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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 19
# Folio 1v, page id 00068268:0002
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quae est, 23β - 88 58. ( f7- 1. eA substitiendo valores ex aeg. 126. 130. 131. fet
eti _ B :  id BN fii ( d5
is
3132-1
quo valore invento in ag. 132. substititi, erit 2 -  - B = 1 B B - c l7 et omnitus ad comminem
3B=1
3B=1
divisorem abjiaentum adudis ( e ( aC C 
2
2 B - 3B + 1, - BF + B - 1,- 5B
BE (B. B57 - 1. reducendo ad comdibis
2B - 2
21
( B N C BC D- p . N P(= n (B 9. 1. adeoqu BY)
sue BF 1 + p a t.  Quo valore ii aeq. 133. inserto, fiet:
2
e + B - 1 B +1
13+- 4 B +1
EDZB. L _. B6 + 3B- B)B  (27),. et reducendo ad com. divis. fiet
B4. 4B21
14- 4 12+-1
CN  +B - , - B2 16 1 C1 1L 1EB)
sed hoc abtandum deberent enim omnia destruit Ergo essol commissus in aliqua ex hris 124. 125. 136
redeatur ad 134.  reducendo ad Com diris. fer: ( β1. ( B Be(B (+ 2 BD - β, - B 9.1
in ex ergo erratum quo et βr
in aeg. 135. frei 2B- 2
B4 B porsus ut ante quem valorem β. inserendo
BE + B B + = 15 + 3B4 3 B7. (118) 1. i quo janis
37.
B- + B+ + B2 1
co, agratinis
adeoque reducendo ad com. divis multiplicatis omnibus per B- 41 + B fier
2, 12(, 2B, ( 14B (i) (= 10 (3 1, ND) ( (p ex + BB) ubi
omnia destruuntur, adeoque de a ipsius calculi re inento certi sumus hue usque
invenimus B _ aq. B5.  ra autem BN L. ex hB F in et  5 . et 8, B = 1
per a. 126. 129. 130. 131. poro supra aeq. 107. et 108. f invenenamus
 Vi 23+ β. 28 B. orrurue vp 38β 1. nn satisfieret scilcet aequation 45, quae
1e
3- 36
 eret: Bv + (v p, D. ( 4 1. sumendo scilicet 3(2) v. B. aequaliane 82. ubi an recte
1- B1
Calculatiu sit,  pro valore ipsius V statim invenimus, sumita B quasi incortarta et valore ejus in ipsius B
 valoibus substitato nam in posteriore valore ipsius v. fiet vB B - B3, = 1 + BV
v
sive multiicando per crocem (o d D. 8 ( ( D H (D. B V- 8 v  8 B. qud cum
B - ( V - B2V +O3
dicta aeq. 45. conicidit. Tunem ipsius B vatorem aq. 39. substituamus in prute iasi V valore, fiet
2
1v 11 B0 + B - r9B +. vβ8β- 58
2BV + B1V
+_∞= 2vBB+ C 
Ev . ex pB- eC 1B  ( Ap e (B D ipeox. BBB
nv. hucip
 et 20, v. r 0fe0 
1 = 1( + (  Uite revendo fiei ( 13, + v. B - v B p v - B + (B v + v (5 B - 8 
quae aequatio dirisa per v. β, dabit vB 1 - V + siB2 quae aequatu a quae rupsusaum
conncudit, itaque calculi  securi sumus. recteque duos ipsius Y valores inven
Et notabile
hic, quom odo factum sit,  ut altius assurgeretur, et depressione esset opus, ad
opendendum calculi prioris cum hoc consensum, com tamen hoc modo videatur aliquid novi
E introductum omnes enim depressiones alternativae, itaque si calculus 81. 82. 83, 84. 85. 107. 108.
xaconsiveretur, et cum hoc exemine conferatur, necesse est apparere, unde
E assurrectio ista orta sit Nunc in valore ipsius ∞. sempliciore, inferamus inventos ipsarm
 B. D. β. valores. eris 
(ent 
1 2 b-ie - 1 B LI, B - B B=
3. DE. 4B+
S DB B = 45 +1
B  1 B+CBR +B+1
5
adesque tanem VZ2 B -1. idem ipsius V rator gdhur semel reperiatur, inserendo
valores Z. β. B. in pros
coresuperiares nemne lsin
-D= 2B -1
B7 q p27 p a B, nC
1+ i sux v B+ BC 14 B. B2B2y. B8 ,
 t
Dq
ui polet nomi od torem pontbers a amgseratorem qui di posse per M- 1. B: 1  13,
VHX
1 B7+
priori, necess e
B
1
2
A. Qui alalus cum don consspliat
in alterutur fuisse endem. Et video sam in pridae calhulo
mesertaser e d. 140.
ergo reducendo ad com. derom. inaegstq
fiet ego md S  (17 D 1, + 13  3B 1 (h43B1 11
(N41, B.1,) 1=1 B 4N 21
hoc V r 18. 2B6 - 2B4 - 2 B41
BE,, B= +M=1
1- N - B4B1F B+ 2B
1
1 - Y D C  13β ,1
B2X +34 i
BS. B: B. 2 1, 1) B4
m qic
 ex 139. est Z Z - PvZ Av- B.
Ergo  X + βF v. et explicando:
1
HE, + D = 1( ∞, + B=, (3.
B+ 4BI D: aV+ 1, B. 1
seu (B 3B G.d+ B.. ( BB
B~ 4 B B W CE dB FiM
seu v. (8) B4
EB.-
ve B+B(149391 - +B 3
1+ β31 β. x0 multiplicando per crucem
) BB + B - 318 Z8. S po  B( - 1, + B38EB3)
3- SuBpv. B.
sed hinc prodit aliu pline aequatio, quam quae produt,
+β  v+ B8V alios duos ipsius v valores aequando, quod quomodo fiat
v7 3+B
1+βZ
equidem miror. Haec praecerea aequatio, 50. ita comparata
st ut in ea ultimo termino secundum B. destructo, destn atu
et penultimus. Latet in his aliquid, quod evolvendum est
fut B3 - B (. - pv. fecimus et v. β  B +- 3B. Ergo (52)
83v+  v.  1+ BV, (- B_ unde sequitur scilicet, vel esse BV p 1.
3C p
vel esse
83, e+ β , + β0. si BVH) erit et
v
d. pa 2. seu v  B. fp. 1. quod
ide
costat
et v 3+ B. at aeg. 153. dabit 30β-1
mulliplicando percrucem, fiet aequatio. B150. Z(3+ B.  BB Bp. 1 1  3
sed mirum varia
nempe 109. Di
haec aequatio cum, 82. fier 213
5o
fier 10302
1. + βV + 3B= 22 3V. et v +
B-30
est nisre est cum alqud El smaber
 novissiniam
multisli recur haec per 300
valorem aequando valori 1_7. fier (D = ~(= ZB) 280 7 3162
quae tres aequationes. 
.
quem
23D+873-86,
ia i  gi dut tei
1 A3B eo
flat exeum nandum
11
tinie
2