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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 138v, page id 00068195:0276
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Calculemus a = X - X +X= Xgy aXyq f B P B+ XXist-
C. XB
+XZ REB- XXGZZ
suppleantur numeri ope negulae supra dictae= XyB
= Xyy B
ubi tollendo Z aq ope aequationis _, habebitur aequatio in qua assurgetur ad ye
V((
quaerata et a, ibi assurgetur ad y3, seu ad Ve sablato Z. Habemus ergo binas ae quationes sine Z
in quarum una est y, in altera y quarum ope tolli poterit y. sed ita nimis alte assurgetura Adhibeamus
10
ergo ad hic aequ ab, et a in qua itidem assuraetur ad y sublato Z; et a abC, ubi itidem assurgetur
Ad v. Denique ad hibeamus a et abSd in quibus assurgitur ad 36 et adeo ad . Et omnes
eus valaes ipsam a ab, a aebc, a abcd vel potus  ponanus l, m, a, p pro a, b cd.
0
Et quendiet ha quantibet ex his aequationibus multipli aultipliemus per fomutam ipsius. ya gy + us, et usue ad
et
p, et componamus done ut evanescat y, habebimus aequationem quae asondet ad Y X
nec otinetat nisi P, end ma Em nep, nam (10 (3, (20 posunt ese hormitolli.
1on
jem aequad
multiplicetur per X . ek. duvec ut ascendatur ad 30 grad pho comparanda priori, tomm
 et hujus comparitionis ope am sunt 25 Teminii comparandi 29 dsteni 30, et literae 25
non vdentur sufee ouaralio ad coparationem a ( ps 5 (45 5 (5m nB.. si assut
un
lap
P7
A B
+
s asturrexissemus solum ad B M d seu (5 sell ad E, seu ad Y3
debriet aequatio N multiplicari
per X+.. et ita habenus comparationes 25, et artitratus totur 20. Et haeremus in eodem incom
modo in abeau fec B multo magis cum habeamus solum tres l
1m emn.
quaso sit aequ. ad Xo p, continens sotum sil B, ln l’ma, lmrip
quid si copuemus _ B = X = Xy + 5XXZ + 5 Xgy  et t = X + qX + rXX + SX
SX
conjungau
et taciamus 15 = t fiet X. 5 +5 XXy 5X
si si fecissenus ( = l et y se. ln =- q
Z seu lun = 5Y
459y
+5C
segXx +rX +s
et β =   (549. 25)= 59: 5
0
Haberenus 13nE per meras X et cognitus net eodem modo (Emn et L m nD
et hacum g sec. quod si jam o his quatuor aeq conjungamus dataim, habentur per et pe
poterit suli x et hab et Et inqualibet habebitur B inS, absolute. sed quia in I5S, valore,
hrabetur XIC, verendum ne dum volumus tollere X, ope aeqq. X, t ne tollatur E. Bmminus
alte V ita hine non habeatur V nisi peraequationem aequalem datae
Omnibs paminatis ergo praestat rediri ad hipotlesu nistra
Aequatio 2ta gradis non habet opustris auxiliis ham tamen huius Hypothescos methadum et ipsi applicemus
sit equalio XdXtq ∞LqX +Y = 0.  X = 8 A  -24 X3= 3Y.  jam X = . Et quicquid rationala
in X nemae 3C = Y devet esse in l3 imo debrt ei aequarii fit ergo lLr. Rursius X = - 243+ ip. et quod rationa
e in X est  =ZAFZrT,. 83. jam t non debet continers rationale aisi in (b+ 2 (3∞ Emra = -eq+rr, it
jem ob B eX erit l= rr 2 d. Ergo pr V’in praecedenti aequatione substituendo valorem, fiet sed hoc non fucce
YF dit quia l  21he = 1Y. Sava si Xm X Y qNI antmplicetur per N 4X Y pet s
XXrXE
gX  9rX
1 r)
rpum
 ex  Y = (+ n qu  g = 3lm 14 = - q = 27 (3 M. m - - 9. 27
= - r - 13. fit 276 + 2r ( = q seu (6+ r(3 = 2G. seu l + r(+ =
=rra =  Sit 13 = -Lr + ( rr + 24, afiet
Y+ (2 tr + 2, 4))  et pari jure mn = (Y (. er +: 37 Ergo tandem fit
 = i C. -E. . 7) + E(. (.... 7) Hino in X3, nihit alius est rationolo quam in B, et sit P. Et videol etiam in X nbhil esse posse
3
adiviradi quam re Sed nine videtur racihare nostra hpothesis nam ba  X - 2934 3rr. Falsum ergo est quod Etia
pers ejus Qvoum X ratio nali sit in  rationale sin quod rationae in quavis potentia cadsis dem. Etm in X3 rationale 3
X 8 + gX nC
est ciptum ejus qud in X ratiorrale. uise erit tres ndices aeqontonibus cubica ex hiben X +Y-0 et getr
des dantur bei xn efict XX + Cx + CC = 0 fit X5 = (- 6 ( 14)  qeu +) 3 Cube+G). Y quod. X perationube, erit
1 C- (2S4 9 eCC 4 ob  seu in  et et in _) 293 A sed in et non crat rationale no
C d et Tuonale
at sunt nveramus Hime vetrotenido siutaei satem quam a  aud adias. terveniemus aded qud est ratibnale in no
Y. hom Erg. in X + B on est catima nist 2 XY Ergo in Z
B
jy
X
es