...that if r be the radius of the circle, its circumference will equal 2 тгг, let ÀCB (fig. 1.) be an angle at the centre of a circle subtended by an arc equal to the radius of the circle ; then, since (Euclid, VI. 33) angles at the centre of the same circle are...

...as '005, or rr^: , that 1 000 is, the 200th part of a unit. PROB. 7. To find the numerical value of the angle at the centre of a circle subtended by an arc equal to the radius. By (240) we know, that the length of an arc subtending an angle of A" at the centre therefore,...

...an arc equal to the radius*. If U° represent that angle, then by equation (1), * К АС В be an angle at the centre of a circle, " subtended by an arc equal to the radius of the circle, then, since by the 33rd Proposition of the 6th Book of Euclid, the angles...

...the 90th part of a right angle is taken for the unit of angular measure, to find its measure where the angle at the centre of a circle, subtended by an arc equal to the radius of the circle, is taken for the unit, and conversely. The numerical value of ir, the ratio...

...second conclusion. Again: On the Orthodox theory, 57-2957795 1 &c. is the number of degrees contained in the angle at the centre of a circle subtended by an arc equal to radius ; but for the purpose of my argument I may take 57-29573 as a sufficiently close approximation. Now,...

...Mathematician, that -^ = 3-125 (which is Mr. Smith-s o But further : The number of degrees contained in an angle at the centre of a circle subtended by an arc equal to radius is —, jT and on the theory that 8 circumferences are exactly equal to 25 diameters = - ". • = 57-6...

...a circle, of which the diameter is unity. But he adds that " the number of degrees contained in an angle at the centre of a circle, subtended by an arc equal to the radius, is — ; and on the theory that 8 circumferences of a circle , TT are exactly equal to...

...intercepts the adopted unit of arc 27 XIV. To find the number of degrees, minutes, and seconds in an angle at the centre of a circle subtended by an arc equal to the radius 30 EXERCISES (3) 32 PART II.—SURFACES. I. PLANE SURFACES. I. To find the area of a rectangle,...

...Art. 54, II.). In the circular measure of an angle and its intercepted arc, the unit of angle is an angle at the centre of a circle, subtended by an arc equal to the radius of the circle ; and this arc is the unit of arc. 79. The angle at the centre of any circle...

...radius of the circle is called the circular measure of tho angle. The unit angle in circular measure is the angle at the centre of a circle subtended by an arc equal in length to the radius. Angles may l>e compared by means of certain functions which we proceed to...