Elements of Geometry and Trigonometry |
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Page 18
... equal to the same thing , are equal to each other . 2. If equals be added to equals , the suns 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 suns 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 ...
... 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 ...
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 r 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 . at Let AB and DE intersect C : then will the opposite r vertical angles be equal . The ...
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- B C ...
... 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- B C ...
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
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence