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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 265r, page id 00068201:0529
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a b X + CX2 + d X + e exciletur L Itum
O
b X +2b∞ + 2 + 2bCX
+C +2d, +2ICX
X + p X + qX + + X + sX +X + v
+ 2bc +2d. + 2be + 2ce tide. + e
+ C. + 2d + d2
 4 d. +2de X + e
Ubi manifestum Unum aequationis latus  smistum scilicet esse quadratum, i ergo simstrum quoque tale reddatur, ope aritratictum
b. c. d. e. Conferatur cum alio quadrato, ibi venc in mentem compendium elegans, si successus respondet tum
d
si coincideent, ergo aequantur nulto magii. Si aequantur, ergo (6) a 20D + S  Z(02) Ergo 2OD , quae
aidem Jani superest, ut non tantum aequar, sed coincider quoque ostendamus estatem. Ubi hoc saltem lucramur ut omnes quantitates in quibus
P F X +2f9X +2fghX + 2flX
92  tigh - +2gl X
(its . 2t. 2df. 2es.
+ h. =+ rhlX + l
2b9. 2cg. 2d9. 2eg.
2bh. 2ch. 2dh. reh.
2b1. 2cl. 2d1. 2el
P 40 h c d
+s h
tollantur, adeoque non nisisi
torm
Unde sine calculo statim scribemus: d) +1 - 2 lh - tv + hP
Extem bp 4- f Exem. ult. eriV. C
is
2
  se invirem, statim
N extmll. b4 p. 19 cf ixtem pnit. es t - 2hl. - adl
) 1 X LpX +GX ArX +sN +tX AV B
Jam etiam tres valores ipsius e examinemus, 
 et quoniam perfecte similes sunt ha
tres priores, tribus illis posterioribus, ideo tantum pro pon
faciemus pro a
ponemus 
f
1
9 d
Extem. H bp7 9. 259. 5. 40s e9
posu
2h
Excotlatis duabus prioribus ipsius b. valolibus tieb:
7da 1osn (g pt. 29- us sie cri Ps s9 datos
ex collatis primo et ultimo,
95 - 2529 - 9f - 2d f = 2c95 cs h. - h5 2
2
et c e 9f-2529. 9f 2d f, -ha + hf
295
et duos ipsius C valores aequando fiet:
pf.9  59 -92t 9 f  45 - 2f9(9 5) - 2d f3 ab f + ts
uc dri 95-sg- alit + h53 1s9 +50 +9a - 55
quisqe e istamerntia
et CF SM -13h -v9l + 9B, - F IM + P. L. + hi v -  junvenimus ergo duos ipsatum d. et c. valores. nde duoi noved
vsultabunt aequationes sine ipsis, invenimus ergo b. c. d. e. quaedam calculi satis ordinati specie. Ubi notabile est
Ex tribus valoribus ipsarum b et e. unum esse, quem nec c. nec e ingrediunbum  quod rursus ad calculum contrahendum
magni est momenti rursus ex valiribus ipsarum d. et C, possumus eligere breissimos breviorem. Et ex Termino medio
seu quante habebitur. (1) (+4gh fV, +FVFCa fI et 15 9(-Hsd) -to f g (+ hlS, + Ps 1H ((  rB - gat h (d s Y n
+ a lf (= Vf), 1 Y5 
4
Supersunt jam aequationes duae ex duobus ipsarum d etc. vatoribus, quae duae aequa
tiones inter se simillimae sunt servatis tantum substitutionibus quas dixi, ac primum collatis duobus valoribus ipsius d, fiet.
+152 - hf3 - ho f + hV F 9f 1 25 g1 - alif l(+ hf 1) - pf9 l’ + f5 l +gal  S 1 Et sinliter satis drolus catuibo iestus
literae C, fiet
pf1 - 2f9l3 = ga 1 (+95 BF S1 f - 2Bhf - v9l5 49135) - + Ihf + Prefe etiB - h 15 7 8
Habemus ergo tres aequationes eleganti quadam ratione congruentes; et pro illis resolvendis, quatuor literas indeter-
manatas, f. 9. h. l. Faciamus _ fl n c. et gl 1  A et hf  8. et fiet
veof tAf -hg vf
aco P p9 1 - hg a 1 B et rco2
Grodsi jam ponamus in aequatione abesse terminum
medium  quod semper effici potest interventu
= + a f 11g cor  eeb- a12
2coA..
=p cost
+a)
N Ng fcel-co292
aequationis cubicae, i explicando incognitam saltem explicatione minori
et Zp cokI sco - vAf
=20. + c0g
+ d.
aeqes.
+ 82 
+v92
=D Hl vel - co ep A2
si item faciamus preterea +V a, quod semper fieri potest p per radicem puram quadrato. subicam, si denique faciamus p, AtA
prisna extubus equationibus novisimis dividi potenit per f4l
exitque acc + p9 - hga p0
sive
-2p2 +13
-qY
pee rsph
+ah
spFho+
teo ig  duabus residuis aequationibus
hvs
phist
et Ap 18, svi 914 Phf
afl +phf -ngerio. erit Ae P Z
Vii  ex Granda him dieruum coripinaum, S ag l +qu paot  ad A 9s et 1 pti = B +t
Explicando jam 9. et l. habebrimus in
sph H+ - it f
eth
Crp
 afl = pht
na
X + pX + + aX + Y X + SN + F X + B 10