I. If  two  strait  lines  falling  upon  another  strait  line  be  parallel,
the  lines  reflected  from  them  shall  also  be  parallel. — 2. If
two  strait  lines  drawn  from  one  point  fall  upon  another
strait  line,  the  lines  reflected  from  them,  if  they  be  drawn  out
the  other  way,  will  meet  in  an  angle  equal  to  the  angle  made
by  the  lines  of  incidence. — 3. If  two  strait  parallel  lines,
drawn  not  oppositely,  but  from  the  same  parts,  fall  upon  the
circumference  of  a  circle,  the  lines  reflected  from  them,  if
produced  they  meet  within  the  circle,  will  make  an  angle
double  to  that  which  is  made  by  two  strait  lines  drawn  from
the  centre  to  the  points  of  incidence. — 4. If  two  strait  lines
drawn  from  the  same  point  without  a  circle  fall  upon  the
circumference,  and  the  lines  reflected  from  them  being  pro
duced  meet  within  the  circle,  they  will  make  an  angle  equal
to  twice  that  angle,  which  is  made  by  two  strait  lines  drawn
from  the  centre  to  the  points  of  incidence,  together  with  the
angle  which  the  incident  lines  themselves  make. — 5. If  two
strait  lines  drawn  from  one  point  fall  upon  the  concave  cir
cumference  of  a  circle,  and  the  angle  they  make  be  less  than
twice  the  angle  at  the  centre,  the  lines  reflected  from  them  and
meeting  within  the  circle  will  make  an  angle,  which  being
added  to  the  angle  of  the  incident  lines  will  be  equal  to
twice  the  angle  at  the  centre. — 6. If  through  any  one  point
two  unequal  chords  be  drawn  cutting  one  another,  and  the
centre  of  the  circle  be  not  placed  between  them,  and  the
lines  reflected  from  them  concur  wheresoever,  there  cannot
through  the  point,  through  which  the  two  former  lines  were
drawn,  be  drawn  any  other  strait  line  whose  reflected  line
shall  pass  through  the  common  point  of  the  two  former
lines  reflected. — 7. In  equal  chords  the  same  is  not  true. —
8. Two  points  being  given  in  the  circumference  of  a  circle,  to
draw  two  strait  lines  to  them,  so  that  their  reflected  lines
may  contain  any  angle  given. — 9. If  a  strait  line  falling  upon
the  circumference  of  a  circle  be  produced  till  it  reach  the


CONCERNING  BODY. 