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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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Pure mathematics, Volume 1

Edward Atkins - 1874
...together with the square on AC. Therefore, if a straight line, &c. 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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Pure mathematics, Volume 1

Edward Atkins - 1874
...together with the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts,...contained by the whole line and one of the parts, toget/ier with the square on the other part, is equal to the square on tlie straight line which is...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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. Construction. Upon AB describe the square ACDB (I....
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let AB...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...together with the square on AC. Therefore, if a straight line, &c. Q. E, D. 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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Elements of Geometry Containing Books I. to VI. and Portions of Books XI ...

James Hamblin Smith - Geometry - 1876
...be drawn from G to B and from (f to D, shew that BO D ia a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by ike whole line and one of the parts, together with the square on the other part, is equal to the square...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...AB:BC = AD:DE. PROBLEM XX. To divide a straight line in extreme mean ratio — that is to say, so that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. Let AB be the straight line. Construct the square ABDE...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...other part. Let AB\vt 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 FO CK 1) Upon AB describe the square A CDB ; (I. 46.)...
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SYLLABUS OF PLANE GEOMETRY

1876
...several parts into which the other is divided. COR. T. If a straight line is divided into two parts, the rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the rectangle contained by the two parts. COR. 2....
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