wonder of this effrft to the rtafbn which he hath laid fb fair a 

 foundation upon another occasion, had he bur reflected upon 

 it. For in his fourth dialogue of motion he hath demonftratcd 

 that a natural! moveabie defcending in the quarter of a circle, 

 from what part focver it begin neth,fpcndeth equall time to come 

 to the lo A eft point, as if it came from any other part : fb that a, 

 pendant being brorght tip to any height by the force of a for- 

 mer motion downwards, it will be fure to ipcnd as much time 

 in going down from thence to the perpendicular, as it did at the 

 hrft when it was let fall from the grcateft height. Now I fub- 

 fume , that the pendants afcending, being the effect of the 

 velocity of its motion gained in defcending immediately before* 

 the faid velocity muft be able to carry it in the fame time to a 

 height, that is proportionate to that height unto which the velo- 

 city gained in the firft fall did caufe the pendant to mount. As 



_/\j , __, for example : if the pendants firft 



; deicent were from A to E, the fe- 

 ^ cond from C to E; bccaufe the time 

 of thofe two is the fame, ( as Gali- 

 leus hath demonstrated ) it follow- 

 eth that their velocities gained in 

 defcending mnft of neeeflity be in the proportion of the line A E 

 to the line C E : therefore, their effects alfo muft be proportio- 

 nable. Let us then put the line E D in that proportion to the 

 line C E, which C E hath to A E, and then the velocity gained 

 in C E will carry the pendant up from E to D, in the fame 

 time in which the defcent AE did carry it up the other way 

 from E to C: wherefore, feeing that the times of its defccnt from 

 A to E, and from C to E arc equall; likewife, the two vibra- 

 tions from A to C and from C to D will be done in equal! 

 times. But that which made Galileo not ice the force of the 

 confequence, was that he did not acknowledge violent motion 

 to be made in the fame proportions., and for the fame rcafons 

 which are found in natural! motion : which we have above 

 fliewed to be Co, where we difcourfed of that matter. 

 > That motion alib which we call T^cfraftion, and is manifefl 



Reflation at to fenfc, oneiy in light; (though peradventurc hereafter more 

 irnVthTre* diligent fcarchcrs of nature , may likc'.vifc find it in fuch other 

 bodies as a re called qualities; as in cold or heat,c. ) is but a 



kind 



