Elements of Geometry and Trigonometry |
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Page 77
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will two - thirds of a right angle . be equal to one - half or PROPOSITION XVIII . THEOREM . An inscribed angle is ...
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will two - thirds of a right angle . be equal to one - half or PROPOSITION XVIII . THEOREM . An inscribed angle is ...
Page 79
... quadrant ( P. XVII . , S. ) . • Cor . 3. Any angle BAC , in- scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in a ...
... quadrant ( P. XVII . , S. ) . • Cor . 3. Any angle BAC , in- scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in a ...
Page 239
... quadrant ( B. III . , P. XVII . , S. ) : hence , the two poles of a great circle are at equal distances from the circumference . Cor . 2. The two poles of a small circle are at unequal distances from the circumference , the sum of the ...
... quadrant ( B. III . , P. XVII . , S. ) : hence , the two poles of a great circle are at equal distances from the circumference . Cor . 2. The two poles of a small circle are at unequal distances from the circumference , the sum of the ...
Page 242
... quadrant • the point C being the pole of the arc DE , the distance CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
... quadrant • the point C being the pole of the arc DE , the distance CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
Page 251
... quadrants . For , since the arcs AB and AC are perpen- B dicular to BC , each must pass through its pole ( P. III . , Cor . 3 ) : hence , their intersection A is that pole , and consequently , AB and AC are quadrants . If the angle A is ...
... quadrants . For , since the arcs AB and AC are perpen- B dicular to BC , each must pass through its pole ( P. III . , Cor . 3 ) : hence , their intersection A is that pole , and consequently , AB and AC are quadrants . If the angle A is ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence