Plane and Solid GeometryMacmillan, 1902 - 370 σελίδες |
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Σελίδα 89
... segment , CD , equal to the exterior tangent , AB . E MEASUREMENT 203. A ratio of two quantities of the same kind is the quotient obtained by dividing the first quantity by the second . Thus , the ratio of two quantities , a and b , is ...
... segment , CD , equal to the exterior tangent , AB . E MEASUREMENT 203. A ratio of two quantities of the same kind is the quotient obtained by dividing the first quantity by the second . Thus , the ratio of two quantities , a and b , is ...
Σελίδα 94
... segment of a circle is a portion of a circle bounded by an arc and its chord . 219. An angle is said to be inscribed in a segment if its vertex lies in the arc and its sides pass through the extremities of that arc . Ex . 345. How many ...
... segment of a circle is a portion of a circle bounded by an arc and its chord . 219. An angle is said to be inscribed in a segment if its vertex lies in the arc and its sides pass through the extremities of that arc . Ex . 345. How many ...
Σελίδα 95
... segment , or in equal segments , are equal . 222. COR . 2. An angle inscribed in a semicircle is a right angle . Ex . 346. If in the diagram for Case I , C = 30 ° , how many degrees are in arc CB ? = Ex . 347. If in the same diagram arc ...
... segment , or in equal segments , are equal . 222. COR . 2. An angle inscribed in a semicircle is a right angle . Ex . 346. If in the diagram for Case I , C = 30 ° , how many degrees are in arc CB ? = Ex . 347. If in the same diagram arc ...
Σελίδα 107
... segment of a circle on AB which shall contain △ M. Construction . At A , draw Z BAC = ≤ M. At A , draw AE 1 to AC . Draw the perpendicular - bisector of AB , intersecting AE at O. From O as a center , with a radius equal to OA , draw ...
... segment of a circle on AB which shall contain △ M. Construction . At A , draw Z BAC = ≤ M. At A , draw AE 1 to AC . Draw the perpendicular - bisector of AB , intersecting AE at O. From O as a center , with a radius equal to OA , draw ...
Σελίδα 114
... segments of the hypotenuse . Ex . 465. The sum of the arms and one acute angle . Ex . 466. To find a point in one side of a triangle which is equidistant from the other two sides . Ex . 467. Find the locus of the vertex of a right ...
... segments of the hypotenuse . Ex . 465. The sum of the arms and one acute angle . Ex . 466. To find a point in one side of a triangle which is equidistant from the other two sides . Ex . 467. Find the locus of the vertex of a right ...
Άλλες εκδόσεις - Προβολή όλων
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 the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous homologous sides 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 polyedral angle polyedron prism PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segment similar triangles sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
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 119 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 180 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
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 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 250 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 297 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 105 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference, intersecting the given circumference in B and C.
Σελίδα 276 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =s= GM'. Proof. The lateral edges of GM