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The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock - Softcover
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Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1852 Excerpt: ... to A; and DL is contained by A, DE, because DK, that isd BG, is equal to A; xxxiv. l. and in like manner the rectangle EH is contained by A, EC: Therefore the rectangle contained by A, BC is equal to the several rectangles contained by A, BD, and by A, DE; and also by A, EC. Wherefore, if there be two straight lines, &c. Q. E. D. BOOK H. This may be illustrated by measuring six equal distances from B to G, and terminating the straight line at the end of the sixth, so that BD shall contain three of the distances, DE two, and EG one, and by taking the other straight line A of any length. Through each of the points of the divided line draw lines parallel to B, and the figure will be divided into six equal parallelograms, which are together equal to the first three, and the next two, and the remaining one; or, in numbers, six is equal to three, and two and one added together. PROP. IL THEOR. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C; the rectangle contained by AB, BC; together with the rectangle AB, AC, shall be equal to the square of AB. Upon AB describe the square ADEB, and through C drawb CF, parallel to AD or BE; Then AE is equal to the rectangles AF, CE; N. B. To avoid repeating the word contained too frequently, the rectangle contained by two straight lines, AB, AC, is sometimes simply called the rectangle AB, AC. and AE is the square of AB; and AF is the rectangle contained by BA, AC; for it is contained by DA, AC, of which AD is equal to AB; and CE is contained by AB, BC, for BE is equal to AB; therefore the rectangle contained by AB, AC, together with the recta...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1852 Excerpt: ... to A; and DL is contained by A, DE, because DK, that isd BG, is equal to A; xxxiv. l. and in like manner the rectangle EH is contained by A, EC: Therefore the rectangle contained by A, BC is equal to the several rectangles contained by A, BD, and by A, DE; and also by A, EC. Wherefore, if there be two straight lines, &c. Q. E. D. BOOK H. This may be illustrated by measuring six equal distances from B to G, and terminating the straight line at the end of the sixth, so that BD shall contain three of the distances, DE two, and EG one, and by taking the other straight line A of any length. Through each of the points of the divided line draw lines parallel to B, and the figure will be divided into six equal parallelograms, which are together equal to the first three, and the next two, and the remaining one; or, in numbers, six is equal to three, and two and one added together. PROP. IL THEOR. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C; the rectangle contained by AB, BC; together with the rectangle AB, AC, shall be equal to the square of AB. Upon AB describe the square ADEB, and through C drawb CF, parallel to AD or BE; Then AE is equal to the rectangles AF, CE; N. B. To avoid repeating the word contained too frequently, the rectangle contained by two straight lines, AB, AC, is sometimes simply called the rectangle AB, AC. and AE is the square of AB; and AF is the rectangle contained by BA, AC; for it is contained by DA, AC, of which AD is equal to AB; and CE is contained by AB, BC, for BE is equal to AB; therefore the rectangle contained by AB, AC, together with the recta...
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