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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: 0.89.

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The machine reads it as

  1. CASF HI.
  2. Ds che Proporcion of Solids.
  3. Wrhere che Difterence = X is oiven, And n 25
  4. betore, Wrhich erect perpendicularty ac cicter end
  5. OE Z: Then draw R trom che midale Poinc OF X,
  6. and with ic, 25 a Radius, describe a Semicircle on
  7. the Centre d: SoTall a =I X be che greater Linc
  8. anda che lesser Coush: FOr a X, mulcipliedby
  9. a= m m = bc. R. C. D.
  10. Fhat is, in otter words, il pon tave THE FX
  11. creams, and che Sum and Difterence oF + PFOPOF.
  12. cionals, sou mas sind che Lerms severally.
  13. PROBL F M H.
  14. To findtvo squares, mhose sum or Difference is sid
  15. Reciprocally proportional to evo siven Squares.
  16. C ASF
  17. 8 1. 1 dO lite latile Dale adtel Lte BC, do 310F.
  18. Every Parallelopiped, as a 5, is 10 a Prramid;
  19. Let b ane c DC ie sides ot the Squares siren
  20. and let Sbe equal rorhe sum ot che squares re
  21. quired.
  22. Find a Courct proportional toSB ande; wotrich
  23. suxpose ro be d: Then, by che former Problem
  24. sind 2 Lines reciprocally proporrionable ro b and c,
  25. otose Sum is S: AS suppose che Segmenes s andh,
  26. and draw the Lines a and e, wrhich Mall be the
  27. Sides of the Squares Tought. For sincc S. b: : c. d.
  28. (Or m): Theretore by Similar Frianglcs, 5. a: : c. m.
  29. Wheretore ex equo reciprocally b. a:: e. c. WVhere.
  30. Core cheir Sguares uill be also in che lame Ratio.
  31. P. E. F.
  32. For il von suppole the Alcitude b e, co be divis
  33. ded into any Humber ot equal parts, by Plains
  34. parallel rothe Bale; then because oF the Prramido
  35. bn ekm b, bF DBHIb, _c. beine similar, eH
  36. Balesm n E R and IIBD F, will be in 2 Dupli
  37. care Ratio ot their AItirudes b 8, Db. Llal l
  38. Thele Bales diminist cowards the Veriex l che
  39. Proporrion oF the syuales oF Numbers in Arirhime-
  40. E d che side ot a Square, wotich ie che Disse-
  41. rence ot the Squares required, vere siven; make
  42. 25 d. V. : c. f. a Fourch proporrional; and, by che
  43. Former Poblem, Aind 2 Fines reciprocally proporti-
  44. onal tob andc; wrhich suppole ro be s and d -] 5,
  45. Whose Dinterence is d: Then crect fac Righe An
  46. Bles, and on v.) 5, describe a Semi cirele: AIL
  47. tical Progrestion.
  48. Buc ic was proved abore in Numb. 7. OE arith.
  49. merical Proeression, Thar a Rank oF Tuch Ouanci-
  50. cies are Subxriple ro as any, equal rothe prearel
  51. i. e. 10 Tuch as compole, or are the Flements oF the
  52. Parallelopiped: Wheretore che Parallelopipel te
  53. the Prramid, 15 253 101, C ene oet IS LP1
  54. OE che latrer.
  55. And chiis must holc in all Pritms Ot Wolat PiBure
  56. Toever, in P
  57. vich chem.
  58. And (0 allo in che Proporrion oF Cones ro Cylin.
  59. ders; For a Cone being composed ot Ciicles nnole
  60. Peripheries decrease Arichmerically, che Llabes 0
  61. those Circles must be a Ranke ot Secundans, (Ec
  62. cher are asthe Squares oF cheir R acuS) and conte
  63. quey che whole Rank, or che Cone, vllb
  64. Subrriple oF che Cylinder, wtich is d lank Ot a5
  65. mans Ceems equal io the greatcll.
  66. A Cylinder–
  67. Sp.
  68. idu and Cont
  69. and Heiphe, are 253, 2, and T.
  70. xence ro a Pyramid ot the lame Bale
  71. os chetame Bale
  72. chesquares reguiteu.
  73. ahict dravins a and e, cher Mals be the Sides ot

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/806933011:0671?run=74