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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 95v, page id 00068199:0190
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Superesset investigandum, cum habetur fr9thayt ky elius tedydu = 0
ut si fiat E m + ny =0 unde X am +duy r atus -0 ducatur in ps pary+t dy
fit pdm + pan +pndy
+amrus
 fgr gqy Fhgtus + tequus telgydus Aequydus.
nb =eq eu g- nt: e = pam: f = rdn: H sit dn = fut:  L r - edm . nk
umatuur solubilis jam inventa: m +ny +pdus, quae multiplicetur per r+ ty+ ndus
fiet mr+ arus +prdus
+mtus v
Antgus L ptlsdus
~ syt gqy +hqdys tRquus Alquydys teg aydus
+ nydus + Wp dydu fiet mr- 59 nt = kg W0p = eq
seu im = fg: Y n = kq. t p EG: W. Ex yfil r:t + Lff.r = Dg  habetur t:r aequature quadhalica
Ex
+ mvodus 
Ex du fit (eq.W +10 59. Y = hq datur r.1 per aequationem quadraticam
Tandem
ob ydu fit t ef: W + WKq. t = lq. Et datur t. u aequatione quadratica sed ducendo arvicem
Cns XB Y B KB+ aaf: β ~ 9 seu KB(B agB + aas
seu ββ = aq B + aat seu B - aqe D = 1aagque = aat) de β = a9 + a Y (9g - 4H), : 2k = r. t
t: r et r: W0 habemus +: W adhuc semel
t: r = ag + a . (99 - 4 4FK), : 2f
AKK
 W: r = a h + a (sh - 4ef), : 2f
t: W = al + a YU - 4 eK), : 2C et multiplicando + : 1o per W : r fit
at + a t: r. = a aa , l + s(u - 4K), h + tChh - 4 es) = AG a, 9 + Hgg - 4 fX)
su (a, lA + t...; h + f. ) - 9 = L(gg - 4 fK) et fit
aa V (iL + s.. ., h + f.. . .) - g a (L+ S. . ., h + t: : .) = - 4 fK et habetur 9 per reliqua
namfit g = aa qu (L + ((H- 4 eK), h + (hl - 4e5) + a f K, :, 2, L + ((- 4 ex), h + (hih - 4 es)
aeet
Aliter L dita est f + gy + hdy + kyy + lydys + e dydus = 0 et m + ny + plus =o seu dus = n +ng, ip
tt sp + ge - hm ns fPp + goppy + hpp dy + K ppgy + lpp ydy + epp dydus pdus = -m - ny
et ppaydu = um - amny. +gy fit Spp +grpus Ee -hpm- hpnys + Kpp  lpym-lxyny temm-remny + nngu
fit +spP + oppu _- lxngu = 0 quod differentiandum, et hinc tentanda solutio,
hum
TK PP
+enim
=hon
remn
 nngy
sed quia id prolixius, resumamus mtnytptus multi
plicatum per r+ty+ Wy, et in quodam loco aequa
tionis datae, nempe in hdy substituamus valores ipstus dy
et rursus alio loco ut in lydu, ita plures habebimus
ce quationes compinandas inter se
quaptum ed agendum, ut sint su
quicutum id agendum, ut sint sufficiente
mr + nru + prdus
+nt y
utyus + ptydy
mus dus
Hoc artificium late porrigitur, magnique est usus
non nisi per aequationes ordinarias quaeruntur
f9 + ggy + hadus + K9yy+ lqydy teu dydus
FB + 9βy +  +K Byy + l Bydy + eBdydy ubi in bsdu substituiuu
-pip 6 h sen
et W id = eque cCH P): p W = e (9+B): p + = K G+ B): n
lydu
+ nwoydus + ropdydus
Valorem- m.B
B K (9+ B) +  e (9+ () = l (9+ B) habetur Q per fit PH + n e = l, adeoque habetur  p: n
sit 4 = per t mo, . h
ab solute percysich q = pr + em (4+ β): p seu m  =  phq = ppY, : e (4+ ()
per y fit rem per y fit m = OA+ B) Lh hB~ - nY, . t ubi a est coguita n: p
quos duos valoas aequabimus, fiet b h H tqp. et pp - eg qu Y C) - Ct ae (11 () et (1 ) a p
ubi faciendo eg qu (qB) et (3~ (G+B) - a seu o+B = h Ba: g seu g ha9
fiet 1. 1) seu 9. B - N h: g  - , seu B = 84: v b- 9 et q p l  f9. teh-9G
et htq- rtp = - er (4+ B) , seu p = ht q + er(quB irt seu ht (k - C)
et ex y fit ne
Ex i fit m m = sp. fghas ( h . 5) p = mti X D4 (. oh. 5) s xp ~ f har que vtr 9) - ham 946, e b. 5)- a ppo: t
seu pht 4 p- tq et + erolla : et compendio P= 4V = 4 r; + 
ubi pro p ponendo Nalorem iaventum evamoscit qy era nescit 4 et fit
et in = f(gho (, ovh -9),:  h9(4) (. arh. 9) = Gha q (, vh ∞) hgqu (., eet ns) 
et evanescit g et hajus aequationis ope fit t 2) (, ( + A) - ...) = ( = o 4(p + Z)
es habebitur 1 vel F imo oblitus sum C jam supra inventum.
Explicudo t e m = 9 C9+ () - h C arp = va ppY, : K (4+ B), quem valorem priortque aequindo qui erat phqus - ppY, : e Cq+ B)
poterit utrinque di vide per p: (9+B) et filevg (9+ B) + eh B0  - V V pY = Khq = KpY et habetur
p = e  g (9+B) + etr βaa = Kh4, :, ea vr = KY. Ex i fit _ emp + ntB = fP (9+ 3)
seu m = fp (9+B): rp + hβ, quemo valorem aequando primo pha - pPF, : CCG+B), pervenitur ad pP,
et fiet esqu(qet et fiet e ( que) =  hrgp + hhB9 - rip hBp, et faciendo esfed lt q es qu( 41B) th eq
fiet hrq rep p. hrq r p= hrqpbr h(4 C): Y, sed hura ipsius P
tu esoer
ralum imentus veti  expiores 
aequata
qecuu incentur e) qordtatie nes mito quon
id impedini possit. itaque putorem succed ere