 | George Darley - Geometry - 1828 - 190 pages
...upon right lines, one foot, one yard, &c. &c. in length respectively. ART. 89. " If there be 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... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...divided into any number of partt, the rectangle contained by the tiro lines shall be equal to tht sum of the rectangles contained by the undivided line, and the several parts of the tliridfd line. Let AB and С be two straight lines, of which AB is divided into the parts AI), DE,... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...sake of brevity, be Jj fj. Q " called the gnomon AGK or "EEC." AE DEC PROP. I. THEOR. If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained by tlte two straight lines is equal to the rectangles contained by the undivided line, and the several... | |
 | 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 number...Let A and BC be two straight lines ; and let BC be divid- Book II. ed into any parts in the points D, E ; the rectangle contained l-— v*"' by the straight... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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 number...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 number...undivided line, and the several parts of the divided line. II. If a straight line be divided into any two parts, the rectangles contained by the whole and each... | |
 | 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
...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... | |
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If there be imo 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. 
