Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 43r
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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One image of two folio pages side by side, registered by the library under both labels (also fol. 42v); this page is its right half.
The machine reads it as
- et q
- ubi C et noccurunt
- mm + rr = Il
- pp+nn =mm
- pptrr = qq
- tantum semel nm = l -rr sit m = l+Y, f:a fiet Ur = r, s r, ffiaa = (- r
- seu n 47af:, aa + m = Y, aa +f5 + aa ff, Sr: faa 15, a), seu
- y e. q ae aa aq
- et m = l, a a Aa -
- m -I, ds 1t aat A
- Aursus
- pp = mm-nn sit. p = m+ R, g: a, et fiet
- m+n, gg: aa = m -n seu miq + ngg = aam- aan, seu m H, aa + g9,:, aa gg
- et p = R, aa -99 +aa +g9, (9: a): aa gg seu p= 2ag, aalgg, denique
- seu p= 2agr r, 4aagf
- pp = 49- rY sit p= qtr, h: a fit, qur th.: aa = q- Y
- i seu ghh + phh = aaq - aar Et fit r = q, ua hh, :, aa +hito e
- aa ff, an tg9
- et p = 9, aa thh +aa -hh, hi: a):, aa +hh, seu p = 2ah g:, aa +hR
- = n, aa +99
- Et ob duos valores ipsius M fit l, 2af
- aats
- Et ob duos valores ipsius Y, fit l, aa- ff=
- aa +f
- iinique ob duos valores ipsius p, fit n a ad
- 2
- aa 9d
- aa = 99
- seu L=
- M
- 9, aa th, seu-
- ad +hsi
- =9, rah, seu n = a h,
- aathto
- l= nO = qd fit n = 9d: O = 98, fit tandem D = 90
- Ergo
- aa =hh, aa +f
- a Z= un = ay = nm = ax Ergo ax = mm - nn + ay = U- ay se Ergo ray = H +nn - nn
- ax + ay = U
- ax + az = mm
- a aytaZ = HM
- Ergo 2ay = U+nn = mm 2aX = U + mm -nn 2 aZ = mm +nn - l
- ita ax tay 2ax + ay = ill EaX + 2ag = 2mM et 2ay+ 2aZ = 2 nn
- ax - ay = pp ax - aZ = 49 ay = aZ = YY. Hinc aZ = ay -YY = aX = 99. fit ax = (ay)tqg. rr = pKt ay)
- Hatem 1 G9 = x Y + pP
- ax = tay aZ= ay - rr
- Dx= ay = pp ax - aq = p (A3 7 p X ( ay) t 1Y = 99
- ay YY
- Ergo I1 +mm - nn =, ay t pp = Zax Mm + nn - Il = 2ay -2rr = 2aZ
- 2a9 = l+ (ma) - nn - 2pp = (mm, + nn -U + 2rr, et fiet U = nn +pp + rr, seu l = an +99
- et ate nn = mm. + p p
- Scupirest Lay = U + nn- um = llamm-un tpP et fint 2nn = amm + ipp seu nn = mmt pP
- Ergo res reducta est ad fres aequaliones gq = Yr+PP et q et II = nn +94
- seu 99 - rr = pp et UF nn = 49 fiat fg+ fr = ap et nn - pp = mm
- aap
- fiat ffqs ap GAr = sp: a fiet f9- fr = ap et aq + ar = fp afquaf r afgt asr = si p et fiet
- et fiet 2atq= aap + ssp, et rafr = fp-aap
- seu qu Htaor et aa
- fial ln = gq: a fiet 2agl = 9g9 + aaque et 2agn = 199- aaque l.
- Ergo ragt = 2a92 afl= 24 f999+ 2afaaq seu 4aa fgl = e (99taa) (Ff r ao)p seu l= 39 taa sptan
- Et 2a92a5, = 2a5994- rafaaque seu 4 anfgnr = (99 - aa) (55 +aa) p et n 99- aar fstaap +aasg
- Aaa fg
- ray = 2aX - A seu ray = mM rqg P EpB H vniue 2a2 X mm - 9c
- (2aX = TC + mim -. nn seu 2aX = mm +9
- ) et denique raz = m 94. seu 2ax = Aaa fmm PF _Sp t + 2aa BP et 2az taagnu spp. a dp. 2ep
- 4aa f)
- raass u t P a dpt F ep + rausseD astet
- El 2ay2
- daaff
- (
- Haas
- aem et p= hh- aa m
- rati
- ex 4 et b fil A = 98P- aa, Hi aa hd laa = (ex 5) hh+ am. Eno tandem D9- aaffica, hh-aa = Aaafg. sntua
- 2a6
- Faciamus h=S fieret gg aa. smna 4 aat
- 8∞3fgh
- sed uliter aneca n = m+ pAb fiet nm Fpp + Emp D2bmDibp mm +pp. unde
- Faeciumus f 2. lob. idest _ h~ 4.
- fiet m = bb = 2b p, : 2b - 2p et, no (p. b) 2(ba p) + 2bb + abp; c Cb p) - abb ps bp tubp p P.
- P
- ptb.D
- Et n =: 1b -Ebp) +. 2bp -2pp -(lb(t 2bp: 2b - 2p seu n = 2bpa 2pp -bb9 1, 2b ip
- site m abp -. bb, :9 2p - 2b et n = 2pp + bb - 2bp3 :, 2p - 2b, sed supra n = gg -aa, f taa, p: 4aafg
- et firo tandem 2pp + bb - 2bp =. (99- aa, 55aaa, : 40as9), 2 pp - 2bp
- J seu r = l, aa- :, aa +
- 2af, aa- 94
- dat H, aa +99
- = O
- aa-vld+ - )
- aa- aa +hk
- C
- G, aa +hh
Cite
Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 43r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0085?run=73