The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.

CHAP. VIII.

To measure any kinde of Superficies, as Board, Glass, Pavement, Walnscot, Hangings, Wal∣ling, Slating, or Tyling, by the line of Num∣bers on the outward ledge.

THe way of accounting any number up∣on, or working proportions by, the line of numbers, is sufficiently shewn already, Chap. 6. which I shall not here repeat, only propose the proportions for these Problems, and refer you to those directions.

PROBL. 1.

The breadth of a Board given in inches, to finde how many inches in length make a foot at that breadth, say,

As the breadth in inches is to 12, so

is 12 to the length in inches for a foot at that breadth. Ex. gr. At 8 inches breadth you must have 18 inches in length for a foot.

PROBL. 2.

The breadth and length of a Board given to finde the content.

As 12 is to the length in feet and inches, so is the breadth in inches to the content in feet. Ex. gr. at 15 inches breadth, and 20 foot length, you have 25 foot of Board.

PROBL. 3.

A speedy way to measure any quantity of Board.

The two former Problems are sufficient to measure small parcels of Board. When you have occasion to measure greater quantities, as 100 foot, or more, lay all the boards of one length together, and when the length of the boards exceeds 12 foot, use this propor∣tion.

As the length in feet and inches is to 12, so is 100 to the breadth in inches for an 100 foot. Ex. gr. At 30 foot in length 40 inches in breadth, make an 100 foot of board (reckoning five score to the hundred.) This

found with a rule or line, measure 40 inches at both ends in breadth, and you have 100 foot. When one end is broader than another, you may take the breadth of the over-plus of 100 foot at both ends, and taking half that sum for the true breadth of the over-plus by Probl. 2. finde the content thereof.

When your boards are under 12 foot in length, say,

As the length in feet and inches is to 12, so is 50 unto the breadth in inches for 50 foot of board, and then you need only double that breadth to measure 100 foot as before. In like manner you may measure two, three, four, five, a hundred, &c. foot of board speedily, as your occasion requires.

PROBL. 4.

To measure Wainscot, Hangings, Plaister, &c.

These are usually computed by the yard, and then the proportion is.

As nine to the length in feet, and inches, so is the breadth or depth in feet and inches to the content in yards, Ex. gr. At 18 foot in length, and two foot in breadth, you have four yards.

PROBL. 5.

To measure Masons, or Slaters Work, as Walling, Tyling, &c.

The common account of these is by the rood, which is eighteen foot square, that is 324 square foot in one rood, and then the proportion is.

As 324 to the length in feet, so is the breadth in feet to the content in roods.

Ex. gr. At 30 foot in length, and 15 foot in breadth, you have 1 rood 3/10 and better, or one rood 126/124 parts of a rood.