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 28
... rectangle of two numbers should be great- er than the sum of their squares ; both which are equally impossible : but , as an instance of the impossibility of some sort of questions , when the conclusion comes out negative , let there be ...
... rectangle of two numbers should be great- er than the sum of their squares ; both which are equally impossible : but , as an instance of the impossibility of some sort of questions , when the conclusion comes out negative , let there be ...
Σελίδα 72
... quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are propor- tional , the rectangle of the means divided by either extreme , will give the other extreme . • See Appendix . = For , by the second theorem , ad bc 72 Of Proportion .
... quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are propor- tional , the rectangle of the means divided by either extreme , will give the other extreme . • See Appendix . = For , by the second theorem , ad bc 72 Of Proportion .
Σελίδα 74
... rectangle of the extremes is equal to that of their two ad- jacent terms : and , after the very same manner , it will ap- pear , that the rectangle of the third and last but two , is equal to that of their two adjacent terms , the ...
... rectangle of the extremes is equal to that of their two ad- jacent terms : and , after the very same manner , it will ap- pear , that the rectangle of the third and last but two , is equal to that of their two adjacent terms , the ...
Σελίδα 120
... rectangle = r ; so shall the sum of the two extremes be - + ( хх yy y 1 a s , and their rectangle also = r ( by the nature of the question . ) But ( by problem 68 ) the sum of the squares of any two numbers whose sum is s , and rectan ...
... rectangle = r ; so shall the sum of the two extremes be - + ( хх yy y 1 a s , and their rectangle also = r ( by the nature of the question . ) But ( by problem 68 ) the sum of the squares of any two numbers whose sum is s , and rectan ...
Σελίδα 121
... rectangle by y2 ( see theor . 7. sect . 10 , ) the sum of their squares will ( by problem 68 ) be — a 2y2 and , in the very same manner , the sum of the squares of the two terms ( x and x ) adjacent to the middle one ( y ) will be 2y2 ...
... rectangle by y2 ( see theor . 7. sect . 10 , ) the sum of their squares will ( by problem 68 ) be — a 2y2 and , in the very same manner , the sum of the squares of the two terms ( x and x ) adjacent to the middle one ( y ) will be 2y2 ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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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.