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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 281

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. EL L IPSI
  2. BF A minorem lectore DF. C, quem cum axe facic did.
  3. MCTEE DF.
  4. Ouoniam igicur sector D F. G maior est sectOre BF A
  5. AaEleCEOE FF C aequalislectori BL. A3 _ FL occurrat et
  6. lipsi in C ducacurque BO C; sector BF A cquacur sectori
  7. Fi P C ex constructione hoc est: sectori ad vercicem AF. C.
  8. Ergo DBC. bilecta estm O ab axc A C. anguli ergo adO
  9. recti lunc. pacec ergo angulum BE A aequariangulo AB C,
  10. hoc est angulo FF C, hoc estminorem ese angulo D F Ci
  11. liguecigitur ex primo BF. qua sectorem facit cum axemi
  12. norem axi propiorem eAlc quem D E, quae MaiOTEM.
  13. PROPOSITIO LXLII
  14. Ectangulum sub dimidiis axibus aquale cle PX
  15. Crallelogrammo sub Cemidiametris coniugaris.
  16. Demonstratio.
  17. 2InE ABC elliplisaXCS AC, BD: cen-
  18. Derum E, e guanis semidiameeri coniu-
  19. SaEX EF, BG. actilquE PEF F eE G can-
  20. sencibus qua convenianein FI, X axi AC
  21. OCCUTrAHEIN T_EK: ducaneur ctiam per C
  22. e B linca quae ellipsim concingane in C
  23. _ B: CONVENIANE AUTEM In MI: _E FTR, PF
  24. secenem O, L. N: cum iunctis punctis F. O
  25. agacur per Acanigens, secans F. N lineam
  26. in P. Duoniam cam NO, R F. clince quam
  27. OK3 NE. Sbi muruo aquidistane; crie
  28. NOKF paralleloprammum, diamerro
  29. OF dinilum bitariam: sune aurem eriangula d F OB, F O C aequalia, igitur _E rC. 838. Duius.
  30. liguarriangula PBN, P OK InCCF LCRQUANEUE. Rurlum cum C A P, C. L lineX is huius.
  31. xquidistene, _ AF, C F lineae sincaequales, crie F. C L criangulo xguale crianou-
  32. lum E AP hocEC CF. IF. Ouoniam isitur eriangulum F. C K sequacur criangulo (70. huius.
  33. E BDT d rriangulu TE F crianguloF C L, provortionalia crune quatuor illa erianou.
  34. lai sune vero eciam similia incer se, nimirum F. C R ipA IF F, _ F BN ipA F CL.
  35. ergoreCA KE, P L, N Fs F L, proportionales CUME. quare cum super propOrtIO- S E2. savel.
  36. nalibus indirectum politis consticura sunc eriangula PF F, F GK, IFIKincer Ce simi-
  37. lia ex criangula C L F; P. BN, L M N incer Pe quoque similia, re sunt duo criangula n60. de 163
  38. TFE, FCK ad duo criangula L P. C, PB N, ica hi ctiangulum F HIR ad criangu. nei:
  39. Ium LHNI: Acqui duo triangula PF F, F CK aequancur, re ostendi supra, duobus
  40. TCP; F BN. ergo criam eriangulu PFTR criangulo LMN aequale est; ac proinde
  41. dempris aqualibus paralleloorammum G F P ET sub semidiamerris coniugatis, x-
  42. quacur rectangulo B F C FI lub dimidiis axibus contento. Ouoderat demonstran-
  43. dum:
  44. Corollarium primum.
  45. eMlucutacllipaaua quanilucalametcocala Conu altolco e en latis
  46. PF, F. C. criangula TuPeF F A, PB, P. F, P C in angulis AF. B, FF O, eNcin-
  47. cer se aqualia: lunc enim dimidia pacallelostammorum ae qualium.
  48. Corollarium secundum.
  49. Cquicur secundo patallelosrammalub cocis alamccti Comuzalio celteellea
  50. qualia: cum linc quadrupla eorum que hac propolcione octeula tuneaqualia.
  51. i tt
  52. c 13. Bt1.
  53. t t is p tr ee p

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 281. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:0338?run=74