## A Practical System of Mensuration of Superficies and Solids ... |

### From inside the book

Results 1-5 of 9

Page iii

...

...

**similar**kind , with which I am acquainted . WM . HOPKINS , Principal of the Auburn Academy . AUBURN , April 19th , 1844 . I fully concur in the foregoing opinion of Mr. Hopkins , and will add , that I hope to see the work introduced as ... Page 18

...

...

**similar**in substance to those found in Euclid , are here inserted for the convenience of reference , and to assist those who may be ignorant of Geometry in acquiring some knowledge of that science . I. Four - sided figures are variously ... Page 35

...

...

**similar**polygons are to each other as the squares of their homologous sides , if the square of the side of a polygon be multiplied by the multiplier of the like figure , the product will be the area sought . And hence we have , 12 ... Page 42

...

...

**similar**polygon be circumscribed about the circle , it may be demonstrated that the perimeter of the inscribed D polygon is 6,2831788 , and that of the circumscribed polygon 6,2831928 . Now , the circumference of the circle being ... Page 61

...

...

**similar**and equal , and the sides , connecting these are parallelograms . A prism takes particular names according to the figure of its base , whether triangular , square , rectangular , pentagonal , & c . The parallel planes are ...### Other editions - View all

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.