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 70
... extremes . = For since , by supposition , ba is dc , therefore is b + c = d + a , by transposition . THEOREM II . In any continued arithmetical progression ( 5 , 7 , 9 , 11 , 13 , 15 ) the sum of the two extremes , and that of every ...
... extremes . = For since , by supposition , ba is dc , therefore is b + c = d + a , by transposition . THEOREM II . In any continued arithmetical progression ( 5 , 7 , 9 , 11 , 13 , 15 ) the sum of the two extremes , and that of every ...
Σελίδα 71
... extremes : and in the same manner it will ap- pear , that the sum of any two other corresponding terms must be equal to that of the two extremes . When the number of terms is odd , as in the progres- sion , 4 , 7 , 10 , 13 , 16 , then ...
... extremes : and in the same manner it will ap- pear , that the sum of any two other corresponding terms must be equal to that of the two extremes . When the number of terms is odd , as in the progres- sion , 4 , 7 , 10 , 13 , 16 , then ...
Σελίδα 72
... extremes ) multi- plied by the whole number of terms ; or to the whole sum of the extremes multiplied by half the number of terms . Geometrical Proportion . THEOREM I. If four quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are in geome ...
... extremes ) multi- plied by the whole number of terms ; or to the whole sum of the extremes multiplied by half the number of terms . Geometrical Proportion . THEOREM I. If four quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are in geome ...
Σελίδα 73
... extreme be given , the other extreme may be found . THEOREM IV . The products of the corresponding terms of two ... extremes , and therefore the quantities are proportional , by theorem 2 . L THEOREM VI . If three numbers , a , b of ...
... extreme be given , the other extreme may be found . THEOREM IV . The products of the corresponding terms of two ... extremes , and therefore the quantities are proportional , by theorem 2 . L THEOREM VI . If three numbers , a , b of ...
Σελίδα 74
... extremes , and that of every other two terms , equally distant from them , are equal . For the ratio of the first term to the second , being the same as that of the last but one to the last , these four terms are in proportion ; and ...
... extremes , and that of every other two terms , equally distant from them , are equal . For the ratio of the first term to the second , being the same as that of the last but one to the last , these four terms are in proportion ; and ...
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.