 | Euclides - 1874 - 120 pages
...proposition in Algebra is similarly expressed, and is thus represented in symbols, PROPOSITION 8. THEOREM. If a straight line be divided into any two parts,...line and one of the parts together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that... | |
 | Edward Atkins - 1874 - 426 pages
...together with the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts,...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole line and... | |
 | Edward Atkins - 1874 - 428 pages
...together with the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts,...contained by the whole line and one of the parts, toget/ier with the square on the other part, is equal to the square on tlie straight line which is... | |
 | Euclides - 1874 - 342 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line, and one of the parts, shall be equal to the square on the other part. Construction. Upon AB describe the square ACDB (I.... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let AB... | |
 | Edward Atkins - 1876 - 130 pages
...together with the square on AC. Therefore, if a straight line, &c. Q. E, D. Proposition 8. — Theorem. If a straight line be divided into any two parts,...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole line and... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...be drawn from G to B and from (f to D, shew that BO D ia a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by ike whole line and one of the parts, together with the square on the other part, is equal to the square... | |
 | Richard Wormell - 1876 - 268 pages
...AB:BC = AD:DE. PROBLEM XX. To divide a straight line in extreme mean ratio — that is to say, so that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. Let AB be the straight line. Construct the square ABDE... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...other part. Let AB\vt the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part FO CK 1) Upon AB describe the square A CDB ; (I. 46.)... | |
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If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that... 
