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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 25r, page id 00068197:0049
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Resumamus O aequationem et eme paginae primae W1DrI  Z F 14DGF 2D Z HBDO+,  2O= 0
compendio 12 DG + 11390+, 23 ZOvocemus 10DL + 100L6, et fiet 194 ubi Notu = 1124 + 113 et 10 1 2300
142 1488 + 14. 1448D + 114 DD = 112∞5 = 111. 144. D  - 10. 144 25 - 140. 144h5. Itaque hoc dextium litus
debet etiam esse quadratum, sildensi per constantem mutiplicetur. Eyf  9∞ - 4. 10. 144 5  4. 100. 144. h0
114 - 4. 1. 144  114- 4. IV. 144
Quod comparandum est cum 37∞, DG + sest ergo fiet 2. 10 14.  = a et - 4. 100 144 t 6 = si se
1142- 4. 14. 144
Qu (114 - 4. 11.49) seu (4. 114. 14 - 112, )100. h5 = 10. 144. 4t seu si et
 4. 116. 144 hE
(4. 14. 144 - 1142) 1346 = 144, 1125 + 2. 112. 113. C + 13. _C
sed inde sequeretur C et G rationem habere constantem quod non est permissum
Set si initio fecissemus 1 4 4. M. 144 = 0 feret D- -10oho, Grrot, qui debet esse
integer seu 127C delebet esse divisibilis per N2  + 13C
itaqe praestabuit in faltor, intio statim venire ad divisionem, ob aequationem hajus pugicae primam
si faceremus 1447+ 114D = 0, f et 114 - 111. 144 = 0, superesset D = 100h5: 1otu se et ha valor
Quod videanus au fieri possit
tuea I DD + 1448
 fiat Z - b~  lv + mh, :h
quaeritur ergo modus generaliter efficiendi ut x si Z0 sit divisibilis per bZ + ex fint R-  tath, et dibet esse
erit integer, sec 123GC) erit divsibilis per mQ + 1130
i ut dinisbilis per lov + nhv divsibilis per bZ + . v, id est per +blx + lnitum, pud fiet ergo lnv+ Imto
t b m fit. n = b et In = bl+ ch seu bl = bl + ch, quod non licet, nisi sit c = 0
R eoeamus ergo ad aequationem primam hujus paginae, et videamus a ex qua fit
111DD +14489 = 114 58 = 13DC, :, 112D + 1236 = 3103 + 3030 + 300; 000
410. 410. 144 3 +E. 410. 403. 144 18 + 48). 403 144. CC + 2. 410. 400.144 Dh + 2. 403. 4co1 446h- +. 400 qao 2t hil
sit 8 = 410D + 403 C + 40ch et fiet M AB, :000
et fiet 1et 8.3. 800. 111 DD + 000. 00d. 113
000. 40. 114 DV + 000. 403. 114. 55
+ 000. 400. 1149h
BDD. 112. 310 77 +000.113. 303 9O + 113, 3031C-+000. 112. 300 Dh +000. 123. 300Dh
Redeamus ad aequ. 7 et 8 expressas compendiose, et tollamus simul 44 et 04
000. 123. 310
+ M. 59 +1 YF+ ut ) f + n2 5+ 13D 138O + 12380 =0 2
2D + 14 O8 + 14Y + 1129P + 1130,: 144
fint 144. 223 = 13. 244
ad tollendum OG
seu exsticando 144, 244, 133 229 Ex 24
+21+ D +21282+ 21330,: 21
2a. g2. N. 98 +344. γ1300 + (2314. 4. +525. 11. 4) 04 seu ex a4. 7 t 8 fiet t ( b. h (b - a) (H +hib. 1), g9 (g9. + h (b.c)) = h (b - c) (99 + b - c) h) f. f (5f ilb. - a) h)
seu  100. 144
11a - 4. 14. 144
+= 
=: 212 W + 223 C 4
pel (b- a) 0g = (b- c) ff et ex cgg. 7 et d compositis prodibil L 114. 2447+ 112. 244Q + 11324C + 122. 147
incompendio vocitur  42 F +1 + 42C + 43C; 4 - 144. 2141 - 149 312 8 144. 21C - 144. 2227
 Hinc valor ipsius . substituatur in valorius aq in aequ n13 + 19+ XF + 1 B Y + 1I2 D  + 1330 + 130 =0
en compendio 31. DB + 214 8P+ 3147P+ 312 D9 + 31380 + 34907 = 0
24. 5 22 . 2138. +223
372. 41. H.. +344. 92. 128G + 344. 43. 438(57 F2. 34 45 41. 1  C + 2344. 91. 4310 +2 344. tr. 170g
114- 4. 11I. 144
314 414 311, +
1. 323. 47 44..
 Videamue quibur casibus efficere lieat, sit  Y(22G+ 59300 + 5. 23 8D) extiribilis, posito d et D esse sumplices
H4. 4g. 42
rationales in capitulibus sit b2c; +63(C 460 = 0 seu  = 630 + 69: 62
2.52263.60 -5236062
1(+533.62, 62C0 
=523.69,6300-5236062. Ch
potit . 60 + 32. 63.6 4 5 3, 62 62 - 519. 62. 63
et ee
60 + le tee
 qu (. 2. 522. 63.63 - 5237. 60. 62)
4. (522. 63. 63 +533...)
cur. 60. 80
 522. 63.634533...
fit P = 2. 52267  53 - 523.60. 62, h
522:63163 + 533, b2. 62 - 5 23. 62. 67
fiet qu (2. 522. 69. 67 523,60. 62) = 4. 522. 60. 60, 522. 6363 + 533662. =523,.60. 62
seu qu 63 (4. Su. 6 60 F32f. 62. 65 - 4. sir. 5r2. 60 62. (3, = (1. 52, 65. 60)1 . 522 533. 62. fo - 4. sir. 123. 68. 62
Et divsis omnibus per 52. 60 fiet (525 - 4. 522.533)62 = 4. 522. 523. 63 + 4. 522,523. 60 = 0
 4. 522.523, 63-60.
c
 523.523 - 522.533
seu Sc= 4. 122. 527. 63 - 4. 52 2. 523. 60
Alliter 12027 + 102 vV + 112 3V aequandum quadratae in integris simelicibus capitalibus sit  00 Z = L 1X + 10h 0ov - 21C + 20
ite ZZ + 10 12 523 - et 2. 533
fiet 120. H. IIXX + 120. 2. 11. 10Xh + 120. 10.10 hh, jam ut 30XXF31 Lx +3Chli  sic aequesur quadato, fiet
102. 2. 21 un + 102. 2. 21. 20... + 102. 2c. 20 
u nn iami v.  
303. XX + 30, 21 hX + 9 31 3 h = 4 3. 3ebl - 30. 32hh
30. zoxX + 30. 7C hX + 30. 3 chlr et AL 31. 31hh = 30. 3eth
 nopod  tet
522.60. 60 hk
302. 69. 8 1 t se3. 629