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 13
... give the learner a clear idea of the reason and certainty of such rules . First , then , it is to be observed , that when several quan- tities are to be multiplied continually together , the result , or product , will come out exactly ...
... give the learner a clear idea of the reason and certainty of such rules . First , then , it is to be observed , that when several quan- tities are to be multiplied continually together , the result , or product , will come out exactly ...
Side 21
... gives the true product , AC - BC — AD + BD , as was to be demonstrated . And , universally , if the sign of any proposed term of the multiplier , in any case what- ever , be affirmative , it is easy to conceive that the re- quired ...
... gives the true product , AC - BC — AD + BD , as was to be demonstrated . And , universally , if the sign of any proposed term of the multiplier , in any case what- ever , be affirmative , it is easy to conceive that the re- quired ...
Side 24
... give a learner a distinct idea how the product of two simple quantities , with negative signs , such as -band - c , ought to be expressed , when they stand alone , independent of all other quantities : And I can- not help thinking ...
... give a learner a distinct idea how the product of two simple quantities , with negative signs , such as -band - c , ought to be expressed , when they stand alone , independent of all other quantities : And I can- not help thinking ...
Side 26
... give gives X = - cb + ab ; that is 7 by --- b will - + x ; c by - b , -cb ; and -a by -b , ab ; which appear to be true ; because the products being thus ex- pressed , the same conclusion is derived , as if both sides of the original ...
... give gives X = - cb + ab ; that is 7 by --- b will - + x ; c by - b , -cb ; and -a by -b , ab ; which appear to be true ; because the products being thus ex- pressed , the same conclusion is derived , as if both sides of the original ...
Side 27
... 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 , had been performed alto- gether by real quantities : but notwithstanding ...
... 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 , had been performed alto- gether by real quantities : but notwithstanding ...
Vanlige uttrykk og setninger
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
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.