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

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The machine reads it as

1. In t
2. ence between the Ri
3. L.
4. ines RN and K n, drann from ehe same Point Le aeseride an Fyperbola, having che Fransverse Dia
5. in the Curve to boththe Foci, is alvays equal tothe
6. Transverse Diameter or AXiS I F.
7. mecer D E, and ihe Loci l and n siven.
8. From che Point K in the Curre, lex the Ordinat
9. K Ebe appliec, chen will P Pbe che Abscissa, anc
10. noced cb. Let C. NPor C n; che Distance From the
11. Focus torhe Centre, De called m, 25 in (Cor. 2. 0t
12. Prop. 2.). Then wil IN =- C 1 -] - C N == = 0b
13. eb. 1 m: And Ln = CL = C n = : 0b. +
14. eb. m
15. Square each, and L N Square = 00b B-
16. cbb -] cc b b -] - 0 b m - 2 c b m- mm
17. And In Square=
18. 400bb F 0c bb Y ccbb
19. =ob m. = 2 c b m- = m m.
20. Tocach oF wohich Squares, add the Square oF
21. the Ordinare P. R, Which in ehis Nocarion vill be
22. Conrid ro BC +cm m - 4c em
23. Sec Cor. 3. oE Prop. 3. and chere will arise che
24. Square oE rhe Hyporhenules, KN = 10 400bb
25. = 0bm + 2cbm = mm. 1 + em m.
26. +e e m m
27. 00 and oE K n = = 00 bb = ob m.
28. 2cbm. F mm- p + emm aeemm
29. Out oF which Onantiries extract the Squari
30. ROOIS, 25 may casiy be done, and chere will L
31. toune,
32. R N = = 0b -] - m -)- 2 em
33. And
34. En = : ob = m - 2 e1
35. Whose Sum is just ob. 2. F. D.
36. N. B. LAO EHC LalC, L2 n =0b = p 2 en
37. be an impossible Equarion, vet ris no matter herc
38. vecaule alt se Paco, buc: ob. nec to in 1
39. Addirion.
40. From N, ac any convenient Distance, a5 N F
41. Arike an Ark, and keepins cho Compasles ac char
42. Distance with one Foor in C, mark che Point C ir
43. the Axis continued; then ich che Lenoth C P
44. and one Foor in n, Crols He Formex ArK L, 1O IIIAH
45. vou sind a Point Which is in che Hyperbola; and b
46. chis Hethod repeated, vou may find anocher Poine
47. ffurther on, and (0 a5 manr a5 rou pleale.
48. Th
49. Realon ot ihich is cridene trom chis PropO-
50. Etion.
51. Let the Second Aris or Conjugate Diamerer os the
52. Tirperbola B A, bc dus i adn i placc at is
53. Vertex, paranet 10the Granates, ad L. LBet
54. is from the Centre L, jou dram thro the Points
55. Oand P, tro RM Lius tunnin on insinuets
56. And aster this dram a Parallel to this Diameter
57. Wobidoro oie tesecobtaus ad etrus t sus.
58. Ic will be plainis demonstrable,
59. I. Thatthe Parrs of the produced Ordinates, CC
60. and II R, intercepted between the Curve and the
61. Asymptotes, will alvars be equal.
62. Forthe Prianples C E P and C F R beins Simi-
63. lar, a5 also C F O and CFC:: it must BeaSCF
64. : P O (OF FP):: C F: F Q OF F R. BuEO F
65. and P P’are =: WVheretore (L F and F R must bC
66. equal: From which catins che equal Ordinares
67. che Remainders: FI R and D C must be equal.
68. 2. F
69. Il. The Rectansle under C and er l (or l1
70. and lG) nill ever be equal to the Square of B,
71. For che Friansles C F. O and C FO, beine
72. similaE, C F: F O: : C F : F 9: : (OF 25) thC
73. Square CC: SGlate L.. Hal 15, (b) Cd1. 3
74. Prop. 3.) 25 the Latus Transversum 10 che Latus
75. Rectum. Thac is, by che lame Proposition as che
76. Rectanole DE EiS EO F C Sgnare. And C F Square
77. EO Square:: C F Square: F O Square. BaE iF
78. From CF Square, voû tate avay che Rectangle
79. DF L, chere ill remain C F Square (bY 6.
80. 2 Euclid.) And is FrOm ChC SquAre OF FO, vou
81. cahie uhe Square ot J C. here wil remain che Rrect
82. an81
83. ROP.
84. C2) or eo a souret part os che Figure.

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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/806933011:0428?run=74