 | Robert Potts - 1868 - 434 pages
...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 BCbe... | |
 | 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
...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
...and EL is equal to BG, which is equal to A, Therefore the rectangle contained by the lines A and BC is equal to the sum of the rectangles contained by the undivided line (A) and the several parts (BD, DE, and BC) of the divided line (BC). The beginner must carefully observe... | |
 | 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
...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; 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 BO... | |
 | Edward Atkins - 1874 - 426 pages
...which make the gnomon. PROPOSITIONS. Proposition 1.— 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...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 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. a Let A and BC... | |
 | Euclides - 1874 - 120 pages
...parallelograms which make the ° *-* ^ gnomon. PROPOSITION 1. 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... | |
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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. 
