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" IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Side 58
av Euclides - 1841 - 351 sider
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Annual Report of the Normal, Model, and Common Schools in Upper Canada for ...

Upper Canada. Chief Superintendent of Schools - 1854
...the whole line is equal to the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ; the squares of the unequal parts are together double of the squares of half the line, and of the squares of the line between...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...straight line (AB) be divided into two equal, and also into two unequal parís (in С and D), tlie squares of the two unequal parts are together double of the square of half the line (AC), and of the square of the Km (GD), between the points of section : that is, A D+ DB= = twiee AC?...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 12. If a straight line be divided into two equal and also...square of the line between the points of section. 11. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...and adding c2 to each member of this equality, we shall have, or4a6+c2=(c+2i)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also...unequal parts are together double of the square of halj the line, and of the square of the line between the points of section. Let the straight line AB...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...of AB and В С together. PROP. IX. THEOREM. If a 'traight line be divided into two equal, and aim into two unequal parts; the squares of the two unequal...double of the square of half the line, and of the ajuare of the line between t he points of section. Let the straight line AB be divided into two equal...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...the square on the hypothenuse be fire times that on one of the sides; compare the two sides. 4. If a straight line be divided into two equal and also into two unequal parts; the rectangle contained by the unequal parts together with the square of the line between the points of...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...manifest that the rectangles about the diameter of a square are likewise squares. L. — EUCLID II. 5. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 59 sider
...two right angles. At what angles are the sides of a regular duodecagon inclined to each other? 3. If a straight line be divided into two equal, and also...square of the line between the points of section. If the sum of the squares of the distances of a point P from two fixed points is constant, the locus...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 sider
...and bisect each other, the straight lines joining their extremities will form a parallelogram. 9. If a straight line be divided into two equal and also...square of the line between the points of section. Prove this proposition also by algebra. No. II. OBLIGATORY PORTION. Second Paper. 1. If a negative...
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volum 3

1858
...squares of the two parts, together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided into two equal, and also...square of the line between the points of section. 7. AOB is the quadrant of a circle, whose centre is O ; from any point C in its arc draw CD perpendicular...
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