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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 23, page id 845634801:0039
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.88
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# After the first blank line: the recognised lines in reading order, one per line.

N O Y A L R +OR.
0
Ouod hr ex adereento duorum larerum in sex lingularia plano. Colida, quibus constar
quactaro cudus eea splolum lacerum, lemel sumpra, est aequale differentix cu-
b0 cuborum.
CO N S E C F A R F V M.
Differentia cubo-cuborum si adplicetur ad adgregarum duorum larerum, orienrur
sex lingularia plano. Colida, quibus constar quadrato. cubus differentix iplorum lace-
rum, semelsumpra.
Alind C O N S E CF A R L V M.
Ve differentia lacerum ad adorepacum, ica sex singulatia plano. Colida. quibus constat
quadraco cybus differentix iplorum larerum. Semel lumpca, ad sex lingularia plano-(0-
lida, quibus constat quadraco cubus aderegati iplorum lacerum, sumpra quoque lemel.
Ex propolicionibus praccemrous de ducuntur Theoremata universalia.
Ouod hcexdittetentia duorum lacerum in lingularia homooenea, quibus constat po-
restas adoresati iplorum lacerum, lemel sumpra, est ae quale differentix porestarum eradus
proxime luperioris. Hinc
C ON SE CF A R T V M
Difterentia porestarum Cadplicetur ad differenciam lacerum, oriencur  aa
mogenea, quibus constar poreltas eradus proxime inferioris aderegati iplorum larerum,
Temel TUMPEA. EECOnETa
Differeneia porestarum ( adplicetur ad sinoularia homocenea, quibus constat pore-
stas gradus proxime inferioris adgrepari iplorum laterum, semel lumpea, orietur diffe-
rencialarerum.
T I E O R E M A TL.
Ouod Er ex adoreearo duorum lacerum in singularia homogenea, quibus conttatpo.
cestas differentiae iplorum laterum, semel sumpra, est aequale adgregato vel diHerenrix po-
rectarum ordinis proxime superioris: adgregaco quidem. C impar Fuerie Cingularium ho-
mogeneorum numerus: differenrix reco. _ par tueric Angularium hOMOGCnCOrU nu-
merus. Ilinc
C ON S E C F A R X V M
Adgregacum vel differentia porestarunt  aepulcetur ad adgregacum laterum; oret
cur Cngularia homogenea, quibus constar poreltas ordinis proxime interioris differen-
cixe iplorum larerum, lemel lumpca.
AIIHd C O N S B C F A R E Y V.
Sipar fuerienumerus singulorum homogeneorum, quibus constar porestas adgresatt
vel differentix laterum, crir: ue disferenria larerum ad adererarum; ira sinoularia homo-
Genea, quibus constar porestas differentix iplorum lacerum, lemel sumpra ad singusaria
homogenca, quibus coludc porectas ejuldem sradus, aderegariiptorum lacerum, le
rel Cucpca.
N E O R E M A L
GFNESIS POTESTATUIM ADEEOTARUM
et EEttde allaetictale.
A O P OS F F +O XXV.
Peraacum adFectum ausanecione plans lub latere, adlcita congruentes
sublacerali coefticiente longicudine, componere.
Sic radix binomia A. = B. Coesticiens sublareralis D longicudo. Oportear quadearum
2b8