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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 161

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: 0.83.

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

The machine reads it as

  1. 5aclt
  2. insul
  3. 15(0l
  4. equ
  5. (CCUN
  6. dtat
  7. eOH
  8. AM
  9. o
  10. B.
  11. obes
  12. 10
  13. tum
  14. et
  15. Pheria; CH quoque ee C B eriensperiphCHa D L. Guare cora peripheria B D cer merietuE
  16. Locam peripheriam circularem, _ puletes comencum B C segmentum B F cer merie-
  17. LUE, ducantur aurem subrena B D, D MI, MF. Ouoniam igitur B D; D M aequales
  18. lune, X est AD circumferenria quae relinquitur sublata BD circumfereneia ex semicireu
  19. l0, d M B ea qua relinquicur sublaca dupla iplus B D ex incesro circulo, estigituF M B cir-
  20. cumferencia dupla iplus A D; aegui, ip EM B circumferentix, aequalis est circumterencia
  21. FD, (2quales siquidem (UnE SuBEEn (X BD, D MI, ipAISDMI, M F.) quare circumferen
  22. cia FD, dupla ericip siusD A. Sececuricaque circumferentia F D, bitariam in E: erun
  23. IGITIT CITCUIMFCTEMLIX A D, DE, F. F aequales, de circumferentia A F ipsuS A D eripla
  24. lubrendancur jam rectae A F, B F. Duoniam igicur eriangula rectangula C lB, AD I
  25. Cimilia lunes ericue B Lad BC
  26. ica AIad A D. eAt aurem B L dupla iphus B C, igituE _E A
  27. ipsius A D dupla erir. Est aurem ex demonstraris a nobis Fheoremate sco 2d Angulares
  28. Sectiones, ur lemidiameter ad iplam A D, id estur diameret A B ad ip (am A L, ita A D
  29. ad A B minus BF, quare AB quadracum minus AB in BF, aequabituT A L in AD, hoc
  30. es A Tguadeari (emisi: e adhibica conoruametathesi, AB quadearum minus A L qu2
  31. drari semlle, equabicur A B in B F. Icerum ex iildem eAt, ut A B ad A I, ic2 BF 2d A F Ni-
  32. vuS A D, rectangulum igIEE A B in A F minus A B in A D, aequabituE A I in B E, ergO
  33. eadem ad sumpea alcicudine BF, cric uE A B ad AI, ica A B quadcatum minus A L9u2
  34. draci lemisse ad a L in BE, id est ex secundae aequalitaris analosilmo, ad AB in A P minus
  35. ABin A D: de omnibus duplacis; A B quadearum bisminus A L quadraro cric ad AB in
  36. A F bisInHHAS ABTH A DBIS. _L AB ad A I.
  37. Est quoqueue A B ad A L. ica AB quadrarum ad A B in AI, vel AB in A D BiS: quare
  38. Esimilibus similia aaaAML, eIC A B quaaraCUM CeinuS A L quadraco ad A B in A F
  39. bis, uE A B ad AI. ACprOIdC AB quaalalet in AIminus A L cubo, aequabitur A B
  40. quadcaro I HL OIS. Ouod craclecundo oco ostendendum.
  41. Tecrio: prorratacur ipla AC quancum lacis in C, de Aac B C dupla ipsusBC, quare
  42. iphusB C laceris alterius circa rectum, porerit C C quadraco criplum laceris B G, perpen-
  43. Dicorursus, Colidum eriplum sub A B quadraro in A C, minus cubo ipsUS AC, aqua-
  44. (quandoquidem in criangulo reclaH C B, latus C B oppolicum recto, saruitur du
  45. Plumlareris B C circa rectum.) sus B H C cerria pars est iplius anguli B AP, PCu PC.
  46. cipheria BF, eric angulus A BII, sire peripheria AH cerria pars periphetiae AII F. de quo-
  47. niam eriangula CHI A, C G B Cimilia (UINE, CrIF C A ad A FL, uFC B ad BG, es aurem C B
  48. dupla iphus BC. quare C A ipsius A HI dupla quoque eric. Secetur jam peripheria HF bi-
  49. Cariam in L, dc duicatur recta B L. CrUNE SEGMENEA A FL, H L. L F Xqualia, igicur ex demon
  50. lraco a nobis laepius ciraro Theoremare, crir ur semidiamerer ad A FI, id es A B ad A C
  51. ITA AFLiphuS A C semisisad B A minuSBL. OuarC A B quadracum minus A Bin BL
  52. aquabicur rectanoulo A C in A II, id est A C quadrari semistr. R ursuS ex eodem FheOrC.
  53. iIBace, uE A B ad A C, ita BL. 2d A Fminus A FI, de rectangulum A B in A P minus AB id
  54. AHI, aquale erir rectangulo A C in BL. eadhibica congrua metachesi in priore aquali.
  55. cace, A B quadrarum minus A C quadeari semisse aquabicur AB in BL. ErgO ad lum pT2
  56. communi alcicudine BL, eric A B quadearum minus A C quadrari semisse ad AC in B L
  57. ddattede Cimilia, eric AB quadracum ter minus
  58. AC. minus A C cubo, aequale erir solido sub AB quadearo in A L bis. Ouod eraccertio
  59. Acg: hinc constac lex ab Aucore estimodi xqualicatum consticurioni apposica: est enim
  60. T6Y
  61. L AB F.
  62. Flcorimum circumterentia C D, anoulo D SuOEMI, IMenStOrMS CIrCULArIS peri
  63. quum rectangulum sic criangulam BG C, e lacus B C recto subrensum angulo, duplum
  64. ciculeeCer crianouli AC B
  65. Et Colidotub A B quadraco ee dupla ip sus AL
  66. OppOTEIS C AB, ACB, est aurem A C B cecta pars uninsrecti, sive semiperipheriae
  67. Peorrahacur enim C B donecicerum circumferentiam secer in FI, _t ducatur A YI.
  68. Duoniam ieague angulus AB HL exceriorerianguli AB C, aequarur duobus incerioribus
  69. es ex posterioris aequalicaris analosimo, ad A B in A F minus A B in AFI, uF AB ad
  70. C. de omnibus duplaris, erir AB quadearum bis minus A C quadeoco ad A Bin A P bi
  71. minus A B in A EI bis, uE AB ad A C. est quoque AB quadracum ad A B in A C, vel A B in
  72. AEI bIs AB2d A C, quare similibus
  73. C quadrato ad AB in AF bis, uc AB ad A C. Solidum ergo sub AB quadratorer ir
  74. e ulcimo loco ostendendum
  75. AB diameter, inlcripcatu axima.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 161. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0167?run=74