 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...for instance, let the segments of BC be denoted by 6, c, and d; then, A(6+c+<i)=AJ+Ac+Arf. 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... | |
 | Jeremiah Day - Algebra - 1847 - 358 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two par.ts, the square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving a binomial Let the side of a square be... | |
 | Euclides - 1848 - 52 pages
...rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. 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. COR. From the demonstration, it is manifest, that the parallelograms... | |
 | Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...concise, 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... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts.... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...contained by two straight lines AB, AC is sometimes simply called the rectangle AB, AC. PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts is equal with the rectangle contained by the... | |
 | Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...sides which contain the right angle. Section 3. 1. If a straight line be divided into any two part» the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two... | |
 | Great Britain. Committee on Education - 1850 - 942 pages
...makes the alternate angles equal. — Define parallel lines, and alternate angles. 3. If a line be cut into any two parts, the square of the whole line is equal to the squares of the parts, and twice the rectangle contained by the parts. — Show the same Algebraically. 4. Prove tluit... | |
 | Jeremiah Day - Algebra - 1850 - 348 pages
...language. The proposition, (Euc, 4. 2.) that when a straight line is divided into two parts, tilesquare of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, Ijy involving a binomial. Let the side of a square... | |
 | 1852 - 316 pages
...to a given triangle, and have one of its angles equal to * Riven rectilineal angle. SECTION II. 1. 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 paits. 2. If a straight line be divided into two equal and also... | |
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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. 
