There are also Finite Differences and their Calculus, Figure of the Earth (force to the center), various Attractions (some evidently referring to Maclaurin's), Integrals, Conic Sections, Kepler's Problem, Analytical Geometry, D'Alembert's Theorem, Spherical Aberration, Rotations round three axes (apparently I had been reading Euler), Floating bodies, Evolute of Ellipse, Newton's treatment of the Moon's Variation.

"But who knows or cares for Kepler's great law of Repulsion, or Apergy?

Kepler's second law covers that.

Kepler's merit as an astronomer has long obscured his philosophical importance, although his discovery of the laws of planetary motion was the outcome of endeavors to secure an exact foundation for his theory of the world.

This dissertation gives, further, a deduction of Kepler's laws.

[Footnote Y: Called now Kepler's cascade.]

On page 114, speaking of Kepler's third law, the author says, "And even those extraordinary objects, the revolving double stars, are subject to the same controlling law."

Since Kepler's third law expresses a relationship between the motions of three bodies, two of which revolve around a third much larger than either, it is a logical impossibility that a system of only two bodies should conform to this law.

We can do, it seems, without Kepler's laws, but not without the Decalogue.

Kepler Joins Tycho V. Kepler's Laws VI.

Kepler's knowledge of astronomy was limited to the compulsory school course, nor had he as yet any particular leaning towards the science; the post, moreover, was a meagre and unimportant one.

Kepler's own suggested explanation of the discordances was that they must be due to erroneous measures of the planetary distances, and this, in those days of crude and infrequent observations, could not easily be disproved.

Not many years later Snell discovered the true law of refraction, but Kepler's contribution to the subject, though he failed to discover the actual law, includes several of the adopted "by-laws".

Maestlin and others of Kepler's friends took the opposite view.

CHAPTER V. KEPLER'S LAWS.

FIGURES EXPLANATORY OF KEPLER'S THEORY OF THE MOTION OF MARS.

2.This is not drawn to scale, but is intended to illustrate Kepler's modification of Ptolemy's excentric.

Kepler's first ellipse had M moved too near C.

The angular velocity is not quite constant about E, the equant or empty focus, but the difference could hardly have been detected in Kepler's time.

These are Kepler's first and second Laws though not discovered in that order, and it was at once clear that Ptolemy's "bisection of the excentricity" simply amounted to the fact that the centre of an ellipse bisects the distance between the foci, the sun being in one focus and the angular velocity being uniform about the empty focus.

Napier's invention of logarithms at once attracted Kepler's attention.

Though Eugenists may find a difficulty in reconciling Napier's brilliancy with the extreme youth of his parents, they may at any rate attribute Kepler's occasional fits of bad temper to heredity.

The Jesuits contrived to have Kepler's library sealed up, and, but for the Imperial protection, would have imprisoned him also; moreover the peasants revolted and blockaded Linz.

No attempt at a complete edition of Kepler's works was made for a long time.

Kepler's fame does not rest upon his voluminous works.