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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 285v

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: 0.78.

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The same scan is also registered as fol. 286r; its text is given once, here.

The machine reads it as

  1. +y+Y
  2. Assumatir
  3. Aequatio hujus gradu, interpretando V per Y +Y potest reduci potest ad cunc forman 100 + 101 dy + 1119dy Zo
  4. 200 + 210y + 2209y + 201 dy + 211 y dy =0. seu -ly = 200 + 2r0y + 22477,:, 201 + 211y = 105:, 101 + 11y. Unde per gucem multiplicando fib
  5. . 200. u1. 210 gy + 11I. 220 y (4 = 0 Compendio 30, + 31y Aay ar o poho tad 3 1s tod 3r gy d 31 y 165. =, rocon ao noldus rao agan
  6. = 100. 201 -100 2 11 G
  7. + 101. 200 +1p. 2, 8. 4 101. 220 9y
  8. a31du f 3 2ydy 1 3 3 Eydus apt. + A. ao y 4 qu 1ol guys ra1. 1 qyslyse
  9. 60)
  10. quan
  11. 3. = c L B. 200 y 1 10 v0 rfes 4 10. 220
  12. tutiando ot y) sp P fiat 220 L (o0. 10) (1n dro +2ro du1) et habatur 220 nssob guy dy, fiet, 41 = 3. BB. 33 + 10. 21. ob gy siet 19. 10 + 00 d32 o de seu 19 20 + d (1 O1 o) F M dno r 20dn - 8
  13. O. 20. yay + 19. 211 yydy N
  14. cui addatur assumen 2 mulipicatper 10
  15. et habetur 210 c B yty eb A Gtu fit C 3 00 33 10t + 10. 2H tor ob Idy fit 40 et ty 40. 111 =, 00. 32 +10. 201 ) en 40 M - 2 _ set 220 + 5 11 20 f 10. 20
  16. 220, et, 210, datur et 32
  17. itaque ut aC simpliciter, peducitur ad 2II, ita 40 simpliciter reducitur ad 201 vb du fit 00. 31 = 40. 101 sel gbe in seu . 100. 2n + d roneto L M. 100 - 110 10L
  18. n
  19. db y fit 41. 100 10. 200 +00 d31 seu 3, 2433 100 +10. L11. 100= vo tv. 200
  20. den
  21. sun - 100. 1II. 211 (F 101 III. 2102, 11. I1I. 200 LD (per 1) 2. 101. 101. 220 ( (2) 101. IIL. 218 + 10, 101 201
  22. Ly 300. 33. 100 1 10 2 100 = 00 10 200 + 50 tEm rud avdua het av iend 2I idurroo 1 udevo
  23. irnius ob absolutum sit co cord siu 4e = 00. 111 d30
  24. no reducta A ad aeqqe. 1, 5, t7.
  25. ob su 00. 3 ex. 11I. 3) 2 101. 32 +10. 201 ob y fit 41. 100 ) 10. 200 + 00d31 seu 3 50b. 33 10 et 300100. 33 +10. 100. 211 = 00. 10. 200 + 000b d31
  26. seu 2. 100. 101. 120 , 2. 1M 110 1 100 nol d 1 dioo Eot. D 1H 100 d20G + H1d1o1. 200 + 11. 1et d200
  27. B comprutio sit 21ot.I cao +dt M NO= eo b 57D et fut 2 et 00 H: 101 S1O et nM: 10 Si et fiet 15. 20 = 510. 21 + 5i 200 et 530
  28. e
  29. Deniu al termtnum absolulum est 46. 100 00d30. seu 40 +00 40. 115100 = 00. 111 d30 seu 2.00. 100. 32 + 10. 100. 20=00. 11 d30
  30. E 32 31 et 30. Ex aequ. 17 fib 2, 00. 100. 32 + 10. 100. 201 Z a N. 1 1. 4100. 201 - 111. 100 1 201 = 111 duo1. 200 + 111. 101 d200
  31. et fiet
  32. superest jam ut explicemus
  33. ubi cum 32 sit cognita,
  34. 200, 100. 32 4 (10. 100 - 11 d100) (111. 31 = 2. 101. 32) = 11AB C M1a 31 + d1. 31 = 2 d (10131)) = 11 d101 200 +1.. 101 d200 it habemus binas aequationes 15 2t 181
  35. faciamus 100. 10. 100 201 = Utdioo 201 1g. 100 d20 cujus apo toltatur Et tolatur hinc 201, ope aequ. B3
  36. in quibus explicando 31 _ habemus binas aequationes differentiales simplices ad binas literas 200, et 2 21I. jam sublato 211, sa redutatur
