## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 48

Page iv

...

...

**corresponds**more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been sub- jected . The In ... Page 46

...

...

**corresponding**exterior angle , is equal A E D Ce 18 B to two right angles ( P. I. ) : hence , the sum of all the inte rior and exterior angles is equal to two right angles taken as many times as the polygon has sides . But 46 GEOMETRY . Page 49

...

...

**corresponding**sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . BOOK II . RATIOS AND PROPORTIONS . DEFINITIONS . 1. 4 ... Page 57

...

...

**corresponding**consequent . From the definition of a continued proportion ( D. 3 ) , A : B :: C : D :: E : F :: G : H , & c . , hence , B B whence , BA = AB ; Α A B D whence , BC AD ; A B 11 A 72 F whence , BE = AF ; E B H ; whence , BG ... Page 58

...

...

**corresponding**terms of two proportions are equal , each term of the resulting proportion will be the square of the**corresponding**term in either of the given pro- portions : hence , If four quantities are proportional , their squares ...### 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...