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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 183v

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: 0.86.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 184r); this page is its left half.

The machine reads it as

  1. Sit Aequatio 20XX + O2yy + uXy + 10aXtoray +00 aa = 0. Ita praestanda in
  2. proposita
  3. rationalibus ut prodeat identica si fiat X: a = 10OV = 10Ia,: 200 P + 20. a et y: a = 300B+ hoa,: 200V + 201 a
  4. Et secundum hos valores explicando Aequationem propositam, debet prodire atia cujus termini evanescant
  5. 20XX = 20, 100100V + 2. 100. 101 a V + 101. 101aa
  6. Oryy = 02, 300. 3001∞ +2. 300. 301 = + 301.301
  7. I1Xy = 11, 100. 300.. +1.
  8. 101.300.-
  9. 10ax, = 10, 100. 200.. +1. 100201.. + 101.201..
  10. 101. 200.
  11. O1 ay = 01, 200. 300. +1.
  12. . 201. 301
  13. + 201. 301 oi
  14. 00aa = 00, 200. 200. +2. 200. 201.. + 201. 201..
  15. compendio 20. 100402. 300 =I1. 100. 300 0. 402 et 10, 100 +01. 300- 50: 401
  16. sit 20. 101+ 02. 301 + 11. 101. 301=00.412 10. 101401. 301=00. 4N
  17. 2. 20100.101 +2. 02. 300. 301 F 11. 100. 209 + 11. 101. 300 -00. 4012
  18. fiet (1mo) 208 + 401. 200 + 402 =0 Ex termine summo
  19. (20) 201 + 41. 201 + 412 =0
  20. (3tio) 2.200. 201 + 401. 200 +4012 =0
  21. medio
  22. o = 33 4 - 2.10. 6) = 2.313
  23. Adde compendia ad aeqqu. 12, 15, 16
  24. Sed quoniam arbitrariae videntur sufficere faciamus 4020. Et ex aego. 1. fiet 200 = - 401. unde ex 0g. 3.
  25. seu 201= 4012- 402 :9 2401 - 4 11 (ep ag. 2) - 411 + Y(4. (- 9. 412), : 2
  26. faciamus calculi magis deprimendi causa 4112 - 4. 412 = (8) = o fiet ex nq. 6 et y 2t = tnoz 201 = (9) = = +11: 2
  27. habebimus 2. 401.201 - 4012 + 411. 201 +4012
  28. 1 4012 - 401 = o 401. 411 = = 4112 ob _ qu 4 fiet 308: 100 = 11 m0 = - 11 = Yp5 - 4. 20. 02) , 02 = 12mo per compend - 102: 000
  29. at ob aqu. 8 fiet 10. 10P + 0r. 30 P + 2. 10. 01. 101 301 = 4. 00. 20. 105 4, 00. 02301 4, 00. 11. 101.301. unde per compendium.
  30. adeoque 301 : 104 = 1910 = - 313 + L (313. 313 - 31. 33),: 33 = (15t) - 2 00
  31. explicatis 4012, 401, 481 et pro 300: 100, Idem 301. 10l substitutis ex agq. 12 et valonibus compendiosis fiet
  32. fiet 31. 1014 33. 301 + 2. 313, 101. 301 = 13tio=
  33. 4002
  34. G cell.
  35. sa
  36. 2, v1 1. 000. 102
  37. ∞2104 000. 0
  38. 42. 1081.
  39. + O1. 112. 112...
  40. =2. O1. 102.102.
  41. -4. 1001. 000. 102... +2. 1081. 000112...
  42. ne sit 301: 100 = 101: 100. Et priora duo videns c jege eeter Neque huie malo
  43. videntur hypotheses nostrae restringentes esse obnoxiae. (301: 300 = C112. 108: 000. 100 per
  44. multiplicando scilicet tum 301 : 101, tum ejus valorem est aeq. 15 per 101: 100. Ergo si 301: 300 esset
  45. idem quod 101: 100, foret 112:000 = 1: 1 seu hoc saem (nisi in certis casibus specialibus
  46. quos bransformatione evitares licet) non patitur aeq. 15.. superest ut ostendamus negi
  47. gereratim saltem) esse 301: 300 aut 101 : 100 = 201: 200. Nam ex ag9.5 et 9
