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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 on the other part, is equal to the square on the straight line which is made up of the whole and that... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 85
by John Mason Good - 1813
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. FG it Upon AB describe the square A CDB ; (l. 46.)...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...made up of the half and the part produced. 8. Divide a given 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 of the other part. PRELIMINARY GENERAL EXAMINATION. Christmas, 1864. WEDNESDAY,...
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An elementary course of practical mathematics, Part 1

James Elliot - 1860
...Ex. C), the altitude of the triangle being a and the base b 1 8. A st* line a being divided so that the rectangle contained by the whole line and one of the parts is equal to the square of the other part, compute the lengths of the two parts. Ans. £a ( V 5 —...
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The elements of algebra. [With] Answers

Robert Fowler - 1861
...&c. &c. according to the explanations in p. 7. 5. Divide a line а feet long 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. Let x = the length of the greater part, in feet. ....
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...with the square on AC. Conclusion. — Therefore, if a straight line, &o. QED PROPOSITION 8. -THEOREM. If a straight line be divided into Any two parts,...line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole line and...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...straight line (AB) be divided into ang two parts (at C), Jour times the rectangle (AB, BC) contained bg the whole line, and one of the parts, together with the square of the other part (AC), is equal to the square of the straigh t line (AD), which is made up of the whole andthalpart...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. c KD Upon AB describe the square A CSB; (i. 46.) bisect...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. FG OKD Upon AB describe the square A CDB; (l. 46.)...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...straight line, &c, QED PROP. VIII.— THEOREM. 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 uf the other part, is equal to the square of the straight line which is made up of the whole and that...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 317 pages
...involution, a2 — 2oc+c2=62. This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. • If a straight line be divided into any two parts, four times the rectangle cnntained by the whole line, and one of the parts, together with the square of the other part, is equal...
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