A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the Nature and Use of Logarithms : Being the Second Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
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Page 28
... pyramid is regular , if its base is a regular poly- gon , and if a line from the center of the base to the vertex of the pyramid is perpendicular to the base . This line is called the axis of the pyramid . IX . The height of a pyramid ...
... pyramid is regular , if its base is a regular poly- gon , and if a line from the center of the base to the vertex of the pyramid is perpendicular to the base . This line is called the axis of the pyramid . IX . The height of a pyramid ...
Page 29
... pyramid , is the distance from the middle of one of the sides of the base , to the middle of the corresponding side in the plane above . It is a line passing on the surface of the frustum , through the middle of one of its sides . XII ...
... pyramid , is the distance from the middle of one of the sides of the base , to the middle of the corresponding side in the plane above . It is a line passing on the surface of the frustum , through the middle of one of its sides . XII ...
Page 32
... pyramid is of a prism of the same base and altitude . ( Sup . Euc . 15 , 3 . Cor . 1. ) Therefore the solidity of a pyramid whether right or oblique , is equal to the product of the base into of the perpendicular height . Ex . 1. What ...
... pyramid is of a prism of the same base and altitude . ( Sup . Euc . 15 , 3 . Cor . 1. ) Therefore the solidity of a pyramid whether right or oblique , is equal to the product of the base into of the perpendicular height . Ex . 1. What ...
Page 33
... pyramid is 225.48 feet . 3. What is the solidity of a pyramid whose perpendicular height is 72 , and the sides of whose base are 67 , 54 , and 40 ? Ans . 25920 . PROBLEM IV . To find the LATERAL SURFACE of a REGULAR PYRAMID . 49 ...
... pyramid is 225.48 feet . 3. What is the solidity of a pyramid whose perpendicular height is 72 , and the sides of whose base are 67 , 54 , and 40 ? Ans . 25920 . PROBLEM IV . To find the LATERAL SURFACE of a REGULAR PYRAMID . 49 ...
Page 34
... pyramid whose axis is 12 feet , and whose base is 18 feet square ? Ans . 540 square feet . The lateral surface of an oblique pyramid may be found , by taking the sum of the areas of the unequal triangles which form its sides . PROBLEM V ...
... pyramid whose axis is 12 feet , and whose base is 18 feet square ? Ans . 540 square feet . The lateral surface of an oblique pyramid may be found , by taking the sum of the areas of the unequal triangles which form its sides . PROBLEM V ...
Other editions - View all
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2017 |
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2018 |
A Treatise of Plane Trigonometry: To Which Is Prefixed a Summary View of the ... Jeremiah Day No preview available - 2018 |
Common terms and phrases
ABC Fig ABCD altitude axis base breadth bung diameter calculation cask circle circular sector circular segment circumference column cosecant cosine cotangent course cube cubic decimal departure Diff difference of latitude difference of longitude distance divided earth equal to half equator figure find the area find the SOLIDITY frustum given sides gles greater hypothenuse inches inscribed lateral surface length less logarithm longitude measured Mercator's meridian meridional difference middle diameter miles multiply the sum number of degrees number of sides oblique parallelogram parallelopiped perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods rule secant sector segment ship sine sines and cosines slant-height sphere spherical subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 43 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 69 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 89 - Divide the height of the segment by the diameter of the circle ; look for the quotient in the column of heights in the table ; take out the corresponding number in the column of areas ; and multiply it by the square of the diameter.