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

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### Common terms and phrases

ABCD adjacent altitude base called centre chord circle circumference common comp cone consequently contained convex surface corresponding cosine Cotang cylinder described determine diagonal diameter difference distance divided draw drawn edges equal equations equivalent example expressed extremes faces feet figure follows formed formula four frustum given gives greater half height hence hypothenuse inches included inscribed intersect length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM proportional PROPOSITION pyramid quadrant radii radius ratio rectangle regular remaining right angles right-angled triangle Scholium segment sides similar sine solidity sphere spherical triangle square straight line substitute suppose surface taken tang tangent THEOREM third triangle triangle ABC unit 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 7 - 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.