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 165
... faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two straight lines , one in each face , and both perpendicular to the edge at the same point . A diedral angle may be acute , obtuse , or ...
... faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two straight lines , one in each face , and both perpendicular to the edge at the same point . A diedral angle may be acute , obtuse , or ...
Page 166
... faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but three faces , is called a triedral B S angle ...
... faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but three faces , is called a triedral B S angle ...
Page 183
... faces in the lines AB , BC , CD , DE , and EA . From any point within the polygon thus formed , as 0 , draw the straight lines OA , OB , OC , OD , and OE . B m $ D We then have two sets of triangles , one set having a common vertex S ...
... faces in the lines AB , BC , CD , DE , and EA . From any point within the polygon thus formed , as 0 , draw the straight lines OA , OB , OC , OD , and OE . B m $ D We then have two sets of triangles , one set having a common vertex S ...
Page 184
... faces are each less than two right angles . PROPOSITION XXI . THEOREM . If the plane angles formed by the edges of ... faces ASB and CSB , the lines BA and BC , respect- ively perpendicular to SB : then the angle ABC measures the ...
... faces are each less than two right angles . PROPOSITION XXI . THEOREM . If the plane angles formed by the edges of ... faces ASB and CSB , the lines BA and BC , respect- ively perpendicular to SB : then the angle ABC measures the ...
Page 185
... faces . Draw AC and DF . The right - angled triangles SBA and TED , have the side SB equal to TE , and the angle ASB ... faces ASB and BSC is equal to that of the faces DTE and ETF , then are the remaining plane angles , ASC and DTF ...
... faces . Draw AC and DF . The right - angled triangles SBA and TED , have the side SB equal to TE , and the angle ASB ... faces ASB and BSC is equal to that of the faces DTE and ETF , then are the remaining plane angles , ASC and DTF ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.