 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...one " another. 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...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 - 264 pages
...-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 - 192 pages
...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 - 1840 - 82 pages
...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 - 1842 - 316 pages
...or ' EHC, 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...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 - 688 pages
...one anotker, and the diameter bisects them, that is, divides them 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 lines is equal to the rectangles contained by... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...These signs will be occasionally used for brevity, in what follows." PROPOSITIONS. PROP. I. THEOR. — If there be two straight lines, one of which is divided...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 - 894 pages
...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 - 128 pages
...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 - 128 pages
...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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If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. 
