Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 173r

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.

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

The machine reads it as

  1. 4 = 11. 2
  2. 1 2 12 = 1. 1.t. 3
  3. Sit aequatio generalis
  4. inter y et L
  5. c
  6. l
  7. finita vel infinita relationem exprimens
  8. a ab aaab aaba abiaa 4ba
  9. O= (0, 9 +025 4 03y ete) Z + (-10 + 11y +1y etc) Z + (204 2y ty Z + (30r Hy Brgy CH)
  10. et sit Z = 101y + 102 yy + 103y + 104y2+ 105y etc. ponatur 10=1. flet
  11. 101 = 01
  12. 102 = 02 + 11. 101 +20, 101. 103 = 03+11. 102 +. 12. 101. +2. 20. 101. 102 + 2]. 1012+ 30 5013
  13. 04 = 04 + H. 103 + 12. 102 + 13. 101 +, 20. 101. 103 + 2B. 1022, f21(101. 102 + ax + 22. 101. 1014 3. 30. 101. 102
  14. + d 1027F+ 31. 1013 2 +40 10rt, 105 = 05+ 11. 104+ 12. 103+13. 102+14. 101 F 2, 20.101. 104 +
  15. 2. 20. 102,103 + 2120 10 +2. 21101. 103 + X. 21. 1 102. 102+2, 22. 101. 102. + 33a, ( 23. 101. 101 + 33no
  16. +3. 30 101, 102 + 3.10 3. 30. 101. 103 + 35 10r o3 ∞3. 31. 1012. 102 + ( 32 ter 1 101 + 40. 101. 102
  17. 10b = osque +41. 101+ 50. 101
  18. + 20.103. 103, 106 = 06 4 11. 105 + 12. 102 + 13. 103+14. 102. +13. 101
  19. a
  20. F3. 101. 102 + 2. 29. 1324. 1012 +639, 105. 102. 103 + 30 102 +35, 31. 101102 + Por 103 331. 101. 103
  21. F7. 32. 101. 102 + 33. 101 4540. 101. 102+448. 101. 103, + 4,41. 1013. 1024. 47, (0l 10 1017 1
  22. +50.51012102 + 60 1016.
  23. RRegulagereralis haec est
  24. scribantur ordine literae qua numeri effi. aequalionis dutae , nci, et
  25. ex qui in quovis membro ccurrunt non nisi semel, cum his conjungantur formae
  26. ex literis equationis quaesitae ea lege ut notae dextrae omnium liteparum simul
  27. sumtae equenturnum componant numerum aequalem notae dextrae ertis numt
  28. cujus valor quanitur. forma autem ex numeris posterioribus tot debet esse ingredi
  29. ertium, quoc sunt unitates in nota degtra simistra p numeni posterioris praefixi
  30. enique numeri veri coefficientes sunt pameri transpositionum formae)
  31. Exempli causa quaeritur valor 104 scribo cum nota pref numerus minor
  32. seu eat ex deuinor seu exe datu aequatione sinistram notam habens o, per
  33. regulam nollam ascipttum habe at nundium majrem seu ex quae sita aquaton
  34. notae autem dexhae facere, debeant 4, non scribi potest nisi +og. sequantu
  35. notae numeri minores notam smistram habentes mempe 11, 12, etc. Et it indicat
  36. ascribendum numerum unum majorem (ob notam in 1t sinistiam 1) eumque debere facere
  37. is ergo a 3 nota dextra, isem eit cam 1 nota dextra in I1 componat 4 ergo non
  38. pligerit quam 103, eti fit + 1. 103. Indescribo 12, cut pari jure ascubetur 102,
  39. et fiel + 12. 102 item + 13, 101. jam pergo ad 20, ob 2. notam sinistram deberst
  40. ascribi fonna duorum dimensionum, et ob notam sinistram o, ebent hujusforme notae dextiae
  41. inadnere 4, et filt 20. 103. 183. cui praefigemus numerum verum 2, quia 101. 103
  42. duas habet positiones 101. 103 et 103. 101, et fiet tandem + 2. 20. 101. 103. similiter
  43. siel + 20. 102. 102 et e dende pergetur ad 21. Ergo forma secunda dimensionis
  44. ex numens majoribus ascrbenda est ob 2 in 21; sed cujus notae dextiae componant 3 quia
  45. Cin 21) +3 facil 4 numerum nolam dexlla in 104 cujus valor quaeritur Ergo
  46. fiet 2. 21. 1018 102 nam 2 praefigitur b rationem dictam, 22 dabit 101. 101
  47. seu fiet +22. 101. 101 30 dabitequirit formam 3 dimensionum, abi tres notae
  48. dextrae conflant 4, et fit 1012. 102 ubi 1+ 1+ 2. faciunt 4 et ft praefigitur antem 3
  49. quia (, 101. 102 tribus modis variari pt, adeoque stabil +3. 30. 10F. 102. et
  50. 31 requiret formula frium dimensionum uboe posit 3, quia e3=4 E 1 (in 31) +3 com
  51. point 4, Ergo requiritur 101 adeoque fi T31. 10. denique 40 requi 32 patet scubi
  52. omu et cujus notae faciant
  53. 4 Ergo non potest esse nisi 40. 104. sed hoc ultimu dinittitur, quia 104
  54. ponamus
  55. ni in aequatione data abessent omne termini, ubi y ducitur in e soliqus adeo
  56. non dest ingredi in ipsius 104 vatorem
  57. addessent numeri minores 10, 20, 30, 40 esq cobi g0 posuimus = 1.
  58. 9
  59. Ex literis aute
  60. 50101 104 = 2. 20.101103+
  61. a
  62. et ex y solis seu o1, o2, o3, etc extet soluin. 03 0
  63. 102 = 20. 10(V
  64. fiet 101 = 01.
  65. 103 =20. 2. 20. 101.155
  66. 20. 1 102. 102 + 3. 3. 10(2. 102
  67. +3. 30 10p, 103. + 4140 10r102
  68. 105 = 2. 10. 101. 104 + 2. 20. 102. 103 +3.30, 101. 102173
  69. Et ita porro.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 173r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0345?run=74