## 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 describe 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 right angles RULE scale segment sides similar Sine slant height solidity sphere square straight line subtract suppose surface taken Tang tangent THEOREM third TIIEOREM triangle triangle ABC unit viii yards

### Popular passages

Page 12 - For this purpose it is divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds are marked thus ° ' " ; and 9° 18' 16", are read, 9 degrees 18 minutes and 16 seconds.

Page 60 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 84 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

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 49 - The angle formed by a tangent and a chord is measured by half the intercepted arc.

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 was 33° 45' ; required the height of the tower.

Page 30 - The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and...

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 12 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes; 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.