J21:0010a	-	YBL	<bmajhd>	-	[Oh.
J21:0010b	-	NN1n	INTRODUCTION	introduction	.
J21:0010c	-	YF	+.	-	.
J21:0010d	-	YBR	<emajhd>	-	.Oh]
J21:0010e	-	II	In	in	[O[S[P:p.
J21:0010f	-	NNm	<sect>	-	[Nns.
J21:0010g	-	MC1n	+1	-	.Nns]P:p]
J21:0010h	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:0010i	-	VV0t	investigate	investigate	[V.V]
J21:0010j	-	AT1	a	a	[Ns:o.
J21:0010k	-	JJ	new	new	.
J21:0010m	-	NNc	series	series	.
J21:0010n	-	IO	of	of	[Po.
J21:0010p	-	NN1n	line	line	[Np.
J21:0010q	-	NN2	involutions	involution	.
J21:0020a	-	II	in	in	[P.
J21:0020b	-	AT1	a	a	[Ns.
J21:0020c	-	JJ	projective	projective	.
J21:0020d	-	NN1n	space	space	.
J21:0020e	-	IO	of	of	[Po.
J21:0020f	-	MC	three	three	[Np.
J21:0020g	-	NN2	dimensions	dimension	.Np]Po]
J21:0020h	-	II	over	over	[P.
J21:0020i	-	AT	the	the	[Ns.
J21:0020j	-	NN1c	field	field	.
J21:0020k	-	IO	of	of	[Po.
J21:0020m	-	JJ	complex	complex	[Np.
J21:0030a	-	NN2	numbers	number	.Np]Po]Ns]P]Ns]P]Np]Po]Ns:o]S]
J21:0030b	-	YF	+.	-	.
J21:0030c	-	DD2i	These	these	[S[Dp:S.Dp:S]
J21:0030d	-	VBR	are	be	[Vap.
J21:0030e	-	VVNt	defined	define	.Vap]
J21:0030f	-	IIb	by	by	[Pb:a.
J21:0030g	-	AT1	a	a	[Ns.
J21:0030h	-	JJ	simple	simple	.
J21:0030i	-	JJ	involutorial	involutorial	.
J21:0030j	-	NN1n	transformation	transformation	.
J21:0040a	-	IO	of	of	[Po.
J21:0040b	-	AT	the	the	[Np:101.
J21:0040c	-	NN2	points	point	.
J21:0040d	-	II	in	in	[Fr[Pq:p.
J21:0040e	-	DDQr	which	which	[Dq:101.Dq:101]Pq:p]
J21:0040f	-	AT1	a	a	[Ns:s.
J21:0040g	-	JJ	general	general	.
J21:0040h	-	NN1n	line	line	.Ns:s]
J21:0040i	-	VVZv	meets	meet	[Vz.Vz]
J21:0040j	-	AT1	a	a	[Ns:o103.
J21:0040k	-	JJ	nonsingular	non<hyphen>singular	.
J21:0040m	-	JJ	quadric	quadric	.
J21:0040n	-	NN1c	surface	surface	.
J21:0040p	-	YG	-	-	[Tg[s103.s103]
J21:0050a	-	VVGv	bearing	bear	[Vg.Vg]
J21:0050b	-	AT1	a	a	[Ns:o.
J21:0050c	-	NN1c	curve	curve	.
J21:0050d	-	IO	of	of	[Po.
J21:0050e	-	NN1c	symbol	symbol	[Ns.
J21:0050f	-	FOx	<formul>	-	.Ns]Po]Ns:o]Tg]Ns:o103]Fr]Np:101]Po]Ns]Pb:a]S]
J21:0050g	-	YF	+.	-	.
J21:0050h	-	RTn	Then	then	[S[Rsw:t.Rsw:t]
J21:0050i	-	II	in	in	[P:p.
J21:0050j	-	NNm	<sect>	-	[Nns.
J21:0050k	-	MC1n	+2	-	.Nns]P:p]
J21:0050m	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:0050n	-	VV0v	show	show	[V.V]
J21:0050p	-	CST	that	that	[Fn:o.
J21:0050q	-	DDy	any	any	[Ns:s.
J21:0050r	-	NN1n	line	line	.
J21:0060a	-	NN1c	involution	involution	.
J21:0060b	-	IW	with	with	[P.
J21:0060c	-	AT	the	the	[Np.
J21:0060d	-	NN2	properties	property	.
J21:0060e	-	CST	that	that	[Fn.
J21:0060f	-	MCb	(a)	-	[Iu.Iu]
J21:0060g	-	PPH1	It	it	[Ni:s.Ni:s]
J21:0060h	-	VHZ	has	have	[Vz.Vz]
J21:0060i	-	ATn	no	no	[Ns:o.
J21:0060j	-	NN1c	complex	complex	.
J21:0060k	-	IO	of	of	[Po.
J21:0060m	-	JJ	invariant	invariant	[Np.
J21:0070a	-	NN2	lines	line	.Np]Po]Ns:o]
J21:0070b	-	YC	+,	-	.
J21:0070c	-	CC	and	and	[Fn+.
J21:0070d	-	MCb	(b)	-	[Iu.Iu]
J21:0070e	-	APPGh1	Its	its	[Np:s.
J21:0070f	-	JJ	singular	singular	.
J21:0070g	-	NN2	lines	line	.Np:s]
J21:0070h	-	VV0v	form	form	[V.V]
J21:0070i	-	AT1	a	a	[Ns:o105.
J21:0070j	-	NN1c	complex	complex	.
J21:0070k	-	YG	-	-	[Tg[s105.s105]
J21:0070m	-	VVGi	consisting	consist	[Vg.Vg]
J21:0070n	-	RR	exclusively	exclusively	[R:m.R:m]
J21:0080a	-	IO	of	of	[Po:u.
J21:0080b	-	AT	the	the	[Np:107.
J21:0080c	-	NN2	lines	line	.
J21:0080d	-	DDQr	which	which	[Fr[Dq:s107.Dq:s107]
J21:0080e	-	VV0v	meet	meet	[V.V]
J21:0080f	-	AT1	a	a	[Ns:o.
J21:0080g	-	VVNv	twisted	twist	[Tn[Vn.Vn]Tn]
J21:0080h	-	NN1c	curve	curve	.Ns:o]Fr]Np:107]Po:u]Tg]Ns:o105]Fn+]
J21:0080i	-	YC	+,	-	.Fn]Np]P]Ns:s]
J21:0080j	-	VBZ	is	be	[Vzb.Vzb]
J21:0080k	-	RR	necessarily	necessarily	[R:m.R:m]
J21:0080m	-	IO	of	of	[Po:e.
J21:0080n	-	AT	the	the	[Ns:109.
J21:0090a	-	NN1n	type	type	.
J21:0090b	-	YG	-	-	[Tn[S109.S109]
J21:0090c	-	VVNt	discussed	discuss	[Vn.Vn]
J21:0090d	-	II	in	in	[P:p.
J21:0090e	-	NNm	<sect>	-	[Nns.
J21:0090f	-	MC1n	+1	-	.Nns]P:p]Tn]Ns:109]Po:e]Fn:o]S]
J21:0090g	-	YF	+.	-	.
J21:0090h	-	ATn	No	no	[S[Ns:S.
J21:0090i	-	NN1n	generalization	generalization	.
J21:0090j	-	IO	of	of	[Po.
J21:0090k	-	DD2i	these	these	[Np.
J21:0090m	-	NN2	results	result	.Np]Po]
J21:0090n	-	IIt	to	to	[P.
J21:0090p	-	NN2	spaces	space	[Np.
J21:0100a	-	IO	of	of	[Po.
J21:0100b	-	DAR	more	more	[Np[D.
J21:0100c	-	CSN	than	than	[P.
J21:0100d	-	MC	three	three	[M.M]P]D]
J21:0100e	-	NN2	dimensions	dimension	.Np]Po]Np]P]Ns:S]
J21:0100f	-	YG	-	-	[t111.t111]
J21:0100g	-	VHZ	has	have	[Vzfp.
J21:0100h	-	RGz	so	so	[R:G111.
J21:0100i	-	RRf	far	far	.R:G111]
J21:0100j	-	VBN	been	be	.
J21:0100k	-	VVNt	found	find	.Vzfp]
J21:0100m	-	JJ	possible	possible	[J:e.J:e]S]
J21:0100n	-	YF	+.	-	.O]
J21:0100p	-	YBL	<bmajhd>	-	[Oh.
J21:0100q	-	MCb	1.	-	.
J21:0100r	-	YBR	<emajhd>	-	.Oh]
J21:0110a	-	VV0v	Let	let	[O[S*[V.V]
J21:0110b	-	YTL	<bital>	-	[N:O112.
J21:0110c	S	FOx	Q	-	.
J21:0110d	-	YTR	<eital>	-	.N:O112]
J21:0110e	-	YG	-	-	[Tb:o[s112.s112]
J21:0110f	-	VB0	be	be	[Vjb.Vjb]
J21:0110g	-	AT1	a	a	[Ns:e113.
J21:0110h	-	JJ	nonsingular	non<hyphen>singular	.
J21:0110i	-	JJ	quadric	quadric	.
J21:0110j	-	NN1c	surface	surface	.
J21:0110k	-	YG	-	-	[Tg[s113.s113]
J21:0110m	-	VVGv	bearing	bear	[Vg.Vg]
J21:0110n	-	NN2	reguli	regulus	[Np:o.
J21:0110p	-	FOx	<formul>	-	[FOx&.
J21:0120a	-	CC	and	and	[FOx+.
J21:0120b	-	FOx	<formul>	-	.FOx+]FOx&]Np:o]Tg]Ns:e113]Tb:o]
J21:0120c	-	YC	+,	-	.
J21:0120d	-	CC	and	and	[S*+.
J21:0120e	-	VV0v	let	let	[V.V]
J21:0120f	S	FOx	g	-	[N:O114.N:O114]
J21:0120g	-	YG	-	-	[Tb:o[s114.s114]
J21:0120h	-	VB0	be	be	[Vjb.Vjb]
J21:0120i	-	AT1	a	a	[Ns:e.
J21:0120j	-	FOx	<formul>	-	.
J21:0120k	-	NN1c	curve	curve	.
J21:0120m	-	IO	of	of	[Po.
J21:0120n	-	NN1n	order	order	[Ns.
J21:0120p	-	YTL	<bital>	-	.
J21:0120q	S	FOx	k	-	.
J21:0120r	-	YTR	<eital>	-	.Ns]Po]
J21:0120s	-	II	on	on	[P.
J21:0120t	-	YTL	<bital>	-	[N.
J21:0120u	S	FOx	Q	-	.
J21:0120v	-	YTR	<eital>	-	.N]P]Ns:e]Tb:o]S*+]S*]
J21:0120w	-	YF	+.	-	.
J21:0130a	-	AT1	A	a	[S[Ns:s.
J21:0140a	-	JJ	general	general	.
J21:0140b	-	NN1n	line	line	.
J21:0140c	-	YTL	<bital>	-	.
J21:0140d	S	FOx	l	-	.
J21:0140e	-	YTR	<eital>	-	.Ns:s]
J21:0140f	-	VVZv	meets	meet	[Vz.Vz]
J21:0140g	-	YTL	<bital>	-	[N:o.
J21:0140h	S	FOx	Q	-	.
J21:0140i	-	YTR	<eital>	-	.N:o]
J21:0140j	-	II	in	in	[P:p.
J21:0140k	-	MC	two	two	[Np:115.
J21:0140m	-	NN2	points	point	.
J21:0140n	-	YC	+,	-	.
J21:0140p	-	FOx	<formul>	-	[FOx&.
J21:0140q	-	CC	and	and	[FOx+.
J21:0140r	-	FOx	<formul>	-	.FOx+]FOx&]
J21:0140s	-	YC	+,	-	.
J21:0140t	-	II	through	through	[Fr[Pq:q.
J21:0150a	-	DD1q	each	each	[Dqs.
J21:0150b	-	IO	of	of	[Poq.
J21:0150c	-	DDQr	which	which	[Dq:115.Dq:115]Poq]Dqs]Pq:q]
J21:0150d	-	VVZv	passes	pass	[Vz.Vz]
J21:0150e	-	AT1	a	a	[Ns:s117.
J21:0150f	-	JJ	unique	unique	.
J21:0150g	-	NN1c	generator	generator	.
J21:0150h	-	IO	of	of	[Po.
J21:0150i	-	AT	the	the	[Ns.
J21:0150j	-	NN1n	regulus	regulus	.
J21:0150k	-	YC	+,	-	.
J21:0150m	-	FOx	<formul>	-	.
J21:0150n	-	YC	+,	-	.Ns]Po]
J21:0150p	-	DDQGr	whose	whose	[Fr[Nqp:s117.
J21:0160a	-	NN2	lines	line	.Nqp:s117]
J21:0160b	-	VBR	are	be	[Vab.Vab]
J21:0160c	-	JJ	simple	simple	[Np:e.
J21:0160d	-	NN2	secants	secant	.
J21:0160e	-	IO	of	of	[Po.
J21:0160f	S	FOx	g	-	.Po]Np:e]Fr]Ns:s117]Fr]Np:115]P:p]S]
J21:0160g	-	YF	+.	-	.
J21:0160h	-	II	On	on	[S*[P:p.
J21:0160i	-	DD2i	these	these	[Np.
J21:0160j	-	NN2	generators	generator	.Np]P:p]
J21:0160k	-	VV0v	let	let	[V.V]
J21:0160m	-	FOx	<formul>	-	[N:O118[FOx&.
J21:0160n	-	CC	and	and	[FOx+.
J21:0170a	-	FOx	<formul>	-	.FOx+]FOx&]N:O118]
J21:0170b	-	YG	-	-	[Tb:o[s118.s118]
J21:0170c	-	VB0	be	be	[Vjb.Vjb]
J21:0170d	-	YC	+,	-	.
J21:0170e	-	RAc	respectively	respectively	[R:m.R:m]
J21:0170f	-	YC	+,	-	.
J21:0170g	-	AT	the	the	[Np:e.
J21:0170h	-	NN1c	harmonic	harmonic	.
J21:0170i	-	NN2	conjugates	conjugate	.
J21:0170j	-	IO	of	of	[Po.
J21:0170k	-	FOx	<formul>	-	[FOx&.
J21:0170m	-	CC	and	and	[FOx+.
J21:0170n	-	FOx	<formul>	-	.FOx+]FOx&]Po]
J21:0170p	-	II31	with	with	[P[II=.
J21:0170q	-	II32	respect	respect	.
J21:0180a	-	II33	to	to	.II=]
J21:0180b	-	AT	the	the	[Np:119.
J21:0180c	-	MC	two	two	.
J21:0180d	-	NN2	points	point	.
J21:0180e	-	II	in	in	[Fr[Pq:p.
J21:0180f	-	DDQr	which	which	[Dq:119.Dq:119]Pq:p]
J21:0180g	-	AT	the	the	[Ns:s.
J21:0180h	-	JJ	corresponding	corresponding	.
J21:0180i	-	NN1c	generator	generator	.Ns:s]
J21:0180j	-	VVZv	meets	meet	[Vz.Vz]
J21:0180k	S	FOx	g	-	[N:o.N:o]Fr]Np:119]P]Np:e]Tb:o]S*]
J21:0190a	-	AT	The	the	[S[Ns:s.
J21:0190b	-	NN1n	line	line	.
J21:0190c	-	FOx	<formul>	-	.Ns:s]
J21:0190d	-	VBZ	is	be	[Vzb.Vzb]
J21:0190e	-	AT	the	the	[Ns:e.
J21:0190f	-	NN1c	image	image	.
J21:0190g	-	IO	of	of	[Po.
J21:0190h	-	YTL	<bital>	-	[N.
J21:0190i	S	FOx	l	-	.
J21:0190j	-	YTR	<eital>	-	.N]Po]Ns:e]S]
J21:0190k	-	YF	+.	-	.
J21:0190m	-	RR	Clearly	clearly	[S[R:m.R:m]
J21:0190n	-	YC	+,	-	.
J21:0190p	-	AT	the	the	[Ns:s.
J21:0190q	-	NN1n	transformation	transformation	.Ns:s]
J21:0200a	-	VBZ	is	be	[Vzb.Vzb]
J21:0200b	-	JJ	involutorial	involutorial	[J:e.J:e]S]
J21:0200c	-	YF	+.	-	.O]
J21:0200d	-	YB	<minbrk>	-	[Oh.Oh]
J21:0200e	-	PPIS2	We	we	[O[S[Nap:s.Nap:s]
J21:0200f	-	VV0v	observe	observe	[V.V]
J21:0200g	-	MDo	first	first	[R:t.R:t]
J21:0200h	-	CST	that	that	[Fn:o.
J21:0200i	-	ATn	no	no	[Ns:s.
J21:0200j	-	NN1n	line	line	.
J21:0200k	-	YC	+,	-	.
J21:0200m	-	YTL	<bital>	-	.
J21:0200n	S	FOx	l	-	.
J21:0200p	-	YTR	<eital>	-	.
J21:0200q	-	YC	+,	-	.Ns:s]
J21:0210a	-	VMo	can	can	[Vc.
J21:0210b	-	VV0v	meet	meet	.Vc]
J21:0210c	-	APPGh1	its	its	[Ns:o.
J21:0210d	-	NN1c	image	image	.Ns:o]
J21:0210e	-	ICSx	except	except	[P:p.
J21:0210f	-	II	at	at	[P.
J21:0210g	-	MC1	one	one	[Ms.
J21:0210h	-	IO	of	of	[Po.
J21:0210i	-	APPGh1	its	its	[Np.
J21:0210j	-	NN2	intersections	intersection	.
J21:0210k	-	IW	with	with	[P.
J21:0210m	-	YTL	<bital>	-	.
J21:0210n	S	FOx	Q	-	.
J21:0210p	-	YTR	<eital>	-	.P]Np]Po]Ms]P]P:p]Fn:o]S]
J21:0210q	-	YF	+.	-	.
J21:0220a	-	CSf	For	for	[Fa:121.
J21:0220b	-	CSi	if	if	[Fa:c.
J21:0220c	-	PPH1	it	it	[Ni:s.Ni:s]
J21:0220d	-	VDD	did	do	[Vdx.Vdx]Fa:c]
J21:0220e	-	YC	+,	-	.
J21:0220f	-	AT	the	the	[Ns:s.
J21:0220g	-	NN1c	plane	plane	.
J21:0220h	-	IO	of	of	[Po.
J21:0220i	-	YTL	<bital>	-	[FOx&.
J21:0220j	S	FOx	l	-	.
