Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/29

Rh

Let us now go on to the ret of the Planets. Becaue the revolutions of the primary Planets about the Sun, and of the econdary about Jupiter and Saturn, are phænomena of the ame kind with the revolution of the Moon about the Earth; and becaue it has been moreover demontrated that the centripetal forces of the primary Planets are directed towards the centre of the Sun, and thoe of the econdary towards the centres of Jupiter and Saturn, in the ame manner as the centripetal force of the Moon is directed towards the centre of the Earth; and ince beides, all thee forces are reciprocally as the quares of the ditances from the centres, in the ame manner as the centripetal force of the Moon is as the quare of the ditance from the Earth; we mut of coure conclude, that the nature of all is the ame. Therefore as the Moon gravitates towards the Earth, and the Earth again towards the Moon; o alo all the econdary Planets will gravitate towards their primary, and the primary Planets again towards their econdary; and o all the primary towards the Sun; and the Sun again towards the primary.

Therefore the Sun gravitates towards all the Planets, and all the Planets towards the Sun. For the econdary Planets, while they accompany the primary, revolve the mean while with the primary about the Sun. Therefore by the ame argument, the Planets of both kinds gravitate towards the Sun, and the Sun towards them. That the econdary Planets gravitate towards the Sun is moreover abundantly clear from the inequalities of the Moon; a mot accurate theory of which laid open with a mot admirable agacity, we find explained in the third book of this Work. Rh