| Euclid, James Thomson - Geometry - 1837 - 390 pages
...These signs will be occasionally used for brevity, " in what follows." PROP. I. THEOR. IF there be **two straight lines, one of which is divided into any...number of parts ; the rectangle contained by the two** lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided... | |
| Euclides - 1838
...-parallelograms which make the gnomon.PROP. I. THEOR. If there be two straight lines, one of which is dieided **into any number of parts ; the rectangle contained...lines, is equal to the rectangles contained by the** undieided line, and the seeeral parts of the dieided line. Let A and BC be two straight lines; and... | |
| Euclides - 1840
...contained by two straight lines, of which one is divided into any number of parts, is equal to the sum of **the rectangles contained by the undivided line and the several parts of the divided line.** PROP. II. THEOR. If a straight line be divided into any two parts, the square of the whole line is... | |
| Euclides - 1840
...and AB), of which one (AB) is divided into any number of parts (AF, FH, HB), is equal to the sum of **the rectangles contained by the undivided line and the several parts of the divided line.** From A draw AC perpendicular to AB, make it equal to L, and complete the parallelogram AD (that is... | |
| Euclides - 1842
...at the opposite angles of the " ' parallelograms which make the gnomon.' PROP. I. THEOR. IF there be **two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line.** by A, BD, together with that contained by A, DE, and that contained by A, EC. From the point в draw... | |
| Education - 1844
...into two equal |>orts. 6. If (here be two straight lines, one of which is divided into any number ot **parts, the rectangle contained by the two straight...undivided line and the several parts of the divided line.** 7. If a straight line be divided into any two parts, the squares of the whole line, and of one of the... | |
| Euclid, James Thomson - Geometry - 1845 - 352 pages
...will be occasionally used for brevity, in what follows." PROPOSITIONS. PROP. I. THEOR. — If there be **two straight lines, one of which is divided into any...number of parts ; the rectangle contained by the two** lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided... | |
| Nathan Scholfield - 1845
...PROPOSITION V. THEOREM. If there be two right lines, of which one is divided into parts, the sum of **the rectangles contained by the undivided line and the several parts of the** other, will be equal to the rectangle contained by the two whole lines. Let the lines be AB, AC, of... | |
| Great Britain. Admiralty - Geometry - 1846
...expressed by the words " rectangle of AB and AD j" or by " AB . AD." PROP. XLI. THEOR. 1. 2 En. angle **contained by the two straight lines, is equal to the...several parts of the divided line. Let A and BC be two** str. lines, and let BC be divided into any parts in D and E; then A.BC=A.BD + A.DE+A.EC B DEC Draw... | |
| Great Britain. Admiralty - Geometry - 1846
...words " rectangle of AB and AD;" or by " AB . AD." PROP. XLI. THEOR. ,. 2Eu . angle contained by tlie **two straight lines, is equal to the rectangles contained...several parts of the divided line, Let A and BC be two** str. lines, and let BC be divided into any parts in D and E; then A.BC=A. BD + A. DE+A. EC B DEC Draw... | |
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