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

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: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 3r); this page is its left half.

The machine reads it as

  1. potest etiam tolli litera, duas aequationes considecando semper ut pares dum inferior
  2. multiplicatur, et ita depumendo
  3. _ 10X + 11 = 0
  4. 20x + 21 =0 fit 11 20 10r t ∞0 10. 21 - 11. 22 = 0
  5. +1130 o CtortuFio 22 - 0 M 2CX 2I = 0.
  6. haculm ex ot eo de oa (e nun emuera apgiari esectinu
  7. IOX uXFIXII=o W tuXruxtIS =O F1B2I4 1B. 2X +1023 =0et vslent tn OX 412 2X +11. 24 = 0
  8. Eugo res deneducta est ad (10) X + ( + (12) = 0 et (20X ( 21) + (2) =0 fietque: (0) -71021 611 = 0 ut (19 - F.10 23
  9. et (20= +10 23 (2) = f 11 23 (22) - + 12. 24. Ut ante habetur Ergo lex explicandi Et nolandum semper primum
  10. valorem in secunda explicatione, et altimum in prima coincidere. Hic 10, 11, 12 explicantur
  11. prisi explicatione 20, 21,22. videamus jam an in reductione si aqu. dualus parbus
  12. set et 20X etC. cyntiocatur larpar 10X et. et 20X et
  13. Nempe exdnabus hox ec etroxe
  14. applicate sipia resultans aeque vertio siat X, erit: + 10 21 2(+ 11.22 - 378. 282 1 = 0. Hac explicale
  15. ∞10. 12. 21.21 + 10, 12. 20. 2
  16. + 11. 12. 20. 2
  17. it2. 202= 12. 1. 2020 serest ne in altioribus veurrat depressio
  18. itaque opus depressione: Maeterea ascendetur
  19. etC. eodem modo so habent 10 eri,
  20. us
  21. c q. sirum
  22. non necessarium plititem
  23. Et proinde explicula a umme timcum
  24. 10 et 21 item Eodem
  25. iter pretemur ad a 1ox eu = et 20X e
  26. adeoque et valoris, et sublationis literarum
  27. Considerandum etiam inquisitionem eois divisoris, posset absolvi sola
  28. binl ur Termini 32.
  29. + 2t C -10Y n ne Et
  30. inquisitione solis liter aequationibus, simplicibus inter se conjunctis hoc modo:
  31. sint duae aequ. 10X + uX + 1X +13 =0 et 20X + 21X + 22X +23 20 hamm qua
  32. quaeritur valor ipsius X simplex. id est quaeritur communis divisor qui sit 30X + 31 =0
  33. quaeruntur ergo aequs duae, in duct duisr 3, det 297. et 2 Nempe
  34. sit 40X + 41X+ 42 = d et 5oX +51X + 52 = 0 ita ut (3 in 4 det 1 et 3ins det 2
  35. fit 30. 40 X3 + 30. 41X + 30. 42X
  36. + 21. 40 431. 41 +31. 47
  37. 10.60X + 11.60X +1260 X + 13.6020
  38. 30, 50X + 30. 51 X + 30. SIX
  39. + 31. 50 + 31. 51. + 31. 52
  40. 20. 70(+ 21. 70. X + 22.7cX + 25.70 =0
  41. negligamus 10, 20, 30, 40, 50, 60, quasi esse ut 1. reperietur esse 31 - 11. 3P2 + 12. 31 - 13 = 0
  42. et 313213F + 2. 31 ~23 = 0 sed ita nihil actum; nam hinc tollere 21 seu
  43. ipsius 31 valorem simplicem inverire aeque difficile ac valorem simplicem ipsius X
  44. Aatur aequatia facta
  45. ex() X et ia r explicationes n fet aequatio similis
  46. sint due aequationes ()X es
  47. Sed rursus videndum quomodo habita aeq. c5
