 | Euclid - Geometry - 1845 - 218 pages
...'parallelograms which make the gnomon.' PROPOSITION I. THEOB. — If there be two straight lines, one of which is divided into any number of parts; the...line, and the several parts of the divided line. Let A and BC be two straight lines ; and let BC be divided into any parts in the points D, E; the rectangle... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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 - 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... | |
 | Euclides - 1846 - 292 pages
...angles of the parallelograms which make the gnomon. PROP. I. THBOB. If there be two straight lines, one of which is divided into any number of parts, the...line, and the several parts of the divided line. Let A and BC be two straight lines, and let BC be divided into any parts in the points D, E : the rectangle... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...gnomon AGK •orEHC." D B 49 JJ ' DEC ~ — • -- ' PROP. I. THEOR. If there be two straight lines, one of which is divided into any number of parts ; the...line, and the several parts of the divided line. Let A and BC be two straight lines ; and let BC be divided into any parts in the points D, E ; the rectangle... | |
 | 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...line, and 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... | |
 | 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...line, and 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.... | |
 | Bengal council of educ - 1848 - 394 pages
...angles to a given straight line from one extremity of the same. 3. If there be two straight lines, one of which is divided into any number of parts ; the...undivided line, and the several parts of the divided line. Hence prove that the area of a rectangle is equal to the product of the base and its altitude. 4. The... | |
 | Euclides - 1848 - 52 pages
...complements, is called a gnomon. PROPOSITIONS. PROP. I. THEOREM. IP there be tvvo straight lines, one of which is divided into any number of parts ; the...undivided line, and the several parts of the divided line. PROP. II. THEOREM. If a straight line be divided into any two parts, the rectangles contained by the... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...angles of the parallelograms which make the gnomon." PROP. I. THEOB. If there be two straight lines, one of which is divided into any number of parts; the...undivided line, and the several parts of the divided line. into any parts in the points D, E ; the rectangle contained by the straight lines A, BC is equal to... | |
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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. 
