Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. -

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: 0.85.

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

The machine reads it as

  1. PROPOSTTTONL
  2. every Triansse, ihe sum of all ihe three
  3. eguat 1olo Riehrones; and the external ansl
  4. made by any Side produced, is equal to the sum c
  5. the incernal and its opposite.
  6. ICay, 1. a - b -
  7. a
  8. = 2 b
  9. e
  10. on che ocher hand, it the sides are equal.
  11. the Angles must; for being equal, ther Hust necds
  12. be equally enclined to che Ba(C a D, t C LOIEC,
  13. ohere cher meet.
  14. PR OP. UI.
  15. in ruo Trianeles A B C, and 2B C, is all ehe ctree
  16. Sides, or tvo Sides and onc Angle, or euo angles
  17. and one Side, be respectively equal one to another,
  18. the whole Friancles are equal
  19. Os ibe Properies o Plame Friameles.
  20. F
  21. beins laid one on anocher, ) vill coneur:
  22. N.
  23. (3. e. Y. FVCl.) Wherctore b a 0 = 2l
  24. D. F. D.
  25. Fucl.) ilc beraken trom boru, thete mult remain
  26. 5 = b Y a. 8. F. D.
  27. COROLLARY. 1.
  28. Htence no S can have 2 obrule or2 L.
  29. COROL. II.
  30. In a Riehr-argled A, the 2 oblique Angles mul
  31. make a rieh one berween chem.
  32. C OR OL. HII.
  33. H2 Aneles in one A Be = 102 in anorter, 1
  34. remainins Angles mult allobe equal.
  35. PR OP. I.
  36. In the same Triancle, equal Sides subtend; and are
  37. subtended hy equat Ansles.
  38. T(ay, it a = b, then a c = cb.
  39. Llas, che Triangles a b0 and ebc, havine chc
  40. b0, arel deceen che lame parallel Lires
  41. Drav che prickd Line chrouxh che Vertex
  42. criancles on the same Base, and havine the same
  43. Deiehr, (ehat is, beins betreon che same pacalibt
  44. Lines) are equal.
  45. .
  46. c
  47. Came Ba
  48. parallel torhe Base: Then will che Angles d and e
  49. be sererally equal ro che alternate ones b and c.
  50. (29 e. L FuCL) BUL d 1 = a c = b (bY C OF. 2
  51. dL aned, dec equal.
  52. Dra de and es Parallet e0 ab.
  53. 1. The Priangles d ce and cc f are equal, be-
  54. caule cach equal ro hale the Parallelogram d f..
  55. 2. The Triangles a b e and eb fare allo equali
  56. eins cach equal ro half rhe Parallelosram af.
  57. 3. Bur A ab 0-F Aces = halF he L af.
  58. 4. And L eb c-] A ocs = hals che a5.
  59. Theretore, is ihe A Ces be taten avay trom
  60. borh Sides, ihe Ae bc must remain = e0 rhe
  61. Triongles a b6. 8. F. .
  62. And since c-] fare al(o equa 10 2L (15. e r.
  63. Becaule che Angles a ane b are equal, che Lines
  64. ac and c b must be equally inclined co. rhe Bale
  65. ab; and consequentY, be (0 ac the POinE C; WherC
  66. cher meet, and theretore c must be equidictant
  67. From a and B3 FOr iF C DC neaTeK EO, OF FartHer
  68. from b than a; ic must be because the Angle a is
  69. hettec o srealet Manb, rhicn is contraty 10 Mhe
  70. Dubpotaron.

Cite

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. - . Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/806933011:0840?run=74