Volume Information Source: The American Mathematical Monthly, Vol. 1, No. 12 (Dec., 1894), pp. 446-452 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/2969033 . Accessed: 21/05/2014 02:59 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The American Mathematical Monthly. http://www.jstor.org This content downloaded from 194.29.185.91 on Wed, 21 May 2014 02:59:43 AM All use subject to JSTOR Terms and Conditions
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Volume InformationSource: The American Mathematical Monthly, Vol. 1, No. 12 (Dec., 1894), pp. 446-452Published by: Mathematical Association of AmericaStable URL: http://www.jstor.org/stable/2969033 .
Accessed: 21/05/2014 02:59
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].
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Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access toThe American Mathematical Monthly.
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This content downloaded from 194.29.185.91 on Wed, 21 May 2014 02:59:43 AMAll use subject to JSTOR Terms and Conditions
ALGEBRA (See Solutions and Problems). ARITHMETIC (See Solutions and Problems). 13IOGRAPHIES (With Portraits)- PAGE.
Cagwin, Sanjuel Gardener, by Burleson.....374-375 Halsted, George Bruce, Ph. D., by Dickson.. 337-340 Hendricks, Dr. Joel E., A. M.,by Colaw.. 65 - 67 Hoover, William, A. M., Ph. D., by Finkel. ..35 - 37 Kirkwood, Daniel, A. M., LL. D., by Aley.. 141-149 Klein, Felix, by George Bruce Halsted....417-420 Loomis, Elisha Scott, &. M., Ph. D., by Finkel..2..219-222 Martin, Artemas, A. M., Ph. D., LL. D., by Finkel. 109-1ll Matteson. James, M. D., bv Matz......373-374 Newcomb, Simon, Ph. D., LL. D., by (Jolaw.-............. 2.....253-2.56 NicholSon, Col. James W.. LL. D., by Editors ........ 183-187
Seitz; Prof. E. B., M. L. M. S., by Finkel............ 3 - 6 Sylvester. James Joseplh, A. M.. LL. D., F. RI. S., 1). C. L..
Finkel, B. F., Solution to a Problem in Average. 97 - 98 Fish. Edmund, Curious Process for Maximum and Minimum. 332 Goodmian, E. J., Quadrature of the Circle .246-247 Gridley, A. L., The Nebular Hypothesis.. 224-225 Hal sted, Greorge Bruice, Easy Corollaries in Nori-Eiwl idean
Geomnetry ..................................... , 42 Non-Etl idean Geometrv: H istorical a nd Expository. 7 0-7 2,
Ingraha m, Andrew, A Proof of the Pythagorean Proposition.. . .2.223-224 .Judson, C. H., Remarks on I)ivision of Concrete Numbers. (8 - 69 Kuinstadter, Ralph Hi., Oblique Angled Triangles. . 69 - 74) Lillev, George, Pascal's Arithimetical 'I'riangle.. 426i Lyle, Johln N., Are Differentials Finite QuantitiesP .118-120
Is thle Supplemenitar-y Angle Finite or Not?..3..385-387 Logical D)eductions from the Hypothesis that thie Angle-Sum
is less than two Right Angles ..426-429 Lobatchewsky's Triangle .2 47-248 Notes on Counsellor Dolman's Remarks.4.. ..48-410 Postulate 1. of Euclid's Elemernts .1 - 1 2 The First Differential Coetfficient of a Circle.. 303-309
Matz. F. P., Professor Sylvester's Reciprocants. .3..383-385' The Second Hyperbolic Integral.. ..341-342
Nicholson, J. W., Some Novel and Interesting Formulas . .. 18,-188 Philbrick, P. H., An Unreasonable Rule in Surveying.. 73
Demonstration of the 'Tange nt Propisition, and Others.. 12-13 Tsoperimetry withiouit Curves or Calculus.. 347