  48. ailicet facta est ex Ex g9 (6) Xnat et (7), X mar per explicationes binas
  49. ducenda ex aqy. 1 et 2.
  50. fit aeq. similis (B), inde per explicationes binas fit aeq. 5. Et ipsa aequatio
  51. habita ex aequus Xm, et (10) Xm 3 unde sit aeq. similis (11), et hunc per binas explication
  52. sit aeg. 8. Et ita semper redmendo ad minores, donec veniatur ad x. Atque ita
  53. Incipiama ab 10X + 1 = 0 conbinata cum alius quotcum isi aliis incipiendo _ a 20X + 21 =.
  54. res Analytice exhibetur. At synthetice hoc modo
  55. Tollatur X fiet aq (3) inde interprelandoque 20 per 10. 21 - 11. 20, et 21 per 1. 22 - 12. 20, et ita porro continue, progedica
  56. et ae habebitur aeq. liberata ab X, pro aq. X 20X etc. 20X ell
  57. 20X et. etc cum
  58. jam procedendum ad aequ. conbinandas cum x: et quidem hbr 2.
  59. proponitur 10 X + UX +12 = 0 et 20X + 21 = 0 facta est ex (Dx + et 20X + 21
  60. 10 () ponendo 20 H- H 20 102 20. 11 - 21. 10 seu - 10. 21 + 11. 20; et pro 11 porendo 20. 12- 22. 10, seu -10. 22 +11. 20
  61. aeq. 1. cobinatis.
  62. Hin (x 10X + 11X+B, ect 20x+2, fent fet aq libera ab X unde sidaretur 19. X cum X,
  63. x eau aequala libera prodiret ex aeq. 6. per explicationes n + 1 directas, seu ipsius 20. porro
  64. Hhic datis 10X3 + 1X L M X + 13Eet 20x + 2X + 22 0 fit 29. (9)
  65. Rem actu exhobeamus.
  66. a ho per tomuro, etc. 1
  67. ex aeq. 5 fiet aeq. (7), explicationibus tinis indiretis, 10 pet 20. 1 - 21. 10 seu ) 1. 20- 10. 21
  68. Sit 20X +2X+ 22X+23X +24 =0. Unde projunctis ceq1. R 6 et 8 fiet 4eq. (9) explication bus sinis directis, 20 per 10. 2 - 120, eu
  69. 10X+n = 0 20X12120,
  70. sit 1003+ux+XtBounde
  71. 1,(=10, XI. 20
  72. Lionret
  73. (10 11 4r1. 20 - (-1B 5 11 . 2B, o herm , noitua a- Iutr. 20
  74. 110 2
  75. -12 20
  76. 410. -u Z, F1D. 2 - M. 297 HoM-11. 20XE
  77. Ao LLOSLIO 1Batur -102+2 2BX -102 trro, 1o
  78. Fu 19t411210
  79. si remse Es, . ( - - . - . X t1 =0 2 Var H =0
  80. 1CXFI =O et 20XL + 2IXY 2=0
  81. unde opicatione ua Aatvnosta Lsit equalio 10. 10. 22 - 10. 12. 20 - 10. 11. 21 + 11. 11. 20 =0 Expis qua tuilit X ex 10K + H = 0
  82. ox nxrune mmamrduit ii ag 9 isieret exeq. sxplica r
  83. et ex TeK +O. Et axpaeq. ex aeq. V explicationibus binis ipserum 10,11, fit aq(3) quo Ellil x ex
  84. quae lohit X ex loXZuMX =oet 20X + 2X n = V
  85. et exsqe. 3. ex plicationibus sinis ipsorum 24, 1, 22. fit. cq () quo la lit x - - - . - ex 10 rx FrX F o et 20 4 3 1 1 , 1 BI-
  86. ex 10X uXKE
  87. 1 per = 10. 11+ 12120 12 per - 10. 23 + 17. 20, et
  88. (1120 2 pe 41 12. 12 20 reph Ho. 23 - 15 20 et
  89. equares teducantur ad
  90. is oa e ci tu ere
  91. 10 X +140. 20x =o. 1 0X + 10.
  92. 10X + 11 20 2Xmx + =
  93. 10XXux 2X tuXM =o
  94. Hg Berite

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 10, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068007:0008?run=73