Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
From inside the book
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Page 4
... give 2x + b = a . Now it is manifest that , if it is necessary to add to double of x , or to 2x , the quantity b in ... gives the rule found before , according to which , in order to obtain the less of two parts sought we subtract from ...
... give 2x + b = a . Now it is manifest that , if it is necessary to add to double of x , or to 2x , the quantity b in ... gives the rule found before , according to which , in order to obtain the less of two parts sought we subtract from ...
Page 6
... gives the same rule as the above for determining the greater of the two parts sought . I will not stop to deduce ... give determinate values to the known numbers . I will suppose that the number to be divided is 230 ; that the excess of ...
... gives the same rule as the above for determining the greater of the two parts sought . I will not stop to deduce ... give determinate values to the known numbers . I will suppose that the number to be divided is 230 ; that the excess of ...
Page 15
... ax - 3x = b c gives x = bc a- 3 Also the equation x + axcd is reduced to C- d x = 1+ a for it is necessary to observe that the letter , Equations of the First Degree . 15 To disengage an unknown quantity from multipliers -
... ax - 3x = b c gives x = bc a- 3 Also the equation x + axcd is reduced to C- d x = 1+ a for it is necessary to observe that the letter , Equations of the First Degree . 15 To disengage an unknown quantity from multipliers -
Page 19
... gives this case of the proposed question . simple rule for resolving every Divide the product of the numbers , which denote the times employ- ed by each fountain in filling the vessel , by the sum of these numbers ; the quotient ...
... gives this case of the proposed question . simple rule for resolving every Divide the product of the numbers , which denote the times employ- ed by each fountain in filling the vessel , by the sum of these numbers ; the quotient ...
Page 27
... give them the sign plus . Indeed , if from the quantity a we would take b - c , and should first write ab , we should ... gives for the true result abc . - This reasoning , which may be applied to all similar cases shows that the sign of ...
... give them the sign plus . Indeed , if from the quantity a we would take b - c , and should first write ab , we should ... gives for the true result abc . - This reasoning , which may be applied to all similar cases shows that the sign of ...
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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.