Elements of Plane and Solid GeometryGinn and Heath, 1877 - 398 σελίδες |
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Σελίδα 303
... frustum , and the parallel sec- tion , its Upper base . 563. DEF . The Altitude of a frustum is the perpendicular distance between the planes of its bases . 564. DEF . The lateral faces of a frustum of a regular pyra- mid are the ...
... frustum , and the parallel sec- tion , its Upper base . 563. DEF . The Altitude of a frustum is the perpendicular distance between the planes of its bases . 564. DEF . The lateral faces of a frustum of a regular pyra- mid are the ...
Σελίδα 306
... frustum of a regular pyramid , being composed of trapezoids which have for their common altitude the slant height of the frustum , is equal to one - half the sum of the perimeters of the bases multiplied by the slant height of the ...
... frustum of a regular pyramid , being composed of trapezoids which have for their common altitude the slant height of the frustum , is equal to one - half the sum of the perimeters of the bases multiplied by the slant height of the ...
Σελίδα 311
... ; find the capacity of each in gallons and litres , in bushels and hectolitres ; and find the weight of water in pounds and in kilo- grammes , required to fill each prism . PROPOSITION XX . THEOREM . 578. The frustum of a EXERCISES . 311.
... ; find the capacity of each in gallons and litres , in bushels and hectolitres ; and find the weight of water in pounds and in kilo- grammes , required to fill each prism . PROPOSITION XX . THEOREM . 578. The frustum of a EXERCISES . 311.
Σελίδα 312
... frustum . D F E A A C B Let B and b denote the lower and upper bases of the frustum ABC - DEF , and H its altitude . Through the vertices A , E , C and E , D , C pass planes dividing the frustum into three pyramids . Now the pyramid E ...
... frustum . D F E A A C B Let B and b denote the lower and upper bases of the frustum ABC - DEF , and H its altitude . Through the vertices A , E , C and E , D , C pass planes dividing the frustum into three pyramids . Now the pyramid E ...
Σελίδα 339
... frustum , and the parallel section the Upper base . 648. DEF . The Altitude of a frustum is the perpendicular distance between the planes of its bases . 649. DEF . The Lateral surface of a frustum is the portion of the lateral surface ...
... frustum , and the parallel section the Upper base . 648. DEF . The Altitude of a frustum is the perpendicular distance between the planes of its bases . 649. DEF . The Lateral surface of a frustum is the portion of the lateral surface ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCD altitude arc A B axis base and altitude bisect centre circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided Draw equal respectively equally distant equilateral equivalent figure frustum Geometry given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC limit line A B measured by arc middle point mutually equiangular number of sides opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 132 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 140 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 206 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 353 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 179 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 192 - 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 150 - 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'.