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
Results 1-5 of 49
Page 10
... called a Surface . Now , since that which bounds a solid is no part of the solid itself , it follows , that a surface has but two dimensions , ength and breadth . 5. If we consider a limited portion of a surface , that which separates ...
... called a Surface . Now , since that which bounds a solid is no part of the solid itself , it follows , that a surface has but two dimensions , ength and breadth . 5. If we consider a limited portion of a surface , that which separates ...
Page 11
... called lines . Thus , we say , the straight line AB , is the shortest dis- tance between the two points A and B. The mark AB , on the paper , is A- not the geometrical line AB , but only -В the sign or representative of it - the ...
... called lines . Thus , we say , the straight line AB , is the shortest dis- tance between the two points A and B. The mark AB , on the paper , is A- not the geometrical line AB , but only -В the sign or representative of it - the ...
Page 14
... called the sides of the angle , and the common point of intersection , the vertex . Thus , the part of the plane includ- ed between AB and AC is called an angle : AB and AC are its sides , and A its vertex . An angle is sometimes ...
... called the sides of the angle , and the common point of intersection , the vertex . Thus , the part of the plane includ- ed between AB and AC is called an angle : AB and AC are its sides , and A its vertex . An angle is sometimes ...
Page 15
... called its perimeter . 19. The polygon of three sides , the simplest of all , is called a triangle ; that of four sides , a quadrilateral ; that of five , a pentagon ; that of six , a hexagon ; that of seven , a heptagon ; that of eight ...
... called its perimeter . 19. The polygon of three sides , the simplest of all , is called a triangle ; that of four sides , a quadrilateral ; that of five , a pentagon ; that of six , a hexagon ; that of seven , a heptagon ; that of eight ...
Page 16
... called the hypothenuse , and the other two sides , the base and perpen- dicular . 6. An obtuse - angled triangle is one which has an obtuse angle . 24. There are three kinds of QUADRILATERALS : 1. The trapezium , which has no two of its ...
... called the hypothenuse , and the other two sides , the base and perpen- dicular . 6. An obtuse - angled triangle is one which has an obtuse angle . 24. There are three kinds of QUADRILATERALS : 1. The trapezium , which has no two of its ...
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.