File:I 449 1 - fig 10.png

English: Described in the notes as follows:

"If the planet described a circle, &c. The motion of a planet about the sun, in a circle A B P, fig. 10, whose radius C A is equal to the planet’s mean distance from him, would be equable, that is, its velocity, or speed, would always be the same. Whereas, if it moved in the ellipse A Q P, its speed would be continually varying, by note 39; but its motion is such, that the time elapsing between its departure from P and its return to that point again would be the same whether it moved in the circle or in the ellipse; for these curves coincide in the points P and A."

"Mean motion. Equable motion in a circle P E A B, fig. 10, at the mean distance C P or C m, in the time that the body would accomplish a revolution in its elliptical orbit P D A Q."

"The vernal equinox, ♈, fig. 11, is the zero point in the heavens whence celestial longitudes, or the angular motions of the celestial bodies, are estimated from west to east, the direction in which they all revolve. The vernal equinox is generally called the first point of Aries, though these two points have not coincided since the early ages of astronomy, about 2233 years ago, on account of a motion in the equinoctial points, to be explained hereafter. If S ♈, fig. 10, be the line of the equinoxes, and ♈ the vernal equinox, the true longitude of a planet p is the angle ♈ S p, and its mean longitude is the angle ♈ C m, the sun being in S. Celestial longitude is the angular distance of a heavenly body from the vernal equinox; whereas terrestrial longitude is the angular distance of a place on the surface of the earth from a meridian arbitrarily chosen, as that of Greenwich."

"Equation of the centre. The difference between ♈ C m and ♈ S p, fig. 10; that is, the difference between the true and mean longitudes of a planet or satellite. The true and mean places only coincide in the points P and A; in every other point of the orbit, the true place is either before or behind the mean place. In moving from A through the arc A Q P, the true place p is behind the mean place m; and through the arc P D A the true place is before the mean place. At its maximum, the equation of the centre measures C S, the excentricity of the orbit, since it is the difference between the motion of a body in an ellipse and in a circle whose diameter A P is the major axis of the ellipse."

"Apsides. The points P and A, fig. 10, at the extremities of the major axis of an orbit. P is commonly called the perihelion, a Greek term signifying round the sun; and the point A is called the aphelion, a Greek term signifying at a distance from the sun."