Abbreviations

- (7) If B m denote the brightness of the
**mth**lateral image, and Bo that the central image, we have amp 'cosx' dx= a d (1) (-) m7r B.: Bo= a+d am?r sin' a4 d (1). - Xxvi.) "the numerical orders of the image," are consequently only odd powers; the condition for the formation of an image of the
**mth**order is that in the series for and the coefficients of the powers of the 3rd, 5th. - As in algebra we say that an equation of the
**mth**order has in roots, viz. - We state this generally without in the first instance, or it may be without ever, distinguishing whether these are real or imaginary; so in geometry we say that a curve of the
**mth**order is met by an arbitrary line in m points, or rather we thus, through algebra, obtain the proper geometrical definition of a curve of the**mth**order, as a curve which is met by an arbitrary line in m points (that is, of course, in m, and not more than m,. - We find in it explicitly the two correlative definitions: " a plane curve is said to be of the p ith degree (order) when it has with a line m real or ideal intersections," and " a plane curve is said to be of the
**mth**class when from any point of its plane there can be drawn to it m real or ideal tangents."

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