-
noin A - Xcubo; aquari B cubo2- F D plano in B. Iplaaurem A GE quoque B, igituE
B cubusz F D plaHOM B =B cabo, aequabitur B cubo 2 = F D plano in B. Ouod qui-
demica se habet.
T H EO R EME A V.
FBM A quadr. 3 = D plano in A = A cubo, aquetur BcubO2 =D pla.
nonIB. A Guall. D A2, aequabicur B quact. 2 = D plano.
Odomiam enim A quad.  BH R2, aequarur B quad. 2 = D plano. Ductis omnibusin
B - A. B in A quad. = B guacr. in A2 = A cubo- + B in A quad. 2, ae qua bitur B cubO2
ECaequalicate ordinata. B in A quad. 3 - D plano in A = A cubo, xquabicur B cubo2
309 - 156N - 1 C, aequacur 440. JBiturZ O = 2ON, aequabitur 44. ex fit LN 22.
Duoniam enim proxonicur BIH A quadc. 3 -- D plano in A - A cubo, aguari B Cu-
b02 =D plano in B. Ipla autem A sic quoque B, igirur B cabusz =- D plano in B - B
elbo, aequabicur B cubo 2 = D plano in B. Ouod quidem ica sc habet.
T E E O R E N A VI.
Ad quadrato. quadraticam perrinens.
Sta quad. - quad. = X I A CMDuM 2 -+ Z cuboin A+, Xguetur Z quad.
Quac. 2. X quad. in A Gua. 2 = A quadr.- quadr., a quabitur L quadr.
Duoniam enim Z qua d. in A Guad. 2 - Aquad. quad., aequacur X quad. - quad. 4 - 7
Cabo2 in a X quad. 3: er80 perancichesin, ee ad X cubum 2 communem adplicationem.
uadr. = X  arac. 2 x quabicur V X quacl. 3.
Ecomnibus quadrais, et per Z cHb0. cubum 4 ductis, adhibitaqi congruenter metachicti
Xcubo. cubus in A quad. 16 -  X quade. in A cubo. cubum 4 = A quad. - quad. quad.
Juad. - Z qua d. - quad. in A quad. quad. 12, aequabicur X quad. . quad. - quad. - quad. 4.
Quod quidem ica se habet: enimrero secundum primam aequarionem. Xcubus in A. +
=X1
no in B, aequabimr D planoin B = Bcubo2. Ouod quidem ica (e habet.
b02 -1. B inD planum = D G_ad. in A2 = D plano in A
F D plano in B. Ouod quidem ira sc habet.
300 - F 24N = 2C, aquatur 22 40. fit L N 10.
D plano in B = B quad. in A2 - F D plano in A.
Tisdem postis, AE A quoque D.
=D plano in B. Ouod quidem ita sc habet.
308 - 156N -. 1 Ci, aquarur 440. fit 1 N10.
Quad. 4 =- Z cubo2in V X quad. 3.
puacen