Hydrostatics.

2Z-

II. All Fluids gravitate, or weigh , in pro *portion to their Quantity of Matter ; and thatpot only in the Air, or in Vacuo , but in

proprio

td, (c d being ilrawn perpendicular to AC pro-duced. )

3. Now, ’tis evident this Triangle will be greatest,when cd is a Maximum , that is, when it becomes CD;and consequently the Triangle A C D is the greatestpossible when CD makes a right Angle with AC jand in this Cafe the Point C is in a Semicircle de-scribed on AD as a Diameter. Therefore, also the.other Angle B, being in a Semicircle described on thesame Diameter AB, will make the other Part of theTrapezium a Maximum ; and so the whole TrapeziumABCD inscribed in a Semicircle, will be greater thanany other, whose three Sides AB, BC, CD, are thesame.

4. Since what has been demonstrated of the Trape-zium, is true of any other Polygonal Figures (becausethey may he resolved into Trapezia) and since the Sidesof a Polygon, when infinitely small, do coincide withthe Circle; therefore the Circle is the most capaciousFigupe, or contains the greatest Area under the famePeriphery.

5. For Example; suppose a String C were disposed

into the Form of a Circle ; then as 22 : 7 : : C :

.7 C

22

7 C

za Diameter of the Circle : the Radius therefore is -—

44

and since the Area of a Circle is equal to the Periphery

7 C

multiplied into half the Radius, therefore C x - —

7 C C _88 “

Area of the Circle. Again, suppose the seme

String disposed in the Form of a Square; tsie Side wouldC CC

be —, and the Area — —7-; hence the Area of the4 to

Circle