Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 500

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: 0.90.

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

The machine reads it as

  1. LCL. OIVe.
  2. cur adhuc plato etsipeico f d quod plano fCP rectum lir; Semisuperliciei illius
  3. semistis TS FZ C X P aquabit Semicycloidem C AF; (nempe Semicirculus balis
  4. CZ P tig. 2. aequabir Semicirenlum C Z F tig. L. es Superticies Curra PSF ZCF X
  5. quabie cxiluIcum C A P Z.)
  6. 5. Nam, Sumpro ubiris in Creloidis axe puncto Y, unde paralleta BaSI ducatuF
  7. Y2Z: rectae C X in aXC CyClONiS LumaCuT C Z aequalis in diametro balis Cylin-
  8. drica, unde dueatur Z. lateri CF parallela, diasonali FP Occurrens in v; d per
  9. punctum, plano bati F ZC Parallelo, puta vec, secetur superticies Ciylindrica
  10. sectionem exhribens sc arcum circuli, quae (propter parallelaS) CongrueE arcII
  11. 2 C in basc Csinc hde et alem LC cirenli renitoris, adeoque 2Z. rectae aequa-
  12. lis, (Sicurve congruit rectae X2. Sive inbale Cy lindri sire in circulo generante.)
  13. Duod cum ubiquetiac, erunt omnes currae in luperticie Cylindrica rE F Z CP, ipl
  14. Cparallelae, aequales rectis omnibus ipli ZC. Parallelis in Prilineo Cycloidis C A F 2,
  15. ee lingulae lingulis, ee limiliter polux (in cildem pura Cire 2 bale sire a vertice
  16. diltantiis:) Adeoque, propter aequalem etiam ucriulque tioura alcicudinem, tioura
  17. tigurae aequasto. Iperteles CMaa plano Frilineo; (led e seomenta illius re-
  18. spectiris legmentis hujus, ut paret:) li addaneur urrobique aquales Semicir-
  19. culi C. 2. F, erit agpresacum aggregaco aquale, et duplum duplo, quadruplum qua
  20. deuxto, ac. Hoc elt Superticies FSFLC YF, Semiereloidi AC. L; et Semisuver-
  21. tieles exlindri (quixpe ictius alpu) Cycloidli ACDf; e cora superticies, hujus
  22. 6. EIL iisitIE Cfcloi A C. DF, ehculi genitoris cripla. Ouod sic colligitmr.
  23. Cstindri incexri modo cspolut Lufscurra, aequatur facto ex alcirudine (qua
  24. aqualis elt diameero Batis) in Batrs Circumterentiam; adeoque elt quadrupla Cir-
  25. culi balis: Cui Si basis vrraque adperatur, agoresacum erie, baleos (hoc est cireuli
  26. genitoris) sexcuplum. Fst aurem, ue supra oltensum est, duplum Cycloidis: F. P∞O
  27. Crclois ipsa est circuli Genitoris Lripla. Nempe Prilineum C A F 2 Semicirculi
  28. DFEFZCYF, Secetur actum plano 27 X, quod sic plano elliprico FSF u
  29. Parallelum: Superticies abscista VC YZ, aequabit legmencum Cycloidis CXZ.
  30. Nam, propter Cylindrica superticiei sectiones parallelas, congruet 72. C ips F3C,
  31. hoc est Trilineo CZ L Cycloidis; sed e C. I2 urrobique aqualis; F1GO aBBrC8 2.
  32. 8. Si supex Cycloide CD erisatur Semieylindrus rectus, sire Prilina, (utro-
  33. ris enim nomine dicatur perinde cst) altieu-
  34. dinem habens C a duplam rectae AD; quod
  35. peraxem secet FC a planum, sectionem in
  36. lacere taciens C. a rectam; cui plano incelli-
  37. Batur planum aliud recte inlistens, per rectam
  38. Fae cranliens. Polidum abscindere D A e CD:
  39. Tluic Polido aequatur Poridum factum ex con-
  40. vertione Cycloidis AC. D circa rectam A D
  41. Cum enim lic A D aequalis peripherixe diame.
  42. tri F C; erit iplius dupla C e, aequalis peri-
  43. Pherix Semidiametri F C; adéstue (Propter
  44. angulum F C∞ rectum) criansulum P C ∞
  45. aequatur circulo ex convertione racii FC
  46. Facto. Ec limiliter ostendetur criangulum
  47. XZ E aequale circulo racii ZZ: e bc ubi-
  48. quo. Frgo omnia Priansula omnibus cir-
  49. culis, adeoque solidum lolido RguatuX, S
  50. sexmenta scomentis respectire sumprio: Pura,
  51. tur solido ex convertione plani Z Y C cirea rectam Z Y Facto. Nam _ Hic c0.
  52. dem modo oltendetur, teiangulum un d aequale circulo radii or; de de reliquis simi-
  53. liter.
  54. . Simili-
  55. perticies curra, dupla crilinei C. A F L: d Ex denique si ea Semituperficies bilece.
  56. Crclois
  57. Circula
  58. pripla.
  59. dupla. Duod crat propolicum.
  60. C2. F duplum.
  61. cu axpresato aequale
  62. 7. POTTO, S expolica quae prius superticies (nempe, Semisupersicei Cstindricx
  63. Sogmen-
  64. cum CxZ. Semiss
  65. solidum Z Z EA, Solido ex convertione plani ZZ A tacto; &e sic ubique: Frem
  66. Prilma LLEvPF Tolido ex converlione Lalallelosrammi XZ. PF; adeoque et
  67. Tolidum Z X C ev E Tolido Cylindrice excarato conversione plani Z. Y C circa rectam
  68. A F facto. Sin achue secetur plano EdL Val Parallelo, Peementum e Fun Xe quabi-
  69. Solaum

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 500. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0520?run=74