## Elements of Geometry |

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ABCD according algebraic altitude applied base becomes called centre circ circle circumference coefficient common consequently considered contains Corollary cube Demonstration denominator denoted described determine divided division divisor draw entire equal equation equivalent evident example exponent expression factors fall figure follows four fraction given gives greater half hence homologous inscribed known less letters manner means measure meet method multiplied necessary observed obtain operation parallel pass perpendicular plane polygon preceding prism problem proportion proposition pyramid question quotient radius ratio reason reduced remainder represented respect result right angles root rule Scholium sides similar simple solid solid angle Solution sphere square straight line substitute subtract suppose surface taken term THEOREM third tion triangle units unknown quantity whence whole

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Side 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Side 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.

Side 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.

Side 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.

Side 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.

Side 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.

Side 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.

Side 203 - In every triangle the sum of the three angles is equal to two right angles.

Side 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.

Side 141 - If a pyramid is cut by a plane parallel to its base, the...