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abstract according added addition algebraic analysis Analytical applied apprehend Arithmetic axiom base branch called characters common compared conclusion connection considered consists contains corresponding curved deduced definition demonstration denominate denote difference divided elements employed equal equation example exist explain expressed facts figure fixed foot four fractional Geometry give given Hence hundred idea increased indicate inferred kind knowledge known language length letters limits logical magnitudes marks mathematical means merely mind minus multiplied nature operations performed plane portion principles processes properties proportion proposition proved quantities ratio reasoning referred regarded relation represented respect result right angles scale sides similar simple space species spelled square standard straight line subtraction surface symbols taken term thing tion triangles true truths unit of measure volume weight whole written yard
Page 117 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 41 - All definitions are of names, and of names only; but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word.
Page 130 - The area of a rectangle is equal to the product of its base and altitude.
Page 125 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they are equal in all their parts.
Page 124 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Page 133 - Similar triangles are to each other as the squares of their homologous sides.
Page 165 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Page 109 - A Circle is a plane figure, bounded by a curved line, all the points of which are equally distant from a point within, called the cen- OOU-AJ i