 | Robert Simson - 1806 - 546 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 - 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 - 714 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 - 1814 - 304 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 - 588 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... | |
 | Daniel Cresswell - 1817 - 454 pages
...rectangle contained by those lines. PROP. VIII. (VII.) If a straight line be divided into five equal parts, the square of the whole line is equal to the square of the straight line, which is made up of four of those parts, together with the square of the straight line... | |
 | John Playfair - 1819 - 350 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 - 800 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.... | |
 | Euclides - 1821 - 294 pages
...suppose '8 and 6 are the given quantities : then 6 X 6 -f- 6 X 2 is = to 8 X 8 — 8 X 2. PROP. 4T THEQR. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts On the given line describe... | |
 | 1854 - 1112 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... | |
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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. 
