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As 1 perch to the breadth in per∣ches, so the length in perches to the content in perches.
As 1 is to 30, so is 183 to 5490 (perches.)
As 160 to the breadth in perches, so is the length in perches to the con∣tent in acres.
As 160 unto 30, so is 183 to 34, 31 (in acres and perches.)
It being troublesome to divide the Content in Perches by 160, we may measure the length and breadth by Chains, each Chain bein 4 perches in length, and divided into 100 links, then will the Work be more easie in Arithmetick, or by the Rule; for as 10 to the breadth in Chains, so the length in Chains to the content in Acres.
As 10 to 7.50, so is 45.75 to 34.31 (100 parts of an Acre.)
If the Perpendicular go for the length, and the whole base for the breadth, then you must take half of the oblong for the content of the tri∣angle, by the second probleme, as 160 to 30, so is 183 to 34.31, or else with∣out halfing, say as 320 to the perpen∣dicular, so is the base to the content in acres; as 320 unto 30, so is 183 to 17, 15.
As 20 to the perpendicular, so is the base to the content in acres.
As 20 to 7, 50, so is 45, 75, to 17, 15 parts.
As the length of the second perch, is to the first, so is the content in acres to a fourth number, and that 4th num∣ber to the content in acres required. Suppose a Superficies be measured with a chain of 66 feet or with a perch of 16 1/2, and it contain 34. 31, and it be demanded how many acres it would contain, if it were measured with a perch of 18 foot? these kind of proportions, are to be wrought by the backward rule of Three, after a duplicated proportion: wherefore I extend the Compasses from 165. unto 18, 0, and the same extent doth reach backward, first from 34.31 to 31.45, and then from 31. 45 to 28. 84, the content, in those larger acres of 18 foot to a perch.
Suppose a plain contained 34 acres 31 Centesmes, if I should measure it with a scale of 10 in an inch, the length should be 38 Chains and 12 Centesmes, and the breadth 6 Chains and 25 Centesmes, and the content according to that dimension, would by the 3 Probleme of this Chapter be found to be 23, 82. whereas it should be 34.31, therefore to gain the truth, I divide the distance between 23. 82 and 34, 31 into two equal parts, then setting one foot of the Compasses upon 10, the supposed true scale, I find the other to extend to 12, which is the length of the scale required.
As the length in perches to 160, so is one acre to the breadth in perches. As 40 to 160, so is 1 to 4. Again, as
50 to 160, so is 1 to 3.20, so is 2 to 6 40; or again if you measure by chains, As the length in Chains to 10, so is 1 acre to his breadth in Chains; as 12 50 unto 10, so 1 to 0. 80, or if the length be measured by foot measure, then as the length in feet unto 43560 so is 1 acre to his breadth in foot measure.
So the length of the oblong being 792 feet, the breadth of one acre will be found to be 55 foot, the breadth of 2 acres 110 feet.
The use of this Table is to shew you how many Inches, Centesmes of a Chain, feet, yards, paces, perches, chains, acres, there is in a mile, either long or square, or consequently any of them all, in any of the other that is less; as for example, I would know how many Inches there is in a long berch, I look on the uppermost row for perches, and in the next row under, I find 198 for the quantity of inches in a long perch. But if I would know now many inches there is in a square
perch, then look for perch on the left hand, and in the inch colume you have 39204, for if you multiply 196 by 196, it will produce 39204.
| Inch. | Centesme. | Feet. | Yard. | Pace. | Perch. | Chain. | Acre. | Mile. | |
| Inch. | [1] | 7 92 | 12 | 36 | 60 | 198 | 792 | 7920 | 63360 |
| Centes | 62 7264 | [1] | 1. 515 | 4 545 | 7 575 | 25 | 100 | 1000 | 8000 |
| Feet. | 144 | 2 295 | [1] | 3 | 5 | 16 5 | 66 | 660 | 5280 |
| Yards. | 1296 | 20 655 | 9 | [1] | 1 66 | 5 50 | 22 | 220 | 1760 |
| Pace. | 3600 | 57 485 | 25 | 8 335 | [1] | 3 30 | 13 2 | 132 | 1056 |
| Perch. | 39204 | 625 | 272.25 | 90 75 | 10. 89 | [1] | 4 | 40 | 320 |
| Chain | 627264 | 10000 | 4356 | 1452 | 17424 | 16 | [1] | 10 | 80 |
| Acre. | 6272640 | 100000 | 43560 | 14520 | 1742.4 | 160 | 10 | [1] | 8 |
| Mlie. | 4014489600 | 64000000 | 27878400 | 9292800 | 1115136 | 102400 | 6400 | 640 | [1] |
| Squar. | Inches. | Centesmes. | Feet. | Yards. | Pace. | Perch. | Chain | Acre. | Mile. |
The like is for any other number in the whole Table, an•• is of very good use to reduce one number into another, or one sort of measure into another: as inches into feet, and feet into Yards, and Yards into Perches, and Perches to Chains, and Chains into Acres, and Acres into Miles, or the contrary either long-wise or square- wise: as is well known to them that have occasion for these measures. Thus much shall suffice for Superficial measure, the practice of which will make it plain to any ordinary capaci∣ty.