Solid GeometryG.H. Kent, 1921 - 192 σελίδες |
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Σελίδα 272
... = FD . ( ? ) Δ ACD = Δ FCD . ( ? ) .. ZACE = FCE . ( ? ) A ACE △ FCE . ( ? ) .. AE = FE . ( ? ) Then BE is 1 to AF . That is , AB is 1 to BE . ( ? ) ( ? ) In like manner it may be proved that AB is 272 SOLID GEOMETRY.
... = FD . ( ? ) Δ ACD = Δ FCD . ( ? ) .. ZACE = FCE . ( ? ) A ACE △ FCE . ( ? ) .. AE = FE . ( ? ) Then BE is 1 to AF . That is , AB is 1 to BE . ( ? ) ( ? ) In like manner it may be proved that AB is 272 SOLID GEOMETRY.
Σελίδα 273
Charles Austin Hobbs. In like manner it may be proved that AB is to every line in MN drawn through B. .. AB is 1 to MN . ( ? ) Q. E.D. COR . If two intersecting lines are perpendicular to a third line at the same point , their plane is ...
Charles Austin Hobbs. In like manner it may be proved that AB is to every line in MN drawn through B. .. AB is 1 to MN . ( ? ) Q. E.D. COR . If two intersecting lines are perpendicular to a third line at the same point , their plane is ...
Σελίδα 275
... the plane determined by DC and DE . Then MN is 1 to AB . ( ? ) [ To prove that there can be only one L , use a method similar to that used in Prop . 206. ] Proposition 208 Theorem At a given point in a given LINES AND PLANES IN SPACE 275.
... the plane determined by DC and DE . Then MN is 1 to AB . ( ? ) [ To prove that there can be only one L , use a method similar to that used in Prop . 206. ] Proposition 208 Theorem At a given point in a given LINES AND PLANES IN SPACE 275.
Σελίδα 277
... prove that there can be only one L , use a method similar to that used in Prop . 208. ] Ex . 957. Is it true that if two lines are perpendicular to each other , any plane passed through one of the lines is perpendicular to the other ...
... prove that there can be only one L , use a method similar to that used in Prop . 208. ] Ex . 957. Is it true that if two lines are perpendicular to each other , any plane passed through one of the lines is perpendicular to the other ...
Σελίδα 279
... > BC . = . Conclusion . AC = AD , and AE > AC . First Part . Consult Prop . 8 , Cor . = Second Part . Take BF BC , and draw AF . Consult Prop . 24 . Ex . 958. State and prove the converse of Prop LINES AND PLANES IN SPACE 279.
... > BC . = . Conclusion . AC = AD , and AE > AC . First Part . Consult Prop . 8 , Cor . = Second Part . Take BF BC , and draw AF . Consult Prop . 24 . Ex . 958. State and prove the converse of Prop LINES AND PLANES IN SPACE 279.
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Συχνά εμφανιζόμενοι όροι και φράσεις
A-BCD altitude angles are equal axis bisects centre circle circumscribed Conclusion cone of revolution congruent conical surface Consult Prop cube cylinder of revolution diagonals diameter dihedral angle distance equal respectively equidistant equilateral equivalent face angles Find the altitude Find the area Find the locus Find the ratio Find the volume frustum given plane given point homologous hypotenuse Hypothesis inscribed intersecting planes isosceles lateral area lateral edges lateral faces lower base lune oblique octahedron opposite parallel planes parallelogram perimeter plane determined plane MN plane parallel plane passing planes are parallel polyhedral angle prismatoidal formula Proposition radii rectangular parallelepiped regular polygons regular pyramid right angles right circular cone right prism right triangle skew lines slant height solid sphere is equal spherical polygon spherical triangle square straight line tangent total area triangular prism trihedral truncated vertex vertices zone
Δημοφιλή αποσπάσματα
Σελίδα 260 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 264 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 261 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 280 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane.
Σελίδα 263 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Σελίδα 385 - The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. Let V denote the volume, B the lewer base, b the upper base, H the altitude of a frustum of a circular cone.
Σελίδα 383 - The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'*
Σελίδα 266 - 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 266 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 385 - The lateral area of a frustum of a cone of revolution is equal to the circumference of a section equidistant from its bases multiplied by its slant height.