  37. res, ad 200 2.. 200 +. d200 +.. dd 203, et fiat ad200 = 0: et res reducatur ad 200, 1200 ed quia aderit simul ddx, nonideo ad exitum plavenire
  38. dy ytus sit y - B b v sit dy e v do gdu - d sit e- 1 = 2e 1 fint P = 0. Huc ergr non licet
  39. sit y - bed Idus - B deo dua b da _ quid s g ( y- ero syta ipdco y yt = Y cocot codco-
  40. sit 1012= ton d (101Z) = 100Z + s 111Z = 1oidz + Z d10
  41. 101 100 + cor y + = 10 + ny 1 4. du 100 + 12ogg + 10 ly = R 100y S 100 + 120y9 + 101 dy y = Y 10 + 12v + 101 e V av
  42. 100Z + 101Z dy + 111Z3
  43. 100Zy + 101 Z ydy + 11 Zyy - 0 sit 4(101 Z. 2) -
  44. licebit
  45. i co dco + da 1covt d t co d
  46. data aequatio 100 + 10lby + 1 ydys =o multipliaetur per 20 +ry fiat 100. 30 + 181. 20dy + 111 20 ydy + 100. 21y_ + M yydus = 0
  47. A Gtu fiet et 3.33.U ob gy fit _ 403- + 005 = 8 3
  48. Et psi aep. 3 disferentiatae addatm ipsu aeq.3. Multiplicatar pe dodus
  49. ione constant
  50. a d (Lyy) = 4G est 9y it + Aitylys
  51. Assunatur 30 +31y + 3r gy +33y =0 et differentiantos, 430 +. gldy + 2. 319
  52. 1i(32 + 1. 13 133)
  53. lui addatur 4i 30 + 31y +32 9y +33 y
  54. + 101. 21 y dys
  55. Et ob _tque g.oetum
  56. (um absuit _33, Y tot 40 = eod33. 33 = 00 d32. 32, quae aqua Ergo d 2 2 et 33 sunt ad in D.ca
  57. tante
  58. non licet; nisi et sit determinatio in datis
  59. H1. Et ob habetur 20 = 2. 00. 3
  60. NG +11. 2yy dy
  61. 101. 21 y dy +100. 2
  62. 3.00. 33,+42. 92. 11
  63. 20 + 211 + 22gy, fint
  64. ita binos tesus 21 valores aequando 130, 11, 32 ,e3 si taater et inui lavicem habent relationem simplicem ob f fit JtG3: 3i = ao sin sig. 1 X E1 tatm B quod
  65. An datu multiplicetur per
  66. pona
  67. 0
  68. possumss lotere si
  69. oltiento 30, ustan 32 e 31, nam 30 jnatulatur. 1 t. 3. rdolitub ad S1 It rabmus A epu. lui quibus htm H1. H ast prmose tndo 31 . 1, haletum 4 2per 40
  70. mutienenta per 4 4b + 42 ay, 0. A0. 30 440. 3t nt tu B2. +av. st . 4 g2. B, 4 grigsi . 4 r. 32. . gr. 32 fo l9
  71. habebitur 32 per 3y et 3 per y, et
  72. hatumu hatemus binas a pe quadum
  73. Quod si sic.
  74. 1. 101
  75. 111 - 42. 30. 111, - 101. 101
  76. 00.32t01 + 42.31. 101 2. a g0 ut datas
  77. Tob ge. co ui pt 1 = -
  78. a
  79. obsolulum
  80. aliunde jam habotur cato
  81. eet u di + (01 _dy C0 fiat
  82. nesc
  83. in duas, ut ero
  84. utr, 30, 31, 2
  85. quids aequatdone
  86. _ F = +W =0 = Y ydo -vau gy duo t auluis igo talis aequatio solvi potest
  87. sit aequatio data Y 5y + g = fyyAgu + hdys = o multiplicetur per Z. fit fZet szgy + g gzy + tidus 0 fiet lro = h, A 1 = stidx
  88. bata,
  89. tificari
  90. du = - fv: h
  91. Habentur ergo ∞ et W, adeoque omnis aequatio syis +gy + hdy =0 solvi potest. Hac est insignis promatio calculi nostri
  92. a + W + Cy stgrey fdg r yds (0 sit ydv - vay + Cb 9ydco + + c t f jg = 0 Hini si fiat duo - - ctf. 5 soo W = 5as )
  93. s
  94. prodibit ydo - vdy + cytus = 0 aequatio situbilis. Itaque et haec est solubilis de - vdus + cdy =0 ridiamus ergo an gereralis
  95. f. + fdy + hd possit reddi solubilis
  96. Hep +Wd + Cs
  97. y
  98. n
  99. sed non apparet
  100. =0 fit + ydo + 2so + vdy + vdip + d gydwo + cydys = 0 li absit qus int W constans
  101. I
  102. ipdu
  103. 42 ydlo
  104. +cydep
  105. +du
