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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 262v, page id 00068201:0524
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Sed ut aequationem nostram:
+9+Z + Y5 = 0
c + E0Z + pry
ceplicandam redeamus, dictum est esse (() = + . (2)  2lnig. (p) + dln  + m X = . (4) Cumi. (Y7. +n - 1.
est autem (= + 2 + 2b 1+ a
(1) = + = 2b2c.
Er g. a = 4 + ab + ab. a 1 + a + su i l.
(W= 4c + 4C, 4 f ob +46 4 + 8b + 4b
P3) = 4 + 8b 146, a2 +3
(9) = ac,
5)-
4+8b + 4b 
4 + 3b + 4b
es
(+2
qu
te
+b
+ G
3)
+ m = a
+f6+6 4c
(1) = t tib. 
4i
Ust calculi veritas examinetur, primum Parabolae applicetur, quo casu = significabit , et unitas erit longitudinis
infinitae, idesque  rejectis (Co) erit rejectis cateris,  4b2 cum sit c0 = 4 + ab + 4b1 + 2 + 2x, manife.
stum est, ad eundem dimensionis gradum omnes ejus terminos non uno perduci posse modo; vel enim ad gradum termi
in dimensionis maximae attollentur inferiores multiplicatis omnibus per unitatem; vel ad gradum  termini dimen-
tionis minimae deprimentur, divisis omnibus per unitatem; vel etiam ad alterius cujustaibe intermedii
cormini vel etiam altum quemlibet altiorem inferiorem termini gradum pervenient multiplicatis pere
unitatem inferioribus, divisis per eam superioribus; vel denique omnes attollentur multiplicatione, aut
deprimentur subt divisione ad gradum alium quemlibe vel terminorum omnium gradibus altiorem aut
inferiorem. Sed duos priores modos aequationis homogeneae reddendae experiti sufficit Posita ergo
ea 24
 Uide rejectis cateris
fiet: cot3 4 + vel cd = 4+3 Si omnes alios terminos deprimas ad gradum termini
maxiius; ideo fiet: co 4( + 8bt + abE +
unitate = 4. cate
infimi, qualis qui est , siet    + 8b a 4b   + 2a +
ideoque rejectis
iterum caeteris omnibus fiet ut ante io vel co-  unde patet omnes ad homogeneitutem reduendi
modos eodem redine  cum aequatio proposita multiplicatione duorum polynomiorum fiat, et in
uno, 4 + 8b + 4b terminus alsipt sit 4b, in altero, 1 + +terminus altissimi gradus sit1
ideo caeteris eodem sublatis in quant factore quolibet, fiet:  4l + obt + 4b 1 + 2t +  = cot
et quoniam  infinite majus est quan a, vel b, fiet rejectis caetetis, 4t = cot, vel at = co
Vicissim cum in utrq uno factore termin infimus sit a, in altero = aequatio depressione homogenea
ee
po at antea; ut proinde omnes modi  homogeneam reddendi aequationem eodem redeant; quar unca
ita fiet: 4 f 8b + 40
t 1
quolibet ex illis uti imposterum sufficiet. Eodem 
ut
2+3
Eodem mod Est ergo  (C0)=
et () = 16l2 4  et (47  32c +3.
et eodem nndo (1  16 ct
(r5) = 16t5 - +
15+5
Unde statim patet erratum esse a me in calculo cum haec quidem applicari non
possint ad parabolam, et vero error in eo est quod omnia pert 2 F 2b multi plicavi
cum dividere deberem. Reno ergo ita resumere placet
sed et utile fuerit demittere perpendicularem, in aliquam ari paralletam
non in ipsum axemus ita puto omnia problemata eadem formula solvis
posse