An Introduction to the Elements of Euclid, Being a Familiar Explanation of the First Twelve Propositions of the First Book (Paperback)

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1874. Not illustrated. Excerpt: ... Two straight lines are given, one of which is greater than the other: -- And it is required from the greater, to cut off a part equal to the less. On a page different from that on which, the figure is to be drawn, write thus: '1. Let A B and C L be two straight lines, of which. A B is the'greater.' Then draw these two straight lines; (let C L be about an inch and a half long, and let the nearest extremities of the straight lines be about an inch apart); and add, '2. It is required from A B the greater, to cut off a part equal to C L, the less.' The first step in the construction is: 'I. From the point A, draw a straight line equal to C L (Prop. 2). This at once links this, the third proposition, on to the second, for what you are here told to do is exactly what you were taught to do in the second proposition. Regard then at present only the point A (which is one extremity of the straight line A B) and the straight line C L. And taking A as the given point, and C L as the given straight line, do all the construction of the second proposition over again. Obs.--In the fig. 24a) this construction is given in dotted lines; do you do it in pencil, that it may afterwards be effaced. i. The first step of the construction of the second proposition is from the point A to C, to draw the straight line A C (Post. 1). ii. The second step is to describe an equilateral triangle on AC. To do this we must go back to the first proposition. But in order not to encumber your figure with circles, find the vertex of the equilateral triangle by the intersection of two small arcs according to the method described on p 27; call the intersection of the arcs H, join H A, and to save time and ensure correctness, before removing the ruler, produce H A to any point K. In like manner join H C, ..