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.
531/572 page 511
![distance ? It appears to do so : and it proves this impossibility of known facts at least as much as it proves anything. Let us noiv look at Hegel's proof of Kepler's second law, that the elliptical sectors swept by the radius vector are proportional to the time. It is this: (s). In the circle, the arc or angle which is included by the two radii is independent of them. But in the motion [of a planet] as determined by the conception, the distance from the center and the arc run over in a certain time must be compounded in one deter- mination, and must make out u whole. This whole is the sector, a space of two dimensions. And hence the arc is essentially a Function of the radius vector; and the former (the arc) being unequal, brings with it the inequality of the radii. As was said in the former case, if we could regard this as reason- ing, it would not prove the conclusion, but only, that the arc is some function or other of the radii. Hegel indeed offers (t) a reason why there must be an arc in. volved. This arises, lie says, from the determinateness [of the nature of motion], at one while as time in the root, at another while as space in the square. But here the quadratic character of the space is, by the returning of the line of motion into itself, limited to a sector. Probably my readers have had a sufficient specimen of Ilcel's mode of dealing with these matters. I will however add his proof of Kepler's third law, that the cubes of the distances are as the squares of the times. Hegel's proof in this case («) has a reference to a previous doc- trine concerning falling bodies, in which time and space have, he says, u relation to each other as root and square. Falling bodies however are the case of only half-free motion, and the determina- tion is incomplete. But in the case of absolute motion, the domain of free masses, the determination attains its totality. The time as the root is a mere empirical magnitude: but as a component of the developed Totality, it is a Totality in itself: it produces itself, and therein has a reference to itself. And in this process, Time, being itself the dimensionless element, only comes to a formal identity with itself and reaches the square: Space, on the other hand, as a positive external relation, comes to the full dimensions of the conception of space, that is, the cube. The Realization of the two conceptions (space and time) preserves their original difference. This is the third Keplerian law, the relation of the Cubes of the distances to the squares of the times.](https://iiif.wellcomecollection.org/image/b20999203_0531.jp2/full/800%2C/0/default.jpg)
