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 ... |
From inside the book
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Page 5
... four times , & c . as great as b . then accordingly is c twice , thrice , or four of Notation . 5.
... four times , & c . as great as b . then accordingly is c twice , thrice , or four of Notation . 5.
Page 6
... four times , & c . as great as d . To what has been thus far laid down on the significa- tion of the signs and characters used in the algebraic notation , we may add what follows ; which is equally ne- cessary to be understood . When ...
... four times , & c . as great as d . To what has been thus far laid down on the significa- tion of the signs and characters used in the algebraic notation , we may add what follows ; which is equally ne- cessary to be understood . When ...
Page 22
... the same with that of the multiplicand . And these four are all the cases that can possibly hap- pen with regard to the variation of signs . Other examples in multiplication , for the learner's ex- ercise 22 Of Multiplication .
... the same with that of the multiplicand . And these four are all the cases that can possibly hap- pen with regard to the variation of signs . Other examples in multiplication , for the learner's ex- ercise 22 Of Multiplication .
Page 36
... four are all the cases that can possibly hap- pen in respect to the variation of the signs . SECTION VI . Of Involution . INVOLUTION is the raising of powers from any proposed root , and may be performed by the following rules . 1 ...
... four are all the cases that can possibly hap- pen in respect to the variation of the signs . SECTION VI . Of Involution . INVOLUTION is the raising of powers from any proposed root , and may be performed by the following rules . 1 ...
Page 43
... four times its cube , & c . according as the root to be extracted is a square , cubic , or biquadratic one , & c . and let the quantity thence arising be also wrote down in the quotient , and the whole be raised to the second , third ...
... four times its cube , & c . according as the root to be extracted is a square , cubic , or biquadratic one , & c . and let the quantity thence arising be also wrote down in the quotient , and the whole be raised to the second , third ...
Common terms and phrases
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
Popular passages
Page 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.
Page 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 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.
Page 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.
Page 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
Page 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.
Page 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.