## Elements of Geometry and Trigonometry: With Applications in MensurationA.S. Barnes & Burr, 1863 |

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### Common terms and phrases

A. S. BARNES ABCDE allel altitude angles equal axis base multiplied bisect centre chord circle whose diameter circumference common intersection cone consequently convex surface Cosine Cotang cubic curve cylinder decimal degrees diagonal dicular distance divided draw equal Bk equal to half equivalent feet figure find the area find the Solidity frustum GEOMETRY half the product hence hexagon horizontal hypothenuse inches included angle inscribed Let ABCD lower base measured by half Mensuration of Surfaces nonagon parallelogram parallelopipedon pendicular pentagon perimeter perpen perpendicular plane MN polyedron prism PROBLEM proportional quadrilateral radius rectangle regular polygon Required the area rhombus right angled triangle right angles Bk segment side AC sides is called similar triangles Sine slant height sphere straight line suppose TABLE OF LOGARITHMS Tang tangent THEOREM three sides triangle ABC Trigonometry upper base vertex yards

### Popular passages

Page 10 - 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 54 - Two triangles of the same altitude are to each other as their bases ; and...

Page 95 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.

Page 12 - 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 77 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.

Page 24 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 92 - ... 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 135 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.

Page 145 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.

Page 23 - 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.