Leibniz Legible

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LBr. 57, 2 · Bernoulli, Joh., fol. 186v

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: 0.78.

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. 185r); this page is its left half.

The machine reads it as

  1. § + 3Q + 9R + 275+ 81 5∞ 243 V4 729W p + 39 + gr + 275 + 81 F + 243 u) Qvia igitur P+ 2X+
  2. 8 + 2Q + 4R + 8 5 + 16 5X 32V + 64W p + 29+ 4r + 8. 5 + 16 + +32 u RXX et: ponitur esse
  3. D + Q + R + S + 5+ V + W p + d+ r + 5 +, t +
  4. s
  5. ∞ - 2 + e - 5 + 5 - V + W p - 9 + r - 5 + + -
  6. u divistorlis per p +qu
  7. + XXX etc: oporiet p
  8. U esse partem aliquocam
  9. B - 22 + 4 R - 85 + 165 - 32V + 64 W p - 2 4 + 4r - 85 + 16+ - 343 u ipsius 5 + 2 + R +5
  10. P -32 +9 R - 275+ 81 5-243 V + 729 IV p - 34 + 9r - 275+ 81 +- 243 u) + 5+ V + W, ec p + g
  11. =r + 5 + E + u partem aliquocam ipsius P + QR + 5 + S + V + W, et p = 9 + r - 5 + t - u parcem aliquotam
  12. ipsius 8 - a = R - 5 + 5 -Y + W. et p - 29 + 4r - 85 + 161 - 32u parcem aliquotam ipsils 8.- 22 + 4 R - 85
  13. + 165 - 32V + 64W, etc. quia quando radices datae et quaesitae aequationis utrobique cadem quantitate minuun
  14. tur vel augentur, aequatio ex illa resultans adhuc dirisibilis est per aequationem, quae ex hac, resurgit, adeoque ul
  15. timus terminus hujus dividet ultimum terminum illius aequationis, oporeet enim p + qu F rxX p. esse partem
  16. aliquocam ipsius PF QY + R XX. p. quicunque demum valet pro X substituatur, sive 1. 2. 3. sive o, sive
  17. = 1. - 2. -3 e. Unde patet inter divisores ultrinorum terminorum semper debere esse aliquos sc: hos p+
  18. 39 + gr etc p. + 29 + 45 etc p F 4 + r etc. etc. qui ita progrediunturut supra dictum est, quemadmo
  19. dum videre est ex hac tabella
  20. P. + 39 + gr + 275 + 81t + 243u
  21. P + 29 + 4r + 85 + 162 + 32u
  22. differentiae primae 1 disserent: Edae per (differ. stiae p diss. alo differentiae quin
  23. 4+5r + 195+65t + 211u
  24. p+ q+ r + 5+ t+ usq + 3r+ 75+ 15+ + 31v
  25. p - 9 + Y = 5 + 4 -
  26. p - 29 + 4r = 85 + 16+ - 32 u
  27. q+ r+ 5+ t+ u
  28. dirisae
  29. rt65+25+ + 90u per 3. divisae per
  30. r+35+7+ F 15 a + bt +25u viste.
  31. g- r + 5 - + + usr +05. + = + 0 u5 + 21 + 5 u t + su
  32. q -3r + 75 - 15t - 31u
  33. p- 34 + 9r 275 +81+ 293 19 - 5r + 195 - 657 - 211 u
  34. F- 35 +7 + - 15 a- 2l +5u
  35. + ou
  36. 65+25+9015- bt 125 ust - 5 u
  37. taper 5 divisae
  38. u
  39. Quod autem in qualibet serie differentiarum medius terminus aut primus ex duobus mediis sit summa omni
  40. um possibilium valorum, qui hac expressione continentur, mn = im - IN
  41. 12. 3.M, Ver. 2. 3. . M -1 etc: N. sic patet:
  42. Finge radices aequationis minui successire his quantitatibus a b. c. d. e. f.g ete, quae denotent numeros pro
  43. gressionis itrithmeticae se inricem unitate excedentes, ita quidem ut medius rerminus exgr. d sit =0. et ul
  44. timus g = primo termino sed signo - affecto h. e. = - a, radicibus igitur ita minutis ulrimi termini
  45. aequationum resultantium erunt.
  46. differ: imae, differ. 2dae per 2divisa
  47. p+ ag+ aar + a5 + a 2Z + a5u.5. = (posito nempe N pro ) s: an A N) quorum disse, s: an - b n = N
  48. p + b4 + bbr + 635 + bEt + b5ug. = pi q1riSit. aG. h. e pro s: bn
  49. p. + cg+ cCr + C35 + c2t + C5 Ws = cujusvis termini aequa) s: cn
  50. p + dq. + ddr + d5 + dEt + d’us. = tionis inveniendae coes s: d
  51. p + ed + cer + C F + ett + e ug. = ficiente, et n poro nue s: en
  52. p + fg + Ar + f35 + fEt + fSup. = mero dimensionum e) J: fn
  53. p194 tgr +95 +get +g5 uc
  54. dif: 3tiae per 3. dirisa
  55. s. a2- 36n + 3Cn- an
  56. b -3Cn + 3dn - en
  57. Cn- 3dn + 3en fn
  58. d - 3en + 3fn gn
  59. diferentiae 6tae per6 divisae
  60. jusdem termini
  61. a2- 4b2+6C1- 4d2+ et
  62. 6en.
  63. a -6b + 15c- 20dn + 15C- bfn + gn
  64. 2. 3. 4. 56.
  65. et
  66. N.
  67. sunt s: cn - du H N; S: cn - 2dn + en
  68. Ni S.
  69. GN
  70. es
  71. cs
  72. se
  73. S. g f, N
  74. diff. Ita per 4 divisae
  75. bn -4cn-
  76. Cn
  77. 6
  78. n
  79. n
  80. tenriae 1mae S: Bn -c r
  81. 2dae 3tia
  82. 4ta etc:
  83. sunt
  84. l. ca
  85. S.
  86. (. ar 2b + n
  87. bu 2c2+ dn
  88. Cn- 2dn + em
  89. d
  90. 2en + f1
  91. N
  92. Ns. Cn- 27 n + g X N
  93. differentiae sta pers dirisae
  94. an -56n + 10C2- 10dn + se
  95. Sc + 10d= 100n +5 fn-
  96. 4.5
  97. in
  98. n
  99. In his medii termini aut primi ex duobus mediis
  100. bu -3cn + 3dn - et _ N, S: b2- 4C2 +6d2- 4e2+ f
  101. 3. 4
  102. qu
  103. etc: et generaliter positis M pro numero differentiarum, m pro = M (vel pro. M F1 Xsi Mn sit nume
  104. rus impar) h. e. quia d = 0 pro c, b, d. f. = 1, 2, 3 medius terminus in serie differentiarum cujus
  105. numerus est M, est = S: m - M m - 1 I + M. M. =L m - 3) n M. n = 1. M -2 m - 31 + etc, H V
  106. 1. 2. 3
  107. Divis. per 1. 2. 3... M, h. e. si divisio reipsa instienatur = (. mn
  108. in - 2n
  109. 1. 2. 3.1. 2. 3.. M = 3 etc:
  110. in = Mn
  111. 1. 2. 3. 4.. 1M1
  112. C
  113. in =
  114. m-2
  115. 1. 2. 3. cM 1123. M-1 13 (128. M. 2
  116. t ac V

Cite

LBr. 57, 2 · Bernoulli, Joh., fol. 186v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-3653099:0372?run=74