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104.

[[image:  Drawing of a vertical tube A B C D,base line H M I; semicircle B L O K H; two arcs F O M and G I from the side of the tube to the baseline.  Dotted nhorizontal lines from the tube F to L, N to O, and G to K on the semicircle; dotted vertical lines from L, and K to the baseline.]]

  Let A B C D be a cylindric vessel, or of some other forme pierced in F and G, ye water in F being always kept at ye height A D, H I is an horizontal plane, and if we would know whether ye spouts F and G fall upon ye horizontal plane H I.  Let us suppose that ye side of ye pipe B F G H where ye holes F and G are pierced is of lead upon ye line B H for a diameter having described ye semicircle B L K H, draw F L G K ye perpendiculars to ye line B H unto ye semicircle in L and K, and having made H I double to G K, and H M double to F L, ye spouts will describe ye semiparabolas G J, and F M as hath been said above:  Whence it follows that if N is ye center of ye circle ye spout wch spouts thrô N shall go farthest, since ye line N O wch is ye [[strikethrough]] semicircle [[/strikethrough]] semidiameter is ye greater than all ye ordinates as G K, F L and if we take equall heights above and below N ye spouts will fall upon ye same point in ye horizontal line H I.

  If we would know in a vessel or reservatory A B C D what height ye water is, we must pierce a hole in some places as [[?M ?+]] whether ye spout goeth, draw ye line I H horizontal from ye point [[strikethrough]] goeth [[/strikethrough]] I, and by ye point G ye line G H [[?]] perpendicular to I H, having cut H G into two equal parts, whereof let G K be one, find the line G B a 3d continual proportion after G H and G K, that line G H is ye height of ye water in ye reservatory above ye hole G, which is but ye inverting ye preceding proposition, wch is easy to be seen if we suppose ye height of ye reservatory to be H B above ye horizontal plane H G, and ye hole of ye spout to be in G:  For according to ye 3 lines G H, G R, G B are in a continuall proportion;  wch agrees to what Galileus hath demonstrated in his 5th proportion of ye motion bodys pushed and spouting, where he sayeth that half ye amplitude of ye parabolas of spouts are mean proportionally between ye height of ye semiparabola, and ye height of ye liquor from ye hole of ye spout:

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Transcription Notes:
mandc: Reviewed and revised image description, changed J's to I's. Desaguliers' image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&viewMode=images&mode=imagepath&pn=283&ww=0.1885&wh=0.2272&wx=0.4782&wy=0.4693