Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 be equal to one - half or two - thirds of a right angle . 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 be equal to one - half or two - thirds of a right angle . 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 , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The angles opposite the equal sides are right angles ( P. III . , C. 3 ) : hence , the sides AB and AC are quadrants . B If the angle ...
... quadrants , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The angles opposite the equal sides are right angles ( P. III . , C. 3 ) : hence , the sides AB and AC are quadrants . B If the angle ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following