380

MISCELLANEOUS

TRACT 38.

On referring him to the accompanying demonstration, to sa-tisfy himself of its geometrical truth, I was niucii surprizedby his reply, that he could not understand that, but. he wouldmake the drawing correctly on a large scale, which wasalways his way to trv if such things were true. In mv sur-prize I asked where he had learned geometry, and by whatEuclid or other book ; to which he franklv replied he hadnever learned any geometry, nor could ever understand thedemonstration of any one of Kuchtl’s propositions. Accord-ingly the next morning, with a joyful countenance, hebrought me the construction, neatiy drawn out on a largesheet of pasteboard, saying he esteemed it a treasure, havingfound it quite right, as everv point and line agreed to ahair’s breadth, by measurement on the scale. This problemand the construction he afterwards inserted, with the pro-per acknowledgment, as a curiosity, in his Select MechanicalExercises, p. 123, printed in 1173.

Also, in the beginning of the year 1771, when I com-menced the republication of the Ladies’ Diary Questions, Iinserted the following solution of the question, at pa. S 3 ofthe first volume of that work, viz.

“ This question is to divide a circle, of 60 inches dia-meter, into 7 equal parts, or rings, bounded by concentriccircles; of which the solution will be thus.—The wholecircle, and each inner circle, after the several precedingrings are ground off, must be to each other, by the ques-tion, as the numbers 7, 6 , 5, 4, 3, 2, 1 ; but circles are asthe squares of their diameters; therefore the diameters ofthose circles will be to one another as /7, /6, a/5, /4,j/3, a/2, VI : but the greatest diameter is 60 or 60 V-fitherefore, by proportioning, all the other diameters willcome out thus, 60 /y, 60v/-f, 60s/ 7 -, 60 /^, 60 </y, 60 /y-:Now the last of these is the diameter of the last person’sshare, and the difference between every two adjacent termsbeing taken, will give the double breadth of the rings, or theparts of the whole diameter to be ground off by the otherpersons; viz.