J21:0220k	-	YTR	<eital>	-	.
J21:0220m	-	CC	and	and	[FOx+.
J21:0220n	-	YTL	<bital>	-	.
J21:0220p	S	FOx	l<prime>	-	.
J21:0220q	-	YTR	<eital>	-	.FOx+]FOx&]Po]Ns:s]
J21:0220r	-	VMd	would	will	[Vdc.
J21:0220s	-	VV0t	contain	contain	.Vdc]
J21:0230a	-	MC	two	two	[Np:o.
J21:0230b	-	NN2	generators	generator	.
J21:0230c	-	IO	of	of	[Po.
J21:0230d	-	FOx	<formul>	-	.Po]Np:o]
J21:0230e	-	YC	+,	-	.
J21:0230f	-	DDQr	which	which	[Fr:x[Dq:s121.Dq:s121]
J21:0230g	-	VBZ	is	be	[Vzb.Vzb]
J21:0230h	-	JJ	impossible	impossible	[J:e.J:e]Fr:x]Fa:121]
J21:0230i	-	YF	+.	-	.
J21:0230j	-	RR	Moreover	moreover	[S[R:m.R:m]
J21:0230k	-	YC	+,	-	.
J21:0230m	-	II	from	from	[P:c.
J21:0230n	-	AT	the	the	[Ns.
J21:0230p	-	JJ	definitive	definitive	.
J21:0240a	-	NN1n	transformation	transformation	.
J21:0240b	-	IO	of	of	[Po.
J21:0240c	-	NN2	intercepts	intercept	[Np.
J21:0240d	-	II	on	on	[P.
J21:0240e	-	AT	the	the	[Np.
J21:0240f	-	NN2	generators	generator	.
J21:0240g	-	IO	of	of	[Po.
J21:0240h	-	FOx	<formul>	-	.Po]Np]P]Np]Po]Ns]P:c]
J21:0240i	-	YC	+,	-	.
J21:0240j	-	PPH1	it	it	[Ni:S.Ni:S]
J21:0240k	-	VBZ	is	be	[Vzb.Vzb]
J21:0240m	-	JJ	clear	clear	[J:e.J:e]
J21:0250a	-	CST	that	that	[Fn:s.
J21:0250b	-	AT	the	the	[Np:s123.
J21:0250c	-	JBy	only	only	.
J21:0250d	-	NN2	points	point	.
J21:0250e	-	IO	of	of	[Po.
J21:0250f	-	YTL	<bital>	-	.
J21:0250g	S	FOx	Q	-	.
J21:0250h	-	YTR	<eital>	-	.Po]
J21:0250i	-	II	at	at	[Fr[Pq:p.
J21:0250j	-	DDQr	which	which	[Dq:123.Dq:123]Pq:p]
J21:0250k	-	AT1	a	a	[Ns:s.
J21:0250m	-	NN1n	line	line	.Ns:s]
J21:0250n	-	VMo	can	can	[Vc.
J21:0250p	E	VVZv	meets	meets	.Vc]
J21:0250q	-	APPGh1	its	its	[Ns:o.
J21:0250r	-	NN1c	image	image	.Ns:o]Fr]Np:s123]
J21:0260a	-	VBR	are	be	[Vab.Vab]
J21:0260b	-	AT	the	the	[Np:e.
J21:0260c	-	NN2	points	point	.
J21:0260d	-	IO	of	of	[Po.
J21:0260e	S	FOx	g	-	.Po]Np:e]Fn:s]S]
J21:0260f	-	YF	+.	-	.
J21:0260g	-	RR	Hence	hence	[S[R:c.R:c]
J21:0260h	-	AT	the	the	[Ns:s.
J21:0260i	-	NN1u	totality	totality	.
J21:0260j	-	IO	of	of	[Po.
J21:0260k	-	JJ	singular	singular	[Np.
J21:0260m	-	NN2	lines	line	.Np]Po]Ns:s]
J21:0260n	-	VBZ	is	be	[Vzb.Vzb]
J21:0270a	-	AT	the	the	[Ns:e.
J21:0270b	-	MD	<bital>k<eital>th	-	[Ns.
J21:0270c	-	NN1n	order	order	.Ns]
J21:0270d	-	NN1c	complex	complex	.
J21:0270e	-	IO	of	of	[Po.
J21:0270f	-	NN2	lines	line	[Np:125.
J21:0270g	-	DDQr	which	which	[Fr[Dq:s125.Dq:s125]
J21:0270h	-	VV0v	meet	meet	[V.V]
J21:0270i	S	FOx	g	-	[N:o.N:o]Fr]Np:125]Po]Ns:e]S]
J21:0270j	-	YF	+.	-	.O]
J21:0270k	-	YB	<minbrk>	-	[Oh.Oh]
J21:0270m	-	AT	The	the	[O[S[Np:s.
J21:0280a	-	JJ	invariant	invariant	.
J21:0280b	-	NN2	lines	line	.Np:s]
J21:0280c	-	VBR	are	be	[Vab.Vab]
J21:0280d	-	AT	the	the	[Np:e.
J21:0280e	-	NN2	lines	line	.
J21:0280f	-	IO	of	of	[Po.
J21:0280g	-	AT	the	the	[Ns.
J21:0280h	-	NN1n	congruence	congruence	.
J21:0280i	-	IO	of	of	[Po.
J21:0280j	-	NN2	secants	secant	[Np.
J21:0280k	-	IO	of	of	[Po.
J21:0280m	S	FOx	g	-	.Po]Np]Po]Ns]Po]Np:e]
J21:0280n	-	YC	+,	-	.
J21:0290a	-	ICSt	since	since	[Fa:c.
J21:0290b	-	DD1q	each	each	[Ds:s.
J21:0290c	-	IO	of	of	[Po.
J21:0290d	-	DD2i	these	these	.Po]Ds:s]
J21:0290e	-	VVZv	meets	meet	[Vz.Vz]
J21:0290f	-	YTL	<bital>	-	.
J21:0290g	S	FOx	Q	-	[N:o.N:o]
J21:0290h	-	YTR	<eital>	-	.
J21:0290i	-	II	in	in	[P:p.
J21:0290j	-	MC	two	two	[Np:127.
J21:0290k	-	NN2	points	point	.
J21:0290m	-	DDQr	which	which	[Fr[Dq:s127.Dq:s127]
J21:0290n	-	VBR	are	be	[Vab.Vab]
J21:0290p	-	JJ	invariant	invariant	[J:e.J:e]Fr]Np:127]P:p]Fa:c]S]
J21:0290q	-	YF	+.	-	.
J21:0300a	-	AT	The	the	[S[Ns:s.
J21:0300b	-	NN1n	order	order	.
J21:0300c	-	IO	of	of	[Po.
J21:0300d	-	DD1i	this	this	[Ns.
J21:0300e	-	NN1n	congruence	congruence	.Ns]Po]Ns:s]
J21:0300f	-	VBZ	is	be	[Vzb.Vzb]
J21:0300g	-	FOx	<formul>	-	[N:e.N:e]
J21:0300h	-	YC	+,	-	.
J21:0300i	-	ICSt	since	since	[Fa:c.
J21:0300j	-	FOx	<formul>	-	[Np:s.
J21:0300k	-	NN2	secants	secant	.
J21:0300m	-	IO	of	of	[Po.
J21:0300n	-	AT1	a	a	[Ns.
J21:0300p	-	NN1c	curve	curve	.
J21:0300q	-	IO	of	of	[Po.
J21:0310a	-	NN1c	symbol	symbol	[Ns.
J21:0310b	-	YPL	(	-	.
J21:0310c	-	YTL	<bital>	-	.
J21:0310d	S	FOx	+a	-	.
J21:0310e	-	YTR	<eital>	-	.
J21:0310f	-	YC	+,	-	.
J21:0310g	-	YTL	<bital>	-	.
J21:0310h	S	FOx	+b	-	.
J21:0310i	-	YTR	<eital>	-	.
J21:0310j	-	YPR	+)	-	.Ns]Po]
J21:0310k	-	II	on	on	[P.
J21:0310m	-	AT1	a	a	[Ns.
J21:0310n	-	JJ	quadric	quadric	.
J21:0310p	-	NN1c	surface	surface	.Ns]P]Ns]Po]Np:s]
J21:0310q	-	VV0v	pass	pass	[V.V]
J21:0310r	-	II	through	through	[P:q.
J21:0310s	-	AT1	an	an	[Ns.
J21:0310t	-	JJ	arbitrary	arbitrary	.
J21:0310u	-	NNL1n	point	point	.Ns]P:q]Fa:c]S]
J21:0310v	-	YF	+.	-	.
J21:0320a	-	AT	The	the	[S[Ns:s.
J21:0320b	-	NN1n	class	class	.
J21:0320c	-	IO	of	of	[Po.
J21:0320d	-	AT	the	the	[Ns.
J21:0320e	-	NN1n	congruence	congruence	.Ns]Po]Ns:s]
J21:0320f	-	VBZ	is	be	[Vzb.Vzb]
J21:0320g	-	FOx	<formul>	-	[N:e.N:e]
J21:0320h	-	YC	+,	-	.
J21:0320i	-	ICSt	since	since	[Fa:c.
J21:0320j	-	AT1	an	an	[Ns:s.
J21:0320k	-	JJ	arbitrary	arbitrary	.
J21:0320m	-	NN1c	plane	plane	.Ns:s]
J21:0320n	-	VVZv	meets	meet	[Vz.Vz]
J21:0330a	S	FOx	g	-	[N:o.N:o]
J21:0330b	-	II	in	in	[P:p.
J21:0330c	-	YTL	<bital>	-	[Np.
J21:0330d	S	FOx	k	-	.
J21:0330e	-	YTR	<eital>	-	.
J21:0330f	-	NN2	points	point	.Np]P:p]Fa:c]S]
J21:0330g	-	YF	+.	-	.O]
J21:0330h	-	YB	<minbrk>	-	[Oh.Oh]
J21:0330i	-	ICSt	Since	since	[O[S[Fa:c.
J21:0330j	-	AT	the	the	[Ns:s.
J21:0330k	-	NN1c	complex	complex	.
J21:0330m	-	IO	of	of	[Po.
J21:0330n	-	JJ	singular	singular	[Np.
J21:0340a	-	NN2	lines	line	.Np]Po]Ns:s]
J21:0340b	-	VBZ	is	be	[Vzb.Vzb]
J21:0340c	-	IO	of	of	[Po:e.
J21:0340d	-	NN1n	order	order	[Ns.
J21:0340e	-	YTL	<bital>	-	.
J21:0340f	S	FOx	k	-	.
J21:0340g	-	YTR	<eital>	-	.Ns]Po:e]
J21:0340h	-	CC	and	and	[Fa+.
J21:0340i	-	ICSt	since	since	.
J21:0340j	-	EX	there	there	.
J21:0340k	-	VBZ	is	be	[Vzb.Vzb]
J21:0340m	-	ATn	no	no	[Ns:s.
J21:0340n	-	NN1c	complex	complex	.
J21:0340p	-	IO	of	of	[Po.
J21:0340q	-	JJ	invariant	invariant	[Np.
J21:0350a	-	NN2	lines	line	.Np]Po]Ns:s]Fa+]Fa:c]
J21:0350b	-	YC	+,	-	.
J21:0350c	-	PPH1	it	it	[Ni:S.Ni:S]
J21:0350d	-	VVZv	follows	follow	[Vz.Vz]
J21:0350e	-	II	from	from	[P:q.
J21:0350f	-	AT	the	the	[Ns.
J21:0350g	-	NN1c	formula	formula	.
J21:0350h	-	FOqx	<formul>	-	[S@.S@]Ns]P:q]
J21:0350i	-	CST	that	that	[Fn:s.
J21:0350j	-	AT	the	the	[Ns:s.
J21:0350k	-	NN1n	order	order	.
J21:0350m	-	IO	of	of	[Po.
J21:0350n	-	AT	the	the	[Ns.
J21:0350p	-	NN1c	involution	involution	.Ns]Po]Ns:s]
J21:0360a	-	VBZ	is	be	[Vzb.Vzb]
J21:0360b	-	FOx	<formul>	-	[N:e.N:e]Fn:s]S]
J21:0360c	-	YF	+.	-	.O]
J21:0360d	-	YB	<minbrk>	-	[Oh.Oh]
J21:0360e	-	EX	There	there	[O[S.
J21:0360f	-	VBR	are	be	[Vab.Vab]
J21:0360g	-	JJ	various	various	[Np:s.
J21:0360h	-	NN2	sets	set	.
J21:0360i	-	IO	of	of	[Po.
J21:0360j	-	JJ	exceptional	exceptional	[Np.
J21:0360k	-	NN2	lines	line	.
J21:0360m	-	YC	+,	-	.
J21:0360n	-	CCr	or	or	[Np+:129.
J21:0360p	-	NN2	lines	line	.
J21:0370a	-	DDQGr	whose	whose	[Fr[Nqp:s129.
J21:0370b	-	NN2	images	image	.Nqp:s129]
J21:0370c	-	VBR	are	be	[Vaeb.
J21:0370d	-	XX	not	not	.Vaeb]
J21:0370e	-	JJ	unique	unique	[J:e.J:e]Fr]Np+:129]Np]Po]Np:s]S]
J21:0370f	-	YF	+.	-	.
J21:0370g	-	AT	The	the	[S[Nj:s.
J21:0370h	-	DAT	most	most	.
J21:0370i	-	JJ	obvious	obvious	.
J21:0370j	-	IO	of	of	[Po.
J21:0370k	-	DD2i	these	these	.Po]Nj:s]
J21:0370m	-	VBZ	is	be	[Vzb.Vzb]
J21:0370n	-	AT	the	the	[Ns:e131.
J21:0370p	-	JJ	quadratic	quadratic	.
J21:0380a	-	NN1c	complex	complex	.
J21:0380b	-	IO	of	of	[Po.
J21:0380c	-	NN2	tangents	tangent	[Np:131.
J21:0380d	-	IIt	to	to	[P.
J21:0380e	-	YTL	<bital>	-	.
J21:0380f	S	FOx	Q	-	.
J21:0380g	-	YTR	<eital>	-	.P]Np:131]Po]
J21:0380h	-	YC	+,	-	.
J21:0380i	-	DD1q	each	each	[Fr[Nqs:S.
J21:0380j	-	NN1n	line	line	.
J21:0380k	-	IO	of	of	[Poq.
J21:0380m	-	DDQr	which	which	[Dq:131.Dq:131]Poq]Nqs:S]
J21:0380n	-	VBZ	is	be	[Vzp.
J21:0380p	-	VVNt	transformed	transform	.Vzp]
J21:0390a	-	II	into	into	[P:q.
J21:0390b	-	AT	the	the	[Ns.
J21:0390c	-	JB	entire	entire	.
J21:0390d	-	NN1c	pencil	pencil	.
J21:0390e	-	IO	of	of	[Po.
J21:0390f	-	NN2	lines	line	[Np.
J21:0390g	-	JJ	tangent	tangent	[Jh.
J21:0390h	-	IIt	to	to	[P.
J21:0390i	-	YTL	<bital>	-	.
J21:0390j	S	FOx	Q	-	.
J21:0390k	-	YTR	<eital>	-	.P]
J21:0390m	-	II	at	at	[P.
J21:0390n	-	AT	the	the	[Ns.
J21:0390p	-	NN1c	image	image	.
J21:0400a	-	IO	of	of	[Po.
J21:0400b	-	AT	the	the	[Ns.
J21:0400c	-	NNL1n	point	point	.
J21:0400d	-	IO	of	of	[Po.
J21:0400e	-	NN1n	tangency	tangency	.Po]
J21:0400f	-	IO	of	of	[Po.
J21:0400g	-	AT	the	the	[Ns.
J21:0400h	-	VVNv	given	give	[Tn[Vn.Vn]Tn]
J21:0400i	-	NN1n	line	line	.Ns]Po]Ns]Po]Ns]P]Jh]Np]Po]Ns]P:q]Fr]Ns:e131]S]
J21:0400j	-	YF	+.	-	.
J21:0400k	-	RR	Thus	thus	[S[R:c.R:c]
J21:0400m	-	NN2	pencils	pencil	[Np:S.
J21:0400n	-	IO	of	of	[Po.
J21:0410a	-	NN2	tangents	tangent	[Np.
J21:0410b	-	IIt	to	to	[P.
J21:0410c	-	YTL	<bital>	-	.
J21:0410d	S	FOx	Q	-	.
J21:0410e	-	YTR	<eital>	-	.P]Np]Po]Np:S]
J21:0410f	-	VBR	are	be	[Vap.
J21:0410g	-	VVNt	transformed	transform	.Vap]
J21:0410h	-	II	into	into	[P:q.
J21:0410i	-	NN2	pencils	pencil	[Np.
J21:0410j	-	IO	of	of	[Po.
J21:0410k	-	NN2	tangents	tangent	.Po]Np]P:q]S]
J21:0410m	-	YF	+.	-	.
J21:0410n	-	PPH1	It	it	[S[Ni:S.Ni:S]
J21:0410p	-	VBZ	is	be	[Vzb.Vzb]
J21:0420a	-	JJ	interesting	interesting	[J:e.J:e]
J21:0420b	-	CST	that	that	[Fn:s.
J21:0420c	-	AT1	a	a	[Ns:S.
J21:0420d	-	MC1n	1	-	[Ms.
J21:0420e	-	IIx	+:	-	[P.
J21:0420f	-	MC1n	+1	-	.P]Ms]
J21:0420g	-	NN1n	correspondence	correspondence	.Ns:S]
J21:0420h	-	VMo	can	can	[Vcp.
J21:0420i	-	VB0	be	be	.
J21:0420j	-	VVNt	established	establish	.Vcp]
J21:0420k	-	II	between	between	[P:r.
J21:0420m	-	AT	the	the	[Np.
J21:0430a	-	NN2	lines	line	.
J21:0430b	-	IO	of	of	[Po.
J21:0430c	-	MC	two	two	[Np.
J21:0430d	-	DAz	such	such	.
J21:0430e	-	NN2	pencils	pencil	.Np]Po]Np]P:r]
J21:0430f	-	YC	+,	-	.
J21:0430g	-	RRz	so	so	[R:c.
J21:0430h	-	CST	that	that	[Fc.
J21:0430i	-	II	in	in	[P:m.
J21:0430j	-	AT1	a	a	[Ns.
J21:0430k	-	NN1n	sense	sense	.Ns]P:m]
J21:0430m	-	AT1	a	a	[Ns:S.
J21:0430n	-	JJ	unique	unique	.
