Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

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: 0.91.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. The USC OE he Tables OE LocariibmS.
  2. 2. Zo sind a Logaricbm.
  3. N. B. P here describe onty che Common
  4. Canon oF Lorarichms contrired bY MIF. BrizGS,
  5. and publistred in Sir Zonas NoorS Mathema-
  6. cicts, and in most BoOHS oF Friconometry
  7. Navisation, ec.
  8. Proper, (thac is) a Figure ot one Place lels than
  9. than che Absolure Number, Whole Losarichm is
  10. reguired.
  11. 2. NexE Y vill Mev the may of findins thé
  12. Number ansimerins to a Losarictum siven.
  13. Omining the Characteristick, seek in ihe Ta-
  14. ble For chat Logarithm which is equal Or nexF
  15. lels to the Locarithm siven, the Absolure NTum-
  16. ber in rhe Column under N. wich chac on the
  17. r. IF che Number, Whole Locarithm vou cop over che Locarichm, is che Number desired,
  18. onld Aind, be under r00, rou hare ic alvays
  19. in che sirst PagC: ThuS che Locarithm OF 55
  20. 15 T. 740363.
  21. utich must be ordered accordins 1o che Cha-
  22. racteristick.
  23. Thus e0 sind what Number ansivers ro che
  24. Logarithm 3. 54482L; omitrins che Index 3,
  25. 2. IF chc Number consicts OF chree PlaceS,
  26. chac is, a Number under 1000, l0ol For ic in the find 54482Y 10 ansiver 10 3506, Which the In
  27. Table under N. and the Locarithm is found in dex 3 cherrs to be all Inresers; bur if the Index
  28. the Column under o. Thus the Locarithm oF had been r, then chie Number vould have been
  29. 216 152. 334454.
  30. 3. HF ihe Number bC OF Tour Places, and un-
  31. 35. 06, Thac is, 35 Inregers and. 06 hundred
  32. der 20000, Seek the chrec Arst Figures under N.
  33. a5 betore, and the last Figure on the cop; un-
  34. der wrhich, in thar Column lineally against che
  35. Tirst chree Figures vou have che Locarithm re-
  36. ParIS.
  37. Buc it the Locarithm De nOE exaCtIY cO BC
  38. quired: Thusche Locarithm OF 3583153. 5542473
  39. found in the Tables, and sire Places be requi-
  40. red, sind che Number 1o tour Places (as betore)
  41. notins the common Difference under D. then
  42. cakce rhe Disserence betvixe the Locarirhm gi
  43. sind 358 under N. against which in che Columm, ven, and the Locarithm Found in che Table lels
  44. under 3, Stands your Losarithm.
  45. thau ir; seek the common Difference in theTa
  46. 4. IF che Numiber bC abore 100C0, and un- ble ot Proporional Parrs under D. and in châc
  47. der 100000, rou must find it by che Disserence, Line sind out che Disserence ot the Locarithms
  48. and Pable oF Parrs Proporrional: Thus, it the and ac the rop just abore ic rou tave che fiEct
  49. Losaritum oF 35786 be required, sirst scek che
  50. Cocarithm OF the FOrmer FOur Figures 3578,
  51. wotich will BC 3.553649; and the common Dif-
  52. Figure. Thus if che Locarichm required hac
  53. bcen 2. 543612, the Losarithm next lels is
  54. 54357F, ansiverins r0 3496; the common DiE
  55. ference under D. i5 121: Wich ehis Disserence Ference is r24, che Diserence of the Logarithm.
  56. enter che Table of Pars Proportional, and find is Ar, which in che Pable oF Proportional PartS
  57. 2r in ehe sirst Column under 3; and then against F24 Sires 3; (O FhaE the Ab Colure Num
  58. lineally against Thac Number, and undex 6, the ber i5 34963: And because the Index i5 2, che
  59. last Fioure oF che Number 35786, Found ac the
  60. Hlead oF the serenth Columm, vou Wvill Sind 72,
  61. NTumber Will be 349 Integers and = 38. PAHIS, OF
  62. 349.63.
  63. wvhich beins added 1o che Losarithm OF 3578.
  64. viz. 3. 553649, mates 4. 553721, ihe Locarittom T0 find the Number os a Logarictm, mhose Indes
  65. OF 35786. And che Index must be 4 Decaule
  66. the Absolure Number consists of sire Places.
  67. is 5, or more.
  68. Suppose q to be che Characteristick, and sind
  69. TF che Number DC abore 10000O, and
  70. under 1000000, 25 Suppose 357865: Then sind (by theforesoine Directions) che Locarichm a5
  71. (25 betore) the Locarithm oF che Arst Aire Fi- near 25 You can, ((0 ic be bur le(5) chen sub-
  72. Sures, viz. 35786, and twill be found co bc
  73. Aract ehis Loxarithm From the Losarithm siven:
  74. (omittins che Characteristick 4) 553721; aF- and r0 che Rishe Fland ot che Remainder, il
  75. ter this, mulciply che remainins Fisure (5) ot (che Index be5, ser o; il che Index bc6, let00;
  76. the siven Nuniber bychecommon Ditterence 70, if 7, Pec 000; and (0 on proporrionally. This
  77. (Found under D.) and twill produce 350; then) donc, divide che Sum by chê common Disserence,
  78. CHIEOFF (0) che las Fisure oF che Produet, and and che Ouote sires the Figure or Figures io be
  79. add cheremainins (35) cothe Losarithm 553721
  80. atorelaid, the Sum i5 553756; to erhich presx
  81. the proper Characteristick (5) Becansethe Num-
  82. ber siven hach (x Places, and 5. 553756 isthe
  83. Lozarim LequtCa 1OF357665.
  84. placed on the Righe IIand oF che Number an
  85. sverins ro che tirst Cound Losarichm.
  86. S. IF the Number bc abore 1000000, and
  87. under 10000000. Find che Locarithm oF thC
  88. sirst sire Fioures (as betore) and multiply che
  89. Examplo.
  90. common Difference by che ruo remainins Fi-
  91. Let 6648976 BC Mhe Loearicim piven. Sup.
  92. pose 610 be 4, the nearest Locarithm lelS Will
  93. bc 4. 648974, Wrhose ABsolure Number 15 44563
  94. Substract 4. 648974 from the siven Locarichm
  95. sures; From wtrich Produet CuL OH the tvo che Remainder is 2; i0 che Righe Hand ol
  96. last Fieures, and add the ocher (as Before) pre-
  97. Exins oo a CharacleCR, (9C.
  98. 7. And s0 For any orher Breater Number pro-
  99. wrhich set 00, (Becausethe Characteristick W 256)
  100. porrionably; only De sutC ld Tur oA From che
  101. Sum lo mans fieures ds rou mulcipls che com-
  102. the Sum is 200; Which diride by che common
  103. Difference 97, the Ouorient i5 2, (and an incon-
  104. Siderable Fraction, Which rou inay omir) which
  105. 2 sec on che Righe FLand oF 44563, it makes
  106. 445632; bur since che Index is 6, che Number
  107. mon Difference by; and add the Remainder r0
  108. ibe Losaricbm, auil pretiae he Charactecillick) must hare 7 Places: cheresore (ec 0 op. asi
  109. Riet

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/806933011:0479?run=74