A Practical System of Mensuration of Superficies and Solids ... |
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Page 21
... upper row of this figure , we find the num- ber to be 4 ; in two rows , twice 4 , or 8 ; in three rows , three times 4 , or 12. Hence , to obtain the number of small parallelograms , ce , contained in the large parallelogram , ABCD , we ...
... upper row of this figure , we find the num- ber to be 4 ; in two rows , twice 4 , or 8 ; in three rows , three times 4 , or 12. Hence , to obtain the number of small parallelograms , ce , contained in the large parallelogram , ABCD , we ...
Page 58
... upper end ef 12 feet , and base AB 20 feet ? ( See last problem . ) OPERATION . -3 20 = 400 20 = 8000 -2 -3 12-144 12-1728 256 - diff . of their squares 6272 3 24 - twice the height . 768 25088 12544 768 ) 150528 ( 196 ft . Ans . 768 ...
... upper end ef 12 feet , and base AB 20 feet ? ( See last problem . ) OPERATION . -3 20 = 400 20 = 8000 -2 -3 12-144 12-1728 256 - diff . of their squares 6272 3 24 - twice the height . 768 25088 12544 768 ) 150528 ( 196 ft . Ans . 768 ...
Page 68
... upper base , 3 feet each . ? OPERATION . First , 5x8-40 - perimeter of lower base . 3x8 = 24 = 66 66 upper 64 - sum of the two ends . 42 - slant height . 128 256 2 ) 2688 1344 - area of lateral surface . 69 Ex . 2. How many square feet ...
... upper base , 3 feet each . ? OPERATION . First , 5x8-40 - perimeter of lower base . 3x8 = 24 = 66 66 upper 64 - sum of the two ends . 42 - slant height . 128 256 2 ) 2688 1344 - area of lateral surface . 69 Ex . 2. How many square feet ...
Page 69
... upper base 2 feet 2 inches ? Ans . 110 . Ex . 3. If the slant height of the frustrum of a hexagonal pyramid be 48 , each side of the lower base 26 , and each side of the upper base 16 feet , what is the lateral surface ? Ans . 6048 sq ...
... upper base 2 feet 2 inches ? Ans . 110 . Ex . 3. If the slant height of the frustrum of a hexagonal pyramid be 48 , each side of the lower base 26 , and each side of the upper base 16 feet , what is the lateral surface ? Ans . 6048 sq ...
Page 71
... upper base . 81x36-2916 , and 2916-54 - sq . root of prod . of 2 areas . Then , 117 + 54 = 171 131-1 of the height . 513 171 57 2280 - solidity . Ex . 2. What is the solidity of the frustrum of a regular pentagonal pyramid , whose ...
... upper base . 81x36-2916 , and 2916-54 - sq . root of prod . of 2 areas . Then , 117 + 54 = 171 131-1 of the height . 513 171 57 2280 - solidity . Ex . 2. What is the solidity of the frustrum of a regular pentagonal pyramid , whose ...
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A Practical System of Mensuration of Superficies and Solids: Designed ... J. M. Scribner No preview available - 2017 |
A Practical System of Mensuration of Superficies and Solids J. M. Scribner No preview available - 2022 |
A Practical System of Mensuration of Superficies and Solids: Designed ... J. M. Scribner No preview available - 2017 |
Common terms and phrases
12 feet 18 inches 20 feet 9 feet ABCD ABFD assumed cube avoirdupois axis base 26 breadth centre chord circle whose diameter Circular Sector circular segment circumfer circumference circumscribed contained convex surface Cube Root cubic feet cubic ft cubic inches cylinder cylindrical ring decimal diff divide the product ellipse ends entire surface equal extract the square feet 6 inches feet long find the area find the Solidity frustrum gallon half hypotenuse inner diameter inscribed square lateral surface length miles multiply the sum Nonagon number of degrees number of sides number of square OPERATION parabola parallel sides parallelogram pentagonal pyramid perpendicular distance perpendicular height plane prism PROBLEM radius regular pentagonal regular Polygon Required the area Required the solidity rhombus right angled triangle Rule Rule.-I slant height solid contents sphere spherical segment spheroid square feet square rods square root square yards thickness trapezium zoid zone
Popular passages
Page 53 - RULE. Find the area of the sector which has the same arc, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...
Page 35 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...
Page 79 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 80 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 90 - ... to three times the square of the radius of the segment's base, add the square of its height ; then multiply the sum by the height, and the product by .5236 for the contents.
Page 49 - From 8 times the chord of half the arc subtract the chord of the whole arc, and ' of the remainder will be the length of the arc nearly.
Page 72 - RULE.* To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by £ of the height will give the solidity.
Page 51 - As 360 degrees is to the number of degrees in the arc of the sector, so is the area of the circle to the area of the sector.
Page 91 - From three times the diameter of the sphere subtract twice the height of the segment; multiply this remainder by the square of the height and the product by 0.5236.
Page 39 - A Circle is a plane figure bounded by a curve line, called the Circumference, which is everywhere equidistant from a certain point within, called its Centre.