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" In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 62
των John Playfair - 1819 - 333 σελίδες
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Βιβλίο 1

Euclides - 1853
...divided in K, as was required. Which was to be done. PEOP. XII. THEOE. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the squares of the sides including the obtuse angle, by twice the rectangle contained by either of those sides, and the straight...

Elements of geometry and mensuration

Thomas Lund - 1854 - 192 σελίδες
...obtuse-angled triangle if a perpendicular be drawn from the vertex of either of the acute angles upon the opposite side produced, the square of the side subtending the obtuse angle is greater than the sum of the squares of the sides forming the obtuse angle by twice the rectangle contained by the side...

Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...of the side (AB) subtending thf ebtuse angle is greater than the squares of the sides (В С, С А) containing the obtuse angle, by twice the rectangle contained by the side upon which, when prolonged, the perpendicular falls, and the line, without the triangle, between the perpendicular and...

Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...(c + a - 6)' = 2 (6 + c) 1 . 2. In obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. ABC is a triangle having a right...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...continually. PROP. XIL THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side tubtending the obtuse angle, ii greater than the squares of the sides containing the obtuse angle,...

National Society's Monthly Paper

1856
...rectangle contamed by the parts. 6. In obtuse-angled triangles if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 7. Equal straight lines in a circle...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...the square of the whole line. 7. In obtuse-angled triangles if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 8. If in a circle two straight...

Manual of Method for the use of teachers in elementary schools

W. F. RICHARDS - 1856 - 184 σελίδες
...rectangle contained by the parts. 6. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted .without the triangle between the perpendicular and the obtuse angle. .7. Equal straight lines in a...

general Report on Public Instruction in the lower Provinces of the Bengal ...

JOHN GRAY - 1857
...sides of a triangle are together greater than the third side. the squares of the sides containing it by twice the rectangle contained by the side upon...perpendicular falls, and the straight line intercepted with the triangle between the perpendicular and the obtuse angle. 3. A straight line is drawn from...

Parliamentary Papers, Τόμος 25

Great Britain. Parliament. House of Commons - 1858
...part produced. 8. PROP. XII. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 9. In any isosceles triangle ABC,...




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