...to each other as the squares of their homologous sides. PROPOSITION X. BOOK V. THEOREMS. PROPOSITION I. If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle...

...regular polygon to A D. Therefore — 349. COROLLARY. A regular polygon may have any number of sides. If the circumference of a circle be divided into any number of equal parts, the lines joining the points of division form an inscribed equilateral polygon. How does the number...

...That is, the polygon is equiangular. Therefore, the polygon is regular (?) (416). QEU 418. THEOREM. If the circumference of a circle be divided into any number of equal arcs, and the chords of these arcs be drawn, they will form an inscribed regular polygon. Proof: Chords...

...each of the arcs, AB, BC, etc.? How many degrees are there in each angle? PLANE GEOMETRY 419. THEOREM. If the circumference of a circle be divided into any number of equal parts, and tangents be drawn, at the several points of division, they will form a circumscribed regular polygon....

...(?). That is, the polygon is equiangular. Therefore, the polygon is regular (?) (416). 418. THEOREM. If the circumference of a circle be divided into any number of equal arcs, and the chords of these arcs be drawn, they will form an inscribed regular polygon. Proof: Chords...

...then the joining lines form a regular polygon inscribed in the circle (Of. Euc. IV. 11) 382 Pn.3. — If the circumference of a circle be divided into any number of equal parts, and if tangents to the circle be drawn at the points of division, then these tangents form a regular polygon...