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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 71r, page id 00068255:0141
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In aequ. 1. aitenl praecedentis 16 poterit expliveri U1213. 1L313. atbu Seu W2 61B in 127. q = W121a5 31E + 22. 1. S1
Ergo H213. 1231. ADCL 112. 123: 113 = 112. 125 . 513 + 1223. A ~. 13. 513 + 112. 1B. 512. 523. uside explicando fit
M 125 38 - (12. 123 bb 2. 
Mo3. v2. 123, 513 = V quh qu e. 12) b. it )
adeoque tandem u2Bh. 12313 = ubb. 24. q, BC. 16h + g, 1152
posu asu satorn qegit 
g33us iht Bhh
 Ahl. 9Y (-29hater. 123, 6. E
lit f. 28. in trillnst _ sit b  ( y . ur 1es Ul mol:  t 192) N au. D8
A, 162+ +. VY
sinricin nud 2 2t 3 ila omestandem irrationales ex calcude sunt sublatae
sed absolvamus penitus aegu. 1 et fiet
Gat  M no s s V 2h+, ihaf = Eh + fa9 et fil (Em) me n2. 123,. 512. 513, 2h -f
rgo ob et ex 9 et 3 fiet
FB(12. h23. 52. 123 = atgg: (11 123. sn 525 ta 9)
An sic potius sit s ut e artie 19 aeq.  vel s ut succedat extractio fiat 2h+f = (guo) 13. 523, te  d: 
(ob en artic. 14 aequoo, ut sucxat exi
i 2h +5,  g9 :tfiol f. h
123 1 (13tio) (11223h = fh+. 5) 49
ergo ex aeq. 3. per y et 10 fiet 11223h = (4mo) 112. 123. 512. 523 ad: R, bc
Et duos ipsius h valores aequando   et i 
siet 112. 523 2ibb) + 123. 51 (CC) +. 1. 123. S12. Sig ((. 6y 4 ocC)) = 4 H 13 f12513 (D. bc
fiet 112. 528 (1: b6) + 123. 512( : cc) + 112. 123. 51 2 525 (1 : b6) + (1: Cc)) = 4. 112. 123. 512. 323(1: bc) Unde
faciendo H2. 123. 51 seg ut jam determinavimus oportet
ras nec quicquam h
set si  24. videtur hac aequalit
auluusus heris
112. 523 (1.6) - 11, 312 (1. C) = salua no vi b. b) e
facere aequalem quadrat
licentur in ea f et h
ad quod postea recunitur
et (10mo) 123. 512 = 15. 2312: a. Ergo
ergo praestat statum facere ob aeq.C
(1Imo) 12. 129. 512. 527 = = ( 152. 14232. 2312: aa et 1 - 12. 123, 512. 523 = (12 mo) (1B 15. 1223. 2 212: a
sit ergo (9no). 112. 523 =  e ex 415. 12523: a
exaoqs et 51223 = (13t0) 15. 18237: a + 15. 332.a et 11223 = (14. to) 15. 13523( a) - 15. 23s1 2L. a)
iter se percuntant officia, et cum i 51223 prius contineret + et =, sed 11223 tantum +, nunc fit contra
Ergo in aeq. 4, retinendo 112. 123.
