| Edinburgh univ - 1871
...the other two sides of it; the angle contained by these two sides is a right angle. 3. 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... | |
| Euclides - 1871
...AB, CD = sum of reet. AB, CE and rect. AB, EF and rect. AB, FD. QED Ex. If two straight lines be each **divided into any number of parts, the rectangle contained by the two** lines is equal to the rectangles contained] by all the parts of the one taken separately with all the... | |
| Henry William Watson - Geometry - 1871 - 285 pages
...parallels, the area of the triangle will be half the area of the parallelogram. PROPOSITION 1r. If there be **two straight lines, one of which is divided into any number of** farts, the rectangle of the two straight lines shall be equal to tJ1e sum of tJ1e rectangles of the... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...the signs +, — , and =. They will accordingly be occasionally employed. PBOPOSITION I. If there are **two straight lines one of which is divided into any...contained by the two straight lines is equal* to the** sum of the rectangles contained by the undivided line and the several parts of che divided line. For... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...AB, CE and rect. AB, EF .: rect. AB, 6'/> = and rect. AB, FD. QED Ex. If two straight lines be each **divided into any number of parts, the rectangle contained by the two** lines is equal to •'he rectangles contained^ by all the parts of the one taken '.rn.t.ely with nil... | |
| Henry Major - Student teachers - 1873
...together with the complements AF, FC, is the gnomon AGK, or EHC. I. — If there be two straight linns, **one of which is divided into any number of parts;...and the several parts of the divided line. Let A and** BO be two straight lines ; of which BC is divided into any parts in the points D, E. Then the rectangle... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...ABC = square-Xy; /. square on AB - squares on AC, CB. BOOK II. RECTANGLES. PROPOSITION I. If there be **two straight lines, one of which is divided into any...undivided line and the several parts of the divided line.** a Let A and BC be two straight lines, and let BC be divided into any parts BP, PQ, QC. Then shall the... | |
| Euclides - 1874
...g. 1. — t BOOK II. PROPOSITION I. — THEOREM. (Euc. II. 1.) Jf there be two straight lines, oiie **of which is divided into any number of parts, the...contained by the two straight lines is equal to the** sum of the rectangles contained by the undivided line, and the several parts of the divided line. Let... | |
| Euclides - 1874
...opposite angles of the parallelograms which make the gnomon." PROPOSITION 1.. — Theorem. If there be **two straight lines, one of which is divided into any...the rectangle contained by the two straight lines** ^s equal to the rectangles contained by the undivided line, and the several parts of the divided line.... | |
| Edward Atkins - 1874
...opposite angles of the parallelograms which make the gnomon. Proposition 1. — Theorem. If t/iere be **two straight lines, one of which is divided into any number of parts,** t/ie rectangle contained by the two straight lines is equal to t/ie rectangles contained by the undivided... | |
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