Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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: 0.85.

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The machine reads it as

  1. MEAN Morion of the Sun, in che OId AArO. ( he CtC oF a Semi cirele, ard then erect rhe
  2. nomr, is che Distance (accounced on in che F. Line P perpendicular co che Fwo siren Lines,
  3. eliprick, trom che Beginnins oF Aries) oFche sun ac eler Point os Onion: L Cay, che line L iS che
  4. Fron che Line oF his Mean Motion. Sec Line Mean Proportional (OusA.
  5. of the suns Mean Motion.
  6. MEAN Or Midale Proportional, between any
  7. cvo Lines or Numbers, is chac wtrich hach che
  8. Came Proportion eo a chird Term char che firA
  9. Lhus B is a mean Proporrional becween 2 and
  10. 32, Decause 2: 8:: 8 32. And the chree Num- extract che Square RoOr oF che Product: OE
  11. bees in ehis Case are rhns expressed 2. 8. 32:: Wvtrich see more under Lorarithms, and che r se
  12. Thac is, Tvo, Fishr, and Thiry cwo, are in of Losarichms, Numb. 1L aFid 12.
  13. Continual Proportion; For the lame Proportion is
  14. conctiued from che Midele or Second Perm 10
  15. ehe Lhird, 25 was becveen che First and Se-
  16. cond. Pheretore ris the very Came chins a5 it
  17. che middle Term had Been pur donn ewice. This Famous Problem (Which is the same 2e
  18. NTon because when Four Numbers are Propor- the Duplication of ihe Cube) may be relolvec
  19. rional che Rectangle oF rhe midale Ferms is and demonstrared by means of the Conchoid ot
  20. equal to chac oE rhe Exrreams, ic must be (0 Nicomedes; and vould be Geometrical, it chab
  21. here: Buc here che rvo midale Terims beins rvere a Geomerrical Curre.
  22. che lame Number, cher will makce a Square;
  23. (0 Thac wrhen Phrec Numbers arc in continuat
  24. Proxortion, the Square ot che midale Term is
  25. equal ro the Rectangle of the ExrreamS; and
  26. Etiac midele Term is called a Mean Proportionat
  27. becwech the ocher tvo.
  28. EROPOSFZFON.
  29. The Perpendicular (a d ) is a Mean Propor.
  30. sional betuveen the Scements oF che Hyporhe-
  31. Bears 1O ic
  32. nute (b d and c d.
  33. For 3. L.. L. 8) e Last Proposiion.
  34. Lo find a Mean PFOPOral betmeen any
  35. Mascipir che Numbers ineo one anocher, and
  36. Fo find Lvo Mean Proporrionals betmeen
  37. Evo Civen Lines, AB and BC.
  38. Lno Lrumborsus
  39. Join ehe siren Lines AB and BC rogettret
  40. ac Rishr Aneles, and bissect cach in chie Poines
  41. D and R: Complear che Rectansle A L B C
  42. and atair L. D eill ic meer wich C B produceo
  43. 10 S. Then Wwill S B = A L OE r0 BC
  44. From P. let Fall a Perpendiculat, Wrtich produce
  45. EIIL
  46. F be coual ro A B, WCM will cuc oA
  47. ThC PATE PF. Dat ce LO, ale PataI
  48. 1O ic CFI. Then (by Cor. 2. Prop. 2. OF ch
  49. Cmmus chroushiche Legs oF the Angle R C L
  50. ataW che Lichr Linc LHIE, (0 chac LTK b0
  51. escat ittad ae it e it
  52. TR
  53. dc; and chere
  54. Fore che Square oF a d is equal ro cheRectans
  55. betireen b d and d c.
  56. For the Frianeles c d a and a d b, beins sim
  57. Tat, CWs bC 25
  58. da: db, and co
  59. ceues D d a = D b de
  60. PROBL F H.
  61. Io find a Mean Proporrional to Tno Civen
  62. Lines, A and B.
  63. Le ic cill ic meec wica B A allo producec
  64. in M. S0 wil C K and A ML bC thC ZWO
  65. Mean Proportionals CougHE.
  66. DF. 1 1L(- LL11
  67. L. ec M A bC calld b. LC Or AB = eb anc
  68. BC = c. Then because ot che Similar Pri-
  69. ansleS M AL. and L CR
  70. AM. L C Oc AB.: AL eBC.K
  71. cb
  72. c.
  73. COr CC
  74. Wherctore Cc =CKE. AIIOM A. AD:: SC. CK
  75. .- :: 2C. Cc.
  76. (Because it rou halre one Consequent, rou
  77. must double che ocher Antecedent.) And
  78. SC. CR:: FHI. HK (because C HI is pa
  79. rallel cOSF) Wheretore MA. AD:: LHI. HIK
  80. EL L 1 equat 1O AD OF Z Cb (25 Was taker
  81. chac conore Lle; ate hC Poinc et Bcetion l or b. And conseguemiy MD = FH (Eor bort
  82. Put A and B both into onc Linc, thenbissect abore) Wrheretore FHI must be equal to MI L

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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/806933011:0501?run=74