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35.
Rules for ye Equilibrium of firm bodys whose specific weight is less than that of water.

Rule I

Every firm body weighing more than ye air and lighter than water, being put upon water will a little sink and elevate the water, and all the sunk part shall be to the lift as its specific weight to that of ye water.

 Let there be in the figure following B C D E water whose upper surface surface let be B C, contained in some vessel, and let A F G H be a cubic body specifically lighter than the water, and heavier than the air; I say that it will not remain upon the surface of the water; 

[[Image: drawing of a rectangle (vessel) labeled B E D C with a rectangular body labeled A G H F intersecting line B C at points K R, and dotted lines down form G to I at the bottom of the vessel, and from H to L at the bottom of the vessel.]]

For ye square column of water K R I L would be more pressed than an equal column B E I K since the weight of the body A H would be more there, therefore the weight shall descend and enter into the water, but shall not entirely hid; because that the column K R I L composed of that body and the water would be lighter than an equal column of water B E I K ; let it therefore sink to K R, and let the water that environs it be elevated to B C, wch shall be higher than it was before because that the portion of the body K G H R posseseth the place of one part wch is obliged to be elevated: I say that the water contained in K G H R, whose place the body occupys [[sic]], shall of an equal weight to the weight of the whole body, that is to say that if a quantity of water equal ^[[in]] bulk to K G H R weight as much in the air as the entire body A F G H, it will remain in that situation; another part of the body viz K R G H shall be to the whole as the specific weight of that whole body shall be to that [[t over Y: guess]] of the water.

So, if the body A F G H is to the water in specific weight as 3 to 4, the part A F K R wch shall pass below the water shall be the 4th part of its whole weight; for if it would weigh 12 pound in the air, as much water would weigh 16 pound and by consequence the part K R G H would weigh 12 pound if it was water, it shall weigh therefore but 9 pounds and ye [[strikethrough]] space [[/strikethrough]] part above the water A F K R shall be three pound and ye whole shall weigh 12 pounds as the space of water occupied by ye part of the weight wch enters there, wch shall be 16 pound in the same proportion as 3 to 4. and by the first rule the weight shall

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Transcription Notes:
mcma - I transcribed ye as 'the' but maintained wch [[which]]. I see the choices vary among transcribers. I cannot figure out some words. mandc: These to there; added upper. You should describe the drawing, not just give letters without reference to points in the illustration. http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=119&ww=0.1386&wh=0.1716&wx=0.5828&wy=0.5905 Corrected "For ye square" and J to I, etc. You can read another transcription here (scans 110-12): http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=11&pn=17&mode=imagepath