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

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### Common terms and phrases

20 feet ABCD altitude angles equal base multiplied bisect breadth called centre chains circle whose diameter circular sector circumference column cone consequently convex surface cosine cotangent cylinder decimal dicular distance divide draw equal Bk equal to half equivalent EXAMPLES figure find the area frustum half the arc half the perimeter half the product hence heptagon hypothenuse included angle inscribed square length Let ABCD logarithm lower base measured by half Mensuration of Solids Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular pentagonal pyramid perimeter perpen perpendicular prism PROBLEM proportional pyramid quadrilateral radius ratio rectangle regular polygon Required the area rhombus right angled triangle right angles Bk RULE segment sine slant height solid ft sphere square feet straight line tangent THEOREM three sides trapezoid triangle ABC Trigonometry upper base

### Popular passages

Page 56 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 78 - 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 119 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.

Page 119 - If a pyramid with a polygon for its base be cut by a plane parallel to the base, the section will be a polygon similar to the base.

Page 30 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.

Page 245 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.

Page 119 - ... 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 9 - 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 79 - A are verti' cal, produce the sides GE, CD till they meet in H. The two rectangles ABCD, AEHD, having the same altitude, AD, are to each other as their bases, AB, AE.

Page 10 - 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.