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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 ... - Page 58
by Euclides - 1841
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...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...points of section. Let the straight line AB be divided at the point С into two equal, Ľnd 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, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...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,...square of half the line, and of the square of the Une between the points of section. 3. If two straight lines within a circle cut one another, the rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...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...between the points of section. Let the straight line AB he divided at the point C into two equal, and at D into two. unequal parts ; The squares' of AD, DB...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...a straight line AB be divided into two equal parts AC, CB, and also into two unequal parts AD, DB ; the squares of the two unequal parts are together...square of half the line, and of the square of the tine CD, between the points of section. • . ; Or, AD2 + DB2 = 2AC2 .+ 2CD2. From the point C, draw...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then the squares of the two unequal parts are, together, double of the square of the half line, and the square of the intermediate part. Let any right line AB be cut into two equal...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...PROPOSITION IX. THEOREM. If a right line be any how cut info two equal and two unequal parts, then the squares of the two unequal parts are, together, double of the square of the half line, and the square oftJie intermediate part. Let any right line AB be cut into two equal...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...BC added together in one straight line. Wherefore, if a straight line, &c. GED PROP. IX. THEOR. If a straight line be divided into two equal, and also...unequal parts; the squares of the two unequal parts arc together double of the square of half the line, and of the square of the line between the points...
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Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...will understand this proposi-Prop. xix. tion, which is necessary for our further progress: that if a straight line be divided into two equal, and also into two unequal parts, the square of either of the equal parts (or the rectangle under both) is equal to the rectangle under the...
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - Astronomy - 1831
...angle. 7. If a straight line be divided into two equal, and also into two unequal parts, prove that the squares of the two unequal parts are, together,...square of the line between the points of section. 8. If a straight line touch a circle, and, from the point of contact, a straight line be drawn cutting...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...AC!+4BC'+4BC. AC. Now BC' + BC.AC = AB.BC "(3. 2.) and therefore AD = AC +4 AB.BC. QED" PROP. IX. THEOR. If a straight line be divided into two equal, and also...two unequal parts; the squares of the two unequal purls are together double of the square of half the line, and of the square of the line between the...
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