| Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...to £ (AB+CD)xEF. Hence the theorem; the area of a trapezoid, etc. THEOREM XXXV. If one of two lines is divided into any number of parts, the rectangle contained by the two lines is equal to the sum of the several rectangles contained by the undivided line and the several... | |
| Edinburgh univ - 1871 - 392 pages
...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 - 136 pages
...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... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...signs +, — , and =. They will accordingly be occasionally employed. PBOPOSITION I. If there are two straight lines one of which is divided into any number...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 - 376 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 - 588 pages
...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 - 400 pages
...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 number...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... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...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 - 342 pages
...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 number...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 - 428 pages
...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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