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 158
... of the plane , that line will lie wholly in the plane . Scholium . If any two points of a plane be joined by a straight line , the plane may be turned about that line as an axis , so as to take an infinite number of 158 GEOMETRY .
... of the plane , that line will lie wholly in the plane . Scholium . If any two points of a plane be joined by a straight line , the plane may be turned about that line as an axis , so as to take an infinite number of 158 GEOMETRY .
Page 159
Adapted to the Course of Mathematical Instruction in the United States Charles Davies. axis , so as to take an infinite number of positions . Hence , we infer that an infinite number of planes may be passed through a given straight line ...
Adapted to the Course of Mathematical Instruction in the United States Charles Davies. axis , so as to take an infinite number of positions . Hence , we infer that an infinite number of planes may be passed through a given straight line ...
Page 180
... axis of the pyramid . 12 The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which ...
... axis of the pyramid . 12 The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which ...
Page 210
... axis . E P Thus , if the rectangle ABCD be turned about the side AB , as an axis , it will generate the cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite ...
... axis . E P Thus , if the rectangle ABCD be turned about the side AB , as an axis , it will generate the cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite ...
Page 211
... axes of similar cylinders are proportional to the radii of their bases ( B. IV . , D. 1 ) ; they are also proportional to any other homologous lines of the cylinders . 3 ... axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
... axes of similar cylinders are proportional to the radii of their bases ( B. IV . , D. 1 ) ; they are also proportional to any other homologous lines of the cylinders . 3 ... axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
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Common terms and phrases
AB² AC² 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