  106. apdy + epde
  107. prod si jam absit etiam y, siel du = - ct p. sin v- et 4
  108. Y _ Eyytaitus a ngrsez voq gtae Avaqu sit Zedo. g = v. h et (av iv = sta g h et v- b ( 5
  109. sit jam aequatio data f + gdys + cydus ∞D sed video non sufficere data nisi praeformetur.
  110. dyA s
  111. ea
  112. +Z= b(5.. ). h En. f(gy + hay, b(f.. J 2b) = y. b (
  113. (Ebr g Fg 20 sit ly +7d5+ figduy - 0 ino h r7 solibile
  114. Sgylus
  115. Soyr yes olyr eq . k 20 fit Hlyn 9tf. + fg syplgs r fydh 20
  116. sit data aequatio: rm f angus erpdy argydus = o mulliplicata per arbitrarum r. ft r- 5g. m 2t ro -5 seu r = f. p ob gysit r= fagin et habitur 8g = n. p
  117. fm + lu = h n- hdn stratque adeoque gest inventa, ob ydy fit r= fg: 9 - f. p. ethabetur g - 9. p. Ergo in datis fit d (9. p) = n : p _andim fit ob 9 fit df + fah = (rm) fM. p
  118. si t se0
  119. sit n - c fit l0 +
  120. site ) ndi patet hic A esse superfluaum et tamen sufficere arbitrariis. Anergo sic sIy +9 15 +de a +gy + h =0 et fiet
  121. Syt e
  122. = fdys ayds + de fgyay lesu +fdygy _ fb Vittrnus a rngus + ip dys 1 rq ylys a 6 9b est rq utg seu rufgique se ypte r segin
  123. sit leg Cd =V C0- V
  124. produ 16 + f = du
  125. seu l. b s - hay b
  126. eg +edgs redhi
  127. lon L = s. ded 10co ts 4 hdleo
  128. + fahys
  129. Et ( lo: 4 = q: H et habetur g, habetiu et r. f
  130. ob yd est ih = r( = de, : e = (ob y) rm - d, = edg 3. f sa H. rea . B. g) B p. g er mr rd cu )
  131. ob ly est f +eg = rp et hobr habetur et C: f Nom f= Yrido) sit r. tus )reg rp, et ed B nitol -po:g
  132. Supersunt termini y et p.
  133. sed ita utrobius destruitur dr adeoque evanescit et Y
  134. Alitr fty (segi 345 + de a cf 9 hd + 3sg + dh
  135. 5y+e.
  136. fy+h
  137. + K -o fil i fgytus + ga) yy Agyde + hsty +hde
  138. Halemus quotuor aegus. et tullendo E et (dk. resabunt duae fl. 9.
  139. pro quibus adsunt literae 5 8 R e, f, g, h, quae tra lantur eodem
  140. hydf
  141. esgydus afdg gy nsus ih +egdus +eedh
  142. Weydu
  143. +fgd kpy Hary E ehdk
  144. =P, : 9
  145. = - edg
  146. teim dale ponandis abasse ydy.
  147. g
  148. ydo
  149. V el +rmyarngus + rpaya sit fit c--
  150. Et d ( = h.f - 8g,: p = ch ik
  151. ob d fit
  152. modo exciptis sigms.
  153. Y 10Y + A dy +rEddu = 0 sit y = b fict 10b + 1deo b + 12 ddio b + 12 daedeo ( b = 0 sen 10 + 1i deo At 12delco + 12 daodeo = 0
  154. +W =0 fit puie y A + WA - vsus + yydu A V rL + rmy arn gy + rodus vagr tuo- en dua rap - plr - ob gu sit du = go rn = - rp do- ptr
  155. yd u
  156. a fio pubre vortur votasitorsi sti toit
  157. rdp +pdr + abrn = tm et fit P = m + d p) - p E y : 2B
  158. sed ita calculus fit difficil
  159. e co 100 + 10y + 12099 + 101 dy 20 sit g- f P, tit 10o q uo toss t10r fil +101 Za f. = 0 inq faci coci potest Z
  160. = G sit 1o su y = p EF 531 d fit 10027 + 10532 +u0 Z9 + 120 ff22 + 2120fg2 + 120994 101 Z 2 101 22 t 1 Za- 101 sy a Z) gdq
  161. vuse utus eroisieis in geta qut si qua une tatum quarius aeie tani ottam plae puon sue petumi suones insunte ospuie ra e ogse uste ro pretutum
  162. 120422 +n 2 +1218

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 285v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0566?run=74