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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 423v, page id 00068196:0842
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v-12 sm + estum v + af vB + ag dalot esse aequalis quadrato cujus latus ap + GsIm
a-
+udUlmm
+ 123F un MN
rafvo. +
aLm
+ 4. 112. 123 lmm In C
4. 12. 123n MM VIn
+ 2. 112. 123 af M rin
+2. 12. 1233 a mm.
et m Umm +612 us Enmm +1Eaflm + ag = aa pp + En 49
129 inmm
125 afn M
ubi substituendo valorem ipsius B, siet
4. 1. 125 np  2. n usasnm
Hac aequatione divisa per ln, fint comprndio 9 u ar 49 =  ideterminatis,
299= ar quar- 4c5). Et quia q debet esse ration.
et
eb etiam 29q erit rationalis in ipsis indeterminatis; adeoque   Caarr -44 5) debet esse quantitas rationalis,
quidem talis, ut ea addita vel subtracta respecto ar si proveniat extrahibile, ut tandem in rationalibus
determinatis habeatur q. Porro l, m, n debent esse quantitates rationale
m, et si
n
implae, et ideo
im quarta
et n possunt integre ltohalitar e ica possent L m, n, tamen res e  praestito res reduci posset ex
etiam l, n rationaliter integre simple explicari possent per n, quippe per quam X sit explicari so test
Hinc posset fieri l= 10M + n a et n = 3o + 31 a et ln = 10. 3o mm 4 10. 2, a M + 11 31a a. 
in mm = 30. 30m + 2.30. 31 a m + 31. 31 aamm
1p = 10.38 m X 18. 3Bam + 3.
ArOu. 10m 4, 12. 10. uan + 1t umamm
ar.
13. 30 n, +2. 125. 30. 31 a M 3 + 125 F. 31 31 aanim
612 nJ. 1930)  6.1E. 13. 10. 31 ar3 +B. 12 125. 11. 31 aa mim
16. 12. 25. 1. 30 an . 10 a f rmmt 112. 11 a F m
m qerolia pus
+12330. af mm + 125. 31 f m
2. b. 40. 0. 31 a m 3. + 0.l1.30. 3 aamn A 11. 31s1 a
(4. MEAS. Eo M + 4 1 .19. 1oIam Z. 1E M J. 16 1 SIaaN + 1211E. n5. 1011. 51am + A. M. 13. 13 31 atm
gtens odon
i l hs o s ari +n. 16. 1 . 10. 3oaa n 6 4 4 l. 15. 13. 31 a m r
. l l 16 1 1 15, to ti cum 24 4 112, 123, 10. l1, 30, 31; cum 123,12, 30 31, 10, 1
ue 1n35 6 o  d. f. se toe ta estatit
m si umm mnneactm ra) aqq = sa euillut anm  i s 1)  20 X + 2.2o nX t 2. 20 vaarx ger.
 12 pnnum 123 afn M
6. 1rE. 13 Cnmm
xrationaliter integre simple explicari pet
assumeretur velut X, per quam
ln = 1830m + 102
niuion hon aam 1n S. N. Di _n
+8. 1. 2f. 112. 30 aa M
14. 1 a8. 16. d0 af M + G. 12. 2J. 1011.30a f m 5 + 4. 1 23 pi. 3oafm L + 4. A2. 18. 12. 5. f M
+16.12E113F 10 HZahtaamB
+a 1E. 1232 16.31 a f M + 18. 112. 125. 10. 11. 31 ∞ f 1
idem rarsus, nisi quod permutari debent a, 123, 10, l, 30 3l; cum 123, 112, 30, 31, 0, 11
+qrapq sn
46. 112. 12s bn MM
d
12 aF R M
0 = + a app
+9q ln
8.12.5 n m adeoque
2. 10. 11. 30.30 a + 1010.  mm
H. 11.
+2. 10. 11.30. 31.
Un = 10. 30 m 4246. 11. D aM = 1I. 30aM
+1S. 3F amm t2 1O. 11314 n  17
I = 1030 u + 2.1030. 3, am + 103i a m +. 11.3 a3
11. 302 amm t 2. 11. 30. 31a M
saciamus _ q 10m
(112. 123. 130 aM
+ 1E.123. 10. 3042 3 1 ~ AL. 13. 103  es 1 + 12. 125. 13 a7 M
un -1o ma tu. spsem esiaa
ln.
Compendio fiat a5 = 60 n + 6) m + b2 aam + 63a m + 64 a m +65 a m + b6 L m + 67 a m + 68 a
comprudio fiat = sem 40
a3Y = 50 M  + s1 a M + 52 am + 530m + 54a
So M E+ 2. Go. sta m + 2. soma ni sr soss aur2. so. _ an
5ISI. a m +2. Sus2an t2 31. 53 an f. 251 59 am
75252 a n + 2. . 53. a m + 252. 59 am
153. 53a m L. B. 5iam + 45ta
compendio fiat
ar=
(1E Im + 125n p. + aB) Lmm F. 2. 12. 115 lnmm +2. 12 ar lm F aarr Svestmm +2) + 4 u2. us si un t 1e emtag. 149
es arntr
ap= 1 lm + 123 um tar = 2113. 1g lmm + 112. 123 fm-: 9 seu uiti
e
velmqus 1 . (2. sa nnon.) 2t. rs Cmma + vr. 13 asm brmf.eti aa)
B. p3rEL
sit q tm:a et r= sin t adlage, et prodtunt hae duae aequatores: 2.B stnter 2M a a iaq p 1s snop  sparus    ii la mi itus u ag. betftiaa)
a2 t: glimm, + (t: a) smyl a(t. a) a sag= 2. i. 13 lntr turrs apt 2. 135 snmgs + 2. n ap
13 t. a) tm
Hiac duae aequationes ad m.
2. 112. 10. 50 m + 2. 15. 12 5iam + 2 13 ustaam
190
50. 50 H + 2. 5a51 am
A. s.Soion en
12. 9
n osen
indaltiin  nia taq a
saaco
cis te inor
125 a Ncap. 314
+ratag st a
ii
et s = 10. 5omm 1. stam 4 nsiaa  sa = 30. 50 min + 30 siam + 31. 51 a
An sieprostel. duae aequalionis sunt 2. ir arlm 4+ aarr = 9 102. tigrlarum + 112 astem + a9- b  44
et n= 30m + 31a
S=om 151a. fint A5s n = se  resanitsian
et aegla Farq= 2. ud 2glum rur rasm sed ita encul g aqque pant i  tistius etc l m
t purata e fin sm  t sit anen tme ne    naect atm