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

### From inside the book

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**Given**Loga- rithm , 260 Multiplication by Logarithms , - 261 Division by Logarithms , 262 Arithmetical Complement ...**Angle**with a Protractor ,. 270 Parts of a Plane Triangle , - 271 Plane Trigonometry , Defined ,. 271 Division of ... Page 10

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**given**portion of space , the term surface to denote the boundary of a solid , the term line to denote the boundary ...**ANGLE**is a term which designates the portion of a surface included by two lines meeting at a common point ; and ... Page 20

... given straight line may be bisected : that is , divided into two equal parts . 5. That a straight line may bisect a

... given straight line may be bisected : that is , divided into two equal parts . 5. That a straight line may bisect a

**given angle**. 6. That a perpendicular may be drawn to a given straight line , either from a point without the line ... Page 31

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**angle**BCD = B . Then , in the triangle CDB , we shall A have CD = BD ( P. 12 ) . Now , the side AC < AD + DC ; but ...**given**point , without a straight line , only one perpen- dicular can be drawn to that line . A D- -E B F Let A ... Page 32

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**given**point C , in the line AB , it is also impossible to erect more than one perpendicular to that line . For , if CD , CE , were both perpendicular to AB , the**angles**A- BCD , BCE , would both be right E D V -B**angles**; hence , they ...### Other editions - View all

### Common terms and phrases

adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices

### Popular passages

Page 27 - If two triangles have two sides of the one equal to two sides of the...

Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.

Page 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.

Page 26 - The sum of any two sides of a triangle is greater than the third side.

Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...

Page 93 - The area of a parallelogram is equal to the product of its base and altitude.

Page 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 323 - 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 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.