## Elements of Geometry and Trigonometry from the Works of A. M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United States |

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### Common terms and phrases

altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosē cosine Cotang cubes cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar similar triangles sinē sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices

### Popular passages

Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...

Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...

Page 278 - 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 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 1 - 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 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.

Page 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.

Page 30 - B : hence the 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 : hence, the two triangles are equal (Th.

Page 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.