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

John Playfair - Euclid's Elements - 1806 - 311 pages
...Which was to be done, Book II. 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 side subtending the obtuse aigle is greater than the squares of the sides contain ng the obtuse...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...AH. Which was to be done. 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 side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...was to be done. PROPOSITION 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 side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Geometry - 1835 - 513 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...side upon which, when produced, the perpendicular fulls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 471 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 upon which, tchen produced, the perpendicular falls, and the straight line intercepted between the perpendicular...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...of the sides containing the right angle. 10. 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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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
....'. AS x BH = AH*. 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 Euclid

Euclid - Geometry - 1838 - 416 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 upon which, wnen produced, the perpendicular falls, and the straight line intercepted without the triangle between...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...Which was to be done. PROP. XII. THEOR. In an obtuseangledtriangle, if a perpendicular be drawnfrom 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 figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...obtuse-angled triangle, the square of the side subtending the obtuse angle exceeds the sum of the squares of the sides containing the obtuse angle, by twice the rectangle contained by either of those sides and the produced part of it intercepted between the perpendicular let fall on...
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