## Elements of Geometry and Trigonometry |

### From inside the book

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**homologous**. The corresponding angles are**homologous**angles , the corresponding sides are**homologous**sides , the corresponding diagonals are**homologous**diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS are those which ... Page 118

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**homologous**angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- dicular , each to each , they may have a different relative position from that ... Page 120

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**homologous**sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , BC : AB : : AB : BD , and , BC : AC :: AC : DC , we have ( B. II . , P. I. ) , and , AB2 BC × BD , AC2 = BC x DC ... Page 122

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**homologous**, DE will be parallel to BC , and we shall have , AD : AB :: AE : AC ; hence ( B. II . , P. IV . ) , wę have , A D E ADE : ABE :: ABE : ABC ; that is , ABE is a mean proportional be- tween ADE and ABC . B PROPOSITION XXV ... Page 123

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**homologous**sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F : then will the triangles be to each other as the squares of any two**homologous**sides . Because the angles A and ...### Other editions - View all

Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |

### Common terms and phrases

AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence

### Popular passages

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

Page 100 - The area of a triangle is equal to half the product of its base by its altitude.

Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 59 - A chord is a straight line joining the extremities of an arc.

Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

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.

Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.

Page 123 - Similar triangles are to each other as the squares of their homologous sides.

Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...