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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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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - Algebra - 1848 - 252 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 ...

Euclides, Thomas Tate - 1849 - 108 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,...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: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 317 pages
...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...be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB....
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 226 pages
...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, Volume 1

Great Britain. Committee on Education - School buildings - 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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Minutes of the Committee of Council on Education, with Appendices, Volume 2

Great Britain. Committee on Education - 1850
...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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AN INTRODUCTION TO ALGEBRA, BEING THE FIRST PART OF A COURSE OF MATHEMATICS ...

JEREMIAH DAY, D.D. LL. D. - 1850
...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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 216 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. . Let the line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent...
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ELEMENTARY GEOMETRY, WITH APPLICATIONS IN MENSURATION.

CHARLES DAVIS, L.L. D. - 1850
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two -^ HC parts at the point E : then will the square described on AB be equivalent...
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Papers for the Schoolmaster

1852
...to a given triangle, and have one of its angles equal to * Riven rectilineal angle. SECTION II. 1. If a straight line be divided into any two parts,...together with twice the rectangle contained by the paits. 2. If a straight line be divided into two equal and also into two unequal parts, the squares...
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