Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 3
... positive number , except 1 , may be taken as the base of a system . In the common system , the base is 10 . 2. If we denote any positive number by n , and the corresponding exponent of 10 , by x , we shall have the exponential equation ...
... positive number , except 1 , may be taken as the base of a system . In the common system , the base is 10 . 2. If we denote any positive number by n , and the corresponding exponent of 10 , by x , we shall have the exponential equation ...
Page 4
... positive , and numerically 1 less than the number of places of figures in the given number , - 1 If a decimal fraction lies between 1 and 1 , its loga rithm lies between 1 and 0 , that is , it is equal to plus a decimal ; if a number ...
... positive , and numerically 1 less than the number of places of figures in the given number , - 1 If a decimal fraction lies between 1 and 1 , its loga rithm lies between 1 and 0 , that is , it is equal to plus a decimal ; if a number ...
Page 5
... positive . This fact is indicated by writing the neg- ative sign over the characteristic : thus , 2.371465 , is equiv alent to 2.371465 . It is to be observed , that the characteristic cf the logarithm of a mixed number is the same as ...
... positive . This fact is indicated by writing the neg- ative sign over the characteristic : thus , 2.371465 , is equiv alent to 2.371465 . It is to be observed , that the characteristic cf the logarithm of a mixed number is the same as ...
Page 51
... positive ; consequently , those reckoned in a a con trary direction must be regarded as negative . The arc AB , is called the first quadrant ; the arc BC , the second quadrant ; the arc CD , the third quadrant ; and the arc DA , the ...
... positive ; consequently , those reckoned in a a con trary direction must be regarded as negative . The arc AB , is called the first quadrant ; the arc BC , the second quadrant ; the arc CD , the third quadrant ; and the arc DA , the ...
Page 54
... positive , and N'M ' , BT " , & c . , are negative . All distances estimated from the centre in a direction to towards the extremity of the arc are regarded as positive ; consequently , all distances estimated in a direction from the ...
... positive , and N'M ' , BT " , & c . , are negative . All distances estimated from the centre in a direction to towards the extremity of the arc are regarded as positive ; consequently , all distances estimated in a direction from the ...
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Common terms and phrases
ABē ABCD ACē 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.