Elements of Geometry, Plane and Spherical: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1868 - 262 σελίδες |
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Σελίδα 173
... pyramid . 10. The Vertex of a pyramid is the common vertex of the triangular faces . 11. The Altitude of a pyramid is the perpendicula distance from its vertex to the plane of its base . 12. A Right Pyramid is one whose base is a ...
... pyramid . 10. The Vertex of a pyramid is the common vertex of the triangular faces . 11. The Altitude of a pyramid is the perpendicula distance from its vertex to the plane of its base . 12. A Right Pyramid is one whose base is a ...
Σελίδα 175
... pyramid be constructed , having for its vertex that of the cone , such pyramid is said to be inscribed in the cone , and the cone is said to circumscribe the pyramid . Thus , in the accompanying figure , V - ABCDE , is an inscribed pyramid ...
... pyramid be constructed , having for its vertex that of the cone , such pyramid is said to be inscribed in the cone , and the cone is said to circumscribe the pyramid . Thus , in the accompanying figure , V - ABCDE , is an inscribed pyramid ...
Σελίδα 191
... pyramid parallel to its base , divides its edges and altitude proportionally , and makes a section , which is a polygon similar to the base . Let ABCDE - V be any pyramid , whose base is in the plane , MN , and vertex in the parallel ...
... pyramid parallel to its base , divides its edges and altitude proportionally , and makes a section , which is a polygon similar to the base . Let ABCDE - V be any pyramid , whose base is in the plane , MN , and vertex in the parallel ...
Σελίδα 192
... pyramid , ab is parallel to AB , ( Th . 9 , B. VI ) ; for the same reason , bc is parallel to BC , cd to CD , etc. Now , in the triangle VAB , because ab is parallel to the base AB , we have , ( Th . 17 , B. II ) , the proportion , VA ...
... pyramid , ab is parallel to AB , ( Th . 9 , B. VI ) ; for the same reason , bc is parallel to BC , cd to CD , etc. Now , in the triangle VAB , because ab is parallel to the base AB , we have , ( Th . 17 , B. II ) , the proportion , VA ...
Σελίδα 193
... pyramid , Cor . 1. Since the areas of similar polygons are to each other as the squares of their homologous sides , ( Th . 22 , B II ) , we have area abcde · But , ab hence , therefore , 2 area ABCDE : ab2 : AB ' . AB : Va : VA :: Fl ...
... pyramid , Cor . 1. Since the areas of similar polygons are to each other as the squares of their homologous sides , ( Th . 22 , B II ) , we have area abcde · But , ab hence , therefore , 2 area ABCDE : ab2 : AB ' . AB : Va : VA :: Fl ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Plane and Spherical: With Numerous Practical Problems Horatio Nelson Robinson Προβολή αποσπασμάτων - 1868 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² altitude angle ABC axis base and altitude bisected chord circ circumference circumscribed polygon common cone convex surface cylinder diagonal diameter dicular distance divided draw equal altitudes equal and parallel equal angles equal bases equal sides equation equiangular equivalent four magnitudes frustum given line greater half Hence the theorem homologous edges hypotenuse interior angles isosceles Let ABC line drawn lune measured middle point multiplied number of sides opposite angles parallel lines parallelogram parallelopipe parallelopipedon pendicular perimeter perpen perpendicular plane ST polyedron PROB PROBLEM produced proportion PROPOSITION prove radii radius regular polygon right angles right-angled triangle SCHOLIUM secant segment semi-polygon slant height solid angles sphere spherical polygon spherical triangle square described straight line tangent three angles triangle ABC triangular prisms triedral angles vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 128 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Σελίδα 174 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 254 - 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 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Σελίδα 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.
Σελίδα 160 - THEOREM. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN...
Σελίδα 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 61 - A fourth proportional to three quantities is the fourth term of a proportion, whose first three terms are the three quantities taken in their order. Thus, in the proportion a : b = c : d, d is a fourth proportional to a, b, and c.