AN ELEMENTARY TREATISE ON GEOMETRY, / SIMPLIFIED FOR BEGINNERS NOT VERSED IN ALGEBRA. PART II, CONTAINING SOLID GEOMETRY, WITH ITS APPLICATION TO THE SOLUTION OF PROBLEMS. BY FRANCIS J. GRUND.X BOSTON: PUBLISHED BY CARTER, HENDEE AND BABCOCK. BALTIMORE, CHARLES CARTER. 1831, QA DISTRICT OF MASSACHUSETTS, TO WIT: Be it remembered, that on the tenth day of March, A. D. 1831, in the fiftyfifth year of the Independence of the United States of America, FRANCIS J. GRUND, of the said district, has deposited in this office the title of a book, the right where of he claims as author, in the words following, to wit: 'AN ELEMENTARY TREATISE ON GEOMETRY, Simplified for beginners not versed in Algebra. Part II, containing Solid Geometry, with its application to the Solution of Problems. By Francis J. Grund.' In conformity to the act of the Congress of the United States, entitled 'An act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned; and also to an act, entitled' An act supplementary to an act, entitled, an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned; and extending the benefits thereof to the arts of designing, engraving and etching historical and other prints.' JNO. W. DAVIS, Clerk of the District of Massachusetts. BOSTON CLASSIC PRESS....I. R. BUTTS. THE UNIVERSITY OF GEORGIA APR 6 1944 RECOMMENDATIONS. From Mr G. B. Emerson, late Principal of the English High School. MR F. J. GRUND-DEAR SIR-I have looked over, with as much attention as my time would allow, the Treatise on Solid Geometry which you sent me on the 5th. It seems to me at once concise, clear and easy of comprehension. Most of it, I believe, would be found quite as easy as Plane Geometry, by a person who had learnt the latter. The modes in which you introduce the propositions on the sphere, and the comparison of the three round bodies, are, so far as I know, new in elementary geometry, and strike me as important improvements upon former methods. The skill and success with which you have avoided the indirect modes of demonstration add also to the value of the work as an introductory treatise. I am, respectfully, yours, GEO. B. EMERSON. MARCH 9, 1831. From Mr F. P. Leverett, Principal of the Public Latin School, Boston. Mr Grund's Treatise on Solid Geometry, if I may be allowed to judge from a hasty examination, is remarkable for its intelligibility. The subject is treated in a very judicious manner, and the author, by making his demonstrations more complete than is usually done, instead of leaving the pupil to supply the deficiencies from his previous knowledge, has improved upon the works in general use, particularly as regards its adaptation to young scholars. MARCH, 3d, 1831. F. P. LEVERETT. 107 01 From Mr E. Bailey, Principal of the Young Ladies' High School, Boston. I have not found time to examine so thoroughly as I could wish, the copy of Mr Grund's 'Solid Geometry,' which was sent to me a few days since; I have examined it far enough, however, to become satisfied that it is a very ingenious and valuable work. It is a necessary sequel to his Elements of Plane Geometry;' the same excellent plan has been observed in both works; and, taken together, they form an admirable treatise for the use of academies and the higher order of schools. Very respectfully, yours &c, E. BAILEY. BOSTON, MARCH 7, 1831. From Mr Jacob Abbott, Teacher of the Mount Vernon School. I have examined the sheets of Grund's Solid Geometry, and have formed a favorable opinion of the plan and execution of the work. This treatise, together with the one on Plane Geometry, by the same author, which has been favorably received by the public, seems to me to be well adapted to the wants of academies and schools. ERRATA. JACOB ABBOTT. Page 36, line 8, read Cd instead of cd. " 43, 66 16, ABC instead of AB. ac AC instead of ac X AC. 1, after are read 'proportional' to the solidities, &c. "10, read CD instead of ED. PREFACE. IN offering to the public, the second part of my Elementary Treatise on Geometry, it may perhaps be well to say a few words on its plan and arrangement. With this regard, it is intended to be the sequel to my First Lessons in Plane Geometry; the second edition of which being paged according to the references in this part, may be bound with it as one volume. The division of the subject into sections, &c, is analogous to that in Plane Geometry, the problems forming a section by themselves, for the sake of being more easily referred to. In addition to this, each class of bodies, Cubes, Prisms, Pyramids, Cones, &c, is treated of under a separate head; because it appeared to me the safest plan, and much better calculated to give a distinct idea of them, than the analytic method of treating surfaces and bodies disconnectedly from each other, One principle has been laid down as an axiom, because its truth cannot be denied: Two bodies are equal to one another in solidity, when, having equivalent bases, and equal heights, they have also, in every point of their height, the same thickness. By this means I have not only succeeded in establishing every principle laid down in this book, |
