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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 73r

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: 0.80.

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The same scan is also registered as fol. 74v; its text is given once, here.

The machine reads it as

  1. sunto
  2. it aequationes besbinas habemus
  3. 31o 31 30] 302
  4. 1B.312 20. 31 30 31L 40.312
  5. suli 10, 20, 30, 40, sunt
  6. arbitrarii
  7. ob 312 erit 10. 51 - 11
  8. 20. 61 -21
  9. 30.91 -31
  10. 302
  11. 20320 11. 310 + 12d34 + 21. 2 + 22 d 3 + 31. 300 + 32 d 3D0. F 41. 3d + 42 d301, = c
  12. 51. 350 + 52 dex +61 3 +62 de + 71. 310 + 72 d3ID + 81. 3)B + 82d301 (70
  13. 10. 11. 312 +10. 12 c312
  14. 20. 21
  15. 30. 31..
  16. 40. 41..
  17. g1D. 12..
  18. d20. 22.
  19. d30. 32..
  20. dao. 42.
  21. 20- 22
  22. 30. 32
  23. 40. 42
  24. 13
  25. 3
  26. 10. 51 312 + 10.52 d3120 Hae binae aeque pdnantur edentisicar
  27. 20. 6
  28. 30.
  29. 40 g1
  30. d10. 52.
  31. d2o. 42..
  32. l30.52
  33. d9u. 62 ..
  34. 20.62 Obdy ) Erit 40 = 10(52- 12) + 2c(62- 22) + 30 (72 - 32)
  35. 30. 72
  36. 40. 82
  37. + d10. 5et = 0 se 10. 53 + d10. 59 = Hec arpuntio
  38. d2o 64
  39. 430. 74
  40. c0. 03
  41. 30. 5
  42. d20. 64
  43. d30. 74
  44. multiplicet
  45. per 84 et
  46. - 82
  47. compendio 4 10. 54 + 20. 64 + 30. 749: - 84
  48. et dq=- 8 4F454. 10484 54 d10. _P + d 34 ( 52. 18 3: 84.84
  49. ec
  50. 64. d04. 20884. 64 d20
  51. 40. 83 440. 84 Explicndo cuiernofirt
  52. 34 d74. 30 84.74d30
  53. (7et. 30
  54. . 82. 53. 10 +94. 5951d L 83. 54. 10 + 84. d54.10- de. 5410 f 154. 547di0
  55. 84, 63. 20 84. 64 d20 83.64. 20 +84. d6g. 20- 1. 64 84. 64 d 20
  56. 84. 73. 3084. 14430) 8. 74. 30 +8+ d7430- 184 3130+84. 7 4d30
  57. superest ergo ut eq. 1o applicetur ad data. Ante omnia videamus an a2- 82 non evanescal, ut haberi possit 40. dende videamus an refficientes ipso
  58. 40. 81-41 d40. 84
  59. 30 et deo non evanescant.
  60. 11
  61. 12
  62. 22
  63. 31 32
  64. 41 42
  65. valent eost 11B. 202 00) 12 V0 IBEs -lN2oL 120.210 0
  66. +83. 74
  67. 3i 32 61 62 71 72, 81 82 Eyo gr = 84
  68. 003 19 202 0o7 1a24 10122 0 na2oI - 1eo. 22
  69. + 120. 120 202 (201-210)
  70. Bd. 8 fit 42 - 82 = - 84 = 120. 202 73= 71 - 31 = 202 (101 - 110) itaque 30404 74 = 30 f- 120. 202 (1 2 0 d 202 + 202 d120))
  71. 81- 41 = 83 = 120 (20(-719 74 = 12. 32 = 120. 202
  72. 6C = 62 - 22 = 120. 20]- 120. 210 = 120 (201 - 210) =64
  73. 63 = 61 - 21 = 00 7 - 003 =63
  74. 4= 52 -12 = 202 (101 -110)
  75. 53=9
  76. Ergo tantem ex aequ. 10, fiet , -120 (20- 201) [120. 282. 30
  77. = 202 (110-101
  78. Cadit
  79. +120. 202. 202 (101 - 110)
  80. (1120. 202 (rodror + 2024120))
  81. 120 (10 1. 201)
  82. A. 1B3. 64 (o(2ot. 20) pol vor. ud
