Elements of Geometry and Trigonometry |
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Page 4
... table of logarithms and logarithmic sines , and to apply the principles of geometry to the mensuration of sur- faces and solids . Military Academy , West Point , March , 1834 . CONTENTS . BOOK I. 9 The principles , BOOK II iv PREFACE .
... table of logarithms and logarithmic sines , and to apply the principles of geometry to the mensuration of sur- faces and solids . Military Academy , West Point , March , 1834 . CONTENTS . BOOK I. 9 The principles , BOOK II iv PREFACE .
Page 127
... face , and ascertain if it touches the surface throughout its whole extent . PROPOSITION II . THEOREM . Two straight lines , which intersect each other , lie in the same plane , and determine its position . Let AB , AC , be two straight ...
... face , and ascertain if it touches the surface throughout its whole extent . PROPOSITION II . THEOREM . Two straight lines , which intersect each other , lie in the same plane , and determine its position . Let AB , AC , be two straight ...
Page 139
... face produced can ever meet the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude . PROPOSITION XXI . THEOREM . If two solid angles are contained by three plane ...
... face produced can ever meet the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude . PROPOSITION XXI . THEOREM . If two solid angles are contained by three plane ...
Page 142
... faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a polyedron is called the side , or edge of the polyedron . 3. The prism is a solid bounded by ...
... faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a polyedron is called the side , or edge of the polyedron . 3. The prism is a solid bounded by ...
Page 143
... faces are rectangles . 9. Among rectangular parallelopipedons , we distinguish the cube , or regular hexaedron ... face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the ...
... faces are rectangles . 9. Among rectangular parallelopipedons , we distinguish the cube , or regular hexaedron ... face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex