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Leibniz-Handschriften zur Mathematik LH 35, 7, 11, fol. 2v

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.

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The machine reads it as

  1. des raitons
  2. l’Europe raisennable, ou l’indien informé de ce qu’il y a de plus consideroble dans nos creames et practiques
  3. cum quadruto ametri seu cregmscripto incommen farabilia sint Octogonum sedecangulum, Brangulum, ec quam et omnuo
  4. soligonum quodlunque, quod bilecando fit, quaeritur an hinc demonstrari possit, apsum sirculum qui est ultimus horum polysguncram
  5. etse inconmmensurabilem quadrato dametpi
  6. etunc quantitas-
  7. Si circulus est quadrato diametri commensurabilis 1- + 1 - 2 + - + - = etc
  8. multiplicata per aliquem numerum, integrum, dabit numerum integrum, seu e - e + e - e + e dc poterit
  9. esse numeus integer posito e esse integuum; seu 2e + 3C + 2C etc. erit numoius integer e cum quilibet horum sis.
  10. fractus, seu in integris exprimatur per seriem infinitam, necesse foret omnia destrui additione seu abire in o
  11. 8 1o. 9
  12. u 10. 5 1. 7 1on6 10.3 1. 4 1o03 ont 10. 10r0 Io+I 10t2 1013 1otq ton hons hor ton 3
  13. le nadi1
  14. 1
  15. ago iost Ddt ocst nomt unno pAe aequ i0 hoco roreoo uoreoeo rovroromo
  16. B tonus aequ 10 200 ot
  17. A+B aequ
  18. militer 1ost 10r8. C . . a9. + + 100o + E0 + 8 + 203 etc
  19. 10
  20. 1odo 1000or
  21. 3 3r 41 15 19dc+ + eu
  22. pro iculorit si debeamus aodere L + + + + + 1 (5, 25 2g
  23. 59q euit + + dic + u + i + i ec + L sed inciiculo summaaddendu destructio illa divisore
  24. G81
  25. oetb
  26. 6obi existente decimali oaa que procedit
  27. 1
  28. C
  29. 1000eoo - 10-3
  30. 1 +
  31. 1 + 3
  32. 10 10
  33. - 7
  34. 1
  35. 1
  36. 1
  37. a L1o25 16-9 10- 13
  38. Hec summa tauto propius accedit Circulo, quanto altior
  39. quantitus est numerus e
  40. 3
  41. +3
  42. 103 +
  43. 10
  44. 125
  45. i aegu 10 7 oe 1 3 pxrarise osisiarsi ideoir
  46. 1029 59 1 10C + 7e 1e hc
  47. Et pro quantiale quae magnitudini cicculi in tantum accedat, in quantum
  48. 1 + d + 11 + 1
  49. 10
  50. a
  51. Sc
  52. U
  53. O
  54. 1te
  55. + 112 etC
  56. 10
  57. numeius e assumitur magur, habebitur:
  58. 1+1=171 = 1+ 14 1 +1 aequ. 0
  59. - 3 + 5. - 7
  60. 1
  61. +9 P. 11 +13 ∞ 15. 11 Xa19+ 21Vc ag.
  62. -3+5= 7 + 9 = 1+ 13 15 4 11 19 + 21 Ec
  63. 345 - 7 + 9 - 11 + 13 - 15 + 17 - 19 + 21 dc
  64. 3+ 5t - 7 + 9 - 15t + et - 15 + 15 - 19 121 hc
  65. +2 + 2 +2 + 2 dc.) se psum
  66. 10
  67. 16 +32 + 48+64 + 80 48
  68. 10
  69. 98 + 366. + 866. + 1586 H,
  70. 040
  71. 2.43 La-3
  72. sum de
  73. sum o4 x + 3. R ix + 3
  74. (x. (X, posito X esse numeros naturales
  75. utile autem erit rem ita institui ut per 10, inveniantur omnes summae protermini
