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117.  

  From hence results a very surprising theorem, viz that if we have a flat square of wood glass or some other fragile matter placed upon a square so that its extremities be strongly inserted therein, as when ye insert ye glass square into a [[strikethrough]] small [[/strikethrough]] square frame ye same weight distributed thro^ on its whole extent wch will break it will brake any other square of ye same thickness of what largeness soever:

      Demonstration

A B C D is ye square wch holds fast ye square of glass,  E F is another square smaller holding another square of glass of ye same thickness;

[[left image: Drawing of a square frame A B C D with three vertical bands M N, I L, K S down the center from A C to B D; and a horizontal band G R from A B to C D underneath the vertical band.]]
 
[[right image: Drawing of a square frame F E with a vertical  band Q H from the top of the frame to the bottom, and another band O P from left side of the frame to right side of the frame under band Q H.]]


  I say it will sustain ye same distributed weight for let a small band of paper R H be placed upon ye small square and for ease of calculation let ye band I L in ye other square be double ye length of R H, and of ye same largeness and thickness, it is evident by what Galileus hath demonstrated, that if we put a weight in ye middle of R H precisely sufficient to break it, ye half of that weight placed upon ye middle of I L will break it, but if we double ye largeness of I L and that ye band be M N K S, there must be ye whole weight to break it, for ye lever will remain the same but it will have twice as many parts to disjoyn and if we distribute ye first weight along R H it must be double to break ye band R H as hath been proved by ye same author: therefore ye weight must be also double to break in S ye double of I L; but if we add cross wise another ban up to ye same square, we must double ye weight wch I have confirmed by experience: for a simple band being broken by a little less than 2 1/2 pounds, being made in a cross it required a little more than 4 pounds 11 ounces, wch if somewhat less than ye double, which may proceed from hence that ye square in ye middle was not double, if we therefore put another band crosswise of ye same largeness as I N, it will carry ye same weight as ye cross P O R H, and if we continue to make these crosses larger in ye same proportion, that of ye greatest will support always ye same weight distributed, and at last we may continue them till there remains but 4 very small squares at ye angles of each square  whence we conclude that if we finish ye two squares ye same effect will allways follow, and ye like in all other proportions; for if ye square of ye middle of ye small makes a cross to bear but a weight double  to what ye band bears, so ye square of ye great one will produce ye same effect.

  These rules serve for solids whose maters are fragile, as wood, glass, marble. steel, &c.

  But for supple and pliant matters, wch break only by traction, as paper, tin, cords &c there  might be other rules of wch here is ye principal: 

      Rules

    For those solids wch are souple

  Bands of paper, tin, and other ye like matter are broke equally be they long or short.

Transcription Notes:
Amended image descriptions, changed J's to I's.