...consequently, O* being the centre of gravity, SO' is— r— ^,and VO'=VS— T\i SO'=— . That is, the distance of the centre of gravity of a circular arc...centre of the circle, is a fourth proportional to the arc the radius and the chord of the arc. When the arc becomes a semi-circle, the chord is then 2r double...

...known by applying the formulae, § 61. The distance of the centre of gravity of an arc of a circle from the centre of the circle is a fourth proportional to the radius, the chord, and the arc. POISSON, § 104. The centre of gravity of an arc of a cycloid, that...

...(/я=Нл:,- hence я : x я =R : d, or 2 Z : 2*=rR : d, that is, the distance of the centre of inertia of a circular arc from the centre of the circle is a fourth proportional to the arc, the chord of the arc, and radius. 1 86. When the arc ВАС becomes a semicircle, PC or x is equal...

...therefore / Let c represent the chord of the arc, then c=2r. sin. ^ ; whence and IX=re, wherefore the distance of the centre of gravity of a circular arc,...fourth proportional to the length of the arc, the chord, and the radius. By analogous processes, the centres of parallel forces may be found in other...

...its centre of parallel forces in the radius that divides it into two equal parts ; and its distance from the centre of the circle is a fourth proportional to the arc, the chord, and two thirds of the radius. The distance of the centre of parallel forces of a parabola,...

...equation of the curve referred to the axes AX, AY is so that the distance of the centre of gravity from the centre of the circle is a fourth, proportional to the arc, the radius, and the chord of the arc. When the arc is a semicircle the chord is double the radius,...

...lx\~ac; ACL from which it appears that a;> , the distance of the centre of gravity of an arc of a circle from the centre of the circle, is a fourth proportional to the radius, the chord, and the arc. 71. As the equation of a plane curve makes known one of the two variables...

...a circle is on the radius which bisects the arc, at a point, the distance of which from the centra of the circle is a fourth proportional to the length of the arc, Us chord, and radius. 4° The area of a parallelogram. The centre of gravity of the area of a parallelogram...

...gravity of the arc of a circle is on the radius which bisects the arc, at a point, the distance of which from the centre of the circle is a fourth proportional to the length of the arc, its chord, and radius. 4° The area of a parallelogram. The centre of gravity of the area of a parallelogram...

...points F and E of the arc. Now, 2asin.i(—) = chord ofEAF=C, .•.Jxd$ = aC, .-.G1 = ^ ...... (23). The distance of the centre of gravity of a circular arc from the centre of the circle is therefore a fourth proportional to the length of the arc, the length of the chord, and the radius of...