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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 English Journal of Education - Page 272
1851
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 pages
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. 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 Calendar of King's College, London

1850
...produced, the exterior angle is greater than either of the interior opposite angles. 2. If a right line be divided into two equal parts, and also into...section, is equal to the square of half the line. 3. In every triangle, the square of the side subtending either of the acute angles, is less than the squares...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 pages
...divided into four equal parts. In what case will the diameter bisect the angle of a parallelogram? 3. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 4. Equal straight lines in a circle are equally distant from the centre ; and conversely, those which...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...same 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,...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 pages
...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 pages
...the parallelograms about the diameter of a square are likewise squares. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts,...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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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 pages
...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 Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 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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