Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
From inside the book
Results 6-10 of 47
Page 72
... substituting them in the equations x - y = a , χ y = b c ' we have by the rule for the signs - a + 2a = a , a 10 2a 20 ' equations which are satisfied ; since , by making the reductions , the first member becomes equal to the second ...
... substituting them in the equations x - y = a , χ y = b c ' we have by the rule for the signs - a + 2a = a , a 10 2a 20 ' equations which are satisfied ; since , by making the reductions , the first member becomes equal to the second ...
Page 74
... , shall satisfy the equations of the problem . By substituting them in the equations X- - y = a , Τ y = which answer to the case where b = c , we have by the first , or or lastly , ab ab = α , ab 74 Elements of Algebra .
... , shall satisfy the equations of the problem . By substituting them in the equations X- - y = a , Τ y = which answer to the case where b = c , we have by the first , or or lastly , ab ab = α , ab 74 Elements of Algebra .
Page 76
... substituting this value in the second equation , which is = x y b b it becomes = y y b b The last equation having its two members identical , that is to say , composed of the same terms with the same sign , is verified , what- ever ...
... substituting this value in the second equation , which is = x y b b it becomes = y y b b The last equation having its two members identical , that is to say , composed of the same terms with the same sign , is verified , what- ever ...
Page 86
... Substituting this value in the expression for that of y , I find y = = 46-7 X 4 46-28 = 18 , 6 or y = 3 ; 6 6 and by substituting these values in the expression for that of z , we obtain - - 12- 2 × 3 = 23 z = 23 3 X 4 6 , or z = 5 . It ...
... Substituting this value in the expression for that of y , I find y = = 46-7 X 4 46-28 = 18 , 6 or y = 3 ; 6 6 and by substituting these values in the expression for that of z , we obtain - - 12- 2 × 3 = 23 z = 23 3 X 4 6 , or z = 5 . It ...
Page 87
... substituting this value , the second and third equations . become 19628y63 z 2 25236y81 % 2 + 3y5z = 3 , + 10y11 z = 4 . Making the denominators to disappear , we have - 196 +28 y 63 z + 6y 10 z = 6 , - 25236y81 z + 20 y - · 22 z = 8 ...
... substituting this value , the second and third equations . become 19628y63 z 2 25236y81 % 2 + 3y5z = 3 , + 10y11 z = 4 . Making the denominators to disappear , we have - 196 +28 y 63 z + 6y 10 z = 6 , - 25236y81 z + 20 y - · 22 z = 8 ...
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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.