## Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |

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### Common terms and phrases

ABCD altitude base called centre chord circle circumference circumscribed common comp cone consequently construction contained corresponding cosine Cotang cylinder described determine diagonal diameter difference distance divided draw drawn edges equal equations equivalent example expressed extremities faces fall feet figure follows formed four frustum given greater half height hence hypothenuse included inscribed intersect length less limit logarithm magnitudes manner mean measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular plane polygon prism PROBLEM proportional PROPOSITION pyramid radii radius ratio reason rectangle regular remaining right angles right-angled triangle Scholium segment sides similar sine solidity sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex vertices whole

### 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 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.