Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 , parts hence , AD is equal to DB . A G B equal in all their Again , because CG is perpendicular to AB , at its middle point , 64 GEOMETRY .
... hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , parts hence , AD is equal to DB . A G B equal in all their Again , because CG 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 , AB is equal to AD , and the angle CAB is equal to the angle CAD . gents are therefore equal , and the ...
... hypothenuse AC , and the side BC equal to DC ; and consequently , they are equal in all their parts ( B. I. , P. XVII . ) : hence , AB is equal to AD , and the angle CAB is equal to the angle CAD . gents are therefore equal , and the ...
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 4 : then will BC AB2 + AC2 . = Construct the square BG AH on the side AB , and ...
... 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 4 : then will BC AB2 + AC2 . = Construct the square BG AH on the side AB , and ...
Page 105
... hypothenuse diminished by the square of the other side : thus , AB2 = BC2 - AC2 ; or , AC2 = BC2 — AB2 . Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into twa segments , BD ...
... hypothenuse diminished by the square of the other side : thus , AB2 = BC2 - AC2 ; or , AC2 = BC2 — AB2 . Cor . 2. If from the vertex of the right angle , a per- pendicular be drawn to the hypothenuse , dividing it into twa segments , BD ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB 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 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 mean proportional 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 six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence