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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1847 - 317 sider
...denoted by a and b ; then, PROP. V. THEOR. If a straight linebe divided into two equal parts, andalsoinlo two unequal parts ; the rectangle contained by the...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 definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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, and...section, is equal to the square of half the line. EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...angle is equal to the squares described upon the sides containing the right angle. SECTION III. 1. If a straight line be divided into two equal parts, and...of section is equal to the square of half the line. 2. In any triangle the square of the side subtending contained by either of these sides, and the straight...
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Minutes of the Committee of Council on Education, with Appendices, Volum 1

Great Britain. Committee on Education - 1848
...angle is equal to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts, and...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less...
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Report of the Committee of Council on Education (England and Wales ..., Utgave 1

Great Britain. Council on Education - 1848
...angle is equal to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts, and...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less...
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The English Journal of Education, Volum 2

1848
...Tate's Geometry," &c. page 39, where a new proof is given of this important theorem. SECTION 3. 1. If a straight line be divided into two equal parts, and...parts, the rectangle contained by the unequal parts, togelher with the square of the line between the points of section, is equal to the square of half...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 sider
...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, 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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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...
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The English Journal of Education, Volum 5

1851
...given 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...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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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 sider
...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, and...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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