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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 143, page id 845634801:0149
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.82
# 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.

itact.
20
(nNO.
 d
CTUI
1
od
DI
3h1
u
A OY A X FO N Y II.
Proponacur A quad. quad. F BI A cubum 2, aequari Z. plano- plano. Oporret ta-
cere quodimperarum cA. Sane H quadrarum estinencurabs A quad. + B in A = F. pla-
nO =, CHCIIlua A quad. quad. -  B in A cubum 2   B quad. in A quad. Y F plan. plan. =
Virique isicur aequationis parri addatur id quod deficic ab effecto d̀ starura radice pla-
na quadcaco, concludecur exitaae qualium aequalibus addicione. A quad. quad. L B in A
B in A, aquari Z plano. plano + B quad. in A quad. + L. plano plano = = F. plano in A
Veeaque pars dividarur sub quadrarice, illic revocata ad analy Ein geneti, orietur ma-
nitecto, A quad. -+ B in A - F planO =
Ouod ( alcera equalicaris pars pollet quoque diridi subquadearice, quod oriretur
Foret aquale radicibusillis planis eprima parre orcivis.
Estingendum estigicur quadearum à radice plana, et illud alceri aequalitaris parri, id est
Z Plano plano una cum luis adfectionibus comparandum ee adaequandum, ut cadices
quoque comparentur e adequencur incer se: Racuicor idcirco radix illa plana ettingendi
quadcaci
NB quacl. - L plauo In A.
Sic enum in comparatione eranelcene adfectiones lub A vel ejus pradibus, ee incide-
cur inaqualicarem de P. quo cendendumeR. ERiCtum igITUE QuAdTATUII CLIC =9. 9. - p. 1.
F B quad in A quad. - F. plano in A quad. = F plano in B in A.
ano. plan
Adequandum Z plano- plano una cum reliquis quae illud comicanur et adfciunt ex-
Polris plano. planis, ee deleris urrinque adfectionibus sub A, ec A qua dC1O. v onu a.  evtam. 1.
Ex omnibus ductis in B quad. 4. = F plano 4. E. plano planum in B quad, x quabicur
Z plavo. plano in B quad. 4. + L Plano. plano in B quad. Z. plano. planoin E planum. 4.
Ex deleco urinque F plano plano in B quad, omnibusquerice ordinacis. F. plani cui
bus Y Z plano. plano 4 in E. planum, aquabitur Z plario- plano in B quad. 4.
Innocelcacaucem E planum esse D planum. F.rBO A quad. + B in A - D planO Z, X9u2-
NB quac. D plano in A.
Et aqualicare secundum acEeM OrAIMaTA A quad. + P F an nus. - o vano. in A, aequabitur
EL A proxonacur a quad. quad. = B in A cubum 2, aequari Z plano- plano. R adix
plana estingendi quadraci Aacuecur.  s. . - a vum ,. F N B uad. - E ptano in A, COmp 2.
ranca A quac. 1 B in A -= F. plaHO =
EE S proponacue B in A cubum 2 = A quad. quad., aquari Z. plano-
plano. Licebit argumeneari. A quad. quad. = B in A cubum 2, aquari Z
plano plano. Quod eric auterre aequalia ab aequalibus. Er radix plana ettin-
Bendi quadeaci RaEuCTIE. yv gudu Leptuio. =  Bguad. L. E plano in A, comparanda B in A
+ E plano Z = A quad. Ficiraque omni calure ductio quae imperata est. Finc ordina-
buncur eria reductionis TheorematA.
T H E OR F M A l.
EA quad. quad. + B in A Cubum 2, XguetuE Z plana planO, _ Eplani- cu
bus-Z plano plairo + in LPlanum, a Guecur Z plano- plano in Bquad. 4.
quad. F B. +VvauB. - v otuo IM A, a quabitUT-
B
D qua
E E E O R E M A II
Y D PlaHO 2.
IA quad. quad. = Bin A Cud, alfdletur Z plano. Platio, ee L. planI- Cu-
bus -Zplano- plano + in L platte X quetur Z. plano. plano in B quad. 40
vorrtu  oouno
 DPlalte 2.
Con
L PlAH. II A quad. = F plan. in Bin A.
cubum 2 F B quad. in A quad. F F. plano. plano Z = F. plano in A quad. - F. plano in
quad. = L plano in B in A.
aquabicur Z plano. plano F F plano. plano .
C plano. plano- planio.
D planO = +
et
uac. a.
bicur
Innoreleat autem F planum esse D planum.
Innocelcac aurem Cplanum esse D planum.
A quact. = v vv aus. B vuno iM A, aquabituI