Elements of Geometry and Trigonometry |
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Page 18
Adrien Marie Legendre Charles Davies. AXIOMS . 1. Things which are equal to the same thing , are equal to each other . 2. If equals be added to equals , the sums will be equal . 3. If equals be subtracted from equals , the remainders will ...
Adrien Marie Legendre Charles Davies. AXIOMS . 1. Things which are equal to the same thing , are equal to each other . 2. If equals be added to equals , the sums will be equal . 3. If equals be subtracted from equals , the remainders will ...
Page 20
... equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles . At C , let CE be drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles A- E D ...
... equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles . At C , let CE be drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles A- E D ...
Page 21
... equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE intersect at C : then will the opposite or vertical angles be equal . The ...
... equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE intersect at C : then will the opposite or vertical angles be equal . The ...
Page 24
... equal to two right angles , the one and the same straight line . Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then will CB be the prolongation of AC . D A- B C E For , if not ...
... equal to two right angles , the one and the same straight line . Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then will CB be the prolongation of AC . D A- B C E For , if not ...
Page 25
... equal to DF , the vertex C will coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I ...
... equal to DF , the vertex C will coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
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.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...