Jan, 13, 1876] 



NATURE 



203 



" ologies." We have not formed a high opinion of the 



geometrical attainments of this compiler, nor do we con- 

 sider him to be well versed in the French language, or 

 even in elegant English composition. " Ouis 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. no, H2 : "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 " i^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 ii 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 " spell- 

 ing-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 dis- 

 posed 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, wU pass by 

 point B." 



A parallelogram is defined to be a quadrilateral, of 

 A'hich the opposite sides are equal j in theorem xxxL he 



*c. 



For pp. II, 20, "two triangles are equal as having an equal angle,' 

 C, we should prefer " because they have, &c. 



subsequently proves this. The term lozenge is used in 

 the text, and a note tells us that the figure is called 

 " rhombus in the old-fashioned EucUd." A terrible mess 

 is made of circumference on p. 36. " The circumference 

 is a plane hne, of which all the points are equally distant 

 from one same point situated in the middle and named 

 centre." This is not so bad as the common school-boy 

 definition : " a circle is a plain figure bounded by one 

 straight line, and is such that aU straight lines drawn 

 from a certain point in its centre to the circumference are 

 equal ; " but it is not what we should expect in a text-book 

 for boys. Again, " a circumference is generally described 

 in language by one of its radii." The itaUcised the is 

 easily accounted for when we remember the source from 

 whence the definition is taken ; here, of course, it ought 

 to be rt, but on p. 5 1 we ought to have the for « (" A polygon 

 is inscribed in a circle when its summits are situated on 

 the circumference). Reciprocally (Mr. Moreli's term for 

 the usual conversely), a circle is said to be circumscribed 

 round a polygon," that is, the circle and polygon pre- 

 viously mentioned, otherwise the definition is incomplete. 

 No distinction is made of major and minor arcs. Thus, 

 p. 39 : " of two unequal arcs the greater is subtended by 

 the greater chord ; " this is, of course, only true of minor 

 arcs. On p. 66 he bisects a given arc without having 

 shown how to bisect a given line. On p. 70 C, C have 

 been wrongly printed in three places. On p. 81 homo- 

 logous is derived from ofiolos and \6yos (p. 9, isosceles 

 from laos is doubtless an oversight). On p. 85 occurs a 

 passage we cannot understand ; he has a quadrilateral 

 A B CD, and then draws E F {E on A B, F on CD) 

 parallel to B C; he says rightly the angles of the two 

 figures are equal, but the sides not in the same propor- 

 tion ; then he proceeds to say " in hke manner, without 

 changing the four sides A B, B C, CD, {sic), point B can 

 be brought near or removed from D, without changing 

 the angles." We cannot imderstand it, and so do not 

 see it. 



In the first note on p. 91, boys are informed that M. 

 Chasles is " Professor of Superior Geometry at the Col- 

 lege de France, and one of the first geometers of the 

 present age ;" in the second, " homothetie " is derived 

 from o/xotoj and 6iai.s ; in the third, " radiivectors or vec- 

 tor es are the straight lines drawn from the two foci of an 

 ellipse to any one point of the circumference of an 

 ellipse." On p. 122 we are told that the ratio of the 

 equilateral triangle inscribed in a circle to the radius is 

 v/3, whereas it ought to be (as is proved in the text) the 

 ratio of the side of the equilateral triangle, &c. On this 

 page, and also elsewhere, we have R used for a right 

 angle ; this is, we think, likely to mislead boys : nor do 

 we approve of the expression, "each of these angles 

 will be worth f R." R is usually employed to denote 

 the radius of the circumscribing circle of a triangle. 

 Pages 132, 133, bristle with blunders, due partly to the 

 editor, but principally to the printer. On p. 134, for 

 " pentagon " read " pentedecagon " (a purism for " quin- 

 decagon"). Page 136, on the calculation of the ratio of 

 the circumference to the diameter, we read : " The com- 

 plete solution of this problem belongs to superior mathe- 

 matics. Therefore it is here less aimed at giving a 

 method to calculate this ratio than to give a notion that 

 it is possible to do so." This last sentence strikes us as not 



