| John Playfair - Trigonometry - 1806 - 311 pages
...Therefore AB.BC =AC.CB+BC2. Therefore, if a straight line, &c. QED c B •33 PROP. IV. THEOR. \ -^ **IF a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts together with twice the rectangle contained... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. **IF a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts, together with twice the rectangle contained... | |
| Charles Hutton, Olinthus Gregory - Mathematics - 1811
...is equal to the sum of all the ether rectangles AjJ . AE, AD. EF, AD . FB. c^. ED Corol. If a right **line be divided into any two parts ; the square on the whole line, is equal to** both the rectangles of die whole line and each of the parts. CB THEOREM XXXI. THE Square of the Sum... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...rectangle contained by the two parts, together with the aquarc of the foresaid part. Prop. IV. Theor. **If a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts, together •with twice the rectangle contained... | |
| John Playfair - Trigonometry - 1819 - 333 pages
...therefore AB.BC '= AC.CB -f BC2. Therefore, if a straight -F line, &c. Q, ED — D PROP. IV. THEOR. **If a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts, together with twice the rectangle contained... | |
| Charles Hutton, Robert Adrain - Mathematics - 1822
...the .-11111 of all the other rectangles AD . AE, AD . EF, AD . FB. 4. c. D. E FB Carol. If a right **line be divided into any two parts ; the square on the whole line, is equal to** both the rectangles of the whole line and each of the parts. THEOREM XXXI. THE Square of the Sum of... | |
| 1854
...product. Geometry furnishes us with a parallel to both these cases ; for, as Euclid tells us (II., 4), **if a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts, together with twice the rectangle contained... | |
| Charles Hutton, Robert Adrain - Mathematics - 1825
...sum of ;tll the other «• •* * M rectangles AD . AE, AD . EF, AD . FB. «. ED Corol. If a right **line be divided into any two parts ; the square on the whole line, is equal to** both the rectangles of the whole line and each of the parts. • THEOREM XXXI. THE Square of the Sum... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...CB, together with the square of BC. If therefore a straight line, &c. QED Proposition IV. Theorem. ', **If a straight line be divided into any two parts, the square** or in* ELEMENTS OP KUCUD. 191 vhole line is equal to the squares of the two parts, together with twice... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. **If a straight line be divided into any two parts, the square** of the whole line is equal to the squares of the two parts, together with twice the rectangle contained... | |
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