Geitet CONTENTS. On the Ancient Geometrical Analysis Geometrical Exercises on Book I Note on the Algebraical Symbols & Abbreviations used in Geometry 109 Geometrical Exercises on Book II Geometrical Exercises on Book III Geometrical Exercises on Book IV Geometrical Exercises on Book VI Eleventh Book of the Elements, Props. 1-21 Notes to the Eleventh Book ..... Questions on the Eleventh Book Geometrical Exercises on Book XI. Twelfth Book of the Elements, Props. 1, 2 Geometrical Exercises on Book XII. Solutions, Hints, &c. on Book I. III. 366 378 385 396 399 TRINITY COLLEGE, CAMBRIDGE. Euclid's Elements of Geometry, the First Six Books, and the portions of the Eleventh and Twelfth Books read at Cambridge, with Notes, Questions, and Geometrical Exercises, from the Senate House and College Examination Papers, with Hints, &c. By R. Potts, M.A., Trinity College, Cambridge. The University Edition, the Second, improved, 8vo. cloth, 10s. The School Edition, the Fifth. 12mo. roan, 58. : : cioth, 4s, 6d.: Books I-IV. 3s. : Books I–III. 28. 6d.: Books I, II. ls. 6d.: Book I. ls. The Enunciations of Euclid, 6d. A Medal has been awarded to "R. Potts for the excellence of his works on Geometry" by the Jurors of the International Exhibition, 1862.-Jury Awards, p. 313. “Mr. Potts' Euclid is in use at Oxford and Cambridge, and in the Principal Grammar Schools. It is supplied at reduced cost for National Education from the Depositories of the National Society, Westminster, and of the Congregational Board of Education, Homerton College. It may be added, that the Council of Education at Calcutta were pleased to order, in the year 1853, the introduction of these Editions of Euclid's Elements into the Schools and Colleges under their control in Bengal.” Critical Remarks on the Editions of Euclid. “In my opinion Mr. Potts has made a valuable addition to Geometrical literature by his Editions of Euclid's Elements."-1. Whewell, D.D., Master of Trinity College, Cambridge (1848.) “Mr. Potts has done great service by his published works in promoting the study of Geometrical Science.”-H. Philpott, D., Master of St. Catharine's College. (1848.) “Mr. Potts' Editions of Euclid's Geometry are characterized by a due appreciation of the spirit and exactness of the Greek Geometry, and an acquaintance with its history, as well as by a knowledge of the modern extensions of the Science. The Elements are given in such a form as to preserve entirely the spirit of the ancient reasoning, and having been extensively used in Colleges and Public Schools, cannot fail to have the effect of keeping up the study of Geometry in its original purity.”— James Challis, M.A., Plumian Professor of Astronomy and Experimental Philosophy in the University of Cambridge. (1848.) “Mr. Potts' edition of Euclid is very generally used in both our Universities and in our Public Schools; the notes which are appended to it shew great research, and are admirably calculated to introduce a student to a thorough knowledge of Geometrical principles and methods.”—George Peacock, D.D., Lowndean Professor of Mathematics and Dean of Ely. (1848.) “By the publication of these works, Mr. Potts has done very great service to the cause of Geometrical Science; I have adopted Mr. Potts' work as the text-book for my own Lectures in Geometry, and I believe that it is recommended by all the Mathematical Tutors and Professors in this University.”—Robert Walker, M.A., F.R.S., Reader in Experimental Philosophy in the University, and Mathematical Tutor of Wadham College, Oxford. (1848.) “When the greater Portion of this part of the Course was printed, and had for some time been in use in the Academy, a new Edition of Euclid's Elements, by Mr. Robert Potts, M.A., of Trinity College, Cambridge, which is likely to supersede most others, to the extent, at least, of the Six Books, was published. From the manner of arranging the Demonstrations, this edition has the advantages of the symbolical form, and it is at the same time free from the manifold objections to which that form is open. The duodecimo edition of this work, comprising only the first Six Books of Euclid, with Deductions from them, having been introduced at this Institution as a text book, now renders any other Treatise on Plane Geometry unnecessary in our course of Mathema. "-Preface to Descriptive Geometry, fc. for the Use of the Royal Military Academy, 5. Hunter Christie, M.A., of Trinity College, Cambridge, late Secretary of the Royal letu, &c.. Professor of Mathematics in the Řoval Militaru Academu. Woolrich (1847.) EUCLID'S ELEMENTS OF GEOMETRY. BOOK I. DEFINITIONS. I. II. III. The extremities of a line are points. IV. V. VI. VII. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to each other in a plane, which meet together, but are not in the same direction. IX. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. A B N.B. If there be only one angle at a point, it may be expressed by a letter placed at that point, as the angle at E: but when several angles are at one point B, either of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of these straight lines, and the other upon the other line. Thus the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA; that which is contained by AB, DB, is named the angle ABD, or DBA; and that which is contained by DB, CB, is called the angle DBC, or CBD. When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. XI. XII. XIII. XIV. XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another. XVI. XVII. A diameter of a circle is a straight line drawn through the center, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. XX. Rectilineal figures are those which are contained by straight lines, XXI. XXII. Quadrilateral, by four straight lines. XXIII. Multilateral figures, or polygons, by more than four straight lines. |