Plane and Solid GeometryMacmillan, 1901 - 370 σελίδες |
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Αποτελέσματα 1 - 5 από τα 14.
Σελίδα 24
... either equal or supplementary . Нур . To prove D A 4 B B AB || A'B ' and BC || B'C ' . LB = LA'B'C ' ZB + ZA'B'D = 2 rt . s . [ The proof is left to the student . ] 92. SCHOLIUM . The angles are equal if both the 24 PLANE GEOMETRY.
... either equal or supplementary . Нур . To prove D A 4 B B AB || A'B ' and BC || B'C ' . LB = LA'B'C ' ZB + ZA'B'D = 2 rt . s . [ The proof is left to the student . ] 92. SCHOLIUM . The angles are equal if both the 24 PLANE GEOMETRY.
Σελίδα 42
... Нур . To prove Proof . B ACB is a A. - AB + AC > BC ; and BA > CB – AC . 1o . A straight line is the shortest distance between two points . ( Ax . 10. ) Q.E.D. 2 ° . .. AB + AC > BC . AB + AC > BC . ( above ) AB > BC – AC . ( Ax . 5 ...
... Нур . To prove Proof . B ACB is a A. - AB + AC > BC ; and BA > CB – AC . 1o . A straight line is the shortest distance between two points . ( Ax . 10. ) Q.E.D. 2 ° . .. AB + AC > BC . AB + AC > BC . ( above ) AB > BC – AC . ( Ax . 5 ...
Σελίδα 50
... Нур . D ABCD is a parallelogram . To prove AD = BC ; AB = CD ; ZA = LC ; ≤B = LD . HINT . - What is the usual means of proving the equality of lines and angles ? - 135. COR . 1. A diagonal divides a parallelogram into two equal ...
... Нур . D ABCD is a parallelogram . To prove AD = BC ; AB = CD ; ZA = LC ; ≤B = LD . HINT . - What is the usual means of proving the equality of lines and angles ? - 135. COR . 1. A diagonal divides a parallelogram into two equal ...
Σελίδα 51
... is a parallelogram . A B Нур . To prove D In quadrilateral ABCD AB || CD ; and AB = CD . ABCD is a parallelogram . [ The proof is similar to that in Prop . XXXIII . ] Ex . 193. The bisectors of two opposite angles of QUADRILATERALS 51.
... is a parallelogram . A B Нур . To prove D In quadrilateral ABCD AB || CD ; and AB = CD . ABCD is a parallelogram . [ The proof is similar to that in Prop . XXXIII . ] Ex . 193. The bisectors of two opposite angles of QUADRILATERALS 51.
Σελίδα 54
... Нур . To prove EF || HI || KL || MN , VS = ST = TU . Proof . Draw Then WX = XY = YZ . WO , XP , YR || AB . WVSO , XSTP , YTUR are parallelograms , ( hyp . and con . ) . .. VS WO , ST = XP , TU = YR , = ( opposite sides of parallelogram ) ...
... Нур . To prove EF || HI || KL || MN , VS = ST = TU . Proof . Draw Then WX = XY = YZ . WO , XP , YR || AB . WVSO , XSTP , YTUR are parallelograms , ( hyp . and con . ) . .. VS WO , ST = XP , TU = YR , = ( opposite sides of parallelogram ) ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Σελίδα 180 - Two triangles having 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 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Σελίδα 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Σελίδα 328 - Every section of a sphere made by a plane is a circle.
Σελίδα 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.