Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 58
... or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of proportional quantities are proportionals . BOOK III . ГНЕ CIRCLE AND THE MEASUREMENT OF ANGLES 58 GEOMETRY .
... or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of proportional quantities are proportionals . BOOK III . ГНЕ CIRCLE AND THE MEASUREMENT OF ANGLES 58 GEOMETRY .
Page 59
... MEASUREMENT OF ANGLES DEFINITIONS . } 1. A CIRCLE is a plane figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A ...
... MEASUREMENT OF ANGLES DEFINITIONS . } 1. A CIRCLE is a plane figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A ...
Page 74
... measured by a common unit : then will they be proportional to the intercepted arcs AB and DE . M Z ; Let the angle M be a common unit and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the ...
... measured by a common unit : then will they be proportional to the intercepted arcs AB and DE . M Z ; Let the angle M be a common unit and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the ...
Page 77
... measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle ...
... measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle ...
Page 78
... measured by the arc DE ( P. XVII . , S. ) : hence , the , angle DAE is measured by half of the arc DE ; which was to be proved . B E 2o . Let DAB be an inscribed angle , and let the centre lie within it then will the angle be measured ...
... measured by the arc DE ( P. XVII . , S. ) : hence , the , angle DAE is measured by half of the arc DE ; which was to be proved . B E 2o . Let DAB be an inscribed angle , and let the centre lie within it then will the angle be measured ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
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.