By a plain scale to measure board or timber of equal or unequal sides without the use of numbers

How to measure any board geometrically. In the last you were instructed how to find any line in proportion, which is like unto this, only in your last you had three lines given, to find a fourth, but in this you have three numbers whereby the fourth is found. Only you must observe that the first of the three numbers is always twelve, being the side of a square foot of board, or the side of a cubical foot of timber.

The second number is always the number of feet contained in the length of the board. The third number is always the number of inches contained in the breadth of the board, and the fourth the square feet contained in the whole board, which is the resolution of the question. As for example, I would know how many feet of board is contained in a board 18 inches broad and 14 feet long. Work thus.

Draw two lines at any distance, meeting at one end as you have been taught, as suppose the two lines ABC, which meet at B. Then take 12, your square inches in a side of a foot, and place it from B to D. Having so done, take the length of your board, which is 14 feet, and place it from B to E, then draw the line DE. Having done that, take the breadth of the board, which is 18 inches, placing it from B to F, then take the distance from D to F and draw a line parallel to DE, and it will be the line FG, which from G to B is 21 feet, the content of the whole board. All board is measured in like manner, which is worthy of your observation.

To measure any board under a foot broad. In the last you were shown how to measure any board, stone, or glass which was above a foot in breadth, but in this you shall be instructed how to measure any board, stone, or glass under a foot in breadth, by reason the work differs from the other. As for example, suppose a board of 16 feet long, and 9 inches in breadth. I would know the content thereof in feet. Work thus. Draw two lines as before you were taught, which let be ABC.

Then take from your scale of equal parts 12, which is your side of a foot square, and set one leg of your compasses at C, the other at D. Then take your length, which is 16, and set it from C to E. Then strike the line D and E. Having so done, take your breadth, which is 9 inches, and set it from C to F. Then take your distance from F to D, and draw a line parallel to DE, which will be the line GF, and then is the line GC 12 feet, which is the resolution of the question, and was required to be done.

For in your last question the fourth number exceeded your first work, but in this it is within your first, and the reason is because the last work was above 12 inches broad, and this work, under, which is but 9 inches. And thus have you all measures which are flat, remembering always this - as 12 is to the length in feet, so is the breadth in inches to the content in feet.

To measure any timber geometrically. The beginning of this work is like unto that of board, and differs in the last line, as you see. For example, I would know how many feet of timber is contained in a piece of timber which is 14 feet long, and 15 inches square. Work thus. Draw

two lines as you have been taught, and let them be ABC, meeting like an angle at B. Then take from your scale 12, which is always your side of a foot square, and place it from B to D. Having so done, take 14, the length of the piece, and place it from B to E, then draw the line DE.

Then take 15 inches, your breadth, and place it from B to F and draw the line FG parallel to the line DE, and thus have you one side as was directed in the board's measure. It remains therefore to find the remainder, as thus. Draw a diagonal line from G to D for your last work. Having thus done, set off the distance from F to H. By a parallel line draw the line FI, which will be found from I to B 21 3/4 feet, and so much timber is in the piece demonstrated, which was required to be done. And in like manner are all pieces measured whose sides are equal. It remains to show you how to measure timber whose sides are unequal as in the next plate shall be set down.

To measure timber of unequal sides by geometry. Suppose a piece whose sides are unequal, the one side being 18 inches, the other side 14 inches, and the length 9 feet. Work as the former chapter, by drawing two lines at any distance, meeting at one end like an angle, and let the lines be ABC, meeting at the point B. Then work thus. Take from your scale 12, which is the side of a foot square, and set it from B to D. Having so done, take the length, which is 9 feet, and set it from B to E. Then draw the line DE. Having done that, take 18, the breadth of one side, setting it from B to E, then draw the line HI parallel to ED.

Now have you the superficial content of one side. It remains to find the other, by drawing a diagonal line from I to D, which is the line LM. Having done this line LM, take your side of your scale which is 14 inches, and set it from B to 0. Draw another line parallel to ID, which will be the line OP, which distance from P to B is 15 4/5 feet, the cubical feet of timber in a piece of the dimension propounded. And thus have I given you one demonstration both of equal and unequal sides, which was required to be done. I could give many examples more, but considering that these, well understood, are sufficient, I will pass to the next on the other side.