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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: 0.84.

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The machine reads it as

  1. LLaY, then d c = = R, set ele rvo Triangles
  2. V: =RR; 1. c. coche v: kL, Or20 1: 3 kk
  3. WrheretorezRR =F, Ot 16; Or a b4 == 3Rl.
  4. D. F.. D.
  5. ratins a Letrahedrum, and in lCriBIIS IE I a BIVen
  6. Sphere. Sec Prop. 13. e 13.
  7. sea ande a d, are equal, a5 havins rvo Angles
  8. and one Side Equal in borh. Wheretore che
  9. Square ot e d = = R R; ertich beins subtracted ina Triansle, a Parallet 1o che Base, is 10 che Basc
  10. trom. R R, lcares P P = + RR. Wheretore
  11. P= V. 3 RR; and consequeny ies double a b
  12. N. B. Flereir coundeuuastraset
  13. OP. X
  14. The Sides of a Friangle are cut Proporcionablys
  15. Line drann Parallet to the Base.
  16. Thac 15, it makes, a b : b c : : a d : des
  17. Wraw ihe, LineS b c ala 6 do
  18. t t tolco Atac l cottcit. Abt Et tot C HB etl
  19. Le55.
  20. hac i6, d0: cb: : a d: a0. : 4c: a b.
  21. Dear d5 parallet 10 e b.
  22. Then will f b = d c: ThCLCTOLC CWII DE
  23. f: fc:: d a: d c: And b7
  24. inversion, fc: bf: : d c: d a. And chen b
  25. Composition, fc - - b f (1. C. b c): bf (1. C. d e
  26. 5: dc = d a (1. C. a c): d 4; Or do cb: de:: 40
  27. : d a.
  28. E. D.
  29. irien trverced, ejves dc: cb:: a d: ac
  30. R O P. XII
  31. in a Rixhr angled Friangle (a B C) a L ine (2 d)
  32. dranon fromthe Riche-ansle at the Top, Perpendi-
  33. cular to the FIyporhenuse (DC) divides the Friangle
  34. (ab C) into eivo other Ristc angled Triangles.
  35. robich are similar tothe first Friancte, an 10 one
  36. arehie
  37. B seue
  38. Demonstration.
  39. P. The Triansles bde, and bde, are equal, because
  40. on rhe Came Bale, and berreen che lame Parallels.
  41. Pherclore he Triangle a b a, Wwill hare che lame
  42. Proporrion rochem bott, 2. c. a b d: b dc:: a b d:
  43. b aC. Bur che Prianele a b d, having che Camie
  44. heighe Wvith che o equal Triancles b dc and
  45. bde, ill beco chem as ies to Sides a b and a d,
  46. are corheir Bales b0 and d c.
  47. Theretore a b: cb:: a d: d e.
  48. Trhich Proporrionals, may be consdered and
  49. varied accordins 10 che sereral Species ot Propor.
  50. tion.
  51. ASby inversion, c b: a b: : d c: d a FhC PATES OF
  52. che Lexs belo che Parallel, are Proporrional t0
  53. chole above ir.
  54. ol one Les abore itic P’arallel, isto che l’arrot the
  55. oiher Leg abore che Parallel, a5 the ParES Below
  56. Thelane chine mas be done by composicion d
  57. Division, _C.
  58. aat . dd det st dtt tet
  59. ebo c tato
  60. AIIO alternately, a b: a d:: c b: d c. The ParE
  61. arCFO One anOThet.
  62. r. For all chree Triar e ut L alBlC
  63. And che Trians aleu d, have ihe Anele
  64. common lo boch) and consequens ine Lhirc
  65. 2. The Case is che lame, a5 ro che Friangles
  66. a bc and a dc: Bucche Friangles a a
  67. beins similar ro the grear one a b c, must bc al-
  68. (0 similar tO OnC anOtHCF. 2. F.. D.
  69. From the Similarier ot wrhich chrec Trianeles,
  70. ic ill Follor, thar che Sides abour else Lsctal An-
  71. glesare proporrional (by 4. e 6. FuCL.) and chence
  72. arises he PrOOF oF che nexE Famous LLopbirion, b)
  73. chis means prorelt 2 tourchi War.

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/806933011:0843?run=74