Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 31
Page vii
... Circle , ...... ... To find the Length of an Arc , .. Area of a Circle , ... Area of a Sector , Area of a Segment ,. Area of a Circular Ring ,. 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
... Circle , ...... ... To find the Length of an Arc , .. Area of a Circle , ... Area of a Sector , Area of a Segment ,. Area of a Circular Ring ,. 130 130 131 131 132 138 Area of the Surface of a Prism , Area of CONTENTS . vii.
Page viii
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone ,. Area of the Surface of a Sphere ,. Area of a Zone , Area of a Spherical Polygon , .. Volume of a Prism , Volume of a Pyramid , .. PAGE 134 134 135 136 137 137 ...
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone ,. Area of the Surface of a Sphere ,. Area of a Zone , Area of a Spherical Polygon , .. Volume of a Prism , Volume of a Pyramid , .. PAGE 134 134 135 136 137 137 ...
Page 134
... . If DC is made equal to DB , DX is a third pro- portional to DA and DB , or to A and B. PROBLEM III . To construct a mean proportional between two 134 GEOMETRY . Area of the Surface of a Prism, Area of the Surface of a Pyramid,
... . If DC is made equal to DB , DX is a third pro- portional to DA and DB , or to A and B. PROBLEM III . To construct a mean proportional between two 134 GEOMETRY . Area of the Surface of a Prism, Area of the Surface of a Pyramid,
Page 189
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
Page 190
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
Other editions - View all
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.