Notices of Books. wwwwww A TREATISE ON THE CONIC SECTIONS; CONTAINING AN ACCOUNT OF SOME OF THE MOST IMPORTANT MODERN ALGEBRAIC AND GEOMETRIC METHODS. BY THE REV. GEORGE SALMON, FELLOW AND TUTOR, TRINITY COLLEGE, DUBLIN. SECOND EDITION. (Dublin: Hodges and Smith.) We are extremely glad to see a second edition of this admirable treatise, and we most gladly take the opportunity of introducing it to our readers' notice. This work is not confined exclusively to analytical (i. e. co-ordinate) geometry, (though that forms the basis of the volume,) but treats likewise of those modern geometric methods due to the labours of Poncelet, Chasles, and others, who have cultivated the theory of curves with so much success. It is not our intention to enter into an analysis of the work, or to point out what is most worthy of notice to the mathematician, for this might lead us into a discussion not very suitable perhaps to the majority of our readers. We prefer, therefore, confining ourselves to pointing out to the student, who may take up this volume without any previous knowledge of analytical geometry, to what portions of the work he had better confine his attention at the first reading. It may seem superfluous, indeed, for us to be at this trouble, seeing that Mr. Salmon himself has, in the table of contents, marked with an asterisk such parts of the volume as he would recommend beginners to study at a first reading. Doubtless the course thus marked out is a good one, and probably the best for students at Dublin University; but we are inclined to think that most of our readers, who probably know little or nothing of harmonic and anharmonic properties, &c., and who may have little assistance in their studies, will find the following course of reading better suited to their circumstances : Read chapters i. and ii. Read chapter iii., omitting articles 43 and 44, examples 11, 12, and 13, art. 45; and examples 3 and 4, art. 46.* Omit chapter iv. Read chapter v., from art. 72 to art. 75 inclusive, omitting the remaining articles. Read chapter vi., omitting articles 91 and 92. Omit chapters vii, and viii. Finally, read chapters ix., x., xi. ; omitting articles 142 to 145, the foot-note at p. 141, and articles 153 and 154. * Perhaps some of our readers will find a difficulty with example 5, p. 32, from not knowing what a complete quadrilateral is, the definition of which we shall therefore add. If A B C D be a common quadrilateral, (the reader will easily supply the diagram,) and its opposite sides be produced to meet, namely, A B and C D in E, and BC and A D in F, we shall have a complete quadrilateral, which thus has four sides and six angles (A, B, C, D, E, F); also if A and C, B and D, and E and F be joined, the three straight lines so drawn are termed its diagonals. When the student shall have thoroughly mastered the course here marked out for him, he will have acquired a very fair knowledge of elementary analytical geometry, and possibly some of our readers may not have time for more. Those who may wish to prosecute this branch of mathematics further will of course now read all the portions previously omitted, as well as the remaining chapters (which are by far the most novel and interesting). He will thus obtain an amount of information respecting the conic sections, and the most elegant and powerful methods of investigating their properties, which is not, we believe, to be found in any English work except the present one, and possibly in no other work whatever. Before concluding, we may observe that the student cannot take up the present volume (or, indeed, any other on analytical geometry) with advantage, until he shall have thoroughly mastered Euclid, and good treatises on algebra and analytical trigonometry; and he must be acquainted with so much of the theory of equations as to know that every equation, of the n. th. degree, has n roots real or imaginary; that if a, b, c,... k, I be these n roots, then, n-1 x"+px"1+q x2-2.... + tx + u -(x-a) (x-b) (x−c).... (x−k) (x-1), for all values of x; and that, psum of the roots, q = sum of the products of every two of them, ... tsum of the products of every (n-1) of them, and u continued produced of all the roots, the upper or under signs being taken according as n is even or odd. TWENTY-THREE SHORT LECTURES ON THE CHURCH CATECHISM. BY ARCH DEACON BERENS. Pp. 214. (London: F. & J. Rivington, 1850.) PROGRESSIVE EXERCISES ON THE CHURCH CATECHISM. BY THE REV. II. HOPWOOD, M.A., RECTOR OF BOTHAL, NORTHUMBERLAND, LATE DIOCESAN INSPECTOR OF SCHOOLS FOR THE NATIONAL SOCIETY. PART IV. EXPOSITORY EXERCISES. Pp. 133. (London: J. H. Parker, 1850.) THE long-established custom of public catechising during Lent, suggests the present time as a fitting one to notice the above works, which have both recently appeared. The author of the lectures is already well known by a variety of publications of a practical character, well adapted to parochial purposes. The lectures are short, plain, and scriptural; and in no part open to the imputation of anything like extreme views upon doctrinal points. In preparing them the writer has availed himself of the admirable exposition of Bishop Nicholson, and of the labours of others; amongst which he mentions the lectures of Archdeacon Daubeny, which, he observes, seem to have come but little before the public. The lectures are designed and adapted to be used in a country village, and we would especially recommend for this purpose the six upon the creed, and the ten upon the commandments. The other work, entitled "Expository Exercises," forms part iv. of "Progressive Exercises," of which the three former parts have already been noticed in the Journal. The "Expository Exercises" are in fact a filling up of the "Analytical Exercises" contained in part iii., and are so contrived, that the catechist, by a previous careful perusal of them, may, when engaged with his class, bring their contents to his recollection by a cursory reference to the short "Analytical Exercises." The information given on each portion of the catechism in these "Expository Exercises" is very full, and put in a clear and distinct form. The statements of doctrine are definite, and supported by Scripture, and by quotations from the Prayer Book, and from the works of some of our best divines. A SCHOOL DICTIONARY OF THE LATIN LANGUAGE. BY DR. J. H. KALTSCHMIDT. 