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SECT. XXXVII. Of the violent, crooked, and natural Motion or Course of a Shot discharged out of any Piece of Ordnance assigned.
BY the third and fourth Proposition of the second Book of Tartaglia, his Nova Scientia▪ shews that every body equally heavy, as a Shot in the end of the violent motion thereof, being Discharged out of a Piece of Ordnance, so it be not right up, or right down, the Crooked-Range, shall join with the Right-Range, and to the natural Course and Motion betwixt them both.
The Right-Range being all the Right-Line AB which is properly called his Violent Motion, and BC will be the mixt or Crooked-Range, and CD the Natural Motion, wherein from A to B is the furthest part of the Violent Motion, and from C to d the end of the Natural Motion.
And in the seventh Proposition of the same Book, he proveth that every Shot equal∣ly heavy, great or little, equally elevated above the Horizon, or equally Oblique or Levelly directed, are among themselves like and proportional in their Distances, as the Figure following sheweth, as A:E:F is like and proportional in the Right and Crooked-Ranges unto H:I, and in their Distance or Dead-Ranges AF unto A:I.
And in his fourth and sixth Propositions of the same Book, he proveth that every Shot made upon the Level hath the mixt or Crooked-Range thereof, equal to the Arch of a Quadrant 90 degr. and if it be made upon any Elevation above the Level, that then it will make the Crooked-Range, to be more than the Quadrant.
And if that be made Imbased under the Level, that then the Crooked-Range thereof will be an Arch less than a Quadrant.