How to take an inacceffible Distance, by three flat Sticks or Rulers of equal Length, joined together, thereby making an Equilateral Triangle: As in FIG. VIII.

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ET A be a Tree or other Object, whofe diftance you would know from the place of your ftanding at B, there being a River or the like Impediment between you and the Tree.

Place your Triangular Rulers horizontally upon a staff at B, and ob ferve the Object at A by the fide of the Triangle B D; it fo refting, look at fome other Object (or cause one to be fet up) by the fide of the Triangle BE. Then transfer your Triangle along the line B C, and place it upon divers parts of the fame line, till at length you find a Point C, upon which placing the Triangle, you fhall fee the Point B, by the fide CG, and the Object A, by the fide CF; then I fay the lines CB and CA are equal; so that by measuring the line B C, you have the Distance from B to A.

PROBL. V.

How to take the Distance between Two (or more) Places, without coming near any of them, by a Two Foot Joint Rule.

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FIG. IX. and X.

ET the two remote Places given be A and B, whose distance Į would know, but I cannot approach or come near either of them and I have no other Inftrument but my Two-Foot Joint Rule; however, I make choice of a Place at C, from whence I can fee both the Places, A and B, and there I fet up a staff whereon to reft my Rule, and opening it to a Square Angle, I look by one fide of it, till Iefpy my firft place at A, and there keeping it faft and level, I look by the other fide of the Ruler, and cause a Mark to be fet up in a right Line from C, at a competent diftance from C, as at D, 150 foot; then close in your Rule, till by the fide thereof you fee your fecond place at B; keep your Rule at that Angle:

Then having a sheet of Paper, or upon a Board, as Figure IX. draw two Right Lines thereon, as KL, and L M, making a Right (or Square Angle) at L.

Then bring your Ruler, (it being ftill kept at the Angle it was when you looked to B) and lay the Center of your Ruler upon L, and by the fide of it draw a line LM; and because your measured diftance between C and D was 150 foot, take 150 quarters of Inches (150 of any equal parts that you have upon your Ruler) and fet them down upon your Paper or Board, from L to M.

Then take your Rule and go to D, and fet the Center of it upon the Staff, look by one fide thereof to C, and by the other to A, then bring the Rule to the Board, and lay the Center thereof on M, and one fide upon the line ML, and by the other fide draw a line at length, as the line MO, croffing the line L K in O; fo fhall O upon your Board represent the Place A in the Field: Again, Take your Rule, and go to D, and there refting it upon the Staff, look by one edg to A, and by the other

F 2

to

to B, and keeping it at that Angle, bring it to the Board, and lay one fide upon the line MO, and by the other draw the line M P, croffing the line LN in the Point P, fo fhall P represent upon the Paper the fecond Place B in the Field, and being measured upon the fame Scale whereof L M was measured, it will be found to be 250 foot, and that is the distance from A to B. And by this means you may find the distances of all the Places in the Figure, if you measure them upon the fame Scale as L M, or OP were measured, and fo fhall you find

How to take the Distance between One or more Places, by a Ten Foot Rod (divided into Inches) only.

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FIG. XI, and XII.

Tanding at A, I would know how far it is to the Tree at B, tho I can not come near it.

Standing at A, I measure in a right line from thence

30 foot, from A to 4: And looking towards D, I measure our 30 foot more, as from to: A to C; and measuring the distance a C, I find it to be 25 foot, which laid down upon Paper, do make the Triangle A Ca, of which draw the line A out at length.

Then standing at C, I measure in a right line towards B, 25 foot, from Ctob, and the distance between a and b, I measure to be 20 foot, which makes the Triangle Cab, Draw the fide Cb at length, till it cross the former line A a, extended in B; fo fhall the line A B (being measured by the fame Scale that the other Lines were laid downby) be found to contain 82 foot, and fuch is the distance between A and B.

And according to this Method may the diftances from feveral Places be measured, As in Figure XI. Where ftanding at G and H, you may find the diftance between E and F; and alfo all the other intermediate distances, as from G or H, to E or F, as also the diftances GE, GF, HE, HF, &c. as by Figure XII. is evident.

F%

SECT. III.

of Planometria: Or Land-Measuring Mechanically.

