4. The most important Propositions are,-three, namely, Props, 4, 8, and 26, containing the criteria, or conditions of equality between triangles; one Prop. 32, the equality of the exterior angle to the two interior and opposite angles, and of the three interior angles of every triangle to two right angles; one Prop. 41, the proportion of the parallelogram to the triangle on the same base and between the same parallels; and one Prop. 47, the relation between the hypotenuse and the sides about a rt. angle. These propositions at least must be thoroughly mastered, not by committing them to memory, but by becoming so perfectly familiar with the principles contained in them, and with the connexions which exist between the arguments or reasonings employed, as never to feel at a loss for the demonstration, however diversified may be the figures constructed, nor even though no figure at all be drawn. The great aim should be to understand, and as a means to this, to follow up each proposition regularly through all its gradations, and verify it by its appropriate proofs. BY THE SAME AUTHOR, Price 68. 6d., pp. about 680, Diagrams above 570; EUCLID'S PLANE GEOMETRY, Books I-VI., Practically Applied; With an Explanatory Preface, Algebraical and Arithmetical Illustrations, Explanatory Notes, Synoptical Index, showing the Uses of the Propositions, &c. CRITICAL NOTICES. "This is a most valuable edition of Euclid, and for the purposes of the practical tutor will be found a very great aid." "On the whole, we have met with no edition of Euclid (in a considerable experience) so likely to aid the teacher by its thorough grasp of the subject, and the great variety of its practical illustrations."-The Spectator. "Of this edition of Mr. Green's we can speak very highly. 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