Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Page 6
... suppose that the number to be divided is 230 ; that the excess of the middle part above the least is 40 ; and that of the greatest above the middle one is 60 . Denoting the least part by x , the middle one will be the least plus 40 , or ...
... suppose that the number to be divided is 230 ; that the excess of the middle part above the least is 40 ; and that of the greatest above the middle one is 60 . Denoting the least part by x , the middle one will be the least plus 40 , or ...
Page 41
... ; but this being divided by itself must give unity for the quotient , which becomes the new numerator . Suppose for example the fraction 4 a b c 12 a2 b3 c d ; the factors 12 , a3 , b3 , and c Alg . 6 Division of Algebraic Quantities . 41.
... ; but this being divided by itself must give unity for the quotient , which becomes the new numerator . Suppose for example the fraction 4 a b c 12 a2 b3 c d ; the factors 12 , a3 , b3 , and c Alg . 6 Division of Algebraic Quantities . 41.
Page 62
... suppose the first sum received by the labourer to be 46 francs , and the second 30 , the other circumstances remain- ing as before ; the equations of the question will then be case . 12x + 7y = 46 , 8x + 5y = 30 . The first gives 46-12 ...
... suppose the first sum received by the labourer to be 46 francs , and the second 30 , the other circumstances remain- ing as before ; the equations of the question will then be case . 12x + 7y = 46 , 8x + 5y = 30 . The first gives 46-12 ...
Page 70
... suppose , that the two couriers proceed in the same direction , and that the one who sets out from A is pursu- ing the one who sets out from B , and who is travelling toward the same point C , placed beyond B , with respect to A. Α ...
... suppose , that the two couriers proceed in the same direction , and that the one who sets out from A is pursu- ing the one who sets out from B , and who is travelling toward the same point C , placed beyond B , with respect to A. Α ...
Page 71
... suppose b smaller than c , and take , for example , b = 10 , c = 20 , we find x = y = 10 10 a - 20 10 a α , 10 20 a = = - 2 a . 10 - · 20 - 10 20 a These values being affected with the sign - , make it evident , that the question cannot ...
... suppose b smaller than c , and take , for example , b = 10 , c = 20 , we find x = y = 10 10 a - 20 10 a α , 10 20 a = = - 2 a . 10 - · 20 - 10 20 a These values being affected with the sign - , make it evident , that the question cannot ...
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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.