Elements of Geometry: With Practical Applications to Mensuration |
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Page 186
... frustum of a pyramid is the perpendicular distance between its parallel bases . 449. The SLANT HEIGHT of a frustum of a right pyra- mid is that part of the slant height of the pyramid which is intercepted between the bases of the ...
... frustum of a pyramid is the perpendicular distance between its parallel bases . 449. The SLANT HEIGHT of a frustum of a right pyra- mid is that part of the slant height of the pyramid which is intercepted between the bases of the ...
Page 204
... frustum of a right pyra- mid is equal to half the sum of the perimeters of its two bases , multiplied by its slant height . Let ABCDE - L be the frustum of a right pyramid , and MN its slant height ; then the convex surface is equal to ...
... frustum of a right pyra- mid is equal to half the sum of the perimeters of its two bases , multiplied by its slant height . Let ABCDE - L be the frustum of a right pyramid , and MN its slant height ; then the convex surface is equal to ...
Page 205
... frustum . But the area of either trapezoid , as A H , is equal to ≥ ( A B + G H ) × MN ( Prop . VII . Bk . IV . ) ; hence the areas of all the trapezoids , or the convex surface of frustum , are equal to half the sum of the perimeters ...
... frustum . But the area of either trapezoid , as A H , is equal to ≥ ( A B + G H ) × MN ( Prop . VII . Bk . IV . ) ; hence the areas of all the trapezoids , or the convex surface of frustum , are equal to half the sum of the perimeters ...
Page 209
... frustum of a pyramid is equivalent to the sum of three pyramids , having for their common altitude the altitude of the frustum , and whose bases are the two bases of the frustum and a mean proportional between them . First . Let A B C ...
... frustum of a pyramid is equivalent to the sum of three pyramids , having for their common altitude the altitude of the frustum , and whose bases are the two bases of the frustum and a mean proportional between them . First . Let A B C ...
Page 210
... frustum , and whose base , A B C , is the lower base of the frustum . Pass another plane through the points D , E , C ; it cuts off the triangular pyramid D EF - C , whose altitude is that of the frus- tum , and whose base , D E F , is ...
... frustum , and whose base , A B C , is the lower base of the frustum . Pass another plane through the points D , E , C ; it cuts off the triangular pyramid D EF - C , whose altitude is that of the frus- tum , and whose base , D E F , is ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - 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 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.