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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, the parts read in the University of Cambridge [book ... - Página 62
por Euclides - 1846
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## The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 páginas
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two...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 at the point D ; the...
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## The Calendar of King's College, London

1850 - 398 páginas
...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 two...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...
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## A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 196 páginas
...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, and also into two...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 English Journal of Education, Volumen5

1851 - 502 páginas
...rectilineal angle. upon the same side together equal to two right angles. SECTION II.—1. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. 3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two...
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## The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 páginas
...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 also into two...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 at the point D ; the...
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## A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - 1852 - 348 páginas
...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 - 146 páginas
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts, and also into two...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 at the point D; the rectangle...
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## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 páginas
...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,...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 at the point D ; the...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 336 páginas
...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;...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 in the point D ; the...
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## The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 páginas
...about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts, and also into two...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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