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" 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 up of the whole and that... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 53
by John Playfair - 1855 - 318 pages
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Papers for the Schoolmaster, Volume 2

1852 - 316 pages
...rectangle contained by the whole line thus produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. ANSWERS TO THE EXAMINATION PAPER ON SCHOOL MANAGEMENT* (CONTINUED...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...Proposition are equal to the two squares AE and kc added together.] PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...to the square of the straight line, which is made up of the whole and that part. [This Proposition may advantageously be omitted at the first time of...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle...equal to the square of the straight line which is made up of the whole and that part. Let the straight line AB be divided into any two parts in the point...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...square of AC. Wherefore, if a straight line, etc. QED PROPOSITION VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...to the square of the straight line, which is made of the whole and that part. Let the straight line AB be divided into any two parts in the point C ;...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...of a С. Wherefore, if a straight line, &c. QED PROPOSITION VIII. — THEOREM. If a straight line be divided into any two parts, four times the rectangle...equal to the square of the straight line which is made up of the whole and that part, LET the straight line ab be divided into any two parts in the point...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853 - 474 pages
...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...
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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
...other part. Let AB be the given straight line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing...
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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...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 282 pages
...parallelograms GF, EH is equal to twice the triangle KBD. 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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...divided into any two parts, four times the rectangle con'ained by the whole line, and one of the parís, 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 thai part. Let the straight line AB be divided into any two parts at the point...
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