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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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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...points of section. 3. Prove that 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. Section 4. 1. Divide a given straight...

The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 σελίδες
...was to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...obtuse angle, by twice the rectangle contained by the Me upon which, when produced, the perpendicular falls, and the straight line intercepted without the...

The English Journal of Education, Τόμος 4

1850
...square of the whole line. 3. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...obtuse angle, by twice the rectangle contained by that side upon which when produced, the perpendicular falls, and the straight line intercepted without...

Elements of Geometry: With, Practical Applications

George Roberts Perkins - 1850 - 320 σελίδες
...the three remainders, and it will be the area. PROPOSITION X. THEOREM. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the sum of the squares of the other two sides, by twice the rectangle of the base and the distance of the...

Minutes of the Committee of Council on Education, with Appendices, Τόμος 2

Great Britain. Committee on Education - 1850
...Parallelograms upon the same base, and between the same parallels, are equal. 3. In an obtuse angled triangle, the square of the side subtending, the obtuse angle is greater than the sum of the squares of the sides containing it by twice the rectangle, contained by the base and the...

The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...OF EUCLID. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the sides subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle,...

The Sydney University Calendar

University of Sydney - 1853
...latter side is a right angle. 7. In obstuse 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. 8. The angle at the centre of...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...be done. PROP. XII. THEOREM. 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. Let ABC be an obtuse-angled triangle,...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...be done. PROPOSITION XII. THEOR. In obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...side upon which, when produced, the perpendicular fulls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 σελίδες
...PEOPOSITION XII. — THEOREM. In obtuse-angled triangles, if a perpendicular be drawn froni any of the acute angles to the opposite side produced, the...of the side subtending the obtuse angle is greater tJian the squares of the sides containing the obtuse angle, by twice the rectangle contained by the...




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