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" If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of... "
The first six books of the Elements of Euclid, with numerous exercises - Page 36
by Euclides - 1853 - 147 pages
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...<•! a + xx + aa=(aa + %ax+xx=) a+xf; that is, the rectangle contained by the line produced and part produced, together with the square of half the line bisected, is equal to the square of the line made up of the half, and part produced. QKD Cor. Hence, if three lines ,r, a 4 ,r, and 2rt + ,r...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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 part. Let the straight line AB be divided into any two parts in the point C; four times...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...PROP. VIII. (VII.) If a straight line be divided into five equal parts, the square of the whole line is equal to the square of the straight line, which is made up of four of those parts, together with the square of the straight line which is made up of three of those...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...THEOR. If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together...half and the part produced. Let the straight line AB be bisected in C, and produced to the point A B k) ; the rectangle AD.DB, together with the square...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...bisected, and produned to any point; the rectangle contained hy the whole line thus produced, and Ihe part of it produced, together with the square of half...which is made up of the half and. the part produced. Prop. VII. Theor. If a straight line be divided into any two parts, the squares of the whole line,...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...VII. 9. THEORKM. If a straight line be divided into five equal parts,- the square of the ~vhok line is equal to the square of the straight line, which is made up of four of those parts, together with (he square of the straight line which is made up of three of those...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...THEOR. if a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square nf half the. line bisected, is equal to the square of the straight line which is made up of the half...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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 tip of the whole and that part. j Let the straight line AB be divided into any two parts in the point...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 part. Let the straight line AB be divided into any two parts in the poin С ; four times...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 326 pages
...together with the square of half the line biseeted, is equal to the square of the straight line whieh is made up of the half and the part produced. Let the straight line AB be biseeted in C, and produeed to the point D ; the reetangle AD.DB, together with the square of CB,...
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