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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 39v

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: 0.83.

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. 38r); this page is its left half.

The machine reads it as

  1. in Ellipsi
  2. et PRt RF = dataeFP
  3. FG+GP = datae AV FG: GP:: FR: RB
  4. Ergo erit
  5. PG+ GF: FG PR+ RF: RF. seu ipsa FG sunt
  6. ipsis FR proportionate
  7. tam (FR in GB = esp in
  8. tmo GB ipsis RN proportionales)
  9. pohas ongulis et Z recta
  10. s
  11. i Gp
  12. sit F= p= P et BS pH = h. sit angulus ad E rectus erut
  13. timam. Trianguta sit sit pG = p, et pH- C fiet
  14. et PG+ GF seu A
  15. esse PC
  16. s
  17. et
  18. et PR+ RF seu PF= pertel
  19. R jam et PG+ GF = b et PR + AF = f
  20. jam b : p:: f: PR. Ergo PR = f p: b et FR = f - fp: b et
  21. FG= b - p. jam sit PH = e. posito angulo ad H recto. pat et
  22. esse FG. eii (obtriangula RQF et PHR similia) jore se
  23. FG: B:: FR. RP:: FG: PG:: b - p: p. sergo F9= eb p p cujus quad retum
  24. detructum ab FG dabit data dabit A23, et idem FG detractum, ab
  25. FD dato, dabit qR datu autem ZR habebitur YH ei proportio
  26. habetur ergo tota GH cuisi detratas sed eadem habebitur. Quadrati
  27. Hs detrahas a quadrato GP. habetur ergo aequatio, pro invenienda
  28. quod exequemur: b2 2 bp + p - e b - p - C b- p: pt = Gq
  29. Ergo GQ = b- p Y Sp CV: p est autem Sp= C2 = GH
  30. ergo fiet GQ: GH:: FG: GP Porro RQ - E FR = F et, e
  31. = b- p: B = C b- p: p. Ergo RZ: FG a C: bx
  32. .:
  33. Sf p = bC: bp. seu Rg = b - p S5p - b0: bp
  34. tam AR: RQ:: p: bip Ergo HR = 52p - b C: b
  35. Seu LH
  36. itaque tandem fiet: G b - p Ip C: p 4 (seu G2 + b. p Ss p - 6: bp
  37. +
  38. Ysp = b e: b (seu RH) = p p- C seu GH
  39. quam aequationem ordinando fiet
  40. 2p - b Sp. e :p = (5p - b0: p seu 2p 6 p apet
  41. seu ip -b p - ape + +bpe (He b = fp (b18
  42. et denique firt e = f p - 2p- b p 3: b - p.
  43. et: f- 2p. b :: p: b. p
  44. seu quadratum ipsius. HP est ad quadcatum Epconstans, multatum quadrat
  45. dquadrato differentiae inter AV et duplam BG axem, et duplum
  46. ipsius pseu radii PGse ut radius P ad radium ex foco opposito b= p.
  47. Jam triangula jam quia ML parallela tangenti PH, et angulus ad D rectus
  48. erunt triangula L et HP similia, fiebque jum et erunt
  49. jam LD=aN: p in casu motus at areas aegeales aequalibus lem
  50. poribus abscindentis. Ergo et MD= dp et fiet:
  51. ap e ap: a : p + dp:: c:
  52. to
  53. Ergo dp ex-d et= a n: p seu du
  54. p(12
  55. a
  56. PH: pt
  57. aen: p GH
  58. Ca p: prpp. ee =aa GH
  59. est autem GH = Ap bp - si paA + 2p. b
  60. ap - f p - 2p - b
  61. estante
  62. 3: V - p
  63. p P- sY + 2p.
  64. bp bup p
  65. si sint n ut temporum
  66. inciementa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 39v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0078?run=74