# The Young Geometrician's Companion: Being A New and Comprehensive Course of Practical Geometry ... Containing. An easy introduction to decimal arithmetic .... Such definitions, axioms, problems, theorems, and characters, as necessarily lead to the knowledge of this science. Planometry, or the mensuration of superficies. Stereometry, ot he mensuration of solids. The sections of a cone .... The Platonic bodies ... To which is added a collection of problems shewing that lines and angles may be divided in infinitum; that superficies and solids may be so cut as to appear considerably augmented; and, that the famous problem of Archimedes, of moving the earth, is capable of an easy and accurate demonstration, Volum 6

S. Crowder, 1787 - 240 sider

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Side 95 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to thcsquare of the other part.
Side 181 - Rule: To twice the square of the middle diameter, add the square of the diameter of...
Side 33 - Multiply the two given numbers together, and extract the square root of the product, which root will be the mean proportional sought. EXAMPLES. (1) What is the mean proportional between 4 and 9 ? (2) What is the mean proportional between 16 and 36?
Side 149 - For the surface of a segment or frustum, multiply the whole circumference of the sphere by the height of the part required.
Side 120 - As 7 is to 22, so is the diameter to the circumference. Or as 113 is to 355, so is the diameter to the circumference. • Or as 1 is to 3.1416, so is the diameter to the circumferenc".
Side 138 - This error, though it. is b«! small, when the depth and breadth are pretty near equal, yet if the difference...
Side 175 - To find the solidity of a spheroid. — Multiply the square of the revolving axe by the fixed axe, and this product again by -5236, and it will give the solidity required.
Side 213 - DF'E. Hence the entire area of the (!i GP cycloid is equal to three times the area of the generating circle.
Side 133 - To find the side of a square equal in area to any given superfices.
Side 28 - Divifion, write the anfwer in the Quotient, and alfo on the right hand of the Divifor...