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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 23r, page id 00068197:0045
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S. feret ht +5g =0. firret ex aequ. 1 agh = aaV- est = (ex rg. 2) + a W - b5 +, et s+ = aa (W -)): 4 (bc
1t agh =  a) = caa (1o. 7 )(: 4 (b. d). sin agt baa) (=C aast caa )V  caa D: 4 (b -c) seu gh = a ()- ci)
Ex nt +5g =0 firret  nertih Euu ses h= posio 3) 1g (onc)5--ht: 9 et -het: g- aaso. . 1sb- )
et oV - cld = Falf +br sac. = (a (Yab - sac) + D  IbC) (Yab + Vac). ut st =  V aaY: A (lab - 1ac)
et oh= af (sab = sac) tas, bE,:, 4(ab  Vac) et fiet
=stgh = Bhutt = 5599 = (a - 10) (b) - c1): qu (b.c afr (tab. Yac) +ar ibe j. 1guffaba tuc
ao  et Veniamus jam ad explicationem aequationis ulticmae paginae praeceventis, quae satis
aghu ( (- 8) st qu (Bract Z Sab) =  a agh tacst, - aa B ( e aorb  matcitib. vac) aatile, a act rasa leb talir
Ldagh- astite, taaBEH
et aas t qu (aptiactaz ab) -- aq aer AH,: 4 (sab - 1ac)
Vab lac) +arribe
2+ hhet=
c qu (tit - 95)
4qu (tab- Vac
Ergo tandem frV (Tab- sac) + rr Ibc + af, (Jac - sab) = f(Vab - lac) taar sbc
compendii causa sit vab - sac = A et IbC = V, et habibimus aequationes sequentes
qu (Tab+ tac)
St = aar: 4_ gh = ab f + a NVY,: 4B
hhHt = sigg = a adfI, apr: b66
et tandem fr vor + e B vrr + afs abss = aaf t aaqvr
5= aa invoniamus S et g, siet
5 = aar: +bt g= abf+ acoY,: 4bh fit =s9 = , a, b5+ aY, : 160Bht = ht
Et = a Hadfr Bar r1): 4D =  -59
+ = as (ab fr + aN rY): ADM et 5= - aa
adh
EBa CaBEr+avr)
 Superest aequatio in qua solae sunt fet Y nempe
= -ahr: Y (adsrtavn)
frDD = r D_ + BD Barr. + adH = aab f + aa VY, seu
y  f + a + PBrr- 2aadY =
at +BOrr -2aaBP - 4 a N + qciV: B) r
4aa
+B- 4a = ab + ac = 2 a sbc - 4 a fbc 2aaD + 4 aV : B = 2aadD + 4 
4
4aa
-2na B + 42  Raa, ab- ac + 2albc + 4a eoc, sed nulla hinc compendia
fiet f =  aa = DY + (a +BBIrY + 4 a(v: b) Y): 2a
=gade
= Z aaor
si si velimus facere f =0 fiet BY = aa seu Y = aa: D et foret g = a V: 4BDh
et  F = aavaN: ADb et 5 = - ah: sac et h manet arbitraria
Rspetau Calculies posito f = 0 et ht + 95 =0 EUam firi arVb- aegale (i antaria a ab
a tib Bst
ob B = 7 fit  AA = gan seu aerre- Aagut 4, gatu
seusarre = 4(a3), gatr (+ ht vad + StC, ob h= B fit pp = 4aq. seusartb = a gahs it lab  Stb
plis aegq. fit Regh= stida = _b, vrat: 4a, ques duos valores aequando sit st = r.
o (P. . Apul P lab e plac)
-ye (aagh+ abst + Cant Fags) iab p. q r abt fa) Btacts saba as t dact
+95 val
E qu af.Y)ab) = 4ab5+
gbYaB
A  g5= -ht s = -ht:g = ghrr = ahhlt ,: Ht sit sthH = gghrr + aghat F, et
et fit h= HH- gorr: 4gH et fiet S= fflt + ggrr, : 4g9t
St = - - AH (+ g9rB,  = = (a rr (C. b)  rasr ( C  la b) 9e (u (C. b)
et on -  ggnr,: (El = da f(b- CD+ rafo (btac - etab) : (ina Cb. C)
(+:gu = q adss Cb arr b) agr loca tab) trY 2aBr (Lctrab) .4(P- 9)
aq: H = 2 afB (bsac = C Nab): aa (C - b) Y) et tuanescentibus F .E, 9, 5, r, fint
d, = 4 aa YbC (ab ad):  a qu Cb - C) et fieret, 1bc =- b +C,
sin fes prasse atrr t ragritaet ast abrr F rasr vab;in qacabs  se ele  rai cherteord gs e B)
qu Cb-c)
go, part  aatislab. tretarobe,- aassatriat
contrahitur ponendo ht+ 95 L0  paagh FabSF  a3Fa
qu (Tab + lac)
4(b-C)
et fit 9 = Ahtt, b - C : aa(V - 10) = a (b) - c1): 4h (b -C). sin IBhhit  Ca V1) (. ad
Et explicundo Zet W0 et) fiet X   V. W= Y(Sact  ab) velb 55gg =
act terrab
Est autem, 3a = r(Nab + 1ac)
Tab- saC)
itaque Et aGh qut B. 15) =- a, afeab - a1) (Nab  tac)  Ibc  (abt actratbi)s: A(tabo tac)
e
 et aβ sac + ac s ab = afiac qbe + af ab Baribe = af (Vab q vac) +ur 
itaque - aaghqu (a β - a Z) = - aa, ex afrr (ab a sac) + ar bc, : 4 (tab - Vac ))
et itue fieret 4bc = bb + c = 2 bc seu bb. + cC + 2bC 
e l) C  inttu ali oetitum succede et si catbulus esset bonu
ee= 8bc +9bb = dbb L bb  erfit a 3b -C = 2b+2. seu
c _V, 3=212, quod mrirater, si res hvccasspenti sucideret
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