| Euclides - 1837 - Liczba stron: 88
...showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. **If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts.** * By the rectangle AX BC (the lines A and BC being separate) is' meant the rectangle which may be formed... | |
| Charles Reiner - 1837 - Liczba stron: 215
...the rectangle contained by ac and c b. M.- — Express this truth as a general proposition. P. — **If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts.** The master will, here, have a suitable opportunity of directing the attention of his pupils to a numerical... | |
| Charles Reiner - 1837 - Liczba stron: 215
...twice the rectangle contained by ac and c b. M.—Express this truth as a general proposition. P.—If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** The master will, here, have a suitable opportunity of directing the attention of his pupils to a numerical... | |
| Euclid, James Thomson - 1837 - Liczba stron: 390
...equal to the square of BC, together with the rectangle AC.CB. * If, therefore, &c. PROP. IV. THEOR. **IF a straight line be divided into any two parts,...the squares of the two parts, together with twice** their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is... | |
| Andrew Bell - 1837 - Liczba stron: 240
...twice the rectangle contained by the whole and that part, together with the square of the other part. **Let the straight line AB be divided into any two parts in** the point C ; the squares of AB, BO, are equal to twice the rectangle AB-BC, together with the square... | |
| Euclides - 1838
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part. **Let the straight line AB be divided into any two parts in** the point C : the rectangle AB-BC shall be equal to the rectangle AC-CB, together with the square of... | |
| Jeremiah Day - 1839 - Liczba stron: 332
...than in ordinary language. The proposition, (Enc. 4. 2.) thai when a straight line is divided into **two parts, the square of the whole line is equal to the squares of the** iwo parts, together with twice the product of the parts, is demonstrated, by involving a binomial.... | |
| Great Britain. Committee on Education - 1853
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Sec/ion 2. 1. **If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts.** 2. If a straight line be divided into two equal and also into two unequal parts, the squares of the... | |
| Dionysius Lardner - 1840 - Liczba stron: 314
...several rectangles under the line and each of its parts. (242.) If a line be divided into two or more **parts, the square of the whole line is equal to the squares of the** several parts together with twice the rectangles under every pair of parts. Let theline AB (fig.l 1... | |
| Euclides - 1840
...contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. **If a straight line be divided into any two parts, the square of the** sum of the whole line and one of its parts is equal to four times the rectangle contained by the whole... | |
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