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[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 47

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. Tib. 1
  2. duplum
  3. RX 5PG
  4. 5)
  5. C deimon
  6. ad quoc
  7. eta, 9
  8. lius pet
  9. Vis hac
  10. impressa
  11. sit reCI
  12. retert
  13. uneentt
  14. Fillip)
  15. POdcu
  16. Apol
  17. H, PH
  18. ilu
  19. Dud
  20. PRO
  21. eE CTFOMETETCA LBLMENEA.
  22. eRoPoStTIO La
  23. Fvolvatur corpuo in F quaeritior
  24. Tendentis ad Focum F. llipsis
  25. Sit FIIipS A P M, cujus perimeter d CpOre revolvente describi-
  26. tur; hujus focus sire umbilicus alter s, ad quem dirisitur Vis qud
  27. corpus a mocu rectilineo retractum in Orbita F. Iliptica recinetur:
  28. Ouxritur hujus Lex.
  29. Ducantur KIlipsis axes conjugati LA, C L, I centro c se invicem
  30. decustantes. Ft per quodlibet in ejus perimetro punctum e ducan
  31. tur recta ez Fllipsin contingens, e diameter P M, X huic conjugata
  32. TCK ad P Z Parallela, ad quam ex e demittatur normalis P N. Com-
  33. pleatur parallelosrammum PCrH; rectaque Te F.Niplin continset per
  34. XVII. Lib. T. Conic. Sungatur Se secans lR P. Per B ips P prOxi
  35. mum ducantur BR ad P S, 8
  36. BX ad PZ Parallela, rCCtX SP
  37. IN X, _E MD IN O OCCUETONS.
  38. Vis centripeta ad s tendens
  39. CA (DEF PFOD. ZZXVIT.) rC
  40. ciproce ut Solidum SP ZuBD
  41. Hoc proinde ex FIlipsiS na-
  42. tura est computandum. In
  43. quem tinem FNip(IS Latus
  44. Rectum Principale, sive ad
  45. axem majorem T A perEI-
  46. nens, rocetur L. Ratio ipsiuIS
  47. L XBR ad BDg componitur
  48. exrationibus L = BR ad L X P O, LXPO ad M OKPO, MO= PO ad BOG.
  49. BOg ad BXG, _ BXG ad BDg: Sed ratiO ipHIUS L XBR ad L XPO,
  50. sive (per PCop. T. FI. 6) ipsius BR aut P X ad P0, aequalis es rationi
  51. DE ad PC, (per PrOP. II. FL. 6,) quia XO est paraIlela E C; _ (per
  52. Draced.) PE aequalis a c: Frso ratio ipsius L = B R ad L x P0 aequalis
  53. eAt rationi AC ad P C. POrTO, ratio LXP O ad MON PO est eadem
  54. cum ratione F ad NO. Ft ratio ip(IUS AT OLPO, SIVO MOD rectan-
  55. suli, ad Bog eadem cAt (Per XXI. Lib. T. Conic.) cum ratione
  56. rectanguli MCP (hoC CA CP9) ad TC9. FL, in casu praesenti, ratio
  57. B09 ad BXg eA ratio aequalitatis; nam, cocunte puncto B CUM P.
  58. B0 Tt ipsi B X aequalis. Denique, ratio B Xg ad eDq aequalis est ra
  59. tioni e Eg ad PNg: (Priangula enim BDX, PN P. sunt xquiansula,
  60. ob angulos ad D e N rectos; _ BXD, PF N alternos in duabuS Par-
  61. allelis B X, F N itidem aequales.) FF P Fg est aequale c A9, quia
  62. iP(X reCta (peF PrX CCd.) aequantur: Frso racio BXq ad BDg eadem
  63. CA cum ratIONC CAg ad P HG. POTKO, (Per PrOp. LZXII. Lib. 4.
  64. Crecorii a So. Vincentio, rectansulum Tub cC e c a aequale eAt
  65. parallelosrammo P CFI; hoc CA, rectangulo SUD LC X P N: Ouare
  66. Dex
  67. it
  68. Ten Vis cencrixeta

Cite

[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 47. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1040780814:0065?run=74