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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 349v

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: 0.83.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 348r); this page is its left half.

The machine reads it as

  1. loco. v, W, X, y, Z vex, () (20), (X, (7) (2
  2. Scribatur 117 12, 1, 14, 15, etc 21, 227 23, 24, 25 et
  3. 1t B = 11(1B -g - 13 21+ 1 = 213 23- 21- 29
  4. et similiter
  5. 113. 131 +213. 231 = 2. 131. 12 = 2. 231. 22 = 0 seu 13. 13 -11. 11 +2323 -21. 21 = 2. (13 -11)12 -2. [3-21)22 = 02
  6. 124. 172+324 242 = 2. 142. 13 - 2. 292. 23 =0 1439- 12.1242924. 32. 22 - 2 (14- 17) 13 - 2. (4 - 32) 23 0
  7. 135.153425. 253 = 2. 153,14 = 2253. 24-0 Ah. 15- B. 13+ 25. 25-9. 23- 2(15. 12)54 - 2 (25- 23) 2930
  8. Et eodem modo 22. 2+=12. 12 - bb
  9. 1616- 14. 14 26. 216- 29. 24 4 1 6- 19)15 - 2 (26. 24) 25 1l0
  10. et 23. 23 (4) (13. 13 - bb et 24. 24 - (9), 14 = bb
  11. Iis valores substituendo in aeq9. 1, 2, 3, et fiet EK aequ. 1. 13. 13 - 12. 11 t 13. 13 - rg - X 11. 1 + r9-
  12. =2. (13- 11) 12 = 2 (23 - 21) 22. seu sit 1+8 = lf eritque 5 (13. 13 - 11. 11) - (13 - 11)- (23 21) 2
  13. Harum agg. 11, 12, 13, (4 etc.
  14. Eodemue modo ex Lerit f. (14. 14 - 12. 12) - (14 12)13- 824- 21) 23 =
  15. mequ eramni quantulore, 13 per 1 et 12 Dx ~g. V) ex3 f (15. 15 - 13. 13) - (15-13) 19 -7(25. 25) 24 =
  16. 14 per 12. et 13 X aequ. 12 et 15 per 13et 14 ex a, 3. Ep4, f(16 1b- 1414) (16. 14) 15-8(6 295
  17. Et da porro. quia autem 23 - ((13. 13, g) ideo utto
  18. id tel daZ ad habendum valorem ipsius 13
  19. et ita porio
  20. assequemur, si faciamus +(413. 13-bH) ex trahibilem. sit nempet 13. 13 - bb - 913. 13 - 2913. 3345
  21. opus foret ex altatione. Sed in fatsor brevins quaesitum
  22. seu 2.913. 33 = bb + 33d seu 15 1 9. 13 = bb + 33. 33, : 2. 33 et 23 = 913 - 33,25 23
  23. 23= bb 4 33.33 = 2. 33.33,: 233 seu 23 = bb = 33. 33,:2.33. itaque ex aq. 11. fiet
  24. C(b + 2. 33 bb +351 = 499. 35.11) - 5 29lb33. 12_ +ag293312 449935. 11. 2
  25. = 49933. bb22 42993322 44993321. 22 = 0 Est autem 5 = 99+1.
  26. Et ordinando aequationem F33Y +299. 22. 337 + 25bb33 = 29bb12 33 +fb =0
  27. 4915.. = 299bb 22
  28. + 4g911
  29. ag12.
  30. ultra pa sed 11 etiam ascendisset ad 1142, et 21, 12, 22 ascendisset ad quadratum, quod hoc modo evitatu
  31. Equidem attntis 13 et 23 non
  32. Rlura emersissent membra, nec 13 assutrepisset
  33. +499. 21300
  34. Hinc similiter ex aeq. 12 faciendo 914 = bb +34. 34, : 2. 39 fint 24 = g. bb-34.34, : 2. 34
  35. et f34 + 299. 23. 3_ + Ef.bb 34 = 29bb13. 34 + fb =0
  36. + quooutue
  37. +499 22. 3) fict
  38. = 299bb23
  39. perians ds
  40. per inansos valores
  41. 534+ +gbl. 35) 54 +2 flb3+ 34 - b1. 534 + fb
  42. 24tg9 bb33
  43. Ubicum 33 assurgat ad quadratum, ideo x
  44. = 2bb. 3. tgm
  45. ope aeq. praecedentis pro 33, et hujus tollendo 33
  46. ascenderet 34 ad octavum gradum fiet et haberetur
  47. relatio qua cujus ope haberetur punctum B ope
  48. a anre
  49. +291g bb. 37)..
  50. +2ubt: 33)
  51. -ggbl. 33)
  52. gybbogue.
  53. -21199225.
  54. ad gradum B. sd si omissa explicatione ipsius 13 ex altassemus aequationem 11, ut habete
