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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 underftanding this point, we will fuppofe a point given in the Perimeter of the Plot, from which the faid Plot is to be divided into as many equal parts. as fhall be required Firft, Measure the Area of the whole Plot, then divide that Content by the number of parts to be cut off, and the Quotient fheweth how many measures each part fhall contain; then cut off each part feverally, as you were: taught in the preceeding work..
To divide a Common-Field or Pafture. into as many parts as fhall be required; according to each Man's Propertion of Rent.
Fig, ro8: Let ABCDEFGHIK, be a Common-Field or Pafture, in the Ufe and Occupation of three Men, viz. A,B, C,,and it is agreed by them all, that each Man fhall! have his Proportion of Ground laid our, according to his Quantity of Common int the fame place.
Firft, Meafure the whole Field, and it will be found to contain 35 A. 3 R. 15 P. or 5735 Perches; then confider how many Bale Gates there are in the Pafture, and divide the Quantity of the Field accordingly by the rule of Proportion, thus, faying, if the whole number of Beafe-Gates of A,B, C give the whole Quantity of Perches in the Field 5735, what fhall the number of them belonging to A, be, and the Answer will be his part, and fo work feverally for each Mans part: But we may fuppofe them thus, to A, 1817 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 Scale the diftance on the Plot bet ween H and L, then meafure out the diftance on the Ground from the Angle H to L, alfo from the Angle A, Measure out 3116 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 fet 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 Divifion to run from a Pond in the Field, fo that every one may have the Benefit of the Water, without going over anothers Land.
Firft from the pond draw Lines to every Angles A, B, C, © D, – E, and then is the Figure divided into 5 Triangles each of which measure, and put the Contents feverally; which Contents reduce all into Perches fo will the Triangle,.
The whole Content being 4320 Perches or 27 Acres, each Mans Proportion being 1440. From to any Angle draw a Line for the firft divifion Line as O A.. Then confider, that the firft Triangle A O B. is but 674 Perches and the fecond BC. 390, both together but 1064 Perches, lefs by 376 than 1440, one Mans Portion: You. muft therefore cut off from the third AngleCOD 376 Perches for the firftMan's Dividing Line; which thus you may do: The Bafe DC is 18 Chains; the Content of the
Triangle 1238 Perches: Say then, if 1238 Perches give 18 Chains, oo Links, what fhall 376 Perches give? Answer, 5 Chains 45 Links; which fet from C to F, and drawing the Line F, you have the firft Mans part, viz. AO F.
Secondly, See what remains of the Triangle, COD 376 being taken out, and you will find it to be 862 Perches, which is lefs by 578 than 1440.. Therefore from the Triangle D E cut off 578 Perches, and the point of Divifion will fall in G. Draw the Line G, which with AO and Fdivides the Figure into three equal parts.
To make a Parallelogram having an Angle equal to any Angle given; and a fide of any Eergh, which fhall be equal to the Area of any Right-lined Figurewhat foever.
Fig.111.Let ABCDE reprefent a Field of 5 unequal Sides, and it was required to lay out a Parallelogram that fhall contain the fame Area, draw the prickt Lines E B and DB, then have you made the Field to confift of three Triangles. Make the Triangle a be equal to the Triangle ABE by Prob. & Divide the Bafe eb into two equal parts at z,, and draw the Line a z which divides, the Triangle e ab into two