  83. d. 20 64 = p) =nonor ano cnom no ao holusaro- drc
  84. 463
  85. F12∞ 20200(7- 3)
  86. aguta licccon) eroio sid
  87. (83. 54 = 120 (201 - 210) 202 (o1 u0)
  88. 82 d 54 - 120. 20 CRO2Cdioi - ducKtd2o2(1oL oB)
  89. 323 = 120. 202 0V (7 - 51) - (X. 202 C∞0. 0.) (notrdi r)
  90. s h
  91. Eo 20. 20 ( 12o (u. 1) 1B Zo2. 10 2o lador sq. vorbu 1 robrot en u Catioinl toB)
  92. sed quia tota aequatio dividi potest per 120 (20-201) + 202 110- 101), fit tandem - 120. 202. 30 + 120. 20, 20 + 110. 202. 10120 vel 30 = 120. 210. 20 + I1c. 202. 10, : 120. 202
  93. 22
  94. 40 = (120. 202) 202 (101 - fi 9) 10 f120. 202) 120 (20) (=210) 20 + (120. 202) (120. 210+ 29) + 620. 202110. 209. 10),:. 12072
  95. Et ita putehre satis fit 40= 101. 202. 10 + 120. 201.20, ut 30 = 110. 202. 10 + 120. 210. 20 Hi jam valores substituendi sunt in aeq. 3, imiidentificata est aeq. Y
  96. 20
  97. 200
  98. 120. 202
  99. Ex coefficiente ipsius C d2 12 multiplicato per 10. 202, fiet 120. 202. 110. 202. 10 + 120. 202, 120. 210. 20_ = 120. 202. 110.202. 10 - 120. 202. 120. 2020= 0 Epqu. Crefficiens ipsin) 312 evanescit mate
  100. Quaemmus nunc etiam eoefficientem ipsius 312, multiplicutum per 120. 202
  101. tiet 202. 1b. 202. 10 2or. 10. 20 L d1 20 ,1 20. 202. W01 2b. 1DF 20. 202. 202 d 1o. 10)
  102. Vi
  103. ae (F110. 202. 10. 202. 10) (= 12o. 20. 1el. 202. 19
  104. 120. 202 =110. 21026 =12V. 120. 210. 201. 2OC1o. 12 0. 2∞9dior 2 ruo. 202. 120d20. 20) (+10. 202. 120. 210. 20) =12O2C. 120. 201. 20)
  105. H
  106. 41 20. 2d2. 110. 202. d 10). L trorcoL 1. 21B. d2O 120. 202. 10 d 292. 10- 120. 202. 202 d lio. (0= 120. 202. 110. 202 d10) (̸ u0. 202. 1204 202. 19( 10. 202 202 4 1o. 10)
  107. P2o. 202. 120. 20 d 20)
  108. C120. 202. 120 dio. 20=120. 207210 d12020)= 120. 202. 120. 210 d 20f 120. 20. 120 d20, =0120. 21 6 202 d120 20)
  109. Ergo coefficiens ipsius 312 in aeq 3 vet a, etiam evanescit
  110. postet fai ao aers et 3o uo elanta ad
  111. U ah + e bZ + cD + B dq + fdo sit 5: eibo fiot abi 4 bg +rv + ce du 4 (aV = e ta a h + bZ - cv + l.p 1q7 + C 1 = 0
  112. sit bZ1 cV = gW fir ah + guo + e li+ e gdu. sed ita oporti esse constentes, b, c,9
  113. Mitar sit Ha Z F = gt aZ at Z + adv = oduo a codque fist de gdr + dg W
  114. et
  115. sit qu = 9Z + rv adio = qZ d9 Z + dr V + qu2 a rdio Ergo (W Vdu = (3 aW + Pa duo = Bg + CpV =
  116. Vd Ndr V +) 9Z + Vrdo
  117. qu’od ut coincisal data abzue + ac V +ae dz tafan, fiet β. b et Y Y af: Y = ae: q
  118. ab = B9 + pdque seu ab = (t aedque et ac = Cr + af dx et fit B = acr - a fdr, : 1Y = abq - aedq, : 99 r - 54. C di- tc. gat
  119. et fiet abq ab - aedq ab9 - aC dg. 5: 49) = _ aC59 - 4(4 - af - a ss d9 - af 9 d5 ,: 199)
  120. Repetamus. Esto formula bZ + cD + edzue + fdx. videamus an reduci possit ad hanc ) BW + dW.
