Euclid Simplified Compiled from the most important French works, approved by the University of Paris and the Minister of Public Instruction

Abstract

EUCLID simplified! “My friend M., with great painstaking, got me to think I understood the first proposition in Euclid, but he gave me over in despair at the second.” Had Elia lived in these days of modern geometries perchance he had been a moderate geometer, but his wit might have been dulled. The book before us, however, is not the book we should recommend to a sucking geometer. We look upon it as one of those private ventures which we hope the Association for the Improvement of Geometrical Teaching will extinguish. There is hardly a page without its crop of faults. The title we consider to be a misnomer, for the method of Euclid (the geometer) is departed from altogether. We should look to find in a “Euclid Simplified” something far different from this. The treatise is based upon good geometrical authorities, as will be seen by a reference to the prefatory remarks; it is to the form in which these authorities are presented that we object. Who is the interpreter? A former “H.M. Inspector of Schools.” We have been wont to look upon these gentlemen as masters of one or more tongues, and as having a fair acquaintance with the “ologies.” We have not formed a high opinion of the geometrical attainments of this compiler, nor do we consider him to be well versed in the French language, or even in elegant English composition. “Quis custodiet ipsos custodes?” It is “a work offered for the use of schools;” it is essential, then, that the writer should take all due precaution to be accurate. We think, further, that he should rather be disposed to retain terms with which boys are fairly acquainted, if they are correct, than to be constantly using terms and phrases which betray their Gallic descent. Thus pp. 23, 55: “angles are equal as opposed at the summit;” p. 40: “this corollary gives occasion to;” pp. 110, 112: “shows that to have point c;” p. 141: “operating in the same measure” (? way); p. 166: “three points taken in equal number on the sides of a triangle and in unequal number on its sides produced;” p. 168: the centre of similitude is the meeting-place,” &c.; we shall get to rendezvous in time. The words “passing by a point” (par) occur repeatedly; on p. 108 we have “by point D draw in like maner (sic);” pp. 41, 42, furnish “perpendicular to the centre,” “perpendicular to the middle,” and so on.^* It is hardly good English to say one point becomes confounded with another point, pp. 46, 97, 127; the boy-mind is apt to confound the different steps of the reasoning, and the boy often is tempted to exclaim, “Confound it altogether.” “Cord” of a circle would not be difficult to make out by one who had read French mathematics, but at a “spelling-bee” we should prefer the candidate who spelled it “chord.” But to return to the prefatory remarks. These have no signature, so we cannot be sure that it is Mr. Morell who writes “it is anticipated that it will prove more practically useful than most other school-books on the subject.” We should expect, too, some recognition of the work accomplished by the association referred to above, the more so as Mr. Morell was at one time a member of the association. We should have been disposed to think that he has employed some one to make the compilation and translation, and has not carefully revised the work himself; but then against this we have the title-page. Were we to note and comment upon every passage we have marked, we should tire our readers. We shall content ourselves with culling a few elegant extracts. Many of the enunciations are loosely, if not always incorrectly, worded. Parallels are treated of in p. 21 before any definition of them has been given. On p. 24 we are told the term transversal is new to English schools: “it explains itself,” and we are favoured with its derivation; in like manner, on p. 73 we are informed that harmonics have been “recently introduced in French geometry;” in the same note a specimen is given of “the new and interesting treatment of this question (i.e. harmonics) abroad;” on p. 72 we have a note on the word capable; “this term—used in French treatises—explains itself, if traced to its Latin root, capax, holding, a segment capable of an angle = a segment holding an angle.” And on p. 104: “this circumference, by the well-known construction of the capable angle, will pass by point B.”

Euclid Simplified. Compiled from the most important French works, approved by the University of Paris and the Minister of Public Instruction.

By J. R. Morell, formerly H.M. Inspector of Schools. (London: Henry S. King and Co., 1875.)