## Elements of Geometry and Trigonometry: With Applications in MensurationA.S. Barnes, 1886 - 324 pages |

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### Common terms and phrases

adjacent angles altitude angles equal base multiplied bisect called centre chains chord circle whose diameter circular sector circumference column comp cone consequently convex surface Cosine Cosine D Cotang cylinder decimal diagonal dicular distance divided draw 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 M.
M. Sine measured by half Mensuration of Surfaces number of sides opposite angles parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane prism PROBLEM proportion pyramid quadrilateral radii radius ratio rectangle regular polygon Required the area rhombus right angled triangle right angles Bk S-ABCDE segment side AC similar similar triangles slant height sphere straight line suppose Tang tangent THEOREM triangle ABC upper base 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.