An Introduction to Mensuration and Practical GeometryKimber & Sharpless, 1829 - 252 pages |
From inside the book
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Page 55
... sum of the three sides subtract each side severally . * Demon . Let Ac = α , AB = b , BC = c , and AD = x ; ( See preceding fig . ) Then , since BD = b - x , we ... Multiply the half sum and the three remainders con- OF SUPERFICIES . 55.
... sum of the three sides subtract each side severally . * Demon . Let Ac = α , AB = b , BC = c , and AD = x ; ( See preceding fig . ) Then , since BD = b - x , we ... Multiply the half sum and the three remainders con- OF SUPERFICIES . 55.
Page 56
John Bonnycastle. 2. Multiply the half sum and the three remainders con- tinually together , and the square root of the product will be the area required . EXAMPLES . 1. Required the area of the triangle ABC , whose three sides BC , CA ...
John Bonnycastle. 2. Multiply the half sum and the three remainders con- tinually together , and the square root of the product will be the area required . EXAMPLES . 1. Required the area of the triangle ABC , whose three sides BC , CA ...
Page 59
... Multiply the diagonal by the sum of the two perpendicu- lars falling upon it from the opposite angles , and half the product will be the area . EXAMPLES . 1. Required the area of the trapezium BAED , whose diagonal BE is 84 , the ...
... Multiply the diagonal by the sum of the two perpendicu- lars falling upon it from the opposite angles , and half the product will be the area . EXAMPLES . 1. Required the area of the trapezium BAED , whose diagonal BE is 84 , the ...
Page 60
... Multiply the sum of the parallel sides by the perpendicu- lar distance between them , and half the product will be the area . EXAMPLES . 1. Required the area of the trapezoid ABCD , whose sides AB and DC are 321.51 and 214.24 , and ...
... Multiply the sum of the parallel sides by the perpendicu- lar distance between them , and half the product will be the area . EXAMPLES . 1. Required the area of the trapezoid ABCD , whose sides AB and DC are 321.51 and 214.24 , and ...
Page 61
... Multiply half the perimeter of the figure by the perpen- dicular falling from its centre upon one of the sides , and the product will be the area . Note . The perimeter of any figure is the sum of all its sides . * Demon . Every regular ...
... Multiply half the perimeter of the figure by the perpen- dicular falling from its centre upon one of the sides , and the product will be the area . Note . The perimeter of any figure is the sum of all its sides . * Demon . Every regular ...
Common terms and phrases
9 inches ABCD adba altitude arch axis base Bisect breadth bung cask centre chord of half circle whose diameter circular circular segment circumference cone CONIC SECTIONS conjugate diameter convex surface cube curve cylinder Demon describe arcs cutting describe the arc diagonal distance divided draw the line ellipse equal EXAMPLES feet 6 inches feet 9 figure find the area find the solidity fluxion foot girt give the solidity given line greater end half the arc hexagon hyperbola hypothenuse length less abscissa less end linear side measure multiply the sum ordinate parabola parallel pentagon perpendicular PROBLEM prolate spheroid pyramid quotient radius rectangle regular polygon Required the area Required the solidity rhombus right line roof segment semicircle sine of half slant height SLIDING RULE solid content solidity required specific gravity sphere spheroid square root thickness transverse diameter trapezium ullage versed sine Whence wine gallons yard
Popular passages
Page ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 50 - The areas of circles are to each other as the squares of their diameters.
Page 19 - Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.
Page 125 - To find the solidity of a cylinder. RULE. — Multiply the area of the base by the altitude, and the product will be the solidity.
Page 21 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 56 - Multiply the half sum and the three remainders continually together, and the square root of the product will be the area...
Page 54 - To find the area of a rectangular board, whose length is 12-^ feet, and breadth 9 inches. Ans. 9f feet.
Page 96 - As the conjugate diameter is to the transverse, So is the square root of the difference of the squares of the ordinate and semi-conjugate, To the distance between the ordinate and centre.
Page 16 - A sector is any part of a circle bounded by an arc, and two radii drawn to its extremities. A quadrant, or quarter of a circle...
Page 54 - To find the Area of a Triangle. Rule ] . Multiply the base by the perpendicular height, and half the product will be the area.