J21:0430p	-	NN1c	image	image	.Ns:S]
J21:0430q	-	YG	-	-	[m133.m133]
J21:0430r	-	VMo	can	can	[Vcp.
J21:0430s	-	RR	actually	actually	[R:G133.R:G133]
J21:0440a	-	VB0	be	be	.
J21:0440b	-	VVNt	assigned	assign	.Vcp]
J21:0440c	-	IIt	to	to	[P:u.
J21:0440d	-	DD1q	each	each	[Ns.
J21:0440e	-	NN1c	tangent	tangent	.Ns]P:u]Fc]R:c]Fn:s]S]
J21:0440f	-	YF	+.	-	.
J21:0440g	-	CSf	For	for	[Fa.
J21:0440h	-	AT	the	the	[Np:S.
J21:0440i	-	NN2	lines	line	.
J21:0440j	-	IO	of	of	[Po.
J21:0440k	-	DDy	any	any	[Ns:135.
J21:0440m	-	NN1c	plane	plane	.
J21:0440n	-	YC	+,	-	.
J21:0440p	S	FOx	<pgr>	-	.
J21:0440q	-	YC	+,	-	.
J21:0440r	-	YG	-	-	[Tg[s135.s135]
J21:0450a	-	VVGv	meeting	meet	[Vg.Vg]
J21:0450b	-	YTL	<bital>	-	.
J21:0450c	S	FOx	Q	-	[N:o.N:o]
J21:0450d	-	YTR	<eital>	-	.
J21:0450e	-	II	in	in	[P:p.
J21:0450f	-	AT1	a	a	[Njs.
J21:0450g	-	JJ	conic	conic	.
J21:0450h	-	YTL	<bital>	-	.
J21:0450i	S	FOx	C	-	.
J21:0450j	-	YTR	<eital>	-	.Njs]P:p]Tg]
J21:0450k	-	YC	+,	-	.Ns:135]Po]Np:S]
J21:0450m	-	VBR	are	be	[Vap.
J21:0450n	-	VVNt	transformed	transform	.Vap]
J21:0450p	-	II	into	into	[P:q.
J21:0450q	-	AT	the	the	[Ns.
J21:0450r	-	NN1n	congruence	congruence	.
J21:0460a	-	IO	of	of	[Po.
J21:0460b	-	NN2	secants	secant	[Np.
J21:0460c	-	IO	of	of	[Po.
J21:0460d	-	AT	the	the	[Ns:137.
J21:0460e	-	NN1c	curve	curve	.
J21:0460f	-	YTL	<bital>	-	.
J21:0460g	S	FOx	C<prime>	-	.
J21:0460h	-	YTR	<eital>	-	.
J21:0460i	-	II	into	into	[Fr[Pq:q.
J21:0460j	-	DDQr	which	which	[Dq:137.Dq:137]Pq:q]
J21:0460k	-	YTL	<bital>	-	.
J21:0460m	S	FOx	C	-	[N:S.N:S]
J21:0460n	-	YTR	<eital>	-	.
J21:0460p	-	VBZ	is	be	[Vzp.
J21:0470a	-	VVNt	transformed	transform	.Vzp]
J21:0470b	-	II	in	in	[P:p.
J21:0470c	-	AT	the	the	[Ns.
J21:0470d	-	NNL1n	point	point	.
J21:0470e	-	NN1c	involution	involution	.
J21:0470f	-	II	on	on	[P.
J21:0470g	-	YTL	<bital>	-	.
J21:0470h	S	FOx	Q	-	.
J21:0470i	-	YTR	<eital>	-	.P]Ns]P:p]Fr]Ns:137]Po]Np]Po]Ns]P:q]Fa]
J21:0470j	-	YF	+.	-	.
J21:0470k	-	RR21	In	in	[S[R:m[RR=.
J21:0470m	-	RR22	particular	particular	.RR=]R:m]
J21:0470n	-	YC	+,	-	.
J21:0470p	-	NN2	tangents	tangent	[Np:S.
J21:0480a	-	IIt	to	to	[P.
J21:0480b	-	YTL	<bital>	-	.
J21:0480c	S	FOx	C	-	.
J21:0480d	-	YTR	<eital>	-	.P]Np:S]
J21:0480e	-	VBR	are	be	[Vap.
J21:0480f	-	VVNt	transformed	transform	.Vap]
J21:0480g	-	II	into	into	[P:q.
J21:0480h	-	NN2	tangents	tangent	[Np.
J21:0480i	-	IIt	to	to	[P.
J21:0480j	-	YTL	<bital>	-	.
J21:0480k	S	FOx	C<prime>	-	.
J21:0480m	-	YTR	<eital>	-	.P]Np]P:q]S]
J21:0480n	-	YF	+.	-	.
J21:0480p	-	RR	Moreover	moreover	[S[R:m.R:m]
J21:0480q	-	YC	+,	-	.
J21:0490a	-	CSi	if	if	[Fa:c.
J21:0490b	-	FOx	<formul>	-	[N:s[FOx&.
J21:0490c	-	CC	and	and	[FOx+.
J21:0490d	-	FOx	<formul>	-	.FOx+]FOx&]N:s]
J21:0490e	-	VBR	are	be	[Vab.Vab]
J21:0490f	-	MC	two	two	[Np:e139.
J21:0490g	-	NN2	planes	plane	.
J21:0490h	-	YG	-	-	[Tg[s139.s139]
J21:0490i	-	VVGv	intersecting	intersect	[Vg.Vg]
J21:0490j	-	II	in	in	[P:p.
J21:0490k	-	AT1	a	a	[Ns.
J21:0490m	-	NN1n	line	line	.
J21:0490n	-	YTL	<bital>	-	.
J21:0490p	S	FOx	l	-	.
J21:0490q	-	YTR	<eital>	-	.
J21:0490r	-	YC	+,	-	.
J21:0490s	-	JJ	tangent	tangent	[Jh.
J21:0500a	-	IIt	to	to	[P.
J21:0500b	-	YTL	<bital>	-	.
J21:0500c	S	FOx	Q	-	.
J21:0500d	-	YTR	<eital>	-	.P]
J21:0500e	-	II	at	at	[P.
J21:0500f	-	AT1	a	a	[Ns.
J21:0500g	-	NNL1n	point	point	.
J21:0500h	-	YTL	<bital>	-	.
J21:0500i	S	FOx	P	-	.
J21:0500j	-	YTR	<eital>	-	.Ns]P]Jh]Ns]P:p]Tg]Np:e139]Fa:c]
J21:0500k	-	YC	+,	-	.
J21:0500m	-	AT	the	the	[Np:s.
J21:0500n	-	MC	two	two	.
J21:0500p	-	JJ	free	free	.
J21:0500q	-	NN2	intersections	intersection	.
J21:0500r	-	IO	of	of	[Po.
J21:0510a	-	AT	the	the	[Np.
J21:0510b	-	NN1c	image	image	.
J21:0510c	-	NN2	curves	curve	.
J21:0510d	-	FOx	<formul>	-	[FOx&.
J21:0510e	-	CC	and	and	[FOx+.
J21:0510f	-	FOx	<formul>	-	.FOx+]FOx&]Np]Po]Np:s]
J21:0510g	-	VMo	must	must	[Vc.
J21:0510h	-	VV0i	coincide	coincide	.Vc]
J21:0510i	-	II	at	at	[P:p.
J21:0510j	-	YTL	<bital>	-	[N.
J21:0510k	S	FOx	P<prime>	-	.
J21:0510m	-	YTR	<eital>	-	.
J21:0510n	-	YC	+,	-	.
J21:0510p	-	AT	the	the	[Ns@.
J21:0510q	-	NN1c	image	image	.
J21:0520a	-	IO	of	of	[Po.
J21:0520b	-	YTL	<bital>	-	.
J21:0520c	S	FOx	P	-	.
J21:0520d	-	YTR	<eital>	-	.Po]Ns@]N]P:p]
J21:0520e	-	YC	+,	-	.
J21:0520f	-	CC	and	and	[S+.
J21:0520g	-	II	at	at	[P:p.
J21:0520h	-	DD1i	this	this	[Ns.
J21:0520i	-	NNL1n	point	point	.Ns]P:p]
J21:0520j	-	FOx	<formul>	-	[N:s[FOx&.
J21:0520k	-	CC	and	and	[FOx+.
J21:0520m	-	FOx	<formul>	-	.FOx+]FOx&]N:s]
J21:0520n	-	VMo	must	must	[Vc.
J21:0520p	-	VH0	have	have	.Vc]
J21:0520q	-	AT1	a	a	[Ns:o.
J21:0520r	-	JJ	common	common	.
J21:0520s	-	NN1c	tangent	tangent	.
J21:0530a	-	YTL	<bital>	-	.
J21:0530b	S	FOx	l<prime>	-	.
J21:0530c	-	YTR	<eital>	-	.Ns:o]S+]S]
J21:0530d	-	YF	+.	-	.
J21:0530e	-	RR	Hence	hence	[S[R:c.R:c]
J21:0530f	-	YC	+,	-	.
J21:0530g	-	VVNv	thought	think	[Tn:b[Vn.Vn]
J21:0530h	-	IO	of	of	[Po:u.
J21:0530i	-	YG	-	-	[140.140]Po:u]
J21:0530j	-	IIa	as	as	[P:e.
J21:0530k	-	AT1	a	a	[Ns.
J21:0530m	-	NN1n	line	line	.
J21:0530n	-	II	in	in	[P.
J21:0530p	-	AT1	a	a	[Ns.
J21:0530q	-	JJ	particular	particular	.
J21:0530r	-	NN1c	plane	plane	.
J21:0530s	S	FOx	<pgr>	-	.Ns]P]Ns]P:e]Tn:b]
J21:0530t	-	YC	+,	-	.
J21:0540a	-	DDy	any	any	[Ns:s140.
J21:0540b	-	NN1c	tangent	tangent	.
J21:0540c	-	IIt	to	to	[P.
J21:0540d	-	YTL	<bital>	-	.
J21:0540e	S	FOx	Q	-	.
J21:0540f	-	YTR	<eital>	-	.P]Ns:s140]
J21:0540g	-	VHZ	has	have	[Vz.Vz]
J21:0540h	-	AT1	a	a	[Ns:o.
J21:0540i	-	JJ	unique	unique	.
J21:0540j	-	NN1c	image	image	.Ns:o]
J21:0540k	-	CC	and	and	[S+.
J21:0540m	-	RR	moreover	moreover	[R:m.R:m]
J21:0540n	-	DD1i	this	this	[Ns:s.
J21:0540p	-	NN1c	image	image	.Ns:s]
J21:0550a	-	VBZ	is	be	[Vzb.Vzb]
J21:0550b	-	AT	the	the	[D:e.
J21:0550c	-	DAy	same	same	.D:e]
J21:0550d	-	IF	for	for	[P:r.
J21:0550e	-	DBa	all	all	[Np.
J21:0550f	-	NN2	planes	plane	.
J21:0550g	-	II	through	through	[P.
J21:0550h	-	YTL	<bital>	-	.
J21:0550i	S	FOx	l	-	.
J21:0550j	-	YTR	<eital>	-	.P]Np]P:r]S+]S]
J21:0550k	-	YF	+.	-	.O]
J21:0550m	-	YB	<minbrk>	-	[Oh.Oh]
J21:0550n	-	DD1q	Each	each	[O[S[Ns:s.
J21:0550p	-	NN1c	generator	generator	.
J21:0550q	-	YC	+,	-	.
J21:0560a	-	FOx	<lgr>	-	.
J21:0560b	-	YC	+,	-	.
J21:0560c	-	IO	of	of	[Po.
J21:0560d	-	FOx	<formul>	-	.Po]Ns:s]
J21:0560e	-	VBZ	is	be	[Vzb.Vzb]
J21:0560f	-	RR	also	also	[R:m.R:m]
J21:0560g	-	JJ	exceptional	exceptional	[J:e.J:e]
J21:0560h	-	YC	+,	-	.
J21:0560i	-	CSf	for	for	[Fa:c.
J21:0560j	-	DD1q	each	each	[Ds:S.Ds:S]
J21:0560k	-	VBZ	is	be	[Vzp.
J21:0560m	-	VVNt	transformed	transform	.Vzp]
J21:0560n	-	II	into	into	[P:q.
J21:0560p	-	AT	the	the	[Ns.
J21:0570a	-	JB	entire	entire	.
J21:0570b	-	NN1n	congruence	congruence	.
J21:0570c	-	IO	of	of	[Po.
J21:0570d	-	NN2	secants	secant	[Np.
J21:0570e	-	IO	of	of	[Po.
J21:0570f	-	AT	the	the	[Ns:141.
J21:0570g	-	NN1c	curve	curve	.
J21:0570h	-	II	into	into	[Fr[Pq:q.
J21:0570i	-	DDQr	which	which	[Dq:141.Dq:141]Pq:q]
J21:0570j	-	DD1a	that	that	[Ns:S.
J21:0570k	-	NN1c	generator	generator	.Ns:S]
J21:0580a	-	VBZ	is	be	[Vzp.
J21:0580b	-	VVNt	transformed	transform	.Vzp]
J21:0580c	-	IIb	by	by	[Pb:a.
J21:0580d	-	AT	the	the	[Ns.
J21:0580e	-	NNL1n	point	point	.
J21:0580f	-	NN1c	involution	involution	.
J21:0580g	-	II	on	on	[P.
J21:0580h	-	YTL	<bital>	-	.
J21:0580i	S	FOx	Q	-	.
J21:0580j	-	YTR	<eital>	-	.P]Ns]Pb:a]Fr]Ns:141]Po]Np]Po]Ns]P:q]Fa:c]S]
J21:0580k	-	YF	+.	-	.
J21:0580m	-	DD1i	This	this	[S[Ns:s.
J21:0580n	-	NN1c	curve	curve	.Ns:s]
J21:0580p	-	VBZ	is	be	[Vzb.Vzb]
J21:0580q	-	IO	of	of	[Po:e.
J21:0590a	-	NN1c	symbol	symbol	[Ns.
J21:0590b	-	FOx	<formul>	-	.Ns]Po:e]
J21:0590c	-	ICSt	since	since	[Fa:c.
J21:0590d	-	PPH1	it	it	[Ni:s.Ni:s]
J21:0590e	-	VVZv	meets	meet	[Vz.Vz]
J21:0590f	S	FOx	<lgr>	-	[N:o.
J21:0590g	-	YC	+,	-	.
J21:0590h	-	CC	and	and	[Ns+.
J21:0590i	-	RR	hence	hence	.
J21:0590j	-	AT1e	every	every	.
J21:0590k	-	NN1n	line	line	.
J21:0590m	-	IO	of	of	[Po.
J21:0590n	-	FOx	<formul>	-	.Po]
J21:0590p	-	II	in	in	[P.
J21:0590q	-	AT	the	the	[Np.
J21:0600a	-	FOx	<formul>	-	.
J21:0600b	-	JJ	invariant	invariant	.
J21:0600c	-	NN2	points	point	.
J21:0600d	-	II	on	on	[P.
J21:0600e	S	FOx	<lgr>	-	.P]Np]P]Ns+]N:o]
J21:0600f	-	CC	and	and	[Fa+.
J21:0600g	-	ICSt	since	since	.
J21:0600h	-	PPH1	it	it	[Ni:s.Ni:s]
J21:0600i	-	RR	obviously	obviously	[R:m.R:m]
J21:0600j	-	VVZv	meets	meet	[Vz.Vz]
J21:0600k	-	AT1e	every	every	[Ns:o.
J21:0600m	-	NN1n	line	line	.
J21:0610a	-	IO	of	of	[Po.
J21:0610b	-	FOx	<formul>	-	.Po]Ns:o]
J21:0610c	-	II	in	in	[P:p.
J21:0610d	-	AT1	a	a	[Ns.
J21:0610e	-	JJ	single	single	.
J21:0610f	-	NNL1n	point	point	.Ns]P:p]Fa+]Fa:c]S]
J21:0610g	-	YF	+.	-	.
J21:0610h	-	AT	The	the	[S[Ns:s.
J21:0610i	-	NN1n	congruence	congruence	.
J21:0610j	-	IO	of	of	[Po.
J21:0610k	-	APPGh1	its	its	[Np.
J21:0610m	-	NN2	secants	secant	.Np]Po]Ns:s]
J21:0610n	-	VBZ	is	be	[Vzb.Vzb]
J21:0610p	-	RR	therefore	therefore	[R:c.R:c]
J21:0620a	-	IO	of	of	[Po:e.
J21:0620b	-	NN1n	order	order	[N.
J21:0620c	-	FOx	<formul>	-	.
J21:0620d	-	CC	and	and	[Ns+.
J21:0620e	-	NN1n	class	class	.
J21:0620f	-	FOx	<formul>	-	.Ns+]N]Po:e]S]
J21:0620g	-	YF	+.	-	.O]
J21:0620h	-	YB	<minbrk>	-	[Oh.Oh]
J21:0620i	-	AT1	A	a	[O[S[Ns:s.
J21:0620j	-	JJ	final	final	.
J21:0620k	-	NN1n	class	class	.
J21:0620m	-	IO	of	of	[Po.
J21:0620n	-	JJ	exceptional	exceptional	[Np.
J21:0620p	-	NN2	lines	line	.Np]Po]Ns:s]
J21:0630a	-	VBZ	is	be	[Vzb.Vzb]
J21:0630b	-	JJ	identifiable	identifiable	[J:e.J:e]
J21:0630c	-	II	from	from	[P:c.
J21:0630d	-	AT	the	the	[Np.
J21:0630e	-	JJ	following	following	.
J21:0630f	-	NN2	considerations	consideration	.Np]P:c]S]
J21:0630g	-	YN	+:	-	.
J21:0630h	-	ICSt	Since	since	[S[Fa:c.
J21:0630i	-	ATn	no	no	[Np:s.
J21:0630j	-	MC	two	two	.
J21:0640a	-	NN2	generators	generator	.
J21:0640b	-	IO	of	of	[Po.
J21:0640c	-	FOx	<formul>	-	.Po]Np:s]
J21:0640d	-	VMo	can	can	[Vc.
J21:0640e	-	VV0v	intersect	intersect	.Vc]Fa:c]
J21:0640f	-	YC	+,	-	.
J21:0640g	-	PPH1	it	it	[Ni:S.Ni:S]
J21:0640h	-	VVZv	follows	follow	[Vz.Vz]
J21:0640i	-	CST	that	that	[Fn:s.
J21:0640j	-	APPGh2	their	their	[Np:s.
J21:0640k	-	NN1c	image	image	.
J21:0640m	-	NN2	curves	curve	.Np:s]
J21:0650a	-	VMo	can	can	[Vc.