513: 113 = (16t0) -(15 : 4) 1825. 23str (= (15: a) (1825 = 2312)), - 2 4 (1225 + 2351 2 , ., 12523. 241 2)
fiet f: h -(1560)  12 5t + 2 32, (152) : 12523. 2.3 = (1514)
(17 mo) 513: 113 = (15: a) 1823. 2342. (12523 623)2): aS B1) 112. 123 (12(23 + 23)12)
suppono autem 5_2 et 52
513: 113 Lae quationis 4 sic
Sed per aeg. 15 et 5 - at ot = (19 ab) 12 .2 HE :, 13  B2
Ergo ix 18 per 19 et 9 fit 12. 513;, 113. 512 = (15∞4) 12523. 122Z = 2212 :, 1sL 3. 2g2 (15: a) (12t5 - 2342)
inveniri per 112, 113, 15ca, et r2z et 2712
112. 513, :, 113. 512 = 112. 523, (f = 2h, : h): 112t23
123. 512, f - 2h, : 11223 = (per 10) -(3: a). 2412 (1323 Lyp2. 1223. 2252). (15. aB, 122 = 23E)
112. 513, 1, 113. 512 = (20m0) (12523 : 2392), 1223 - 22423 :, 1243 + 2312
(2205) 123. 513,:, 113. 513 = (2212 12) 2 22 s s
123. 513:, 113. 513 = (21mo)
ii
Fajesi) et 31223  . a) n  (37 : a), 12725 - 23712
  t 
aa et 71225 =(41) (7: af, 12725 + 2371E
L 3f. 1272551533(. 2123 - 23712): (12723 + 2371331253, seu
312. 713:, 313. 712 = (3mo) (12723: 23712), 12723-23712, :, 12723 + 23712 et 323. 713;, 313. 723 -(800) 23712. 127 25) 23712- 12723, :, 25712+ 127 23
et (2do), 373. 712 = - 37. 23712. a et 312. 313. 712. 725
A     apiai ure it
et 713. 313 = (6to) -(37.
aeq. articuli 12 designaitae articuso 1
nat = (5to) 0. quae ne habeatur v: Z divellenda est in duas, et fiet
163 Hinc jam _ at quia per aeg. 14 satis fecimus extra ctroer in. et pari jare 312. 7126 + 323
L51223 YEptC13. 1213 3Z 4 7 122N = (4. to
fint + 12 Si. Amarev + iy 123. pa  - s, tA B nde l) Msir, 1, 3nop2 = 129. 523,: , 321. 723
in   3 1)o et
non
6, 7, 8 duae sufficiuct cum ter
B_AA, :, 721C)C= ubi par  per ag, 11 articuli 14, et autre. qu. 3 artic. 15. apparet utrobique
M2. St. _, :, 312. 7 12BL sra AC:, nBA  Bpu) 12 1. 52 3, id) 2 H  a q
V9( 1121612. 323
123, 523. 312. 712 quod institiariam multiplicat
onem et fet: 5 ed) n. SC2. 12517 13. 15. 125
123. 523. 3I2. 712. nt antem ae quatio
seu 113. 523, :, 5tG. 723 = (1mo) +) 5M, :, on3 H = 112. 512 s’ podit au
2  im. 527d. b_) = 127. 512 tCC)
h- f = (0 mo) 123. 512 ad: E
feliniter exenit extractio
cc. ih. 33 t  s et C 8. y. Jnda  aa b.B, B
et fit (u2 23 (l mm) 16)  2h +, D.
pari pre 31213. 3231+)X
Th 112. 523(: b) + ,29. 5121d: C2)
rachonem
Nita redimus ad eq.t
rst
compuno iasrevhrn
t 12. NS. SM. 523 - -1b, +hil. 1. 
Seu (1m0) S1 = Au 2. 123. 512 125 = 11223 112. 123. 512. 527, - 2, ME. N3. 12 S3) Ergo Aa3 esB3. M. 13. 13 = bb. ih. q Eh.  ist  - 4thr 9- +h r  chi q -  n.  pats. it il g.  . q iB
gutrus 2 l122(71227
 AI: n B
i. 12) en 13. sedium
Pit pari pec ex ajo.  alriansous estpis
3. 113: 
 iu
a 61q 513: 113
1122
112713023712 = (10 mo) otu M.
Sed quia in s, continetu
alitiome et pcab
ilimque duae aequaturs. ies. 2Eu (F
peia
ant rediietionems
 ungur rto  besetes
byg. 10 et 12 artituli 10
1527) (323t723) i E 23. 112∞D m (am
3t 2 V2. 123Si, DI2tII
 ar it si-
 H2. 1L 3
quis duo valpres equandi,
surds otro
2123 (123+523) (327
mysore dis utia nm  aspro, st q. L, v  
nnon, mesusat.n) iss
 ters, et exrqoe
32g  is iti n situ ubi 
n ot mua antu ititand aeuaa ad
Eex as per
ome 713