Page:First six books of the elements of Euclid 1847 Byrne.djvu/21

Rh the angles DBC and ECB, which are those included by the third side BC and the productions of the equal sides AB and AC are equal. Also the angles DCB and EBC are equal if those equals be taken from the angles DCA and EBA before proved equal, the remainders, which are the angles ABC and ACB opposite to the equal sides, will be equal.

Therefore in an isosceles triangle, &c.

Q. E. D. Our object in this place being to introduce the system rather than to teach any particular set of propositions, we have therefore selected the foregoing out of the regular course. For schools and other public places of instruction, dyed chalks will answer to describe diagrams, &c. for private use coloured pencils will be found very convenient. We are happy to find that the Elements of Mathematics now forms a considerable part of every sound female education, therefore we call the attention of those interested or engaged in the education of ladies to this very attractive mode of communicating knowledge, and to the succeeding work for its future developement.

We shall for the present conclude by observing, as the senses of sight and hearing can be so forcibly and instantaneously addressed alike with one thousand as with one, the million might be taught geometry and other branches of mathematics with great ease, this would advance the purpose of education more than any thing that might be named, for it would teach the people how to think, and not what to think; it is in this particular the great error of education originates.