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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... "
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ... - Page 158
by Miles Bland - 1819 - 377 pages
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Lessons on form; or, Introduction to geometry as given in a Pestalozzian ...

Charles Reiner - 1837
...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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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...square of AC. 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided 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 figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...half 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 square...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...the 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 ; join EB,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...straight line, &c. QED PROP. VIII. THEOR. 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...equality, by transposition. PROP. 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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...straight line, &c. QED PROP. 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 equivalent to the square of the straight line, which...
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Proceedings

Scotland free church, gen. assembly - 1847
...on the 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 unequal...
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - Algebra - 1845
...both cases. The first case is equivalent to the following problem. Its firet case stated and solved. " To divide a given line into two such parts that the rectangle contained by the whole and one of the parts shall be equal to the square of the other." If we call x the greater of the two...
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