382-383, 420-4'21. Some General Formul as for Square Numbers with Appl ications 25.6-259
Pratt, Seth, "An Unreasonable Rule". . 247 Robins, Sylvester, Certain Series of Integral, Rational, Scalene
Triangles.. 13-14 Series (of Rational Trialngles. .. 262-263
Smuitb, 1). E., Note on Mr. Ellwood's Renmarks on 1)ivision. 74-75 Stevens, M. C., Logarithms of Negative Nuimbers. . A 11-1 12 Whiitaker, FH. C., A Reply to Mr. Draughon....410-411 Zerr, G. B. M., Solution to a Probability Problem.. 54-5S
Note on Centroid of Plane Areas .120-12., Notes on Areas and Volumes. . 380-381
MECHANICS (See Solutions and Problems). MISCELLANEOUS. (See Soluitions and Problems). NOTES. 29, 58X-.59, 103. PORTRAITS: (See Biographies). PROBLEMS, Arithmetical Unsolved, No. 22 .264 PROBLEMS, Geometrical Unsolved, No. 20. 1 51 356 PROBLEMS. (See Solutions). PERIODICALS, ...... 32, 61.62, 105-106, 180, 2,50, 292, 570, 4192-414
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QUERIES AND INFORMATION. Answer to Prof. Halsted's Query in June No.. by Geno Lorea. 367 Answers to Prof. Lyle's Queries on p. 102, hy Prof. Halsted.. I,5-170. 213-214 "An Unreasontable Rule," by Setht Pratt. ....247
'. " 4 " f. Again by Prof. Philbrick.. 331-332 A Reply to Prof. Whitaker's Comment. by H. W. Drauglion .... 286 A Reply to Mr. Dreaughon, by JI. C. Whitaker..4..410-411 Comment by Prof. Whitaker on Editor's Replv to L. 13., p. 27.... ;5 Curiouis Process for Maximumu and Minimum, by Edmuind Fislh.. ..332-3 Definition of a Fraction-A Query by H. C. K..31
Lobatchewsky's Triangle, by Prof. Lyle.. 247 -248 Mathematics at Brooklyn, by G. B. Halsted.287 N'ote by J. H. Drurmmond t- Prof. I)ickson's Article on TriAingles. Note to Article on p. 42, by G. B. Halsted .102 Note on flayward's Solution to Ex. 3, p. 19, by Bradbury.170 Notes on Couipisellor Dolman's Remarks in April No., by Lyle. 408-41() Proofs In Wenthwortlh's Geometrv-Finkel. . ..176 Quadrature of the Circle, by E. J. Goodwin.24(i Queries by Prof. J. N. Lyle..12 Query by George Bruce Haisted.214 Query by John Dolman. Jr.289 Querv by "Kendrick".....8 Remarks on Prof. Steven's Article in April No., by C. I). Schniitt....214 Remarks on Division, by W. F. Bradbury..248 Reply to a Query.28 Reply to Query of "L. B.", by Editor (1olaw.2 7-28 Rtesolultions at the Caen Congress-Halsted..-. .:68 Solution to a Probability Problem by Editor ..28
SoLUTTIONS AND PROBLEMS. ARITHMETIC.
Acres in hexagonal field when A. equal No. boards in fenve..2..2o Acres in rectanglar " " ' " ' " ".348
Agent for Company, to find bal. of aect..3..309 Animals, buying 100-hiow many different answer.40................43 Board, cuttinig to f(rm a square . . .. .49 Board, cutting trapezoidal into two equal parts... 12i Cliclken, diamond in gizzard-to find gaiii or loss in -ielling.. ..388 Circle, area of part between chords... 195+3 Clock, when and what correct time. . ..26i5' Corn, bushels bought and price.. . 22.i Debt, payment of part..2. .2.6 Discount, date of ..388 Estate divided.. 127 Farm, area of circular. .19:3 Fractions, reduced....1 Horse. tied to sq. building-area grazed..431 House, equallv distant from A, B, C ..1.53 Logs piled-d iam. of top log... 125
Men, No. In militia.....
