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Bøker Bok 2130 av 192If a straight line be divided into two equal parts, and also into two unequal parts;...
" If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Side 56
av John Playfair - 1832 - 333 sider
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...the diameter of a square are likewise squares. V. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained...section, is equal to the square of half the line. COR. From this proposition it is manifest, that the difference of the squares of two unequal lines...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 sider
...equal to the square of one of them. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained...square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB, together with the square of CD, is...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained...square of half the line. Let the straight line AB he divided into two equal parts in the point C, and into two unequal parts at the point D ; the rectangle...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...two equal parts, and also into two unequal parts, the rectangle A contained by the unequal parts, I together with the square of the line between the points...section, is equal to the square of half the line. Proved by showing that BC* = figs. CM + HG +LF; and that these = figs. AH + LF ; and these = AD x DB...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...square on half the line. PROP. V THEOR. If a straight line be divided into two equal parts, and aim into two unequal 'parts ; the rectangle contained...equal parts in the point C, and into two unequal parts at the point D : the rectangle AD'DB, together with the square of CD, shall be equal to the square...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. two unequal parts: the rectangle contained by the...square of half the line. • Let the straight line AH be divided into two equal parts in the point C, and into two unequal parts at the point D ; the...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...half. PROP. V. THEOR. If a straight line (AB) be bisected (in c), and be also divided unequally (in D), the rectangle contained by the unequal parts, together with the square of the part intermediate between the points of section, is equal to the square of half the line. Upon AC describe...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...square of the half. PROP. V. THEOR. If a straight line be bisected, and be also divided unequally, the rectangle contained by the unequal parts, together with the square of the part intermediate between the points of section, is equal to the square of half the line. P E_ AD PROP....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...a square are likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two unequal parts; the rectangle contained...equal parts in the point C, and into two unequal parts at the point D; the rectangle AD, DB, together with the square of CD, shall be equal to the square...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...denoted by a and b; then, (a-\-b)2 PROP. V. THEOR. If a straight line lie divided into two equal parts, and also into two unequal parts ; the rectangle contained...into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB, or AD.DB+CD2= CB2. Upon CB describe...
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