## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 70

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**vertex**; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line meets another the two angles which they form are called adjacent angles . Thus , the A- angles ABD and DBC are adjacent . 12. A ... Page 25

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**vertex**B will coincide with the**vertex**E ; and because AC is equal to DF , the**vertex**C will coincide with the**vertex**F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide ... Page 26

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**vertex**C will coincide with the**vertex**F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the**vertex**A being at the same time on the lines ED and FD , it must be at their intersection D ... Page 30

... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the angle C be equal to the angle B. A AD Join the

... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the angle C be equal to the angle B. A AD Join the

**vertex**A and the middle point 30 GEOMETRY . Page 31

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**vertex**of an isosceles triangle to the middle of the base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal ...### 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

ABē ABCD ACē 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...