| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...straight line &c. QED B t> PROPOSITION 8. THEOREM. If a straight line be divided into any two parti, **four times the rectangle contained by the whole line and one of the parts, together with the square** en the other part, is equal to the square on the straight line which is made up of the whole and that... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...BC, together with the square on AC. Wherefore, if a straight line &c. QED A PROPOSITION 8. THEOREM. **If a straight line be divided into any two parts, four times the rectangle contained** l)ij the whole line and one of the parts, together with the square en the other part, is equal to the... | |
| Robert Potts - 1868 - 410 pages
...BC, together with the square on AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. THEOREM. **If a straight line be divided into any two parts,...four times the rectangle contained by the whole line,** mid one of the parts, together with the square un the other part, is equal to the square on tlte straight... | |
| James Maurice Wilson - 1869
...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 - 1870
...arithmetical progression; as 324, 1G4, and 4, — the com. dif. being 160. PROP. 8. — THEOR. If a st. **line be divided into any two parts, four times the...together with the square of the other part, is equal to** tlie square of the st. line which is made up of the whole and that part. Coxs. — Pst. 2. A terminated... | |
| Euclides - 1871
...If straight 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,...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 - 349 pages
...be drawn from 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,...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
...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
...squares of A] ! and 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
...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... | |
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