Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 sums 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 sums 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 . . A C , let CE be drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles E D A ...
... 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 . . A C , let CE be drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles E D A ...
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 . at Let AB and DE intersect C : then will the opposite or vertical angles be equal . E ...
... equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . at Let AB and DE intersect C : then will the opposite or vertical angles be equal . E ...
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 of the at C , making the sum angles DCA and DCB equal to two right angles : then will CB be the prolongation of AC . D A ...
... equal to two right angles , the two lines met will form one and the same straight line . Let DC meet AC and BC of the at C , making the sum angles DCA and DCB equal to two right angles : then will CB be the prolongation of AC . D A ...
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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Common terms and phrases
ABē 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