Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 169

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. P
  2. 3A
  3. e
  4. CIRCV LV
  5. Femicirculo A F B, crune similia triangula e
  6. aequalia ABF, E B C: vnde _ AP, F C Xqu2 - 3
  7. les lune lincx.
  8. Ouarto. Contingar recta C D, circulum dia-
  9. merri AB in A, adeog d punctum F, idem sic
  10. cum puncto A. cum igicur D C sc ContinsenS,
  11. erune B AD, B A C anguli recti: lune aurem
  12. aequales anguli ADB, ACB, aequalium sc-
  13. mencorum; igicur criangula ADB, ABC, A-
  14. milia Cunt e xequalia. uod fuit demonstrandum.
  15. PROPOSITIO III
  16. luilo circulo in sex parces aequales, punctis A, B, C, D, C, F. ductis.
  17. Que BF, C F, PONANEuE BD, F D, Occurrentes C L. in C de HI.
  18. Dico C. F. lineam in C 8 HI eritariam esse divilam.
  19. Demonstratio.
  20. Vm enim arCUS BD, DF, F B pONAnEuEX-
  21. quales, eric BDF criangulum aequilacerum.
  22. inde cum CF, aequidistee BF, crit _ GDHI
  23. aequilacerum: CA aueC GD aequalis b C C+ eCFID
  24. aequalis FTF; igicur C G, GTF, FTE linex, lunE
  25. incer lexquales, ex CF in C e II critariam di-
  26. vila. Quod erat demonctrandum.
  27. PROPOSITIO IV.
  28. Ecent seinuicem equales duo circuli ABC, DEF- per mutua cen
  29. DEra C, F, tranleuntes: linex vero BD, per veriulque contrum actx,
  30. parallelaponacur quaenis HIC, occurrens perimetro in F; de per F li-
  31. nea C F A.
  32. Dico GF, F A, aquales este.
  33. Demonstratio.
  34. VCaCUE F FI; quoniam FTG quidisAE BC CFIE AM-
  35. suluS FHIP aequalis angulo HIF B. e quia arcus
  36. HB, FF ob circulorum equalicarem xequales quoque
  37. Cune, erit angulus FC F. xequalis angulo HIFB, adcoque
  38. ansulo FHIF; unde parallelogrammum vel Rhombus eA
  39. CHI: de HIF lincx aequalis C F, id elt CF; estaurem
  40. rectansulo CF A, Cqualec HIF C rectangulum; ixieur
  41. AF, C F linex dquoque inter le equantur. Juod tuie de-
  42. monstrandum
  43. Corollarium.
  44. Inclequitur HF, BF lineas quoqueincer le requari
  45. CUm HIF linca aquetuE ip(I F C: _ quia IIC cA
  46. quaecumque aquidistans diametro BC, sequirur paral.
  47. lelasomnesrecta. BF. caua circuli ABC, e conuexa
  48. PFD peripheria incercepras, esse inter se aequales, cum
  49. singula xquencur ipli BF.
  50. B Deducien
  51. 1x105
  52. lit
  53. C35. 21r1i
  54. sexsi

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 169. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:0226?run=74