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
... SUBTRACTION 11 SECTION IV . MULTIPLICATION 13 SECTION V. DIVISION 28 SECTION VI . INVOLUTION 36 SECTION VII . EVOLUTION 42 SECTION VIII . THE REDUCTION OF FRACTIONAL AND RA- DICAL QUANTITIES 45 SECTION IX . OF EQUATIONS 1. The Reduction ...
... SUBTRACTION 11 SECTION IV . MULTIPLICATION 13 SECTION V. DIVISION 28 SECTION VI . INVOLUTION 36 SECTION VII . EVOLUTION 42 SECTION VIII . THE REDUCTION OF FRACTIONAL AND RA- DICAL QUANTITIES 45 SECTION IX . OF EQUATIONS 1. The Reduction ...
Σελίδα 2
... subtracted . Thus ab shows that the quantity represented by b is to be subtracted from that represent- ed by a , and expresseth the difference of a and b ; so that , if a was 5 , and b 3 , then would a · b be 5 - 3 or 2. In like manner ...
... subtracted . Thus ab shows that the quantity represented by b is to be subtracted from that represent- ed by a , and expresseth the difference of a and b ; so that , if a was 5 , and b 3 , then would a · b be 5 - 3 or 2. In like manner ...
Σελίδα 9
... subtracting the coefficient of the lesser from that of the greater , and adjoining the letters common to each ; to which difference prefix the sign of the greater . 1 . 3 . Examples of this Rule may be as follow . Sum 12a 5b - 3a + 2b ...
... subtracting the coefficient of the lesser from that of the greater , and adjoining the letters common to each ; to which difference prefix the sign of the greater . 1 . 3 . Examples of this Rule may be as follow . Sum 12a 5b - 3a + 2b ...
Σελίδα 11
... Subtraction . SUBTRACTION , in Algebra , is performed by changing all the signs of the subtrahend ( or conceiving them to be changed ) and then connecting the ... subtraction , may be as follow : of Subtraction . 11 SECTION III SUBTRACTION.
... Subtraction . SUBTRACTION , in Algebra , is performed by changing all the signs of the subtrahend ( or conceiving them to be changed ) and then connecting the ... subtraction , may be as follow : of Subtraction . 11 SECTION III SUBTRACTION.
Σελίδα 12
... subtraction , may be as follow : From 20ax + 5bc From 7√ax + 9√ by - 7aa take 12ax 3bc - - 5aa take - - 5√ax + 12 ... subtracted is less than 5a by 3b , too much has been taken away by 3b ; and therefore the true remainder will be ...
... subtraction , may be as follow : From 20ax + 5bc From 7√ax + 9√ by - 7aa take 12ax 3bc - - 5aa take - - 5√ax + 12 ... subtracted is less than 5a by 3b , too much has been taken away by 3b ; and therefore the true remainder will be ...
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.