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ABCD according algebraic altitude applied base becomes called centre circ circle circumference common consequently considered contained Corollary cylinder Demonstration denominator described determine diameter divided dividend 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 obtain operation parallel pass perpendicular plane polyedron polygon preceding prism problem proportion proposed pyramid question quotient radius ratio reason rectangle reduced remainder represented respect result right angles root rule Scholium sides similar simple solid angle Solution sphere square straight line substitute subtract suppose surface taken term THEOREM third triangle units unknown quantity whence whole
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 153 - 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 78 - 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 27 - 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 54 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 162 - 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 205 - In every triangle the sum of the three angles is equal to two right angles.
Page 164 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.