Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 307
gth of the diameter; its end points, theextremities of the diameter. Problem. What is the locus of the mid-points of a set ofparallel chords of an ellipse ? i . In the special case of a circle, the locus is a diameter, con-sidered as a line-segment. This is true, also, for the generalellipse. For,… … Fig. 1 (1) b\ a2 and let X (=?t: 0) be the slope of the chords. Consider a variablechord of slope X moving always parallel to itself. Its mo- 288 DIAMETERS. POLES AND POLARS 289 tion we express analytically by taking jS, its intercept on theaxis of y, as auxiliary variable. The equation of the…
