Plane and Solid GeometryMacmillan, 1901 - 370 σελίδες |
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Σελίδα 2
... coincide . 17. Equal magnitudes are those that can be made to coincide . 18. Proof by superposition is the method of proving the equality of two figures by means of coincidence . QUESTIONS 1. What is the path of a moving point ? 2. What ...
... coincide . 17. Equal magnitudes are those that can be made to coincide . 18. Proof by superposition is the method of proving the equality of two figures by means of coincidence . QUESTIONS 1. What is the path of a moving point ? 2. What ...
Σελίδα 3
... coinciding in part , coincide throughout , ( b ) two straight lines can intersect only once , and ( c ) two points determine a straight line . The expression , straight line , is used to denote both an un- limited straight line and a ...
... coinciding in part , coincide throughout , ( b ) two straight lines can intersect only once , and ( c ) two points determine a straight line . The expression , straight line , is used to denote both an un- limited straight line and a ...
Σελίδα 9
... coincides with BA . Then EF will fall on BC ( straight lines coinciding in part coincide throughout ) . Hence DEF Z ABC . = 53. All right angles are equal . Q.E.D. ( Ax . 7. ) 54. At a given point in a given line there can be but one ...
... coincides with BA . Then EF will fall on BC ( straight lines coinciding in part coincide throughout ) . Hence DEF Z ABC . = 53. All right angles are equal . Q.E.D. ( Ax . 7. ) 54. At a given point in a given line there can be but one ...
Σελίδα 13
... coincide .. △ ABC = △ A'B'C ' . Q.E.D. 69. NOTE . This method of proof ( superposition ) is employed in fundamental propositions only . The student should place those parts upon each other whose equality is known , and , by successive ...
... coincide .. △ ABC = △ A'B'C ' . Q.E.D. 69. NOTE . This method of proof ( superposition ) is employed in fundamental propositions only . The student should place those parts upon each other whose equality is known , and , by successive ...
Σελίδα 14
... coincide BA will take the direction of B'A ' , ( LB = LB ' by hyp . ) . The point A will fall upon the point A ' , ( AB = A'B ' by hyp . ) . .. AC will coincide with A'C ' . .. AABC and A'B'C ' coincide . : A ABC = A A'B'C ' . = Q.E.D. ...
... coincide BA will take the direction of B'A ' , ( LB = LB ' by hyp . ) . The point A will fall upon the point A ' , ( AB = A'B ' by hyp . ) . .. AC will coincide with A'C ' . .. AABC and A'B'C ' coincide . : A ABC = A A'B'C ' . = Q.E.D. ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal base angles bisect bisector chord circumference circumscribed cone 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 vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 146 - 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 248 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 165 - The area of a rectangle is equal to the product of its base and altitude. 1\ u Hyp.
Σελίδα 303 - 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 45 - ... the third side of the first is greater than the third side of the second.
Σελίδα 117 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 29 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 178 - 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 150 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 148 - If, from a jwint without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and UK external segment.