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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 68v, page id 00068049:0136
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m h, 2a + 2ohaa L, er5B M
ov + ua 2 = 20V + et a 5 = 30V + 3a O = 200V+ -01a D = 300v + 301 a
a=motu Zica i mote
axx + am = ) a, ga t 2130Y48
axx + a = L a, Dat 3130 16.
denique sit
aX =  Ex6sit aXx = 120. k2 + 2. 120 20 2 _t6. quo valore suesituto in aeq. 2. et itentificando
fiet 112044 et explicardo sigao aequationum let notas aequanonum l2,3 , f denique
F1120. 1020 vV + M2D. 1an X +MO u2Ia = 2. 1120. 1920. 20V  L f 5 + 2. 120. 32021a 1ti6
13c6 coefficientes ipsius 
Ex aq.2 fint
+ 1310 50.20.
2150 1 30
110. 3a 2120 +1328. 312)aa CL C. c. 2
ei   (10)
200. aa vV +220120 + 20i 
ns+ 
+2200. 2130 aV 1+8 +2. 201. 21 30aa 1t6
Quam equationem faciendo idetitatem assumendo ut identitatem
fiet ex identificatis terminis irrationalibus 200a = 1170. 1320. 20: 2130 et 2014 = 1120. 1320. 21 : 2130
E+ ex tatorulibus 26 200 a + 213, 5. 10. 30 = 1125. 10. 20p re d. 30. 20 2 138. 11 31 A C E m = 1120 121 20 321
2. 200, 201 a+ 2130310. 31 = 1125. 1021 + 1328. 304.
valores ex agq. 11 et 12 substituamus in aeg4. 13, 14, 15. 
Ex 13 fit 1120. 1320. 20 + 2135.10.30= 1120, 10. 20. 2130 + 1320. 30.20. 2138
Exerfit. rureoast. at 1128. 132. 2s  + 2135. 1. 37 4 aM. 2130 = 1120. 1. 21. 2307. 1326. 31. 21. 2130
Ex 4 fit 1120. 1320. 27 + 2136. 11. 31 == 1128. 11. 21. 2138 + 1320. 31. 21. 2130
+a n. 2130
2.1120.7396. 17 + 2130t. 10.31  1128. 102. 2130 + 132 8. 30. 21. 2130
Ex his aequationibus inveniamus ante omnia, per valorem, abque tollamus 21302
A Tollamus aut inveni
  aequantem Aequatio autem 16 habet hanc formam  e CX b. 238 +, r. 1130 + d = 0. unde
bb. 212 + b. 2130. C + bd = 0 seu bb. 2130 + b2130. C + CC = L CC = bd. seu - C + Si cc- bd
olaq exari 15 fit 10. 30. 210 = L. Md n  + smonio pe nimo esie ( 10. B1o. 10 50 20C
aa 9 reapse procedit extractio.
tam Hinc pari pire qui valor substituendus in ae49. 17. 18. TatecyHaem autam calculus eut pro
22.1320.3020 451310. 30. 20
Jide m antem calculus est pro aequ. 8 praestanda tantum pro 2136, 200, 201, ponendo 3130. 300, 30)
sed quia valor ipsius 2136, adeoque et ipsi reo et ipsius 201. differre debet a ralore ipsis 310E, quia alioboi m et
 coinciderent si eadem esset aeq. in qua a, (nempe aequ. 17) cum aeq. in qua erit aer; ideo ex duobus
diversus valoribus ipss ipsuis 2130, unus erit pro squ. 17, altera  alter pro alie simiti qe laequatione
2etiam 6q9. 17 et 14 destrimi possent, ut repressa est aequib calculus foret tanto facilior, sed facile
conlinente a.
sed nec pro aeq. 18 procedit extractio nam fiet
10. 31 2136 = = 1120. 10. 2 + L1320. 30. 21 + 41120. 10. 28
B3ed Gay) + L. 126. 13 20. 1030 n1 21 - 2 NE6. 13E0. 10 2 j r 21
n. 30 it unde patet non succedere extractionem, quae successiset si in aeq. 18 pro 2. 1120. 1310
slin in aeq. 20. sit +∞ et fiet
=ae 12o. 20.30 Et exta quale
Et exoq u per nefiel (120) 1320. 21. 307 4 1126. 25. 11 31 = 112. 20. 112I. 30 + (112591326. 303127 20
Eexaep.i8 per 2 fitt (~(iuo 13io (u 30 + i ro an   u dio + (120) 1325  ud 20 30
E2 est 1316 = g2S. , BI 30∞3a2 - 31 20 1. ~7 2. 20. 11. 20. 3, - 71. 30 + ae g. 2030,:, 2.30 B 20. 3) = 21. 50
quos duos varlores 25 et2) inter
120. 10. 20. 51 - 21307:, 30. 20. 31 - 21. 30 seu,  1320= 128. 10: 30
se aequando, fiet: 112O o I_202 10. 21 - 11.20= aa mm. 20)80: 21. 20. 31 - 21. 30
Si in ag. 20 sit 4 .  -. pro 313 , i 513 Ex 59. 20. transmusa ypio aann, fiet 3130 = 1320, 20:10. Undi ex aeg. 17
Et ex 24 est 1328 2
1(2 aamm. 204 X. 20.31 - 21. 30, -20. 11 + 21. 10
transuntasa fiet  120 (132C) c 2I. 10 + (1320)1320, 20.  1. 3F= 1128. 11. 21 (1320. 2010 + (1320) 31. 21. 1320. 20. 50
1126 Cpi r2d. (Eo 0 +710) qa 1320. Ed10
a n(32r0.10
Ex 3 est  112O 1328. 20. 31. 20.M - 21010 + à n 20. ju, : 921. 10. R20. 1 - 2110
coincidilcum aeq. 27
Efex ayifit 1120 = 2920. 30. 20. n- 1. 10; 10. 2011 -  2110 seu 1120= 1310. 30: 10 quae aequat
adeoque (quod utile est) ad  nullam novam determinationem dicit dicit aequand
p  20  olo D_ (per 27).
Caxnn 20. 10
quando jam duos valores 33 et 35, fret 13202. 21. 30 -20. 3]
per 1320) 20.  a n _: XP. W 2011- 21. 10. =20314 2130. 2x29 et37 fit
sed in sed inde fit mpmnn seu duo quaprata in idem recidunt, quod est contra intentum
taque res non successit
adeo depressionem Aequationis 17 non prucedere. ob intervenentem am. alioqui procederet extractio prosuntuau, it
iuteum si etiam
ae (12920. 30
(suplez 12d. 193970. 20. 21
seu fiet
20 1-2110