| Euclides - Euclid's Elements - 1837 - 112 pages
...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, the...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... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...BC is equal to the rectangle AC • CB, together with the square of BC. PROPOSITION TV. THEOREM. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares... | |
| Euclid - Geometry - 1837 - 410 pages
...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...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... | |
| Euclides - 1838 - 264 pages
...IV. THEOR. If a straight line be divided into any two parts, the sqtmre of the whole line is equal in **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 in C ; the square of AB shall be equal to the... | |
| Jeremiah Day - 1839 - 354 pages
...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 - School buildings - 1853 - 1218 pages
...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, the...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 - Curves, Plane - 1840 - 386 pages
...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 - 194 pages
...by the parts. F T» PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), **the square of the whole line is equal to the squares of the** parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;... | |
| Euclides - 1840 - 82 pages
...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... | |
| Euclides - 1841 - 378 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, the...together with twice the rectangle contained by the parts.** Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares... | |
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