The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
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Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 3
... drawn from A , a point without the plane ; and let AC be any other line drawn from A to the plane ; then AC cannot be perpen- dicular to MN . Draw the line BC . Now , since AB is perpendicular to the plane MN , it is also perpendicular ...
... drawn from A , a point without the plane ; and let AC be any other line drawn from A to the plane ; then AC cannot be perpen- dicular to MN . Draw the line BC . Now , since AB is perpendicular to the plane MN , it is also perpendicular ...
Σελίδα 4
... drawn perpendicular to the line AB at a given point A ; and let MN be a plane passing through A , and perpendicular to AB ; then will AE lie in MN . For , if AE does not lie in MN , pass through AE and AB a plane BAE ; and let AE ' be ...
... drawn perpendicular to the line AB at a given point A ; and let MN be a plane passing through A , and perpendicular to AB ; then will AE lie in MN . For , if AE does not lie in MN , pass through AE and AB a plane BAE ; and let AE ' be ...
Σελίδα 5
... Draw the lines AC and A'C ' . Now these lines are paral- lel . For , they lie in the same plane , i.e. , the plane of the parallel lines AA ′ and CC ' ( 11 ) ; and they cannot meet , since they lie in the parallel planes MN and PQ ( 5 ) ...
... Draw the lines AC and A'C ' . Now these lines are paral- lel . For , they lie in the same plane , i.e. , the plane of the parallel lines AA ′ and CC ' ( 11 ) ; and they cannot meet , since they lie in the parallel planes MN and PQ ( 5 ) ...
Σελίδα 7
... draw through C , any line CF , and parallel to CF draw AE ; then the angles BAE and DCF will be equal ( 19 ) . But BAE is a right angle ( 4 ) ; therefore DCF is a right angle . Then , since DC is perpendicular to CF any line in the ...
... draw through C , any line CF , and parallel to CF draw AE ; then the angles BAE and DCF will be equal ( 19 ) . But BAE is a right angle ( 4 ) ; therefore DCF is a right angle . Then , since DC is perpendicular to CF any line in the ...
Σελίδα 8
... Draw the line AC ' piercing PQ at D ; then draw BD and DB ' , also draw AA ' and CC ' . Now BD is parallel to CC ' , and DB ' is parallel to AA ' ( 18 ) . Hence , AB : BC :: AD : DC ' , and A'B ' : B'C ' :: AD : DC ' ( 361 ) . Therefore ...
... Draw the line AC ' piercing PQ at D ; then draw BD and DB ' , also draw AA ' and CC ' . Now BD is parallel to CC ' , and DB ' is parallel to AA ' ( 18 ) . Hence , AB : BC :: AD : DC ' , and A'B ' : B'C ' :: AD : DC ' ( 361 ) . Therefore ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle EDC-O equal with respect equivalent faces is called feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA lune MN and PQ mutually equal O-ABCD oblique parallelopiped parallel planes parallelogram pass perimeter perpen perpendicular to MN plane angle plane MN plane PQ polar triangle polyedral angle prisms whose bases radii radius regular polyedrons regular polygon right angles right circular cone right prism right section SCHOLIUM sides slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tetraedron THEOREM triangles ABC triangular prism triangular pyramids triedral
Δημοφιλή αποσπάσματα
Σελίδα 48 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Σελίδα 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Σελίδα 4 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Σελίδα 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Σελίδα 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Σελίδα 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Σελίδα 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Σελίδα 56 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.