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" Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 154
by Daniel Cresswell - 1817 - 436 pages
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853 - 474 pages
...both are answers to the question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less part,...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...to be proved. PEOP. VIII. THEOE. If a straight line be divided into any two parts : then four times the rectangle contained by the whole line and one of the parts, together with the square of the other part shall be equal to the square of the line which is made up...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...&c. QED PROPOSITION VIII. — THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...line, etc. QED PROPOSITION VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...straight line, &c. QED PROP. VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight line to a point such that the rectangle...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 282 pages
...parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight line to a point such that the rectangle...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...into any two parts, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and one of the parts, together with the square of the other part. 5. To construct a square equal to a given rectangle. 6....
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...upon the sides which contain the right angle. 6. If a straight line be divided into anу two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square of the aforesaid part....
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...do the rectangles contained by the parts become ? 4. Divide a given straight line into two parts, so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. NATURAL SCIENCES. By MAJOR-GEN. PORTLOCK, RE, LL.D., FRS,...
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