Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 79
... quadrant , is taken as a unit . If , therefore , any angle is measured by one half or two thirds of a quadrant , it is equal to one half or two thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by ...
... quadrant , is taken as a unit . If , therefore , any angle is measured by one half or two thirds of a quadrant , it is equal to one half or two thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by ...
Page 81
... quadrant ( P. XVII . , S. ) . Cor . 3. Any angle BAC , inscribed in a segment greater than a semicircle , is acute ; for it is measured by half the arc BOC , less than a semi - circum- ference . Any angle BOC , inscribed in a seg- ment ...
... quadrant ( P. XVII . , S. ) . Cor . 3. Any angle BAC , inscribed in a segment greater than a semicircle , is acute ; for it is measured by half the arc BOC , less than a semi - circum- ference . Any angle BOC , inscribed in a seg- ment ...
Page 94
... quadrant or quarter of a circumference , as CD , is , for convenience , divided into 90 equal parts , each of which is called a degree . A degree is denoted by the symbol ° ; thus , 25 ° is read 25 degrees , etc. Since a quad- rant ...
... quadrant or quarter of a circumference , as CD , is , for convenience , divided into 90 equal parts , each of which is called a degree . A degree is denoted by the symbol ° ; thus , 25 ° is read 25 degrees , etc. Since a quad- rant ...
Page 254
... 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 255
... quadrant DFA round the point D , its extremity A will describe an arc of a great circle . PROPOSITION IV . THEOREM ... quadrants , the lines OD , OE , are perpendicular to OA , BOOK IX . 255.
... quadrant DFA round the point D , its extremity A will describe an arc of a great circle . PROPOSITION IV . THEOREM ... quadrants , the lines OD , OE , are perpendicular to OA , BOOK IX . 255.
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence