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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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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice the rectangle contained by the whole line and one of the parts is equal to twice the square upon that part, together with twice the rectangle contained by the parts....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...half and the produced part. PROP. XI. PROB. To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ;...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...and the produced part. .n. . PROP. XI. PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...twice the rectangle AB, BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. IF a straight line be divided into...parts, together with the square of the other part, is equivalent to the square of the straight line, which is made up of the whole and that part. ELEMENTS...
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Proceedings

Scotland free church, gen. assembly - 1847
...other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 317 pages
...2 —2ac+c 2 =6 2 . This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into...one of the parts, together with the square of the olher part, is equal to the square of the straight line which is made up of the whole and thefirst-mentioned...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...of two lines, is equal to the square of their difference, together with four tunes their rectangle. PROP. VIII. THEOR. — If a straight line be divided...parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the reel" angle contained by the whole line, and one of the parts, together with the square of the other...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...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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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853
...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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