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

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  1. Proportion, as the Numbers ther ansiver ro do ) Losarithm oF 9, che Tourid a midale PrOPOF.
  2. in a Geometrical onc. AS For Fxaiple,
  3. tionat berrveen the ablolure Numbers r and 10
  4. 2. 4. 8. 76, 32,. 64. F28: 256. are NNum- encreased wich seren Crphers cach: Then ctiac
  5. bers procecdlins from Vnier, in a Geometrical Number noc beins exactly the absolute Numi:
  6. Propoirion continued. Nou il over thele vou ber 9, but bigger ox lesser chan 9, (wich seven
  7. place a Series of Numbers, (beginning wicho
  8. Erphers added r0 ic) cher accordinsly found
  9. in an Arichmetical Proportion, ther vill sand our neu Geometrical mean Proportionals De-
  10. chuS,
  11. treen char Number and 10, il ic vere less;
  12. and betreen that and the next lels chan ic, a5
  13. 1. 2. 4. 8, 16. 32, 64. 128, 256, 572, 690. Soon as ir came robe bigger, Coc. rill at last, 2F-
  14. ter a prodigious Number oF Tria(S, (viZ. 25.
  15. and the Numbers abore, beginming with (0) ther came ro the absolure NTumber 8, 9999998.
  16. and Rrichmerically Proporrional, are called Lo- which approacheth very neaF 1O 9, 0000000
  17. Sarithms.
  18. 2. The Addirion and Substraction OE Loga
  19. And in order to find the Locarithm ot this Num-
  20. ber 8, 9999998, ther found an Arichmerical
  21. richms ansivers t0 che Mulriplication and Diri- mean Proporional between the Locarithm otc
  22. sion oF the Numbers ther ansiver 1O. Thus the and 10 (2. e. betreen 0000000 and 10000000.)
  23. Locarithm 2 added ro 4, makes the Logarithm And then anocher becween that so found, and
  24. oF 6, Whole correspondins Number is 64, (the 10000000 again; and (0 on, rill at last chey
  25. Product oF the Number + mulriplied into 16.
  26. AIO rhe Lorarirhm 5 Tubstracted trom 9 leares
  27. the Lozarichm oF 4, Wrhose Number i5 16, (c
  28. qual 2o 5F2 dirided by 32.
  29. And the Case vould be the lame if any orher
  30. Rank oF Numbers in an Arichmerical PFOPOE-
  31. tion vere made ro anliver ro the Numbers be.
  32. came 10 0, 95424250, the exact Losarithm
  33. OE 9
  34. They vere Corced to proceed aster the same
  35. manner also t0 sain the Locarithm OF 5; BUE
  36. then cheir Work oreu somethins calier, and
  37. more expeditious.
  38. T. For since by diridins 10 bY 5, che Ouo-
  39. Lor. Andtheretore chere mar be manz Porrs of rient is 2; cheretore the Losarithm oF 5, sub.
  40. Losarithms, 25 indeed there are.
  41. Aracted from ehe Losaritum oF 10, must sire
  42. And chus also ill FxEraCtIOn OF ROOrS bC the Locarithm OF 2
  43. pertormed by biffectinq the Lorarithms oF any
  44. 2. And as r0, mulriplied b7 2, sires 203
  45. Numbers For the Square ROOr, and trisectins (cheretore che Lorarithm oF 2 added ro rhe Lo5a-
  46. them For the Cube: A5 For Instance,
  47. T0 extract che Square R0orOF 256, divide
  48. its Losarithm 8 by 2, and ic ill quore 4; Which
  49. Cocarichmick Number 4, hach For ies absolure
  50. Number 16, and cherefore 16 is the Square
  51. ROOT OF 256.
  52. To extract the Cube ROOEOF 64, divide its
  53. Cosarithm 6by 3, and che Ouore will DC 2:
  54. wtrich is the Locarithm OF 4, the Cube ROOr
  55. OC 64.
  56. 3. T0 apply chis Mattes For the matins oF
  57. Cannon Or Table oE Lorarithms, thac Bould an-
  58. Tiver ro Common Numibers in cheir natural Or
  59. der, che Inrenters procceded in this Merhod:
  60. Ther pirched on those which are naturalI
  61. Ceometrically proporrional; a5,
  62. Fy YO, 10O, 1O9O, 1OGDO, 269D0O, 1000009, 1000000D, C.
  63. And co chesether sirted nor che sinele Locarichms.
  64. 6, 2, 29 3, (90. 25 in oux Instance (NNumb. L. )
  65. abore, bur those auxmenced ich many Cy-
  66. rithm ot 10, sires the Lozarithm Ot 20.
  67. 3. Since che Square ROOr oF 9 is 3, there-
  68. FOre The Locarithm oF 9 beins divided bY 2, OF
  69. halved, must sire the Locarithm oF 3
  70. 4. BY substractins the Losarithm oF any one
  71. known Number, from that oF another, voi
  72. have the Locarithm oF che Duorient oE che FOF-
  73. mer Number diridins the latrer
  74. And atrer this ox the like manner they pro-
  75. cecded rill chey trad compleaced che C annOn OF
  76. Locarithms eo Numbers reachinq +O 10000.
  77. It ron ould sec au easie and expeditions
  78. Way oE makinu several TOrES OF Locarithms 1O a
  79. larse Radius, consule CapF. Fdm. FTalley5 Dis-
  80. course in Phil. Trans. NV. 216. WWhero From thc
  81. pure Consideration DF Numbers, and wichal by
  82. the Lelp oF MIT. I. NemronS Mechod ot findina
  83. the 2noiae ot the Numbers ot a Binomial Pou-
  84. ex, he Mens horr ro tind readily the Locarithms
  85. oF all Numbers r0 abore 30 Places; and he
  86. sires there sereral Series For this Purpole, some
  87. universal, aud some appropriared io peculiar
  88. phers, in OrdeE FO AE PFOPeF Locarithms FOF aII POrES OF Locarithms
  89. intermediare Numbers between L and 10, 10
  90. and 200, 700 and 1000, C9c. Ther made
  91. cheretore 0000000 10 bc the Locarithm oF 1
  92. and 10000000r0 be the Locarithm oF 10; alsc
  93. 20000000 they pur For the Locarithm OF 100
  94. and 30000000 For the Lorarithm of 1000, ma
  95. Kins Aillthe Index Or Characteristick OF the Loga
  96. rithm co be one lels chan the Number ot Places
  97. Nicholas Mercator also did a g00d wrhile since
  98. make some improvements in this AHair, ot
  99. utck rou hare Dr. WallisS Fhouxlus in Phil.
  100. Trans. N. 38.
  101. And Zohn Grexory hach also Mewd a way 10
  102. mate Losarichms 20 25 Places, by means ot chc
  103. Fsyperbola
  104. For che Characteristicke oC a Losariibm: sec
  105. in the Absolure Number, because ches appoinced in Index.
  106. wich chole appointed For 1, 10, 100, 10000, C.
  107. extrieh victi most indetatisable lals allu Calc
  108. Mey canie etelet ta otde (2. 2) 10 8ec e
  109. 0000000 a5 the Lorarithm ot 1.
  110. 3. Duc then che grearest Ditticuler and l’ains
  111. Was vet eo come, vrtrich Wvas ro And Locarithms
  112. For all che iutermediare Numbers correspondine

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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/806933011:0478?run=74