## Elements of Geometry and Trigonometry: With Applications in Mensuration |

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altitude base called centre chord circle circumference column common cone consequently contain convex surface corresponding Cosine Cotang cubic cylinder decimal described diagonal diameter difference distance divided draw drawn entire equal equal to half equivalent EXAMPLES extremity feet figure follows formed four frustum given gives greater hence horizontal inches included inscribed intersection length less Let ABCD logarithm measured meet minutes multiplied opposite parallel parallelogram pass perimeter perpendicular plane polygon prism PROBLEM proportion pyramid quadrilateral quantities radius ratio rectangle regular remaining right angles RULE scale segment sides similar Sine slant height solidity sphere square straight line suppose surface taken Tang tangent THEOREM third TIIEOREM triangle triangle ABC unit viii yards

### Popular passages

Page 44 - Let ABC be a triangle, of which the side AC is greater than the side AB; the angle ABC shall be greater than the angle BCA.

Page 11 - A circle (Fig. 38) is a figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within, called the center.

Page 12 - 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 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 130 - ... or cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a...

Page 209 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.

Page 58 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they are equal in all their parts.

Page 159 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.

Page 70 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.