354 FHILOSOl'HICAI. TRAN8ACTIOW8. [aNNO 1687. 



for the line of descent, of the same body, are all equal, each to each : because 

 g, the new impulse of gravity, in each moment, is supposed to be the same. 



24. But what is the proportion of J" to g, that of the force impressed, to 

 the impulse of gravity in each body, remains to be inquired by experiment. 

 This proportion being found for one known force ; the same is thence known 

 as to any other force of which the proportion to this is given, in the same uni- 

 form medium. And this being known as to one medium ; the same is thence 

 known as to any other medium, the proportion of the resistance to that of this 

 being known. 



25. If a heavy body be projected downward in a perpendicular line; it descends 



therefore at the rate — , — , — , &c. of f. the impressed force, increased by 



fnm 



■^' m + ^' m + ^ + ^' ^^' °^ S the impulse of gravity ; because both 

 forces are here united. — 26. If in a perpendicular projection upwards ; it ascends 

 at the rate of the former, abated by that of the latter : because here the impulse 

 of gravity is contrary to the force impressed. — 27. When therefore this latter, 

 continually increasing, becomes equal to that former, continually decreasing, it 

 then ceases to ascend ; and thenceforth descends at the rate by which the latter 

 continually exceeds the former. 



28. In an horizontal or oblique projection : if to a tangent the increments 



of which are as FL, L M, M N, &c. that is as -/, &c. be fitted ordi- 



nates, at a given angle, the increments of which are as FL, F M, FN, &c. 



that is as —s, &c. the curve answering to the compound of these motions, is 



that in which the projectile is to move. This curve, being hitherto without a 

 name, may be called linea projectorum ; the line of projects, or things pro- 

 jected ; which resembles a parabola deformed. — 29. The celerity and tendency, 

 as to each point of this line, is determined by a tangent at that point. — 30. And 

 that against which it makes the greatest stroke or percussion, is that which, at 

 that point, is at right angles to that tangent. 



31. If the projection, at art. 21, be not infinitely continued, but terminate, 

 suppose, at N, so that the last term in the first column or series erect be u ; and 

 consequently in the second, mc, in the third, mm a, &c. each series having 

 one term fewer than that before it ; then the aggregates of the several columns, 

 or series, will be ^-^, ^-^, \::mma ^^^ ^^ ^j,, ^^^ multiple of a b&- 



coming = i, the progression vanish. 



32. Now all the abatements here, a, ma, mmoy &c. are the sanae with the 



