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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. "
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 117
by Charles Reiner - 1837 - 215 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...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 - 434 pages
...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 pages
...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, the...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 to the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...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, the...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 squares...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...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 - Algebra - 1847 - 358 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 - 710 pages
...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 pages
...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, the...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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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...concise, than in ordinary language. The proposition, (Euc 4. 2,) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...rectangle AC, CB together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to...
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