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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...equal to the square of BC, together with the rectangle AC.CB.* If, therefore, &c. PROP. IV. THEOR. — If a straight line be divided into any two parts,...the squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...line is equal to four times the square of half the line. Also, if a line be divided into any three parts, the square of the whole line is equal to the squares of the three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...two parts in the point C, the proposition becomes the following. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts, together with twice the rectangle contained by the parts. Cor. 2....
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) the square of the whole line is equal to the squares of the parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. c B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part, Let the straight line AB be divided into any two parts in the point C : the rectangle AB, BC shall be equal to the rectangle AC, CB, together with the square...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1847 - 332 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two par.ts, the square of the whole line is equal...squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving a binomial Let the side of a square be represented...
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Minutes of the Committee of Council on Education, Volume 2

Great Britain. Committee on Education - School buildings - 1847
...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to be equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. Prove the angle in a semicircle to be a right angle. 518 mities 36 201 and 60 10* ; required...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square...
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