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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...line be divided into any two parts, four times the reetangle eontained by the whole line, arid ohtt of the parts, together with the square of the other part> iS H equal to the square of the straight line whieh is made up of the whole and the first-mentioned part....
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...solutions. For example, if it be required to divide a given straight line 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; this problem is determinate. If on the other hand,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...together equal to the square of the whole line. ..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 rectangle contained by the two parts together with the square of the foresaid part....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...twice the rectangle contained by the lines together with the " square of the difference of the lines. PROP. VIII. THEOR. If a straight line be divided into...rectangle contained by the whole line, and one of I he parts? together with thesquare of the other part, is equal to the square of the straight line...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...twice the rectangle contained by the lines together with the " square of the difference of the lines." PROP. VIII. THEOR. If a straight line be divided into...parts, together with the square of the other part, is equalto the square of the straight line which is made up of the whole and the jir si-mentioned part....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...with the square of AC. Wherefore, " if a straight line," &c. QED PROP. VIII. THEOR. JJ F E a 34. 1. If a straight line be divided into any two parts,...and one of the parts; together with the square of t/ie other part, is equal to the square of the straight line which is made up of the whole and that...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 471 pages
...the rectangle contained by the " lines together with the square of the difference of the " lines." PROP. VIII. THEOR. If a straight line be divided into...contained by the whole line, and one of the parts, togetiier with the square of the other part, is equal to the square of the straight line which is made...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...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,...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 - Geometry - 1837 - 390 pages
...of two lines, is equal to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into...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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