
I s m a ë l B o u l l i a u  P a r i s 1645 P r i n c i p l e s o f P h i l o l a i c A s t r o n o m y Translated by Robert A. Hatch© 
I. Planets have a simple motion in a simple line. II. Planetary revolutions are equal, perpetual, uniform. III. They should be regular revolutions or composed of regular revolutions. IV. They can only be circular; V. Or composed of circles. VI. Motions should have a principle of equality. VII. Because they admit a certain inequality, the center of the zodiac must be the reference point of inequality. VIII. This point is in the Sun. IX. Half of the inequality is attributed to eccentricity, the other to another cause which makes the planet slower at aphelion, less slow at perihelion, without disturbing the equality of motion or transposing it to some other location, whether the circle or surface. X. When the planet, moving from aphelion, comes to quadrature on the same surface with equal motion, it should differ from the apparent motion of the first inequality completely or nearly so; but because the other half [of the inequality] is due to the distance [between] the circles, the center of planetary motion must be between the points of true and apparent motion. XI. Since the equal motion in the first quadrant is greater than the apparent motion, that part of apparent motion must be greater; hence, from the first quadrant to perihelion the arc described moving toward perihelion must be larger than the first. XII. All revolution is composed of circular parts; the same is true of each part. XIII. Equal motion is uniform; thus, the motion in coming from aphelion corresponds to the larger parallel circles, which increase from aphelion to perihelion. This equal motion does not correspond to a single circle but to several unequal circles to which the apparent motion also corresponds; the apparent motion includes all the circles on the same surface. The motion must also be eccentric and inclined. XIV. These circles follow one another in a continuous series and are all parallel among themselves; they do not overlap or enclose one another; the apparent motion forms a solid surface containing larger and smaller circles. 
rah.viii.98
