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.

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    and XC the meafure of the prelfure upon C. T're<51: the Perpendiculars LO, MP^ NO, CR equal refpe&ively to LS, MT, NP\ CX9 and imagin the like Conftru&ion to be made for all the other Points of the Line AC, and the fum of all thofe Perpendiculars, that is the Triangle ACR will be the meafure of the prelfure upon the whole Line AC, If this Line AC be fuppos’d to reprefent a Parallelogram as before, then the Triangle ACR. will as before become a Prifm, and the weight of that Prifm of Water, which we are taught by Luclid how to meafure, will be the prelfure fuftain’d by the Parallelogram. I have hitherto fuppos’d that the Line CA or the Parallelogram repre- fented by it coincides with the Surface of the Water at A\ if that does not happen but the higheft part of the Line or Parallelogram is at fome di« fiance from the Surface, a Computation of the prelfure will Hill be ealy enough. Suppofe MC in the 8 Figure were the Line or Parallelogram propos’d, the Prelfure upon the Line MC will be meafur’d by the Tra¬ pezium or four lided Figure MCRP, and the prelfure upon the Parallelo¬ gram reprefented by that Line will be a Prifm, having that Trapezium for¬ ks ba'e, and the other lide of the Parallelogram which is fuppos’d parallel to the Surface of the Water for its Altitude. From what has been faid of thefe few particular Inftances we may nowr underftand, that the prelfure upon any Plane of what ever Figure and Situation is equivalent to the weight of a Solid of Water, which is form’d by erecting Perpendiculars upon every point of the Plane propos’d, equal to the refpedive diftances of thofe points from the upper Surface of the Water. For the Perpendiculars being the meafure of the prelfure upon the Points from which they are ere&ed, the Sum of thofe Perpendiculars, or the Solid form’d by them, will be equal to the Sum of the prelfures upon the Points, or the total prelfure upon the whole Plane. Or we may thus exprefs the fame thing after another way, and fo take in all curv’d Surfaces as well as Planes, that the prelfure upon any Surface is equal to the Sum of all the Products which are made by multiplying every indefinitely fmall part of the Surface into its diftance from the top of the Water. For the prelfure upon each of thofe Parts is equal to a Column of Water having the Part for its Balls and the diftance from the top of the Water for its Altitude, and every one knows who has the leaft skill in Geometry, that thofe Columns are meafur’d by multiplying their Bafcs by their Altitudes, therefore the Sum of the Produ&s of all thofe Bafes or little Parts by their Altitudes or refpe&ive diftances from the top of the Water will be equal to all the Columns upon every little Part, and therefore to a Body of Water whofe weight will be equivalent to the total Prelfure upon the whole Surface. Now to find the Sum of all thefe Produ&s or a Body of Water equal to that Sum, is a very difficult Problem in rnoft Cafes. Stevims in his Hydroftaticks has at- B tempted