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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 71r

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: 0.75.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 66v); this page is its right half.

The machine reads it as

  1. In aequ. 1. aitenl praecedentis 16 poterit expliveri U1213. 1L313. atbu Seu W2 61B in 127. q = W121a5 31E + 22. 1. S1
  2. Ergo H213. 1231. ADCL 112. 123: 113 = 112. 125 . 513 + 1223. A ~. 13. 513 + 112. 1B. 512. 523. uside explicando fit
  3. M 125 38 - (12. 123 bb 2.
  4. Mo3. v2. 123, 513 = V quh qu e. 12) b. it )
  5. adeoque tandem u2Bh. 12313 = ubb. 24. q, BC. 16h + g, 1152
  6. posu asu satorn qegit
  7. g33us iht Bhh
  8. Ahl. 9Y (-29hater. 123, 6. E
  9. lit f. 28. in trillnst _ sit b ( y . ur 1es Ul mol: t 192) N au. D8
  10. A, 162+ +. VY
  11. sinricin nud 2 2t 3 ila omestandem irrationales ex calcude sunt sublatae
  12. sed absolvamus penitus aegu. 1 et fiet
  13. Gat M no s s V 2h+, ihaf = Eh + fa9 et fil (Em) me n2. 123,. 512. 513, 2h -f
  14. rgo ob et ex 9 et 3 fiet
  15. FB(12. h23. 52. 123 = atgg: (11 123. sn 525 ta 9)
  16. An sic potius sit s ut e artie 19 aeq. vel s ut succedat extractio fiat 2h+f = (guo) 13. 523, te d:
  17. (ob en artic. 14 aequoo, ut sucxat exi
  18. i 2h +5, g9 :tfiol f. h
  19. 123 1 (13tio) (11223h = fh+. 5) 49
  20. ergo ex aeq. 3. per y et 10 fiet 11223h = (4mo) 112. 123. 512. 523 ad: R, bc
  21. Et duos ipsius h valores aequando et i
  22. siet 112. 523 2ibb) + 123. 51 (CC) +. 1. 123. S12. Sig ((. 6y 4 ocC)) = 4 H 13 f12513 (D. bc
  23. 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
  24. faciendo H2. 123. 51 seg ut jam determinavimus oportet
  25. ras nec quicquam h
  26. set si 24. videtur hac aequalit
  27. auluusus heris
  28. 112. 523 (1.6) - 11, 312 (1. C) = salua no vi b. b) e
  29. facere aequalem quadrat
  30. licentur in ea f et h
  31. ad quod postea recunitur
  32. et (10mo) 123. 512 = 15. 2312: a. Ergo
  33. ergo praestat statum facere ob aeq.C
  34. (1Imo) 12. 129. 512. 527 = = ( 152. 14232. 2312: aa et 1 - 12. 123, 512. 523 = (12 mo) (1B 15. 1223. 2 212: a
  35. sit ergo (9no). 112. 523 = e ex 415. 12523: a
  36. exaoqs et 51223 = (13t0) 15. 18237: a + 15. 332.a et 11223 = (14. to) 15. 13523( a) - 15. 23s1 2L. a)
  37. iter se percuntant officia, et cum i 51223 prius contineret + et =, sed 11223 tantum +, nunc fit contra
  38. Ergo in aeq. 4, retinendo 112. 123.
  39. 513: 113 = (16t0) -(15 : 4) 1825. 23str (= (15: a) (1825 = 2312)), - 2 4 (1225 + 2351 2 , ., 12523. 241 2)
  40. fiet f: h -(1560) 12 5t + 2 32, (152) : 12523. 2.3 = (1514)
  41. (17 mo) 513: 113 = (15: a) 1823. 2342. (12523 623)2): aS B1) 112. 123 (12(23 + 23)12)
  42. suppono autem 5_2 et 52
  43. 513: 113 Lae quationis 4 sic
  44. Sed per aeg. 15 et 5 - at ot = (19 ab) 12 .2 HE :, 13 B2
  45. Ergo ix 18 per 19 et 9 fit 12. 513;, 113. 512 = (15∞4) 12523. 122Z = 2212 :, 1sL 3. 2g2 (15: a) (12t5 - 2342)
