Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 34
Page v
... Ratios and Proportions , - - 47 BOOK III . The Circle , and the Measurement of Angles ,. Problems relating to the First and Third Books , - - BOOK IV . 57 76 Proportions of Figures - Measurement of Areas , Problems relating to the ...
... Ratios and Proportions , - - 47 BOOK III . The Circle , and the Measurement of Angles ,. Problems relating to the First and Third Books , - - BOOK IV . 57 76 Proportions of Figures - Measurement of Areas , Problems relating to the ...
Page 46
... equal : whence , it follows , that the angles AEB , BEC , are equal , and therefore , the two diago- nals of a rhombus bisect each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . DEFINITIONS . 46 GEOMETRY .
... equal : whence , it follows , that the angles AEB , BEC , are equal , and therefore , the two diago- nals of a rhombus bisect each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . DEFINITIONS . 46 GEOMETRY .
Page 47
... ratio of A to B is expressed by B A A and B are called the terms of the ratio ; the first is called the antecedent , and the second , the consequent . 3. The ratio of magnitudes may be expressed by num- bers , either exactly or ...
... ratio of A to B is expressed by B A A and B are called the terms of the ratio ; the first is called the antecedent , and the second , the consequent . 3. The ratio of magnitudes may be expressed by num- bers , either exactly or ...
Page 48
... ratio between the straight lines CD and AB , which we will suppose commensurable . From the greater line AB , cut off a part equal A to the less CD , as many times as possible ; for ex- ample , twice , with the remainder BE From the ...
... ratio between the straight lines CD and AB , which we will suppose commensurable . From the greater line AB , cut off a part equal A to the less CD , as many times as possible ; for ex- ample , twice , with the remainder BE From the ...
Page 49
... ratio in numbers . Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall then have , FD - 2 ; but EB contains FD once , plus GB ...
... ratio in numbers . Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall then have , FD - 2 ; but EB contains FD once , plus GB ...
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
adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosē Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line 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 opposite parallel 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 sinē sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...