and because the square on GH} therefore the rect. BE, EF, with the square on GE and therefore the rect. BE, EF = = squares on GE and the EH, the squares on GE and EH (ax. 1), =the square on EH (ax.3). But the rect. BE, EF, is the rect. BE, ED, for EF therefore the rect. BD But the rect. BD = ED; =the square on EH. the figure A (cons.). Therefore, it is proved, as required, that The square described on EH = the rectilineal figure A. Q. E. F. ADDENDUM. EUCLID, BOOK II. The chief difficulty the learner has in remembering, as well as in learning, the Propositions of Euclid, Book II., arises from the verbal similarity in many of the Enunciations. This difficulty may be lessened, in preparing for an examination at least, by taking the following Propositions in the classes referred to. A. Properties of a straight line divided into any two parts. Props. 2, 3, 4, 7, and 8. Let AB be a straight line divided into any two parts in C. Then, Prop. 2, The rectangles contained by the whole and each of =the square on the whole line. the parts |