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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 29v

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: 0.84.

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. 30r); this page is its left half.

The machine reads it as

  1. sed ut definiamus progressum conatuum centralium paracentricorum
  2. intelligantur tangentes seu elementa curvae, 1C2C inst et 2C3C in H sitque pH ex Peducto
  3. perpendiculanter occumens ipsi 2C3C productae in H et porro occurrens ipse
  4. denique in 1C2CN recta sumatur A, sic ut sit H parallelqu Rve
  5. eut _ 3CK: MH: 2C3C: LE_ CH. Rursus ob tiangula
  6. ZCPN, et H similia erit MH: H:: CP. e ve (PH seu
  7. + fick 2CK
  8. HV. CP 3 2(7C: CHSCK. PH. H. CP
  9. Verrim ut note inveniamus WHAH et Hps
  10. intelligatur evolvicurva _ CC, et quidem
  11. ordine retrogrado 3C=C,C, ata ut (it er
  12. OIV = FBC, et 2(2V = L3C2C jam
  13. in CEY sumatur, utsit .V W parallel. CD
  14. erit
  15. ussq
  16. 3CK: 1V W i 2CZCC: CV
  17. 1V B: IV2V :: CP: PH
  18. Ergo 3CK. PH: IVEV. aP
  19. 2C3C.
  20. Ergo ipsae 3Ckautr conatis paracentrici, sunt
  21. go 3CK = IVEV. CP. 2BC: PH. CV. jan atunde seu ipsae ces
  22. conatus parrcentrici 3CK, sunt in directa ratione, radiorum (ce)elementorm
  23. curvae motus ( 2C3C), elementorum curvae molisis evolutione descripto (iv
  24. et in neciproca ratione distam distantiarum gentu a langente (seu ipsarum
  25. et curvae evolutae (seu CV,
  26. vel in recipioca, ratione triangulorum CpV
  27. ipsaesist
  28. porro ipsae sEY sunt in composita lationeerementa curvae el evolution
  29. descriptae sunt in composita ratione arcum evolutorum (CV) et angulorum
  30. VC2Y seu 3C2CK ergo is cum 3Ckissint ut 1V 2V. CP. 2C3C: PHCt
  31. et IVLV sint ut anguli deflexuum set CV, ergo 3CK fient ut
  32. anguli deflexn aui
  33. deflexus et2 (3C. CP: PH. Assumaluo directrix
  34. Faliqua vel axis AB id nered cui ex p occunnt PR ad anguo
  35. ectos, et ex A educatur alia ad AQ perpendicularis, t AE, et
  36. psis AE APi opus productae occuptie occurrat tangens CH BCH, in
  37. dq et in f idem vero jam poterat ex superiribus derivari nec proinde opus faisset
  38. lineae evolutione, nam invenimus 3ck 3CK. PH: H CP: 2C3C: CH. Ergo
  39. F ipsae 3CK, sunt in directa ratione HN CP, 2C3C et recipioca PH. CH jam ipsae H
  40. H sunt in con (ob angulum HNC recto aequivalente) sunt ut in composita
  41. coratione ipsarum CH, et sinuum angulorum fexus N2CH, ergo quos
  42. directa ratione elme velocitatis in curva (2C3C, singulus sinuum angulorum
  43. a centro pH; paulo apte autem eadem invereramus, iisi quod pro simubus
  44. deflexus prodieiant ipsi anguli deflexus, sed in angulis inassignabilibus
  45. sinus sunt angulis proportionales. ducantur duae puraltelae AE, et RF
  46. et velocitatum in va, e centro p, est parallita axicurrae A ARi ee A plam Cui
  47. educatur Es occurrens ipsi ps ex pendemaliter
  48. S. Ep L: pC. CH, ergo quia Ep constars feat Es, ut BC. CH
  49. centra Leqdimatur ducatur si placet recta constans quaecunque positione et magnitudinet motu regulam semper gyrari circa curba, mobile ipsum
  50. dete iminata, seducta si plac ut Ps ed pE (educta si placet
  51. et angulo PES, aequali
  52. (ita ut 25 seuper cadam in rplinter parallelas AE
  53. HC
  54. educta
  55. P
  56. et reciproca PH, CH, ergus erunt ipsae 3CK in directa ratione E, C p rC3C.
  57. deflexus (3) et radiorum CP, et reciproca distantiarum dengentis
  58. finus vocabimus Z. erit erunt ipsae 3CK, ell in directa ratione Z, CH, CP, 2C3C.
  59. et reciproca pH seu conntus centi paracentrisi sunt ut anguli in
  60. (quarum siplacetun eR transeat per P centrum, at Ex centro p
  61. a perpendicularis ex curva occunt inp
  62. pa
  63. e
  64. id
  65. M
  66. tenta
  67. E
  68. 2
  69. e
  70. sec
  71. multi
  72. DEs detCBH
  73. ens
  74. deniu data
  75. conatus in aqua
  76. quacuns hassumto
  77. cantro quodum
  78. conalus par
  79. _MC K)
  80. unt in componitara
  81. 2C
  82. desce
  83. Rac
  84. set
  85. sesgntium angne
  86. pura
  87. indentiae
  88. ad tex
  89. tento
  90. insu
  91. in radi DC ad mngente pule
  92. prbulis
  93. x Cis.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 29v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0058?run=74