their Truth.
The Tenth Proposition contains a Problem, untouch'd by Torricellius, which is of the greatest use in Gunnery, and for the sake of which this Discourse was principally intended: It was first Solved by Mr. Anderson, in his Book of the Genuine Use and Effects of the Gun, Printed in the Year 1674; but his Solution required so much Calculation, that it put me upon search, whether it might not be done more easily, and thereupon in the Year 1678 I found out the Rule I now Publish, and from it the Geometrical Construction: Since which time there has a large Treatise of this
Subject, Intituled, L'Art dejetter les Bombes, been Published by Monsieur Blondel, wherein he gives the Solutions of this Problem by Messieurs Buot, Romer and de la Hire: But none of them being the same with Mine, or, in my Opinion, more easy, and most of them more Operose, and besides mine finding the Tangent, which generally determines the Angle better than its Sine, I thought my self obliged to Print it for the use of all such, as desire to be informed in the Mathematical part of the Art of Gunnery.
Now these Rules were rigidly true, were it not, as I said before, for the Opposition of the Medium, whereby not only the direct imprest Motion is continually retarded, but likewise the increase of the Velocity of the Fall , so that the Spaces described thereby, are not exactly as the Squares of the Times: But what this Opposition of the Air is, against several Velocities , Bulks , and Weights , is not so easie to determine. 'Tis certain that the weight of Air to that of Water , is nearly as 1 to 800, whence the weight thereof, to that of any Project is given; 'tis very likely, that to the same Velocity and Magnitude , but of different Matter, the Opposition should be reciprocally as the weights