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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: 0.87.

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The machine reads it as

  1. In oire Cale Cheretore Ille Laprecion is Pohrire
  2. in ehe octier Negatire. Buc a5 the Potns SO L
  3. apprOaCk1O L, The Cmanciries B F and B F de.
  4. Crease continually, and at the Point F are equal 10
  5. norhins.
  6. Sochac ie is plain, Thac chere is no parting From
  7. a Positire toa Negarire Exprection, inthis Calc ot
  8. Y. In chose Curres thac tave a Point OF IH
  9. Rection, har the Abscista A P encrealerh conrin
  10. ally; and, chac the Patr A T, oF ihe Diamerer, in-
  11. tercepred berween A ehe Orixinal oF a, and Y che
  12. concourse of the Pangent and che Are, enereasert
  13. till such rime as the Poine P Fall upon F, and asier
  14. thac it again begins eo diminist: From wvhence ic
  15. 2 Ouantier continually decreasine, Withour pastins is apPareNE, ChaEA T must become che Maximuni
  16. chro noching. FOrrhe otheF pATE.
  17. Let us consider the TAnGeHES (aS D A OF FTI)
  18. curoH by Lirres continually dracon trom L rhe Poin
  19. ot the Cireles coritact. IF, C B; OF C F, DC DUF
  20. equal roy; che Exprection of ans suchi Tangene,
  21. will bc = , BE
  22. AL, utien che PoinE P FalIS uxon che Poisc F re-
  23. quired.
  24. 2. In thole Curres thac have a POInE OF Retro
  25. pression, ris evidene, MaE THC PArE A T CnCrCasech
  26. continually; and chiar che Abscirta encreaseth (0
  27. accordins as we rake lons, eilletie Poine T FalI uxon L, ascer whichi ic 2
  28. it on che one or on the orter side oF the PoinEF;
  29. ir ore ense cheretore tis Politire, in ehe orher Ne-
  30. satire. Buc as the Points B or F approach 1o F,
  31. he Targents D A and EP P enCrease ContinualIY,
  32. and ac the Poine P chey become Infinice. There.
  33. Tore a Guanvies chac contininally encreasech, cannor
  34. pals trom a Posirire 20 à Nepatire Exprestion,
  35. vithoui Decomine Infinice.
  36. AII ehis is Oniversally erue, Whecher ic be a Fi-
  37. nice Ouantier or a Fluxion chiar ve consider. Phere
  38. eain diminisech: From whence ic is clear, Thac
  39. A P must become a Maximum, When the Point Y
  40. FalIS upon L.
  41. Nou is A E BE pUE = X, EF = y, ehen vill
  42. ALBC = 7= = s, whose Fluxion, Wotictae i5
  43. =à (suxposine i invariable) beine
  44. is no chansins From Positire ro Nesarire, withour dirided by X, che Fluxion oF A F must become
  45. pastins chro Nochins or Insinice.
  46. Applyins ehis cheresore to Fluxions, ic will Fol. Nochins or Insinice; chat is - = Norhing e
  47. Jon trom hence, Tharche Pluxion oF a Ouancier
  48. thac expresses a Maximum, Or a Minimum, must
  49. be equal ro Noching or rointinite. And upon this
  50. Foundation re may no casily procecdiothe spe
  51. culacion oE chie Poines ot inptection and Retro
  52. cression.
  53. Insitile: S0 chac mulcipivins by j, and divi-
  54. dins by = y, y willbe = co Nochins or Intinice
  55. Which in the Sequel will Serre For a general Form
  56. t0 sind F che Point or InRection or Rerrogrestion.
  57. In order ro sind a General TheoteM to altist us FOF Mhe NatuTC OF ihC Curre A F H beins Birem
  58. che Value oC y may be sound in x; and catine che
  59. Fluxion oF chis Value, and supposine x inrariable;
  60. he Vatue oF y will be Found in X, Which beins
  61. Duc equal eo Wochins, or Intnier, serres in cicher ot
  62. thele Suppohtions eo And sucti a Value ot A P, 25
  63. char che Ordinare P F Mall intersect che Curve
  64. A PKL in P che Point oF InRection or Rerroprectiori
  65. OEchis Y Mall orils no trom che Analyse des insic
  66. niment Petits, sive one
  67. ENampte
  68. Wvhose Diaheter is che Righe Line AB; andits
  69. thro che Point l’be dramn che Catnace applicate
  70. in ehis Matrer, ler us consider che Curre AFH,
  71. Ordinares PMI, cF, Patallel 10 onc anocher. II
  72. E F, cogecher wich che Tansene P. L; and trom
  73. any ortiex Poine a5 MI, on che lame side wich A P
  74. be dravn ette Ordinare pae M P, 25 litrerise
  75. che Tangenr H P: Mis evidem.
  76. Lec AF K, be a prorracted Semi cyeloid, whor
  77. Base is lonper chan ehe Circumterence oF che gene
  78. rarins Cirele ADB, Wvhose Centre is C. Tisre
  79. quired ro sind P in ehe Diamerer A B, PO thac lC
  80. Ordinace Applicare B F, Mallcur che Semi crciot
  81. ot. ce ceonre es cenuaes tileacon
  82. ot

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/806933011:0442?run=74