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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 125v, page id 00068124:0252
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 126r); this page is its left half.
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a+ b aqu a + Z a b + 2. 5-1 a b + 22 2 a b + 2F12. 723,
sit Laequ L. fiet.
Si Zaequ  fiet:
in decimalibus si addas
duplum orom esti
1 + i
3141 + 3, - 1
4-
12
1, 2,3
X 1672
1,23, 4
asy 5
4 4
ab+ 2722 a b+ 2Ea
+ 2567 2
n nominatores progressionis Geometricae triplae, et ita porro. Quare utia est in numeris adhiberi algorithmum dyadicum pro extractione
radicis quadratae, ternarium pro extractione radicis cubicae. Et nihil ominus semper apparebit ratio transferendi ex una in alteram,
Caelerum ex his etiam apparebit quomodo nomina numeratores procedere debeant
- 1
1 + 008 aequ 14 0001 A = 0000001.
81
4 0000009001
10
24373
 ese
d082304537a
aequ 1 +000051D8DB. - 0000 0BD12500 +00000000000b250V erc summa
+ 280
1d C)) 8)50bC
sit l+ e. cujus cubus l + 31 e + 3le + e. dividatur in duas partes l + 3le, et C + 3e l. ex quibus prior fiat aequal. a. posterior aequal. b. et quaeritur (7) a + b
seu radix cubica ex 13+ 3le + e + 3C12. id est quaeritur l. e. Series proveniet hujus modi:
3+1 + e
er. 25.
80  se
B) Pt 3e ( 3el
mtn aequ. 1. 01
m +n. aequ m + 2mn+ n. sit maequ. 1. et n aequ fiet: mn aequ, 1 + or + 001 aequ 1. jam, 2 aequ 10 fiet 1 + 010 + 001. aequ 1. 011 quod est quadr. de 1. 01
V + 21 laequ. 1 + ot aequ. 1 + e2 - 00 441
10601
10001000
avs100100001
100100001
10001
100500001
l
1+01 sit seu + + et 1 + 0110 + oi ( 1. +  1 + 0b1 aequ AB. t 1001
Y 1 + ou aequ. 1 + 001  00 001001 + 00000011011 cu equ
(10 equ 10 00 t +
2)raequ Y10. aequ
10001
. 100 1000110001
6
dobodd
0011b00101 f+H
Y 10. 01 aequ (, 4101 aqu , + 0101
Nhabeatus una Radix ejus _ R - p R - q. hunc
subtuhendo a priore fieri X R3 - p X + pR aequ. 0.
+ 10010001
- 0000000100100001
= 10010000
00000vVOVVOIIe
dividendo per X -R. fiet: X + R X + R aequ. 0.
et X aego +RX + p p - Z N et x + = R B Y p - 2 t seu Xp Sp. 2 f - L R
At aequ. = 1 + s.3 Exgo E si jame . multipiretur per 3 quia h. 1 idem quod R.
recte multiplicari potest
ero et Yh, idem quod ith in c. ergo quia S1 nes habet valores unum 1. alteropndios - 1 4+S.3
etiam 3str duos habebit natores, unum h. alterum Th in  alterum YE in =1 + sa
Hinc quique 35 + s- 2 aequ. - 1 +. s - 2. multiplicando per - 1 4 f.3 fict: + L 4, sa3 -+ s. 14 1 s6
5+ f- 2 aequ. L + V-  - s.  4 (3 Eodemmodo S5+ s. 2 aequ- 1 + Su2 nulti per - 1 + f.3
5 = S.2 aequ. L = s. 3 + Y-= 
+13
Ergo 25 5. Y- 2 + Y5 - S. 2 aequ. 1 f 16. quod
em, nam extidendo radice eu his duobu binonous X
i
1100 ( +qu. V + 0010001 aequ. l _ + 00010001  = 000 300O1001000D1+ 0000000VVV1001000110001
x - g X - pX - quequ. 0.
ve
 2440, xqu. 16,
+
unde puto nominalores semper non alios forequam progressionis Geometricae duplae
+ 3
 aesi atb 3r an BZa
fiet:
10001
000
seriem infinitam prodiit: 3. +49 ex) id est 1+ 16. est
curtium binomium multiplicandum per V =1 Sad
 rarilibus. Regula vulgaris.. ne
72913
+10000d00000000000000
+ 0000500000
0000000 125000
00
At ∞
00
+ 1
101 c
10
0001
101