On the philosophy of discovery : chapters historical and critical / by William Whewell. Including the completion of the 3d ed. of the Philosophy of the inductive sciences.
- William Whewell
- Date:
- 1860
Licence: Public Domain Mark
Credit: On the philosophy of discovery : chapters historical and critical / by William Whewell. Including the completion of the 3d ed. of the Philosophy of the inductive sciences. Source: Wellcome Collection.
Provider: This material has been provided by the Harvey Cushing/John Hay Whitney Medical Library at Yale University, through the Medical Heritage Library. The original may be consulted at the Harvey Cushing/John Hay Whitney Medical Library at Yale University.
539/572 page 519
![§ 240. (r) And now first, as to what concerns the Form of the Path, the Circle only can be conceived as the path of an absolutely uniform motion. Conceivable, as people express it, no doubt it is, that an increasing and diminishing motion should take place in a circle. But this conceivableness or possibility means only an abstract capability of being represented, which leaves out of sight that Determinate Thing on which the question turns. The Circle is the line returning into itself in which all the radii are equal, that is, it is completely determined by means of the radius. There is only one Determination, and that is the whole Determination. But in free motion, in which the Determinations according to space and according to time come into view with Differ- ences, in a qualitative relation to each other, this Eelation appears in the spatial aspect as a Difference thereof in itself, which therefore requires two Determinations. Hereby the Form of the path returning into itself is essentially an Ellipse, (s) The abstract Determinateness which produces the circle appears also in this way, that the arc or angle which is in- cluded by two Radii is independent of them, a magnitude with regard to them completely empirical. But since iu the motion as determined by the Conception, the distance from the center, and the arc which is run over in a certain time, must be comprehended in one determinateness, [and] make out a whole, this is the sector, a space-determination of two dimen- sions: in this way, the arc is essentially a Function of the Kadius Vector; and the former (the arc) being unequal, brings with it the inequality of the Radii. That the determination with regard to the space by means of the time appears as a Determination of two Dimensions,—as a SuperBcies-Determi- (r) nation,'—agrees with what was said before (§ 26G) respecting Falling Bodies, with regard to the exposition of the same Determinateness, at one while as Time in the root, at another while as Space in the Square. Here, however, the Quadratic character of the space is, by the returning of the Line of motion into itself, limited to a Sector. These are, as may be seen, the general principles on which the Keplerian Law, that in equal times equal sectors are cut off, rests. This Law becomes, as is clear, only the relation of the arc to the Radius Vector, and the Time enters there as the abstract](https://iiif.wellcomecollection.org/image/b20999203_0539.jp2/full/800%2C/0/default.jpg)
