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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 15r, page id 00068197:0029
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=29
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yA- A V aequandus quodrato.
sit  e: a = fg: aa = hi: aa
Y+B-D, insia y - vr - 1 = img: a
3to = nh: a 9- v = ni: a
Z2- aabt = EL
L
cosab -v
fint ist v
aqpondus
2y = m f+g, m: a 2v =  f - 9, m: a -,
29 = h+I, n: a 2V = h -1, n: a
m: n = hti,: s+g = Hh - I, :  f- g
superest i = fg:h, et fiet
hae
omnet quantitases
tih +f9 Lihh- 1g, et tand extuberde in inagus
h. f+g
h, f-g
et tandem (hli s). ihg + st gE Fgg (hbs t lilus 5sg P sag
fiet . tih =0 seu h = + f. Ergo 1 = +g
et fa +s +8 = +5 +d. 4
Et tandem hls- hhgs + Hg - sgg = -1, Shh   litgs . ftg. fgg
titif. ( - -1) - lihus (1+ Y- 1) + fg (1 + - 1) - 99t ( - L. 1)
hf (hh - ggi  - f. 1) 5 = s lita (hih -. 55) (1 + f. 1) )
hh = f59 (1 1-1) -fg9 (1 - Y -1) hoc in integis efficien
um
(1+ Y- 1)9 = (1 - 1- 1) f
hh =  f (. + 1. 1) - 9 (1 - 1. 1) =
9(1 +  - 1) = f (1 - Y- 1)
videtur posse fieri th: fg = b: a posita b constante
et fiet  f: 9 constans ratio et h. f constans ratio
et
h:i constans ratio, et m. n constans ratio
Alitrri fiat Sd. f(it .1) - 9 (1- 5.1 = 5508vo
etbs  s
su 
gg ag199  5 = + gvr + 9 V _)
3d= 5oC it no vol cpt.
sit Z - nabb aequanda formula quadrato, fiet fiat G Z = a 3: _ fiet  a y - aa bb I : 214
dibet etust -abb aequari quadrato, sid _   sab = va, fiet a y - a  aeq. quadrato vel
tandem yt- vt debet aequani quadrato siat yy+ vo = mme:a et gy -on = nne: a et sit
Ee e: a = fg: aa = hi: aa y + v. + -1 = mf: a et y - v  -1 = mg: a, et 2y = m, Htg: a
et 2v -1 = m, f- 9, : a seu 20 = m, f-g, : a -1 y + v =nh:a y -v = ni: a sy 2y -n, hti, : a
et 20 = n, h-i, :a. Ergo ex duobus valoribus ipsius 2y fit min= hai,:, f+g Et similiter ex duobus
seu m:n = L1y h- 1:, f-9 quas duos ipsins m: n
Valoribus ipsius 20 fit m: n = h - 1, i, (f - g, : - 1)
valores aequando fit  f. quos duos ipsias m: n Valores aequando sit hti = s-1, h. 1, adeoque fiet
 pro i substituatur ipsuis valor fgih, fiat hh+ f9 f.1, lit B9, adeoque hiti s - tit g tts g. sgg chli J. s getihius Ggu sas
h,5+9
h, 5.
et fit hh f (1 - + -1) = hhg (14 f -1) = -fg (1+ . 1) Tes + f99 (. - Y - 1)
seu hh= F9, f (1+ + - 1) - g (1 - 1 - 1)  g (1+ + . 1) = f(, - + - 1)
ffggaa
= = ht
vv qu (9 (Hl. 1) -f (1 - Y- 1))
9 (1+ 1 - 1) - f(1 - f- 1) fiet f(i+ 1.1) -g (1- L.1), in, 9 (1+ . 1) - f (1- - 1) = fgaa: vv
sat 592+ -1 - fgei 2f - 299 = fg aa: vv seu H+ gg = - fgaa: hvV
sinliceret facere videamus an licent facere fgaa. Evo = Bfq + ax ab. seu aafg = 2β fgre + 2aaD vv
4 = dd =09 = 1699v + g9 a
seu sg raadvo  a 20 ff +2s dqon daa
sed ita aciditur in priora
16 v2