| John Playfair - Mathematics - 1806 - 320 pages
...rectangles A.BD, A.DE, A.EC. Therefore, if there be two straight lines, &c. QED Book II. PROP. II. **THEOR. IF a straight line be divided into any two parts, the** rectangles contained by the whole and each of the parts are together equal to the square of the whole... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...with the square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. **THEOR. IF a straight line be divided into any two parts, the** squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the... | |
| John Mason Good - 1813 - 714 pages
...equal to the square of the «traight line which U made up of the half and the part produced. Prop. VII. **Theor. If a straight line be divided into any two parts, the** squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the... | |
| Euclides - 1814 - 560 pages
...rectangle AC'. CB, together with the square of BC. If therefore u straight line, &c. QED PHOP. IV. THKOR. E **IF a straight line be divided into any two parts,...equal to the squares of the two parts, together with** twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts... | |
| Jeremiah Day - Algebra - 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 a binomial. Let the side... | |
| Euclides - 1816 - 588 pages
...rectangle 1"" "Y"*"' AB, BC, is equal to the square of AB. If therefore a straight line, &c. QED PROP. III. **THEOR. IF a straight line be divided into any two parts, the** rectangle contained by the whole and one ofthe parts is equal to the rectangle contained by the two... | |
| John Mason Good - 1819 - 800 pages
...equal to the rectangle 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.... | |
| Jeremiah Day - Algebra - 1820 - 352 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, together with** twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square... | |
| Euclides - 1821 - 294 pages
...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... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 pages
...BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IP a straight line be divided into any twq **parts, the square of the whole line is equal to the squares of the two** pai ts, together with twice the rectangle contained by the parts. Let the straight line AB be divided... | |
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