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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 207

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.

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

The machine reads it as

  1. 1
  2. t
  3. c.
  4. en
  5. DE VERTBOS ET MOTIBOS CORPORUM. LIB. II. 207
  6. arithmeticam proeressionem ascendentem constituentes, et per singula-
  7. rum terminos transeant ordinatae AB, CD, TCTD, 2C2V, exc. jua-
  8. ta proeressionem arithmeticam decrescentes, definire curvam BDFDZI)
  9. per sincularum ordinatarum terminos B, D, AD, ZD, transeuntem.
  10. Per puncta D agantur parallelae ipsi AHI, ec in prima DE prO-
  11. duCta LUatUE PF =DE, ac per F ducta FP parallela AB, in linca
  12. TFTO a linea FP deortum ponatur xOeF aequalis excessui, quo se
  13. cunda divisio CFC primam AC, vel tertia secundam, Peu quarta
  14. tertiam, atque ita deinceps, excedunt, ducaturque per puncta L et
  15. EF, recta FO; CTUNEque AC =DF = EV, item CTC = TRTV, d
  16. XC2C = 2F 2F, atquO SIC POFTO. AdCOquC A2C = 2F 2F L TRTF L FF.
  17. Veruim 2E, 2F = rec- IO 2E 2F. 2R FR : 2E FB, _E TL PF = RCC-IO TPPF.
  18. TEE: AEB; ergo quia 2R TR = FHE = F B ex hypocheli quandoqui-
  19. dem AB, CD, TCFD, 2C2D (secundum hypochelin) Cunt in PrO.
  20. Gressione arithmetica, erit 2F2F F TE TF = (xCc- lum H ER + rec- 10
  21. ITF): BF; haec vero rectangula simul Cumpta quotcunque corum
  22. FUICFINE, XGUANtUT trapCZIO LFZF2F Simul cum triangulis TPXF,
  23. IETFZF, quX TUNE eXtra trapeZIUM LFZFZB, e dicta triangula
  24. simul aequantur rec- 10 sub dimidia 202F, ex 2F 1F vel BF: ergo
  25. 2EZF L TEFF = (EF2F2H + 5. 2OZF. BF ): BR =FF2F2F: BB
  26. = 5. 2O2F; ac proinde A2C =F F2FEF: BF, + 3. 2O2F L R F -
  27. 2FQF + TEEF + FF; eodem aroumento probatur esse indefinite AC
  28. vel od =EF fe: BF, + i. pf + PF vel ep, vel bisecta ps ing ductaque
  29. Per g recta FgQ, crit ed = F F fe: BF, + p9 + ep = LL fe: BF, + eg;
  30. adeoque ed. BF =FF fe + eg. BE; atqui trapezium P. P fe = rec- 10
  31. eg. et; ergo ed. BF = eg. F C F eg. BP = BC. eq; hinc CuEVX QuX (IEX
  32. haec est proprietas, ut de vel cA ubique siE ad homologam eq ut
  33. Be ad BF, quae proprietas parabolae communi competit.
  34. TT. Nam si quaedam T AIaE ad RB, SICUE RM (quXe reTUIEaE a COn-
  35. cursu MI rectae OF productae cum recta AB itidem protenta) ad
  36. EF; hinc erit etiam eg: CM (= FF: FM) =BF: YI, CUIEVX VerO
  37. modo recensitae proprietas exhibet de: eg = Be: BF, ergO CX Xquo
  38. de: eNt = Be: T, et de. T = MIe. Be = NTe =NB, bisecta scilicet
  39. BM in N; hinc de. Y + NVB: = Ne =raE; eE SIV sIE FCREIa PFOPOE-
  40. tionalis ad T ex BN erit T. V = BN., atque adeo de. T + P. V
  41. (=de. T + NB) =rd, idcirco, si inrN perpendiculari ad AB prO-
  42. auCta VerSUS S, SLatE NR =V, erit T. Rr =rd, acque adeo
  43. CUrrA GUIXSITa RBDFD eAt parabola, cujus parameter eA L, e ver
  44. tex in R; in qua I est quarta proporcionalis act datas EF, E. M

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 207. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0235?run=74