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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 79

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. L R C F.
  2. X.
  3. lineamque V P F tanGaL recta F T. irem lineaM V R E Fangat recta
  4. FS. Fst ergOSD (a) = 2 TD. aEquiD E XDT (b) =VDEL.
  5. 4) 5. Tect.
  6. 1Z0.
  7. erBODE XSD = C2VDEZ =) FDg. unde constat angulum (b) Cor. prac.
  8. DFSrectum esse. quod Provolitum erat.
  9. Adjungam es illis cognata haeC.
  10. XIII. Sic curra quaevis AC F.Z, punctumque quoddam D (a quo
  11. projectx D A, DC, DE, 55 6. ab initio D A continuo decresCanE) F1s. II2-
  12. cum altera (IE Curra D R E, priorem interlecans in P, naturaque Ca-
  13. lis, ut a D utcunque project a recta D R C (QuIX CUIEVAM A F L. PeCeF
  14. In C, CUrYAI D R E iN R) sit perpetuO rectangulum CX DR, _ de-
  15. signaca quadam linea R aequale spatio ADC; tum ductâ D I ad
  16. DF perpendiculari, sIE DY = 2 R; e connectatur YF; hXC
  17. curram D R F. ConingCE.
  18. Nam Cumpto quoris in Curra D K F punCtOR, ducatuE rectADRC.
  19. _ TumPEA DL == DR, duCatuE L R ad D T parallela (secans ipsam
  20. DC in Z). TUM PeF F duCatuF F X ad D P perpendicularis (hXC
  21. VeTO CXTTA CUTVaM A F Z, ad partes Z cadet, quia decrescune proje-
  22. Atx vertus Z; unde P X versuS A intra curram F C A cadet; Cate-
  23. nus Taltem, quatenus huic Proposiro latistaciet). Sit jam primo pun-
  24. ctum C supea F, versus inirium A, ∞ obTD. DF:: RL. L F;
  25. adeoque R L. XD F = T D X L F (∞) = 2 RX LF (a) L 2CDF
  26. = 2 DFZ = EX XD E. CrBORL C EXC LY. EA aurem
  27. punCtU Y exETa CUEVa, quiA DZE DL =DR; ergo magis
  28. punetum R elE exEra CuEVaI.
  29. Sic rurlus punctum C intra punctum Fi. versus Z; ceque rursus.
  30. uei prius, R L XD R = e GDE =I ETrIAnS. FDX = FX XDF.
  31. Cet) eroo punctum R ruxsus extra curram existie. Liguidum est igi-
  32. quod ducta lic DKC; _ HaC D C. DR:: R. P; SuMaturqUe
  33. DI == 2 P; _ connectatur TC; cum ducatur R S ad C Y paralle.
  34. la; reCtA RS CUIVaM D R E tanSeF.
  35. Nam conciviarur curra DOC, per C transiens, talis, ut recta
  36. quacunque DON a D projecta (quae curram DOO secet in O,
  37. CurVam L H F in M, CUIEVaM A G F in N) SIC semper DOX P X.
  38. qualis spatio AD N; erit ideo D MI XR = DO X P; ac proinde
  39. DM. DO:: F. R. unde linea DK E, DOG analOBX CTWNE. Ve
  40. E18, 113.
  41. (a) Hyp.
  42. unde A F, == F. X = L Y. Fs aNTEM reCTA L Y eXTFA CUITVAI PR.
  43. FOTA, (RAMA CFIAM CXEFA AFCUM L R CUXVX R F. circumduetum tora ja-
  44. tur rectam TF R curram D R E tansere.
  45. Duod si punctum aliud in CurrA DR P deliBRCtUT, PUTA R; pex
  46. xitir

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 79. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0303?run=74