  55. sin AB ex datis A et D, sed quae assurgeret
  56. quadrat 23, Ldinabimus sic 23. 22 = f5 (13 - 2: 13. 1 11 +. 1) - 251512+25 1315+25 11. 13N- SII. 12
  57. + 2517 2 32 A = 2515. 21. 22 4 13. 17 -7. 13. 11. 12 + 11 12 + -2. 13,. 12. 21. 21 F. 11. 1. H. R
  58. 213. 22 - X bb 22 et ordinando seundum
  59. 15 - 25l21) - 255 15 13 +4f 1112 13 + 5511
  60. videndum an haec communislex determi-
  61. 2 ur
  62. possit ex seriibus aequation qua lubitia 2
  63. fandumentatiam
  64. an equo
  65. 2. 11. 12 21
  66. a2. 12. 21. 2..
  67. Quodsi ergo depressio melior statiar in aegq. ar. 1ra
  68. H depressiones inseremus fiet
  69. ef 23- 21 = 1(X 13. 13 - bb) - Fr1. 1 bb)
  70. = 2f11312
  71. =2f1. 11. 22
  72. 22, 11. 12. 11. 22
  73. + bb 22
  74. Calculus institutus est, tanquam manentebqu semper punctis praecedentibus
  75. nA, B, etc var epuncta C, D, etc. semper alia ali alia essent
  76. sed scopus est rem ita risdlocia, ut manente semper netimoprimo et ultimo nunc
  77. nunc tres nunc quatuor ete. hodae equales inseribantur. Sit ergo
  78. punctum determinatur per H1 et 21 altimum determinetur per 19 et 20
  79. Eodem habeditur
  80. ut hoc aequatio es
  81. inter 13, 22, 82, 21, 11
  82. habelituenter 1a 29, c3, 22, 12
  83. sed ili tae quae etia
  84. est aei gnd prn 14 sed
  85. ut tollatur 23 per 13 assur
  86. getur ad gr. 8, et 13
  87. ad gr. 4. unde cm
  88. 13 in duabus aeq
  89. ad cendat ad e.+
  90. Follendo 13 altissime
  91. assur pet 14. ideo
  92. metibr videtum de
  93. pressio
  94. eteaque pro duabus chordi inseridendis habemus aeprationem has ex cet sutus parpinae 419. 19 429.29 - 29- 11) M = dantur invicem 11e1 21
  95. ergo ut et quaeritur semper punctum B, s seu recta AB, bis, velter) etc. repetenda
  96. -2s29. ∞1
  97. pordis aequalibus achitende aq. Ba 2 hocmodo 113. 13 823 23 = 2 ()- 11) tt9 19 + 2929 - 2(19. 79730
  98. 13 qu
  99. 1. 1 =21. 21 = 2(2] -_ X
  100. 2 422. 3 - 2(292 21) 23
  101. ae quatibus adhivead 5 1. 2. 3 = 11. H = 2 et = 23 2g L 12 , - 2(243 d
  102. e15.13 deste - 2(2923)G
  103. ubi solum ponuntur aeqq. 1, 2, B, 4 etc nisi quod semper in ultima pro summique abscissa ponitur B9 et pro
  104. Tamma ordinata 29. Itaque produabus a tribus, quamor, etc. chaedis aequalibus pro 13, 23; 14, 24; 15, 25 et espective poni
  105. debent 19, 29. Quibns a44. accedet demum proprietas invae exhibens relationem inter 11 21, velM, 2, vel
  106. =.13, 23, etc vel 19, 29 ordinata. Semperant -e = 11. 11 + 12. 12 - 2. 11.12 + 21. 21 + 22. 22 - 2. 21 22
  107. I1 autem et 2_ item r9 et 29 semper sunt datae, itaque tantum opus inveniri 12 vel 22, quod non potest si
  108. sed t cum chordae u aequales arcui inscrbendae sunt plures duabus nob plotest fier nisi intervenientibus pluribus, ut 1 item
  109. penste pro tribus chordis, ipsis 223 pro quatuor etiam 14, 20 quio et etium 15, 25 et ila por
  110. quacam seestio ducbus e
  111. versaeassi
  112. 22. 213,225 3 14, 324, 19, 29 et it. portos ila quaeronda progressio.
  113. ea relatio communis aiquot ternor oinuore

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 349v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0694?run=74