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" Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. "
A Supplement to the Elements of Euclid - Page 349
by Daniel Cresswell - 1819 - 410 pages
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The Calendar of Owens college, Manchester

Manchester univ - 1877 - 544 pages
...contained by the parts of a straight line will be greatest when the parts are equal. 7. To divide a straight line into two parts such that the rectangle contained by the whole line, and one of the parts may be equal to the square on the other part. If AB bo the straight line, ABCD the square...
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The Mathematical Gazette, Volume 2

Mathematics - 1904 - 500 pages
...this, he reduced the problem of the construction of the isosceles triangle required to the cutting of a straight line into two parts, such that the rectangle contained by the whole line and one part is equal to the square on the other part, and this he put into the second book, where it stands...
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The Elements of Plane Geometry

Euclid - 1845 - 336 pages
...in Prop. 8 or (b -a) ins. in Prop. 10; then (a + 6) (a - b) = a? - b*, or 183. PROP. 12. To divide a straight line into two parts such that the rectangle contained by the whole line and one part may be equal to the squares on the other part. To divide the given straight line AB into two parts...
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Report of the examination held (Dec. 1859)-73

Cowley Oxon, dioc. school - 1860 - 318 pages
...parts. Give the proof. 10. Describe a square which shall be equal to a given rectilineal figure. 11. Divide a given straight line into two parts such that the rectangle contained by the two is the greatest possible. 12. What sort of triangles as to their angles are those whoso sides are...
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Calendar

University of St. Andrews - 1905 - 682 pages
...the points of contact. MATHEMATICS (FIRST PAPER). TUESDAY, MARCH 21, 1905 — 9 TO 11 AM 1. Divide a line into two parts such that the rectangle contained by the whole line and one part may be equal to the square on the other part. If the length of the line be 10, find to two places...
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Calendar

University of St. Andrews - 1900 - 670 pages
...point D ; show that the rectangle AD, DB together with the square on CD is equal to the square on CB. Divide a given straight line into two parts such that the rectangle contained by them shall be the greatest possible. 17. Two circles touch one another internally ; show that the straight...
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Calendar

University of St. Andrews - 1891 - 440 pages
...and AB respectively of a triangle ABC. Show that BD- + CE2 + AF2 = CD2 + AE2 + BF:!. 3. To divide a straight line into two parts, such that the rectangle contained by the whole and one part may be equal to the square on the other part. If the given straight line be 10 inches...
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modern geometry

Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - Geometry - 1963 - 198 pages
...E. Prove that X {KCZD} = {EALD} = X {KCYD}, and that XYZ is a straight line. APPENDIX. THE PENTAGON. To divide a given straight line into two parts such that the square on the greater part may be equal to the rectangle contained by the whole line and the smaller...
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Elementary Geometry

Geometry - 1973 - 204 pages
..., 345 APPENDIX I. Euclid II. 14 353 Euclid in. 35, 36 354 APPENDIX II. THE PENTAGON. CONSTRUCTION. To divide a given straight line into two parts such that the square on the greater part may be equal to the rectangle contained by the whole line and the smaller...
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Paractical Geometry Based on the Various Geometry Books by Godfrey and Siddons

480 pages
...this can be done by employing the properties of similar triangles. CONSTRUCTION OF REGULAR PENTAGON. To divide a given straight line into two parts such that the square on the greater part may be equal to the rectangle contained by the whole line and the smaller...
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