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 sider |
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Side 26
... sides thereof , as to leave the remaining quanti- ties negative ; and then it is , chiefly , that the multiplica- tion by quantities absolutely negative takes place . Thus if there were given the equation a- = c b ( in order to find x ...
... sides thereof , as to leave the remaining quanti- ties negative ; and then it is , chiefly , that the multiplica- tion by quantities absolutely negative takes place . Thus if there were given the equation a- = c b ( in order to find x ...
Side 27
... sides we shall have x2 ― = √c ī -- = a ; and this multiplied by ✓ , will give ✓2 ( or x ) ✓cb + ab : which also appears to be true , because the result , this way , comes out exactly the same , as if the operations , for finding x ...
... sides we shall have x2 ― = √c ī -- = a ; and this multiplied by ✓ , will give ✓2 ( or x ) ✓cb + ab : which also appears to be true , because the result , this way , comes out exactly the same , as if the operations , for finding x ...
Side 58
... sides of the equation , ac- cording as the sign thereof is positive or negative . Thus , in the equation x + 6 = 16 ( which by transposition be- comes x = 16- 6 10 ) the number 6 is subtracted from both sides ; and in the equation x - 4 ...
... sides of the equation , ac- cording as the sign thereof is positive or negative . Thus , in the equation x + 6 = 16 ( which by transposition be- comes x = 16- 6 10 ) the number 6 is subtracted from both sides ; and in the equation x - 4 ...
Side 59
... side ( by rule 1 ; ) and then , if both sides be involved to the power denominated by the surd , an equation will arise free from radical quantities ; unless there happen to be more surds than one , in which case the operation is to be ...
... side ( by rule 1 ; ) and then , if both sides be involved to the power denominated by the surd , an equation will arise free from radical quantities ; unless there happen to be more surds than one , in which case the operation is to be ...
Side 61
... power of a may be positive ) gives xxbx ab . But the same conclusion may be otherwise brought out , by first changing the sides of the equation ax + ab + bx = ax + xx ; which thereby becoming ax + xxax + Of Equations . 61.
... power of a may be positive ) gives xxbx ab . But the same conclusion may be otherwise brought out , by first changing the sides of the equation ax + ab + bx = ax + xx ; which thereby becoming ax + xxax + Of Equations . 61.
Vanlige uttrykk og setninger
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Populære avsnitt
Side 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.
Side 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Side 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.
Side 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.
Side 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
Side 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.
Side 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.