The American Mathematical Monthly; The Official Journal of the Mathematical Association of America Volume 8

The American Mathematical Monthly; The Official Journal of the Mathematical Association of America Volume 8

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ...follows. It will be noticed that there is not a suspicion of anything pertaining to the evolute until we reach equation (5), and that then by conjunction of conditions the thing snaps into place and the a, b locus becomes, willy nilly, the a, ft locus or evolute, and the r similarly becomes R, the radius of curvature. The terminology applied to a, b, r is ineffective. II is the conjunction of conditions that decide what they should be called. DEPARTMENTS. SOLUTIONS OF PROBLEMS. ARITHMETIC. 142. Proposed by M. J. CRAWFORD. Principal oi Crawford's Academy, Savannah, Ga. A gentleman has a garden 400 feet long and 300 feet wide, which he wishes to raise 9 inches higher by means of the earth to be dug out of a ditch 6 feet wide and surrounding the entire garden. How deep must the ditch be? Solution by G. B. M. ZERR, A. H Ph. D Professor of Chemistry and Physics, The Temple College, Philadelphia, Pa. 400x300xT=90000 cubic feet of earth necessary to raise the garden. 2(412]300) X 6=8544 square feet, area of surface of ditch. 9O0O0-r-8544=10, Vs feet, depth of ditch. S ALGEBRA. 117. Proposed by G. B. M. ZERR, A. M., Pb. D. Professor of Chemistry and Physics. The Temple College, Philadelphia, Pa. Rationalize J4-f-m-f-n + xS-f j/4 + 2 = 0. Solution by the PROPOSER. Letu--pu4 + qu3--ru-su+t=0, be the equation having H, mi, n, x, j/4, 2 for its roots; then u-j-put+qu + ru+sw- + t=0 is the equation having I, m, n, x, y, z for its roots..." it3 +pws+ru+f+-4 (Lqu--8)=0 oru+2pul+(ps+$r)u+(.2t+2pr-q)u + (r8 +2pt-2qs)uf! +(2rt-s )u 4 t=(). Let a=l-f-m + n--x--y--z='S, l). 6--lm--ln--lx + ly + lz--mn + mx + my + mz 4-nx--ny + nz + xy+xz-f yz 2(/m). c=lmn-=lmx--lmy--hnz--lnx--lny--lnz--lxy + lxz + lyz-innx--mny--mnz--vvry-mxz + myz--nxy more

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  • Paperback | 70 pages
  • 189 x 246 x 4mm | 141g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236535987
  • 9781236535986