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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 on the line between the points of section, is equal to the square on half the line. "
The first and second books of Euclid explained to beginners, by C.P. Mason - Page 144
by Euclid, Charles Peter MASON - 1872
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...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 also into...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. 4. Equal straight...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...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 also into...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. Let the straight...
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A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - Algebra - 1852 - 352 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 first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 pages
...parallelograms 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...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 Une. LET the straight...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...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...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. Let the straight...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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,...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. Let the straight...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 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;...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. Let the straight...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...the segments, together with twice the rectangle under * each pair of segments. / The rectangle under the unequal parts, together with the square on the line between the points of section, is equal in area to tho square on half the line. .The sum of the squares on the unequal parts is equal in area...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 532 pages
...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 H 46 I. "upon С В describe the square С F : draw BE ; through...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...one of its angles equal to a given rectilineal angle. Is this a determinate problem? 6. If a straight line be divided into two equal parts, and also into...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. Prove this proposition...
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