The commands for the ‘Figures’ menu.

    		 commands for drawing figures
     
    d-line (Figures menu) 
    A d-line (or disc line) through two points is that part of the arc of a circle that lies inside the disc boundary and cuts the disc boundary at right angles. To display a d-line, choose (that is, ‘click on’) two points p1 and p2 that lie inside the disc and then choose the disc circle itself. The points of intersection of the d-line and the disc circle are not shown as the points on the disc circle (or disc boundary or horizon as it sometimes called) are not part of the hyperbolic space. Note, the second point chosen can lie on the boundary of the disc.
    d-line (bnd points)
    Use this command if you want both points to lie on the disc circle. These are the points that the d-line, if extended, will cut the circle orthogonally.
    d-segment  (or arc) ( Figures menu) 
    Choose two points p1 and p2 and then the disc circle. The result is that part of the d-line joining the two points. This is a d-segment or part of a line, sometimes referred to as an arc, since Cabri will label some of the images of d-segments as an ‘arc’. 
    d-triangle  (Figures menu) 
    Choose three points p1, p2 and p3, inside the disc and then the disc circle. The result is the triangle as shown. Note that Cabri will label each of the sides of the triangle as an ‘arc’ (which they are in Euclidean space) but as sides of a d-triangle they are to be thought of as line or d-segments.
    d-quad  (Figures menu) 
    Choose four points p1 to p4 for the vertices of a quadrilateral and then the disc circle. Note that the points must be chosen in clockwise (or anti clockwise) order around the required quadrilateral, as the sides are drawn in sequence.This and the triangle object are included to facilitate the drawing of such figures. Figures with more sides can  be drawn by choosing the vertices and then connecting them by line segments.
    d-circle  (Figures menu) 
    Choose a centre point p1, a point p2 to be on the circumference of the circle, and then the disc circle. The result is the d-circle as shown, the centre point being the non Euclidean centre point of the circle. The figure can be changed by dragging either of the two defining points within the disc circle.
    horocycle
    These are circles in the disc that touch the disc circle at one and only one point.  Again note that this point is not a part of the curve in H2. Any two horocycles are equidistant from one another.
    hypercycle
    This curve is equidistant from a given d-line and extended it passes through the points on the disc that the d-line passes through. In this model the curve is a circular arc.
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