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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. "
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ... - Side 14
af Miles Bland - 1819 - 377 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 sider
...AD2=AC2+4BC2+4BC.AC. Now BC* + BC.AC = AB.BCb ; therefore AD2=AC2+ U3.2. 4AB.BC. QED" Book II. PROP. IX. THEOR. 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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 sider
...and 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 into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Bind 5

John Mason Good - 1813 - 714 sider
...equal to the square of the straight line which is made up of the whole and that part. Prop. IX. Theor. If a straight line be divided into two equal, and also into two unequal parts; the tqniMN of the two unequal parts arc together double of the square of half the line, and of the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 sider
...straight line. Wherefore, if a straight line, &c. QED TIL F ACBT z .... 6 K / P R / PROP. IX. THEOR. 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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 sider
...divided; then will nil lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and also into two unequal parts, and be |>roduced, so that the part produced may have to the whole line so produced, the same ratio that the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 sider
...AD3=AC3+4BC3-HBC.AC. Now BC3-f BC.AC=AB.BC(3. 2); " and therefore ADs=AC3+4AB.BC. q. ED" PROP. IX. THEOR. 'If /a straight line be divided into two equal, and also into too untquai parts ; the squares of the two unequal parts are together double of the square of half...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1821 - 898 sider
...divided ; then will all lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and...of unequal section from one extremity of the given line, from its middle point, from the extremity of the part produced, and from the other extremity...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 sider
...together in one straight line. Wherefore, if a straight line, &c. Q. ED. PROP. IX. THEOR. • . | IP 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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 sider
...added together in one straight line. ^herefore, if a straight line, &c. QED Proposition IX. Theorem, 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 326 sider
.../ P R C. Now BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V PROP. IX. THEOR. ., 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...
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