In order that the language of his astronomy may be understood, it is necessary to mention briefly some of the older theories. When it had been discovered that the planets did not move regularly round the earth, which was supposed to be fixed in the centre of the world, a mechanism was contrived by which it was thought that the apparent irregularity could be represented, and yet the principle of uniform motion, which was adhered to with superstitious reverence, might be preserved. This, in its simplest form, consisted in supposing the planet to move uniformly in a small circle, called an _epicycle_, the centre of which moved with an equal angular motion in the opposite direction round the earth.[187] The circle D_d_, described by D, the centre of the epicycle, was called the _deferent_. For instance, if the planet was supposed to be at A when the centre of the epicycle was at D, its position, when the centre of the epicycle had removed to _d_, would be at _p_, found by drawing _dp_ parallel to DA. Thus, the angle _adp_, measuring the motion of the planet in its epicycle, would be equal to DE_d_, the angle described by the centre of the epicycle in the deferent. The angle _p_E_d_ between E_p_, the direction in which a planet so moving would be seen from the earth, supposed to be at E, and E_d_ the direction in which it would have been seen had it been moving in the centre of the deferent, was called the equation of the orbit, the word equation, in the language of astronomy, signifying what must be added or taken from an irregularly varying quantity to make it vary uniformly.
As the accuracy of observations increased, minor irregularities were discovered, which were attempted to be accounted for by making a second deferent of the epicycle, and making the centre of a second epicycle revolve in the circumference of the first, and so on, or else by supposing the revolution in the epicycle not to be completed in exactly the time in which its centre is carried round the deferent. Hipparchus was the first to make a remark by which the geometrical representation of these inequalities was considerably simplified. In fact, if EC be taken equal to _pd_, C_d_ will be a parallelogram, and consequently C_p_ equal to E_d_, so that the machinery of the first deferent and epicycle amounts to supposing that the planet revolves uniformly in a circle round the point C, not coincident with the place of the earth. This was consequently called the excentric theory, in opposition to the former or concentric one, and was received as a great improvement. As the point _d_ is not represented by this construction, the equation to the orbit was measured by the angle C_p_E, which is equal to _p_E_d_. It is not necessary to give any account of the manner in which the old astronomers determined the magnitudes and positions of these orbits, either in the concentric or excentric theory, the present object being little more than to explain the meaning of the terms it will be necessary to use in describing Kepler's investigations.