The faithfull surveyour discovering divers errours in land measuring, and showing how to measure all manner of ground, and to plot it, and to prove the shutting by the chain onely ... / by George Atwell.

CHAP. V. Of round t••mber.

BEcause to every circle there belongeth 3 squares, first the square without the circle, or the square of the diame∣ter; secondly, the square equal to the circle, not in Peripherie, but in the area; for if the area of a circle of a mile round, and a mile about in a square be compared, we shall finde the square to contain just 40 acres, whereas the circle of the same Pe∣ripherie containeth 50 acres, 3 roods, 25 poles 5/11; and thirdly the side of the square within the circle: therefore we will first shew the manner of making these 4 scales, and then the mea∣suring of round timber: yet before we shew the making of them our best way is to take Virgil's advice, and to do as he doth with his Bees.

Principio sedes apibus statióque petenda.

So before we shew the making of them we will first finde out a seat for each of them, and then the making of them one after each other. First; in the beginning of the first cha∣pter we shewed that we would have one of the edges on one side besild off: and the rest of that side divided length wise into eight equal columns with 7 Gage-strokes upon the besill, ½ the length of the Rule, you may set a scale of 20 in the inch dividing each inch into halves and quarters. Numbring each half-inch with 10, 20, 30, &c. save that half-inch next the beginning, which must not be accounted for any of the tens: but that must be divided into ten equall parts by it self, to take the odd inches above even ones, that any round block or circle is about.

Besides this, you have three other scales that are for round measure, that shew the three squares belonging to the circle: and any of these four being known, all the rest are known onely by taking the number thereof upon its proper scale with your compasses, and apply that distance to the scale proper to the thing desired: and these three scales for these squares are

one for the Diameter, or side of a square without the circle, and that each side thereof toucheth the circle. Another is the side of a square within the circle, or of the chords of 90 degr. and the other is a side of a square, whose content is equal to the content of a circle. For Example. Let a block be girded about with a nealed wyer, and then that wyer laid along upon the block, being found to be 88 inches, I set one foot of the compasses in 80 of the said circle scale, and the other foot in 8 of those 10 odd parts next the beginning of the Rule, rec∣koned from ten upward, being the contrary way to the other 80. If then you desire to know the Diameter of the circle, or side of the square including the circle, you shall finde it just 28 inches, by setting one foot of the compasses in 25 of the Diameter scale, and the other will fall in three odd parts, which added make 28: for all these three last scales must be divided into fives, and numbred with 5, 10, 15, &c. and five odd ones above, at the beginning. Likewise if you apply the same wideness of the compasses to the scale of the square within the circle, that is, to the square, that a block being round will be, being hewed just to the four edges: then set one foot of the compasses in one of those great divisions by fives, so that the other may fall amongst the odd small divisi∣ons, and it gives you 19¾ feré.

And lastly, if you apply the same wideness of the compasses to the scale for the square equal, setting one foot in the great divisions, so that the other may fall in the five odd small ones, it gives 24 and about ⅔.

And in like manner if any of the other three scales be given, as if the Diameter 14 be given; if you take 14 upon the Diameter, and carry that to the circle; it gives 44; if to the square equal, it gives about 12⅓, and so of the rest.