Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 65v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.79.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 72r); this page is its left half.

The machine reads it as

1. Itaque ex HvD H. 31 VY + 123. 5232y = 1G. S1Z vZ +100p 500t U-mm
2. HB. 51, 13) i. 523L H3. 512
3. 2t513 3 5 1M223S
4. Hmm) 11223. 5123.
5. 10rb destructis jam irrationalibus in aequatione articuli 4 restat in eadem aequatione pars rationalis
6. 112. 512 vy + 13. 522Zy + e) + 100 p. 500 F + 113. 513VZ =nill oum, ubi substituenus
7. valores y et et 500C inventos articulo 6 et 7. jam 100 p = M. H2V + 12313Z: 5123 et
8. seol= aq si ul jam 100β = - 12. 112. 513 V + 123. 123, 513 Z,
9. 12. 527 et 5ot permutando 1 et 5. fi
10. seu 500 = + 512. 11213V2313Z.: 51223. Ergo 10dp 5oot =. L812 u2IZ vB + 112. siZ 11213. 12B3VZ,: 5122S
11. Seot - - 312. 113 A~, .
12. Siz. 123 - 523. 11
13. Rursus ex artic. 7. est y = 1121y. 5I213V ~ 12313, 52313Z.3:, 11223,51223: Elyo
14. +II2. 5I2. 51223, 11213.51213VV - 112. 512. 51223, 12313. 523131)
15. = Bur2z. Snz si (ill- im m)
16. 123.523. 52317. 11213. 51213 --. 4 123.523. 52g1. 12313. 5231377
17. ubi 123 permutantur 12 et Ncum 23 et Z
18. 12. 512, 11223. 11213. 112B3VV f 1122211225. 112B. 123B ... = 123, 523. 131 2 1291. 123132
19. l.Fid est 2. 12. Su 12313. 1113)
20. 2312 2se - 51223
21. jam coefficiens ipsius vo est +112. 512. 11213 (151223. 512I3 = 11223. 11213). A 11. 512. 11213 fa - b) (1. r)- + b) m) seu
22. fr2. 123)SI2 C N13- sIL. 113) -
23. as. i 3 4 113, 513 11223. 51223, 52312...
24. 1 su ns, , tr 2.112. 515. 1∞21Z, 12713
25. 2112. 512. U2B3Am + bC) seu- 2. 112. 312. 113a3(112 SI. 13. 3241. 512: 12I
26. us in quibus siru, hac
27. et prius quaerat nempe meuorum primum secundum et quartum. Et quibem proprim
28. siS qu - 112. S1 (12313. 32343 dat 112. 512. 51) seu H 2. 512: (123. 513 115. 5252),
29. 123,523. 51223, 11213. 5213 dat 123.523. 512131 seu + 13. 523 (112, 55- 115, 512).
30. uttermia terminus ( 13. 513. 11223. Axs. 1M23 dat
31. pro sccuntus terminis qua rumus
32. + 1125. 11223. 293 1_B da
33. 112. 523 +SI1) 113. 313
34. 112 13. 12313 =, 112. sey + u3. fIr, tBt H s = siL S23. 113. pE. 14. 113 +
35. certius denique
36. +12, 512. 5257112, 523.
37. =112. 512. 525 123. 512X
38. = 123, 523. 512, 112. 523
39. f123. 523. 512 123. 512
40. +512. 523 112,52)
41. 45(2. 527 125. 51
42. n2 SI2. 523. 51125 113
43. 3. iEius sasis
44. (42. 512. 513. 112. 123. 512.523)
45. seu 2. 112, 512. 525 115. s s M h ar. 12.
46. . _. 123. is
47. 112. SIL. 125. 5I22
48. . 12. jur
49. se 2.512. 523. 112.523
50. -113.513 si. S25 = 123. 512), 51223
51. (12 en. se 1) 11227
52. SB B- 12223. 5p23. SI22Z 113, 515
53. 11. 525 = 1232 51 + 2. 112. 123. 9n. 523 2 113. 51
54. Machigue. bes+ i ac FEcitus oege
55. 12) Ergo tandem aequatio explicata sic. stabit