J21:0650b	-	VH0	have	have	.Vc]
J21:0650c	-	ATn	no	no	[Np:o.
J21:0650d	-	JJ	free	free	.
J21:0650e	-	NN2	intersections	intersection	.Np:o]Fn:s]S]
J21:0650f	-	YF	+.	-	.
J21:0650g	-	II	In	in	[S[P:m.
J21:0650h	-	JBo	other	other	[Np.
J21:0650i	-	NN2	words	word	.Np]P:m]
J21:0650j	-	YC	+,	-	.
J21:0650k	-	DD2i	these	these	[Np:s.
J21:0650m	-	NN2	curves	curve	.Np:s]
J21:0650n	-	VH0	have	have	[V.V]
J21:0650p	-	RRx	only	only	[R:m.R:m]
J21:0660a	-	JJ	fixed	fixed	[Np:o.
J21:0660b	-	NN2	intersections	intersection	.
J21:0660c	-	JJ	common	common	[Jh.
J21:0660d	-	IIt	to	to	[P.
J21:0660e	-	PPHO2	them	they	[Nop.
J21:0660f	-	DBa	all	all	.Nop]P]Jh]Np:o]S]
J21:0660g	-	YF	+.	-	.
J21:0660h	-	RTo	Now	now	[S[Rw:c.Rw:c]
J21:0660i	-	AT	the	the	[Ns:s143.
J21:0660j	-	JBy	only	only	.
J21:0660k	-	NNL1n	way	way	.
J21:0660m	-	II	in	in	[Fr[Pq:h.
J21:0660n	-	DDQr	which	which	[Dq:143.Dq:143]Pq:h]
J21:0660p	-	DBa	all	all	[Np:s.
J21:0670a	-	NN2	curves	curve	.
J21:0670b	-	IO	of	of	[Po.
J21:0670c	-	AT	the	the	[Ns.
J21:0670d	-	NN1c	image	image	.
J21:0670e	-	NN1n	family	family	.
J21:0670f	-	IO	of	of	[Po.
J21:0670g	-	FOx	<formul>	-	.Po]Ns]Po]Np:s]
J21:0670h	-	VMo	can	can	[Vc.
J21:0670i	-	VV0v	pass	pass	.Vc]
J21:0670j	-	II	through	through	[P:q.
J21:0670k	-	AT1	a	a	[Ns.
J21:0670m	-	JJ	fixed	fixed	.
J21:0670n	-	NNL1n	point	point	.Ns]P:q]Fr]Ns:s143]
J21:0670p	-	VBZ	is	be	[Vzb.Vzb]
J21:0680a	-	TO	to	to	[Ti:e[Vi.
J21:0680b	-	VH0	have	have	.Vi]
J21:0680c	-	AT1	a	a	[Ns:o145.
J21:0680d	-	NN1c	generator	generator	.
J21:0680e	-	IO	of	of	[Po.
J21:0680f	-	FOx	<formul>	-	.Po]
J21:0680g	-	DDQr	which	which	[Fr[Dq:s145.Dq:s145]
J21:0680h	-	VBZ	is	be	[Vzeb.
J21:0680i	-	XX	not	not	.Vzeb]
J21:0680j	-	AT1	a	a	[N:e.
J21:0680k	-	NN1c	secant	secant	.
J21:0680m	-	CCB	but	but	[Ns+.
J21:0680n	-	AT1	a	a	.
J21:0680p	-	NN1c	tangent	tangent	.Ns+]
J21:0680q	-	IO	of	of	[Po.
J21:0680r	S	FOx	g	-	.Po]N:e]Fr]Ns:o145]Ti:e]
J21:0680s	-	YC	+,	-	.
J21:0690a	-	CSf	for	for	[Fa:c.
J21:0690b	-	RTn	then	then	[Rsw:t.Rsw:t]
J21:0690c	-	DDy	any	any	[Ns:S.
J21:0690d	-	NNL1n	point	point	.
J21:0690e	-	II	on	on	[P.
J21:0690f	-	DAz	such	such	[Ns.
J21:0690g	-	AT1	a	a	.
J21:0690h	-	NN1c	generator	generator	.Ns]P]Ns:S]
J21:0690i	-	VMo	will	will	[Vcp.
J21:0690j	-	VB0	be	be	.
J21:0690k	-	VVNt	transformed	transform	.Vcp]
J21:0690m	-	II	into	into	[P:q.
J21:0700a	-	AT	the	the	[Ns.
J21:0700b	-	NNL1n	point	point	.
J21:0700c	-	IO	of	of	[Po.
J21:0700d	-	NN1n	tangency	tangency	.Po]Ns]P:q]Fa:c]S]
J21:0700e	-	YF	+.	-	.
J21:0700f	-	ICSt	Since	since	[S[Fa:c.
J21:0700g	-	MC	two	two	[Np:s.
J21:0700h	-	NN2	curves	curve	.
J21:0700i	-	IO	of	of	[Po.
J21:0700j	-	NN1c	symbol	symbol	[Ns.
J21:0700k	-	FOx	<formul>	-	.Ns]Po]
J21:0700m	-	II	on	on	[P.
J21:0700n	-	YTL	<bital>	-	.
J21:0700p	S	FOx	Q	-	.
J21:0700q	-	YTR	<eital>	-	.P]Np:s]
J21:0700r	-	VV0v	intersect	intersect	[V.V]
J21:0710a	-	II	in	in	[P:p.
J21:0710b	-	FOx	<formul>	-	[Np.
J21:0710c	-	NN2	points	point	.Np]P:p]Fa:c]
J21:0710d	-	YC	+,	-	.
J21:0710e	-	PPH1	it	it	[Ni:S.Ni:S]
J21:0710f	-	VVZv	follows	follow	[Vz.Vz]
J21:0710g	-	CST	that	that	[Fn:s.
J21:0710h	-	EX	there	there	.
J21:0710i	-	VBR	are	be	[Vab.Vab]
J21:0710j	-	FOx	<formul>	-	[Np:e147.
J21:0710k	-	NN2	lines	line	.
J21:0710m	-	IO	of	of	[Po.
J21:0710n	-	FOx	<formul>	-	.Po]
J21:0710p	-	DDQr	which	which	[Fr[Dq:s147.Dq:s147]
J21:0720a	-	VBR	are	be	[Vab.Vab]
J21:0720b	-	JJ	tangent	tangent	[Jh:e.
J21:0720c	-	IIt	to	to	[P.
J21:0720d	S	FOx	g	-	.P]Jh:e]Fr]Np:e147]Fn:s]S]
J21:0720e	-	YF	+.	-	.
J21:0720f	-	RR	Clearly	clearly	[S[R:m.R:m]
J21:0720g	-	YC	+,	-	.
J21:0720h	-	DDy	any	any	[Ns:S.
J21:0720i	-	NN1n	line	line	.
J21:0720j	-	YC	+,	-	.
J21:0720k	-	YTL	<bital>	-	.
J21:0720m	S	FOx	l	-	.
J21:0720n	-	YTR	<eital>	-	.
J21:0720p	-	YC	+,	-	.
J21:0720q	-	IO	of	of	[Po.
J21:0720r	-	DDy	any	any	[Ns:149.
J21:0720s	-	NN1c	bundle	bundle	.
J21:0720t	-	YG	-	-	[Tg[s149.s149]
J21:0730a	-	VHG	having	have	[Vg.Vg]
J21:0730b	-	MC1	one	one	[Ms:o.
J21:0730c	-	IO	of	of	[Po.
J21:0730d	-	DD2i	these	these	[Np.
J21:0730e	-	NN2	points	point	.
J21:0730f	-	IO	of	of	[Po.
J21:0730g	-	NN1n	tangency	tangency	.Po]Np]Po]
J21:0730h	-	YC	+,	-	.
J21:0730i	-	YTL	<bital>	-	.
J21:0730j	S	FOx	T	-	.
J21:0730k	-	YTR	<eital>	-	.
J21:0730m	-	YC	+,	-	.Ms:o]
J21:0730n	-	IIa	as	as	[P:j.
J21:0730p	-	NN1c	vertex	vertex	.P:j]Tg]Ns:149]Po]Ns:S]
J21:0730q	-	VMo	will	will	[Vcp.
J21:0730r	-	VB0	be	be	.
J21:0730s	-	VVNt	transformed	transform	.Vcp]
J21:0740a	-	II	into	into	[P:q.
J21:0740b	-	AT	the	the	[Ns:151.
J21:0740c	-	JB	entire	entire	.
J21:0740d	-	NN1c	pencil	pencil	.
J21:0740e	-	YG	-	-	[Tg[s151.s151]
J21:0740f	-	VHG	having	have	[Vg.Vg]
J21:0740g	-	AT	the	the	[Ns:o.
J21:0740h	-	NN1c	image	image	.
J21:0740i	-	IO	of	of	[Po.
J21:0740j	-	AT	the	the	[Ns.
J21:0740k	-	MDo	second	second	.
J21:0740m	-	NN1n	intersection	intersection	.
J21:0750a	-	IO	of	of	[Po.
J21:0750b	-	YTL	<bital>	-	[FOx&.
J21:0750c	S	FOx	l	-	.
J21:0750d	-	YTR	<eital>	-	.
J21:0750e	-	CC	and	and	[FOx+.
J21:0750f	-	YTL	<bital>	-	.
J21:0750g	S	FOx	Q	-	.
J21:0750h	-	YTR	<eital>	-	.FOx+]FOx&]Po]Ns]Po]Ns:o]
J21:0750i	-	IIa	as	as	[P:j.
J21:0750j	-	NN1c	vertex	vertex	.P:j]
J21:0750k	-	CC	and	and	[Tg+.
J21:0750m	-	VVGi	lying	lie	[Vg.Vg]
J21:0750n	-	II	in	in	[P:p.
J21:0750p	-	AT	the	the	[Ns:153.
J21:0750q	-	NN1c	plane	plane	.
J21:0750r	-	YG	-	-	[Tn[S153.S153]
J21:0750s	-	VVNv	determined	determine	[Vn.Vn]
J21:0760a	-	IIb	by	by	[Pb:a.
J21:0760b	-	AT	the	the	[N.
J21:0760c	-	NN1c	image	image	.
J21:0760d	-	NNL1n	point	point	.
J21:0760e	-	CC	and	and	[Ns+:155.
J21:0760f	-	AT	the	the	.
J21:0760g	-	NN1c	generator	generator	.
J21:0760h	-	IO	of	of	[Po.
J21:0760i	-	FOx	<formul>	-	.Po]
J21:0760j	-	DDQr	which	which	[Fr[Dq:s155.Dq:s155]
J21:0760k	-	VBZ	is	be	[Vzb.Vzb]
J21:0760m	-	JJ	tangent	tangent	[Jh:e.
J21:0760n	-	IIt	to	to	[P.
J21:0770a	S	FOx	g	-	.P]Jh:e]
J21:0770b	-	II	at	at	[P:p.
J21:0770c	-	YTL	<bital>	-	.
J21:0770d	S	FOx	T	-	.
J21:0770e	-	YTR	<eital>	-	.P:p]Fr]Ns+:155]N]Pb:a]Tn]Ns:153]P:p]Tg+]Tg]Ns:151]P:q]S]
J21:0770f	-	YF	+.	-	.
J21:0770g	-	AT1	A	a	[S[Ns:S.
J21:0770h	-	NN1n	line	line	.
J21:0770i	-	II	through	through	[P.
J21:0770j	-	MC	two	two	[M.
J21:0770k	-	IO	of	of	[Po.
J21:0770m	-	DD2i	these	these	[Np.
J21:0770n	-	NN2	points	point	.Np]Po]
J21:0770p	-	YC	+,	-	.
J21:0770q	-	FOx	<formul>	-	[FOx&.
J21:0770r	-	CC	and	and	[FOx+.
J21:0770s	-	FOx	<formul>	-	.FOx+]FOx&]
J21:0770t	-	YC	+,	-	.M]P]Ns:S]
J21:0780a	-	VMo	will	will	[Vcp.
J21:0780b	-	VB0	be	be	.
J21:0780c	-	VVNt	transformed	transform	.Vcp]
J21:0780d	-	II	into	into	[P:q.
J21:0780e	-	AT	the	the	[Ns:157.
J21:0780f	-	JB	entire	entire	.
J21:0780g	-	JJ	bilinear	bilinear	.
J21:0780h	-	NN1n	congruence	congruence	.
J21:0780i	-	YG	-	-	[Tg[s157.s157]
J21:0780j	-	VHG	having	have	[Vg.Vg]
J21:0780k	-	AT	the	the	[Np:o.
J21:0790a	-	NN2	tangents	tangent	.
J21:0790b	-	IIt	to	to	[P.
J21:0790c	S	FOx	g	-	.P]
J21:0790d	-	II	at	at	[P.
J21:0790e	-	FOx	<formul>	-	[FOx&.
J21:0790f	-	CC	and	and	[FOx+.
J21:0790g	-	FOx	<formul>	-	.FOx+]FOx&]P]Np:o]
J21:0790h	-	IIa	as	as	[P:j.
J21:0790i	-	NN2	directrices	directrix	.P:j]Tg]Ns:157]P:q]S]
J21:0790j	-	YF	+.	-	.O]
J21:0790k	-	YB	<minbrk>	-	[Oh.Oh]
J21:0790m	-	AT1	A	a	[O[S[N:s.
J21:0790n	-	JJ	conic	conic	.
J21:0790p	-	YC	+,	-	.
J21:0790q	-	YTL	<bital>	-	.
J21:0790r	S	FOx	C	-	.
J21:0790s	-	YTR	<eital>	-	.
J21:0790t	-	YC	+,	-	.
J21:0800a	-	VBG	being	be	[Tg[Vgb.Vgb]
J21:0800b	-	AT1	a	a	[Ns:e.
J21:0800c	-	FOx	(1,1)	-	.
J21:0800d	-	NN1c	curve	curve	.
J21:0800e	-	II	on	on	[P.
J21:0800f	-	YTL	<bital>	-	.
J21:0800g	S	FOx	Q	-	.
J21:0800h	-	YTR	<eital>	-	.P]Ns:e]Tg]
J21:0800i	-	YC	+,	-	.N:s]
J21:0800j	-	VVZv	meets	meet	[Vz.Vz]
J21:0800k	-	AT	the	the	[Ns:o.
J21:0800m	-	NN1c	image	image	.
J21:0800n	-	IO	of	of	[Po.
J21:0800p	-	DDy	any	any	[Ns:159.
J21:0800q	-	NN1n	line	line	.
J21:0810a	-	IO	of	of	[Po.
J21:0810b	-	FOx	<formul>	-	.Po]Ns:159]Po]
J21:0810c	-	YC	+,	-	.
J21:0810d	-	DDQr	which	which	[Fr[Dq:O159.Dq:O159]
J21:0810e	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:0810f	-	YG	-	-	[t161.t161]
J21:0810g	-	VH0	have	have	[Vf.
J21:0810h	-	RR	already	already	[R:G161.R:G161]
J21:0810i	-	VVNt	found	find	.Vf]
J21:0810j	-	YG	-	-	[Ti:o[s159.s159]
J21:0810k	-	TO	to	to	[Vib.
J21:0810m	-	VB0	be	be	.Vib]
J21:0810n	-	AT1	a	a	[Ns:e.
J21:0810p	-	FOx	<formul>	-	.
J21:0810q	-	NN1c	curve	curve	.
J21:0810r	-	II	on	on	[P.
J21:0810s	-	YTL	<bital>	-	.
J21:0810t	S	FOx	Q	-	.
J21:0810u	-	YTR	<eital>	-	.P]Ns:e]Ti:o]Fr]
J21:0810v	-	YC	+,	-	.Ns:o]
J21:0820a	-	II	in	in	[P:p.
J21:0820b	-	FOx	<formul>	-	[Np.
J21:0820c	-	NN2	points	point	.Np]P:p]S]
J21:0820d	-	YF	+.	-	.
J21:0820e	-	RR	Hence	hence	[S[R:c.R:c]
J21:0820f	-	APPGh1	its	its	[Ns:s.
J21:0820g	-	NN1c	image	image	.
J21:0820h	-	YC	+,	-	.
J21:0820i	-	YTL	<bital>	-	[N@.
J21:0820j	S	FOx	C<prime>	-	.
J21:0820k	-	YTR	<eital>	-	.N@]
J21:0820m	-	YC	+,	-	.Ns:s]
J21:0820n	-	VVZv	meets	meet	[Vz.Vz]
J21:0820p	-	DDy	any	any	[Ns:o.
J21:0820q	-	NN1n	line	line	.
J21:0820r	-	IO	of	of	[Po.
J21:0820s	-	FOx	<formul>	-	.Po]Ns:o]
J21:0830a	-	II	in	in	[P:p.
J21:0830b	-	FOx	<formul>	-	[Np.
J21:0830c	-	NN2	points	point	.Np]P:p]S]
J21:0830d	-	YF	+.	-	.
J21:0830e	-	RR	Moreover	moreover	[S[R:m.R:m]
J21:0830f	-	YC	+,	-	.
J21:0830g	-	YTL	<bital>	-	.
J21:0830h	S	FOx	C<prime>	-	[N:s.N:s]
J21:0830i	-	YTR	<eital>	-	.
J21:0830j	-	RR	obviously	obviously	[R:m.R:m]
J21:0830k	-	VVZv	meets	meet	[Vz.Vz]
J21:0830m	-	DDy	any	any	[Ns:o.
J21:0830n	-	NN1n	line	line	.
J21:0830p	-	FOx	<formul>	-	.Ns:o]
J21:0830q	-	II	in	in	[P:p.
J21:0840a	-	AT1	a	a	[Ns.
J21:0840b	-	JJ	single	single	.
J21:0840c	-	NNL1n	point	point	.Ns]P:p]S]
J21:0840d	-	YF	+.	-	.
J21:0840e	-	RR	Hence	hence	[S[R:c.R:c]
J21:0840f	-	YTL	<bital>	-	.
J21:0840g	S	FOx	C<prime>	-	[N:s.N:s]
J21:0840h	-	YTR	<eital>	-	.
J21:0840i	-	VBZ	is	be	[Vzb.Vzb]
J21:0840j	-	AT1	a	a	[Ns:e.
J21:0840k	-	FOx	<formul>	-	.
J21:0840m	-	NN1c	curve	curve	.
J21:0840n	-	II	on	on	[P.
J21:0840p	-	YTL	<bital>	-	.
J21:0840q	S	FOx	Q	-	.
J21:0840r	-	YTR	<eital>	-	.P]Ns:e]S]
J21:0840s	-	YF	+.	-	.
