A Treatise of Algebra: Wherein the Principles are Demonstrated ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems ...M. Carey & sons, 1821 - 408 σελίδες |
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Σελίδα 42
... a frac- tion , or consists of several factors multiplied together , its root will be extracted , by extracting the root of each par- ticular factor . Thus the square root of a2b2 will be ab ; 42 Of Evolution , SECTION VII EVOLUTION.
... a frac- tion , or consists of several factors multiplied together , its root will be extracted , by extracting the root of each par- ticular factor . Thus the square root of a2b2 will be ab ; 42 Of Evolution , SECTION VII EVOLUTION.
Σελίδα 45
... extracting the roots of compound quantities ; which , sometimes , bring out the conclusions rather more expeditiously ; but as these are confined to particular cases , and would take up a great deal of room to explain in a manner suf ...
... extracting the roots of compound quantities ; which , sometimes , bring out the conclusions rather more expeditiously ; but as these are confined to particular cases , and would take up a great deal of room to explain in a manner suf ...
Σελίδα 54
... extracting the square root of 4 , becomes 27 : also ✓ab is reduced to a x ; which , by extracting the root of a2 , becomes ab : likewise a3b4c2 , or abc is reduced to ab3 × be , or abybe2 : 4a3x -4a2x2 bc2 moreover - x 4a2 is reduced ...
... extracting the square root of 4 , becomes 27 : also ✓ab is reduced to a x ; which , by extracting the root of a2 , becomes ab : likewise a3b4c2 , or abc is reduced to ab3 × be , or abybe2 : 4a3x -4a2x2 bc2 moreover - x 4a2 is reduced ...
Σελίδα 99
... extracting the square root , on both sides thereof : thus in the equation x2 ab , the value of x is given ✓ ab ( for if two quantities be equal , their square roots must necessarily be equal . ) The method of solution when the equation ...
... extracting the square root , on both sides thereof : thus in the equation x2 ab , the value of x is given ✓ ab ( for if two quantities be equal , their square roots must necessarily be equal . ) The method of solution when the equation ...
Σελίδα 100
... extracting the root , or finding the value of x , is the same in all three , except that , in the last of them , the root of the known part , on the right - hand side , is to be expressed with the double sign before it , x having two ...
... extracting the root , or finding the value of x , is the same in all three , except that , in the last of them , the root of the known part , on the right - hand side , is to be expressed with the double sign before it , x having two ...
Συχνά εμφανιζόμενοι όροι και φράσεις
added algebraic arch arithmetical progression ax² become biquadratic circle co-sine coefficient common difference completing the square consequently CONSTRUCTION cube cube root cubic equation DEMONSTRATION denominator dividend divisor draw equa equal example expressed extracting find the numbers former fraction geometrical progression given angle given equation gives greater Hence latter likewise manner Method of Calculation moidores multiplied negative number of terms number sought perpendicular PROBLEM proportion proposed Q. E. D. Method quadratic equation quan question quotient radical quantities radius ratio rectangle reduced remains required numbers right-line rule second term sides sine square root subtracted supposed surd thence theorem third three numbers tion tity trapezium triangle unknown quantity value being substituted vulgar fraction whence wherein whereof whole number
Δημοφιλή αποσπάσματα
Σελίδα 241 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 64 - ... then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
Σελίδα 251 - ... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base.
Σελίδα 87 - A composition of copper and tin containing 100 cubic inches weighed 505 ounces. How many ounces of each metal did it contain, supposing a cubic inch of copper to weigh of ounces, and a cubic inch of tin to weigh 4т ounces ? Ans. 420 of copper, and
Σελίδα 88 - ... half of what he had left, and half a sheep over ; and, soon after this, a third party met him, and used him in the same manner, and then he had only five sheep left. It is required to find what number of sheep he had at first, Ans, 47 sheep.
Σελίδα 254 - The following particular directions, however, may be of some use. 1st, In preparing the figure, by drawing lines, let them be either parallel or perpendicular to other lines in the figure, or so as to form similar triangles. And if an angle be given, it will be proper to let the perpendicular be opposite to that angle, and to fall from one end of a given line, if possible.