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: 0.86.

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

The machine reads it as

  1. U
  2. Form of Fractions; cher must (it Etiey have HOE ( à = L e. We may conclude; That co Square any
  3. one) be reducedro a common Denominator in ihe
  4. least Perms; and then eo find our the Rational
  5. Ouorients, rou necd oniy divide che rwo Nem
  6. NumeraTOES, by cheir srearest common Dirilor
  7. and chen sou must e0 on as abore, in Intecrat
  8. Surds.
  9. Thus, H ehe Sum and Diference oF V: 24 anc
  10. y: = vere required: When reduced to 2 com
  11. mon Denominaror, they will be V: ands:
  12. and chese dirided by cheir greatest common Divi.
  13. Sor V: itie Ouores are V: and V: 95, Or
  14. 6Y: and 5 V: =, Wotose Sum isY : 1L
  15. and heis Disterence L V:
  16. NV. IE Etic Simple Surds xiven ro be added, or
  17. Tubrracted, are Incommensurable, then ther can on
  18. ly (generalls speakins). De added or subtracted b3
  19. the Sions J and -: For neictier Sum nor Ditte.
  20. renice can be exprels d by any, single ROOT. AnC
  21. tromthis Addicion and Subrraction oE simple Surds
  22. onty by che Siens, ariles wtrat ther call a Surd Bi
  23. nomial, Ox Residual R0ot.
  24. Thus, V: 6- V: 7, is a Dinomiat Surd, anC
  25. 1: 7 =- : 615 a Residuat Surd.
  26. BuE LrOm Prop. 4. and 7 OF Fuclid S second B0ek
  27. there arises a Rule erhich helps us 1o sind che Sur
  28. or Ditierence ot Incommensurable Square ROorS
  29. Wrhich Rule is chis.
  30. 20 d siom the Sum of the sgantes s ie
  31. Surd Ro0tS, add, or subtract, their double Ret
  32. angle. and the Square Root of the Sum, or Re
  33. mainder, is else sum, or Disserence souxtra
  34. . 81.
  35. Fosind the Sum ana iHterence OL V. 14. ai
  36. N: 12, cheir Squares beins r4 and 12, their Sum
  37. will BC26, and etie Double Rectansle oF Y: 14
  38. into V : 12, 152V : 168. WVherctore
  39. SSum
  40. V: 26 1 = 2 Y : 168. is che 3 DiRerence 5 te
  41. quired.
  42. es Compouna Surds.
  43. The Aricturierick oE Compound surds, depende
  44. on che Rules abore siren about simple Surds, aud
  45. on therrue knomledse oF che Sisns :) and in
  46. Algebraick Addirion, Suberaction, Mulciplicarion,
  47. and Dirision; only fome parricular Directions maz
  48. be oiven asro Binomials and Residuals: AS,
  49. Y. Is any Binomiat be 20 be moleiplied by ile
  50. correspondins Residual, the Difference ot cheir
  51. Squares is the erue Product; and rheretore will
  52. Come OuE ~ R arional Oiantity, 25 il ~: a - - 0
  53. bemulriplied by V: a = e, cheProduet will bc:
  54. Rarional Ouanirs, viZ. 4 a = e e.
  55. and mont casily pertormed by a Table OE POrvers:
  56. Binomial Whacloever, vou need on y ad d the dou
  57. ble Rectangle oF che ParIS; t0 ihic Sum oF he
  58. Squares ot those Parrs; or take thie double Rcct
  59. aetote dedita lltal vlt i i DE a dichcllata
  60. III. L’ox Dirition in Compound surds, ris conve-
  61. nient, if nor necellary, to redisce them Arstto lOmE
  62. berer, and when ir can be done, 10 2 RatiOnat
  63. FORL. ANd,
  64. (L.) IF a Binomial, consistins os rul M