  48. habetur 202201: 200 = V 4 (119n0 = 411 : 2401 = 10 101 +01. 3013:
  49. 2(10. 100 + 01. 300)= 10. 000. 101 + 01. 112. 101, :2 (10. 000. 100 + 01. 102100 quod
  50. (10,000 + 01. 112, : 2 (10. 000. + 01. 102)) 101: 100. Ergo non aequat regulititer) psi 101 : 100
  51. sed nec aequatur (regulariter) ipsi 301: 300, seu per 18 ipsi 112. 101: 300. 100
  52. alioqui foret 10. 000 +01 112, : 2 (10.000 +01. 102) = 112: 000, quod utique regu-
  53. Veniamus ad exemplum quo iudigemus sico =a (C +aXX, :, aC + ag XZ)
  54. lariter locum non habet
  55. quaeritur (CD)dX. siat ZZ = thX et fiet ( 2+Z = hdX L ch
  56. ot du = h dx: Y2RX et Cix AZ =hat (aE + 2FhX, :, (a C + aghX) 2hX) debet
  57. ergo a C FrafghiX, ac + raGhX, 2hX aequari quadrate. Quoisi ergo res praestari
  58. otest faciendo X = 100V rioIa,:, 20ov+ roia, su effici potest, ut aa C+ rfhX, aact 2h X
  59. Liet 02 = -A1., et 20 = mn: a et n 20 et 01 =0 et 10 = ac con + t et men,ic et 00 = aa
  60. quadrato quod sittjus fietque
  61. per 5 erit 200 = C=(M+n: C) 100. Et per 9 erit 201 = - (mt 2 (m +n: 2C) 101
  62. 33= = 4. 44 : CC sed 313 =0. Ergo per aqu. 15 fiet 301: 101 seu 112:000
  63. 10. 10 seu 101 -C 2mod + nirueumqus + ammus - m M L- a nin (bmmnid 41e n +(3 mmuB)
  64. seu majus quam um + ns + Bm + B n. si MLn hoc non proc
  65. 10X = - 4 11 4 3 (1. 4.10. 13)
  66. +12 mmnon resse majus quam 44 (in + n) quodsi alterutra m, vel n sit quantitas negativa
  67. saltem nmmi
  68. 10. 10XX + G. 10X. 11 +10.12
  69. (A (aa : CC)q (m -n: C)): (= 4aa : cc) seu A (m - n,: C) a(a: C): (- 4da :cc) = f m. n ). 2a = 1 : a
  70. Denique ex aequ. 16 fiet + 4. ma 1100. 181 - 2. si + _) 100. 108 tq. F) 101. 101 =0
  71. rp. velbreniter A. 20 - 2. 10. 10) 106. 101 + 101. 101 - 2 = 0
  72. Et 101 = - 2. 20+10. 10 + ((4. 20 4+102 - 4. 20. 10. 19 6 - 2 10t)
  73. ubi videndum an fieri Bossit ab irrationalis sit quantitas reali
  74. non iideo quid obstet, sed si ambae sint affirmativae debet esse
  75. d obi mo
  76. nam soli
  77. sed quia Quia 11 =0 fiet mn. 100 = a a. 3 d = cc. 402. Ergo si 402 =0 fi et 300: 100 = Imn: a = 102:000
  78. sed 412 = Mn. 1012 - 4a. 3012, : cC 401 = mn (m+n,: C) 100 41 = (m +n, : C) 101 Ergo
  79. Ergo 201: 200 = _. 101 1 00 101 : 2. 100. porro 31 = 4 mn- mm - hm - 2mn, : Cc se
  80. seu 31 = qu (m - n, : C)
  81. =4 mn (mmenn)
  82. jus
  83. 10XX + 10X. 11 + L. 11
  84. aequetur quadrato, facile effici potest, ut deinde et iha aequetur quadrato. Par fh scribemusn
  85. prorfg scuibamus am, et pro 29h scribamus an, et ac + nX, ac + nX debet aequari
  86. mEX ju + mnXX +acmX + aa d =0. itaque
  87. unde 101 : 100 = (B, 2) 17mo = - 59, + Y 50. 51): 51 oe
  88. ubi tantum cavendum ne sit 101: 100, neque 301: 300, aequ. 201: 200
  89. qu et denique ne sit 301: 300 = 101: 100.
  90. Ubi tantum cavendum ne sit 101 : 100 = 201. 200, neque 301. 300 = 201 : 200, ac demque
  91. 42 001. 1o2 12 ...
  92. 40. 100 + g1. 102 +,GD1. 100. 101 - = d
  93. 100. 100

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 183v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0366?run=74