  46. inveniri per 112, 113, 15ca, et r2z et 2712
  47. 112. 513, :, 113. 512 = 112. 523, (f = 2h, : h): 112t23
  48. 123. 512, f - 2h, : 11223 = (per 10) -(3: a). 2412 (1323 Lyp2. 1223. 2252). (15. aB, 122 = 23E)
  49. 112. 513, 1, 113. 512 = (20m0) (12523 : 2392), 1223 - 22423 :, 1243 + 2312
  50. (2205) 123. 513,:, 113. 513 = (2212 12) 2 22 s s
  51. 123. 513:, 113. 513 = (21mo)
  52. ii
  53. Fajesi) et 31223 . a) n (37 : a), 12725 - 23712
  54. t
  55. aa et 71225 =(41) (7: af, 12725 + 2371E
  56. L 3f. 1272551533(. 2123 - 23712): (12723 + 2371331253, seu
  57. 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
  58. et (2do), 373. 712 = - 37. 23712. a et 312. 313. 712. 725
  59. A apiai ure it
  60. et 713. 313 = (6to) -(37.
  61. aeq. articuli 12 designaitae articuso 1
  62. nat = (5to) 0. quae ne habeatur v: Z divellenda est in duas, et fiet
  63. 163 Hinc jam _ at quia per aeg. 14 satis fecimus extra ctroer in. et pari jare 312. 7126 + 323
  64. L51223 YEptC13. 1213 3Z 4 7 122N = (4. to
  65. fint + 12 Si. Amarev + iy 123. pa - s, tA B nde l) Msir, 1, 3nop2 = 129. 523,: , 321. 723
  66. in 3 1)o et
  67. non
  68. 6, 7, 8 duae sufficiuct cum ter
  69. B_AA, :, 721C)C= ubi par per ag, 11 articuli 14, et autre. qu. 3 artic. 15. apparet utrobique
  70. M2. St. _, :, 312. 7 12BL sra AC:, nBA Bpu) 12 1. 52 3, id) 2 H a q
  71. V9( 1121612. 323
  72. 123, 523. 312. 712 quod institiariam multiplicat
  73. onem et fet: 5 ed) n. SC2. 12517 13. 15. 125
  74. 123. 523. 3I2. 712. nt antem ae quatio
  75. seu 113. 523, :, 5tG. 723 = (1mo) +) 5M, :, on3 H = 112. 512 s’ podit au
  76. 2 im. 527d. b_) = 127. 512 tCC)
  77. h- f = (0 mo) 123. 512 ad: E
  78. feliniter exenit extractio
  79. cc. ih. 33 t s et C 8. y. Jnda aa b.B, B
  80. et fit (u2 23 (l mm) 16) 2h +, D.
  81. pari pre 31213. 3231+)X
  82. Th 112. 523(: b) + ,29. 5121d: C2)
  83. rachonem
  84. Nita redimus ad eq.t
  85. rst
  86. compuno iasrevhrn
  87. t 12. NS. SM. 523 - -1b, +hil. 1.
  88. 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
  89. gutrus 2 l122(71227
  90. AI: n B
  91. i. 12) en 13. sedium
  92. Pit pari pec ex ajo. alriansous estpis
  93. 3. 113:
  94. iu
  95. a 61q 513: 113
  96. 1122
  97. 112713023712 = (10 mo) otu M.
  98. Sed quia in s, continetu
  99. alitiome et pcab
  100. ilimque duae aequaturs. ies. 2Eu (F
  101. peia
  102. ant rediietionems
  103. ungur rto besetes
  104. byg. 10 et 12 artituli 10
  105. 1527) (323t723) i E 23. 112∞D m (am
  106. 3t 2 V2. 123Si, DI2tII
  107. ar it si-
  108. H2. 1L 3
  109. quis duo valpres equandi,
  110. surds otro
  111. 2123 (123+523) (327
  112. mysore dis utia nm aspro, st q. L, v
  113. nnon, mesusat.n) iss
  114. ters, et exrqoe
  115. 32g is iti n situ ubi
  116. n ot mua antu ititand aeuaa ad
  117. Eex as per
  118. ome 713

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 71r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0141?run=74