  65. Sguare ROOES, OF OF OnC Square ROOF and a LALI
  66. onal Ouancier. be mulciplied by iis correspondine
  67. Residuat, chie Produet ill alvays be. 2 Ratioral
  68. Duancier.
  69. ttnta tetaft maus ust ut eltt sebisus ett a
  70. silt de eant idde destate lolo, e et e
  71. beins mulciphied, as is betore lata, b) us Binomial
  72. ic produces à Lattoas uanrier.
  73. (3.) IF a Prinomial, having chree Simple Squares
  74. Roors, be multiplied by ic self, with one ot chic
  75. Siens chansed; ihe Product will be cither a Bino-
  76. mial, oe Rehidual, which beins mulciplied by is
  77. correspondenr Relidual, or Binomial, Wvill sive im
  78. che Product, a Ouanciry encixely Rarional.
  79. Siduat; BUF COnJOYHCA IN CHC BLHOMITAL. Bγ =, and
  80. tet ettu eetctta 1). ale altllabisut
  81. al ox Kehdual, Will be a Omancies entirels Ra
  82. TenCaS, ThC uLL bC FeduCCaIO a COMIMIOL
  83. Radical Sign.
  84. conneet chole parcicular Lroduets rogether by cheis
  85. Siens; buc it che Birilorbe a Binomial, Lrinomi
  86. al, or Ouacrinomial, 59c. ot such kind as betore
  87. is specihed, reduce FHaE Biven DIrIIOE EO 2 new
  88. Diritor thar may be a Simple Racional Ouantier
  89. Reduce allo, the siren cene 1o a he Diri
  90. dend, by multiplrins che tormer by ic Clantirie
  91. chac vere Mulriplicarors, in reducins che siver
  92. Dirilor ro a Racional Ouantier; chen diride che
  93. new Diridend by che new Dirilor: Buc wtienctic
  94. Diritor cannor be reduced ro a Simple Rationas
  95. Ouancier, sec rhe Diridend 25 2 NuMETaTOI, OVet
  96. che Dirilor as a Denominator.
  97. Ouorient i5 4
  98. V. : 33 V : 22 = V: 15 diri
  99. Ae becaule we sec chac a a = 2 a c c e = D ded by V: 3, chc Ouoriene is Y: 7 y:
  100. (2.) IF 2 BIrOMIIAt COMMInS eF Euvo Biquadra
  101. Ouanciey; if chis be mulriplied by ies correspond.
  102. . clat, the Produet Wvis be a Residuat con
  103. Sgnare RoOr a Rarional Ouanrier; Which Residuat
  104. IV. IF a Binomial or Rehidual, consisting oF rvo
  105. Simple Cubick or Biquadrarick ROOrS, (9C. Or
  106. ot onc Cubick or. Biquadrarick ROOc, 69c. and a
  107. Rational Onanus l proposed for a Divisor; sind
  108. (0 many continual Proportionals in che Proporrion
  109. OF the Patts O ie Binomial Or Relidual proposed
  110. s chere be Vnices inthe Index of che Radical
  111. Sten, ale luch whose Radical Sion may be che
  112. Pame wich char ot eC Lales et omial Or RC-
  113. concraril), in che Proporriotials by -1-, and in che
  114. Lelidual by -) and--; che Produet of thelalut
  115. Proportionals (0 connexed, multiplied into che Bino.
  116. rional. Attex che Pame manner mas a Binomin
  117. Ox Rchdual, arB 566, Sc. o ene Mdex Ot
  118. Coon Radical Sign oF che Loots, De secuceu
  119. a Duantiry enrirely Rarionalo
  120. And Nore, thar when he RooS are oF Ditte
  121. V. TCthe Divisor be a Simple Onanrieyr, divide
  122. cach parr ot che Diridend by che Dirilor, ane
  123. II. Involurion in Dinomials and Residuals, is BCA
  124. ThuS, 12 -F= V : 63 divided by 3, ihe Ouoriere
  125. 15 4 - I V: 73 and 8 = V: 12 dirided by 2, che

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/806933011:0793?run=74