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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 19
# Folio 10v, page id 00068268:0020
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X. y. Z
X
Y 5.8 a suno
Ixtiy 17a. ix dy B b. Ergo iXB a - 1y p b 4 1y. er 9p 177 - b. 4, 1X,  a L
a - b +Zip c. et a - b - Z1p, d. Ergo 1Zp) c  +  + 4 - b - 42
et et fuer e+ d p a - V. Rursus  novissime a +  tiZ p g. et a +b - iZ  h2
enitque 1Z H ae + B -Hi  g - 4 4b. et fiet a + b 1 9 + ti Supersunt ergo nobis
solvendae aequationes duae: b d d 5a. et a + b A 9 + si seu a- h e 9 - b
seu a+h a - h, 9+ bg- b. sit ia +it p l 9+b) fier l a -t B 1 g- b
ex unde ia_ (1g (+ H f ih p e ig - db, +  et .hp 19 + 1b - ia, a rusus h altibajus
quos duos vulores aequando: Pg + l l(=ila  ial + Pb - Pg. et 9  2ial + i1b - f.b
quem valorem inserendo in invento valore h, fiet hp al - al i2 + ibl 2 - (3b - 19l + 1- 21a  
restat aequatio a B B +C + d, quae illud ingens habet commodum
aut h, in ipsam intrent. Ergo ponendo ap C+ malsiei rem + ne p B. f, d
er Cr. 6 + - m. et a  V +
ut per se subsistat neque
sed unn adhuc restat aequuatio inter. iz valorem ex duplici toppositione conditione, penultima
et ullima nempe e (aes+ b
2 12 t ) - h. seu C + ho r a vel 3 +d p ae
2
sit dei vel d  F h2 - b
a
+ m
3 supro p 2 ial - b
Resumendo a +Bi s + h. et b+ C+ d a
A. 1. Apera bpi 3. e Cx   ae. His hibus aequationibus satisfaciendum est.
a= h  9 - B. seu ath auh  9+b9- b. et  C7 a - t. ergo Ep art a. h
sit . 4 R 1 2ach. ergo ex  P  arhp a- h et ap pK = 1
2
i
 Ph et et a - c  = Ph destant resolvendo aequationes. 2. et 4.
aequatio 2 b + d2 p a - C p7 a - c a +C  - Ph, at c  b d
a  VetB  StCta V9 +te B ergo (et tep BCCd. ergo hp
a p C xhi. eit Cs a M. piei (a  (a arma m + li et ar  + M. et 1 - 
et c  H - R + . ess + 13 n. +N. + d, 9  H( b)
4m
em
(E+ hi p V(D +S sit bp h - n. fei (  hn + + 8 ex h e dn +  et bp  
sperest aequatio ad huc una, ut CDe, dCti  sit bp hun trei h  +n. et bs -
superest e (1o,
Iso
+19
et 
2
+
= q
g2(4h7 - bv. seu h+
4;4
Que  +  p g - d + 3 - = sit E79n. sei
4n2
414 E +1 A F. et + rt - pr
2i2
 17 4. ergo M h i 2 ∞ +1
sive mp S. n
41 Ep + 1 BY ergo   F2 si X ⊓9 - vn
 a + b n9 ( H) Ergo Ct tp 9.
Habemus ergo tes aequationes vilde singliaes: c  bi p a. d 49  a b4 e . 9
ubi explicab quaeliber aequatio literam habet, sibi soli prosuram sn hp Tanc. devaue
b17 V92-e
et e sn a+b fC. et a-bf
cur h H 3et c ay 5C- c. p5(+ C. a CH sec - f c aet fC+ f
Codem modo proh. a. c. f. C. 1. ponento d. a. g. M. n. p. fiet de map. et ap  M n + mp. er gu mn. mpo
et aequando a duos vulores frei fC + f12 Omn 4 mpr. seu  nt 
T. dem modo pro s a: C. f. e. l. substitendo b. g. c. 9. 7. 5. fet hp qus. G1 qu + 9S ex Cp qu2 qsu. aequandoque duos valores ipsius
fo. et aequando duos valors ipsius C, fiet fp  s  Multiplicandi aq. D et t m se inicem siet:
p p. so
 foi q
7+ fu e e 10
21
at edem jam f ru+ F fiet ergo aequatio novissua p n - pB Y gr n po
+ p
et reducendo: (n re  nVY + se p pt  C
p2 5= 10)
p
en) re Se( seB (  r C
e
u
d)
et fiet: Mr  ps  rC  + S e N. qua aequatione divisa in duas  s  e. seu nlr ex.
altera p sit  suen. seu ple en eit: lr en H ex. adeoque 111P. seu n p P. Ergo eps L.
sed hoc admitti non potest, feret enim erio. ergo nec haec divussio
pone nerija rprp fsp sre no- suso pr. sit nrl+ rep p + sen+sip fietu;
nrl - rep p) = sen - sEp ertque Z (F) ~ en -le (A ena 
unde miso
Anbruinuus ner pesa
1
sui. Hola enx, - l en le (en t pn (psed en
ilo ex H D ultex
CBi fori non deberlt, quia nondum a generalitate discesim
nisus tit pAB. fer V465  B 4S tundem sit i
reprrs en. sit le eN. fier: Xry + py, r sK
fer V   B Bs + ( V H B2 (3 + 1
fer vi B +divide in duu Ov + B v P 2DBV 1 et 2BRV  DB
fiet; OD - βBH + L et 2V7 dB
eutque Dp +L.P B 2 V. et fiet + P+ BB B aB hi vr B. Pai 41+  Y, .y3B Uux Cs eni fi, quod qunder poesito )
litem sabi opus it 1Y . Y opetu quadinto Y. g1. fei ay. 1 FiYG. Lpsi cs a. Sa s. fer. rosi po  i cot i t ogra H E b
C N 1b ri a
res cgeaec
a + b p 9 + t
exte pa oraeri
b2 4f t et b 92
Sed tribus harum aequationum
quibus libet satis fieri sufficit
ex quibus tribus utcunque assuntis,
semper una erit litera cuilibet
propria ut poterit inveniti
h
Notetur haec inserendi
mettrodus.
a
C + h B a
aex   9 +hi. Crg. C abi gr c Xh)
b +C + d p a. g0 9 4+ d 7 a
n 11