teaching Geometry, in the Public Schools, of the City and County of Philadelphia; and indeed in all other schools of like grade. Concurrent: JAMES M'CLUNE, Principal of the Master St. Grammar School. JOSHUA RHOADS, M.D., Principal of Palmer St. Gram. School. A. H. BROWN, Principal of Zane St. Grammar School. W. W. WOOD, Principal of S. W. Grammar School. W. H. PILE, Principal of N. E. Grammar School. B. E. CHAMBERLIN, Principal of Buttonwood St. Gram. School. W. S. CLEAVENGER, Principal of Locust St. Gram. School. Central High School, Philadelphia, February 24, 1845. Having examined a Chart of Geometry, prepared by MR. D. M'CURDY, containing the diagrams and propositions* of Euclid, in the order of Simson's and Playfair's editions, we are of opinion that the use of it, as "First Lessons," in schools, would conduce to the more general diffusion of Geometrical knowledge, and be very helpful to those who may want the time and facilities for a more liberal Mathematical education. The Chart appears to be correct and neatly executed. E. OTIS KENDALL, Prof. of Theoretical Math. and Astronomy. Professor of Practical Mathematics. Lancaster, Pa. March 1, 1845. I concur very cordially with Professor Johnson of Philadelphia, in the recommendation of MR. M'CURDY'S Geometrical Chart, No. 1. DANIEL KIRKWOOD, Principal of the Male High School of Lancaster. I have examined the Chart of Geometry, No. 1, and feel warranted in adding a cordial concurrence with the Professors and Principals who have subscribed their names in testimony of its great utility. JAMES DAMANT, Principal of the Ladies' Seminary of Lancaster, Pa. The Committee on books of the Public Schools for Lancaster County, consisting of the Rev. Clergy of the City of Lancaster, passed a resolution on the day above mentioned, to recommend the adoption of the Geometrical Charts to the Board of Directors of which they are a Committee. Columbia, Lancaster County, Pa. March 4, 1845. I have examined the Chart of Geometry prepared by MR. D. M'CURDY, exhibiting the diagrams and propositions in the order of Simson's * The propositions were attached to the first plate of the Chart, which are now contained in the book, called "First Lessons." and Playfair's Euclid, and pronounce it superior to any work of the kind, that has come to my knowledge, for facilitating the study of those elements. THOMAS W. SUMMERS, Principal of the Columbia Academy. I am decidedly of opinion, that the Chart of Geometry, in the hands of judicious teachers, would be very useful in our Primary Schools, in giving to the young some knowledge of this important branch of science. STEPHEN BOYER, Principal of York Co. Academy. March 5, 1845. I cordially concur with the Rev. Mr. Boyer, in the opinion that MR. M'CURDY'S plan of teaching Geometry could be used to great advantage in our Primary Schools of the South Ward, also that it would facilitate the study more than the usual books, and with less expense. WILLIAM R. STOUCH, Teacher, York, Penn. Washington, March 18, 1845. DEAR SIR-I have examined your Geometrical Charts, and am much pleased with the plan and arrangement; and believing it to be the very best system to instruct the youthful mind in the principles of this invaluable science, I will introduce a bill into the Councils next Monday, to make appropriation for the purchase of a set of those Charts, for each of our Public Schools. The simple fact of having those figures before the eyes of the children familiarizes their minds with them; and the questions they will naturally ask in relation to them, will so impress them on their minds, that the study itself in more advanced years will be comparatively easy. In fact I consider the pictorial plan of instruction as much of an improvement on the old system, as steam and magnetism are on the plans of locomotion. Very tfuly, your friend, JOHN WILSON, Alderman of the Second Ward, Washington. D. M'Curdy, Esq., Washington, D. C. The Mayor of Washington certifies that on the 2d of June, the Board of Trustees ordered the purchase of a set of the Charts, &c., for each of the Public Schools. Respectfully submitted to the Secretary of War. The course of practical Geometry, after the method of Mr. M'Curdy, may be introduced with advantage amongst the non-commissioned officers and soldiers of the army. We have schools at many of our military posts, where the men receive gratuitous instruction from their officers, in the ordinary branches of an English education; and I would regard the addition of Mr. M'Curdy's Geometrical Charts, as an important first step, towards bringing into our service, a system of instruction kindred to that adopted for the non-commissioned officers of the British army, and with so much success, at the Royal Military School of Woolwich. WINFIELD SCOTT. A true copy. H. L. SCOTT, Aide-de-camp. The Chart and First Lessons have been introduced into the Union Public Schools, and several private Academies in Wilmington, Del. Also in Georgetown, D. C.; in Camden and Burlington, N. J.; in Frankford, Germantown and Bristol, Pennsylvania; and in several Academies in Philadelphia. And the Commissioners of Public Schools in the city of Baltimore, in August last, ordered the Charts and First Lessons to be used in the schools of that city. New York, Oct. 18th, 1845. We have examined M'Curdy's Chart of the diagrams of Euclid, and the book of "First Lessons" connected therewith; and think his plan well adapted to the purpose of teaching large classes, and children of immature minds. Its use is a desideratum in the schools. (Signed) Concurrent. DAVID PATTERSON, M.D. Teachers of the Male Teach. of the Female ISAAC F. BRAGG, Prin. Male High School. I have examined M'Curdy's "First Lessons and Chart;" and have no hesitation in stating my belief, that they will prove a valuable auxiliary to the acquisition of the important study of Geometry. (Signed) Concurrent. JOHN W. KETCHAM, Prin. Pub. School No. 7. MR. FOULKE,-Dear Sir,-Mr. M'Curdy will show you a map to facilitate the study of Geometry, with a very concise little work on the subject, which we, the school officers, think well of. If you approve of the same, I authorize you to take one set of the maps and a dozen of the books, and send the bill to me. Yours, truly. Tuesday, Nov. 11, 1845. HENRY NICOLL. Having hastily examined the work above referred to, I have no hesitation in saying, that I think the plan of the author well adapted to the * In these Institutions teachers are prepared for the Public Schools.