J21:0840t	-	RR	Therefore	therefore	[S[R:c.R:c]
J21:0840u	-	YC	+,	-	.
J21:0850a	-	AT	the	the	[Ns:s.
J21:0850b	-	NN1n	congruence	congruence	.
J21:0850c	-	IO	of	of	[Po.
J21:0850d	-	APPGh1	its	its	[Np.
J21:0850e	-	NN2	secants	secant	.Np]Po]
J21:0850f	-	YC	+,	-	.
J21:0850g	-	REX21	that	that	[REX=.
J21:0850h	-	REX22	is	be	.REX=]
J21:0850i	-	AT	the	the	[Ns@.
J21:0850j	-	NN1c	image	image	.
J21:0850k	-	IO	of	of	[Po.
J21:0850m	-	AT1	a	a	[Ns.
J21:0850n	-	JJ	general	general	.
J21:0860a	-	NN1c	plane	plane	.
J21:0860b	-	NN1c	field	field	.
J21:0860c	-	IO	of	of	[Po.
J21:0860d	-	NN2	lines	line	.Po]Ns]Po]Ns@]
J21:0860e	-	YC	+,	-	.Ns:s]
J21:0860f	-	VBZ	is	be	[Vzb.Vzb]
J21:0860g	-	IO	of	of	[Po:e.
J21:0860h	-	NN1n	order	order	[N.
J21:0860i	-	FOx	<formul>	-	.
J21:0860j	-	CC	and	and	[Ns+.
J21:0860k	-	NN1n	class	class	.
J21:0860m	-	FOx	<formul>	-	.Ns+]N]Po:e]S]
J21:0860n	-	YF	+.	-	.
J21:0860p	-	RR	Finally	finally	[S[R:t.R:t]
J21:0860q	-	YC	+,	-	.
J21:0860r	-	AT	the	the	[Ns:s.
J21:0860s	-	NN1c	image	image	.
J21:0870a	-	IO	of	of	[Po.
J21:0870b	-	AT1	a	a	[Ns.
J21:0870c	-	JJ	general	general	.
J21:0870d	-	NN1c	bundle	bundle	.
J21:0870e	-	IO	of	of	[Po.
J21:0870f	-	NN2	lines	line	.Po]Ns]Po]Ns:s]
J21:0870g	-	VBZ	is	be	[Vzb.Vzb]
J21:0870h	-	AT1	a	a	[Ns:e165.
J21:0870i	-	NN1n	congruence	congruence	.
J21:0870j	-	DDQGr	whose	whose	[Fr[Nqs:s165.
J21:0870k	-	NN1n	order	order	.Nqs:s165]
J21:0870m	-	VBZ	is	be	[Vzb.Vzb]
J21:0870n	-	AT	the	the	[Ns:e.
J21:0870p	-	NN1n	order	order	.
J21:0880a	-	IO	of	of	[Po.
J21:0880b	-	AT	the	the	[Ns.
J21:0880c	-	NN1n	congruence	congruence	.
J21:0880d	-	IO	of	of	[Po.
J21:0880e	-	JJ	invariant	invariant	[Np.
J21:0880f	-	NN2	lines	line	.Np]Po]Ns]Po]
J21:0880g	-	YC	+,	-	.
J21:0880h	-	REX	namely	namely	.
J21:0880i	-	FOx	<formul>	-	.Ns:e]
J21:0880j	-	CC	and	and	[Fr+.
J21:0880k	-	DDQGr	whose	whose	[Nqs:s165.
J21:0880m	-	NN1n	class	class	.Nqs:s165]
J21:0880n	-	VBZ	is	be	[Vzb.Vzb]
J21:0890a	-	AT	the	the	[Ns:e.
J21:0890b	-	NN1n	order	order	.
J21:0890c	-	IO	of	of	[Po.
J21:0890d	-	AT	the	the	[Ns.
J21:0890e	-	NN1c	image	image	.
J21:0890f	-	NN1n	congruence	congruence	.
J21:0890g	-	IO	of	of	[Po.
J21:0890h	-	AT1	a	a	[Ns.
J21:0890i	-	JJ	general	general	.
J21:0890j	-	NN1c	plane	plane	.
J21:0890k	-	NN1c	field	field	.
J21:0890m	-	IO	of	of	[Po.
J21:0890n	-	NN2	lines	line	.Po]Ns]Po]Ns]Po]
J21:0890p	-	YC	+,	-	.
J21:0900a	-	REX	namely	namely	.
J21:0900b	-	FOx	<formul>	-	.Ns:e]Fr+]Fr]Ns:e165]S]
J21:0900c	-	YF	+.	-	.O]
J21:0900d	-	YBL	<bmajhd>	-	[Oh.
J21:0900e	-	MCb	2.	-	.
J21:0900f	-	YBR	<emajhd>	-	.Oh]
J21:0900g	-	AT	The	the	[O[S[Np:s.
J21:0900h	-	JJ	preceding	preceding	.
J21:0900i	-	NN2	observations	observation	.Np:s]
J21:0900j	-	VV0v	make	make	[V.V]
J21:0900k	-	PPH1	it	it	[Ni:O.Ni:O]
J21:0900m	-	JJ	clear	clear	[J:j.J:j]
J21:0900n	-	CST	that	that	[Fn:o.
J21:0900p	-	EX	there	there	.
J21:0910a	-	VV0i	exist	exist	[V.V]
J21:0910b	-	NN1n	line	line	[Np:s.
J21:0910c	-	NN2	involutions	involution	.
J21:0910d	-	IO	of	of	[Po.
J21:0910e	-	DBa	all	all	[Np.
J21:0910f	-	NN2	orders	order	.
J21:0910g	-	JJR	greater	great	[Jh.
J21:0910h	-	CSN	than	than	[P.
J21:0910i	-	MC1n	1	-	.P]Jh]Np]Po]
J21:0910j	-	IW	with	with	[P.
J21:0910k	-	ATn	no	no	[Ns.
J21:0910m	-	NN1c	complex	complex	.
J21:0920a	-	IO	of	of	[Po.
J21:0920b	-	JJ	invariant	invariant	[Np.
J21:0920c	-	NN2	lines	line	.Np]Po]Ns]
J21:0920d	-	CC	and	and	[P+.
J21:0920e	-	IW	with	with	.
J21:0920f	-	AT1	a	a	[Ns:167.
J21:0920g	-	NN1c	complex	complex	.
J21:0920h	-	IO	of	of	[Po.
J21:0920i	-	JJ	singular	singular	[Np.
J21:0920j	-	NN2	lines	line	.Np]Po]
J21:0920k	-	YG	-	-	[Tg[s167.s167]
J21:0920m	-	VVGi	consisting	consist	[Vg.Vg]
J21:0920n	-	RR	exclusively	exclusively	[R:m.R:m]
J21:0930a	-	IO	of	of	[Po:u.
J21:0930b	-	AT	the	the	[Np:169.
J21:0930c	-	NN2	lines	line	.
J21:0930d	-	DDQr	which	which	[Fr[Dq:s169.Dq:s169]
J21:0930e	-	VV0v	meet	meet	[V.V]
J21:0930f	-	AT1	a	a	[Ns:o.
J21:0930g	-	VVNv	twisted	twist	[Tn[Vn.Vn]Tn]
J21:0930h	-	NN1c	curve	curve	.
J21:0930i	S	FOx	g	-	.Ns:o]Fr]Np:169]Po:u]Tg]Ns:167]P+]P]Np:s]Fn:o]S]
J21:0930j	-	YF	+.	-	.
J21:0930k	-	PPIS2	We	we	[S[Nap:s.Nap:s]
J21:0930m	-	RTo	now	now	[Rw:t.Rw:t]
J21:0930n	-	VMo	shall	shall	[Vc.
J21:0940a	-	VV0v	show	show	.Vc]
J21:0940b	-	CST	that	that	[Fn:o.
J21:0940c	-	DDy	any	any	[Ns:s.
J21:0940d	-	NN1c	involution	involution	.
J21:0940e	-	IW	with	with	[P.
J21:0940f	-	DD2i	these	these	[Np.
J21:0940g	-	NN2	characteristics	characteristic	.Np]P]Ns:s]
J21:0940h	-	VBZ	is	be	[Vzb.Vzb]
J21:0940i	-	RR	necessarily	necessarily	[R:m.R:m]
J21:0950a	-	IO	of	of	[Po:e.
J21:0950b	-	AT	the	the	[Ns:171.
J21:0950c	-	NN1n	type	type	.
J21:0950d	-	PPIS2	we	we	[Fr[Nap:s.Nap:s]
J21:0950e	-	YG	-	-	[t173.t173]
J21:0950f	-	VH0	have	have	[Vf.
J21:0950g	-	RR	just	just	[R:G173.R:G173]
J21:0950h	-	VVNt	described	describe	.Vf]
J21:0950i	-	YG	-	-	[o171.o171]Fr]Ns:171]Po:e]Fn:o]S]
J21:0950j	-	YF	+.	-	.O]
J21:0950k	-	YB	<minbrk>	-	[Oh.Oh]
J21:0950m	-	TO	To	to	[O[S[Ti:c[Vi.
J21:0950n	-	VD0	do	do	.Vi]
J21:0950p	-	DD1i	this	this	[Ds:o.Ds:o]Ti:c]
J21:0950q	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:0950r	-	YG	-	-	[t175.t175]
J21:0950s	-	VMo	must	must	[Vc.
J21:0950t	-	MDo	first	first	[R:G175.R:G175]
J21:0960a	-	VV0v	show	show	.Vc]
J21:0960b	-	CST	that	that	[Fn:o.
J21:0960c	-	AT1e	every	every	[Ns:s177.
J21:0960d	-	NN1n	line	line	.
J21:0960e	-	DDQr	which	which	[Fr[Dq:s177.Dq:s177]
J21:0960f	-	VVZv	meets	meet	[Vz.Vz]
J21:0960g	S	FOx	g	-	[N:o.N:o]
J21:0960h	-	II	in	in	[P:p.
J21:0960i	-	AT1	a	a	[Ns.
J21:0960j	-	NNL1n	point	point	.
J21:0960k	-	YTL	<bital>	-	.
J21:0960m	S	FOx	P	-	.
J21:0960n	-	YTR	<eital>	-	.Ns]P:p]Fr]Ns:s177]
J21:0960p	-	VVZv	meets	meet	[Vz.Vz]
J21:0960q	-	APPGh1	its	its	[Ns:o.
J21:0970a	-	NN1c	image	image	.Ns:o]
J21:0970b	-	II	at	at	[P:p.
J21:0970c	-	YTL	<bital>	-	.
J21:0970d	S	FOx	P	-	.
J21:0970e	-	YTR	<eital>	-	.P:p]Fn:o]S]
J21:0970f	-	YF	+.	-	.
J21:0970g	-	TO	To	to	[S*[Ti:c[Vi.
J21:0970h	-	VV0v	see	see	.Vi]
J21:0970i	-	DD1i	this	this	[Ds:o.Ds:o]Ti:c]
J21:0970j	-	YC	+,	-	.
J21:0970k	-	VV0t	consider	consider	[V.V]
J21:0970m	-	AT1	a	a	[Ns:o179.
J21:0970n	-	JJ	general	general	.
J21:0970p	-	NN1c	pencil	pencil	.
J21:0970q	-	IO	of	of	[Po.
J21:0970r	-	NN2	lines	line	.Po]
J21:0970s	-	YG	-	-	[Tg[s179.s179]
J21:0980a	-	VVGt	containing	contain	[Vg.Vg]
J21:0980b	-	AT1	a	a	[Ns:o.
J21:0980c	-	JJ	general	general	.
J21:0980d	-	NN1c	secant	secant	.
J21:0980e	-	IO	of	of	[Po.
J21:0980f	S	FOx	G	-	.Po]Ns:o]Tg]Ns:o179]S*]
J21:0980g	-	YF	+.	-	.
J21:0980h	-	IIb	By	by	[S[Pb:m.
J21:0980i	-	MCb	(1)	-	.Pb:m]
J21:0980j	-	YC	+,	-	.
J21:0980k	-	AT	the	the	[Ns:s.
J21:0980m	-	NN1c	image	image	.
J21:0980n	-	IO	of	of	[Po.
J21:0980p	-	DD1i	this	this	[Ns.
J21:0980q	-	NN1c	pencil	pencil	.Ns]Po]Ns:s]
J21:0990a	-	VBZ	is	be	[Vzb.Vzb]
J21:0990b	-	AT1	a	a	[Ns:e181.
J21:0990c	-	VVNv	ruled	rule	[Tn[Vn.Vn]Tn]
J21:0990d	-	NN1c	surface	surface	.
J21:0990e	-	IO	of	of	[Po.
J21:0990f	-	NN1n	order	order	[Ns.
J21:0990g	-	FOx	<formul>	-	.Ns]Po]
J21:0990h	-	DDQr	which	which	[Fr[Dq:S181.Dq:S181]
J21:0990i	-	VBZ	is	be	[Vzp.
J21:0990j	-	VVNv	met	meet	.Vzp]
J21:0990k	-	IIb	by	by	[Pb:a.
J21:0990m	-	AT	the	the	[Ns.
J21:0990n	-	NN1c	plane	plane	.
J21:0990p	-	IO	of	of	[Po.
J21:0990q	-	AT	the	the	[Ns.
J21:1000a	-	NN1c	pencil	pencil	.Ns]Po]Ns]Pb:a]
J21:1000b	-	II	in	in	[P:p.
J21:1000c	-	AT1	a	a	[Ns.
J21:1000d	-	NN1c	curve	curve	.
J21:1000e	-	YC	+,	-	.
J21:1000f	-	YTL	<bital>	-	.
J21:1000g	S	FOx	C	-	.
J21:1000h	-	YTR	<eital>	-	.
J21:1000i	-	YC	+,	-	.
J21:1000j	-	IO	of	of	[Po.
J21:1000k	-	NN1n	order	order	[Ns.
J21:1000m	-	FOx	<formul>	-	.Ns]Po]Ns]P:p]Fr]Ns:e181]S]
J21:1000n	-	YF	+.	-	.
J21:1000p	-	II	On	on	[S[P:p.
J21:1000q	-	YTL	<bital>	-	.
J21:1000r	S	FOx	C	-	.
J21:1000s	-	YTR	<eital>	-	.P:p]
J21:1000t	-	EX	there	there	.
J21:1000u	-	VBZ	is	be	[Vzb.Vzb]
J21:1000v	-	AT1	a	a	[Ns:s183.
J21:1010a	-	FOx	<formul>	-	.
J21:1010b	-	NN1n	correspondence	correspondence	.
J21:1010c	-	II	in	in	[Fr[Pq:p.
J21:1010d	-	DDQr	which	which	[Dq:183.Dq:183]Pq:p]
J21:1010e	-	AT	the	the	[Np:s185.
J21:1010f	-	FOx	<formul>	-	.
J21:1010g	-	NN2	points	point	.
J21:1010h	-	YG	-	-	[Tn[S185.S185]
J21:1010i	-	VVNv	cut	cut	[Vn.Vn]
J21:1010j	-	II	from	from	[P:q.
J21:1010k	-	YTL	<bital>	-	.
J21:1010m	S	FOx	C	-	.
J21:1010n	-	YTR	<eital>	-	.P:q]
J21:1010p	-	IIb	by	by	[Pb:a.
J21:1010q	-	AT1	a	a	[Ns.
J21:1010r	-	JJ	general	general	.
J21:1020a	-	NN1n	line	line	.
J21:1020b	-	YC	+,	-	.
J21:1020c	-	YTL	<bital>	-	.
J21:1020d	S	FOx	l	-	.
J21:1020e	-	YTR	<eital>	-	.
J21:1020f	-	YC	+,	-	.
J21:1020g	-	IO	of	of	[Po.
J21:1020h	-	AT	the	the	[Ns.
J21:1020i	-	NN1c	pencil	pencil	.Ns]Po]Ns]Pb:a]Tn]Np:s185]
J21:1020j	-	VV0i	correspond	correspond	[V.V]
J21:1020k	-	IIt	to	to	[P:q.
J21:1020m	-	AT	the	the	[Ns.
J21:1020n	-	NNL1n	point	point	.
J21:1020p	-	IO	of	of	[Po.
J21:1020q	-	NN1n	intersection	intersection	.Po]
J21:1030a	-	IO	of	of	[Po.
J21:1030b	-	AT	the	the	[N.
J21:1030c	-	NN1c	image	image	.
J21:1030d	-	IO	of	of	[Po.
J21:1030e	-	YTL	<bital>	-	.
J21:1030f	S	FOx	l	-	.
J21:1030g	-	YTR	<eital>	-	.Po]
J21:1030h	-	CC	and	and	[Ns+.
J21:1030i	-	AT	the	the	.
J21:1030j	-	NN1c	plane	plane	.
J21:1030k	-	IO	of	of	[Po.
J21:1030m	-	AT	the	the	[Ns.
J21:1030n	-	NN1c	pencil	pencil	.Ns]Po]Ns+]N]Po]Ns]P:q]Fr]Ns:s183]S]
J21:1030p	-	YF	+.	-	.
J21:1030q	-	ICSt	Since	since	[S[Fa:c.
J21:1030r	-	YTL	<bital>	-	.
J21:1030s	S	FOx	C	-	[N:s.N:s]
J21:1030t	-	YTR	<eital>	-	.
J21:1040a	-	VBZ	is	be	[Vzb.Vzb]
J21:1040b	-	JJ	rational	rational	[J:e.J:e]Fa:c]
J21:1040c	-	YC	+,	-	.
J21:1040d	-	DD1i	this	this	[Ns:s.
J21:1040e	-	NN1n	correspondence	correspondence	.Ns:s]
J21:1040f	-	VHZ	has	have	[Vz.Vz]
J21:1040g	-	YTL	<bital>	-	[Np:o187.
J21:1040h	S	FOx	k	-	.
J21:1040i	-	YTR	<eital>	-	.
J21:1040j	-	NN2	coincidences	coincidence	.
J21:1040k	-	YC	+,	-	.
J21:1040m	-	DD1q	each	each	[Fr[Dqs:s.
J21:1050a	-	IO	of	of	[Poq.
J21:1050b	-	DDQr	which	which	[Dq:187.Dq:187]Poq]Dqs:s]
J21:1050c	-	VVZt	implies	imply	[Vz.Vz]
J21:1050d	-	AT1	a	a	[Ns:o189.
J21:1050e	-	NN1n	line	line	.
J21:1050f	-	IO	of	of	[Po.
J21:1050g	-	AT	the	the	[Ns.
