Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Page viii
... perfect squares Method of determining whether the root found is too small To find the square and square root of a fraction Every prime number , which will divide the product of two num- bers , will necessarily divide one of these ...
... perfect squares Method of determining whether the root found is too small To find the square and square root of a fraction Every prime number , which will divide the product of two num- bers , will necessarily divide one of these ...
Page 105
... perfect square . If we look at the table given , page 100 , we shall see that between the squares of each of the nine primitive numbers , there are in- tervals comprehending many numbers , which have no assignable root ; 45 , for ...
... perfect square . If we look at the table given , page 100 , we shall see that between the squares of each of the nine primitive numbers , there are in- tervals comprehending many numbers , which have no assignable root ; 45 , for ...
Page 107
... square of the fraction 99. From this last proposition it follows , that entire numbers , except only such as are perfect squares , admit of no assignable root , either among whole numbers or fractions . Yet it is evident , that there ...
... square of the fraction 99. From this last proposition it follows , that entire numbers , except only such as are perfect squares , admit of no assignable root , either among whole numbers or fractions . Yet it is evident , that there ...
Page 108
... perfect square . The root of the greatest square contained in the numerator will then be that of the proposed number expressed in parts , the value of which will be denoted by the root of the denominator . If we convert , for example ...
... perfect square . The root of the greatest square contained in the numerator will then be that of the proposed number expressed in parts , the value of which will be denoted by the root of the denominator . If we convert , for example ...
Page 111
... square , we find , which , subtracted from 2 or , gives for a remainder this case the formula - · • In becomes N ... perfect square . This is done by multiplying the two terms of the pro- posed fraction by the denominator . If it were ...
... square , we find , which , subtracted from 2 or , gives for a remainder this case the formula - · • In becomes N ... perfect square . This is done by multiplying the two terms of the pro- posed fraction by the denominator . If it were ...
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Common terms and phrases
a² b³ algebraic Algebraic Quantities Arith arithmetic becomes binomial changing the signs coefficient common divisor consequently contains courier cube root decimal deduce denominator denoted divided dividend division employed entire number enunciation equa evident example exponent expression extract the root figures follows formula fraction given in art given number gives greater greatest common divisor last term letters logarithm manner method multiplicand multiplied negative number of arrangements observed obtain operation perfect square polynomials preceding article proposed equation proposed number quan question quotient radical quantities radical sign reduced remainder represented resolve result rule given second degree second member second term simple quantities square root subtract suppose taken tens third tion tities units unity unknown quantity vulgar fractions whence whole numbers
Popular passages
Page 9 - 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 44 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 101 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 122 - ... is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots.
Page 180 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
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 185 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Page 164 - 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.