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" If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 53
av Euclid, Robert Simson - 1821 - 516 sider
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...may be shown of any other division of 8, as into 6 and 2, or 7 and 1.] BOOK II. PROP. V. THEOR. If a straight line be divided into two equal parts, and...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - 1852 - 336 sider
...c=3. Then 12=9+3; And 4Xl2X9+3 2 =(3X2X9) 2 ; 441 = 441. THEOREM XIII. 17O. If any quantity or number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts will be double the squares of half the quantity, plus twice...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts, and...points of section, is equal to the square of half the Une. LET the straight line ab be divided into two equal parts in the point С, and into two unequal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 sider
...line is divided be denoted by a and b; then, (a+6)* PROP. V. THEOR. If a straight line bcdividedinto two equal parts, and also into two unequal parts;...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...diameter of a square are likewise squares. PROPOSITION V. THEOR. If a straight line be divided inio two equal parts, and also into two unequal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Bok 1

Euclides - 1853
...proved. PEOP. V. THEOE. If a straight line be bisected, and also divided into two unequal parts : then the rectangle contained by the unequal parts together with the square of the part of the line intercepted between the points of section, shall be equal to the square of half the...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...л straight line (AB) be divided into two equal parts (inC), and also info two unequal parts (in D), the rectangle contained by the unequal parts, together with the square of (CD), the line between the points of section, is equal to the square of hilf the line : that is, DB...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...T) B PROP. V. THEOR. If a straight linele divided into two equal parts, andalsointo twounequalparts; the rectangle contained by the unequal parts, together...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the- point C, and into two unequal parts...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...into turn equal parts, and also into two unequal part'; the rectangle contained by the unequal parta, together with the square of the line between the points of section (or division), is equal to the square of half the line. Let the straight line AB be divided into two...
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