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 v
... Third Books ,. Exercises , 61 84 95 BOOK IV . Proportions of Figures - Measurement of Areas , 97 Problems relating to the Fourth Book , 133 Exercises . 140 BOOK V. Regular Polygons - Measurement of the Circle , Exercises , 142 163 BOOK ...
... Third Books ,. Exercises , 61 84 95 BOOK IV . Proportions of Figures - Measurement of Areas , 97 Problems relating to the Fourth Book , 133 Exercises . 140 BOOK V. Regular Polygons - Measurement of the Circle , Exercises , 142 163 BOOK ...
Page 10
... third power . The Radical Sign , V : Thus , VA , B , indicate that the square root of A , and the cube root of B , are to be taken . When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ...
... third power . The Radical Sign , V : Thus , VA , B , indicate that the square root of A , and the cube root of B , are to be taken . When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ...
Page 26
... third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , is greater than C the distance measured on ...
... third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , is greater than C the distance measured on ...
Page 27
... third , and the difference of any two must be less than the third . PROPOSITION VIII . THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two ...
... third , and the difference of any two must be less than the third . PROPOSITION VIII . THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two ...
Page 28
... third sides are unequal ; and the greater side belongs to the triangle which has the greater included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the angle D : then is BC ...
... third sides are unequal ; and the greater side belongs to the triangle which has the greater included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the angle D : then is BC ...
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Common terms and phrases
ABē ACē altitude angle is equal apothem Applying logarithms axis base and altitude base multiplied bisects centre chord circumference cone consequently convex surface corresponding cosec cosine cotangent cylinder denote diagonals diameter distance divided draw drawn edges equal altitudes equal in volume equilateral feet find the area formula frustum given line given point greater hence homologous hypothenuse included angle inscribed circle inscribed polygon intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROBLEM.-To PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium segment similar sine slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices 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.