| John Playfair - Euclid's Elements - 1835 - 336 pages
...brevity, be called the gno' mon AGK or EHC." A. E H I 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 straight lines is equ2l to the rectangles contained by the undivided line, and the several parts of the divided line.... | |
| Mathematics - 1835 - 684 pages
...Rectangles under the par Is of divided lines. PROP. 30. (Eue. ii. 1.) If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two lines shall be equal to the sum of the rectangles contained by the undivided line, and the several... | |
| Mathematics - 1836 - 488 pages
...together with the two complements, is called a Gnomon. PHOP. I. If there be two straight lines, one of which is divided into any number of parts ; the...contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. II. If a straight... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the parallelograms which make the gnomon. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number of parts, the...contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided into any number of parts, the...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
...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
...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 of parts; the...contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC... | |
| 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 by the two straight lines, is equal to the rectangles contained by the undieided line, and the seeeral parts of the dieided line. Let A and BC... | |
| Euclides - 1840 - 82 pages
...THEOR. The rectangle 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...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 - 192 pages
...=L'HB. Therefore, L'AB, or the rectangle contained by the two lines, is equal to L'AF+L'FH+L'HB, or the sum of the rectangles contained by the undivided line and the parts of the divided line. PROP. II. THEOR. If a straight line (AB) be divided into any two parts (AF,... | |
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