74 Some of the elements are of more general use in demonstrations than others, and are more frequently quoted. Of such is the equality of radii; -of triangles identical (as in p. 4 of b. 1), and those upon the same or equal bases and between the same parallels; also of parallelograms in similar case; of angles by position vertical and opposite, alternate, and in alternate segments of a circle made by a chord meeting a tangent, interior, exterior and adjacent; -of the opposite sides and angles of parallelograms; -of the square of the side subtending to the squares of the sides containing a right angle;--of the squares and rectangles upon lines divided equally and unequally, or bisected and produced ;-of ratios; and of similar rectilineal figures. These equals are among the most useful of the elements, and will claim the learner's attention. The object of the First Lessons is to furnish the entire text, unencumbered with comment, which has ever precluded the general diffusion of these useful elements. The chart furnishes the diagrams, as an auxiliary to the acquirement of the text, which is the great desideratum. They do not speak from experience who say that students cannot learn the enunciations without the demonstrations: their doubts, however, will be received as arguments only by the indolent, "who stand by the brook until it shall have discharged all its waters." On the other hand, no one will pretend to say, that the demonstrations can be effected without that familiarity with the propositions provided for in the Chart and First Lessons. The time has arrived when the elements of geometry should obtain a place in the common education. Abstracts for the use of Surveyors, Navigators, Builders, &c., are insufficient: the qualification for an occupation, or office, should precede the exercise of it, and be the common portion of junior citizens. The old plan proves to be impracticable by the public destitution of this most useful knowledge: and it is by far too costly for large schools. The plan here proposed is accessible to every reader, and requires only the test of experiment. A book worth 25 cents, in the hands of willing teachers, will effect the general diffusion of these inestimable elements of natural science in the schools: not merely in view of the future occupations of the students; but as the basis of that general knowledge required by every citizen of the United States; -as the best remedy for the contagion of the turbid streams now inundating town and country under the name of literature; which robs youth of its time for improvement, and leads many into the imitation of vices, at least palliated if not approved. In regard to the manner of using the Chart and First Lessons, it would seem unnecessary to say more. The preface to the book contains forms of questions applicable to the diagrams and propositions. We shall add the substance of the foregoing directions. If any difficulty remain, it must be that of invincible incredulity: for what can be more simple than to read the book and understand what you can of it;--to repeat the same and learn more and more; to follow out the directions given and make your knowledge perfect? The readings and recitations are all the text of Euclid, without comment;-the collective wisdom of the past; by which the remote parts of the earth have been discovered, rendered habitable, and adorned with cottages, cities and temples to the praise of Him who reigns. VALUABLE BOOKS PUBLISHED BY COLLINS, BROTHER & CO., 254 PEARL STREET, NEW YORK. OLMSTED'S NATURAL PHILOSOPHY: Designed as a Text Book for Colleges and Academies. Compiled from various authorities, by Denison Olmsted, A.M., Professor of Natural Philosophy and Astronomy in Yale College. 1 vol. 8vo. Sheep. Price $3 00. The rapidity with which this work has been sold and introduced into various Colleges and Academies in the United States, is sufficient evidence of the estimation in which it is held. OLMSTED'S ASTRONOMY: For the use of Colleges. By Denison Olmsted. 8vo. Sheep. Price $2 00. Nearly all who have written treatises on Astronomy designed for teachers, appear to have erred in one of two ways; they have either disregarded demonstrative evidence and relied on mere popular illustrations, or they have exhibited the elements of the science in naked mathematical formule. The former are usually diffuse and superficial; the latter technical and abstruse. In the above work the author is thought to have fully succeeded in uniting the advantages of both methods. He has, firstly, established the great principles of Astronomy on a mathematical basis; and, secondly, rendered the study interesting and intelligible to the learner by easy and familiar illustrations. OLMSTED'S SCHOOL ASTRONOMY : Containing the Elements of the Science, familiarly explained and illustrated. With the latest Discoveries. Adapted to the use of Schools and Academies, and of the general reader. By Denison Olmsted, A.M., Professor of Natural Philosophy and Astronomy in Yale College. 