 | 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...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 be represented... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...rectangle AC, CB together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...parts, the square of the whole line is equal to the squares of the two parts, together with tvtice the rectangle contained by the parts. Let the straight...be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB.... | |
 | 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.... | |
 | 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...parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole... | |
 | 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 be represented... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. . Let the line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two -^ HC parts at the point E : then will the square described on AB be equivalent... | |
 | 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,...together with twice the rectangle contained by the paits. 2. If a straight line be divided into two equal and also into two unequal parts, the squares... | |
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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. 
