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

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### Common terms and phrases

adjacent angles allel altitude angles equal base multiplied bisect called centre chains chord circle whose diameter circular sector circumference column comp cone consequently convex surface Cosine Cotang cylinder decimal diagonal dicular distance divided draw drawn equal altitudes equal Bk equal to half equivalent figure find the area frustum greater half the arc half the product hence horizontal hypothenuse inches included angle inscribed intersection Let ABCD logarithm lower base measured by half Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane prism PROBLEM pyramid quadrilateral radii radius rectangle regular polygon Required the area rhombus right angled triangle right angles Bk segment side AC similar similar triangles Sine slant height sphere straight line subtract suppose Tang tangent THEOREM three sides triangle ABC upper base yards

### Popular passages

Page 24 - 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 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 55 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line; it is required to divide it into two equal parts.

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 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 25 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

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 124 - 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 133 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.