12mo. Sheep. Price 75 cents. This work having been used as a class book in many schools and academies, the publishers have been favoured with testimonials of approbation, among which are the following: From Charles Henry Alden, Principal of the Philadelphia High School for Young Ladies. I have examined with great care "Olmsted's Compendium of Astronomy," and have taken a highly intelligent class in my institution critically through it. We have long felt the want of a Text Book in this most interesting science, and the author of this merits the thanks of the profession for a Treatise so entirely methodical and lucid, and so admirably adapted to our more advanced classes. Judging of its merits by the interest evinced by my pupils, as well as from its intrinsic excellence, I cannot too strongly recommend its general adoption. From Samuel Jones, A. M., Principal of the Classical and Mathemat ical Institute, South Seventh Street, Phil. I am using "Olmsted's Compendium of Astronomy" in my school, and fully concur with the Rev. Mr. Alden in his opinion of the work. From Charles Dexter Cleveland, A. M., late Professor in Dickinson College, Carlisle, Pa. GENTLEMEN, I have not vanity enough, I assure you, to suppose for a moment that any thing I can say will add to the fame of Professor Olmsted's Works on Natural Philosophy; but as you ask me my opinion of his " Compendium of Astronomy," I will say, that I intend to introduce it irto my school, considering it the best work of the kind with which I am acquainted. This work has also been very favourably noticed in various periodicals. The following discriminating remarks from the New Haven Record, are understood to be from the pen of an able and experienced teacher of Astronomy. OLMSTED'S SCHOOL ASTRONOMY. It is with peculiar pleasure we notice the appearance of this work, small in size, but containing more. matter than many larger books. There is probably no instructor of much experience who has not felt serious inconvenience from the want of a proper text book in this department of science, as taught in our academies and higher schools. The treatise before us, however, is one which, after a careful perusal and the use of it as a text book, we can most cheerfully recommend as eminently adapted to supply the vacancy heretofore existing. Our author is particularly happy in the arrangement and division of the various subjects discussed; each occupying its appropriate place, involving no principle which has not been previously considered. He aims to fix in the mind the great principles of the science, first by stating them in the most concise and perspicuous terms, and then by lucid and familiar illustrations, without entering into an indiscriminate and detailed statement of a multiplicity of statistics, which only burden the memory and discourage the student. The learner is early made acquainted with the use of the globes, which greatly assists him in understanding the causes of various phenomena which otherwise would be wholly unintelligible. The student in his progress finds himself in possession of the keys of knowledge, and is highly pleased and encouraged in being able to anticipate effects and assign their true causes, which before seemed a mystery. Indeed, we feel assured, that this compendium need only be known to competent and judicious instructors, in order to secure its cheerful introduction into our schools and academies as an important auxiliary to science. Those who have had the misfortune to toil for many a tedious hour in treasuring up insulated facts in this science, without a knowledge of the principles upon which they depend, and consequently without any knowledge of the subject, will be fully convinced, after a patient perusal of the work under consideration, that the study of Astronomy is not necessarily dry and uninteresting, but that the difficulty arises in a great measure from an erroneous method of studying the subject. A. OLMSTED'S RUDIMENTS OF NATURAL PHILOSOPHY AND ASTRONOMY: Designed for the Common Schools and younger classes in Academies, with numerous Wood Cuts. By Denison Olmsted. 18mo., half bound, cloth sides. Price 62 çents. ELEMENTARY AND HIGHER GEOMETRY, TRIGONOMETRY, AND MENSURATION: In Four Parts. By Nathan Scholfield. (Each Part sold separately.) The above is the title of a work just published, containing many valuable discoveries and improvements in mathematical science, especially in relation to the Quadrature of the Circle, and some other curves, as well as the cubature of certain curvilinear solids; designed as a text book for Collegiate and Academic instruction, and as a practical compendium on mensuration. The first part consists of the Elements of PLANE GEOMETRY, and the mensuration of plane figures. The second part consists of the Elements of SOLID GEOMETRY, and the mensuration of elementary solids. The third part treats of SPHERICAL GEOMETRY, ANALYTICAL, PLANE, AND SPHERICAL TRIGONOMETRY, with their applications; the application of Algebra to Geometry; and on the Ellipse, Hyperbola and Parabola. The fourth part treats of the species and quadrature of the sections of a cone-the relations of cylindrical and conical segments and ungulas-a new class of curvilinear solids termed revoloids, and of such other solids as are subjects of the HIGHER GEOMETRY. Also, on some new curves termed the revoloidal curve, and curve of the circles quadrature; by the investigations of which, some important properties of the circle are developed, furnishing us with geometrical methods of approximating to the circles quadrature to any desirable extent; and by the same investigations are developed means of computing the area of any segment of a circle, when the arc of the segment and its sine are given, with as little labour as that of a triangle whose base and perpendicular are known. A new method of notation is also introduced, by which the relations of magnitudes, whose elements are a series of variable factors, may be intelligibly investigated; by means of which notation, is obtained a definite expression for the circle's quadrature, in positive and known functions of the diameter. The first principles of the differential and integral calculus are introduced, and the principles on which most of the operations of that science are performed, are rendered more intelligible by means of the notation above referred to. The series closes with the mensuration of such surfaces and solids as depend on the higher geometry. |