 | Robert Potts - 1868 - 434 σελίδες
...double of the squares on AC, CD ; but DG is equal to DB; BOOK II. PROP. XI. PROPOSITION XI. PROBLEM. To divide a given straight line into two parts* so that...and one of the parts, shall be equal to the square on the other part, Let AB be the given straight line. It is required to divide AB into two parts, so... | |
 | Edinburgh univ - 1868 - 336 σελίδες
...Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 4. To divide a given straight line into two parts, so that...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. 5. The angles in the same segment of a circle are equal... | |
 | 1868 - 876 σελίδες
...bisected, is equal to the square of the straight line which is made up of the half and the part produced 25 5. Divide a given straight line into two parts, so that the rectangle contained by the whole mid one of the pails shall be equal to the square of the other part 25 100 B. Latt of Pupils recommended... | |
 | Washington Hudson - 1868 - 80 σελίδες
...other in the required ratio, which is represented by the squares с b г/and ach i. Fi«. 104. То divide a given straight line into two parts, so that the rectangle contained by the whole line and lesser part, shall be equal to the square on the other. Let AB be the given line. On AB as... | |
 | Euclides - 1870 - 270 σελίδες
...exercises for the learner." — LARDNER'S Euclid, pp. 79 and 80. PROP. 11. — PROB. To divide a given st. line into two parts, so that the rectangle contained...one of the parts shall be equal to the square of the oilier part. SOL. — 46. I. To describe a square on a given st. line. 10. I. To bisect a given finite... | |
 | Cambridge univ, exam. papers - 1870 - 272 σελίδες
...by the straight lines BD, CD ; prove that the angle BDC is half the sum of the angles ABG, ACS. 2. Divide a given straight line into two parts, so that...rectangle contained by the whole and one of the parts may be equal to the square on the other part. Produce a given straight line, so that the rectangle... | |
 | Alexander Charles Ewald - 1870 - 292 σελίδες
...bankrupt, pays 12s. 6d. in £1, what does the merchant gain or lose by the transaction ? 2. Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other part. 3. Prove that equiangular parallelograms have to one... | |
 | Robert Wallace - 1870 - 164 σελίδες
...cube, the product shall be 216. Ans. 3 or — 2. 6. Divide 20 into two such parts that the product of the whole and one of the parts shall be equal to the square of the other. Ans. 10^5 — 10 and 30— l0-V5. 7. A merchant sold a quantity of brandy for £39, and gained ns much... | |
 | Euclides - 1871 - 136 σελίδες
...every respect. NOTE. This Theorem has been already deduced as a Corollary from Prop. E, page 43. Ex. 5. Divide a given straight line into two parts, so that the square on one part shall be double of the square on the other. Ex. 6. If from one of the acute angles... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...every respect. NOTE. This Theorem has been already deduced as a Corollary from Prop. B, page 43. Ex. 5. Divide a given straight line into two parts, so that the square on one part shall be double of the square on the other. Ex. 6. If from one of the acute angles... | |
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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. 
