A Treatise on the Elements of Algebra |
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Common terms and phrases
algebraic algebraic quantities ANSW arithmetic arithmetic series binomial chord circle coefficients Conic Sections consequently cosine cotan cubic equation curvature curve denominator diameter divided divisor Ellipse equa equal equation A)=0 equation whose roots EXAMPLE expressed Find the sum Find the value Formula fraction geometric geometric progression given equation greater greatest common measure Hence Hyperbola impossible roots last term latus-rectum least common multiple limiting equation logarithm manner multiplied negative roots nth root number of terms Parabola parallel perpendicular plane positive powers PROPERTY quadratic equation quadratic surd quotient radius ratio right angles rule secant second term shewn side simple equations sine and cosine square root substituted Subtract surd tangent THEOR Theorem triangle unknown quantities whole number
Popular passages
Page 38 - MOMENTUM, from moveo, to move ; the product of the numbers which represent the quantity of matter and the Velocity of a body, is called its momentum or quantity of motion. MUCILAGINOUS ; resembling mucilage or gum. MULTIPLE, from multiplico, to render manifold ; a quantity is said to be a multiple of another when it contains that other quantity a certain number of times without a remainder. N.
Page 103 - Prob. 7. Two persons draw prizes in a lottery, the difference of which is 120 dollars, and the greater is to the less, as the less to 10. What are the prizes 1 Prob.
Page 58 - Thus, in the case of 53361 (whose square root is a number consisting of three figures) ; since the square of the figure standing in the hundred's place cannot be found either in the last period...
Page 123 - If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth. (Alg. 364.) Thus, if a : b : : c : d, then |=|, and"=^.
Page 129 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 58 - For the square of tens can give no figure in the first right hand period ; the square of hundreds can give no figure in the first two periods on the right ; and the square of the highest figure in the root can give no figure except in the first period on the left.
Page 1 - Notation. 1. Quantities whose values are known or determined, are generally expressed by the first letters of the Alphabet, a, b, c, d, &c. ; and unknown or undetermined quantities are commonly represented by the last letters of the Alphabet, x, y, z, &c.
Page 90 - The sum of those digits is 5 ; and if 9 be added to the number itself, the digits will be inverted.
Page 128 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...