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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 191v

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: 0.77.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 192r); this page is its left half.

The machine reads it as

  1. Et(et DF
  2. videaum saltem an non aliter un data (urva conicae extensione, possit
  3. ergo
  4. perveniri ad (om superficiem cond scaleni
  5. Elementum Conicum invenimus esse
  6. hh + 2tx + hXX, :, itX YXX) vel dx tib + 1)
  7. pehs chxtex
  8. sit alxip -gus sie - 2itu
  9. et Hy: heta, seo dx ylisiht si faciomus Multiplicemus omnia per q.h. et q + - hy pti9)
  10. +3
  11. dx se
  12. fiet dx
  13. S(tq + EgX + XX, :, 29X + xx sit 49 + dgX + XX - 99 = 22 -99
  14. pusito ZZ qul +, q- x) se Z = q. X fiet etaq + a7 = dx
  15. e
  16. 1+
  17. et x- Aryehq) qua
  18. AX -+ (4 gy 149- q
  19. =44) seu saZ 1 (hg - l99 - h 2 + Z2P:, 1399.)
  20. 1+
  21. seu + Z B e + dy ((- 2 +42B:, - 49 + 22) fiet 22 - a 2i eto
  22. q
  23. et dq = dv: (4) 2se, faciamus (Y) _ = 4 fiet dq = ad t edv: 2Y V, et xElementum
  24. conicae centralae erit 2dv. + (- 2 + CV, : - 99 ev + eevv sit 945:, 1+h = ef
  25. et fiet = edo ((. f +V, :, 29V + evo) Res ergo eo redit, ut qqu + erv, v.f sial extrahibile
  26. (ev +9q ur + fqq V) = C
  27. 3
  28. sevr
  29. ex = fggo sebet aequari quadrato, nan fit edre
  30. Qquten
  31. Prosec Elemento (omi scalem habemus 1 Sob Y (am + n t (, : k p + p 4) =
  32. fiet a
  33. 1+ Y
  34. (posito 1 =a)
  35. fam K P + nk Vp +x VV +) quod in radice est multiplicatum per 4
  36. +am ipip + n iph + 2
  37. gi 2020aa + naa 2. 20. 21 acs + 1ua 429
  38. 13a p
  39. paa. 130 a
  40. fit
  41. perlinum in di sic explicato tollere
  42. 21. 30aa K 9 + 21. 31 k Ge). 3oito ae 1 ho1 as ha 1
  43. 2020a + 2. 20. 21439 + 21. 21aacg
  44. 21a: K et fi f20. 3oaK + 21. 3uaatie: 2o. guaa +, 30. 2a + 2t 1aa = h p+ 9
  45. v=
  46. 1
  47. Eua
  48. 30. 21 a3
  49. 20. 20 a
  50. et fiet dep, 3 XG E8 f(am +n Y YY, vida rodaque
  51. L + 20.2a
  52. mus et imus
  53. sed e sed poterimus simfliciter videre brevo
  54. Terminum suaum Explicemus K Y + YV
  55. RIV = 3_ 3oak t K 20. 30 aK = 20. 31 aa K
  56. fit1 3 = , 307 (in ratyr L V_, e Dea +21 48) r0 toaex arisonius,, qu ( vax rut aues)
  57. el
  58. com
  59. compendio scribemus 10cF 1Z + +B a +14
  60. =20 20aa + 2 ag,: 30 a +31 8, prodiit formula in qua tolli potest
  61. 1030. 35da + 10ca. 2. 30. 3, 48 + 10a a 31 3t g
  62. et faciendo
  63. 10t
  64. 31 -
  65. s. rouiu t.
  66. + 2 30aa t
  67. 28. 30aK +20.214 8
  68. 20. a
  69. 20. 30 ak +. 21. Paakes
  70. Ou (t a+) 21 4 8), 2a 20ct 20 21ag
  71. 30 =0, vel 20 =0 ser
  72. non simul utrumque
  73. = 230 21d (31 2 a porro explicanta ad huc per es
  74. ag, 20. 4. ades . 21. 3. 908
  75. qu (304 + 31 8)
  76. vi, u
  77. am +n +
  78. palis t
  79. am. 3oqoaa + an 2) d tam. A MEI. 2 CPC 20.3ORK + 21. 70aa k)
  80. Ck
  81. ) 20.20t 20.2148
  82. na. 20. 3oaa + na 20. u a gr a
  83. na 2.30 ac 2f Ma. 2121 4 98
  84. unicae, nempe
  85. Hoc maltplicatum per ( 3ok + , conferri poterit eo quodatur per curo,
  86. Hocmnliplicatum per 3oa+ 2 . seu per 2o k +G_ dat A en sisabile pt
  87. caru clomentim sunnabile ope altervis
  88. carde (onicae hujusmodi qualis fuitC
  89. 21 a: K
  90. 0. 30aK + 2. 3vaa K∞s
  91. Horum pdact Harum summarum differentia cum sit 2030aK+0. 20a 30H, in summationem psorum )
  92. i per 21. quaa k + 20. 2a
  93. sed idem (multiplicatum per joroar 20u
  94. dati et summationem Elementi quaesiti seu oni scaleni, ope survae sonicae in rectam extensae.
  95. 2
  96. 21. 30aa K +20. 218
  97. ed verto it eadem Nescio autem an eadem curva sonica possit inservire utrique, an vero opuis sit
  98. 31. 30aa k 120. 21 8
  99. adhibere diversas, quod quidem non noceret, etsi reddat constrectionem magis compositam
  100. incqudica spesserdisibnti usitaru nitiurer notudo p a Be
  101. Y
  102. +
  103. oe yG + 28fZ + B (et dividendo) faeret Z2 ((fer = 1)X
  104. ex XX - 2rX fietet _ ex- 2+ 2rt
  105. er er
  106. Nmsrator Hb qu( r.X) durr, seu b ( lrra l( bbgu( r - eZ- f) r + ez
  107. quem dividendo per E fiet. Utr-qul1 +) A +
  108. ee
  109. irr
  110. et AG qust. s) r etZ
  111. ee:
  112. et ita contentum in fractine cyliadii scaleni, erit
  113. Jam tranfformemus etiam expressionem Elementi sonici,
  114. Dee 77
  115. =Urr - Gu (r - f) e - et y -
  116. ec:rr
  117. CiYr
  118. AB+2t 2(t, - 1) 1LZ + Z
  119. 1e:
  120. tam
  121. + firrerit.
  122. possumus quidem et aliud puncto, assumere, sed ita sorum constans accederet
  123. vel delederet ipsi X. quod si loco diametri, assumeremus parallelam diametro
  124. et ita rectam quamcunque tantum u angeretur constante.
  125. ee

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 191v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0382?run=74