Other editions of book Mathematical Questions, With Their Solutions, From the "Educational Times", Vol. 40: With Many Prayers and Solutions Not Published in the "Educational Times"

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. 1872 Excerpt: ...mathematical and nonmathematical, may obtain approximate solutions to some of the probability questions which appear in it from time to time, and so test the correctness of the more scientific solutions supplied by the mathematical contributors. As an example of the class of problems to which I refer, I would here propose for solution the following question:--"A point is taken at random on a window consisting of nine equal square panes, and through this point a line is drawn in a random direction. What are the respective chances of the line so drawn cutting one, two, three, four, or five panes?" Experimentally this may be solved as follows. Take a circular piece of white card-board; draw a straight line across the centre on one side, and through the centre on the opposite side insert a pin. Move the cardboard round this pin as a pivot till the stiffness is so far gone that when the pin is held by the point head downwards, a slight jerk of the finger will make the card-board revolve easily and rapidly. This may be a rude contrivance, but it will answer the purpose. Now draw a figure on paper representing the window; twirl the card-board, and while it is spinning mark with a pencil a point anywhere on the figure. If the rotatory motion of the card-board still continues, arrest it suddenly, so as to economize time; then place the card-board on the paper so that the pin's head shall fall on the pencil mark, or near it, extreme accuracy upon this point not being at all necessary. Observe now how many panes the line drawn across the centre of the card-board would cut through if produced; and register accordingly. Mark another point with the pencil, and proceed as before; and so on as long as you please; taking care, however, to distribute the points as ...

Excerpt from Mathematical Questions, With Their Solutions, From the Educational Times, With Many Papers and Solutions Not Published in the "Educational Times", Vol. 16: From June to December, 1871Martin, Rev. H. M.a., late Examiner in Ma the'matics and Natural Philosophy in the University of Edinb h.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ...A, 0 This determinant is, when worked out, (/+ g cos C) (g + h cos A) (A +/cos B) + (A + g cos A) (/+ h cos B) (g +/cos C), which breaks up identically into the product of sin A + g sin B + h sin C into gh sin A + A/sin B + _/j sin C; this result determining the locus of (/, g. A), according to what we all know, to be the circle circumscribing the original triangle. The geographical statement of this theorem homographically transformed, runs thus: Consider two fixed points joined by a line intersecting the three sides of a triangle; to each point of intersection successively let there be taken the harmonic conjugate with the fixed points as a pair of conjugates: join each point so determined with any point on the conic passing through the fixed points and the vertices of the triangle; the intersections of these connectors each with the "corresponding" side of the original triangle, lie in a straight line. And, analytically stated, the proposition is as follows; Let (a,/8, 7), (a', /8', 7') be the two fixed points, and (/, g, h) the arbitrary point on the conic circumscribing the triangle of reference. The coordinates of the "harmonic conjugates" spoken of above are as follows; viz., x: y: z = y'a. + 7o': /$ + yff: 277' for that corresponding to the point of intersection on the side x, and similar expressions for the other two. The coordinates of the point where the line joining this conjugate with the point (f, g, h) intersects the side 2, are x: y: z = h (7'a + 7o')--2/77': h (y'0 + y0')--2gyy': 0, with similar expressions for the other two points of intersection; and the condition that these three should lie in a straight line is 0, f(a'0 + a$')-2gaa', f (a'y + ay')-2haa' 1 0 03a' + iS'o)-ye/', 0, g (#7 + 0Y)-2 W-0....

Excerpt from Mathematical Questions, With Their Solutions, From the "Educational Times", Vol. 38: With Many Papers and Solutions Not Published in the "Educational Times"Ficklin. Joseph; Professor Mathematics and Astronoui in the University of Missouri. Fosrsv. H. Bellurv, Madras Presidency. Seems. P. W., b.a.; Chelsea. Foster. Prof.g.carby. F.rs.; fuortes, E. University of Naples. GA um (tn. Roml m.a.; gale, kate knight; Com tonterr..brlghton. GA lton. Francis, m.a.. F. G.s.; London. Gallatlt, W b.a.; Earl's Court, London. Genese. Prof.. M.a.; Univ. Coll., Aberystwith. Gerrans. H. 'l' b.a.; Stud. Of Oxford. Glaiau. J. W. L. F'.r.s Fellow of Trinity College. Éemhria golnarro. Professor M.' Moscow. Graham, R. A m.a.; Trinity College, Dublin geeenpield, Rev. W. J. College greenwood, james Kirksville, Missouri geieeith,w. Superintendent of Public Schools, New London, Ohio, United States. Grieeiths, G. J m.a.; Fell. Ch. Coll Cam'i. Griffiths J m.a. Fellow of Jesus Coll., Oxon. Grove; W. B b.a.; Perry Bar, Birmingham. Hadamard, Prof.; Paris. Hamh E., d.a., d.sc.; King's Sch Warwick hall, Professor asaph, m.a.; Naval Observa tory, Washington. Hammond,j m.a.; Buckhurst Hill, Essex. Harhema O.; University of St. Petersburgh. Harley. Rev. B.. Princxpnl of Builders field College. Harhis, I]. W., b.a.; Trinity College, Dublin. Harris. J. R. M.a.; Clare Lollcge, Cambridge hart. Dr. David S.; Stoninirtou. Connecticut. Hart. Pl; rm. Aca'lemv, Woolwich. Hahmiton, Rev. Trin.coll Dubl. Hu'asn, J ma. Hum ad. Hendricksj. S., Moines. Iowa. Heppkl, m.a.; Hammersmith. Kingalfred's scll,wantsge. Herman. R. A.. M.a.; Trin. Coll., Cambridge. Hermite, Cm; Mvmbrc do l'lnstltut. Paris. Hill. Rev. E m.a.; St. John's College, Camb. Hillary. H. M.a.; Tunbridge. Hinton C. College. H1 Hsr, Dr. T. A.. Director of Studies in tho Roval Naval College, Greenwich. Hopkins, Rovli. H m.a.; Stratum, Comwall hopkinson. J., d.sc.. B.a.: Konsington. Hudson.c. T. LLD.° Munilln hi'dson. Proliw. N. If inn leby. C. M., m.a.. LL.D.; London. Jelly. J. O.. B.a.; Magdalen C illcge, Oxford. Jenkins. Morgan. M.a.; London. Johnron. J. M b.a.; wloy College, Abingdon. Johnson. Prof.. Lll.a.; Anna hs, Maryland. Johnston. Wpr; Trin. Col Dublin. Jones. L. W., h.a.; Morton College, Oxford. Kealy. J. A.. Ma. Wilmiu n. Delaware. Kirhman Rev. T. R, mal. Croft Rec tory, Warrin on. Kitchin, Rev. L., m.a.; Heavitree, Exeter. Kittudge, lizzie A.; Boston, United States. KN isely, Rev. U.j.; N ewcomerstown, Ohio. Know] Es, R., b.a., Totteuham. Liadd, christine Professor of Natural Science and Mathematics. Union S rings. New York larmor, J. M.a Queen's ollege, Galway laverty, W. H m.a Public Examineriu Lb University of Oxford. Lawrence, E. J ex-fell. Trin. Coll Cami). Lei dhold R., Finsbury Park. Levett. R m.a.; King Edw. Sch., Birmin ham. Lrudesdore.c., m.a.; fel.pe nbrokecoll., xon. Lowry, W. H m.a. Blackmck. Dublin. Mcadam, D. S.; Nashin on, Penns lvania. Mcalister, donald, It. A., d.sc.; ambridge. Mccay, W. S., m.a.; Fellow and Tutor of Trinit College, Dublin. Mccoll, b.a. 73 Rue sibliquin,boulogne. Macdonald, W. J m.a. Edinburgh.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.