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laying out Grounds, whether into parts equal or unequal; which every Surveyor ought well to acquaint himself with.
For the better understanding this point, we will suppose a point given in the Perio meter of the Plot, from which the faid Plot is to be divided into as many equal parts as shall be required. First, Measure the Area of the whole Plot, then divide that Content by the number of parts to be cut: off, and the Quotient sheweth how many measures each part shall contain; then, cut off each part severally, as you were: taught in the preceeding work.
To divide a Common-Field or Pasture into as many parts as shall be required according to each Man's Propertion of Rept.
Example: I Fig; ro8: Eet ABCDEFGHIK, be al Common-Field or Pasture, in the Use and Occupation of three Men, viz. A,B,C,, and. it is agreed by them all, that each Man shall have his Proportion of Ground laid our, according to his Quantity of Counmon in the same place
First, Measure the whole Field, and it will be found to contain 35 A. 3 R. 15 P. or 5735 Perches ; then consider how many B-ale. Gates there are in the Pasture, and divide the Quantity of the Field accordingly by the rule of Proportion, thus ; saying, if the whole number of Bease-Gates of A,B,C give the whole Quantity of Perches in the Field 5735, what shall the number of them belonging to A, be, and the Answer will be his part; and so work severally for each Mans part: But we may suppose them thus, 10 A, 1819 Perches, to B, 1716 Perches, to C,2202 Perches. Then to lay out every Mans Plot, I divide the Figure by the Directions aforegoing by the Lines B L and CM, which to lay out upon the Ground, take from your Scalethe distance on the Plot bet ween H and L, then meafure out the dia stance on the Ground from the Angle H to L, also from the Angle A, Measure out 31.16 to B, then draw the Line BL; a. gain take from your Scale the Quantity of LM 28.00, which measure on the Ground from L to M, and there set a Mark : and in like manner Measure from B to C upon the Ground 25: 10, equal to BC upon the plot, drawing the Line CM: So is your plot divided according to every Mans juft Quantity and Proportion.
Example II. Fig. 109. But suppose it was required to divide this Field between three Persons, viz. A,B,C, according to each Mans proportion of Rent: As suppose the whole Grounds to be 20 Pounds a Year, whereof A pays 9 l.B.7 l.. C 41. the Question is, how many Acres, Roods and Perches belong to each Man, according to his Proportion of Rent, which by the Rule of three argue thus, fort for A) If 201 the whole Rent, give 5735 Perches, (being the Content of the whole Field in Perches,) what will 91. give? viz. 2581 Perches, or 16 A o R. 21 P. being the proportion of Ground belonging to A, for bis 91. Rent. In like manner, B will have 12 A. 2 R. 07 Perches, being his Quantity of Ground proportionable to hisRent of 71. and C for his 42. Rent, will have 7 A, O R 27 Perches. Then to lay out these parts upon the Ground, observe the directions in the former Example.
To divide a Field into three equal parts, and each Man to have the Benefit of a Pond about the middle of the Field.
Suppose Fig. I . containing 27Acres is to be divided between three Men, each to have q
Acres, and the Lines of Division to run from a Pond in the Field, so that every one may have the Benefit of the Water, without going over anothers Lund.
First from the pond o draw Lines to every. Angles o A, O B, C, D, E, and then is the Figure divided into s Tria angles each of which measure, and put the Contents feverally ; which Contents reduce
; all into Perches so will the Triangle,
The whole Content being 4325 Pera ches, or 27 Acres, each Mans Proportion being 1440. From o to any Angle draw a Line for the first division Line as O A.. Then consider that the firft Triangle A O B. is but 67-4 Perches and the second BOC 390, both together but 1064 Pärches, less by 376 than 1-440, one Mans Portion : You. muft therefore cut off from the third AngleCoD 376 Perches for the firstMap's Dividing Line , which thus you may do: The Bale DC is 28 Chains, the Content of the 18
Triangle 1238 Perches: Say then, if 1238 Perches give 18 Chains, oo Links , what fhall 376 Perches give Answer, s Chains 45 Links ;, which fet from C to F, and
, drawing the Line o F, you have the first Mans part, viz. A OF.
Secondly, See what remains of the Triangle, COD 376 being taken out, and you
will find it to be 862 Perches, which.is less by 578 than 1440. Therefore from the Tria angle DO E cut off 578 Perches, and the point of Division will fall in G. Draw the Line O G, which with A O and op die vides the figure into three equal parts..
PRO B L E M X.
To make a Parallelogram having an: Angle equal to any Angle given; and ai side of any Ergih, which Thall be equal to the Area ot any Right lined Figurewhatsoever.
Fig. 111.Let ABCDE represent a Field of 5 unequal Skes, and it was req ired to lay out a Parallelogram that fall contain the fame Area, draw the prickt Lines EB: and DB, then have you made the Field to confift. ot three Triangles. Make the Triangle a be equal to the Triangle ABE by Prob. & Divide the Base e b into two e qual parts at 2;, and draw the Line a z; which divides, the Triangle eab into two