The Pascal Hexagram.
By Miss Christine Ladd, Johns Hopkins University.
I wish to propose a new notation for the lines and points connected with the Pascal Hexagram, to give a brief account of the discoveries of Veronese on the subject and to develop a few additional properties of the figure.
The vertices of the hexagon inscribed in the comic, 
are 
the lines tangent to the conic at these vertices respectively are 
In general, a large letter will represent a point, a small letter a line. Lines joining vertices of the inscribed hexagon are called fundamental lines; intersections of sides of the circumscribed hexagon are called fundamental points. The intersection of the two fundamental lines 
is called 
the line joining two fundamental points, 
is called 
It is evident that 
is the pole of 
There are 
points 
and lines 
The Pascal line obtained by taking the vertices of the hexagon in the order 
is called 
It passes through the points 
Similarly, the intersection of the lines 
is the Brianchon point 
of the hexagon 
the pole of
The three Pascal lines which meet in a Steiner point are (Salmon's Comic Sections, 5th ed., note, p. 361) 
We shall call the Steiner point in which they meet 
In this symbol, the relative cyclic order of the letters in each group of three is all that it is necessary to observe; for instance, 
and 
are the same as Given a 
point, the 
lines through it are obtained by taking one group of three in a fixed order for the odd letter and permuting cyclically the other group of three for the oven letters. The Pascals which pass through the conjugate point are 
and the symbol of that point is 
hence two