56. = 2. 112.515. 512. 52. 1B32 ∞V = 2. 125. 525, 512. 51. 113
57. 12. r3.. 513
58. 11223. 11223. 11213....
59. 4 4. 112. 123. 512.523. 113. 513
60. Z2. + 2. s12 113 1pi vis. 115
61. + 2. 112.123.2
62. I23 H3SB +4 12. 123. 512. sig. 1B S
63. supere (t coefficiens ipsius vZ. quem ut explicemus, ita procedetur
64. B. HB S
65. + 11515]3, 1123. 51223. 12312
66. seu 4123. 513 (112. 513 - 113. 515), Su2er u3)..
67. + p227. 1229. 11213. 12313 seu + 112. 123.513 + 51. 513 11 Q 11223 B
68. 5(2254 51225 + 4. 112. 13 512. 523
69. et coefficiens ipsius vZ est 25. 5 l1223 S. 113 + 2. 12. 123, sf2 + 4 (1r2. 123. M2. 523. 113. 513.
70. A st23 + 11225 est 2. 112. 513 + 2. 123512 )eu r. Js E
71. 112). itaque tandem aequatio ex rationalibus explicata sic ctabit
72. 25512. 523. 132 (+IIE. SIE VV
73. I223.15. 5B, +125.523 2
74. +E(tirS(Sn 6C3. 113
75. D. Hrar 5 (312. 52 3 113 + 112. 123. 5152) = L. H1223, 112. 123. 512. 51313513
76. quam aequationem compendio scribemus 120VVI Z IV voaa - 0. Et cum ex
77. seu dividendo ft 112. 512 VV + 123. 523
78. 13) Alia similis aequatu fiet ex ex rationalibus subtatis riationatibus valoris ipsius E, d- O, tantum
79. 1 et 5 troturum initialium permatando cum 3 et 7. quam compendio similiter
80. seribemus, 220vV 202ZZ+ etvZ+ 200 aa 0; Ias duns aequationes
81. latere radix esse ( 112. 512V + 123. 523Z et fiet - 2. 112. 512. 123. 523(2 11213. 12313 = l2X 235(,1 12G.
82. se fiet L1c. 523. SI2. S23. 113 + 2= 112. 525 1 123, 515 + 1t 525. A. 1223, 112 1)SIL. 313. 113. 513 =
83. +2. H12. S1]13. 513... . ..
84. +2. 112. 5121359. 504.:
85. B1 en sis quae aquatia q
86. quae aequabib dividi potest per u2 23 seu per 112. 513 + (3. 512 et fi
87. .512. 523113 + in 2312. 123.515 + 4. 112. 133.512. 523. 113. 513=0
88. Et pari re modo
89. tractando G, D. O fiet 31223. 712723, 315 4 31213. 312. 325. 7132+ 4. 312. 323. 711. 715. 313. 713=0
90. IVZ = 11223. st. 13. 5231 2(l. m C
91. l 2. 1123. 112. 123, 512. 529. 113.513
92. 11223.51225 (inise
93. 2. 11213. 2313
94. quasi ab uno
95. =11223.51225, 52312 (l mon)
96. =12. 5I2. SI213. 1313 32313 seu - 1. sir (125. 51 - 15. 113), Su Mn (SB + sM2, Z13
97. = 123.523, 51212. 11213. 51213
98. seu -113. 513 (1123. 523 - 113. 512), 51229
99. 11223. 13. 51348
100. Et coefficiens ipsius ZZ est + 123, 523. 12313 (4 52312. 52313 - 12312. 12313) sin 1stus uesn (ib. a f t. ) (B Y a) f19) - - ( c m nus vidi sotas
101. sed b9 + af = 123.523. 113. 512 + 123. 523. 112. 513. Ergo fil coefficient ipsius Z2 -2. 123. 52512313. 11213
102. je surorest coefficiens ipsius ez. ubi primum excersamus et explicenus ter
103. ipso omisso, entice
104. et ordinai
105. p. S pr13. 123B3 BV +
106. vq i edre auimm
107. uie art asnse

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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 65v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0130?run=74