Elements of Geometry and Trigonometry |
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Page 126
... plane . 2. A line is parallel to a plane , when it cannot meet that plane , to whatever distance both be produced . Conversely , the plane is parallel to the line . 3. Two planes are parallel to each other , when they cannot meet , to ...
... plane . 2. A line is parallel to a plane , when it cannot meet that plane , to whatever distance both be produced . Conversely , the plane is parallel to the line . 3. Two planes are parallel to each other , when they cannot meet , to ...
Page 127
... plane , and partly out of it . For , by the definition of a plane , when a straight line has two points common with a plane , it lies wholly in that plane . Scholium . To discover whether a surface is plane , it is ne- cessary to apply ...
... plane , and partly out of it . For , by the definition of a plane , when a straight line has two points common with a plane , it lies wholly in that plane . Scholium . To discover whether a surface is plane , it is ne- cessary to apply ...
Page 128
... planes . This line will lie wholly in the plane AB , and also wholly in the plane CD ( Book 1. Def . 6. ) : therefore it will be in both planes at once , and conse- quently is their common intersection . C E B F PROPOSITION IV . THEOREM ...
... planes . This line will lie wholly in the plane AB , and also wholly in the plane CD ( Book 1. Def . 6. ) : therefore it will be in both planes at once , and conse- quently is their common intersection . C E B F PROPOSITION IV . THEOREM ...
Page 129
... plane , but that it always must be so , when ever it is perpendicular to two straight lines drawn in the plane ; which proves the first Definition to be accurate . Cor . 1. The perpendicular AP is shorter than any oblique line AQ ...
... plane , but that it always must be so , when ever it is perpendicular to two straight lines drawn in the plane ; which proves the first Definition to be accurate . Cor . 1. The perpendicular AP is shorter than any oblique line AQ ...
Page 130
... plane , may be found by marking upon N that plane three points B , C , D , equally distant from the point A , and then finding the centre of the circle which passes through these points ; this centre will be P , the point sought ...
... plane , may be found by marking upon N that plane three points B , C , D , equally distant from the point A , and then finding the centre of the circle which passes through these points ; this centre will be P , the point sought ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex