The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

Planimetry, or, The most Exact and Curious Arts of Surveying Lands, &c. after the newest and most Experienced Method and Practice, &c.

PLanimetry, or Surveying, is numbered among the Curious, and deserves wor∣thily here to take place; and to be exact in this, have (beside other Instruments pro∣per to the matter) a Ruler of about 7 or 8 Inches long, and an Inch and a half broad, and place two Scales, one of 12, and the o∣ther of 11, in an Inch describing a line of Cords 2 Inches long, or somewhat less than 60 or 90 degrees, the Radius of which or 60 degrees, being equal to the Semidiameter of the same Circle, and after the order of these on the other side, place several other scales which may be of 16, 20, 24, or the like in an Inch, whereby you have an In∣strument necessary for sundry occasions, and for this scale in its use you must be provi∣ded with a pair of Brass Compasses, also a curious pair of Calem Compasses, having screws to alter the points, as to draw as oc∣casion requires to the beautifying the Plats with black Lead or the like; being provid∣ed with Instruments, and all things sitting for measuring, you must consider the Mea∣sures, and reduce that which is called Sta∣tute

Measure into such measure as is Custo∣mary and Usual, for by an Act of the 23 of Edward the I. an Acre of Land was to con∣tain 160 Perches or Poles to be made out square, &c. but by Custom in divers pla∣ces of this Kingdom, this has been altered by the varying of Perches in the number of feet, as, 18, 20, 24, and sometimes 28 foot to the Perch, and this requires the Surveyers diligence to reconcile the one to the other, of which we shall give some insight.

Suppose you are to Reduce 5 Acres, 2 Roods, 20 Perches measured Statute mea∣sure by 18 foot the Perch, in this case seek the least proportional terms between 18 and 16 foot and a ½, and to effect it, be∣cause the latter carries with it a fraction, reduce it into halves, and that they may be of one denomination, let the 18 foot be likewise halved, and you will find them in this manner 33/36, which you must abbrevi∣ate by 3, in saying, how many times 3 shall I find in 33, and the Answer will be 11 times 3, and the same do by 36, and you will find it 12 times 3, and thereup∣on the two proportional terms between 16½ and 18, will appear to be 11 and 12 which being done, reduce the Given Quan∣tity of 5 Acres, 2 Roods, and 20 Perches all into Perches, by which means you will find them to be 900 Perches; then observe what is the Proportion, the Square 11,

which is found 121, bears to the square 12, which is found 144, the same does the Acre containing 16 and a half feet to the Perch, bear to that that contains 18 feet to the Perch or Pole.

Always observe, in this was particularly that the greater measure is to be reduced into the lesser, then multiply the Quanti∣ty Given, viz. 900 Perches by 144 the larger square, and you will find the Pro∣duct to be 129600, and that divided by 121, you will find the Quotient to be 1071 Perches, and 9/121 parts, which reduced in∣to Acres, gives us 6 Acres, 2 Roods, and 31 Perches, and 9/121 parts of a Perch, and this compeers with the Quantity of Acres Parallel with Statu••e measure; but on the other hand, if it had been required for the reducing Statute Measure into Custo∣mary Measure, you must then Multiply 900 perches, your given measure or quantity, by 121, which is the lesser square, because the lesser is to be reduced into the greater, and you will find the Product to be 108900, which if you divide by the greater square 144, you will have the Quotient 756 ••/4, which being reduced into Acres, is 4 Acres, 2 Roods, 36½ Perches; and this rule is to be taken with what ever Customary quan∣tity is proposed in their difference, and degrees, as when the Perch is 20, 24, or 28 foot, or other disproportions of num∣ber.

If in this Mensuration, you are required to reduce Perches into Acres, and so on the contrary, observe that by the Afore∣mentioned Statute, an Acre of Ground should contain 169 square perches or poles, being every Rood 4 square perches, so that if you find any number of perches, that must be done into Acres, the given number must consequently be divided by 160, and the Acres are shewed by the Quotient, but if there be remainder, and it be under 40, they are perches, but if they are found to exceed 40, divide by 40, which you will find to be the number of perches contained in a Rood, so that the Quotient will be Roods, and the Remainder Perches.

But to reduce Acres into Perches, there is no great difficulty, considering it is but turning it as it were backward, for in the other to bring Perches into Acres, the di∣vision was by 160, but in this case, to turn Acres into Perches, it must be multiplied by 160, which being observed, we come now to more nearer particulars, as to the matter in hand. If the piece of ground you measure be square, having considered well that the Acre is 160 Perches, then multiply one of the sides by the other joyn∣ing to it, & you will find the sum is to be di∣vided by 160, and suppose your Ground be 40 poles one way and but 20 another, these multiplyed, make 800 Poles or Per∣ches,

which divided by 160, shews 5 Acres to be the content.

In measuring a Triangular piece of Ground, you must first observe to mea∣sure the longest side of the Triangle, as also the Perpendicular opposed to the said long side, then multiplying the half of one by the whole of the other, you must di∣vide by 160.

Suppose the side be 60, the Perpendicu∣lar 40; 60 must be multiply'd by 20, or 40 by 30, which so done, make 1200, which being divided by 160, renders 7 Acres and ½ for the true content.

If you are to measure that which we call a Trapezia, or a double Triangle, then both the Perpendiculars must be multiply'd by the Diagonal Line, as being the usual or common Base of both the Triangles, and must be divided by 160 in this manner. Let the Diagonal Line be 40, and one of the Perpendiculars 15, the other 8, which be∣ing put together make 23, which being multiplyed by 20, which is half the Dia∣gonal Line, make 460, and that divided by 160, renders two Acres, three Roods, and 20 Poles.

If the Ground be Circular, then half the Diameter must be multiplyed by half the Circumference, and the product divided by 160, whereby the Diameter of the Cir∣cle being found to be 140 poles, the Circum∣ference

is 440 poles, and the half of these two producing 220, and 70, they are to be multiplyed together, and then produce 15400 Perches, which being divided by 160 produce 96 Acres and a ¼.

If the piece of Ground given, be Oval, suppose it to be 30 Perches one way, and 40 the other, to know the content, mul∣tiply the length 40 by the bredth, which as aforesaid is 30, and you will find it make 1200, which again divided by 203 7/101, and you will find it yield 5 Acres, 3 Roods, and 23 Perches, and by this last number so working, you may find the number of A∣cres contained, in a Semicircle, a quarter or sixth part, or any section or division of a Circle greater or lesser, multiplying the half Diameter.

If you are to measure wood Land, which is the difficultest of all, you may fix a mark at either corner of the Wood, that 3 marks may be seen at once, then having a Quadrant in your hand, lay it flat there∣on, and take sight to two of the marks on each side▪ and then upon paper, mark the degrees of the Angle, and measure to the two marks in sight, and place them on the same paper by your line of equal parts, and do so to all other corners, till you have closed up the Plat or Wood, which then may be easily brought into Acres by the line of equal parts. And Note here, if your

Quadrant be too small, you may joyn two together, or do it by a board for want of a plain Table, so your Plat upon the paper make 3 Triangles, and to mea∣sure one of them, measure for one Tri∣angle the longest doted line, by half the middle doted line, or Perpendicular, which gives the content, and by so wor∣king the other two Triangles you have compleated it.