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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 87r

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. sint aequatun data 50d = 5ocd + 60Z + 51 deo + 6i dq + 5b0 ( =3t70co + 30 Z+ 21duo + g1 dZ + 780 = () -0
  2. sit co = Dy + dv et Z - n y + H V.
  3. 5050c0 = 50Dy + 50Av
  4. 1560
  5. 1780=
  6. 60Z = 60py + 60HV
  7. S1 deo = 51ABy + SIdA V + 51Ddy + SiA dv + sbC
  8. 61 dZ - 61 deny +6i d n v + 61 p dy +617 dv
  9. 70W = 7oby + 70A∞
  10. 80Z = 60piy + G0 r V
  11. 7Idco = nidby + 71 ds v + 71Bdy, 715 dv 478
  12. e1dZ - B. dpiy + B1 dr V + 81 n ly r S1 r dv
  13. Et ex aeggus. datis, interpretando cd et Z fiet
  14. (3) 70 Hae novae aequationes componitae intelligantur in unum
  15. ne
  16. it
  17. identificentur jam aequationes 5 et 6
  18. per y fiet
  19. 715B. 81fM
  20. fa. difa
  21. ib
  22. multiplicatione prioris facta per e, et posserioris per f.
  23. paeterea Et videatur an aequatio composita possit reddi
  24. tractabilis, si possit coincedentiari identificari osi
  25. huic C + K d0 + n multiplicatae per 1. posito
  26. 3 = gy + h D, +dO = dgy + dh V = gdy + h dv. Et fit
  27. igy + ih v
  28. ikdgis + ikdliv + ik gdys + ik h do + ik n
  29. e et perire
  30. 51 eB +b1 e , et (51C)B + Sie AB +((51 2) n + 61 e de
  31. 615
  32. Pa715
  33. 7Sat
  34. 670
  35. 1 SeteD +B1 C)
  36. t de + E lic use 8 sp
  37. I usa BiSM et s (o) _se A F BC LA + d(B C)X+ B1 edX + dix ed + 6 )
  38. S1 fdu
  39. it
  40. hoed +boee +5, edB +6i ede (L sig ik dg =) d su e) B+ 5ue
  41. 71 fd N
  42. 0d+bIB ScK d
  43. C12)
  44. 20fD 80f 1fdB 81 fde
  45. -
  46. AS dat
  47. ubi evan in qua aequatione apte eva nescunt dd et dM, et habetur B: n =
  48. Eodem modo per v habebitur A: H: ubi tantum cavendum est, ne sit A: N = B: n, sed hoc fiet
  49. Nensee scecse, fiot 60 si has literas conservamus uod si velimius destmere _ et M, (undetram destruentur A et I
  50. rota incidemus in difficilem nimis inont inquisitionem ipsarum e et f
  51. Itaque istis quoleunque comparatio machinas non licet efficere, ut aequatio ex trans datis transfor
  52. Si in aeqqe 3 et 4 liceret facere, ut coefficientes duorum quorandam terminorum unius
  53. matis composita reddatur tractabilis
  54. aequationis haberent inter se eandem rationem quam habent coefficientes duorum respon–
  55. dentium terminctum alterius aequationis, possent posset componi aequatio in qua illi
  56. Si F Itaque si simul vellemus tollere dy et do fieret
  57. 51D +61 n, :, 51A + bI7 = 7IA +BIM, :, 71N + 8II. Unde multiplicando peo crucem, fit
  58. termini deessent simul
  59. (51. 71 AB) + 11. 71 X n + 51. 81DH (+ 61.81 (n 1 = (51. 7IAD) + 61. 61XB + 51. 81 A n (+61. (B1 n ri
  60. unde fit 61. 27 (51. 81 - 61. 71) (2C = nD) = 0 und sed non licet facere An = 18, seu K B: = p: H, ut
  61. jam dictum est.
