## analytically

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**Analytically**, it is defined by an equation of the second degree, of which the highest terms have real roots (see Conic Section).**Analytically**the hyperbola is given by ax2+2hxy+by2+2gx+ 2fy+c=o wherein ab>h 2 .- Viewed
**analytically**in its developed nature, magic is a wonder-working recognized as such, the core of the mystery consisting in the supposed transformation of suggested idea into accomplished fact by means of that suggestion itself. **Analytically**expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the focal point) was equal to A 2 /X 2 f2.- By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or
**analytically**that this is a minimum.