Elements of Geometry |
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Page 58
... an angle of the one equal to an angle of the other and the sides about these angles proportional , are similar . Demonstration . Let the angle A = D ( fig . 122 ) , and let AB : DE :: AC : DF , the triangle ABC is similar to the ...
... an angle of the one equal to an angle of the other and the sides about these angles proportional , are similar . Demonstration . Let the angle A = D ( fig . 122 ) , and let AB : DE :: AC : DF , the triangle ABC is similar to the ...
Page 63
... an angle of the one equal to an angle of the other and the sides about the equal angles proportional , are similar ( 208 ) , conse- quently the angle BCA = GHF . These equal angles being subtracted from the equal angles BCD , GHI , the ...
... an angle of the one equal to an angle of the other and the sides about the equal angles proportional , are similar ( 208 ) , conse- quently the angle BCA = GHF . These equal angles being subtracted from the equal angles BCD , GHI , the ...
Page 64
... an angle of the one equal to an angle of the other and the sides about the equal angles propor- tional ; they are therefore similar ( 208 ) . We might proceed in the same manner to demonstrate , that the remaining triangles are similar ...
... an angle of the one equal to an angle of the other and the sides about the equal angles propor- tional ; they are therefore similar ( 208 ) . We might proceed in the same manner to demonstrate , that the remaining triangles are similar ...
Page 69
... an angle of the one equal to an angle of the other and the sides about the equal angles proportional , are similar ( 208 ) ; therefore But the proportion gives , by division , MP : MQ :: CP : CM or CA. CP : CA :: CA : CQ or therefore CP ...
... an angle of the one equal to an angle of the other and the sides about the equal angles proportional , are similar ( 208 ) ; therefore But the proportion gives , by division , MP : MQ :: CP : CM or CA. CP : CA :: CA : CQ or therefore CP ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...