  62. si simu vellemus tollere, D et de
  63. 50R + 60H + 51 dA + 6, d H
  64. fieret
  65. 7on +807 + 7id + 81 de comperi non licere facere rationem
  66. 7I A + 81N
  67. itaque ciet: + 507XX + G0. _ RH (+ SP. Y. Add + 51. BIrd X
  68. 5I A 46IN
  69. + 60. 8IHII + 60. YI NH = 80. 71 AdX - 61. 71 nd X
  70. = 51. 70NA = 51. 80NH
  71. =61. 8OMM - 61. 8O N H
  72. -51. 70
  73. + 61. 8I rdu
  74. = 61. 80
  75. + 61. 71 A dH
  76. - 61. 81 Hdu - 51. 817 dH
  77. G+ 8
  78. constantem ipsarum 51A+6I, et 71 A + 8I H,
  79. ita enim explicato H evanescet A
  80. AA AN AX XA SL d T
  81. co
  82. N = B RN = 88
  83. N. 6271
  84. sed ita deo evanescit
  85. - 61.71
  86. i- deo b bedtes
  87. +61. -1
  88. sit, A = b et ( = cs (d fit dA = dco b et dn = des b + pdco b. Itaque fiet
  89. ex aeq. 1. fier 30 + 318 + 32deo +,d. 2x aeq. 2 fit 40 + 4 G + 42 deo + 43 de
  90. 438deo
  91. Ex caq. 1. fit 30p + 31c F 32 d ip +33d9 +32deo = 0 Ex aeg. 2 fit 40Y + 415 + +2 d ep + 43 d 9 + 42 deo
  92. Muttiplic etur illa aequatie per 43, haec per 33, et 30. et a se invicem subtrahantur, fiet
  93. Goded
  94. 43Gdeo
  95. multiplicetur illa per e, haec per f, et coaddantur
  96. =0 d( l. V + mg) ~ di y + dm 8 + ld V + mde
  97. 3. 43G. t 3143 +32. 43d V + 33. 43 des 1 32
  98. + 30 Crp + 31C4. = 32 C d p + 33C des
  99. +32 deo Y F 33 edco.
  100. -40f2Y 4158 - 42 5d4 - 43 fdes.
  101. ∞32le Y - 433 de es
  102. vd3ge 1 Gd 33fC 5
  103. +424 d f +438d54
  104. +dg2hf 1d43f9
  105. ABec 3ge9
  106. arfgip +43058
  107. datur huic aequationi
  108. Ht3rgdet + 33)de G
  109. +ge fers 13des
  110. -424 dfy -43259
  111. diffip 13df 8
  112. + 32eg +33914
  113. fit l = 32C - 42f M = 33e - 43f
  114. (et erit 30c = 40f a 2e +32 de d4 f + df = 0
  115. 4259 1 - 4395
  116. pdc
  117. - 61. 715F 1pdg inf + 51. 81 9 4 deo . 51. 81 Ve duo
  118. Aliter A = b ( = 8b ds = Idco b + dip bo et dn = c)dco b + d9 bco
  119. 33
  120. (2)
  121. 30 d + 31 n + 32 d a +33d n =0 40N 41 + q2 dR + 42 dpr = 0
  122. 61. 70
  123. A 4.X + 40 + 31 dx + 41 dn =0
  124. +33 deo
  125. elo
  126. fin 1. Vi 1 8g +. ps . S. 9 plo F. 19 0
  127. 11
  128. 3adio e gr cof
  129. 31C 7- 414
  130. 37deoe -43 dco f
  131. dise +3y de-dgrs + df -
  132. cofficientium ipsins g. astat equatio actabiliis quae est (g (3 e) + (d e)G
  133. sed video u vel deo, ad idem reduci, seu atterurum ( d sore Aeg
  134. altenntium non prodesse itaque potest poni 9-0
  135. 435.
  136. jam aedendee sunt injiceum aega. una en sibi scrpposilis, altera ex sibi suppositis
  137. divisa prius illa per 42, hac per 43, habebitur aequalio sinc ef letiam etiam tollitur f non possumus efficere
  138. , bis. Ergo habebitur des ter log. C. Et hoc videtur
  139. necedere; sit sc. f= βC. firt da= 41 β3 + 1; 13 = 43βd4 4b2 (2 deo = . 3) + 4B + aZ Bd 42 + 32 de - q2de, :, 32 qu
  140. sed im prori de simpliciter. Et proinde dues ipsius deo ralores aequando evanescit. Ha patet ipso deo noss
  141. f in
  142. sed ita inubiliter
  143. evanescit deo
  144. ta divelli potest in tres, una coefficientium ipsius sibi suppositorum, altera similite

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 87r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0171?run=74