 | George Darley - Euclid's Elements - 1836 - 172 pages
...extremities of equal arches, and not intersecting, are parallel, 64. ART. 89. If there he two right lines, one of which is divided into any number of parts, the rectangle under the two lines is equal to the sum of the rectangles under the undivided line and the several... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...opposite angles of the parallelograms which make the gnomon. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number...undivided 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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...apply to the demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided into any number...contained by the two straight lines is equal to the & rectangles contained by the undivided line, and the several parts of the divided line. JL LH CB Proved... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...angles of the paral- H 'lelograms which make the gnomon.' F D K BGC PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number...undivided 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... | |
 | 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 - 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 equal to the... | |
 | 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 - Geometry - 1841 - 378 pages
...the opposite angles ' of the parallelograms, which make the gnomon.' PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number...undivided 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... | |
 | Euclides - 1842 - 316 pages
...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 number...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... | |
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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. 
