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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. "
Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry - Página 80
por John Playfair - 1829 - 186 páginas
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 páginas
...CB, together with the square of BC. If therefore a straight line, &c. QED PROPOSITION IV. THEOB. — If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 páginas
...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 - 546 páginas
...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 - 444 páginas
...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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 páginas
...rectangle AC, CB, together with the square of BC. Wherefore, If a straight line ScQED PROP. IV. THEOR. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C : the square of AB shall be equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 páginas
...therefore, multiplying both members of this equality by c, we shall have ac=ic+c2. PROP. IV. THEOR. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 páginas
...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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1847 - 358 páginas
...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, Volumen2

Great Britain. Committee on Education - 1847 - 710 páginas
...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 - 52 páginas
...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...
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