...still stronger reason CF^> CI. But CF = CO, since the chords AB, DE, are equal. Therefore CG > CI, and of two unequal chords the less is at the greater distance from the centre. THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fig. 54. radius AC, is a tangent...

...circumference can pass through three given points. THEOREM. 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (Jig. 53). Bisect Fig. 33: these chords by the perpendicular...

...circumference can pass through three given points. THEOREM. o 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (fig. 53). Bisect Fig. 53. these chords by the perpendicular...

...would make one and the same circumference. THEOREM. 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (fig. 53). Bisect Fig. 53. these chords by the perpendicular...

...still stronger reason CF > CI. But CF = CG, since the chords AB, DE, are equal. Therefore CG > CI, and of two unequal chords the less is at the greater distance from the centre. THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fig. radius AC, is a tangent...

...common points, they must have the same centre, and form one and the same circumference. THEOREM. 109. Two equal chords are equally distant from the centre...the less is at the greater distance from the centre. First. Suppose the chord AB= DE. Bisect those chords by the perpendiculars CF, CG, and draw the radii...

...circumferences passing through the same three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally...the less is at the greater distance from the centre. 'First. Suppose the chord AB — DE. Bisect these chords by the perpendiculars CF, CG, and draw the...

...circumferences passing through the same three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; andofttno unequal chords, the less is at the greater distance from tfi* wntre First. Suppose the...

...III. 47 PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; andoftwo unequal chords, the less is at the greater distance from the centre. First. Suppose the chard AB = DE. Bisect these chords by the perpendiculars CF, CG, and draw the radii...

...three points; which has been shown by the proposition to be impossible. PROPO8ITION VIII. THEOREM. equal chords are equally distant from the centre ;...the less is at the greater distance from the centre. First. Suppose the chord AB = DE. Bisect these chords by the perpendiculars CF, CG, and draw the radii...