A HISTORY OF SCIENCE 



the moon, and there, together with the moon, deprived 

 of all motion, to be let go, so as to fall together towards 

 the earth, it is certain, from what we have demonstrated 

 before, that, in equal times, they would describe equal 

 spaces with the moon, and of consequence are to the 

 moon, in quantity and matter, as their weights to its 

 weight. 



" Moreover, since the satellites of Jupiter perform 

 their revolutions in times which observe the sesquipli- 

 cate proportion of their distances from Jupiter's centre, 

 their accelerative gravities towards Jupiter will be re- 

 ciprocally as the square of their distances from Jupi- 

 ter's centre that is, equal, at equal distances. And, 

 therefore, these satellites, if supposed to fall towards 

 Jupiter from equal heights, would describe equal 

 spaces in equal times, in like manner as heavy 

 bodies do on our earth. And, by the same argu- 

 ment, if the circumsolar planets were supposed to 

 be let fall at equal distances from the sun, they would, 

 in their descent towards the sun, describe equal spaces 

 in equal times. But forces which equally accelerate 

 unequal bodies must be as those bodies that 

 is to say, the weights of the planets towards the sun 

 must be as their quantities of matter. Further, that 

 the weights of Jupiter and his satellites towards the 

 sun are proportional to the several quantities of their 

 matter, appears from the exceedingly regular motions 

 of the satellites. For if some of these bodies were 

 more strongly attracted to the sun in proportion to 

 their quantity of matter than others, the motions of 

 the satellites would be disturbed by that inequality 

 of attraction. If at equal distances from the sun 



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