 | John Playfair - Geometry - 1855 - 350 pages
...involution, a2 — 2oc+c2=62. This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. • If a straight line be divided into any two parts, four times the rectangle cnntained by the whole line, and one of the parts, together with the square of the other part, is equal... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 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 - 424 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 - 434 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 - 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 - 1870 - 270 pages
...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 - 136 pages
...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 - 376 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 - 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 - 588 pages
...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... | |
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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... 
