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Leibniz-Handschriften zur Mathematik LH 35, 4, 10, fol. 3r

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: 0.82.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.

The machine reads it as

  1. sublatio literarum
  2. Sublatio literae
  3. 10X + 11 = 0
  4. 20Xt2I = 0 (+10. 20XF 11. 20 20 vel horffrmat (20
  5. = 10, 20X) - 10. 21
  6. 10X +11 = 0 2OX L UIX + n o (YID20X)H1O. IX F1B. 22 LO NL M 30X L IBIX(I
  7. = 10.20 - 11. 20. characteres
  8. ubi notandum aequ. 3 et 4 eo inter se disterre, quod aequationes literae ab initio, sumtue eodem modo
  9. permutantur res pondentibus a fine. Hinc ex 1 et 3 fit + 10. 1021 X) + 10. 10. 22 =0. 1x 1et 4 111. 1 20X F um21
  10. Generiliter patet cxaeq. 1 et2 oriri aeg. 5. si pro
  11. pro X ( in ag. 2 substituos =H. 10 ex 29. 1.
  12. - 10. 10. 21 ( - 10. 11. 27
  13. + 10. 1. 20 + 1. H. 20
  14. 10X + 1X + 12 =0 20X + 21X + 22 =0 +1, 20X + 12. 20 = 10. 21X + 10. 22
  15. simoliter I. 12X + 1. = i. 4X + 1220 inversibns liferairum. s i tate gura
  16. B Ergo 13 - 10. 21 = 12, 21 - 11. 22 similiter 10. 22X + 11. 22 == 12. 20X + 12. 21 inversiore lterarum
  17. Et Unde ha duae aequationes dant unam 5, ut initio in primo calculo 1 et 2 dant unam 4 (vel 3)
  18. Et fit + 11. 20211. 2
  19. 10. 215) -13.21
  20. GB) in (21) ( (1) in B.d
  21. C11. 20 = 12. 2
  22. 1X L IX +1 =0 20X+ 2IX + 22X + 23
  23. acqtimo
  24. 1. 20X + 12.20X. X 2 19. 21X + 1032X + 10. 23 Et inversione it a 2.
  25. seu 110. 21 X2 + 10. 22X +10. 23 20 IL. 20X + 12. 21X +1
  26. 1. 23 + 1B. 23X X = 12. 22 +12. 2IX + 12. 20X
  27. possunt, ut 1. et 2
  28. 26 quae duce aequatones
  29. fit enim (10) = 10. 21 - 11. 20 (11) = 10. 22 = 12.20 (12 =10. 23.... et anse, aisi quod accedit 12 = 10. 23 carum seu
  30. (20) = 12. 20 (21) = 12. 21 - 10.23 (22) = 12. 22 - 11. 23... consentit priori inversione literrumi chanactus
  31. - 11. 20 - 12. 20
  32. Non est opus nunc scribere actu ipso, et explicite fiet suo loco
  33. ed Bilot sine notarum inversione salent
  34. HNTHXA rx et
  35. instituere, ut ipsa notarum inversio sit separatim pro exumine
  36. et depressione. ut: viser enim sit ordinem et simplicililem molius servari hoc tuodo:
  37. V. 10. 21X + 10. 22 =0. Et habemus duas aequationes
  38. +1921. X3 + 10. 2X + 10. 13X + 10 2420
  39. . 20 1220
  40. nempe 2 et 3. e Unde ad tollendam X calculus erit similis calculo quo sustulimus ex
  41. 10X L IX+ 12 =0 20X= + 21X + 22=0
  42. aequ. (30 X + 2X + 22 = 0 et (10) X + (1) = 0. tantumque Eratque + b0 19 22 - po ( 21 + (11 (1) 20 = 0
  43. vel si maluissemus, H0X + HX + 12 = 0 et, (2o (1) = 0 fieret 10. (21(2) - 11(20. (21 ) + 12. (20) (20)=0
  44. ubi (20) = 10. 21 - 11. 20 et (21) = 10. 22 - 12. 20. Sed si in ag. sed si mage in aega substituas
  45. valores (21) et (22), vide oritur aequatio in qua dimensionis uno gradu justo altioris seu diprimibilis,
