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Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 18r

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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The machine reads it as

  1. observation de mons de Mariotte,
  2. soitur les generaleuis oes Triangles ictan
  3. gles eu nomtres : 1. 2. 2. 1+(32) 5 2 + 35) 12 6. 5+(2)12)
  4. n
  5. 25
  6. de
  7. e
  8. sive progressionis: cujus temmino uno posito a.b. sequaus per. sit b at2b et
  9. 29
  10. primum omnium sit 1. 2. Ert Triangulum a generatoribus, a
  11. later ahabei, b. habebit latera:
  12. a. 2ab. a + b. Tiangulum proxime sequens t:
  13. a +4ab+4b.
  14. et ab +4b2. et b+ a + +ab f 4B2 seu a + 4ab +5 . Ait Mariu observati
  15. in
  16. a 12
  17. a se inductione quod ia hac progressione riangulo productorum latera lircu rectae habeant
  18. differentiam unitatem. sive + a 4 4 ab +3b
  19. 2ab+ 4b p7 1.
  20. sive: fa + 2ab jb2 p 1. Erpor + Hoc demonstrandum.
  21. eut a +2ab - V p) 4 c. et a +2 ab +b p 2b2XC
  22. est ergo quod non nisi unitas dupto quadrato
  23. haberetur desideratum
  24. generator
  25. a. b.
  26. si a +2 abY b24 1. erit a + 2b+ b2+
  27. vel 2a45b
  28. sit p c
  29. si probarip
  30. olendiset
  31. vet subtracta
  32. addita faciat quadratum
  33. sed proposito generalius.
  34. prioris posterivis Trianguli in
  35. 6. atib a+ 2b 6+2a+4b 2a +5b
  36. Sa 4 12b
  37. a
  38. id est secundus
  39. a + 2b, 4a+ 10b
  40. 54 + 126
  41. 2a+ 5t 410a + pb Ad exemplum hujus inductione cyquiri poterunt, quorum
  42. 12a + 29b
  43. lascrum if triangulonum latera differant binario; vel
  44. temario, et ita porro. Et eorum quarentur generatores.
  45. a. b a + 2bf b +2, a + rb. (a + 2b +2 b+ 2arb) b + 2 a r 2b + 2 a + 2b + Fbrrarit
  46. seu
  47. b
  48. +27
  49. 2a
  50. sive
  51. 2b Ta
  52. 2t 24
  53. a. bsagib) 2a + 2b (2a 2b
  54. et quonim b12a; fiec
  55. a
  56. 2b
  57. d
  58. a
  59. b
  60. 2b
  61. 22b
  62. 2a
  63. 24
  64. 3a
  65. e + ea Xb
  66. va.
  67. 23b
  68. a. 24 la,2a)2a + 2a. a +2a +2a+ 2a. ) 2a + 2a +2’ a + 2 a +2a
  69. unde potent continuando era et simplicissima erin hujus progressionis enuntatio, qua habita
  70. non erit credo difficile demonstrare theorema, cum ipse calculus tunc exhibiturus sis, unde in
  71. talibus aertis maximae gevocare progressionem ad reguiam
  72. 2 +23, 2 + 24 2+8
  73. 2 + 2 + 2
  74. 3
  75. 1. (2. ) 1+22) 2+2+277 2+23. )142,+242(218, +2+d+2127+24242,213(22
  76. 2
  77. 1+2+8+2+ 224 3 +2 p +2+45+2 Jerc. sed ut adhuc alia exprssio
  78. quaeratur, eum aliae similes invicem addudtur, id utit tnotari seu designari
  79. W EtASI+K, A
  80. +k + KH 1 +E vi
  81. 80782,195025. 43083 A k 11 2+ A + ra R7
  82. te
  83. + C I ∞st E+ 1 AC (, 1208L
  84. 825
  85. 13D
  86. Ai -k L
  87. Generaloris lam lalem
  88. f. 12
  89. 12. 29
  90. 29. 7u
  91. 1
  92. 2∞. 21. 29. Uternatre -.2.
  93. 3. 4.
  94. 119. 120. 169
  95. munc latus
  96. pno
  97. 695. 697.985 pavmuiu.
  98. 4osg. 70bo. 5741.
  99. 2+. AE + A. d 0+201 +k
  100. 5. 122 29. 70 1169. 10.90: 1960. 33461
  101. a
  102. 1bed
  103. s

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 18r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0035?run=73