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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 51r

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: 0.76.

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The machine reads it as

  1. Disideramus, ut e productum ext X +b, X+C, x+d aequetur quidrato. Alumo
  2. oe et esse LLMm (x+ b) = ABCd + b LLMM = EEFGEt LL MM(XIC) = ABCd + Cf LmM. Et A B. Sa B au Mm =rGaa na
  3. Enim productum ex X+b, X+C, X +d erit quadratus EEFFGGHH IIKK: L M. Ubi quaevis sitera signilicet formulam simplitem
  4. Fiet A qualis est. H +.. a
  5. Omnes autem aequationes quae sequuntur sunt coinidentiae ideunficationes
  6. Eliu medium, ABCd = IIKK - CLLMM. itaque seponi potest _ ABCd, donec I, K, L M, sint inventae;, inde cum statiae dabitur
  7. Sed quia etiam ABCd = EEFG- b LLMM et ABCd = FGHH - dLLMM. Hinc fit idKK = EEFG + (C- b) LLMM, et iIKK = FGHH H (C- d) LLMy
  8. At c et sit C b = β et c- d = d fiet EEFG = IIKR - 3LMM et FGHH = IiKK- t LLMM. Hinifiat
  9. HH su (X + LM 1B K Im tC) EEFG A, IK + LM Vo HH LM Ad) FGHH Ex his quatuor sinistris hacum duarum aequation
  10. B(IK + LM +B) in f (iK. LM sB) = EEFG et A (IK+ LMS) in Z (IK- LM YS) = FGHH. Ex his quatuor sinistris harum duarum
  11. aequationum binas formulas, aquali quadratis, vol ad quadrata EE, HH, rationes constant a habentibus, non licet;; aliequi enim binae altere
  12. aeuate qui
  13. videa deberent habere rationem constantem inter se, quod commodum non erit Hac ergo resolutione omissa ali tentanda erit,
  14. p
  15. EP
  16. tuc tame
  17. Ex IK + LMIS =HF. K: d IK + LMd = HF L: K
  18. vil HF. 9
  19. Vet H∞. 1.9
  20. iK- LM+B= EED: BC
  21. s in piori pari, nihil resent cui attriouss F vel G; in poseriore, quia refert post electam jam in priore F vel G) adhibetur signum ambiguum, ita
  22. nin
  23. pursus nis refert: Ex his quatuor aequationibus fit ik = Ep. EF + E EG = Z9. HF + = HG. addende inuilen po runus moscem
  24. ubi sufici ik iton 2
  25. hi coincdentiantur
  26. Hinc E=
  27. dincidentiari alterubi suerum valorum, quia
  28. er
  29. F+ G
  30. et
  31. PF+ G
  32. =
  33. 1B, 9F - 4G
  34. os
  35. ip. EF - EG = 2q. HF ig HG subtutento a primasocurdum, ta tetia quantum
  36. LM= +B
  37. 418, pF- G ubi rursus sufficit E coincidentiari alterutii valorum, quia hi coinsat atantur ater se
  38. Multiplicatione ergo per ceucem instituta, fit +8, pgeF G(K 2) FG = YB, p9FF - GG + Cq - P) FG. jam com–
  39. pendii causa paFF. F GG vocetur R, et (Y-4) ve FG vocetur S, fint +d, R+5 = +B, R- 5, seu
  40. R (1β +8) = S(1B 488) sou (1B. f 18) CpgFF- 1 GG) = (+β + 15) (L. 2) FG dividatur haec aequatio
  41. 1B + ss (f -Z) FG seu compendio FF- rrGG = at FG. Htoc jam
  42. per (AB = 15) p9, et fict FF - poqu GG = YB+ is
  43. tandem aequatione identificatoria praestandum est.
  44. fiet +10. 10aa yy + 2. 10. 11 a3y + 11.1 a
  45. Sit F = 10y , 11a, et G= 20y +21 a
  46. =20 orrgy - 2. 20.21 arrys - 21. Maart ~ 10. 20 at yy + 10. 21 auty + 11. 21 cet
