Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 47
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . For , draw the diagonal BD . Then , because AB and DC are parallel , the angle DBA is equal to its alternate D A B angle BDC ( P. XX . , C. 2 ) : and , because AD ...
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . For , draw the diagonal BD . Then , because AB and DC are parallel , the angle DBA is equal to its alternate D A B angle BDC ( P. XX . , C. 2 ) : and , because AD ...
Page 48
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D C the sides of the one equal to the sides of the other , each to each ; and ...
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D C the sides of the one equal to the sides of the other , each to each ; and ...
Page 49
... ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and the ...
... ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and the ...
Page 79
... ABCD , are together equal to two right angles ; for the angle DAB is measured by half the arc DCB , the angle DCB by half the arc DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence , their sum ...
... ABCD , are together equal to two right angles ; for the angle DAB is measured by half the arc DCB , the angle DCB by half the arc DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence , their sum ...
Page 90
... ABCD ; join the point A with the points of intersection D and B : then will both AD and AB be tangent to the given circle , and there will be two solutions . For , the angles ABC and ADC are right angles ( P. XVIII . , C. 2 ) : B hence ...
... ABCD ; join the point A with the points of intersection D and B : then will both AD and AB be tangent to the given circle , and there will be two solutions . For , the angles ABC and ADC are right angles ( P. XVIII . , C. 2 ) : B hence ...
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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.