| James Maurice Wilson - 1869 - 260 pages
...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 - 136 pages
...lines be drawn from G to B and from G to Z>, shew that BGD is a straight line. /i as a If. a straight **line be divided into any two parts, four times the...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 the... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...G to B and from G to D, show that BGD is a straight line. PROPOSITION VIII. THEOREM. If a straight **line be divided into any two parts, four times the...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 up of the \ and the first... | |
| Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...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... | |
| Henry Major - Student teachers - 1873 - 592 pages
...BC are equal to twice the rectangle AB, BC. together with the square of AC. VIII. — If a straight **line be divided into any two parts four times the rectangle contained by the** wJwle line, and one of the parts, together with the square oftha other part, is equal to the square... | |
| Euclides - 1874 - 120 pages
...Algebra is similarly expressed, and is thus represented in symbols, PROPOSITION 8. THEOREM. If a straight **line be divided into any two parts, four times the...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 - 424 pages
...the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight **line be divided into any two parts, four times the...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
...the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight **line be divided into any two parts, four times the...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 - 234 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... | |
| 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.... | |
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