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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 174r, page id 00068194:0347
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Habetur solutio generalis  formulae
C_ byy +RCy +d quadrata ev aequanda
pro scopo meo solutio in determinatae, anqua saltem ipsae
iadeterminatae y, et V, sint extra vincula radicalia non
curando de coefficientibus. Nam Et quidem si b vel e
sint quadrati, res etiam numerice praestari potest. Sed
centraliter fiat V = y1b + X et fiet (byy+ cy+ d= byyt 2xy1b
seu y = Xx - d,: , c = 2X 1b.  Sed rg +XX + 2Xb y 20
D
Sca Surgamus jam ad altiora. sit formula, cubica aequanda
quadrati sit surgumus jum ad altiora sit formuta subrea
b1 + Cy + dY + e = vr
sed video magis, uniformiter nos processuros, si semper
ima tollamus. sit Ergo  sit b + c + dgy = vv et
fiat v = 1b + Xy Ergo ex 1 et2 fit, b + cy + agus = b + 2xy 1b 4 Xx yy
seu c+ 3y2XYb + Xxy seu y = C - 2X 1b,: Xx- d qui valor
tantum est prioris reciprocus
furgamus jum ad altiora: sit formula subica aequanda quadrato
nempe  b + cy + d ys+ C Y = ov sit v = ( sb+ c: 216y + xy
et fiet b + cy + dsG +Cy = b + cy + Bx gy + cirbX 5 + XX 1t
seu destructis destruendis XX YY + c. st Y  b + X
et fui b + cy = dyy + e = b+ Cy+ xtv yy  + ab XGG n d
Et destructis destruendis: +X sb
als
C: 4b
+ C. +b X Y + XX
+ C. b = AC
4
seu Beb) + (C) y +cd) yG, = 0 Unde per aeq. 4 calculi procedentis
per compendrum
(5
d
habetur y. pro b, c, d ponendo valores ipsarum (6), (C) (d) ex
ibi repertis
comparatione aequationum 4 et 5, et pro X ibi reperto, ponendo
et siet. +ZZ seu per compludium (6) + (C) Y +Cd) yy. 6 sua non quae
ita x ita res redit ad aequationis quadratica resolutione
sit ergo Faciamus X = 1. Z. Et ex 0g. 4 fiet
6
+q sb + C: 5b Z y + yy = 0
sed ob 229, video hnc
huni non dari solutionem
si jam voluissemus facere Xtb + c: ab - d = 0 seu determinare X
+ c: abZ2 = eZZ.
res redacta esset ad solutionem determinatam. Sed pro generali
= Z
solutione cum sit sit pro compendium yy + Cs my +n =0 et fit
yy + my Lnm: 4 =  um- an : a et y = Vmm- qn = m,: 2
ei debet min- an aequari quadrato. Et habetur formulaaquanda quadrato
in qua extant 74. 73,  q. abestantem absolutus; Et video nem
successuram si absit terminus h simplex ita enim prodibe formula
p2X Z
Z,  et absolutus. ut quidem si lnqullet face
iliccris facere b =0, haberetur desideratum sed hocmonlicet si faciamus y- PZ+ Y
aequanda quadrato, in qua sunt 2
Puce
Ileu Zet absolutum 17