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2. Set up your Instrument at F. and direct the Sights on Fig. IX. the Diameterthereof; to the other place at G. and there fix it : Which done, direct the Sighis to the several Places, A, B, C, D and E, noting what Degrees of the Instrument are cut by the Index at every Observation.
3. Then removing your Instrument to the second Place G, direct the Sighis which are upon the Diameter thereof, back towards the Firl Place at F, where fix it: Then, turning the Index about, direct it to the several Places, A, B, C, D and F, as before ; noting the Degrees cut by the Index. Which we will suppose to be such as are nored in this Table.
And the Distance from F to G 1oco.
of the several Places.
1. Upon a Sheet of Paper, draw a Right Line, as F G, to contain 1000 Foor, of any Scale, which represents the Line of the Distance of the Two Places, where you Observed at F and G.
2.. Place the Center of a Protra&ter upon F, and the Diameter thereof upon the Line FG, and there holding it fast, make Marks against the several Degrees that were cut by the Index, when the Sights were disečted to the several Objells at A, B, C, Ec. when you Observed at F, and through those Points draw Right Lines, at Pleasure; as FA, FB, FC, FD, F E.
3. Lay the Center of the Protractor to the Point G, and the Diameter thereof upon the Line F G, and there holding it fast, make Marks against those Degrees of the Protraflor, as the Index did cut upon the Instrument, when you made Observation at G; and through those Points, and the Point G, draw Lines; as GA, GR, GC, G D, and G E, crossing the former Lines (drawn from F,) in the refpe&tive Points, A, B, C, D and E. Which Points will lye upon your Paper, in the fame Position as the Places you took notice of, were fituate on the Ground on which they Hood: And being thus laid down, if you take with your Com
Fig. IX. passes the Distance between any Two of them, and measure it up
on the same Scale you laid down the Line F G by, it will give you the Distance between those Two Places.
But, their Distances may be more exact and accurately attained unto by Trigonometrical Calculation.
For, in every Triangle, as in F G A, F GB, FGC, FGD, and F G E, there is given, (1.) The Angle A F G, obseryed at F. (2.) The Angle AGF, observed at G; and, (3.) The Side FG, (the Stationary Distance) included between them, to find the other Sides, A F and A G. The Practice whereof I commit to the Ingenuity of the Practitioner.
CHA P. III.
Of PL ANOMETRI A.
A Logar. of 27:32
Of the Mensuration of Plain Superficial Figures.
1.436481 Logar. of 27.32
1.436481 Logar. of 746.38
2.072962 The Superficial Content of the Square in Feet. II. Of the Parallelogram (or Long Square) E F G H, whose Length
EF is 27.25 Yards, and Breadth EG, 6.29 Tards.
As 1 : 27.25 :: 6.29 : 17.03
1.4353665 Logar. of 6.25 ,
0.7958800 Logar. of 17.03
III. Of the Triangle K L M, whofe Longest Side L M is 267.26
Pole or Perches ; and its Perpendicular LN 160.25 Perches. As+P: L M 133.63 P :: L N 160.25 P: 21414 P. Logar. 160 25
2.204798 Logar. 133.63
2.J 25904 Logar. of 21414
4.330702 IV. Of the Trapezit (or Figure of Four in.egu..? Sides) O POR:
The Dirgonal, whereof O Q is 27:32 Perches, ibe Perpendicular P S 9.53 P. and the perpendicular R T, 21.06 P.
As I : 10P 13.66 . : : PS +RT 30.59 : 417.85 Fig.XIII. Logar, of half O Q 13.66 . Q
1.135451 Logar. of P S and K T, 30.59
1.485579 Logar. of 417.85 Perches.
-2.62 1030 Which is the drea, or Content in Perches. IV. Of an Irregular Plot, consisting of many inequal Sideš und A2
gles: As the Figure ABCDEFG.
Before such Irregular Figures can be measured, they must be re- Fig. XIV. duced in Triangles or Trapezii's, by drawing of Lines from Angle to fingle at the best Advantage, as in this, by the Lines FC and F C, which Two Lines divides the whole Plot into the Two Trapezia's A B CF; F C D E, and One Triangle F E G. And then the Bafes and Perpendiculars being such as are expressed in the Figure, they may bo measured, as is fliewed in the Two foregoing Sc&tions hereof; and according to the following Operations.
1:084933 Logarithm of B H and H F, 8.13 5 11
1.112605 Logarithm of CL and E M, 23.1 I
1.263800 the area of FCDE 299.51