An extract of some physico-mathematical discourses contained in Mr. Cotes's Hydrostatical and pneumatical lectures : printed for the use of those that go the course of experiments.

  • Cotes, Roger, 1682-1716.
Date:
[1740?]
Catalogue details

Licence: Public Domain Mark

Credit: An extract of some physico-mathematical discourses contained in Mr. Cotes's Hydrostatical and pneumatical lectures : printed for the use of those that go the course of experiments. Source: Wellcome Collection.

    4/28 (page 4)
    Xvill the Triangle ACD reprefent a Prifm having the (aid. Triangle for its Bafe and the fide of the Square for its Altitude. Idle weight of that Prifm -of Water is therefore equivalent to the preffure made againft the Square or lide of the Cube. That Prifm is equal to half the whole Cube as we learn from Euclid’s Elements, therefore the preffure againft the Square is equivalent to half the weight of the whole Water contain’d in the Veffel. There are 4 (uch hides of a Cube belides the Top and Bottom, and each of thofe 4 lides for the fame reafon doth fuftain the fame preffure, there¬ fore altogether do fuftain 4 times half the weight, that is twice the whole weight of the Water. And the Bottom by what has been prov’d above does it felf fuftain a preffure equal to the whole weight of the Water; therefore the Bottom and Sides together of a Cubical Veffel fill’d with Water do fuftain a preffure from the Water equal to thrice the weight of it. I have endeavour’d to make the thing as eafy as I believe the nature of it will permit. Elowever fince that part of this dedu&ion where I told You the Triangle ACD did at the fame time reprefent the Prifm when the Line AC reprefented the Square, might be perhaps a little obfcure I will endeavour to clear up this matter fomething further. Let then ACFE (Fig* 7O reprefent the Square Side of the Veffel, and CDGF reprefent the Square Bottom of the fame. It was prov’d before that the preffure exercis’d upon the Line AC was meafur’d by the Triangle ACD> by the fame way of reafoning it may be prov’d that the preffure upon the Line EF is meafur’d by the Triangle EFG, and the preffure upon any other Line HI which is parallel to thefe two and fttuated between them is meafur’d by its refpedive Triangle HI1C If we imagin the Square ACFE to be made up of an Infinite Number of fuch interme¬ diate Lines as HE the preffure upon the whole Square will be made up of the fame Infinite Number of fuch equal Triangles as HIK> now the Sum of all thofe Triangles make up the Prifm AEGDCF and this Prifm is half the whole Cube, as in the former Scheme the Triangle ACD is half the Square ACDB. If the Plane AC FE inftead of being a Square were a redangled Parallelogram having its Sides AE either longer or fhorter than AC> it would follow from the Principles that the preffure to which it is expos’d would be equivalent to the weight of a like Prifm of Water, having the Triangle ACD ior its Bafts, and the Side AE for its Altitude. I have been hitherto fpeaking of Planes which are either parallel or per¬ pendicular to the Horizon, it will be no difficult matter to apply what has been laid of Perpendicular Planes to thofe which are oblique. Let AC ( Fig. 8.) reprefent any fuch oblique Plane and let the upper Surface of the Water be AB. The meafure of the preffure upon the Point L is LS the Altitude of the Water above that Point, fo 'FAF is the meafure *>f the preflure upon AT, VN the meafure of the preffure upon A7,