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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 89r, page id 00068049:0179
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Calculus paginae precedentis viam nobis offerre videtur ad huc
faciliorem, edm scilicet in aeq. 31 efficiendo, ut fractionis nominator vel numerator
sit extrahibilis, quod praestat  vel sola aeq. 35 quae dat bat = + Crr Quod adlo sufficit
Hia
quod si similiter ob nominatorem faciamus bb- B. bbrr- aaH = (2) bbr- pat, ubipro e
at substituamus ejus valorem + Brr: b siet WB - BB. bbrr -Br: bb = 4 (2) bbr AB Crr.: b
seu (bor3- bb BY- β ber (+ p,  b Er 81  Ept, et divisis
A
44
omnibus per 1X, sit 3b + 5 (r = B seu b f- b Pr - Bb + B1 = 4br. b 5 ab p (7
VY. Br -p + seu 48bBr - b (βY - Bb+ = 3b + 3B= Y. Hanc aequationem utiliter
resolvere in duas, faciendo bB p = n B3Cr. seu r= b_ et 8B3 a - pibβ- βb = 3b +3(72
b 3. 9p - p -1 = 3b L 3β2  bB). eu 3b 43 2b46 (2b ( - b (5 1an - p - 1. adeoque)
bβ N4 - e- 1
= b + β Sed haec aequatio producit aliquid impossibile
nam fit bB. 2(B - ( 2- 1 = 3 b + 3 ( n - 63 nb
seu bβ11 = 13. = β. quod evitandum qua licet
3β+a bbB: Y = = B b - 3b
Ergo omissa divulsione aequationis () in duas nodo acto fciamus er = 8B
seu Y - 4b = (16b 37 - 3β - 3β b - p 1 368 β
3β41
3B+ b(
s
3β + b2B
seu r = + 4b3Bb 8bB. 3(L, B
3B3+ b B
2bbβB non minor quam 3 bt + 3β - 6bb (3β. sin bBt2 non minuerquam (+)67+) B2 13
faciamus aequales, ut calculus sit, tanto brevior, fiet: β (4) F2. 3bβ = ( bb: 13. adeoque
B _ = (4)  2 (4) b: 56 p.  (3 + E seu B = B (+) 11 +r 3 b
et Y =
+4b
3β2+6
4b
+ 4b
143G +2. 13 + , 17 -
seu β = (4) 1b1f 312
45
x
B+r = 3(+ -
() 2 (+) 1216 +136V2(D1812
et =
(414)
s
3
s Hetds
3
bbrr= (+ 1(4) (4)613
V6
et at = bb  (4) 16(+ 116 13
b Ad =.-
16 _12+) f)613
bb = at = (+ 5 16(1 912  bb
L) 1816
B3 = 1b 241213 = 2+1B3 bb et bb = βB = 
36
4(+)(+)213(4.
bb
1+ H.3. 
8 312(4 (+1 18013
aat
8
104 + (+ 60 8
27
bbrr- a a H = 36 = _ 104 (+ (4) 18 s3 (4) (4160d34-- 63(+) (4) 42 13 s
jam multiplicentur invicem bb = AB, et bbrr  aate, fiet: ( -19+ (+ ( +) 110 Y3 
oportet ergo esse (+) = (+) et sed tam quia productum hoc de set esse affirma-
tivum quispue quale quadrato 4 (2) bor= Bat. sed video hoc non
succedere, quia 194 major est quam 110 13
1)
Calculus ergo resumendus duae sunt aequationes una: bat = + Brr
(3)
altera bb - BB. bbrr- aau = (2) bbr = Bat. seu bb est btr bat -t Br - Bbat
seu B B: (p p2, (e per  B2  quominus error surre pat, adhibeamus
ubique numeros sit b = 5 et at, 184 et BA C et Y, C; 3142 fit 314 () =b266
ubi in rei veritate est (61, hic vero numeros supplet G  6b. 3322- 1144
porro 33 =22. 3366 -1144 =(2) 336-214 - (576) Hac arte ubique
instituere licebet probationem per abjectionem novenarii, aequationem 2, utrobique multipli–
162
Cabimus per 33, et tum pro 34 substituemus valorem ex aeq. s. fit 53. 22. 33336b - 331144 = (2) 3336- 2314  h F iiq ng4
seu  (3666- 39 635+26.6)- 22566(+ 267: (6)  566) 13626) (26: 63 308
st deprimendo pit 3322bb fit - 66 : 67 - 33 = 4 136. (6) -576) 4 6 17033 (1548 4b
omissis jam fictitiis (6) et (576) fiet 66 +33 4 1) 36 =0 seu fit 6 = 8_ +3
seu fit i ergo at - r = + b et at = +βb (quod si Br = at esse debeat
fint +BV = + Bb, et r = +b, hoc ergo succedit in casu Hyperbolae) substimamus iam
valores inventos sit numeroter exhuohendos fractionis: b
X 2bSXX + 16 1a
num b +C NB Minatornit +bb XX + 2b X + b4 + 2eC B. +ee BBBE
eB
et fict
(B
ssm
a
Eao = ex (+et
Ae(b. = Bbb Aubi rursus surcedit extram hio) 1B  +ee b
st teced bHC
Xr + 2bX +bb astr. B +) Hoc mido quod mirum est tota fractio (F
2
IX
3
dit50
16L 575b4(1b
estconstans. deu de integro exteriatuur.
fiecet ∞s, 3. 2 quod absudum hoti
17
seu
+ioqe
e
reo
162
12
60
60 42
6470
120
92
id
308
8 194
Ab for
184, 40ode
2(16 194
40. 194
776
1746
194 5