 | Euclides - 1833 - 304 pages
...EGF. END OF FIRST BOOK. THE SECOND BOOK, IN GENERAL TERMS. PROPOSITION 1. THEOR. If there be two right lines, one of which is divided into any number of parts, the rectangle under the two linns is equal to the sum of the rectangles under the undivided line and the several... | |
 | Euclid - 1835 - 540 pages
...opposite H B B K C ' angles of the parallelograms which make the gnomon.' PROP. I. THEOR. If there be two straight lines, one of which is divided into any...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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...for the ' sake of 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...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
...miles. SECTION 5. 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
...parallelograms about a diameter, together with the two complements, is called a Gnomon. PHOP. I. If there be two straight lines, one of which is divided into any...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... | |
 | 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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...ready to apply to the demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided into any...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the 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...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... | |
 | 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
...opposite 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...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... | |
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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. 