  76. se
  77. constat autem alunde quae sit
  78. quorum denominatores sunt infra 10; per
  79. 10 omnes quorum denominatores sint infra 100
  80. ita porro.
  81. per 10 omnes quorum denominatores, sunt infra 1000. Ditems 2= item rono- qu s 1
  82. Et ita terminus ultimus addendorum, O, est
  83. 10-9
  84. 100-90
  85. summae autem omnium X, X, X, erc. praecedentium semper in caleulo sunt anterendae.
  86. (1 egx posito X termino ultimo seu
  87. sX aego fX- t + si ego (xt + x. jam fx + sai aequ X
  88. Superest ut quaeraumus summas omnium hA, X, X, et.
  89. maximo
  90. oem adhibemus.
  91. (X sii aequ
  92. et (X- (X-, aequ. X etC.
  93. (N - 2sX + Si aequ SX - 25X + X. Ergo per 1 et 2 fiet sx agu X + Y seu B apo AX+
  94. et TX - (X - 1, ai
  95. Jam SX = 1 aequ. SX - 51. Ergo per 1 et 10 erit si aque
  96. Manifestum est, essex (X = sX1 aq. X
  97. -
  98. 491
  99. 1X + 5 X 1 X
  100. r 198Gden 3 scarear X
  101. SX. agb. sX 4GXL 6 SX- 4 sx + Srop s 4s+ (6. 3, X , 3. nda -n - a XEx 1 ∞) y 2 2 S aqu. X3+ B- s ausi
  102. item SX aeq Sx3SX + 3 Sx - si aequ sX a 35X 4 L. ) X L X. Ergo per 12 et 3 erit
  103. Et ita habetur progressio in infinitum qua
  104. a
  105. similiter sx-1 aequ
  106. (x sive D aequ. X + 6C - + B+ . A
  107. Lceno)
  108. quod in nostro
  109. se invicem derivantur.
  110. Daequ. X + 6C - 4B+ 14. E aequ. X + 15 D - 15C + 5B - 1A. Et ita porro
  111. et eodem modo olinuando: E sive Sxt aequ. X +15D - 45C + 5B - 1 A
  112. adtoque per sere et
  113. casu sufficit nec opres est rem reduci ad ipsas potentias
  114. Aago X Baego X + 1A
  115. C ag. 1X + 3B - 1A
  116. Baequ AIX At aX. Caequ. 21 t 3. Ox + 3i x
  117. .2.3
  118. AX = 153, 2 1X = 15. 6. 3+ X 15. 6.9. X
  119. 4 +X
  120. - 15. 3. 4. 1X
  121. 44 15. 2+
  122. 33 17
  123. 2. 3
  124. 2. 3X + 69. 2,
  125. 2
  126. eti
  127. Daeg. 3. 2. 1X + 6. 2. 1 X + 631X = 6. 21 X
  128. = 3. 4. 1 + - 3 . 1X
  129. 1. 2. 3. 4
  130. F5. 2. 1X
  131. de summis potentiarum
  132. qu
  133. -3
  134. 16-7
  135. aqu
  136. 144
  137. erc la e est X
  138. 9d
  139. 3. 7. 11 dc est 4X + 32 diff. 2. f. 53 2e
  140. 5. 9. (3dtc est 4X+ 5
  141. 16X + 24X + 9
  142. 18
  143. diff. 19245
  144. 23. 7 64X + (49X + 108X + 27 2di 96X g2 +9B
  145. 33. 97 S4 x 2+ 24OX + 300X + 1 25) (en 3. 165 X+ 3 4 5. 5 X
  146. +4.4. X+64. 3 xt 4+ 3r) Bisserentia ent
  147. s isis
  148. 2
  149. 29Z
  150. 491.
  151. 22G
  152. 125
  153. 323
  154. 343
  155. 12
  156. 34.
  157. 386
  158. 306+
  159. 169
  160. 7
  161. 169
  162. od
  163. 386
  164. . 48 19
  165. 88 288
  166. Era rit
  167. sum. 4. 473 +
  168. 18- 41
  169. Haec (alia scheda accuratius
  170. exhibui, et penitus absolvi

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 11, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068082:0004?run=73