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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 19r, page id 00068197:0037
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Videtur casus dari, quo s rrcc - irs (rssu f5 XX
2YX = XX
deprimi possit
reddendo scilicet numeratorem divisibilem per nominatoris divisorem 2X-X
nempe multiplicetur 2Y - x per nec +s hex ner + rpX, prodibit
2nYd = nIrX = rPXX ~ rrcc - 2rf(r+f) X + ffXX
+ 2IrpX
X fit 2nP = rrce seu n = Cc: 2r Ob ex fit p = - ff: Y ob X fit 21f (21f) = ntr - 2rrp
sen 25(Y+ 5) = nr - 2rp, hoc est 25 (r+5) = =cc + 2ff  seu (Cc = qus +4- 4f.
sime
seu denique CC =2f, (S) V Adeoque ABaerit media proportionalis, inter f seu CD, et  a bis
est autem =a, ilem quod (C)d, posito C eadere inta circulum Ce
Et c seu AB eritu media proportionalis duplum mediae proportionalis inter radium
inter  OA radium, su seu Y; et inter OC, seu f
Itaque si inter C A si circa CA describatur Circulus; erg ejus chorda
angulo recto ad CA transiens per O, erit aequalis rectae AB, _ et centro A
radio qui sit aequalis dictae chordae, descriptus in cent plano 
plano, normaliter ad AC  eductam, in B vertice quaesito Coni scaleni
normali educam et angule,
cto
cujus superficies haberi potest. Itaque dato puncto C, dabitur conus scalemus
superficiei mensurabilis, ei respondens
prodibit ergo
art -Ert(risIX + ffXX.
2YX = XX
X - 2r dividat ffxx -erf (rts)X + 4Vs F ffX - Errf
X
2
+2rfsX
2rrs -
sed hoc fiustra, nam
chorda minor est quamfuns
diameter Circuli ergo minorqua
CA, ergo ex A noa poste potest
 pertingere dius
ad rectam exc normlaliter
edactu
videamus jam, qua quadhatura haberi possit dx Carrs. Bx, : X) - de
af dao: dx = f
Fingamus r+F =O, seu B imminer ipsi A die urr+ EX
2rX - XX
jam SSXX + CCrr = GX + er1-1, fx - eFY-1
Sx +c +GX-2Er, fiet c = + t 2f: 8- 1 - b
sed ita b constini non potest.
pr X assumamus Z7, et vi si esset r+f = + c, haberemus
etiam intentum, nam numerator esset extrahibilis
Y+ f = CA, sed se E = AB c = BA, itaque
sed BA et C A non possunt esse aequales, ergo nec r+f- +c
videamus, quid fial si r+f = -c, fiet rr+ ff + 2rf = Cc=
bb +rY + aar taa. Et sit. sed f- atr et fiat
YD+ (aa rar rn +2 rat im = bb + (41 n (+ 4art aa)
e
Ob
et fint b =0, quod est absurdum
nam lonicam, methado illa altiore, qua possumus  bx + xt ex +5) _rationalisandum reducere 
citoo b
hl_V + hfsu + fe ab vi  LabrvFabrr. = h∞ + ff + (∞ + 1 lb, hv+f-(ver) lab 
a, vv+ un ir
X Ab XDC, sit X=
ha ve+ alisu + ac vrae racw e urr
ves thv + (+)C, lv- 1f + (V er) Vac
ad est +gyrghus + rationalsandum. B