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 18
... 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 be equal . 4. If equals be added to unequals , the suns will be ...
... 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 be equal . 4. If equals be added to unequals , the suns will be ...
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 Ε D B ...
... 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 Ε D B ...
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 ...
... 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 ...
Page 24
... equal to two right angles , the two lines met will form 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 . A- PBE ...
... equal to two right angles , the two lines met will form 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 . A- PBE ...
Page 25
... equal in all their parts . For , let ABC be applied to DEE , in such a manner that the angle A shall coincide with ... equal to DE , the vertex B will coincide with the vertex E ; and because AC is equal to DF , the vertex C will ...
... equal in all their parts . For , let ABC be applied to DEE , in such a manner that the angle A shall coincide with ... equal to DE , the vertex B will coincide with the vertex E ; and because AC is equal to DF , the vertex C will ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence