Of the Properties of Bodies. 7

SOLIDITY, sometimes called the Im-penetrability of Matter, is that Proper-ty

{which in this Cafe is called the Area, or Superficial Con-tent) is thus expressed, ABXBC=4X2=8; that is,there are eight small Squares, which are square Inches,square Feet, £sV. according to the Measure of theSides.

q. If this Surface be compared with any other, asEG, whose Length is EF—3, and Breadth FG — 2; Plate I.then their Magnitudes will be to each o.her as ABxBC Fig. 3.to EFXFG, that is, as 8 to 6, or as 4 to 3. And be-cause in this Comparison each Term consists of twoParts, or there is a twofold Ratio of Length to Lengthand Breadth to Breadth, therefore this is said to be aDuplicate Ratio-, and so all Surfaces are to each otherin the. Duplicate Ratio of their Sides.

4. In like Manner all Solid Bodies, which have threeDimensions, have their Magnitudes exprefs’d by thePro- Plate I.duel of their Length, Breadth, and Depth together. Thus Fig. 4, 5.if there be one Solid AG, whole Length AB —4, itsBreadth AE—2, and Depth AD —3 ; and another Solid

HO, whose Length HI=3, Breadth HM=i, and DepthHL = 2 ; then will their Magnitudes be to each other asABxBExAD to HIxHMxHL, that is 4X2X3—24 to3X 1X2—6, or as 24 to 6. And therefore Solids are saidto be in a triplicate Ratio, viz. of their Length, Breadth,and Depth or Thickness; and the Standard Measure rnthis Cafe is call’d a Cubic Inch, Foot , &c. because of itsbeing in the Form of a Dye, or Cube, which Figure iscontained under 6 equal and rectangular Planes.

5. And here it will be necesiary to advertise the Rea-der, that any Quantity is generally denoted by a singleLetter, as A, B, t 5 c. and the Square of that Quantityby AX A or AA, or A"-, B\ Uc. and the Cube by A*or Bh And when we express the Ratio of two Quanti-ties A and B, it is usually thus, A: B; and when wecompare this Ratio with any other, as of C to D, weexpress it thus, A : B :: C : D. If both Terms of theRatio increase or decrease together, the Ratio is said tobe direct, and exprefs’d as before: But if one Quantity

B 4 increases