MATHEMATICAL PAPERS. 25 



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No. L 



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A method of Jinding the Area of a feld arithmetically^ 



4r ELIZtJR WRIGHT, A. M. 



X HE invefligation of the area of a field, performed 

 according to the two modes of operation,^ Geometrical and 

 Arithmetical, has in each its peculiar excellences and defeats. 

 The lines and figures, arifing in a geometrical operation, aflifl 

 the imagination, and give an exadl image and idea of the form 

 of the field. The operation is at the fame time eafy and ex- 

 peditious. But the aritlimetical method is capable of a higher 

 degree of accuracy, and enables vis to approach to a greater 

 nearnefs to truth. The minutes of a degree, or the decima 

 parts of a chain, when geometrically confidered, approach fo 

 near to a point, that it often becomes impradllcable to lay 

 them down on paper ; which occafions a fenfible error in the 

 operation, fo that furveyors will frequently differ very 

 confiderably in computing tlie area of the fame field. For 

 thefe reafons it will be doing an acceptable fervice to furnifli 

 the ingenious artifl with an univerfal method of finding the 

 area of a field by numbers, that fhall exhibit an eafy and 

 natural order, fo that the operator may proceed without per- 

 plexity or danger of miflake : arid alfo afford a fiiort ami con- 

 cinnous folution, performed with the leafl poflible, number of 

 figures. Having had occafion to turn my thoughts to the 

 computation of areas, I hit upon a numerical method of find- 



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