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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 42, page id 175906937X:0066
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+2
P R L H C F P E A
Ouod si, Tubductis quadratis parcium dati binomii a se invi-
cem, reliqui radix quadrata e major pars binomii communican.
tes non fuerint: Catius erit ipsi binomio lignum univertale radi-
cis quadratae praefigere. IIt ad extrahendam radicem quadratam
Cx = = a. = V = a a + bb scriboV = = a L V = a a + bb. Gux radio
ces rulso appellantur Univertales.
DE REDVETIOHE AEOYATTONVH.
TToniam ad resolrendum aliquod Problema, id ipsum sup-
Ponendum est ut jam factum, atque nomina imponenda
Tune quanticacibus tum datis, tum quaesitis; et quidem prodatis
a D. Des-Cartes ordinarie ponuntur priores licera Alphabeti
a, b, 6, _C. pro quae sicis aurem polteriores Z, V, X, _C: HIE UE Per-
currendo Droblematis difficultatem, eo ordine, quo omnium na-
turalissime paret, qua ratione dicta quantitates, nullo inter co-
onitas ee incoonitas Facto discrimine, a se inricem dependent,
eandem inreniatur ria quantitatem aliquam duobus imodis expri
mendi. id quod Aquatio rocatur. IInde cum xequatio nihil aliud
SIE, quam mutua comparatio duarum rerum ae qualium, quae varie
denominantur: Facile constat, quantitates halce cognitas e in-
coonitas, prout direrlimode lunt aftecta atque dispolitae, direr-
Pas efticere posse Equationum formulas, qua tamen per sequen-
ces regulas reduci queunt ad halce limilesre species:
V
Z∞b, aut
∞- aZ + bb, aUE
3∞. F a ZZ F bbZ - c3, auF
∞ = a Z3 F bbZ2
132
De Reductione per Additionem.
T P hrabeatur aequatio inter Z - 3_ F2, hoc est, Si fuerit
 3 ∞ T2: guoniam s aequalibus aequalia vel idem addas,
ea quae tiune sune aequalia; hinc si uerinque addatur L 3, fet
D 15. HaM 3 X  L 3 addita FaciunEO.
Sic _e Si fueric Z - b ∞ 0, adden do verinque b, Het Z ∞ b. AUE
s1
Pa8. 6.