Plane and Solid Geometry |
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Page 179
... Frustum of a pyramid is a trun- cated pyramid whose bases are parallel . The Altitude of a frustum is the perpendicu- lar distance between the planes of its bases . 444. The lateral faces of a frustum of a regular pyramid are equal ...
... Frustum of a pyramid is a trun- cated pyramid whose bases are parallel . The Altitude of a frustum is the perpendicu- lar distance between the planes of its bases . 444. The lateral faces of a frustum of a regular pyramid are equal ...
Page 183
... frustum of a cone of revolution is equal to one - half the sum of the circumferences of its bases multiplied by its slant height . If R and R ' denote the radii of the lower and upper bases of the frustum of a cone of revolution , and L ...
... frustum of a cone of revolution is equal to one - half the sum of the circumferences of its bases multiplied by its slant height . If R and R ' denote the radii of the lower and upper bases of the frustum of a cone of revolution , and L ...
Page 186
... frustum , and for their bases the lower base , the upper base , and a mean proportional between the bases , of the frustum . Let AF be a frustum of a triangular pyramid . Denote the area of the lower base by B , the area of the upper ...
... frustum , and for their bases the lower base , the upper base , and a mean proportional between the bases , of the frustum . Let AF be a frustum of a triangular pyramid . Denote the area of the lower base by B , the area of the upper ...
Page 187
... frustum . Hence ( by 464 ) P = } h × B. ( 1 ) And the pyramid Q has for its altitude the altitude of the frustum , and for its base the upper base b of the frustum . Hence Q = hxb . ( 2 ) Now the pyramids E - ABC and E - ACD may be ...
... frustum . Hence ( by 464 ) P = } h × B. ( 1 ) And the pyramid Q has for its altitude the altitude of the frustum , and for its base the upper base b of the frustum . Hence Q = hxb . ( 2 ) Now the pyramids E - ABC and E - ACD may be ...
Page 188
... frustum of any pyramid is equivalent to the sum of three pyramids , having the same altitude as the frustum , and whose bases are the lower base , the upper base , and a mean pro- portional between the bases , of the frustum . 471. COR ...
... frustum of any pyramid is equivalent to the sum of three pyramids , having the same altitude as the frustum , and whose bases are the lower base , the upper base , and a mean pro- portional between the bases , of the frustum . 471. COR ...
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Common terms and phrases
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Popular passages
Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 108 - 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.
Page 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Page 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.