Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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: 0.87.

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The machine reads it as

  1. eles are Lguaterat (bY l4C. )
  2. prearex han 2 Lipsc AnSles, and Lels Clati 6 AIBI
  3. Ones.
  4. Forn_ F m X = F m n = 4 L (B7 121)
  5. Thar is,
  6. ther are Equiansulur, ee eus ncal Frian-
  7. 2: The Lees oE che Righr angle are or ctie same
  8. Kind wich the opposire Anoles. So in che Triangle
  9. BD A, bccause D A is Grearer thau a Ou2
  10. deanc D P, che Ansle D B A is GreateE Than che
  11. Richc-ansle D BP. And inthe Friansle BC A
  12. becaule A C is leser than che OuadranEP C, the
  13. Ansle C B A is lels chanthe Righr- angle C BP,
  14. 2. YF che Legs (and consequentty che Angles)
  15. are ot che Came or disserene kinds; the TIrpOTI
  16. nuse is accordinslr lesser or grearer than a Oua
  17. drant: S0 in che Friangles P D A, F C A, the
  18. IIypochenuse A P is lesser than a Ouadram, ou
  19. in che Priansle BD A, che Fyporhenuse A B, is
  20. Greater thanche Ouadrane B P
  21. sles are Equilateral, (BY LAth) and cheretore Pqui
  22. angular (by sch) and cheretore che provoled Trian
  23. 17. First, The3 Angles oF every Friangle, are
  24. 6
  25. 1. 0. 2L = D. )- 6 fl.
  26. 2ay, The Sum oF che internal Angles, is le
  27. than ehe Sum oE the Incernal and External boch
  28. erhrich in all, matie buc siX Righe Angles.
  29. 18. OE leveral Arks oF srear Circles Fallinsfrom
  30. thie Pame Poine of the Spheres Surtace on another
  31. Circle, the greacest is thac which palses chroush
  32. che Pole ot the Circle, andche nexerothis, is grea
  33. ter than thac ertich is Faxcher OH.
  34. For suppose P che Pole oF che Circle C a L
  35. and the lole ot ll C; then iS AL
  36. AF = AC; andche Arch B aC = BP
  37. Jors trom che WO lall.
  38. 3. IFHC LSPOHeMUICIS LCIS Os SICateL CMAH a
  39. Ouadrant, CiFMCL LCD WSCIE Les aacCse LInole, I5
  40. accordinsly oE che lame ox ditterent Lind, 25 F0l-
  41. D - C = TI
  42. L
  43. For che viewing che Sines, Cosines, and orter
  44. Riohe Lines oF Arks, Wrhich are noc visible in a
  45. common Sphere; Let the Arks ot chree orcal CH
  46. eles oE Card Past. board be put roserter; do al
  47. Armillar Sptiere.
  48. 19. A great Circle pastins chrouph che Poles
  49. anocher srear Circle, curs it ac Righe angles; at
  50. On the contrarr, if ie curs ic at Righe-angles, i
  51. passes chroush iis Poles. Thus the Angle P BL
  52. -. = POD = PDB, 21(0 = 10 a AC.
  53. 20. In an oblique ansled Friangle, il che An-
  54. eles at the BasC are like, Or of the same Kind, i. c. borH
  55. Acure, or boch Obcule; che Perpendicular FalIS
  56. richin che Triansle, and the Ouadrantal ArH
  57. withoue: Bur is ches be untike, the Perpendicular
  58. Falls withour, and che Ouadrant within. FOr che
  59. Frianele F A F has the Angles F and F ACurC, and
  60. the Perpendicular AC Falls victiin, and ehe Oua-
  61. drane A Writhour. AIO the Triangle B AC hatH
  62. B and C obtuse; and the Perpendicular AD wvichim
  63. and che Ouadrant A u Wwithour: Bur che Triansle
  64. BA F haS the Angles B, L OF different Kinds, and
  65. che l’erpendicular AC wirhour, and che Ouadrant
  66. A a Wrichrim.
  67. AIIO, by che Paus LISuC lsmanitere, ho ene
  68. ambiruities ot Rishc ansed Prianples may be
  69. Colred, viz.
  70. AS SupPOTC ThC ENO ACRS DL, D R, and ChaL
  71. BP II, The Plane ot the greater WeC CIHC
  72. round B FI, eill thac a Righe Line Fallins trom
  73. pervendicular ro the Plane B A H, mas tall 01
  74. Lome Poine of che line CA, suppole on ; 10
  75. in chat Poluion L’a B WillDe aSpesek Hlal.
  76. Righe ansled ac A, and B P chc FIyporhenule, B A
  77. che Bale, P A rheperpendicular Arct.
  78. And suppose PA (in thenexE Figure) BC equal PA
  79. OE the Frianole, and sicred accordins ro irs Letrers
  80. cherein, and dra A F, P FPerpendicular tO BC
  81. (0 A B, P B, PD, Will bC Sines oF the ANtS B A
  82. B P, P A, and cheir Co sines will be E C, F C
  83. DC.
  84. Thele

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/806933011:0857?run=74