Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 36
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles will be equal in all their parts . A Let the right - angled tri- angles ABC and DEF have the hypothenuse AC equal to DF ...
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles will be equal in all their parts . A Let the right - angled tri- angles ABC and DEF have the hypothenuse AC equal to DF ...
Page 64
... hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , A D equal in all their parts hence , AD is equal to DB . Again , because CG 1 is perpendicular to AB , at its middle point 64 GEOMETRY .
... hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , A D equal in all their parts hence , AD is equal to DB . Again , because CG 1 is perpendicular to AB , at its middle point 64 GEOMETRY .
Page 90
... hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in all their parts ( B. I. , P. XVII . ) : hence , hence , AB is equal to AD , and the angle CAB is equal to the angle CAD . gents are therefore equal ...
... hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in all their parts ( B. I. , P. XVII . ) : hence , hence , AB is equal to AD , and the angle CAB is equal to the angle CAD . gents are therefore equal ...
Page 104
... hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the other two sides . Let ABC be a triangle , right - angled at A : then will BC2 AB2 + AC2 . = Construct the square BG on the side BC , AH on ...
... hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the other two sides . Let ABC be a triangle , right - angled at A : then will BC2 AB2 + AC2 . = Construct the square BG on the side BC , AH on ...
Page 105
... hypothenuse diminished by the square of the other side : thus , AB2 BC2 AC2 ; or , AC2 BC2 - AB2 . BC2 = = Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into two segments ...
... hypothenuse diminished by the square of the other side : thus , AB2 BC2 AC2 ; or , AC2 BC2 - AB2 . BC2 = = Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into two segments ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following