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[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 240

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: 0.88.

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

The machine reads it as

  1. 2.4.0
  2. ALSLRONOMTA PAZSTOA
  3. perimeter; invenienda est F. Iip Seos istius diaeter quaedam FP, est
  4. que conjusata XY, magnitudine e positione. Ducta incelligantur
  5. recta data puncta conjungentes, (ut in schemato,) quarum dua qua
  6. dam aut parallela sunt, aur dua nulla. Hloc autem Facile perlpi
  7. citur; cum enim dentur puncta N, MI, L, R, E, danEUE FCCLA BIMLIES
  8. ea omnitariam conjunsentes, e anguli inter rectas iltas compre
  9. henti. Si ergo deprehendatur angulos duos alternatim positos (ex.
  10. EY. RMET, MMN) elso aequales, concludetur reCtaS dUAS MK, NII, IN
  11. quibus praedicti ansuli alternatim tunt potiti, esse inter se parallelas.
  12. Cas. I. Ponatur primo duas qua(dam MK, NE esse paraIlelaS. Bi-
  13. secentur la in B et A, ex juncta B a producatur, donec FIipsi OC.
  14. currat in P e P; erit haec (ex Flementis Conicis) Pllipleos diame
  15. TEF, _ quidem (per 26. Dat.) positione data:
  16. quippe per data puncta B ec a transiens. Du
  17. Catur per L ipHI E F Parallela L X, F IipA in X,
  18. recta MK in D, Q NE in C OCCUETONS. FF jun
  19. Eta ZK, L MI OCCUFTANE FCCIX HN (RI OpUS CA
  20. producta) in punctis Pe C. PeF PFOD. RVIT.
  21. TIB. HIT. Flem. ConiC. Apollonii CR rECTanSU.
  22. lum XDL ad rectansulum NDK ut ZF9 ad
  23. ZYg. LLem ZCL. NCH:: ZFg, ZY9. FF isitur
  24. XDL. NDR:: XOL. NCF. Scd (ut intra ostendetur) CA X DF.
  25. NDR:: XCL. GCD. EE igItUT (PEF PrOP. IX. FleM. V.) CCL N CH rect
  26. ansulum aequale rectansulo ccr. Atqui rectangulum N CE datur,
  27. quoniam ejus latOTA NC, CH dantuT; tota enim N E initio datur tam
  28. magnicudine quam positione, item recta L C positione, (per 28. Dat:)
  29. quare (per 25. Dat.) dabitur e c punctum: item recta EC, quippe
  30. cujus termini a ec c dantur; datur ergo (per 57. Dat.) ee magni-
  31. tudine: Sed ee positione; ergo ipsum e punctum datum eAt. Datur
  32. etiam _E K punctum; ergo e puncta illa COnjunGOnS rCCTA RP POF
  33. tione datur, de proinde (per 25. Dat.) punctum x in FIlipsi (ubi
  34. Politione data L.C, RP COnCUEruNE) etiam datum cA. Jungantur
  35. reCta NX, L H dIaEEEO PF (R OpuS CA produetX) occurrentes in
  36. R ec 5: Critque (per supra citatam PrOP. XVIT. LiB. TIT. Flem:
  37. Conic.) TUm NCH ad XOL, CUM N A E ad E A F, SICUL Z Z9 ad ZFG:
  38. unde NCF. XCL :: NAF. EAF. EF per inferius demonstratum est
  39. NOF, ZCE: : N AFF. R AS; Quare (PeF IX. FI V.) e aS rectangulum
  40. reCtanSMIIO E AF aequale clE. Sed E AS datur, (cum tria punCta A, R
  41. _e S dentur, a quidem ut supra ostensum, R e S Per 25. Datorum;
  42. nempe datae positione rectae FF cum potitione datis rectis XN, HL
  43. COnCUEFUS:) rectangulum isituE E A F datum crit. Simili ratione
  44. invenietur EBF rectansulum: _ dantur puncta A e B; ergo e ipla
  45. F F magnitudine, ut deinceps ostendemuo: Sed prius inventa crat
  46. ejus positio; quare diameter Pr positione d magnitudine data
  47. CIC. POrTO, TFq CA ad E FGUE NCF ad XCL, UE supra ostentum est;
  48. hoc CA, (Per T. Dat.) in ratione data, ob data NCF, X CF rectangula;
  49. quare e prioris subduplicata ratio, nempe ratio FY ad PF (Per 24.
  50. Dat.)
  51. ID. IIL
  52. dlic
  53. DuIN
  54. e

Cite

[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 240. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1040780814:0258?run=74