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 62
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet ... semi - circle · ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB ...
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet ... semi - circle · ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB ...
Page 79
... semi - circumference BOD , or by 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 ...
... semi - circumference BOD , or by 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 ...
Page 81
... half of the arc AMC . M For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVI . , S. ) ; the angle DAC is measured by half of the arc DC ᎠᏟ ( P. XVIII ...
... half of the arc AMC . M For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVI . , S. ) ; the angle DAC is measured by half of the arc DC ᎠᏟ ( P. XVIII ...
Page 121
... semi - circumference BAC , chords be drawn to the B D extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right angled tri- angle , right - angled at A ; and from what was ...
... semi - circumference BAC , chords be drawn to the B D extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right angled tri- angle , right - angled at A ; and from what was ...
Page 223
... difference of their radii , one is wholly within the other : 6o . When this distance is equal to zero , they have a common centre , or , are concentric . DEFINITIONS . 1o . If a semi - circumference be BOOK VIII . 223.
... difference of their radii , one is wholly within the other : 6o . When this distance is equal to zero , they have a common centre , or , are concentric . DEFINITIONS . 1o . If a semi - circumference be BOOK VIII . 223.
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Common terms and phrases
ABē ACē 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence