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Published online by Cambridge University Press: 15 September 2017
I desire in the first place to express my thanks to the members of the London Branch of the Mathematical Association for the honour they have done me in electing me to the office of president. I esteem it a privilege to take part in the efforts the Association is making to bring about improvements in the methods of teaching Mathematics.
In what position does the work of the Association now stand ? Is it in fact in the position described by Sir J. J. Thomson in his address to the Association of Public School Science Masters? He is reported to have said that he had come to the conclusion that if you have intelligent masters and small classes it does not matter much what theory of education you adopt, and if you have not these, well, it does not much matter either.
* These so-called algebraic proofs are applicable only to ratios of commensurable magnitudes. The proofs in the Fifth Book (which is a treatise on Algebra and not on Geometry) are applicable to the ratios of Incommensurable Magnitudes.
page note 325 Bd. 28, p. 152, 1897.
page note 326 *
method of holding or having, mode or kind of existence.
page note 326 †
for which there is no English word; it means relative greatness, and is the substantive which refers to the number of times or parts of times one is in the other.
page note 329 * To this book I owe a very great debt, as it set me upon the track which I have since followed. I have developed and made use of the idea of Relative Multiple Scales in the first edition of my Contents of the Fifth and Sixth Books of Euclid and in the papers in Vols. XVI. and XIX. of the Cambridge Philosophical Transactions, but I abandoned it in the second edition for what seemed to me a simpler treatment.
page note 330 * For a proof of this, see Heath, l.c. Vol. II. p. 130.
page note 330 † (Encyklopädie der mathernatischen Wissenschaften, Vol. I. A. 3, p. 51.)
page note 331 * Vorlesungen über allgemeine Arithmetik, Theil I. p. 87 (1885).