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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 on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the... "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page 96
by Robert Potts - 1860 - 361 pages
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...AH. Which was to be done. PROP. XII. THEOR. In obtuse-angled Mangles, if a perpendicular be dratcn 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...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 38

Perry Fairfax Nursey - Industrial arts - 1843
...Eu.) it is.— " The square of the side subtending the obtuse angle is greater than the squares of the sides containing the 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 317 pages
...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 rectangle contained by the side uponwhich, when produced, the perpendicular falls, and the straight line intercepted between the perpendicular...
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The British Annals of Education for ...: Being The Scholastic ..., Volume 1

Education - 1844
...is equal to the square of half the line. 7. 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...square of AH. QE r. PROPOSITION XII. 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 subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...=2b(a + b+ a 8 . 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 square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...(a + b} + a'. 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 square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...square of the 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 square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...between the 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 square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849
...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 rectangle contained by the Me upon which, when produced, the perpendicular falls, and the straight line intercepted without the...
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