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Money, borrowed and loaned (unsolved). . .'64 Note, how long disc. before due.. .153 Note, given at bk.-to find 'p. c. paid.. 152 Profit and Loss, problems in.. 19, 76, 226 Pyramid. Vol. of pentagonal.. .76 Quotation, No, of ways can be read... 310 Rope, length to draw from well.. 127 Ship, division of purchlase money....310 Spider, how long to crawl in rect. hall. .264 Stakes, how many driven in square. 191
ALGEBRA. Age problem.0.. 8 Algebraic equations solved....21, 78, 128, 129, 228, 349, '92 Apples, to find names of boys stealing.. .158 Bonds, price at which Gov. must sell. 230 Eggs, selling in market . ..79 Equation. to tind lost coefficient ................. ...194 Field, area and dist. from tree to corners. 80 Horse, working capacity given to find formula for value . 391 Inequality, solved. .351
M1oney-box, amt. drawn out daily. 154 Money loaned, to find payment made. 196 Oarsman problem ....... 89 Pole. three lads climbing ......................................... 155 Potatoes, digging and pulling vines.. ..350 Problem, the "Little German" .392 Series, problems in . . 78, 313, 432 Tobacco, price of mixture.. 266 Track, money divided for ploughing circular .267
Trains, how pass theni. 196 Traveling, to find rate and distances. 195 Triangle, dists. from pt. to angles to find sides.. 195, 312 Vessel, fllling bv pipes. 79
GEOMETRY. Circle, thro' 2 points to draw two circles tangent to a.. 271 Circle,s 3 touch and tangent3 meet, etc .. 82 Circles, 2 intersect, etc.. 160 Circles, thro' 2 points to pass four circles tangent to two. .232, 269 Circles, circle bisectitg circumfs. of 3 circles.. .270 Circles, from pt. in cirf. lines drawn to angles of inscribed triangles. .315 Circles, two intersecting have com. area-to ffnd radiuis .......395 Cistern, height water rises when cyl. laid in ..... ...... 315-316 Conoidal surface, to find vol. of.... ....355 Ellipse, to flnd value of eccentric angles ........... .......... 352 Ellipse, equilat. triangle described on chor. ....... ....... 198 Farm, 8 circular within--to find areas ........ ... 197 Field, how far walk before turning in circular 10-acrea ..... 233 Lights, flnd pt. in plane of 3 aqually illuminated.. . . 269 Field bound, etc., and containing a spring ... . 435
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Parabola, chord thro' straight line touching ....1........... 131, 160 Plane, to find minimum dist. from points to ..161 Quadrilateral board, to find max. rect.. sq., and triangle 'in.... 354. 434 Quadrilateral, bisectors intersect, etc.. 23 Sphere, thro' 3 pts. to pass 2 sphl. surfs. tangent to ..... ........... 394 Spheres, to pass 4 sphl. surfs. tangent to two. 199 Trapeziuml, sides of inscribed-to flnd diam. of circle. :13(. 159 Triangle, angles drawn to sides of isosceles ..83 Triangle, to prove isosceles . ..131 Triangle, to find sides, etc ..316 Triangle, line parallel to base in isosceles.. 355 Triangle, length of parallel bet. sides=sum of segmenits. .395 Triangles, to flnd base of two rt. triangles. 3.3.53 Trigronometricail problem ...51 Wallis, expression for 7r, to find .1.. . t1, 82
CALCULUS. Circle, area bet. locus of P and asymptotes=twice area of cir.... 2 2, 436. Cuip, Cyl. of max. capacity fromn nmaterial .04 Curve of pursuit in circular room. .2 73 Cylinder, Vol. Com. to and Vol. generated by cueirve. 87 Cylinder, ldist. dove flies in unwiniding string ...88, 318 Differential equation, solved. . .396
Equiation, to find d3f foI reO . = 0.203 d.r
Equation, diff erentiated . .234 F (x), to determine, ete . .132 Indeterminate form, to find value when x0. ..89 Integral, to find Ellipitic of eq..356 Parabola, to find moment of inertia in . ..........5 ...... .8 President receiving, when to join line to suffer least dela . . 437 Prism, length of ribbon and of curve in unwindin 2..2 02 Room, race in circular .............. ..... 27 03 Segment, to find Vol. gerierated by circular.4. . 320 Solids, eqs. of given,when centres are coincident, to fincd Vol. of eaclh
and Vol. common t( both ...3...... .. . . ...... .. 163 Steamers, one crossing course of another. etc . . ... ..... 203, .320 rrangent, determine at point of a req'd locus9 ... . 9, Towns, 3 in St. line-time to travel frorm B to C .. . 87 Tree, board cut ouit in logging off ....13 Triangle, to find max. area of, etc . ... . 8(6, 3p8 Triangle in circle, to find curve to which leg is tangent .. 204 Triangle. equilateral-Vol. of solid generated by revolvinigo figture
about altitude .... 357.
