TRACT 38.

PROBLEMS.

381

60 ^ 7 - 60./ f X 60=4-450794 the 1st person’s share

60v'J-60\/f=^^x 60=4-839951 the 2d

V'

60\/t-—60 \/7 X 60 = 5" 353518 the 3d

V 7

60 v /^-60>/f= A/4 ~/ 3 X 60=6-076516 the 4th

60 A /|-60 v /|.=:^^?x 60=7-207871 the 5thv”

60 v / 7--60v'f=^^x 60=9-393480 the 6th

V 7

60v'-f-60v'y = —^r—x 60 = 22-677870 the 7th

“ The Construction will be thus.—Divide the radius ab ofthe given circle into 7 equal parts; and at the points of di-vision erect perpendiculars meeting the circle, described onAB as a diameter in d, f, h, k, m, o ; then with the centrea, and radii ao, am, ak, &c, circles being described, thething is done.—For, by the nature of the circle, the squaresof the chords or radii, ao, am, ak, &c, are as the versedsines an, al, ai, 8tc.

“ Scholium. It is evident that the above method of cal-culation and construction will both hold true also whenthe shares are unequal in any proportion ; by using the re-spective proportional numbers in the former, and dividingthe radius ab in the same proportion in the latter.

Very soon after the first publication of the solution of theDiary question as above, it was seized by a shameful pla-giary, in the person of a Mr. Samuel Clark, who had com-menced, after mine, a republication of the Diary questions,under the title of ‘ The Diarian Repository.’ When this