# Algebraically Sentence Examples

- To form a conception of this problem it is to be noted that since the position of the body in space can be computed from the six elements of the orbit at any time we may ideally conceive the coordinates of the body to be
**algebraically**expressed as functions of the six elements and of the time. - Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved
**Algebraically**(1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888). - (2), (3), (4),...(n), and say that with ao, we have an
**algebraically**complete system. - Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An
**Algebraically**Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed. - (v.) Permutations and Combinations may be regarded as arithmetical recreations; they become important
**algebraically**in reference to the binomial theroem (ï¿½ï¿½ 41, 44)ï¿½ (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers. - Thus, to divide i by i +x
**algebraically**, we may write it in the form I+o.x+o.x 2 +o.x 3 +o.x 4, and we then obtain I I +0.x+0.x2+0.x3 '+0.x4 = I' x+x2 - x 3 + x4 I+x I+x' where the successive terms of the quotient are obtained by a process which is purely formal. - He solved quadratic equations both geometrically and
**algebraically**, and also equations of the form x 2 "+ax n +b=o; he also proved certain relations between the sum of the first n natural numbers, and the sums of their squares and cubes. **Algebraically**expressed, if x and y be the required mean proportionals and a, 2a, the lines, we have a: x :: x: y :: y : 2a, from which it follows that x = 2a3.- Let these projections be denoted
**algebraically**by x1, xi,. - It may be shown
**algebraically**that under theseconditions the n roots of the above equation in r2 are all real and positive. - The periodic variations can be represented
**algebraically**as the resultant of a series of harmonic motions in the following way: Let L be an angle which is increasing uniformly with the time, and let n be its rate of increase. - The longitudes, latitudes and radii vectores of a planet, being
**algebraically**expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions. - One more covariant is requisite to make an
**algebraically**complete set. - The general equation of degree 5 cannot be solved
**algebraically**, but the roots can be expressed by means of elliptic modular functions.