Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 10v
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: 0.86.
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The machine reads it as
- . p
- sind numeri C, m, n, differentiae l - M = Y l - n = n
- = Y + X
- M- H = 5
- aEt F C = m + Y = n + n m = n m + n
- M = A = Y + n = s L n. Ergo = A + Y, ut constat, ne
- itaque ex datis tribus differentiis non possunt haberi termini. Quia revera
- data sunt fantum duo, cum ex duabus differentis detur tertia
- + m N l+n =M men = L
- = N - m = M = n fit m = N - M + n = L - n . Ergo n = L + M - N, 12
- Ergo ex datis tribus summis d dantu res numeri. Itaque si tres
- summae sunt quadrati s _ seu pro L, M, N, scubabum LL, MM, NN, fiet
- 2C = MM + NN - LL 2m = LL + NN -MM 2n = LL +MM = N V
- sint jam et disferentiae quadrati l - m = VV
- Ln = nM m - n = AA
- Erit et + N_ a 2l = _a VV + NN 2m = LL + M
- finc
- MM - (a iu
- LL - X X
- =te + M M + L L
- VV = MM = LL
- etiam
- = + (M + MM
- = -H + MM + NN
- = NN- VV
- = = AM+ LL+ NN
- Hin 2LL = YV L MM- MM = A A = 4 Y
- NN
- MM = NN = LL
- Hinc M(M = XA + VV
- Ex summis El = MM + NN = LL 2m = LL + NN - MM
- AX = NN - MM
- 2n = LLTMM - XN
- ex differentiis, non possunt invoniri l et n absolute sed supposito m, Erg
- +VV
- n = na AI
- fint 2l = 2NV +L +) XN ( 2MM
- 2= Mm NNL LL
- G = m = X fint 2n = (3LL +(D N N (= MM, = 2X X
- b=
- 1) MM ( XN
- Ergo ex duplici valore a fit 2VV + 3LL + NN = 3MM
- ipsius 21,
- Et duplii valore ipsius 2n fit
- 2AN F3MM = LL + 3NN
- Eu YV = MM _ = LL
- a = MN (FNN. - LL = 2VV + LL(+ NN) - MM Zo
- 2n = (LL MM - XN = (L D + NN - MM = 2 dc
- unde quia rr+M = pn. sequitur NN - LL = M
- NN MM
- Tantum ergo pus
- est solvi has bina, aequationes tras vr = MM - LL, XA = XN - Mm
- et tandem
- 14+ a= N NtrV = e
- n=
Cite
Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0020?run=73