Everard (1727)

1. A Superficies is a Figure incompassed about with a Line or Lines, and is either Round or Angular.

2. A Round Figure is that which is contained by one round Line, and is either a Circle (as Fig. 1.) or an Ellipsis (as Fig. 2.)

3. An Angular Figure is that which doth consist of three or more Angles, from the Number of which they are denominated, as a Figure of three Angles is called a Triangle; of four, a Quadrangle, &c.

4. A Triangle is a Superficies comprehended by three Right Lines (as Fig. 3.) of these there are six Variites, which I shall forbear to mention, they being all measured by one and the same Rule.

5. A Quadrangle is a Figure comprehended by four Right-Lines, and is either a Parallelogram or Trapezium.

6. A Parallelogram is a Figure whose opposite Sides are parallel, having equal distances from one another in all places, and is either Right or Oblique.

7. A Right-Angled Parallelogram, is that whose Angles are all Right, and is either a Square (as Fig. 5.) or an Oblong (as Fig. 4.)

8. The Oblique-Angled Parallelogram, is that whose Angles are all Oblique, and is either a Rhombus (as Fig. 7.) or a Rhomboides (as Fig. 6.)

9. A Trapezium is a Quadrangular Figure, in which no two Sides are equal and parallel (as Fig. 8.)

10. Figures consisting of more Sides than four, are almost innumerable, but are reducible unto two sorts, Regular and Irregular, either of which are also called Polygons.

11. Regular Polygons are such, whose Sides and Angles are equal; they take their Names from the Numbers of their Sides, as that of five Sides is called a Pentagon (as Fig. 9.) that of six Sides, an Hexagon, &c. Of Irregular Polygons ’tis needless to say any thing, they being measured after the same manner as a Trapezium.

I should next proceed to shew the Use of the Rule in the measuring of Lines, Superficies, and Solids: But in order to this I must premise,

1. That every Magnitude must be measured by some known kind of Magnitude that is Homogeneal (or like) to it. A Line is measured by a Line, as one Lineal Inch, Foor or Yard, &c.

A Superficies is measured by a Superficies, as one Square Inch or Foot, &c. A Solid is measured by a Solid, as one Cubick Inch, one Cubick Foot, &c.

2. That the Measures of Capacity commonly used in England are of two Sorts, one for wet Commodities, as Beer, Cyder, Wine, &c. the other for dry Commodities, as Corn, &c.

And, I here take it for granted, that there are three several Gallons, whose Contents are allowed to be as followeth,

Ale	}		{	282	}	Solid
Wine	}	Gallon	{	231	}	Inches.
Corn	}		{	268.8	}

Now, from hence are derived the following Tables, shewing how many Solid Inches are contained in any of the other Measures respectively contained in them.

A TABLE of Beer-Measure

Inches.
35¼	Pints.
70½	2	Quarts.
282	8	4	Gallons.
2538	72	36	9	Firkins.
5076	144	72	18	2	Kilderkins.
10152	288	144	36	4	2	Barrels.

A TABLE of Ale-Measure

Inches.
35¼	Pints.
70½	2	Quarts.
282	8	4	Gallons.
2256	64	32	8	Firkins.
4512	128	64	16	2	Kilderkins.
9024	256	128	32	4	2	Barrels.

By an Act of the First of William and Mary, 34 Gallons is the Barrel, both for Beer and Ale, in all places, except within the weekly Bills of Mortality.

A TABLE of Wine-Measure

Inches.
28⁷/₈	Pint.
57¾	2	Quart.
231	8	4	Gallon.
4158	144	72	18	Rundlet.
14553	504	252	63	3½	Hogshead.
19404	672	336	84	4²/₃	1²/₃	Tericon.
29106	1008	504	126	7	2	1½	Pipe.
58212	2106	1008	252	14	4	3	2	Tun.

This Table shews, that in 1 Tun there are 2 Pipes, 3 Tericons, 4 Hogsheads, 14 Rundlets, 252 Gallons, 1008 Quarts, 2016 Pints, and 58212 solid Inches. The Tables for Beer and Ale are like this, and need no Explanation.