  46. fit enim 5 otatum cum supra, ubic adhibuimus inversionem aliterarum, fuerit solum
  47. praestatet ergo redire ad modum priorem. Etsi hic constantior futura fuerit progressio
  48. Nam pergento ad 10X +X +2 = et quam antequam hinc abeamus exponere placet apergendo:
  49. IOX F uX 12 L0 20X + 2IX F 2yC + 23 (10 +10. 21X + 102L X +0. 23 =0. Ubi res redit ad
  50. quatuor notarum
  51. Calculua praecedentem quasi fuiffet ge proter aq. 10. affuiset (20) X + (21) X +(22) =0
  52. =11.20 -12. 20
  53. 10X LIXH E =0 20X + 21X + 22X + 23X+ 2420 et HID. 2IX+10. 22X Z 10. 23X + 1024 20
  54. iffet (20) =, 10. 21 - 11. 20 21= 10. 22 - 12. 20
  55. Unde perinde est ac si essent ducae aequationes 10X uX A M = 0 et (20) 1 (2X +(23) = 0. fictqu (20 =-102, -120
  56. et (21) = 10. 22 - 12. 20 et (22) = 10. 23 et (23) = 10. 24
  57. ed placet totam rem repraesentare
  58. sit 10X + 11X + 12 = 0
  59. on rto 1oulouro 102
  60. Et sc eodem etiam modo semper proceditur in infinitam. Sita ubi hoc unum turat quod basis isse progressimis ex eadem lege
  61. ZDX +EIX+ 22 =0 = +10. 5
  62. 20X +X+ UXIB=OL
  63. aumo lonido ren iro
  64. Poterimus ergo sic procedere: 10X + 1X + 12 = 0
  65. 11. 29, 21.
  66. xGr+14 =0 = 16. 2
  67. ua i ie uua
  68. Et ita porro. Et haec compendiosissima videtu r iteram ope duarum aequationum tollendi.
  69. aequatio 10X +HX + 12X +0 compinetur cum aliis ordinie assumtis, procedetu nempe
  70. ondo tantum se per
  71. CoxtEIX, UO=
  72. x+n
  73. ojuntionem jam solatam ex calculo praecedenti,
  74. prodit utique ut ante 10, 213 - 11. 2. 20 +12. 21. 20+ 13, 20.=0
  75. res reducitur ad aeq. simplicem. Had
  76. quem cutum e
  77. puu it
  78. u 10(7 4- 11 C20 20)
  79. 102)22 2 (10(11)21 + (112) 20 =0 a (0) = 10. 25 - 10. 20. 22 ~ 11. 20. 21 + 12. 20 _ (11) = 10. 21. 21- 1120.251i e ad
  80. Has jam si sit . 10X + UX + 12X+13=0 et Guicaccedat 20X + 2X + 2X + 23 = O. multiplisan fictH10. 2IX +18. 2IX +10. 23 =0 RC
  81. sent 1_ Di o- 11. 20. 2HO 2 I C
  82. duas aequationes 1oxSFX FuX LB =Det (1D) XH (21)X + (22) et fiet (20 = 10. 21 - 11. 20 et (1) = 10. 22- 12. 20
  83. et alia quae sit proxime inferiscasita; si datae posteriiris coefficientibus positis 20, 21, 2, etc. m proxime inferioris coefficientibus 10), (1), (22) erc. datae autem communus
  84. sencealim; cum tollendae est litera per duas aequationes; inficit poterit per aequation
  85. 10.2- 11. 20; 10. 2 - 12. 20; 10. 23-13. 20; 10. 24 -14. 20,
  86. =X quia -13. 20 deest, cum
  87. ut ut ante. Vanc ergo habemus regulam
  88. ad iss damen incuis
  89. in sonpe atus userais hadsferteur ad possne
  90. in tequoitione t periater. Ha cere hotis neeu
  91. Accedat jam 20X + 21X + 22 Verum hanc conjungendo cum
  92. ioda nam sit aequalu
  93. 1D. 12. 21 + 11. 12. 20 e (20) = 10,22

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 10, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068007:0005?run=73