Hints, theoretical, elucidatory and practical, for the use of teachers of elementary mathematics

by Olinthus Gregory

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. 1840 edition. ... not fallen under the contemplation of Euclid. The synopses of the data of triangles by Lawson, Leybourn, and Farey, have added very greatly to the rich varieties of this kind of classification. (A similar course, of greater or less extent, according to circumstances, may be adopted at the end of each book of the elements.) These and other matters, which might have been specified, but which will occur to the experienced teacher, are not verbal niceties, but are essential to scientific accuracy and perspicuity. Regarding them or neglecting them constitutes a main distinction between logical, scientific instruction, and perfunctory lessons in which memory is substituted for the active investigating powers of intellect. 40. The word rectangle often occurs in the enunciations and demonstrations of the second book; but in several editions of Simson, that word is not defined; when such is the case, let definition 1 be amended to run "Every right-angled parallelogram is called a rectangle, and is said to be contained by any two of the straight lines which contain one of the right angles." (a.) In demonstrating the propositions of this book, students who have been allowed to employ Williams's symbolical Euclid, instead of Simson's, are very apt to use the algebraical terms plus, into, &c, instead of the corresponding geometrical phrases together with, rectangle under, or rectangle contained by; let them be especially guarded against this loose, and ungeometrical mode of expression, as it is calculated to fill the mind with vague ideas. (b.) In the demonstration of prop. 4, instead of the sentence " for CG is parallel to BK," &c. down to " and CGKB is rectangular," let this be substituted; "for KBC...

36 pages, Paperback

First published April 19, 2013

About the author

Olinthus Gilbert Gregory (29 January 1774 – 2 February 1841) was an English mathematician, author and editor.

He was born on 29 January 1774 at Yaxley in Huntingdonshire. Having been educated by Richard Weston, a Leicester botanist, in 1793 he published a treatise, Lessons Astronomical and Philosophical. Having settled at Cambridge in 1796, Gregory first acted as sub-editor on the Cambridge Intelligencer, and then opened a booksellers shop. In 1802 he obtained an appointment as mathematical master at the Royal Military Academy, Woolwich through the influence of Charles Hutton, to whose notice he had been brought by a manuscript on the Use of the Sliding Rule; and when Hutton resigned in 1807 Gregory succeeded him in the professorship. Failing health obliged him to retire in 1838, and he died at Woolwich on 2 February 1841.