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Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 1v

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: 0.71.

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

The same scan is also registered as fol. 3r; its text is given once, here.

The machine reads it as

  1. quae est, 23β - 88 58. ( f7- 1. eA substitiendo valores ex aeg. 126. 130. 131. fet
  2. eti _ B : id BN fii ( d5
  3. is
  4. 3132-1
  5. quo valore invento in ag. 132. substititi, erit 2 - - B = 1 B B - c l7 et omnitus ad comminem
  6. 3B=1
  7. 3B=1
  8. divisorem abjiaentum adudis ( e ( aC C
  9. 2
  10. 2 B - 3B + 1, - BF + B - 1,- 5B
  11. BE (B. B57 - 1. reducendo ad comdibis
  12. 2B - 2
  13. 21
  14. ( B N C BC D- p . N P(= n (B 9. 1. adeoqu BY)
  15. sue BF 1 + p a t. Quo valore ii aeq. 133. inserto, fiet:
  16. 2
  17. e + B - 1 B +1
  18. 13+- 4 B +1
  19. EDZB. L _. B6 + 3B- B)B (27),. et reducendo ad com. divis. fiet
  20. B4. 4B21
  21. 14- 4 12+-1
  22. CN +B - , - B2 16 1 C1 1L 1EB)
  23. sed hoc abtandum deberent enim omnia destruit Ergo essol commissus in aliqua ex hris 124. 125. 136
  24. redeatur ad 134. reducendo ad Com diris. fer: ( β1. ( B Be(B (+ 2 BD - β, - B 9.1
  25. in ex ergo erratum quo et βr
  26. in aeg. 135. frei 2B- 2
  27. B4 B porsus ut ante quem valorem β. inserendo
  28. BE + B B + = 15 + 3B4 3 B7. (118) 1. i quo janis
  29. 37.
  30. B- + B+ + B2 1
  31. co, agratinis
  32. adeoque reducendo ad com. divis multiplicatis omnibus per B- 41 + B fier
  33. 2, 12(, 2B, ( 14B (i) (= 10 (3 1, ND) ( (p ex + BB) ubi
  34. omnia destruuntur, adeoque de a ipsius calculi re inento certi sumus hue usque
  35. invenimus B _ aq. B5. ra autem BN L. ex hB F in et 5 . et 8, B = 1
  36. per a. 126. 129. 130. 131. poro supra aeq. 107. et 108. f invenenamus
  37. Vi 23+ β. 28 B. orrurue vp 38β 1. nn satisfieret scilcet aequation 45, quae
  38. 1e
  39. 3- 36
  40. eret: Bv + (v p, D. ( 4 1. sumendo scilicet 3(2) v. B. aequaliane 82. ubi an recte
  41. 1- B1
  42. Calculatiu sit, pro valore ipsius V statim invenimus, sumita B quasi incortarta et valore ejus in ipsius B
  43. valoibus substitato nam in posteriore valore ipsius v. fiet vB B - B3, = 1 + BV
  44. v
  45. sive multiicando per crocem (o d D. 8 ( ( D H (D. B V- 8 v 8 B. qud cum
  46. B - ( V - B2V +O3
  47. dicta aeq. 45. conicidit. Tunem ipsius B vatorem aq. 39. substituamus in prute iasi V valore, fiet
  48. 2
  49. 1v 11 B0 + B - r9B +. vβ8β- 58
  50. 2BV + B1V
  51. +_∞= 2vBB+ C
  52. Ev . ex pB- eC 1B ( Ap e (B D ipeox. BBB
  53. nv. hucip
  54. et 20, v. r 0fe0
  55. 1 = 1( + ( Uite revendo fiei ( 13, + v. B - v B p v - B + (B v + v (5 B - 8
  56. quae aequatio dirisa per v. β, dabit vB 1 - V + siB2 quae aequatu a quae rupsusaum
  57. conncudit, itaque calculi securi sumus. recteque duos ipsius Y valores inven
  58. Et notabile
  59. hic, quom odo factum sit, ut altius assurgeretur, et depressione esset opus, ad
