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

### From inside the book

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**equal to twice as many right angles as the figure has sides**, less four right angles , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the ...### Other editions - View all

### Common terms and phrases

ABCD altitude axis base called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding Cosine Cotang cylinder denote described diameter difference distance divided draw drawn edges equal Examples extremity faces feet figure formed formula four frustum given greater half hence homologous included inscribed intersect less logarithm lower base manner mean measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular placed plane plane MN polyedron polygon position prism PROBLEM proportional PROPOSITION proved pyramid radii radius rectangle regular respects right angles right-angled triangle Scholium segment Show shown sides similar sine solution sphere spherical triangle square straight line supplement taken Tang tangent term THEOREM third triangle triangle ABC unit vertex vertices volume whence

### Popular passages

Page 28 - If two triangles have two sides of the one equal to two sides of the...

Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...

Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.

Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.

Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.