Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 8r

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.

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

The machine reads it as

  1. quaeritur solutio hujus aequationis differentialis
  2. primi gradus dy: de yy + xx,: aa. compendio scribamus
  3. =dy: de =O: D e ubi C, et D datae, assumumuus quaesitam aequationem
  4. dy: dx Z 2: T. fiet Ot D4. et disserentiando +C Ax + C at dx- 4 d ) d - D d. E dx
  5. = - dOdy - C d h dy + 2 = D dy + D 4 dy, seu fiet dy: dx-,Oth. 2 d D. 944:
  6. , +0 + Odh - 2 +D- 9 d 4 = C:D. Ergo landem fiet
  7. Oh+O +OOdt- 02 +9-0) 44 = D540 +0) dG- D4 d D - D7 42.
  8. Si hoc loco C = yy + XX dO = 2Xdx, dO = 2ydy D = aa d3 =0 4) =0
  9. qu
  10. sit pro quaesitis 4 = 30 3 + n9 ayyt 3 et t sit 41) +4 a, fietque
  11. d4 = y+30 + aysd31 + a) d3 Va 13) a 2 = 3. 307y dy + 2 31) dy = 1. 32
  12. dt =aa egy dgo + ay dq + aa d4u dG =
  13. Ergo liis vatoribus substitutis in aequ. 6. fiet
  14. 1. 4 aidys
  15. (+ ad33
  16. (yy + XX) (41ay +42aa) 2X dx + ( + 2yy XX + X) a (ay d9 1 F aa d 42) - aa (yytX X) (1) ho raytgutaslu
  17. Aqu. aa (4ay F graa) 2y 4 , aa (yy +XX) 1. 41 a 4 = at (3. 307 + 2. 31 . Et ordinando fiet
  18. taa Y d41 + yt ad42 + yy41ay2X + yy 42aa 2X + XX 41 ay2X + XX42Aa2X
  19. aa y5d30 = a3y d31 + 2GyXX aayd41 + 2yy a aad42 + xT a ayd4 + xt a aa dqe
  20. = aagyaa 432 - aagy d33 - au Xx aa) d32 - aa XX ad33
  21. aa xx y3 d30 - aa XX ayy d31
  22. = aa 41ay2y = aqe 4244 = Aa XX 1. 41 a
  23. =0
  24. =aa yg1. 41a + a. 231 ay + 3. 1. 32aa
  25. + a,38yy
  26. Haec aequatio coincidentienda cum aeq. 4 multiplicata per 50y +51 ipsa ag. 4
  27. explicata dat (yy + XX) (quagu f 41 aay +42 a) = aa (30y + 31ayy + 32 aay =+ 338)
  28. inde
  29. 50gqa + 5oy’ 41aay + 50y42 a
  30. +50yX X quagy +5OyXX 4l aay + soyxxqa
  31. + Et yy quaqu + Sigy 41aay + Syy 42a
  32. +5IXX 40ayy F SIXX 41aay + SIXX42a
  33. - 50 44y 305 - 50949 31yy = 50aay 32aay - 50 aa y 3343
  34. .51443013 -514a31 ayy - 514a 3244y -51 a a33a
  35. Si a l Jaret 28 - 41 bC sepenieposse Cum 440
  36. omissis multiplicationibus possemus fortasse er sex aequationes coincidentiales
  37. praestare, fiere per solas sex quaesitas 30, 31, 32, 37, 41, 42
  38. (et 41 = 30 + b et 42 = 31 +C et pro Terminis y et yt, et
  39. Ex y fiet 2a _ 2041 ax + 2d41 a aXX - a2432 = 41 - 30 a
  40. seu 2. 30 a X + 2. a b X + 2. d3d aa Xx = a+ d32 = (30a) + a b (- 30a) Heebetur d32
  41. X
  42. = 31 aXX + CaXX = a31. Ita habemus vatorem ipsius d33
  43. an
  44. supersunt duae 5e49. per y et Y, ubi occurrunt 32 et 33, una cum d32 et d33.
  45. Tollantur d32 et d33 per valores inventos et differentientur 32 et 33, pervenietur
  46. ad ede tollentur. 3 32 et 33 prorsus, sed descendetur ad dd30 et dd31 ubi
  47. si velimus collere, dd 3C 3, novissima aequatio descendet ad d30 qua alibi
  48. qualia in simplicibus resolvi posse ostendimus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0015?run=74