44. If two circles touch each other externally, and also touch a straight line, prove that the part of the line between the points of contact is a mean proportional between the diameters of the circles.

45. Any regular polygon inscribed in a circle is a mean proportional between the inscribed and circumscribed regular polygons of half the number of sides.

46. ABC is a triangle, and O is the point of intersection of the perpendicular from ABC on the opposite sides of the triangle: the circle which passes through the middle points of OA, OB, OC, will pass through the feet of the perpendiculars, and through the middle points of the sides of the triangle.

47. Describe a circle to touch a given straight line and a given circle, and to pass through a given point.

48. A and B are two points on the same side of a straight line which meet AB produced in C. Of all the points in this straight line find that at which AB subtends the greatest angle.

49. Inscribe a square in a given pentagon.

50. ABCD is a quadrilateral figure circumscribing a circle, and through the centre O, a line EOF equally inclined to AB and BC is drawn to meet them in E and F: prove that AE : EB :: CF : FD.

CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

By the same author.

SOLID GEOMETRY

AND

CONIC SECTIONS,

WITH APPENDICES ON TRANSVERSALS

AND HARMONIC DIVISION.

FOR THE USE OF SCHOOLS.

THIRD EDITION.

Extra fcap. 8vo., price 3s. 6d.

MACMILLAN AND CO., LONDON.

NOTE BOOK ON PRACTICAL, SOLID, OR DESCRIPTIVE GEOMETRY. Containing Problems, with help for Solution. By J. H. EDGAR, M. A. and G. S. PRITCHARD. New Edition, revised and enlarged. Extra fcap. 8vo. 35.

A GEOMETRICAL NOTE-BOOK, containing Easy Problems in Geometrical Drawing preparatory to the Study of Geometry. For the use of Schools. By F. E. KITCHENER, M.A., Mathematical Master at Rugby. New Edition. 4to. 25.

SYLLABUS OF PLANE GEOMETRY. (Corresponding to Euclid, Books I.-VI.) Prepared by the Association for the Improvement of Geometrical Teaching. New Edition. Crown 8vo. Is.

NATURAL GEOMETRY: an Introduction to the Logical Study of Mathematics. For Schools and Technical Classes. By A. MAULT. With Explanatory Models based upon the Tachymetrical works of Ed. LAGOUT. 18mo. IS.

Models to illustrate the above, in box, 12s. 6d.

ELEMENTS OF DESCRIPTIVE GEOMETRY.

By

J. B. MILLAR, C.E., Assistant Lecturer in Engineering in Owens
College, Manchester. Crown 8vo. 6s.

MODERN METHODS IN ELEMENTARY GEOMETRY. By E. M. REYNOLDS, M.A., Mathematical Master in Clifton College. Crown 8vo. 3s. 6d.

MACMILLAN AND CO., LONDON.

A CATALOGUE

OF

EDUCATIONAL BOOKS,

PUBLISHED BY

MACMILLAN AND CO.,

BEDFORD STREET, STRAND, LONDON.

CLASSICAL.

ÆSCHYLUS-THE EUMENIDES. The Greek Text, with Introduction, English Notes, and Verse Translation. By BERNARD DRAKE, M.A., late Fellow of King's College, Cambridge. 8vo. 3s. 6d.

ARISTOTLE-AN INTRODUCTION TO ARISTOTLE'S RHETORIC. With Analysis, Notes and Appendices. By E. M. COPE, Fellow and Tutor of Trinity College, Cambridge, 8vo.

145.

ARISTOTLE ON FALLACIES; OR, THE SOPHISTICI
ELENCHI. With Translation and Notes by E. POSTE, M.A.
Fellow of Oriel College, Oxford. 8vo. 8s. 6d.

ARISTOPHANES-THE BIRDS. Translated into English
Verse, with Introduction, Notes, and Appendices, by B. H.
KENNEDY, D.D., Regius Professor of Greek in the University
of Cambridge. Crown 8vo. 6s.

BELCHER-SHORT EXERCISES IN LATIN PROSE
COMPOSITION AND EXAMINATION PAPERS IN
LATIN GRAMMAR, to which is prefixed a Chapter on
Analysis of Sentences. By the Rev. H. BELCHER, M.A.,
Assistant Master in King's College School, London.
Edition. 18mo. Is. 6d. Key, Is. 6d.

New

BLACKIE-GREEK AND ENGLISH DIALOGUES FOR

USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh. Second Edition. Fcap. 8vo. 10,000. 7. 78.

2s. 6d.

a