A Practical System of Mensuration of Superficies and Solids ... |
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Page 39
... quarter of the circumference ; as , AB ( fig . 2. ) B 2 6. An Arc is any portion of the circumference ; as AC B ( fig . 3. ) 7. A Chord is a straight line , which joins DEFINITIONS . 39 OF THE CIRCLE AND ITS PARTS, General Principles, 39- ...
... quarter of the circumference ; as , AB ( fig . 2. ) B 2 6. An Arc is any portion of the circumference ; as AC B ( fig . 3. ) 7. A Chord is a straight line , which joins DEFINITIONS . 39 OF THE CIRCLE AND ITS PARTS, General Principles, 39- ...
Page 40
... chord of the arc ACB , ( fig . 3. ) з с A B 8. A Circular Segment is the space contained between an arc and its chord ; as , ACB ( fig . 3. ) The chord is sometimes called the base of the segment . The height of the segment is the ...
... chord of the arc ACB , ( fig . 3. ) з с A B 8. A Circular Segment is the space contained between an arc and its chord ; as , ACB ( fig . 3. ) The chord is sometimes called the base of the segment . The height of the segment is the ...
Page 49
... chord is 120 , and whose height is 45 ? OPERATION . 120 ÷ 2-60-1 chord of the arc . NOTE . The chord of half the arc is equal to the square root of the sum of the squares of the height and half the chord of the whole arc . C 60-3600 45 ...
... chord is 120 , and whose height is 45 ? OPERATION . 120 ÷ 2-60-1 chord of the arc . NOTE . The chord of half the arc is equal to the square root of the sum of the squares of the height and half the chord of the whole arc . C 60-3600 45 ...
Page 52
... chord of the whole arc add of the chord of half the arc . II . Then multiply the sum by the versed sine , or height of the segment , and 1 of the product will be the area of the segment , very nearly . Ex . 1. Required the area of a cir ...
... chord of the whole arc add of the chord of half the arc . II . Then multiply the sum by the versed sine , or height of the segment , and 1 of the product will be the area of the segment , very nearly . Ex . 1. Required the area of a cir ...
Page 53
... chord 70 . - 35 + 19.2-4D . Ans . 947.86 . Ex . 3. What is the area of a circular segment whose chord is 16 , and the diameter of the circle 20 ? Ans . 44.680 . Ex . 4. If the base or chord of a segment be 10 feet , and the radius of ...
... chord 70 . - 35 + 19.2-4D . Ans . 947.86 . Ex . 3. What is the area of a circular segment whose chord is 16 , and the diameter of the circle 20 ? Ans . 44.680 . Ex . 4. If the base or chord of a segment be 10 feet , and the radius of ...
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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.