OR the Measuring of Land (by a Chain only without any other Graduated Inftrument, which I call) Mechanichally: The best Chain that I can advise you to, is one that is commonly known by the name of Gunter's Chain, and it contains in length four Rods, Poles, or Perches (which are all one), and each Pole contains 16 foot and a half: So that this Chain is 66 foot in length, and is divided into 100 equal Parts or Links, which are diftinguished by having a Brafs Ring at every Ten Links end: And one of thefe Chains in Breadth, and Ten of them in Length, do make One juft Acre of Land according to the Statute: And

thus

thus much concerning the Chain it self. And now, before I come to fhew you how to take the Plot of a Field by help thereof, without any other Graduated Inftrument, I think it convenient, firft to fhew you how any Piece of Land measured by fuch a Chain may be caft up; that is, to know how many Acres, Roods, and Perches, fuch a Piece of Ground fo measured doth contain. And in order thereunto I shall begin with the Menfuration of Squares, Triangles, &c.

I. To Measure a Square Piece of Land.

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your Piece of Ground be exactly four Square, and have all the fides of equal length, and at right (or square) Angles, as the figure A B CD; and by your Chain you find that each fide thereof contains 12 Chains, and 25 Links; you have no more to do, but multiply 12 C. 25 L. by 12 C. 25 L as you fee done in the Margent. And the Product is 1425625, from which (always) cut off five Figures towards the Right hand, by a Point or Line, and then the Product will be 14.25625; that

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25625 4

is 14 Acres, and.25625 hundred thousand parts of an Acre; and to know how many Roods and Perches that is, multiply .25625 by 4, (because there are 4 Roods in one Acre) and the Product will be 1.02500; and five figures cut off, there is 1 beyond the Prick, which is 1 Rood, and .02500 remaining, which multiply by 40, (because there are 40 Perches in a Rood) and the Product will be 1.00000; from which five figures being cut off, there will remain 1. which is one Perch: So that this Square Piece of 'Land thus measured, will contain 14 Acres, 1 Rood, and 1 Perch.

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R1.02500

02500 40

P1.00000

II.To measure a Square Piece of Land,whose Length and Breadth are unequal.

ET CDEF be a Furlong in common Field, or the like; and let thereof Links,

thereof

16272

5424 24408

27. 12 thereof FH 9 Ch. 26 L. Multiply 27. 12. by 9. 26; 9.26 and the Product will be, five figures being cut off 25. 11312, which is 25 Acres; and the remainder 11312 multiplied by 4, the Product (five figures being cut off), is o. 45248, which is o Roods: And the remainder 45248 multiplied by 40, and five Figures cut off, will be 18.09920, which is 18 Perches; fo that this Piece of Land contains 25 Acres, o Roods, 18 Perches. As is feen in the Margent.

A. 25.113 12

4

R. 0.45248

4. 67

T

O measure Triangular Pieces of Land, you muft multiply Half the length of the Bafe by 4.26 the Perpendicular, and that Product fhall give the Content of the Piece.

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So in the Triangular Piece of Land KLM, the length of the line K Mis 9 Ch. 34 L. the half thereof is 4 Ch. 67 L. this multiplied by 4 Ch. 26 L. the length of the Perpendicular L N, the Product (five figures being cut off) is 1 Acre, and .98942 remaining; which multiplied by 4, the Product is 3 Roods, and .95768 remaining; which multiplied by 40, it produceth 38 Perches, &c. as in the Margent: So that this Triangular Piece of Land contains 1 Acre, 3 Roods, and 38 Perches; which is 2 Acres wanting only 2 Perches.

IV. How to measure an irregular Piece of Ground, of Four, unequal Sides.

Supp

Uppofe the figure OPQR to be fuch a Piece of Land to be meafured by the Chain only.

12.36

7.76

7416

8652

8652

First, measure the Length or Diagonal thereof OQ, finding it to contain 12 Chains, 36 Links, which fet down; then measure the Perpendiculars PT and RS, finding one to be 7 C. 24 L. the other 8 C. 28 L. which added together makes 15 C. 52 L. the half whereof is C. 76 L. which mul tiplied by the length OQ, 12 C 36 L. the Product is 9 Acres, and .59136, which multiplied by 4, the A. 9. 59136 Product is Roods, and .36544 remaining; and that multiplied by 40, produceth 14 Perches, &c. as in the Margent and the whole Content of the Triangle is 9 Acres, 2 Roods, and 14 Perches.

4

R. 2.36544

40

P. 14.61760

V. Of Irregular Pieces of Ground of many Sides, how to reduce them into Triangles, and to measure them.

ET ABCDEFGH be a Field to be measured In regard that I the Field is irregular, it must therefore be firft reduced into Triangles by drawing (or imagining) lines to be drawn from one Ang'e to another, as the lines A D, D B, A E, and FH; by which lines fo drawn (or imagined) the whole Figure will be reduced into Six Triangles, namely,