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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. "
Examination papers collected by A. Clark as a student and as an examiner - Página 38
1867
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 páginas
...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 square of the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 páginas
...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 square of the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 square...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 páginas
...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 square of the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 páginas
....: EB : GI :: EH : HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH :: FG : HG. (23.) If a straight line be divided into two equal, and also into two unequal parts, and be produced, so that the part produced may have to the whole line so produced the same ratio that...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 páginas
....-. EB : GI :: EH . HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH . FG . HG. (23.) If a straight line be divided into two equal, and also into two unequal parts, and be produced, so that the part produced may have to the whole line so produced the same ratio that...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 páginas
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 páginas
...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 square of the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 páginas
...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 square of the...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - 1825
...given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight Hue 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...
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