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" ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse... "
The student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 páginas
...AB.BH is equal to the square of AH. Which was to be done, Book II. PROP. XII. THEOR. IN obtuse angled triangles if a perpendicular be drawn from either...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 - 1827 - 513 páginas
...rectangle AB, BH is equal to the square of AH. Which was to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either...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
...the rectangle AB, BH is equal to the square of AH. Which was to be done. PROPOSITION XII. THEOR. — In obtuse-angled triangles, if a perpendicular be...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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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 páginas
...subtending the right angle is equal to the sum of the squares of the sides containing the right angle. 10. In obtuse-angled triangles, if a perpendicular be...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 - 1837 - 88 páginas
...ie, fig FK = AB% ie, fig. AD, 4. that FH = HD, 3. that .'. AS x BH = AH*. PROPOSITION XII. Theorem. In obtuse-angled triangles, if a perpendicular be...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 [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 Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 páginas
...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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The British Annals of Education for ...: Being The Scholastic ..., Volumen1

1844
...between the points of section, 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
...divided in H, so that the rectangle AB, BH is equal to the square of AH. QE r. PROPOSITION XII. THEOREM. In obtuse-angled triangles, if a perpendicular be...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 - 1846
...2a (a + b) + b>. Or(« + bf + 6 8 = 2b (a + b} + a'. PROP. XLVII. THEOR. 12. 2 Eu. In obtuse angled triangles, if a perpendicular be drawn from either...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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