  60. opendendum calculi prioris cum hoc consensum, com tamen hoc modo videatur aliquid novi
  61. E introductum omnes enim depressiones alternativae, itaque si calculus 81. 82. 83, 84. 85. 107. 108.
  62. xaconsiveretur, et cum hoc exemine conferatur, necesse est apparere, unde
  63. E assurrectio ista orta sit Nunc in valore ipsius ∞. sempliciore, inferamus inventos ipsarm
  64. B. D. β. valores. eris
  65. (ent
  66. 1 2 b-ie - 1 B LI, B - B B=
  67. 3. DE. 4B+
  68. S DB B = 45 +1
  69. B 1 B+CBR +B+1
  70. 5
  71. adesque tanem VZ2 B -1. idem ipsius V rator gdhur semel reperiatur, inserendo
  72. valores Z. β. B. in pros
  73. coresuperiares nemne lsin
  74. -D= 2B -1
  75. B7 q p27 p a B, nC
  76. 1+ i sux v B+ BC 14 B. B2B2y. B8 ,
  77. t
  78. Dq
  79. ui polet nomi od torem pontbers a amgseratorem qui di posse per M- 1. B: 1 13,
  80. VHX
  81. 1 B7+
  82. priori, necess e
  83. B
  84. 1
  85. 2
  86. A. Qui alalus cum don consspliat
  87. in alterutur fuisse endem. Et video sam in pridae calhulo
  88. mesertaser e d. 140.
  89. ergo reducendo ad com. derom. inaegstq
  90. fiet ego md S (17 D 1, + 13 3B 1 (h43B1 11
  91. (N41, B.1,) 1=1 B 4N 21
  92. hoc V r 18. 2B6 - 2B4 - 2 B41
  93. BE,, B= +M=1
  94. 1- N - B4B1F B+ 2B
  95. 1
  96. 1 - Y D C 13β ,1
  97. B2X +34 i
  98. BS. B: B. 2 1, 1) B4
  99. m qic
  100. ex 139. est Z Z - PvZ Av- B.
  101. Ergo X + βF v. et explicando:
  102. 1
  103. HE, + D = 1( ∞, + B=, (3.
  104. B+ 4BI D: aV+ 1, B. 1
  105. seu (B 3B G.d+ B.. ( BB
  106. B~ 4 B B W CE dB FiM
  107. seu v. (8) B4
  108. EB.-
  109. ve B+B(149391 - +B 3
  110. 1+ β31 β. x0 multiplicando per crucem
  111. ) BB + B - 318 Z8. S po B( - 1, + B38EB3)
  112. 3- SuBpv. B.
  113. sed hinc prodit aliu pline aequatio, quam quae produt,
  114. +β v+ B8V alios duos ipsius v valores aequando, quod quomodo fiat
  115. v7 3+B
  116. 1+βZ
  117. equidem miror. Haec praecerea aequatio, 50. ita comparata
  118. st ut in ea ultimo termino secundum B. destructo, destn atu
  119. et penultimus. Latet in his aliquid, quod evolvendum est
  120. fut B3 - B (. - pv. fecimus et v. β B +- 3B. Ergo (52)
  121. 83v+ v. 1+ BV, (- B_ unde sequitur scilicet, vel esse BV p 1.
  122. 3C p
  123. vel esse
  124. 83, e+ β , + β0. si BVH) erit et
  125. v
  126. d. pa 2. seu v B. fp. 1. quod
  127. ide
  128. costat
  129. et v 3+ B. at aeg. 153. dabit 30β-1
  130. mulliplicando percrucem, fiet aequatio. B150. Z(3+ B. BB Bp. 1 1 3
  131. sed mirum varia
  132. nempe 109. Di
  133. haec aequatio cum, 82. fier 213
  134. 5o
  135. fier 10302
  136. 1. + βV + 3B= 22 3V. et v +
  137. B-30
  138. est nisre est cum alqud El smaber
  139. novissiniam
  140. multisli recur haec per 300
  141. valorem aequando valori 1_7. fier (D = ~(= ZB) 280 7 3162
  142. quae tres aequationes.
  143. .
  144. quem
  145. 23D+873-86,
  146. ia i gi dut tei
  147. 1 A3B eo
  148. flat exeum nandum
  149. 11
  150. tinie
  151. 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068268:0002?run=74