  47. Is
  48. 11. 20 aaty
  49. identificando teocoefficientes ipsius yy, fit 10. 10 aCD - 10 at = W, Au 10. 10
  50. 8.2C
  51. Eodem
  52. 2c
  53. 10
  54. 20.20 20 a
  55. 12
  56. -
  57. + na
  58. Et + 4rr
  59. Aaa
  60. 20= ta+CAtarr. pari jure acusi Eodem modo coincidentinadidentificando voessicientes ipsius y
  61. seu 10
  62. Eodem modo identificando coeficientes ipsius y, fit 1P. 11a0- 11 at = Y Y, unda ad discrimen prisrisfiet,:
  63. 21.2
  64. = F- HCH+ arr)
  65. la
  66. Tandem identificando coefficientes ipsius y fit 10. UIaa = 20. 21 EY = (10. 21 +. 11.20) at, seu dividendo per 20. 21,
  67. S.aa - rr = (180 + 1) at, et fint Et - H - a Iaa - rY = L + Y (H + arr) + L - s (H + arr) at
  68. fit 10.
  69. et fipt -Err = FE et fit to
  70. 4aa
  71. +
  72. a
  73. t 2
  74. Tra
  75. A ser Arp =- 2tt et (H +ari) = (H - 2H) = H tat F f-
  76. 10 = E
  77. 1 1 + Y-1
  78. Ea
  79. et IR = F, 1 - -1
  80. et
  81. a
  82. t:
  83. 2D
  84. 1β+
  85. jam quia -2rr = H, siet 1a = Btd +21Bd pp 44
  86. c
  87. ut 24
  88. A+S FZ +Bd
  89. PtS L2+
  90. peisa B+d + 2 1βd
  91. F
  92. seu = YI- 2 = F fiet
  93. unde st=
  94. a
  95. l-2
  96. L 10 = aa l- 2 - 12
  97. (p 2 yu = 1ay Zu2 aa
  98. Ergo fiet Ik = _ LM
  99. a 2a
  100. 13+ 18 - seu
  101. et i - aa, L.2 + 2 seu 10 aa
  102. jt fiab F et hut asensur, et
  103. et hiIK- LMS) fier
  104. et A(IK + LM S) fieret = FG =
  105. +F 30yy + 31 ay + F 32aa
  106. + F d 4oyy + F 1S. H ay L F 18 42aa
  107. le
  108. et
  109. 1- 2 = pp
  110. YB + 1s
  111. L-1 + 1 et 11 = ea
  112. 2 AH= pE t G. m
  113. h.d
  114. Tentemus ante omnia
  115. postremum; sit ik = 30y9 + 31a 1+ 32 aa et. LM = 40yy + 41ay +42 aa
  116. +p2R yy + (2a. y +32 aa
  117. X
  118. Epet
  119. + t-Epp4q, seu eaa r- 1 =
  120. ao Y. 2 =
  121. 1β+ 1s
  122. et E Y. - 2 = a l- 2 fit Y = a
  123. veluti si B(IK + LMB) fioret = EEm
  124. ex (1KC L M feret = FG+,
  125. 94
  126. pP
  127. 4
  128. 10
  129. fiet
  130. per has tres identificationes qu
  131. dabitur raho constans 20 ad A,
  132. 40 ad 30, et A ad 31, 42 ad 3 d
  133. et quidem semper eadem, et fiet
  134. 40:20 L 41 : 31 = 42: ZL
  135. et fiet DitE + Ba t BV LM + LM+ B - EE et LM - YS LM = H H 1
  136. ergo etiam E et H erunt in ratiore constante. Ergo etiam EEFG et FGHH erunt in ratione 2 constante, (labe
  137. sed ita etiam X + b, et x+ d erunt in ratione constante, quod non licet
  138. procedit,
  139. et (iK DLM = FG
  140. itaque seposita iniErethidus non ps
  141. possemus ad huc unam tlatare sepositam, verb. gr. faciendo B(IK + LM YB= Et sur
  142. et A(IK + LMId) = FHX et ZCIK- LmB) = lC H = hac methodus
  143. videtur extum bossehabere, et absolvenda est, it vid atur quae exduabus possibilibus sit commodedes
  144. ita vin
  145. 1- 1 - 1
  146. pa
  147. ideu
  148. Pa12
  149. i
  150. ito
  151. x

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 51r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0101?run=74