1. LATIN-ENGLISH. (Edinburgh: W. & R. Chumbers, 1850.) THIS Dictionary is part of Chambers' Educational Course. We are told in the preface, that "the feature which distinguishes the present Dictionary from all others" is, that it "gives, as far as possible, the etymology of every word, not only by tracing it to its Latin or Greek root, but to roots or kindred forms of words occurring in the cognate languages of the great Indo-Germanic family." With this information from the editor, we opened the body of the work, and in turning over a few of the leaves we came upon the following specimens of Dr. Kaltschmidt's etymological system : Miror (akin to merus, spero, vereor). Mendax (mentior). Mentior (mendax). Mora, f. (moror). Moror, 1. (mora). Mæreo (akin to murrio, burrio, fremo). Moles (akin to bolus). Mollis (akin to pellis, vellus). Moveo (akin to paveo and vivo). Mugio (akin to voco). Mulier (akin to filia). Mordeo (akin to mependa). Metus (akin to vito). Murmur (murrio, burrio, fremo). Amo (Sanscrit am, to see; akin to opto). Anus, i. m. (akin to animus, from Sanscrit an, to breathe, to blow) the fun dament, &c. Alea (akin to ala). Ansa (akin to ensis). Adulor (* ulo, ulor ululo, I howl). Cogito (Sanscrit chank; Icelandic huga, to think). Colo (Kλdw, I break). Ico (Sanscrit agh, to beat, hurt; ach, to penetrate), Jaceo (Sanscrit gah, to be dense, firm, keμα). Fœdus, eris (Todow, to bind). Fortis (akin to fartus). Fides and fidis (akin to vestis), a thread, a string, &c. Obscurus (perhaps akin to creperus). Oppidum (ops, do). Palam (akin to palpebra and Bλétw). Pampinus (akin to vinum). Potis, pote (allied to -pte, -pse, -met, akin to fidus). Prope (akin to privus). Sobrius (so, bria). Ebrius (bria, vat). Tribuo (perhaps from Sanscrit trip, to satiate). Usquam (us; akin to ad, quam). Usque (us; akin to ad, que). Verbum (from eños; akin to sermo, from oro, ¿pw, elpw). Vox (voco). It is difficult to know which most to admire-1. The circular mode of derivation by which the nouns mendax, mora, and vox flow from the verbs mentior, moror, and voco, and at the same time these verbs flow from the nouns; 2. The missing of evident etymologies, as the relation of cogito to agito, which is as certain as that of cogo to ago; and the close connection, amounting to almost identity, of ico, jacio, and jaceo, as well as of anus and annus, or annulus; 3. The introduction of such non-existing or doubtful words, as murrio, burrio, and the preposition us; or, 4. The utter disregard of connection in respect of meaning, which runs through the whole series. A CATECHISM ON THE HOLY SCRIPTURES. BY THE REV. E. S. PHIPPS. Pp. 98. (Masters.) QUESTIONS ON THE OLD AND NEW TESTAMENTS; WITH REFERENCES AND ANSWERS. BY THE REV. J. HARRIS. Pp. 120. (Hamilton, Adams & Co.) THESE little works, though both in the form of questions and answers upon the Holy Scriptures, differ in their arrangement and subject matter. The first, as expressly stated in the title, is for the use of Church Schools. Accordingly, it begins with a direct reference to baptism and the Church. Its design is to convey, in an easy and interesting manner, a general knowledge, chiefly historical, of the Holy Scriptures, to the minds of school children. The answer immediately follows each question, and nearly to every answer is added a reference to the chapter and verse from which the answer may be derived. The author's plan in his own schools is to furnish each child with a Bible containing the Apocrypha, and a Prayer Book; and then to ask one of the questions and give the reference, requiring the child to look it out, and from it to supply an answer. This, he observes, creates interest, prevents the work from becoming merely a mechanical rote, and, while it affords work which each child can do, yet requires of him some little mental exertion to accomplish it. The epitome contained in this Catechism is of course brief, but it affords a useful, continuous, and general narrative, the recurrence to which will, as the author justly remarks, prevent a tendency to diffuse and desultory statements. The questions are arranged in divisions upon each book of the Bible in succession. The other work is, as expressed in the title page," for the use of schools and biblical students." It consists of two parts. The first contains 600 questions upon the Old and New Testaments, and may be had separately. The second part forms a key to the questions in the first, pointing out the passages containing the required answers, and giving information on those questions which could not be answered from the text of Scripture itself. Most of the questions are upon the historical books, and are generally arranged in chronological order. There are also chronological tables of the kings of Israel and Judah, and of the principal events in Scripture history. Both works may be used with profit by the same person. The first is more adapted to a regular course of Scripture reading; but the second will be found very serviceable as a test of the knowledge gathered in reading the Bible, and as a means of fixing in the memory those particulars which a systematic perusal of Scripture may have failed to impress upon it. ANSWERS TO THE MATHEMATICAL QUESTIONS. QUES. 90.-Proposed by Mr. J. Brown. A SOLID lost 1 oz. when weighed in water, and 1 oz. when weighed in spirits; required the specific gravity of the spirits. Answered by Mr. F. R. Crampton, Mr. Sothern, Mr. Barnacle, and Mr. Gillingham. Weight of water equal in bulk to the solid = 1 oz. QUES. 91.-Proposed by Tom Tomkins. Required the same as in Question 88 of the last number of the Journal, when the fluid is mercury in the place of water. Answered by Mr. Righton, Mr. Royds, Prismoid, and Mr. Yoel. = Let the height of the mercury in the glass, then we find, after the method adopted in the solution to question 88, 22-42x = -36 .. x=8754 inches. QUES. 92.-Proposed by the same, A right cone is cut out of an upright cylinder; it is required to find the work requisite to overturn the remaining portion of the solid on the edge of its base. |