  121. q E sit aW qq + rV erit adu = at. d9 Z+ de V + gdZ + rdo et aBu +du ext ent B9Z + βrV
  122. (6)
  123. Identificando teminos deb sit 9= af: Y et teminos dzue sit V = aC : q. Ergo r= qF r - 59: C et di . 41o s posta V dgZ + qaV =+ Ga Vrd
  124. Vaeztevtetz efdo
  125. constante quod in arbitrio est
  126. Ob terminos identificandos, f ope aq.7 fit BY + a fdr. r= ac seu β acr - afdr, : H. Rursus opt ae 4. 8 fit BOb termnos Z, ope ag. 5 sit B9+ aed9 u9 = ab
  127. seu B = abg - aedg,: gq. quos duos ipsius B valores aequando sit acr - afdY, : rr abq- ae dque: qu et ex 9 et 10, pro Y et dr substituend
  128. 1
  129. valores, fiet abq - aedque, : 49 = ac fq: C = a ff dq: e - afqdf: C, :, sf 49: ee, seu b fgC efdq = ceg ( fe dq - egdf, ergo
  130. tandem fiet in da evanescente q siet in datis edf = ce ce - bf. sed haec non est ipo in pte
  131. 1op) + updus + 12 pldus an redigi potest ad fC + gde posito () = 20y + 21 dus ubi d0 = droy + 20 dy +2, ddys
  132. a2 du
  133. Gdroy +920 dy +921 ddy 10p y. + up dus + 12 p ddy fit p = 29. 12 = 205 + duo 9: 10 seu _ 10219 = 12. 20f + 2d209
  134. f20y + f 21 dy
  135. superest aequatio 21f + 209 + d 2 g = 11 P, ubi substituantur valoes f et p. Multiphicet hoc aeq. per 12. 20 fint 21. 1. 21 - 21.12420 +12. 20. 20 + 12. 20d21 - 11. 2021
  136. fiet:
  137. fiet f = 9, 10.21 - 12d20, :, 12. 20
  138. Quodsi fiat 21 = 2m 20m: a, fint 20. 20. 10mm (= 12. 20d20) am + 12. 20. 20aa +1 20312. 20. 20dma + . 20 dio and = 11. 20. 20 a m
  139. Es d21 dy
  140. 10y + 11 dy + 12 ddus, divitatur in duas partes Bato + = 10 ay + 1 adus +oopdus + 124, ddus prior pars sit differentia ipsius osus, poserae itus gda
  141. qua divisa per 20, habetur ita ve evanescit 20. nec profectum est quicquam
  142. liet 0s df y + oif dus ~ 10au + u aydys siet f. f o. 00 et f et a Agdus + aoa gdus ~ vop gdus + 12agibus sit pg = ar
  143. d
  144. vop d
  145. r = dg g = 00g: 12 = df 00 00df: 10 f. oof q r = 19 - 00 5, . d
  146. 119 - 00f 500 fit dg. 9. 10 = 25.5 + 119df = - af5 + 11 dtdf00: 10
  147. 200 a + 210Z+ 201V + 200 dz +202 dv =o Ex 1 et 2 fiet ngo 200. 2oa (+ 210. 1207 ) 2o1. noV (220. nodZ +, 1no. 202 dv = 100. 220 a +10 220Z (u0. mo
  148. c
  149. n4 13
  150. arg
  151. = 10g: 12
  152. ldg = 119 -005, :00
  153. fiet ad prro. 200) + _ 120. 201 dv + d120. 201) V + (120. 20+) ddio + d (120. 202) dv = (10. 290 - 120. 210 ) dZ = d (10. 20 - 1B. 20)Z andent tolltu Z et aZ, fiet
  154. 00. F29
  155. 1005
  156. il fdZ
  157. 100 a + 10 = + 120 1Z = 0
  158. =20oga = 2019p - 202 9 dv
  159. 21947
  160. + 110 fZ
  161. +21097
  162. F= 120, 210 - 110. 220-2209, : 120
  163. F = d (120. 210 - 110. 210) - 21093: 11C
  164. 27

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 73r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0145?run=74