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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 73v, page id 00068255:0146
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(10) Has 4 aequationes articuli praecedentis aliter sexprimemus, est autem 1121 = 12. 513+ 113. 51 2.
et nyis 13 83+ 1g 323 et sit 12 5=
.sit
AD 123 = a ab 133 = c+d 131215  a- b 533 = c- d
122. 51=C
31213 =+6) sit 112. 513 = a  134612 = b 312. 713 =c
123. 513 = (a) 1. 113. 523 =(6)
fiet 11213 = a + b 13(3 = (a) +16)
323. 713 =()
4 323 =8 et fiet
31213 = e+ d 32913 = (C)H(d)
S12I = a b.  52313 = (a) - 1(6)  X213  c - d 71313 = (C) - (d)
313, 712 = d
313. 723 = (d)
Hinc ex . Articuli 9 aequatione 1. sit (a - b,: cud = (imo) 112: 312 a
S (1) -6), 51 ( (3) = (2d0 123: 323
a + b 3:, etd = 3tio) 312: 712
(4 (b), : (1 (d) = ato = 523: 723
ex ifit eud = aub, 3t. 12 cx3 fit E+d = atb, 712. 512. Ergo 2C = (6t) sa b) p12: 12) + (a + b(712 :512) Et st
et ad = Cto) (b- a) β312. 112) + (a +b) (71  (612) et pari jure ex 2 et 4 fit 2(C) -. (mo) ((2) - (6)) 383. 123 + (a)+ b)) (23: 573)
et 210) _ = (8B0) ((6) - (a)) (377 2122) f(a) + (b) ) (723: 523) jam c. 312 = 713 = ( (C): 323. Ergo 323C 311C)
Ergo ex 5 et Y fit, (a, b) (3e2. 323: 11)  (a+b) ( (71292Z: 512) = ((a) = (6)) (312. 323 : 123) + (() +(b)) (312. 7231523).
Et eodem modo 723 d= 7121d) et fiet ((b- a) (312. 7 3. 12) et (a + b) (712. 723): 512 = (19mo) (6) (a)). _ 72 3 A(1 +(b )) (Ep2. 313. t
et ex aequ. _ et 10 et 12 poterunt inveniri a et b
compendii causa scribumi oe  ex  bgo + (a+ b1 = a (a. b) 1 3 + (at 372
pro aequ  b7 331  (476) 73s (a -b) e + (a+b) = (13tro) ((a) = (6) 9 + ((a) + (l)) h
et pro aequa (b- a)  + (atb)  = (gto) (1b) - (2)) 7 + (a + (b)) 12
agus 1y milliplicetur per E, et ag. 14 per e, fa et addantur un anjum fiet
sambE) + (t6) 52 ((a) - (b)) gC ut (a) +67) _E  in conjungantur jam a et () item b et (
e
b et fiet
tex 19 firt +a e + af (a)o - (a h  Ab e = bf - 1b) 9+ (b) h jam (a) = ~r 123a1112. 
(b- a) e2 + (a1b) g (B) (1) Ve + ((a) + ()) it
ex 14 fint = aE + a∞ + (a)V = (a) 1 = - bE - b 8 + (b) γ + (b) 
(6) 18) 523b : 512
ergo ar ob 17 et 18 etraque aequatio, is et 16 multiplicetia per 112. 512, et pro (a) et b) substituatur vald
fietque: +12. S1 a + 12. 512fa = 123. 51Z Ga= 123. 512ha L) 112. 512 ed = 113. 512 fb - 112. 5239b + 112. 523Ab
112gG. Sit 343. 71L. 123, (7a7 13: 523 1(20m0)
 tC Ea L m. SiGa + 122. 3ILya = 13. SIEBa,   12. S12Eb, - i. sm gb + 112. 523Y b + 112. 523, 1b
112. 7:1IL
unde ex agurg fit (129. gt2. 312. 313) 4. 112. 323. H ( Gr EsBir. 125, 12S 5 t2. 312. 723, a   5 2. 523, 312. 729 -- 1121513 37 p , 1. 515. 142. 3 + 12. 123 53, 312. 723, b
tex
Hic suspectum mili erois, quod 23 sepius reperitur in mentris harum duaum ag9. quam