| Euclid - 1835 - 540 pages
...the squares of AC, CD. Wherefore, " if a straight line," &c. QED PROP. XI. PROB. To divide a given **straight line into two parts, so that the rectangle contained by the whole,** and one of the parts, shall be equal to the square of the other part. Let AB be the given straight... | |
| Mathematics - 1835
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, **the rectangle contained by the whole line and one of the parts,** shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid... | |
| Mathematics - 1836 - 472 pages
...of the difference of the lines. VIII. 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 of the other part, is equal to the square of the straight line which is made... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given **straight line into two parts, so that the rectangle contained by the whole** and one of the parts shall be equal to the square of c KT~i the other part. Steps of the Demonstration.... | |
| Euclid - Geometry - 1837 - 410 pages
...Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. To divide a given **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. Let AB be the given straight line... | |
| Charles Reiner - Geometry - 1837 - 254 pages
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice **the rectangle contained by the whole line and one of the parts** is equal to twice the square upon that part, together with twice the rectangle contained by the parts.... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...square of AC. 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 of the other part, is equal to the square of the straight line which is made... | |
| Euclides - 1838 - 264 pages
...of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. To divide a given **straight line into two parts, so that the rectangle contained by the whole,** and one of the parts, shall be equal to the square of the other part. Let AB be the given straight... | |
| Euclides - 1841 - 378 pages
...of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 To divide a given **straight line into two parts, so that the rectangle contained by the whole** and one of the parts, shall be equal to the square of the other part. Let AB be the given straight... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given **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. Let AB be the given straight line... | |
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