-ED. purpose of teaching Geometry to large classes of pupils who are about entering upon the study of this important science; and of supplying a manifest defect now existing in our schools. THOMAS FOULKE, Prin. W. School No. 14, N. Y. We have examined the Chart of Geometry and "Book of First Lessons," prepared by D. M'Curdy, and believe them to be well adapted to the purpose of teaching this science in public schools. In our opinion, a pupil, by using these charts, and aided by the teacher, will obtain a clearer idea of Geometry, besides saving time, than by any other method. WM. KENNEDY, Prin. W. School No. 2, N. Y. JOHN J. DOANE, Asst. W. School No. 2. The undersigned, members of the Book Committee of the Ward School Teachers' Association, having examined a chart of the diagrams of Euclid, connected with a book called "First Lessons," and prepared for public schools by Mr. D. M'Curdy, respectfully REPORT: That the design of said book and chart appears to be to supply a défect in the elements of a sound practical education, the existence of which your committee must readily admit. The cause of this defect, however, is not in the want of books on Geometry; but in the oppressive strictness in which the subject is usually presented to beginners. The plan now presented obviates this difficulty by omitting the demonstrations, and requiring learners to read the propositions, recite the proofs and draw the diagrams, as occasional exercises, on slates. Questions are also suggested to teachers in view of the book and chart, which, if followed out, must inevitably render the subject familiar to both teachers and pupils; and prepare them to demonstrate the propositions of Euclid with facility and success. Your committee therefore recommends this work to the patronage of the Association as worthy of its unanimous support, and offers the following resolution : Resolved, That this Association recommend M'Curdy's geometrical chart of the diagrams of Euclid in connection with the book of "First Lessons," with a view to their introduction into the Ward Schools of this city. Signed, SENECA DURAND, EDWARD M'ILROY. At a regular meeting of the Ward School Teachers' Association on the 17th Dec., 1845, the above report of the committee was approved and the resolution unanimously adopted. JOSIAH RICH, President W. S. T. Asso. FURTHER DIRECTIONS FOR THE USE OF THE CHART OF GEOMETRY AND BOOK OF FIRST LESSONS. Respectfully submitted to the Officers and Teachers of the Public Schools. GENTLEMEN,-In reply to a question proposed, How are the Chart and. First Lessons, to be used?-permit me to explain in a few words. Each student requires a copy of the book; one chart will be sufficient for a large class. The students read the definitions, postulates, axioms and propositions, in order; and recite the proofs at each proposition, as directed. The teacher should not embarrass himself or his class, by exacting from them more than they can perform: he ought not to stop, in the first course, except to explain the meaning of terms. The object is to make the enunciations familiar to the students. The six books of Euclid and plane trigonometry occupy forty-three pages; these may be read and recited every six months, without any material abatement of other studies. In the second course of reading, slates and pencils may be used :-in order to draw a straight line from one point to another-to produce the same in a straight line-and to describe a circle about a point with any radius. This is the permission sought in the postulates; and it embraces every thing that is to be done by hand. Next, in connection with the definitions, the class draws straight lines, parallel, and at right and oblique angles to each other; also radii, diameters, and other chords in a circle;-triangles equilateral, isosceles and scalene-right angled and oblique ;-squares and other rectangles, rhombuses, rhomboids, and a variety of trapezia: then they should make several angles at the same point, and read them distinctly by their proper letters. In short, the class should draw every line and figure spoken of in the definitions, and call it by its proper name: for then they will take an interest in it as their own production. In view of the axioms, every relation should be expressed by appropriate lines, angles, or areas; illustrating each according to the tenor of it: this exercise will impress the use of these simple propositions upon the learner's memory, and be to him a pleasing introduction to the process of ratiocination: axioms are always invincible proofs. The teacher will now direct the class to copy from the chart as many of the diagrams as he thinks proper for the day's lesson: he will examine whether they have done it well or ill; and ask, in relation to each diagram, what proposition it illustrates, and what proofs are adduced ;-all of which the class will answer: and as they recite proof after proof, he will point to the proper diagram on the chart, and say-"This is the illustration-How does it apply to the case?" He cannot expect answers in all cases: but the question will elicit attention. The definitions and axioms are properly quoted as proofs: for although they are not separately represented on the chart, they are found all over it. The postulates prove only this, that the geometer asks permission to draw such lines as he requires: the fact of his drawing them shows that he has permission. |