| Robert Potts - 1868 - Liczba stron: 410
...on the 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. FQ Upon AB describe the square A CDB ; (I. 46.) bisect AC... | |
| James Maurice Wilson - 1869
...therefore remembering that AD = DC, we obtain by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a **straight line into two parts such that the rectangle contained by the whole line and one of the parts** is equal to the square of the other part. Let AB be the given line. Construction. Draw a square ACDB... | |
| Euclides - 1871
...that BGD is a straight line. /i as a 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... | |
| Euclid, Charles Peter Mason - 1872
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, **the rectangle contained by the whole line and one of the parts** is equal to the square on that part together with the rectangle contained by the two parts. The propositions... | |
| Euclides, James Hamblin Smith - 1872 - Liczba stron: 349
...straight line. PROPOSITION VIII. THEOREM. 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 otJter part, is equal to the square on the straight line which is made... | |
| Euclides - 1874
...square on CD. QED PROP. XI.— PKOBLEM. (Euc. II. 11). To divide a straight line into two parts, so **that the rectangle contained by the whole line, and one of the parts,** may be equal to the square of the other part. Let AB be a straight line, it is required to find a point... | |
| Francis Cuthbertson - 1874 - Liczba stron: 349
...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... | |
| Edward Atkins - 1874
...line, &c. QED Proposition 8. — Theorem. 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... | |
| Euclides - 1874
...line, &c. QED PROPOSITION 8. —Theorem. 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... | |
| Euclides - 1874
...represented in symbols, PROPOSITION 8. THEOREM. 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... | |
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