| Robert Simson - Trigonometry - 1806 - 518 pages
...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 by the parts. Let the straight... | |
| John Playfair - Euclid's Elements - 1806 - 320 pages
...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 by the parts. Let the straight... | |
| John Mason Good - 1813 - 722 pages
...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 by the parts. Prop. V. Theor.... | |
| Jeremiah Day - Algebra - 1814 - 303 pages
...than in ordinary language. The proposition, (Euc. 4. 2.)] that when a straight line is divided into **two parts, the square of the whole line is equal to the** squares of the two parts, togedier with twice die product of the parts, is demonstrated, by involving... | |
| Euclides - 1816 - 528 pages
...together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. Is 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 by the parts. Let the straight... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...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 by the parts, Let the straight... | |
| John Mason Good - 1819 - 740 pages
...contained by the two parts, together with tiie square of the furesaicl part. Prop. IV. Theor. If a straight **line be divided into any two parts, the square of the whole line** n equal to the squares of the two parts, together with twice the rectangle contained by the parts.... | |
| 1854 - 1110 pages
...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 by the parts ; and, were we to... | |
| Charles Hutton - Mathematics - 1822 - 618 pages
...is equal to 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... | |
| Charles Hutton - Mathematics - 1825
...equal to the 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... | |
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