J21:1050h	-	NN1c	pencil	pencil	.Ns]Po]
J21:1050i	-	DDQr	which	which	[Fr[Dq:s189.Dq:s189]
J21:1050j	-	VVZv	meets	meet	[Vz.Vz]
J21:1050k	-	APPGh1	its	its	[Ns:o.
J21:1050m	-	NN1c	image	image	.Ns:o]Fr]Ns:o189]Fr]Np:o187]S]
J21:1050n	-	YF	+.	-	.
J21:1050p	-	RR	However	however	[S[R:c.R:c]
J21:1050q	-	YC	+,	-	.
J21:1060a	-	ICSt	since	since	[Fa:c.
J21:1060b	-	AT	the	the	[Ns:s.
J21:1060c	-	NN1c	pencil	pencil	.Ns:s]
J21:1060d	-	VVZt	contains	contain	[Vz.Vz]
J21:1060e	-	AT1	a	a	[Ns:o.
J21:1060f	-	NN1c	secant	secant	.
J21:1060g	-	IO	of	of	[Po.
J21:1060h	S	FOx	g	-	.Po]Ns:o]Fa:c]
J21:1060i	-	PPH1	it	it	[Ni:s.Ni:s]
J21:1060j	-	RR	actually	actually	[R:m.R:m]
J21:1060k	-	VVZt	contains	contain	[Vz.Vz]
J21:1060m	-	RRx	only	only	[R:m.R:m]
J21:1070a	-	FOx	<formul>	-	[Np:o.
J21:1070b	-	JJ	singular	singular	.
J21:1070c	-	NN2	lines	line	.Np:o]S]
J21:1070d	-	YF	+.	-	.
J21:1070e	-	TO	To	to	[S[Ti:c[Vi.
J21:1070f	-	VV0t	avoid	avoid	.Vi]
J21:1070g	-	DD1i	this	this	[Ns:o.
J21:1070h	-	NN1n	contradiction	contradiction	.Ns:o]Ti:c]
J21:1070i	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1070j	-	VBZ	is	be	[Vzb.Vzb]
J21:1070k	-	JJ	necessary	necessary	[J:e.J:e]
J21:1070m	-	CST	that	that	[Fn%:s.
J21:1080a	-	YTL	<bital>	-	.
J21:1080b	S	FOx	C	-	[N:s.N:s]
J21:1080c	-	YTR	<eital>	-	.
J21:1080d	-	VB0	be	be	[Vjb.Vjb]
J21:1080e	-	JJ	composite	composite	[J:e.J:e]
J21:1080f	-	YC	+,	-	.
J21:1080g	-	IW	with	with	[W:b.
J21:1080h	-	AT	the	the	[N:s.
J21:1080i	-	NN1c	secant	secant	.
J21:1080j	-	IO	of	of	[Po.
J21:1080k	S	FOx	g	-	.Po]
J21:1080m	-	CC	and	and	[Ns+.
J21:1080n	-	AT1	a	a	.
J21:1080p	-	NN1c	curve	curve	.
J21:1080q	-	IO	of	of	[Po.
J21:1090a	-	NN1n	order	order	[Ns.
J21:1090b	-	FOx	<formul>	-	.Ns]Po]Ns+]N:s]
J21:1090c	-	IIa	as	as	[P:e.
J21:1090d	-	NN2	components	component	.P:e]W:b]Fn%:s]S]
J21:1090e	-	YF	+.	-	.
J21:1090f	-	RR	Thus	thus	[S[R:c.R:c]
J21:1090g	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1090h	-	VVZv	follows	follow	[Vz.Vz]
J21:1090i	-	CST	that	that	[Fn:s.
J21:1090j	-	AT	the	the	[Np:s.
J21:1090k	-	NN2	secants	secant	.
J21:1090m	-	IO	of	of	[Po.
J21:1090n	S	FOx	g	-	.Po]Np:s]
J21:1100a	-	VBR	are	be	[Vab.Vab]
J21:1100b	-	RR	all	all	[R:h.R:h]
J21:1100c	-	JJ	invariant	invariant	[J:e.J:e]Fn:s]S]
J21:1100d	-	YF	+.	-	.
J21:1100e	-	CCB	But	but	[S+.
J21:1100f	-	CSi	if	if	[Fa:c.
J21:1100g	-	DD1i	this	this	[Ds:s.Ds:s]
J21:1100h	-	VBZ	is	be	[Vzb.Vzb]
J21:1100i	-	AT	the	the	[Ns:e.
J21:1100j	-	NN1c	case	case	.Ns:e]Fa:c]
J21:1100k	-	YC	+,	-	.
J21:1100m	-	RTn	then	then	[Rsw:t.Rsw:t]
J21:1100n	-	AT1	an	an	[Ns:S193.
J21:1100p	-	JJ	arbitrary	arbitrary	.
J21:1100q	-	NN1c	pencil	pencil	.
J21:1110a	-	IO	of	of	[Po.
J21:1110b	-	NN2	lines	line	.Po]
J21:1110c	-	YG	-	-	[Tg[s193.s193]
J21:1110d	-	VHG	having	have	[Vg.Vg]
J21:1110e	-	AT1	a	a	[Ns:o.
J21:1110f	-	NNL1n	point	point	.
J21:1110g	-	YC	+,	-	.
J21:1110h	-	YTL	<bital>	-	.
J21:1110i	S	FOx	P	-	.
J21:1110j	-	YTR	<eital>	-	.
J21:1110k	-	YC	+,	-	.
J21:1110m	-	IO	of	of	[Po.
J21:1110n	S	FOx	g	-	.Po]Ns:o]
J21:1110p	-	IIa	as	as	[P:j.
J21:1110q	-	NN1c	vertex	vertex	.P:j]Tg]Ns:S193]
J21:1110r	-	VBZ	is	be	[Vzp.
J21:1110s	-	VVNt	transformed	transform	.Vzp]
J21:1120a	-	II	into	into	[P:q.
J21:1120b	-	AT1	a	a	[Ns:195.
J21:1120c	-	VVNv	ruled	rule	[Tn[Vn.Vn]Tn]
J21:1120d	-	NN1c	surface	surface	.
J21:1120e	-	IO	of	of	[Po.
J21:1120f	-	NN1n	order	order	[Ns.
J21:1120g	-	FOx	<formul>	-	.Ns]Po]
J21:1120h	-	YG	-	-	[Tg[s195.s195]
J21:1120i	-	VHG	having	have	[Vg.Vg]
J21:1120j	-	FOx	<formul>	-	[Np:o.
J21:1120k	-	NN2	generators	generator	.
J21:1120m	-	JJ	concurrent	concurrent	[Jh.
J21:1120n	-	II	at	at	[P.
J21:1130a	-	YTL	<bital>	-	.
J21:1130b	S	FOx	P	-	.
J21:1130c	-	YTR	<eital>	-	.P]Jh]Np:o]Tg]Ns:195]P:q]S+]
J21:1130d	-	YF	+.	-	.
J21:1130e	-	ICSt	Since	since	[S[Fa:c.
J21:1130f	-	AT1	a	a	[Ns:s.
J21:1130g	-	VVNv	ruled	rule	[Tn[Vn.Vn]Tn]
J21:1130h	-	NN1c	surface	surface	.
J21:1130i	-	IO	of	of	[Po.
J21:1130j	-	NN1n	order	order	[Ns.
J21:1130k	-	YTL	<bital>	-	.
J21:1130m	S	FOx	n	-	.
J21:1130n	-	YTR	<eital>	-	.Ns]Po]
J21:1130p	-	IW	with	with	[P.
J21:1130q	-	YTL	<bital>	-	[Np.
J21:1130r	S	FOx	n	-	.
J21:1130s	-	YTR	<eital>	-	.
J21:1130t	-	JJ	concurrent	concurrent	.
J21:1131a	-	NN2	generators	generator	.Np]P]Ns:s]
J21:1140a	-	VBZ	is	be	[Vzb.Vzb]
J21:1140b	-	RR	necessarily	necessarily	[R:m.R:m]
J21:1140c	-	AT1	a	a	[Ns:e.
J21:1140d	-	NN1c	cone	cone	.Ns:e]Fa:c]
J21:1140e	-	YC	+,	-	.
J21:1140f	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1140g	-	VVZv	follows	follow	[Vz.Vz]
J21:1140h	-	RR	finally	finally	[R:t.R:t]
J21:1140i	-	CST	that	that	[Fn:s.
J21:1140j	-	AT1e	every	every	[Ns:s.
J21:1140k	-	NN1n	line	line	.
J21:1140m	-	II	through	through	[P.
J21:1150a	-	AT1	a	a	[Ns.
J21:1150b	-	NNL1n	point	point	.
J21:1150c	-	YC	+,	-	.
J21:1150d	-	YTL	<bital>	-	.
J21:1150e	S	FOx	P	-	.
J21:1150f	-	YTR	<eital>	-	.
J21:1150g	-	YC	+,	-	.
J21:1150h	-	IO	of	of	[Po.
J21:1150i	S	FOx	g	-	.Po]Ns]P]Ns:s]
J21:1150j	-	VVZv	meets	meet	[Vz.Vz]
J21:1150k	-	APPGh1	its	its	[Ns:o.
J21:1150m	-	NN1c	image	image	.Ns:o]
J21:1150n	-	II	at	at	[P:p.
J21:1150p	-	YTL	<bital>	-	.
J21:1150q	S	FOx	P	-	.
J21:1150r	-	YTR	<eital>	-	.P:p]
J21:1150s	-	YC	+,	-	.
J21:1150t	-	CSA	as	as	[A:m.
J21:1150u	-	VVNt	asserted	assert	[Vn.Vn]A:m]Fn:s]S]
J21:1150v	-	YF	+.	-	.O]
J21:1160a	-	YB	<minbrk>	-	[Oh.Oh]
J21:1160b	-	RTo	Now	now	[O[S*[Rw:t.Rw:t]
J21:1160c	-	VV0t	consider	consider	[V.V]
J21:1160d	-	AT	the	the	[Ns:o197.
J21:1160e	-	NN1n	transformation	transformation	.
J21:1160f	-	IO	of	of	[Po.
J21:1160g	-	AT	the	the	[Np.
J21:1160h	-	NN2	lines	line	.
J21:1160i	-	IO	of	of	[Po.
J21:1160j	-	AT1	a	a	[Ns.
J21:1160k	-	NN1c	bundle	bundle	.
J21:1170a	-	IW	with	with	[W.
J21:1170b	-	NN1c	vertex	vertex	[Ns:s.
J21:1170c	-	YC	+,	-	.
J21:1170d	-	YTL	<bital>	-	.
J21:1170e	S	FOx	P	-	.
J21:1170f	-	YTR	<eital>	-	.
J21:1170g	-	YC	+,	-	.Ns:s]
J21:1170h	-	II	on	on	[P:p.
J21:1170i	S	FOx	g	-	.P:p]W]Ns]Po]Np]Po]
J21:1170j	-	DDQr	which	which	[Fr[Dq:S197.Dq:S197]
J21:1170k	-	VBZ	is	be	[Vzp.
J21:1170m	-	VVNt	effected	effect	.Vzp]
J21:1170n	-	IIb	by	by	[Pb:a.
J21:1170p	-	AT	the	the	[Ns.
J21:1170q	-	NN1c	involution	involution	.
J21:1180a	-	IIa	as	as	[P.
J21:1180b	-	AT1	a	a	[Ns.
J21:1180c	-	NN1c	whole	whole	.Ns]P]Ns]Pb:a]Fr]Ns:o197]S*]
J21:1180d	-	YF	+.	-	.
J21:1180e	-	II	From	from	[S[P:c.
J21:1180f	-	AT	the	the	[Np.
J21:1180g	-	JJ	preceding	preceding	.
J21:1180h	-	NN2	remarks	remark	.Np]P:c]
J21:1180i	-	YC	+,	-	.
J21:1180j	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1180k	-	VBZ	is	be	[Vzb.Vzb]
J21:1180m	-	JJ	clear	clear	[J:e.J:e]
J21:1180n	-	CST	that	that	[Fn:s.
J21:1180p	-	DAz	such	such	[Ns:S.
J21:1180q	-	AT1	a	a	.
J21:1180r	-	NN1c	bundle	bundle	.Ns:S]
J21:1190a	-	VBZ	is	be	[Vzp.
J21:1190b	-	VVNt	transformed	transform	.Vzp]
J21:1190c	-	II	into	into	[P:q.
J21:1190d	-	PPX1h	itself	itself	.P:q]
J21:1190e	-	II	in	in	[P:h.
J21:1190f	-	AT1	an	an	[Ns.
J21:1190g	-	JJ	involutorial	involutorial	.
J21:1190h	-	NN1n	fashion	fashion	.Ns]P:h]Fn:s]S]
J21:1190i	-	YF	+.	-	.
J21:1190j	-	RR	Moreover	moreover	[S[R:m.R:m]
J21:1190k	-	YC	+,	-	.
J21:1200a	-	II	in	in	[P:p.
J21:1200b	-	DD1i	this	this	[Ns.
J21:1200c	-	NN1c	involution	involution	.Ns]P:p]
J21:1200d	-	EX	there	there	.
J21:1200e	-	VBZ	is	be	[Vzb.Vzb]
J21:1200f	-	AT1	a	a	[Ns:s.
J21:1200g	-	NN1c	cone	cone	.
J21:1200h	-	IO	of	of	[Po.
J21:1200i	-	JJ	invariant	invariant	[Np.
J21:1200j	-	NN2	lines	line	.
J21:1200k	-	IO	of	of	[Po.
J21:1200m	-	NN1n	order	order	[Ns.
J21:1200n	-	FOx	<formul>	-	.Ns]Po]Np]Po]
J21:1200p	-	YC	+,	-	.
J21:1200q	-	REX	namely	namely	.
J21:1210a	-	AT	the	the	[Ns@:199.
J21:1210b	-	NN1c	cone	cone	.
J21:1210c	-	IO	of	of	[Po.
J21:1210d	-	NN2	secants	secant	[Np.
J21:1210e	-	IO	of	of	[Po.
J21:1210f	S	FOx	g	-	.Po]
J21:1210g	-	DDQr	which	which	[Fr[Dq:s199.Dq:s199]
J21:1210h	-	VV0v	pass	pass	[V.V]
J21:1210i	-	II	through	through	[P:q.
J21:1210j	-	YTL	<bital>	-	.
J21:1210k	S	FOx	P	-	.
J21:1210m	-	YTR	<eital>	-	.P:q]Fr]Np]Po]Ns@:199]Ns:s]S]
J21:1210n	-	YF	+.	-	.
J21:1210p	-	RR	Hence	hence	[S[R:c.R:c]
J21:1220a	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1220b	-	VVZv	follows	follow	[Vz.Vz]
J21:1220c	-	CST	that	that	[Fn:s.
J21:1220d	-	AT	the	the	[Ns:s.
J21:1220e	-	NN1c	involution	involution	.
J21:1220f	-	II	within	within	[P.
J21:1220g	-	AT	the	the	[Ns.
J21:1220h	-	NN1c	bundle	bundle	.Ns]P]Ns:s]
J21:1220i	-	VMo	must	must	[Vcb.
J21:1220j	-	VB0	be	be	.Vcb]
J21:1220k	-	AT1	a	a	[Ns:e.
J21:1220m	-	NN1n	perspective	perspective	.
J21:1230a	-	NP1s	de	de	[Nns.
J21:1230b	-	NP1s	Jonquieres	Jonqui<egrave>res	.Nns]
J21:1230c	-	NN1c	involution	involution	.
J21:1230d	-	IO	of	of	[Po.
J21:1230e	-	NN1n	order	order	[Ns.
J21:1230f	-	FOx	<formul>	-	.Ns]Po]Ns:e]
J21:1230g	-	CC	and	and	[Fn+.
J21:1230h	-	AT	the	the	[Ns:s.
J21:1230i	-	JJ	invariant	invariant	.
J21:1230j	-	NN1c	locus	locus	.Ns:s]
J21:1230k	-	VMo	must	must	[Vc.
J21:1240a	-	VH0	have	have	.Vc]
J21:1240b	-	AT1	a	a	[Ns:o.
J21:1240c	-	JJ	multiple	multiple	.
J21:1240d	-	NN1n	line	line	.
J21:1240e	-	IO	of	of	[Po.
J21:1240f	-	NN1u	multiplicity	multiplicity	[Ns.
J21:1240g	-	LEe	either	either	[N.
J21:1240h	-	FOx	<formul>	-	.
J21:1240i	-	CCr	or	or	[N+.
J21:1240j	-	FOx	<formul>	-	.N+]N]Ns]Po]Ns:o]Fn+]Fn:s]S]
J21:1240k	-	YF	+.	-	.
J21:1240m	-	AT	The	the	[S[Ns:s.
J21:1240n	-	MDo	first	first	.
J21:1240p	-	NN1n	possibility	possibility	.Ns:s]
J21:1250a	-	VVZt	requires	require	[Vz.Vz]
J21:1250b	-	CST	that	that	[Fn%:o.
J21:1250c	-	EX	there	there	.
J21:1250d	-	VB0	be	be	[Vjb.Vjb]
J21:1250e	-	AT1	a	a	[Ns:s201.
J21:1250f	-	NN1n	line	line	.
J21:1250g	-	II	through	through	[P.
J21:1250h	-	YTL	<bital>	-	.
J21:1250i	S	FOx	P	-	.
J21:1250j	-	YTR	<eital>	-	.P]
J21:1250k	-	DDQr	which	which	[Fr[Dq:s201.Dq:s201]
J21:1250m	-	VVZv	meets	meet	[Vz.Vz]
J21:1260a	S	FOx	g	-	[N:o.N:o]
J21:1260b	-	II	in	in	[P:p.
J21:1260c	-	FOx	<formul>	-	[Np.
J21:1260d	-	NN2	points	point	.Np]P:p]Fr]Ns:s201]Fn%:o]
J21:1260e	-	YS	+;	-	.
J21:1260f	-	AT	the	the	[S-[Nj:s.
J21:1260g	-	MDo	second	second	.Nj:s]
J21:1260h	-	VVZt	requires	require	[Vz.Vz]
J21:1260i	-	CST	that	that	[Fn%:o.
J21:1260j	-	EX	there	there	.
J21:1260k	-	VB0	be	be	[Vjb.Vjb]
J21:1260m	-	AT1	a	a	[Ns:s203.
J21:1260n	-	NN1n	line	line	.
J21:1260p	-	II	through	through	[P.
J21:1270a	-	YTL	<bital>	-	.
J21:1270b	S	FOx	P	-	.
