Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1862 - 490 páginas |
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Página 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 ...
Página 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 ...
Página 205
... frustum . But the area of either trapezoid , as A H , is equal to A E D N B ( AB + GH ) × 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 ...
... frustum . But the area of either trapezoid , as A H , is equal to A E D N B ( AB + GH ) × 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 ...
Página 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 ...
Página 210
... frustum , and whose basc , 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 DEF - C , whose altitude is that of the frus- tum , and whose base , DE F , is ...
... frustum , and whose basc , 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 DEF - C , whose altitude is that of the frus- tum , and whose base , DE F , is ...
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Términos y frases comunes
A B C ABCD adjacent angles altitude angle ACB angle equal base bisect centre 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 interior angles 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 Required the area 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
Pasajes populares
Página 28 - 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.
Página 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.
Página 79 - Two rectangles having equal altitudes are to each other as their bases.
Página 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Página 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.
Página 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Página 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Página 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 4 - 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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Página 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.