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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 ... - Seite 41
von Euclides - 1816 - 528 Seiten
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1847 - 358 Seiten
...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, Band 2

Great Britain. Committee on Education - 1847 - 710 Seiten
...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 Seiten
...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 - 1848 - 264 Seiten
...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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 332 Seiten
...parts, the square of the whole line is equal to the squares of the two parts, together with tvtice the rectangle contained by the parts. Let the straight...CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB. Upon AB describe (Prop. 46. 1.) the square ADEB, and join BD, and through...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 Seiten
...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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Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 252 Seiten
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts....
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Minutes of the Committee of Council on Education, Band 1

Great Britain. Committee on Education - 1850
...sides which contain the right angle. Section 3. 1. If a straight line be divided into any two part» the square of the whole line is equal to the squares...parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1850 - 348 Seiten
...language. The proposition, (Euc, 4. 2.) that when a straight line is divided into two parts, tilesquare of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, Ijy involving a binomial. Let the side of a square be represented...
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Minutes ...: Correspondence, Financial Statements, Etc., and Reports ..., Band 2

Great Britain. Committee on Education - 1850 - 914 Seiten
...makes the alternate angles equal. — Define parallel lines, and alternate angles. 3. If a line be cut into any two parts, the square of the whole line is equal to the squares of the parts, and twice the rectangle contained by the parts. — Show the same Algebraically. 4. Prove tluit...
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