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 2
... - tinually together ; so that , if a was 5 , b 4 , and c 3 ; then - would a + b + cxa − b + cxa of Notation . The sums of compound Progressions, arising from a series of powers drawn into the terms of a geo- metrical progression.
... - tinually together ; so that , if a was 5 , b 4 , and c 3 ; then - would a + b + cxa − b + cxa of Notation . The sums of compound Progressions, arising from a series of powers drawn into the terms of a geo- metrical progression.
Σελίδα 3
... draw a line over the given quantity , and at the end thereof place the exponent of the power . Thus a + b2 denotes the same as a + b x a + b , viz . the second power ( or square ) of a + b con- sidered as one quantity : thus also , ab + ...
... draw a line over the given quantity , and at the end thereof place the exponent of the power . Thus a + b2 denotes the same as a + b x a + b , viz . the second power ( or square ) of a + b con- sidered as one quantity : thus also , ab + ...
Σελίδα 4
... drawn below √ ) signifies that the square root of ab + bc is to be first taken , and afterwards divided by d : so that , if a was 2 , b 6 , c 4 , and d 9 , then would ✓ab + be d 36 be or 9 6 Jab + bc 36 but is 56 , or / 4 , which is 2 ...
... drawn below √ ) signifies that the square root of ab + bc is to be first taken , and afterwards divided by d : so that , if a was 2 , b 6 , c 4 , and d 9 , then would ✓ab + be d 36 be or 9 6 Jab + bc 36 but is 56 , or / 4 , which is 2 ...
Σελίδα 241
... drawn from one ex- tremity of an arch to the other ; thus BE is the chord or sub- tense of the archBAE , or BDE . 5. The sine ( or right sine ) of an arch is a right line drawn D G H K I B C ابع F A from one extremity of the arch ...
... drawn from one ex- tremity of an arch to the other ; thus BE is the chord or sub- tense of the archBAE , or BDE . 5. The sine ( or right sine ) of an arch is a right line drawn D G H K I B C ابع F A from one extremity of the arch ...
Σελίδα 245
... draw the subtenses AE and BE ; and let CQ bisect the arch AE in Q and its chord ( perpendicularly ) in D ; then since the angle BEA is a right one ( by Euc . 31. 3. ) the triangles ABE and ADC are similar ; and therefore , AC being AB ...
... draw the subtenses AE and BE ; and let CQ bisect the arch AE in Q and its chord ( perpendicularly ) in D ; then since the angle BEA is a right one ( by Euc . 31. 3. ) the triangles ABE and ADC are similar ; and therefore , AC being AB ...
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.