Elements of Geometry and Trigonometry: With Practical Applications |
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Page 238
... CONE is a solid which may be described by the revolution of a right- angled triangle turning about one of its ... cone is the circle de- scribed by the revolution of the side . BC , which is perpendicular to the im- movable side . B A ...
... CONE is a solid which may be described by the revolution of a right- angled triangle turning about one of its ... cone is the circle de- scribed by the revolution of the side . BC , which is perpendicular to the im- movable side . B A ...
Page 239
... cone is the point A , where the hy- pothenuse meets the immovable side . The AXIS of the cone is the straight line joining the vertex to the centre of the base ; as the line A B. The ALTITUDE of a cone is a line drawn from the vertex ...
... cone is the point A , where the hy- pothenuse meets the immovable side . The AXIS of the cone is the straight line joining the vertex to the centre of the base ; as the line A B. The ALTITUDE of a cone is a line drawn from the vertex ...
Page 242
... cone is equal to the cir- cumference of the base multiplied by half the slant height . Let A B C DEF - S be a cone whose base is the circle ABCDEF , and whose slant height is the line SA ; then its convex surface is equal to ABCDEF ...
... cone is equal to the cir- cumference of the base multiplied by half the slant height . Let A B C DEF - S be a cone whose base is the circle ABCDEF , and whose slant height is the line SA ; then its convex surface is equal to ABCDEF ...
Page 243
... cone is equal to half the sum of the circumference of the two bases multiplied by its slant height . Let ABCDEF - M be the frustum of a cone , and AG its slant height ; then the convex surface is equal to half the sum of the ...
... cone is equal to half the sum of the circumference of the two bases multiplied by its slant height . Let ABCDEF - M be the frustum of a cone , and AG its slant height ; then the convex surface is equal to half the sum of the ...
Page 244
... cone , whose base is ABCDEF , and alti- tude SH ; then its solidity is equal to ABCDEFX SH . S In the base of the cone inscribe any regular polygon , ABCDEF , and on this polygon construct a reg- ular pyramid , having the same vertex ...
... cone , whose base is ABCDEF , and alti- tude SH ; then its solidity is equal to ABCDEFX SH . S In the base of the cone inscribe any regular polygon , ABCDEF , and on this polygon construct a reg- ular pyramid , having the same vertex ...
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Common terms and phrases
A B C ABCD adjacent angles altitude 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 less Let ABC line A B logarithm logarithmic sine mean proportional 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 sine slant height solidity solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 35 - 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 57 - 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 117 - 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 50 - If any number of magnitudes 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; then will A : B : : A + C + E : B + D + F.
Page 77 - Two rectangles having equal altitudes are to each other as their bases.
Page 158 - 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.
Page 313 - FRACTION is a negative number, and is one more tftan the number of ciphers between the decimal point and the first significant figure.
Page 314 - 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 100 - 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'.
Page 244 - RULE. — Multiply the base by the altitude, and the product will be the area.