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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 9r, page id 00068021:0017
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f se 35 antes e
Ergo y5- ∞f cs
hogo y -5 +Sinrs
v
ss
lique vt
Invencendus ergo valor ipsarum C, et f.
est autem e = 53 = 75 + yf + y + +5 + vS + W
=s+ f.
et f= - y5 + e5 + y + +s + vs + W
et substiluendo proie ejus valorem,
hobebitur vator ipsius f. sinc et et per consequens fate rulor quoque ipsius e, sine f et
- y + c.
utrisque sine f, et e. et, quia ubilibet liut substituere et pros et epro y facile
inde fieri potest valor qui libaerit. Sd ansstre autemmodor haberitur aequatio forman
habeus similem datae, et eaque duarum radicum aequanlium. Sed artis foret ista
bregsei atque eleganter consequi Posse. Bartholinus non trodidit. Beamal non tradidit modum
invemiendi quae de limitibus aequationum prodidit, sed hoc modo videtur id semper fieri et
no
ostitutiae
Datae aequationi alia ejusdem formae constitui posse caeterum dic fatilitas eo mapot quid
signa pro arbitrio assumi possunt
siu brcvisu  y s yf = v s. Ergo 5 2 f = n. Et qir f
e5t52 + vs Ergo C = +s +v
Ergi  - +5 + v =
S +ny maneat
 5.e
e
a
Ergo y Mulls pliants fieh: sy = +5  Vs - Syh ts =vs +- tsnyrhs
Eror in calculo resumatur: 25 - Vf = y. Ergo s - f = 4. ny. (= 0.)
= es = +5 + vs. Eigo C = - +s - v etandemque 9f = W. rgo f -W
= 5 - nyd. Set 5 e6+ b. Ego f W = C + V- ny
et y = e+ v
4
+
n e
 Unde et ipsius e valre ale habetur et
pehravalorem e valar ipsius f. sola exu incignitis Y. tantum concurrente. Valoribus
alis substitutis in eorum locum. factaque mulliplicare prodhici debet ny s Vs. W. sed
et si cong in aequalione a illa n. W = e + V. ny pro ny poneretur ne
uti certe fieri potest; ob aequalitatem unc patet e, pariter e. f. absolue
haberio ac ptroinde radicum V et S, valorem purum. Indeque institui pe
aequationis huique arbitiariae, cum datu comparao, quae necessario olvet
problema
0 imclius utex: a. 6 = . 4
qu
Cartesius tradidit methodum complendi omnia loca aequationis
cum una est incognita. Tradtenda methodus compeendi cum sunt
plures
s
Nc
V5 = yf es + ef y+ ts = , ddit: an. S 25f- (Cy5) eys +y5 +5 As entes
u
Unt 95 + tys f V sate S ctsed
eys- tes
sive -saV- te S He S sresa
luadem
fiet
ma Ateita
luy
je
un
a
e
enca
+nes-ves,
Ax
tetes
a uis
5
COF =O Comparanda cuu ra  - ar5 + raS- at
ex
+ a
f= - r. +- ay o r- uy=ratae
Ergo V- Y ra- ego W = a
aptra nreHar. sin  fY Ecce aqvationem
 r41 Xa2rat vust
Itr Rt SY
in jaa loguitis experiri plactt.
Locs e Al non actom jansita
L1 25,5
identicam eusdem secu 1p50
ex
el
 0 quanquam autem de calculo non
e
responderim, methodum tamen detectam
artitioo alcum et acuratam quis