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Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 12v

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: 0.80.

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. 13r); this page is its left half.

The machine reads it as

  1. Resumamus calculum
  2. X: a = (1) SddZ: dZu et y: a (1) dv: dZ et dx: a = (3) d d Z: d7
  3. et dy: a = (4). dq ddv - dvddz,: dz dZ. sit jam aequatio tangentialis
  4. ad resolvendum data dy. Unde dy: dx = d Zddv - d vddz,: (dZ d2:
  5. d ddz (: az = ddv: ddz - dvZ dv: dZ = (5) dy: ax.
  6. sit jam aequatio tangentialis ad resolvendum data dy: dx = (5) exryy: aa
  7. fet Unde per 1,2, 5. fiet adv: dedzue - du: dz = (7) qu sal Z: dz + dudo: dzdZ, quam multiplicand
  8. pe C per dZue fiet dZddv: ddz -dv = dz qu (dd Z: d + dudo: d2. sit jam
  9. dZ ddv: ddz - dv dv:dz = (8) deo constansi, et ex praecedenti aquatione fiet
  10. et ex proxima aequatione, fiet deo = (8) dque qu sddz:dz + du, quam
  11. differentiando, prodibit erit 0 = 2 dZ (sdaz. d2) aa (idZ + ddzue qu saaz: a +adv seu
  12. Ju Sddzidz + 2 Sddz. dz + dav: daz = 0. Et extrahendo radicem ex hac aequa–
  13. tione, fiet fddz: dz L = 1 + Y(1 = ddv: daZ) C unde
  14. qu. Sdaz: dz = (11) 2 - ddv: ddz + 2 + (. - ddv: dd Z) per 2 = (12) ddv: ddz - dv. 4Z = dvdv: did
  15. seu - 2 Ysi - dav: daz) = Y dv: dZ + dpav: di dZ + 2 - 2 ddv: ddZ, et
  16. compendio fiat dv: dz tdvdv: dzdz +2 = (13) 2d: de et ex proxima
  17. aequatione fiet - L + - ddv: ddZue) =4 fd: du = Zddv: daz, et quadrando
  18. 1 =- ddv: ddque dip d: deodeo - x dr 3dip ddx: dZ deo dd Z + ddvddv: de Z dd Z
  19. itaque ut extrahamus sl deda: deda Lc
  20. iel
  21. davat A- 3g) ddv + a () (1 - 2 de) = 1 - 4. lex + 4 d d.s) + 4 - 4 dis d) : 4
  22. da t ad Z
  23. o daz
  24. deo
  25. deo duodeo)
  26. dodco
  27. unde cum dip: deo detur
  28. et prodibit ddv = d - = + L ((5 - 448)
  29. per do: dz ex aeg. 13, hinc ettam t hinc res redacta est ad qadraturas;, sed
  30. des
  31. hanc tentemus reddere rationalem, et 5 4dpido oetur e seu (per 13
  32. 144) - 2dv: dz - dedv. d7dZ (, aequetur quadrateo (17) 1+. dvdg. d t dode: dZ
  33. ab 1 = dvdg: dzdZ, it fiet (d) - 2du idque - Av dv a2dZ = (1 - 2 dvdes: dy dz + dvardisle: dz
  34. et divisis omnibas per dv: dz fiet + 2 v: due L d: de - dv dedg: d ZdZdZ, atque adeo
  35. (v: dque (17) 2 d8 2Z, dz dZ des d et quia t5- 4+4. duo) - 1 dvds : did
  36. ibi substituto varore ipsius deidq modibit B 4duido- didz des (Ed9+ 2de dZ:de
  37. 27 (def. dZ, 1): (de df: dadZ) t1) 27 d8: dz =1, id de: didz +
  38. u du 2 dessie E A d2 : ds19
  39. seu du: dz d 9aZ- dzdZ,: d d9 + did, quo valore
  40. substituto in (5- 4dib), seu in 5 _+ seu Cer) in + 2dvidque d
  41. a2 42
  42. deo
  43. 1- dv des: dzdZ, fiet di d dq 2td ed edZ 1 d2 - = d9 d3 + 2d didz
  44. sive dZ aZ - dv des, : d7dZ = (dZ d Z de d9 e d7 d Z + Ed( d73;d2 + dz u des l
  45. yl17)
  46. dyd - dvda ee ed 1 =2do: d3 = dodv: 47dz aequant debet quadrato ab
  47. I= avda: dZdz, seu ad dZ dz = 2d0 d2- dudo aequari debet quadrato a
  48. ipsi de et dedz- d 2dvdg + evdr d8s: dydzue, et
  49. fiat - 2 dZ = dv = 2d9 + dv
  50. 1 5 ++, , 4 daq a d 1Z - 4 das dg d 7. 7 - 3dg a 3 + 4 dZ
  51. disdes + dea
  52. 4s + dq d3 (2 ( d5 + d3 dZ)
  53. M
  54. seu dest d tdatus ereque +ded ( a di d d9des adid + 4 d adodestdsses
  55. itaque ((5 - 4 d p. 10) debet aequari quadrato seu per aquis a debet
  56. ac aequari quodrato AtA) - 2dv: dZ - do dv: a2 dz (4), aequari quadrato
  57. itaque 1 = 2dv: dz dvdr: dzdz aequetur quadrato ab 1- odG: dydzue tvardfdes. d
  58. erit S5 = + d 1: aco) = 1 - dxdg: dzdz. et erit (1) 2dv: dq Edvdv: d 7dZ = (1) - 2 d vdg. d7 d2
  59. + duav dedg: d3 et divisis omnibus per du fiat -2 -, dv: dZ = - 2 de: d3e + dxdis de: d3
  60. seu du: dz = (19) (dg. d _ 2, de: dz - 1,: d8 d8: d2d7 +2 His rntor substituatu
  61. i 2d23,; d9 des +az d7
  62. seu du
  63. seu do = (20) dy dZ de - d33: ddgdyd Hic vator substituatur in 1- 2dr: d2
  64. ia aqu. 17. fint
  65. -ErdridZdZ (it Ac 4d8dBL Zdc. = l3d82+ dZ + d3dZ d ed5 dyaz de des
  66. s () dz 4 did de de + la) dides Edzat ttidzi didz rajar ds des + Mxt d des djurte.
  67. ndrat dic +4ax dg 142):, (lesdes + 2dide)
  68. At seu
  69. avid Z2
  70. e 1zde d7d
  71. ds +d2dZ

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0024?run=73