J21:1270c	-	YTR	<eital>	-	.P]
J21:1270d	-	DDQr	which	which	[Fr[Dq:s203.Dq:s203]
J21:1270e	-	VVZv	meets	meet	[Vz.Vz]
J21:1270f	S	FOx	g	-	[N:o.N:o]
J21:1270g	-	II	in	in	[P:p.
J21:1270h	-	FOx	<formul>	-	[Np.
J21:1270i	-	NN2	points	point	.Np]P:p]Fr]Ns:s203]Fn%:o]S-]S]
J21:1270j	-	YF	+.	-	.
J21:1270k	-	II	In	in	[S[P:r.
J21:1270m	-	DD1q	each	each	[Ns.
J21:1270n	-	NN1c	case	case	.Ns]P:r]
J21:1270p	-	YC	+,	-	.
J21:1270q	-	NN2	lines	line	[Np:S.
J21:1280a	-	IO	of	of	[Po.
J21:1280b	-	AT	the	the	[Np.
J21:1280c	-	NN2	bundles	bundle	.Np]Po]Np:S]
J21:1280d	-	VBR	are	be	[Vap.
J21:1280e	-	VVNt	transformed	transform	.Vap]
J21:1280f	-	IIb	by	by	[Pb:a.
J21:1280g	-	NN2	involutions	involution	[Np.
J21:1280h	-	II	within	within	[P.
J21:1280i	-	AT	the	the	[Np:205.
J21:1280j	-	NN2	pencils	pencil	.
J21:1280k	-	PPHS2	they	they	[Fr[Nap:s.Nap:s]
J21:1290a	-	VV0v	determine	determine	[V.V]
J21:1290b	-	YG	-	-	[o205.o205]
J21:1290c	-	IW	with	with	[P:w.
J21:1290d	-	AT	the	the	[Ns.
J21:1290e	-	JJ	multiple	multiple	.
J21:1290f	-	NN1c	secant	secant	.Ns]P:w]Fr]Np:205]P]Np]Pb:a]S]
J21:1290g	-	YF	+.	-	.
J21:1290h	-	II	In	in	[S[P:r.
J21:1290i	-	AT	the	the	[Ns.
J21:1290j	-	MDo	first	first	.
J21:1290k	-	NN1c	case	case	.Ns]P:r]
J21:1290m	-	AT	the	the	[Np:s.
J21:1290n	-	JJ	fixed	fixed	.
J21:1290p	-	NN2	elements	element	.
J21:1300a	-	II	within	within	[P.
J21:1300b	-	DD1q	each	each	[Ns.
J21:1300c	-	NN1c	pencil	pencil	.Ns]P]Np:s]
J21:1300d	-	VBR	are	be	[Vab.Vab]
J21:1300e	-	AT	the	the	[N:e.
J21:1300f	-	JJ	multiple	multiple	.
J21:1300g	-	NN1c	secant	secant	.
J21:1300h	-	CC	and	and	[Ns+:207.
J21:1300i	-	AT	the	the	.
J21:1300j	-	NN1n	line	line	.
J21:1300k	-	YG	-	-	[Tg[s207.s207]
J21:1300m	-	VVGv	joining	join	[Vg.Vg]
J21:1300n	-	AT	the	the	[Ns:o.
J21:1310a	-	NN1c	vertex	vertex	.
J21:1310b	-	YC	+,	-	.
J21:1310c	-	YTL	<bital>	-	.
J21:1310d	S	FOx	P	-	.
J21:1310e	-	YTR	<eital>	-	.
J21:1310f	-	YC	+,	-	.Ns:o]
J21:1310g	-	IIt	to	to	[P:q.
J21:1310h	-	AT	the	the	[Ns:209.
J21:1310i	-	NN1n	intersection	intersection	.
J21:1310j	-	IO	of	of	[Po.
J21:1310k	S	FOx	g	-	[N.
J21:1310m	-	CC	and	and	[Ns+.
J21:1310n	-	AT	the	the	.
J21:1310p	-	NN1c	plane	plane	.
J21:1310q	-	IO	of	of	[Po.
J21:1320a	-	AT	the	the	[Ns.
J21:1320b	-	NN1c	pencil	pencil	.Ns]Po]Ns+]N]Po]
J21:1320c	-	DDQr	which	which	[Fr[Dq:s209.Dq:s209]
J21:1320d	-	VDZ	does	do	[Vze.
J21:1320e	-	XX	not	not	.
J21:1320f	-	VV0i	lie	lie	.Vze]
J21:1320g	-	II	on	on	[P:p.
J21:1320h	-	AT	the	the	[Ns.
J21:1320i	-	JJ	multiple	multiple	.
J21:1320j	-	NN1c	secant	secant	.Ns]P:p]Fr]Ns:209]P:q]Tg]Ns+:207]N:e]S]
J21:1320k	-	YF	+.	-	.
J21:1320m	-	II	In	in	[S[P:r.
J21:1320n	-	AT	the	the	[Nj.
J21:1320p	-	MDo	second	second	.Nj]P:r]
J21:1320q	-	YC	+,	-	.
J21:1330a	-	AT	the	the	[Np:s.
J21:1330b	-	JJ	fixed	fixed	.
J21:1330c	-	NN2	elements	element	.Np:s]
J21:1330d	-	VBR	are	be	[Vab.Vab]
J21:1330e	-	AT	the	the	[Np:e211.
J21:1330f	-	NN2	lines	line	.
J21:1330g	-	DDQr	which	which	[Fr[Dq:s211.Dq:s211]
J21:1330h	-	VV0v	join	join	[V.V]
J21:1330i	-	AT	the	the	[Ns:o.
J21:1330j	-	NN1c	vertex	vertex	.
J21:1330k	-	YC	+,	-	.
J21:1330m	-	YTL	<bital>	-	.
J21:1330n	S	FOx	P	-	.
J21:1330p	-	YTR	<eital>	-	.
J21:1330q	-	YC	+,	-	.Ns:o]
J21:1330r	-	IIt	to	to	[P:q.
J21:1340a	-	AT	the	the	[Np:213.
J21:1340b	-	MC	two	two	.
J21:1340c	-	NN2	intersections	intersection	.
J21:1340d	-	IO	of	of	[Po.
J21:1340e	S	FOx	g	-	[N.
J21:1340f	-	CC	and	and	[Ns+.
J21:1340g	-	AT	the	the	.
J21:1340h	-	NN1c	plane	plane	.
J21:1340i	-	IO	of	of	[Po.
J21:1340j	-	AT	the	the	[Ns.
J21:1340k	-	NN1c	pencil	pencil	.Ns]Po]Ns+]N]Po]
J21:1340m	-	DDQr	which	which	[Fr[Dq:s213.Dq:s213]
J21:1340n	-	VD0	do	do	[Ve.
J21:1350a	-	XX	not	not	.
J21:1350b	-	VV0i	lie	lie	.Ve]
J21:1350c	-	II	on	on	[P:p.
J21:1350d	-	AT	the	the	[Ns.
J21:1350e	-	JJ	multiple	multiple	.
J21:1350f	-	NN1c	secant	secant	.Ns]P:p]Fr]Np:213]P:q]Fr]Np:e211]S]
J21:1350g	-	YF	+.	-	.
J21:1350h	-	AT	The	the	[S[Np:s.
J21:1350i	-	JJ	multiple	multiple	.
J21:1350j	-	NN2	secants	secant	.Np:s]
J21:1350k	-	YC	+,	-	.
J21:1350m	-	RR21	of	of	[R:m[RR=.
J21:1350n	-	RR22	course	course	.RR=]R:m]
J21:1350p	-	YC	+,	-	.
J21:1350q	-	VBR	are	be	[Vab.Vab]
J21:1360a	-	JJ	exceptional	exceptional	[J:e.J:e]
J21:1360b	-	CC	and	and	[S+.
J21:1360c	-	II	in	in	[P:r.
J21:1360d	-	DD1q	each	each	[Ns.
J21:1360e	-	NN1c	case	case	.Ns]P:r]
J21:1360f	-	VBR	are	be	[Vap.
J21:1360g	-	VVNt	transformed	transform	.Vap]
J21:1360h	-	II	into	into	[P:q.
J21:1360i	-	NN2	cones	cone	[Np.
J21:1360j	-	IO	of	of	[Po.
J21:1360k	-	NN1n	order	order	[Ns.
J21:1360m	-	FOx	<formul>	-	.Ns]Po]Np]P:q]S+]S]
J21:1360n	-	YF	+.	-	.O]
J21:1370a	-	YB	<minbrk>	-	[Oh.Oh]
J21:1370b	-	NN2	Observations	observation	[O[S[Np:S.
J21:1370c	-	JJ	similar	similar	[Jh.
J21:1370d	-	IIt	to	to	[P.
J21:1370e	-	DD2i	these	these	.P]Jh]Np:S]
J21:1370f	-	VMo	can	can	[Vcp.
J21:1370g	-	VB0	be	be	.
J21:1370h	-	VVNv	made	make	.Vcp]
J21:1370i	-	II	at	at	[P:p.
J21:1370j	-	DD1q	each	each	[Ns.
J21:1370k	-	NNL1n	point	point	.
J21:1370m	-	IO	of	of	[Po.
J21:1370n	S	FOx	g	-	.Po]Ns]P:p]S]
J21:1370p	-	YF	+.	-	.
J21:1380a	-	RR	Hence	hence	[S[R:c.R:c]
J21:1380b	S	FOx	g	-	[N:s.N:s]
J21:1380c	-	VMo	must	must	[Vc.
J21:1380d	-	VH0	have	have	.Vc]
J21:1380e	-	LEe	either	either	[N:o.
J21:1380f	-	AT1	a	a	.
J21:1380g	-	NN1n	regulus	regulus	.
J21:1380h	-	IO	of	of	[Po.
J21:1380i	-	FOx	<formul>	-	[Np[J.
J21:1380j	-	YH	+<hyphen>	-	.
J21:1380k	-	FA	+fold	fold	.J]
J21:1380m	-	NN2	secants	secant	.Np]Po]
J21:1380n	-	CCr	or	or	[Ns+.
J21:1390a	-	AT1	a	a	.
J21:1390b	-	NN1n	regulus	regulus	.
J21:1390c	-	IO	of	of	[Po.
J21:1390d	-	FOx	<formul>	-	[Np[J.
J21:1390e	-	YH	+<hyphen>	-	.
J21:1390f	-	FA	+fold	fold	.J]
J21:1390g	-	NN2	secants	secant	.Np]Po]Ns+]N:o]S]
J21:1390h	-	YF	+.	-	.
J21:1390i	-	RR	Moreover	moreover	[S[R:m.R:m]
J21:1390j	-	YC	+,	-	.
J21:1390k	-	CSi	if	if	[Fa:c.
J21:1390m	-	FOx	<formul>	-	[N:e.N:e]Fa:c]
J21:1390n	-	YC	+,	-	.
J21:1390p	-	ATn	no	no	[M:s.
J21:1390q	-	MC	two	two	.
J21:1390r	-	IO	of	of	[Po.
J21:1390s	-	AT	the	the	[Np.
J21:1390t	-	JJ	multiple	multiple	.
J21:1400a	-	NN2	secants	secant	.Np]Po]M:s]
J21:1400b	-	VMo	can	can	[Vc.
J21:1400c	-	VV0v	intersect	intersect	.Vc]S]
J21:1400d	-	YF	+.	-	.
J21:1400e	-	CSf	For	for	[Fa.
J21:1400f	-	CSi	if	if	[Fa:c.
J21:1400g	-	DAz	such	such	[D:e.D:e]
J21:1400h	-	VBDR	were	be	[Vwb.Vwb]
J21:1400i	-	AT	the	the	[Ns:s.
J21:1400j	-	NN1c	case	case	.Ns:s]Fa:c]
J21:1400k	-	YC	+,	-	.
J21:1400m	-	LEe	either	either	.
J21:1400n	-	AT	the	the	[Ns:s.
J21:1400p	-	NN1c	plane	plane	.
J21:1410a	-	IO	of	of	[Po.
J21:1410b	-	AT	the	the	[Np.
J21:1410c	-	MC	two	two	.
J21:1410d	-	NN2	lines	line	.Np]Po]Ns:s]
J21:1410e	-	VMd	would	will	[Vdc.
J21:1410f	-	VV0v	meet	meet	.Vdc]
J21:1410g	S	FOx	g	-	[N:o.N:o]
J21:1410h	-	II	in	in	[P:p.
J21:1410i	-	DAR	more	more	[Np[D.
J21:1410j	-	CSN	than	than	[P.
J21:1410k	-	YTL	<bital>	-	.
J21:1410m	S	FOx	k	-	.
J21:1410n	-	YTR	<eital>	-	.P]D]
J21:1410p	-	NN2	points	point	.Np]P:p]
J21:1410q	-	CCr	or	or	[Fa+.
J21:1410r	-	YC	+,	-	.
J21:1420a	-	RR	alternatively	alternatively	[R:m.R:m]
J21:1420b	-	YC	+,	-	.
J21:1420c	-	AT	the	the	[Ns:s.
J21:1420d	-	NN1n	order	order	.
J21:1420e	-	IO	of	of	[Po.
J21:1420f	-	AT	the	the	[Ns:215.
J21:1420g	-	NN1c	image	image	.
J21:1420h	-	NN1n	regulus	regulus	.
J21:1420i	-	IO	of	of	[Po.
J21:1420j	-	AT	the	the	[Ns.
J21:1420k	-	NN1c	pencil	pencil	.Ns]Po]
J21:1420m	-	YG	-	-	[Tn[S215.S215]
J21:1420n	-	VVNv	determined	determine	[Vn.Vn]
J21:1430a	-	IIb	by	by	[Pb:a.
J21:1430b	-	AT	the	the	[Np.
J21:1430c	-	MC	two	two	.
J21:1430d	-	NN2	lines	line	.Np]Pb:a]Tn]Ns:215]Po]Ns:s]
J21:1430e	-	VMd	would	will	[Vdcb.
J21:1430f	-	VB0	be	be	.Vdcb]
J21:1430g	-	RGf	too	too	[J:e.
J21:1430h	-	JJ	high	high	.J:e]Fa+]Fa]
J21:1430i	-	YF	+.	-	.
J21:1430j	-	CCB	But	but	[S+.
J21:1430k	-	CSi	if	if	[Fa:c.
J21:1430m	-	ATn	no	no	[Np:s.
J21:1430n	-	MC	two	two	.
J21:1430p	-	NN2	lines	line	.
J21:1430q	-	IO	of	of	[Po.
J21:1430r	-	AT	the	the	[Ns.
J21:1430s	-	NN1n	regulus	regulus	.
J21:1440a	-	IO	of	of	[Po.
J21:1440b	-	JJ	multiple	multiple	[Np.
J21:1440c	-	NN2	secants	secant	.
J21:1440d	-	IO	of	of	[Po.
J21:1440e	S	FOx	g	-	.Po]Np]Po]Ns]Po]Np:s]
J21:1440f	-	VMo	can	can	[Vc.
J21:1440g	-	VV0v	intersect	intersect	.Vc]Fa:c]
J21:1440h	-	YC	+,	-	.
J21:1440i	-	RTn	then	then	[Rsw:t.Rsw:t]
J21:1440j	-	AT	the	the	[Ns:s.
J21:1440k	-	NN1n	regulus	regulus	.Ns:s]
J21:1440m	-	VMo	must	must	[Vcb.
J21:1450a	-	VB0	be	be	.Vcb]
J21:1450b	-	JJ	quadratic	quadratic	[J:e.J:e]
J21:1450c	-	YC	+,	-	.
J21:1450d	-	CCr	or	or	[S+.
J21:1450e	-	II	in	in	[P:m.
J21:1450f	-	JBo	other	other	[Np.
J21:1450g	-	NN2	words	word	.Np]P:m]
J21:1450h	-	YC	+,	-	.
J21:1450i	S	FOx	g	-	[N:s.N:s]
J21:1450j	-	VMo	must	must	[Vcb.
J21:1450k	-	VB0	be	be	.Vcb]
J21:1450m	-	LEe	either	either	[N:e.
J21:1450n	-	AT1	a	a	.
J21:1450p	-	FOx	<formul>	-	.
J21:1450q	-	CCr	or	or	[Ns+.
J21:1450r	-	AT1	a	a	.
J21:1450s	-	FOx	<formul>	-	.Ns+]
J21:1460a	-	NN1c	curve	curve	.
J21:1460b	-	II	on	on	[P.
J21:1460c	-	AT1	a	a	[Ns.
J21:1460d	-	JJ	nonsingular	non<hyphen>singular	.
J21:1460e	-	JJ	quadric	quadric	.
J21:1460f	-	NN1c	surface	surface	.Ns]P]N:e]S+]S+]
J21:1460g	-	YF	+.	-	.O]
J21:1460h	-	YB	<minbrk>	-	[Oh.Oh]
J21:1460i	-	PPIS2	We	we	[O[S[Nap:s.Nap:s]
J21:1460j	-	RTo	now	now	[Rw:t.Rw:t]
J21:1460k	-	VV0v	observe	observe	[V.V]
J21:1460m	-	CST	that	that	[Fn:o.
J21:1470a	-	AT	the	the	[Ns:s217.
J21:1470b	-	NN1c	case	case	.
J21:1470c	-	II	in	in	[Fr[Pq:p.
J21:1470d	-	DDQr	which	which	[Dq:217.Dq:217]Pq:p]
J21:1470e	S	FOx	g	-	[N:s.N:s]
J21:1470f	-	VBZ	is	be	[Vzb.Vzb]
J21:1470g	-	AT1	a	a	[Ns:e.
J21:1470h	-	FOx	<formul>	-	.
J21:1470i	-	NN1c	curve	curve	.
J21:1470j	-	II	on	on	[P.
J21:1470k	-	AT1	a	a	[Njs.
J21:1470m	-	JJ	quadric	quadric	.Njs]P]Ns:e]Fr]Ns:s217]
J21:1470n	-	VBZ	is	be	[Vzb.Vzb]
J21:1470p	-	JJ	impossible	impossible	[J:e.J:e]
J21:1470q	-	CSi	if	if	[Fa:c.
J21:1480a	-	AT	the	the	[Ns:s.
J21:1480b	-	NN1c	complex	complex	.
J21:1480c	-	IO	of	of	[Po.
J21:1480d	-	JJ	singular	singular	[Np.
J21:1480e	-	NN2	lines	line	.Np]Po]Ns:s]
J21:1480f	-	VVZi	consists	consist	[Vz.Vz]
J21:1480g	-	RR	exclusively	exclusively	[R:m.R:m]
J21:1480h	-	IO	of	of	[Po:u.