MECHANICS. Air-bubble-spherical, to find diam. at point of starting.. ...134 Bar. falling-to find angular velocity .238 Cavalry, effect of charge between liglht and beav'y . .205 Ladder, height man may ascend before begins to slip. .31
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Lomnis, to find locus of foot of Perpendicular from center of ei-rcle upon resultant accelerati(in .167
Parabola, po.sition of focal cllord down wlhich body rolls in least time. .90, Paraboloid, floating in a liquid-ratio of densities, etc ........ .... 321 Race cour.se, mian, hio(rse and buggy in-find pressure on ground ... 400 Sphere, h1ow filled withl water freezing-timeof descent down plane. .205.
236, 276. Sphere, show that will slide and not! roll rouigh inclined plane . ....... 35t' Table, ball on 3 legged table to find weight on each leg.etc ... ... 166 'Table, find pressure uipon at thiree points ......... ..... 3 99,. 43S Trraveling, A and B from point in plane--to flnd dist. apart ..... ... 90
DIOPHANTINE ANALYSIS. Eqquation. find valiue of x to render a square .......... .. .. . 97, 13t Fouir numbers, suim of fourth power3 a square ........ ....... 4013 Numbers-two. dilfl. of squares a cube, and diff. of cubes a square.95, 32,. Numbers-three, sq. of sum of two less sq. of other eqtual ai square..361 Odd squiare of form 4a+1: valuie of a for nth odd squiare. .209 Odd squares. diff. of two . 8; sunm of two times odd No...439 Square number, to divide into two parts each squares . .94, 32:, Three numbers, sum of sq. of any two less their product a square.... 208 'T'hree numbers, sum of cubes a square, an.d sum of square a eube.. .. 363 Three whole numbers in Arith. prog.--sum of every two a square.96, 136,169 Three wholoe numbers, sum of any two a cube.. .208, 279 Trhiree numrribers sumii of whose 4th powers a square .279! Two numbers, each of themi and theirsum and diff. pluis 1 squares.280,325. Triangles, find initial ternis in three series .402 Xt2-q2 =?I1, Solved bv A. H. Bell .53, 93 169 239-
AVERAGE AND PROBABILITY. 13ox-rectangular, equal No. of white and black balls in-proba. of
contact of white balls.. 211, 363. Circles, Av. area of all circles tangent to two-Finkel.. .97 [)eer, chance wotunded will drop dead in park.. 170. 209 Diamieters, avr. length of all in given ellipse....242, 28i Dice, flnd expectation in thirowing..9..9.. .. .. .. .. .. ..911 Dice, probability of tlhrowing, by Zerr.. ..5, Ellipse, find mean area of octagonal surface within....210, 241 Letter. probability came from Oshkosh.. ..283 Numbers, 4 multiplied to find proba. last digit is 0. .328 Regular polvgon thrown at random upon a ruled surface. .441 Surface 1 ft. square, chance coin touches or intersects both dliigonals.404 Triangle, find avr. area of, formed by joining angle of square with 2
pts. with in.. 137. Triangle, find av. area of, formed by joining corn r of cube with 2
pts..within . ...405. Triangle, mean area of all Ls's with vertices upon surf. of given
Z, and bases parallel to base of given A= (ares of giv3en .~~~~~~~~~~~~~~~326.
AMISCELLANEOUS. Axes. find position in space at any assigned instant.. 101
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Cloud, two observations taken r eq'd direction of wind ............ . 284 Comet, how long can remain within earth's orbit .. ............... 406 Qycloid, to divide are of into 8 equal parts .... . ....99-00 Grindstone, to flnd thickness of outer edge that each may grind off
18 inches.173, 330. Grindstones, two circular wearing out and No. of revolutions.... 172, 32$4 Man, course of who walks towards sun from morning till night .....212 Rain, how many tons will fall from cubic mile of air cooled...... . . 173 Trapezoids, give dimensions of 13 rational with given bisector....100 Triangle, general expression for co-ordinates of.. ..244 Wires of 5 metals soldered, to find strenth of current in.. ..244
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