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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... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 55
av Euclid, Robert Simson - 1821 - 516 sider
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...are equal to twice the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four...equal to the square of the straight line which is made up of the whole and the first mentioned part. Let the straight line AB he divided into any two parts...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...KF, and that these = 2 AH + KF ; ;and that these = 2 AB x BC + AC*. CBD PROPOSITION VIII. Theorem. If a straight line be divided into any two parts, four...square of the other part, is equal to the square of the line made up of the whole and that part. R In the construction of the figure it is necessary to show...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into any two 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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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 sider
...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...rectangle AB, BC, together with the square AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Ir a straight line be divided into any two parts, four...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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...AC. Wherefore, if a straight line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided into any two parts, four times the rectangle contained...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 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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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 Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...AB, BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Iff a straight line be divided into any two parts, four...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...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...equal to the square of the straight line which is made up of the whole and the first-mentioned part. Let the straight line AB be divided into any two parts...
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