Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Page viii
... decimal figures in the square double the number of those in the root Method of approximating roots 107 108 ib . 109 · ib . ib . Method of abridging , by division , the extraction of roots To approximate a root indefinitely , by means of ...
... decimal figures in the square double the number of those in the root Method of approximating roots 107 108 ib . 109 · ib . ib . Method of abridging , by division , the extraction of roots To approximate a root indefinitely , by means of ...
Page xii
... decimal powers The characteristic of logarithms Of the logarithms of fractions The arithmetical complement - ib . 247 249 251 - 253 To change a logarithm from one system to another 254 The logarithm of zero ib . The use of logarithms ...
... decimal powers The characteristic of logarithms Of the logarithms of fractions The arithmetical complement - ib . 247 249 251 - 253 To change a logarithm from one system to another 254 The logarithm of zero ib . The use of logarithms ...
Page 108
... denominator , may evi- dently be applied to any kind of fraction whatever , and more readily to decimals than to others . It is manifest 108 Elements of Algebra . What is meant by the term incommensurable or irrational ·
... denominator , may evi- dently be applied to any kind of fraction whatever , and more readily to decimals than to others . It is manifest 108 Elements of Algebra . What is meant by the term incommensurable or irrational ·
Page 109
... decimal figures in the square is always double that of the decimal figures in the root . The truth of this remark is further evident from the rule observed in the multiplication of decimal numbers , which requires that a product should ...
... decimal figures in the square is always double that of the decimal figures in the root . The truth of this remark is further evident from the rule observed in the multiplication of decimal numbers , which requires that a product should ...
Page 110
... decimal places , we obtain 0,59 , which must be added to 181 ; the result will be 181,59 for the root of 32976 , which is accurate to within one hundredth . In order to prove that this method is correct , let us designate the proposed ...
... decimal places , we obtain 0,59 , which must be added to 181 ; the result will be 181,59 for the root of 32976 , which is accurate to within one hundredth . In order to prove that this method is correct , let us designate the proposed ...
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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.