Elements of Geometry and Trigonometry: Translated from the French of A.M. Legendre by Daniel Brewster : Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 19
... base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB AI + IB ; therefore , GC + AB < GI + AI + IC + IB , or , which is the same thing , GC + AB < AG + BC . Take away AB from the one side , and ...
... base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB AI + IB ; therefore , GC + AB < GI + AI + IC + IB , or , which is the same thing , GC + AB < AG + BC . Take away AB from the one side , and ...
Page 20
... base BC . Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to ... base , is perpendicular to the base , and divides the angle at the vertex into two equal parts . In a triangle which ...
... base BC . Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to ... base , is perpendicular to the base , and divides the angle at the vertex into two equal parts . In a triangle which ...
Page 21
... base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be ...
... base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be ...
Page 42
... base AB retaining its position , the curve line AEB must fall exactly on the A curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a ...
... base AB retaining its position , the curve line AEB must fall exactly on the A curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a ...
Page 68
... base . Thus , AD is the altitude of the triangle BAC B 6. The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- A gram DB ...
... base . Thus , AD is the altitude of the triangle BAC B 6. The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- A gram DB ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex