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

### From inside the book

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Page 179

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**Parallelopipedon**is one whose lat- eral edges are perpendicular to the planes of the bases . A Rectangular**Parallelopipedon**is whose faces are all rectangles . . A Cube is a rectangular**parallelopipedon**whose faces are squares . 1 8. A ... Page 186

... , will be equal in all their parts to the faces which include the corresponding triedral angle of the other , each to each , and they will be similarly placed . PROPOSITION VI . THEOREM . In any

... , will be equal in all their parts to the faces which include the corresponding triedral angle of the other , each to each , and they will be similarly placed . PROPOSITION VI . THEOREM . In any

**parallelopipedon**, the 186 GEOMETRY . Page 187

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**parallelopipedon**, the opposite faces are equal in all their parts , each to each , and their planes are**parallel**. A E B Let ABCD - H be a**parallelopipedon**: then will its opposite faces be equal and their planes will be**parallel**. For ... Page 188

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**parallelopipedon**. PROPOSITION VII . THEOREM . If a plane be passed through the diagonally opposite edges of a**parallelopipedon**, it will divide the**parallelopipedon**into two equal triangular prisms . Let ABCD - H be a**parallelopipedon**... Page 189

From the Works of A.M. Legendre Adrien Marie Legendre. because their opposite sides are

From the Works of A.M. Legendre Adrien Marie Legendre. because their opposite sides are

**parallel**, each to each ...**parallelopipedon**AG , which has the same triedral angle A , and the same edges AB , AD , and AE . PROPOSITION VIII ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence

### Popular passages

Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.

Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

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

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 99 - The area of a parallelogram is equal to the product of its base and altitude.

Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.

Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.