 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...therefore their surfaces are as the squares of the circumferences. Cor. 2. It follows also, that similar arcs are to each other as the radii of the circles to which they belong, for they subtend equal angles at the centres (Def. 2. B. VI.) and each angle is to four right angles... | |
 | Denison Olmsted - Physics - 1838 - 376 pages
...infinitum, then the polygons ABCD, abed, become similar curves, in falling down which no velocity is lost. Suppose the curves to be circular arcs; then, since...to each other as the square roots of their radii. THE PENDULUM. 170. DEFINITIONS.—A Pendulum is a body suspended by a right line from any point, and... | |
 | Charles William Hackley - Trigonometry - 1838 - 338 pages
...of itude will be measured he arc ia of the equator, and since (Geom., Prop. 11, Cor. B. 5,) similar arcs are to each other as the radii of the circles to which they belong, we have CB : ci : : dist. BD : diff. long. ia. But CB is the cosine of the latitude IB to the radius... | |
 | Denison Olmsted - Physics - 1844 - 618 pages
...infinitum, then the polygons ABCD, abed, become similar curves, in falling down which no velocity is lost. Suppose the curves to be circular arcs; then, since...to each other as the square roots of their radii. THE PENDULUM. 170. DEFINITIONS.—A Pendulum is a body suspended by a right line from any point, and... | |
 | Denison Olmsted, Ebenezer Strong Snell - Physics - 1845 - 612 pages
...which no velocity is lost. Suppose the curves to be circular arcs; then, since similar circular ares are to each other as the radii of the circles to which...they belong, the times of descending through these ares will be to each other as the square roots of their radii. THE PENDULUM. 170. DEFINITIONS. —... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...therefore their surfaces are as the squares of the circumferences. Cor. 2. It follows, also, that similar arcs are to each other as the radii of the circles to which they belong ; for they subtend equal angles at the centres (B. Ill, Def. 12), and each angle is to four right angles... | |
 | John Radford Young - Nautical astronomy - 1848 - 412 pages
...longitude will be measured by the arc Id of the equator, and since (Geom., prop. 12, Cor. 2, B. 7) similar arcs are to each other as the radii of the circles to which they belong, we have cB : CI :: dist. BD : diff. long. IQ.. But cB is the cosine of the latitude IB to the radius... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...therefore their surfaces are as the squares of the circumferences. Cor. 2. It follows, also, that similar arcs are to each other as the radii of the circles to which they belong; for they subtend equal angles at the centres, (B. III. Def. 12,) and each angle is to four right-angles... | |
 | Henry Barnard - Military education - 1862 - 412 pages
...5, I0, 20, 40 sides. Begular polygons of tho same number of sides are similar, and their perimeters are to each other as the radii of the circles to which they are inscribed or circumscribed.—The circumferences of circles are to each other as their radii. To... | |
 | Education - 1862 - 752 pages
...of 15, 80, 60 sides. Kegular polygons of the same number of sides are similar, and their perimeters are to each other as the radii of the circles to which they are inscribed or circumscribed.— The circumferences of circles are to each other as their radii.... | |
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ABCD, abed, become similar curves, in falling down which no velocity is lost. Suppose the curves to be circular arcs; then, since similar circular arcs are to each other as the radii of the circles to which they belong, the times of descending through... 
