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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... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 53
by John Playfair - 1855 - 318 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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, four times the rectangle...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 Pierce ...

Mathematics - 1835 - 684 pages
...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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...contained by the lines together with the square of the difference of the lines. VIII. If a straight line be divided into any two parts, four times the rectangle...equal to the square of the straight line which is made up of the whole and the first mentioned part. Сок. 1. Hence, four times the rectangle contained...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected is equal to the square of the straight line, which is made up of the half of the part produced." 10. Some very useful problems may be performed by means of the...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected is equal to the square of the straight line, which is made up of the half of the part produced." 10. Some very useful problems may be performed by means of the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...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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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle...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 - Euclid's Elements - 1837 - 112 pages
...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 times the rectangle...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 - 410 pages
...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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