J21:1480i	-	AT	the	the	[Np:219.
J21:1480j	-	NN2	lines	line	.
J21:1480k	-	DDQr	which	which	[Fr[Dq:s219.Dq:s219]
J21:1490a	-	VV0v	meet	meet	[V.V]
J21:1490b	S	FOx	g	-	[N:o.N:o]Fr]Np:219]Po:u]Fa:c]Fn:o]S]
J21:1490c	-	YF	+.	-	.
J21:1490d	-	CSf	For	for	[Fa.
J21:1490e	-	DDy	any	any	[Ns:s.
J21:1490f	-	NN1c	pencil	pencil	.
J21:1490g	-	II	in	in	[P.
J21:1490h	-	AT1	a	a	[Ns:221.
J21:1490i	-	NN1c	plane	plane	.
J21:1490j	-	YG	-	-	[Tg[s221.s221]
J21:1490k	-	VVGt	containing	contain	[Vg.Vg]
J21:1490m	-	AT1	a	a	[Ns:o.
J21:1490n	-	FOx	<formul>	-	[J.
J21:1490p	-	YH	+<hyphen>	-	.
J21:1490q	-	FA	+fold	fold	.J]
J21:1490r	-	NN1c	secant	secant	.
J21:1500a	-	IO	of	of	[Po.
J21:1500b	S	FOx	g	-	.Po]Ns:o]Tg]Ns:221]P]Ns:s]
J21:1500c	-	VHZ	has	have	[Vz.Vz]
J21:1500d	-	AT1	an	an	[Ns:o223.
J21:1500e	-	NN1c	image	image	.
J21:1500f	-	NN1n	regulus	regulus	.
J21:1500g	-	DDQr	which	which	[Fr[Dq:s223.Dq:s223]
J21:1500h	-	VVZv	meets	meet	[Vz.Vz]
J21:1500i	-	AT	the	the	[Ns:o.
J21:1500j	-	NN1c	plane	plane	.
J21:1500k	-	IO	of	of	[Po.
J21:1500m	-	AT	the	the	[Ns.
J21:1500n	-	NN1c	pencil	pencil	.Ns]Po]Ns:o]
J21:1510a	-	II	in	in	[P:p.
J21:1510b	-	FOx	<formul>	-	[Np.
J21:1510c	-	NN2	lines	line	.
J21:1510d	-	YC	+,	-	.
J21:1510e	-	REX	namely	namely	.
J21:1510f	-	AT	the	the	[N@.
J21:1510g	-	NN2	images	image	.
J21:1510h	-	IO	of	of	[Po.
J21:1510i	-	AT	the	the	[Np:225.
J21:1510j	-	NN2	lines	line	.
J21:1510k	-	IO	of	of	[Po.
J21:1510m	-	AT	the	the	[Ns.
J21:1510n	-	NN1c	pencil	pencil	.Ns]Po]
J21:1510p	-	DDQr	which	which	[Fr[Dq:s225.Dq:s225]
J21:1510q	-	VV0v	pass	pass	[V.V]
J21:1520a	-	II	through	through	[P:q.
J21:1520b	-	AT	the	the	[Ns.
J21:1520c	-	NN1n	intersection	intersection	.
J21:1520d	-	IO	of	of	[Po.
J21:1520e	S	FOx	g	-	[N.
J21:1520f	-	CC	and	and	[Ns+.
J21:1520g	-	AT	the	the	.
J21:1520h	-	JJ	multiple	multiple	.
J21:1520i	-	NN1c	secant	secant	.Ns+]N]Po]Ns]P:q]Fr]Np:225]Po]
J21:1520j	-	YC	+,	-	.
J21:1520k	-	CC	plus	plus	[Ns+.
J21:1520m	-	AT1	an	an	.
J21:1520n	-	JJ	additional	additional	.
J21:1530a	-	NN1c	component	component	.
J21:1530b	-	TO	to	to	[Ti[Vi.
J21:1530c	-	VV0v	account	account	.Vi]
J21:1530d	-	IF	for	for	[P:u.
J21:1530e	-	AT	the	the	[Np.
J21:1530f	-	NN2	intersections	intersection	.
J21:1530g	-	IO	of	of	[Po.
J21:1530h	-	AT	the	the	[Np.
J21:1530i	-	NN2	images	image	.
J21:1530j	-	IO	of	of	[Po.
J21:1540a	-	AT	the	the	[Np.
J21:1540b	-	JJ	general	general	.
J21:1540c	-	NN2	lines	line	.
J21:1540d	-	IO	of	of	[Po.
J21:1540e	-	AT	the	the	[Ns.
J21:1540f	-	NN1c	pencil	pencil	.Ns]Po]Np]Po]Np]Po]Np]P:u]Ti]Ns+]N@]Np]P:p]Fr]Ns:o223]Fa]
J21:1540g	-	YF	+.	-	.
J21:1540h	-	RR	However	however	[S[R:c.R:c]
J21:1540i	-	YC	+,	-	.
J21:1540j	-	CSi	if	if	[Fa:c.
J21:1540k	-	EX	there	there	.
J21:1540m	-	VBZ	is	be	[Vzb.Vzb]
J21:1540n	-	ATn	no	no	[Ns:s.
J21:1540p	-	JJ	additional	additional	.
J21:1540q	-	NN1c	complex	complex	.
J21:1550a	-	IO	of	of	[Po.
J21:1550b	-	JJ	singular	singular	[Np.
J21:1550c	-	NN2	lines	line	.Np]Po]Ns:s]Fa:c]
J21:1550d	-	YC	+,	-	.
J21:1550e	-	AT	the	the	[Ns:s.
J21:1550f	-	NN1n	order	order	.
J21:1550g	-	IO	of	of	[Po.
J21:1550h	-	AT	the	the	[Ns.
J21:1550i	-	NN1c	image	image	.
J21:1550j	-	NN1n	regulus	regulus	.
J21:1550k	-	IO	of	of	[Po.
J21:1550m	-	AT1	a	a	[Ns.
J21:1550n	-	NN1c	pencil	pencil	.Ns]Po]Ns]Po]Ns:s]
J21:1550p	-	VBZ	is	be	[Vzb.Vzb]
J21:1560a	-	RR	precisely	precisely	[R:m.R:m]
J21:1560b	-	FOx	<formul>	-	[N:e.N:e]S]
J21:1560c	-	YF	+.	-	.
J21:1560d	-	DD1i	This	this	[S[Ds:s.Ds:s]
J21:1560e	-	VVZt	contradicts	contradict	[Vz.Vz]
J21:1560f	-	AT	the	the	[Np:o.
J21:1560g	-	JJ	preceding	preceding	.
J21:1560h	-	NN2	observations	observation	.Np:o]
J21:1560i	-	YC	+,	-	.
J21:1560j	-	CC	and	and	[S+.
J21:1560k	-	RRz	so	so	[Rs:c.Rs:c]
J21:1560m	-	YC	+,	-	.
J21:1570a	-	II	under	under	[P:c.
J21:1570b	-	AT	the	the	[Ns.
J21:1570c	-	NN1c	assumption	assumption	.
J21:1570d	-	IO	of	of	[Po.
J21:1570e	-	DD1i	this	this	[Ns.
J21:1570f	-	NN1n	paper	paper	.Ns]Po]Ns]P:c]
J21:1570g	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:1570h	-	VMo	must	must	[Vc.
J21:1570i	-	VV0t	reject	reject	.Vc]
J21:1570j	-	AT	the	the	[Ns:o.
J21:1570k	-	NN1n	possibility	possibility	.
J21:1570m	-	CST	that	that	[Fn.
J21:1580a	S	FOx	g	-	[N:s.N:s]
J21:1580b	-	VBZ	is	be	[Vzb.Vzb]
J21:1580c	-	AT1	a	a	[Ns:e.
J21:1580d	-	FOx	<formul>	-	.
J21:1580e	-	NN1c	curve	curve	.
J21:1580f	-	II	on	on	[P.
J21:1580g	-	AT1	a	a	[Ns.
J21:1580h	-	JJ	quadric	quadric	.
J21:1580i	-	NN1c	surface	surface	.Ns]P]Ns:e]Fn]Ns:o]S+]S]
J21:1580j	-	YF	+.	-	.O]
J21:1580k	-	YB	<minbrk>	-	[Oh.Oh]
J21:1580m	-	VVGv	Continuing	continue	[O[S[Tg:b[Vg.Vg]
J21:1580n	-	IW	with	with	[P:u.
J21:1590a	-	AT	the	the	[Ns:227.
J21:1590b	-	NN1c	case	case	.
J21:1590c	-	II	in	in	[Fr[Pq:r.
J21:1590d	-	DDQr	which	which	[Dq:227.Dq:227]Pq:r]
J21:1590e	S	FOx	g	-	[N:s.N:s]
J21:1590f	-	VBZ	is	be	[Vzb.Vzb]
J21:1590g	-	AT1	a	a	[Ns:e.
J21:1590h	-	FOx	<formul>	-	.
J21:1590i	-	NN1c	curve	curve	.
J21:1590j	-	II	on	on	[P.
J21:1590k	-	AT1	a	a	[Njs.
J21:1590m	-	JJ	quadric	quadric	.
J21:1590n	-	YTL	<bital>	-	.
J21:1590p	S	FOx	Q	-	.
J21:1590q	-	YTR	<eital>	-	.Njs]P]Ns:e]Fr]Ns:227]P:u]Tg:b]
J21:1590r	-	YC	+,	-	.
J21:1590s	-	PPIS2	we	we	[Nap:s.Nap:s]
J21:1590t	-	MDo	first	first	[R:t.R:t]
J21:1600a	-	VV0v	observe	observe	[V.V]
J21:1600b	-	CST	that	that	[Fn:o.
J21:1600c	-	AT	the	the	[Ns:s.
J21:1600d	-	MDo	second	second	.
J21:1600e	-	NN1n	regulus	regulus	.
J21:1600f	-	IO	of	of	[Po.
J21:1600g	-	YTL	<bital>	-	.
J21:1600h	S	FOx	Q	-	.
J21:1600i	-	YTR	<eital>	-	.Po]Ns:s]
J21:1600j	-	VVZi	consists	consist	[Vz.Vz]
J21:1600k	-	RR	precisely	precisely	[R:m.R:m]
J21:1600m	-	IO	of	of	[Po:u.
J21:1610a	-	AT	the	the	[Np:229.
J21:1610b	-	NN2	lines	line	.
J21:1610c	-	DDQr	which	which	[Fr[Dq:s229.Dq:s229]
J21:1610d	-	VV0v	join	join	[V.V]
J21:1610e	-	AT	the	the	[Np:o.
J21:1610f	-	MC	two	two	.
J21:1610g	-	JJ	free	free	.
J21:1610h	-	NN2	intersections	intersection	.
J21:1610i	-	IO	of	of	[Po.
J21:1610j	S	FOx	g	-	[N.
J21:1610k	-	CC	and	and	[Np+.
J21:1610m	-	AT	the	the	.
J21:1610n	-	NN2	planes	plane	.
J21:1620a	-	II	through	through	[P.
J21:1620b	-	DDy	any	any	[Ms.
J21:1620c	-	MC1	one	one	.
J21:1620d	-	IO	of	of	[Po.
J21:1620e	-	AT	the	the	[Np.
J21:1620f	-	JJ	multiple	multiple	.
J21:1620g	-	NN2	secants	secant	.Np]Po]Ms]P]Np+]N]Po]Np:o]Fr]Np:229]Po:u]Fn:o]S]
J21:1620h	-	YF	+.	-	.
J21:1620i	-	CSf	For	for	[Fa.
J21:1620j	-	DD1q	each	each	[Ds:s.
J21:1620k	-	IO	of	of	[Po.
J21:1620m	-	DD2i	these	these	[Np.
J21:1620n	-	NN2	lines	line	.Np]Po]Ds:s]
J21:1630a	-	VVZv	meets	meet	[Vz.Vz]
J21:1630b	-	YTL	<bital>	-	.
J21:1630c	S	FOx	Q	-	[N:o.N:o]
J21:1630d	-	YTR	<eital>	-	.
J21:1630e	-	II	in	in	[P:p.
J21:1630f	-	MC	three	three	[Np.
J21:1630g	-	NN2	points	point	.
J21:1630h	-	YC	+,	-	.
J21:1630i	-	REX	namely	namely	.
J21:1630j	-	MC	two	two	[N@.
J21:1630k	-	NN2	points	point	.
J21:1630m	-	II	on	on	[P.
J21:1630n	S	FOx	g	-	.P]
J21:1630p	-	CC	and	and	[Ns+.
J21:1630q	-	MC1	one	one	.
J21:1640a	-	NNL1n	point	point	.
J21:1640b	-	II	on	on	[P.
J21:1640c	-	MC1	one	one	[Ms.
J21:1640d	-	IO	of	of	[Po.
J21:1640e	-	AT	the	the	[Np.
J21:1640f	-	JJ	multiple	multiple	.
J21:1640g	-	NN2	secants	secant	.Np]Po]Ms]P]Ns+]N@]Np]P:p]Fa]
J21:1640h	-	YF	+.	-	.O]
J21:1640i	-	YB	<minbrk>	-	[Oh.Oh]
J21:1640j	-	RTo	Now	now	[O[S*[Rw:t.Rw:t]
J21:1640k	-	VV0t	consider	consider	[V.V]
J21:1640m	-	AT1	an	an	[Ns:o231.
J21:1640n	-	JJ	arbitrary	arbitrary	.
J21:1650a	-	NN1n	line	line	.
J21:1650b	-	YC	+,	-	.
J21:1650c	-	YTL	<bital>	-	.
J21:1650d	S	FOx	l	-	.
J21:1650e	-	YTR	<eital>	-	.
J21:1650f	-	YC	+,	-	.
J21:1650g	-	YG	-	-	[Tg[s231.s231]
J21:1650h	-	VVGv	meeting	meet	[Vg.Vg]
J21:1650i	-	YTL	<bital>	-	.
J21:1650j	S	FOx	Q	-	[N:o.N:o]
J21:1650k	-	YTR	<eital>	-	.
J21:1650m	-	II	in	in	[P:p.
J21:1650n	-	MC	two	two	[Np.
J21:1650p	-	NN2	points	point	.
J21:1650q	-	YC	+,	-	.
J21:1650r	-	FOx	<formul>	-	[FOx&.
J21:1650s	-	CC	and	and	[FOx+.
J21:1650t	-	FOx	<formul>	-	.FOx+]FOx&]Np]P:p]Tg]Ns:o231]S*]
J21:1650u	-	YF	+.	-	.
J21:1650v	-	CSi	If	if	[S[Fa:c[Fa&.
J21:1660a	S	FOx	<agr>	-	[N:s.N:s]
J21:1660b	-	VBZ	is	be	[Vzb.Vzb]
J21:1660c	-	AT	the	the	[Ns:e233.
J21:1660d	-	JJ	multiple	multiple	.
J21:1660e	-	NN1c	secant	secant	.
J21:1660f	-	IO	of	of	[Po.
J21:1660g	S	FOx	g	-	.Po]
J21:1660h	-	DDQr	which	which	[Fr[Dq:s233.Dq:s233]
J21:1660i	-	VVZv	passes	pass	[Vz.Vz]
J21:1660j	-	II	through	through	[P:q.
J21:1660k	-	FOx	<formul>	-	.P:q]Fr]Ns:e233]
J21:1660m	-	CC	and	and	[Fa+.
J21:1670a	S	FOx	<bgr>	-	[N:s.N:s]
J21:1670b	-	VBZ	is	be	[Vzb.Vzb]
J21:1670c	-	AT	the	the	[Ns:e235.
J21:1670d	-	JJ	simple	simple	.
J21:1670e	-	NN1c	secant	secant	.
J21:1670f	-	IO	of	of	[Po.
J21:1670g	S	FOx	g	-	.Po]
J21:1670h	-	DDQr	which	which	[Fr[Dq:s235.Dq:s235]
J21:1670i	-	VVZv	passes	pass	[Vz.Vz]
J21:1670j	-	II	through	through	[P:q.
J21:1670k	-	FOx	<formul>	-	.P:q]Fr]Ns:e235]Fa+]Fa&]
J21:1670m	-	YC	+,	-	.
J21:1670n	-	CC	and	and	[Fa+.
J21:1680a	-	CSi	if	if	.
J21:1680b	-	FOx	<formul>	-	[N:s.N:s]
J21:1680c	-	VBR	are	be	[Vab.Vab]
J21:1680d	-	AT	the	the	[Np:e237.
J21:1680e	-	NN2	points	point	.
J21:1680f	-	II	in	in	[Fr[Pq:p.
J21:1680g	-	DDQr	which	which	[Dq:237.Dq:237]Pq:p]
J21:1680h	S	FOx	<agr>	-	[N:s.N:s]
J21:1680i	-	VVZv	meets	meet	[Vz.Vz]
J21:1680j	S	FOx	g	-	[N:o.N:o]Fr]Np:e237]Fa+]
J21:1680k	-	YC	+,	-	.
J21:1680m	-	CC	and	and	[Fa+.
J21:1680n	-	CSi	if	if	.
J21:1680p	-	FOx	<formul>	-	[N:s.N:s]
J21:1680q	-	VBZ	is	be	[Vzb.Vzb]
J21:1680r	-	AT	the	the	[Ns:e.
J21:1690a	-	NN1c	image	image	.
J21:1690b	-	IO	of	of	[Po.
J21:1690c	-	FOx	<formul>	-	.Po]
J21:1690d	-	II	on	on	[P.
J21:1690e	-	AT	the	the	[Ns.
J21:1690f	-	NN1c	generator	generator	.
J21:1690g	S	FOx	<bgr>	-	.Ns]P]Ns:e]Fa+]Fa:c]
J21:1690h	-	YC	+,	-	.
J21:1690i	-	PPH1	it	it	[Ni:S.Ni:S]
J21:1690j	-	VVZv	follows	follow	[Vz.Vz]
J21:1690k	-	CST	that	that	[Fn:s.
J21:1690m	-	AT	the	the	[Ns:s.
J21:1690n	-	NN1c	image	image	.
J21:1690p	-	IO	of	of	[Po.
J21:1700a	-	AT	the	the	[Ns.
J21:1700b	-	NN1n	line	line	.
J21:1700c	-	FOx	<formul>	-	.Ns]Po]Ns:s]
J21:1700d	-	VBZ	is	be	[Vzb.Vzb]
J21:1700e	-	FOx	<formul>	-	[N:e.N:e]Fn:s]S]
J21:1700f	-	YF	+.	-	.O]
