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" IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Side 58
av Euclides - 1841 - 351 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...+ 4BC. AC. Now BC2+ BC.AC = AB.BC " (3. 2.) and therefore AD2=AC+ 4AB.BC. QED" PROP. IX. THEOR. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...line. Wherefore, " if a straight line" &c. QED HL A. M X CB D / G K M 0 P / R / PROP. IX. THEOR. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts : The squares of AD, DB are together...
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Solutions of the Cambridge Problems, from 1800 to 1820, Volum 2

John Martin Frederick Wright - 1836
...parallelogram equal to a given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight line be divided into two equal, and also...square of the line between the points of section. 3. If two straight lines within a circle cut one another, the rectangle contained Ъу the segments...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...is also manifest, that the square of any line is quadruple of the square of half that line. IX. If a straight line be divided into two equal, and also...square of the line between the points of section. X. If a straight line be bisected, and produced to any point, the square of the whole line thus produced,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...CB, the square of any line is quadruple of the square of half that line. PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; the squares of AD, DB, are together...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...or4ai+c2=(c-|-2i)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...XH ; and that these = 4 AK + XH, and that these last = 4 AB x BC + AC*. PROPOSITION IX. Theorem. If a straight line be divided into two equal and also into two unequal parts, the squares of the two un- ^ equal parts are together double / GJ.^J? of the square of half the line, and /'^..^ \ \ \ of...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...and BC added together in one straight line. * Wherefore, if a straight line, &c. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the unequal parts are together double of the square of half the line, and of the square of the line between...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. IF a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts : the squares of AD, DB are together...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. If a straight line be divided into two equal, and also...the squares of the two unequal parts are together doable of the square of half the line, and of the square of the line between the points of section....
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