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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: 0.90.

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The machine reads it as

  1. buc a very (inall Distance From cach other:
  2. To find any Number of mean Proportionals bermixt Then imagine a Curre Line deawn chrougt
  3. any tuo Numbers.
  4. all che Extremities oE chese parallel Lines, 25
  5. eou deha, and chis is called the Lozarith-
  6. Fake the Disserence oF the Locarithms OF che micat Line
  7. trvo giren Numbers, which diride by a Tum-
  8. IF chis Figure vere drann on a verr larse
  9. ber more by one than che Numbex OF MeanS Table, and ith all requisire Exactnels, cactr
  10. desired; and chis Logarichmick Ouorient added Part, AB, BC, (9c. mighe be divided nOL
  11. torhe Locarithm of che least, gires the Locarichm
  12. OnlY InEO An 1OO OF 1OOO, BUIE CVeN InEO 10000,
  13. ot che first mean nexr ic; and chen added ro che 100000 equal Parts, and more. So haL AB
  14. last Sum, Ands the nexF, (9C.
  15. beins 10000O, AC ould bC 200000; AD
  16. As suppose ic vere required t0 sind 3 mean 300000, 9c. as must alwars be in an Arictne.
  17. Proxortionals berween 4 and 64; che Lozarithm rick PFOSreNION.
  18. OF 4, 150. 602060; 0f 64, i5 1. 806180; Their
  19. TheLine Pe beins supposed eo contain 10000
  20. Difference, r. 204+20, dirided by 4, (1. c. 3-] 1) Parrs, lec us imagine chrough cach ot chole Di-
  21. sires 0.301030; Which added eo che Locarithm visions a Parallel co be drann eo che Line AP
  22. OF 4, makes 0. 903090, the Losarithm oE B, che currins che Curre in (0 many Points, v. gr. let
  23. first mean; and again, added co rhe last Sum, the Line io be dravn chrough the Dirision 9900
  24. Sires T. 204120, the Losarithm oF 16; and 2- oE the Line Fe, and wrhich curs che Curre in
  25. Bain added, sires che Losarithm oF 32: Which che Point o. Let chere be allo supposed. the
  26. are the threc Means berwixt 4 and 64.
  27. Parallel O0, cuttins the Line A P. in che Divi-
  28. TOGARTTEMICK-Line of Pardie, iS a Sion 399563: Then any one may Hnon thaE
  29. Curre which discorers perfectiy all the Myste
  30. ries of the Locarithms, wich sereral orher very
  31. 399563 is che Lozarithm oF che Number 9900.
  32. In like manner, if S u passed chroush che Divi
  33. excellent Properries and Vses; and is thus deli- sion 9000 oF the Line Fe, the Line Vu Were
  34. neaced.
  35. drann curtins AF. in 395424, then vould haE
  36. Tet the Righr Line AP be dirided into the Line u V bC The Locarithm OF 900O, COC.
  37. equat ParS AB, BC; CD, DF, C9C. From tnC
  38. Sochac by chis means a Table ot Losarithms
  39. Points A, B, C, D, P, (90. Let che Lines A a, From + t0 20000 may casili be made; and Far-
  40. Bb, Cc, D d, and P e, be drann all perpen- cher, by producins the Line AP
  41. dicular 10 AF, and consequemis parallel r0 onc
  42. another:
  43. Note, T0 obtain aIl the LOsarithusS FFOM L 1O
  44. 10000, twill be enough to seck the Locarithms
  45. From 1000 10 10000; that is Charins drann
  46. che Parallel d+) 10 cake ehe Lozarirhms oF all
  47. che Dirisions From +toe; which Locarithms are
  48. aI concaincd between F and D: For by this vou
  49. Wvill have the Locarithms OF aII the Parrs thaL
  50. are between s and F, and whole Locarithms lic
  51. berreen D and A. For Fxample: Since O0 is
  52. 9900 Parrs, and ies Logarithm 399563, the Pame
  53. Number may be caken For che Losarithm oF 990.
  54. wrhichis NVn; 25 alto oE che Number Xy 99
  55. chanoino onty the Ars Figure 3. Becaule, ac
  56. cordins ro che Composicion oF chis Linc, OP
  57. Or TY y oustc e0 bc equal 1O F D OFD C; 25
  58. anr one mas casils prore. S0 chat O N OrN)
  59. will contain 100000; and because A O id
  60. 399563, Tubstractins ON 100000, there wilt
  61. rest 199563 FOr Ay. And after che same man-
  62. ner, havins Ay 395424 For the Locarithm ol
  63. Vu, irhich is9000; rou mar have al(0 09542
  64. Cor che Losarithm of X x, Which is 9: O
  65. 195424 FOr thC Locarithm OF 90; OF 295424
  66. FOT ehe Locarithm Ot900.
  67. HI this may be reduced co Practice FOr C al
  68. uotrac ve have here explained, is susticient ro sain
  69. Let each oF the equal ParIS, E D, DC, CB,ihe KnoWledse oF che Nature and Composition
  70. Tho inaced chere will noc arise Cuch Adran
  71. between
  72. And let them all be in a Geometrical Progrel-
  73. FOn : 25, let A a bC L, Bb 1O, CC1OO, D d
  74. 1003, F e 20000, (90. Then Mall wre havecvo
  75. Prosrestions oF Lines, Arichmerical and Ceome- cularion, writhout actually dramins chese Fi
  76. in Arichmerical Progression, Ox 25 1, 2, 3, 4,5, (90. For by che Rules oF common Arichmerick, we
  77. and (o do represent the Locarithms, to Which may find out FF, the mean Proporrional BerWeer
  78. correspond
  79. E9c. be dirided equally again in F, C, HI; and ot ihe Locarithms.
  80. dec the ParallelS Ff, C 5, (c. bC drawn, and
  81. De Mean Proxortionals Berween the Collaterat cage For makino Lorariihms by this Oblerra-
  82. ones: chacis, EC: Ff:: Ff: Dd:: Dd: 68, (90. rion, a5 ic may ac firtt Sishr Coem 10 promile,
  83. dramn trom che midele of each Subdirision and 10000, Whose Locarichms must be Founc
  84. FF, FD, D6, (90. and (0 on, rill chese paral- also; and buc 900 Betreen 100 and 1000
  85. el Lines sromine verr numerous, have al lalt aut bur 90 bereen 10 and 100, and buc
  86. trical: For the Lines AB, AC, AD, AF, are gures, buc ontr imaginins chem to be dravn.
  87. the Geomerrical Lines A a, Bb, Cc, (96. d0 dD and FF, Or between F f arid F c, EC. BUI
  88. Let there allo be more Mean Proportionals because chere are 9000 Mmbers berween 100C

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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/806933011:0481?run=74