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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 Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...PROP. XLVII. THEOR. 12. 2 Eu. 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. A V str. line BD is divided into...

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

Euclid, John Playfair - 1846 - 317 σελίδες
...square of AH. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...squares of the sides containing the obtuse angle, 6y twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and...

The London University Calendar

London univ - 1846
...angle of a regular octagon ? 4. In any obtuse-angled triangle, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...is greater than the squares of the sides containing it, by twice the rectangle contained by the side on which when produced the perpendicular falls, and...

Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 σελίδες
...47; (/) ax. 3 of b. 1. 12 Th. In any obtuse angled triangle, if a perpendicular be drawn from one of the acute angles to the opposite side produced ; the square of the side subtending the obtuse angle equals the two squares of the sides containing it, and two rectangles of the produced side and its...

Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...to AB. PROPOSITION XII. THEOREM. In any obtuse angled triangle (as BAC) the square of the side (AB) subtending the obtuse angle, is greater than the squares of the sides (BC and CA) which contain the obtuse angle, by twice the rectangle contained under either of these...

The Mechanic's Magazine, Museum, Register, Journal and Gazette, Τόμος 38

1843
...EK also subtends the obtuse angle EPK of the triangle EPK, and by (12 Prop. 2 Book Eu.) It is.— " The square of the side subtending the obtuse angle...obtuse angle, by twice the rectangle contained by one of the sides about the obtuse angle, and the line intercepted without by a perpendicular to it...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 σελίδες
...the three remainders, and it will be the area. PEOPOSITION 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...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - 1847 - 478 σελίδες
...the squares of the sides containing the right angle ; but in an obtuse-angled triangle (Euc. n. 12), the square of the side subtending the obtuse angle is greater than the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the...

Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 σελίδες
...(AC + BC) . (AC - BC) = AB . (AD + BD) in the 1st fig. THEOREM XXVJU. 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 one of the sides containing the...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...other part. 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. PROP. XIII. THEOREM. In every...




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