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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... "
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 134
by Charles Reiner - 1837 - 215 pages
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...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...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852 - 152 pages
...equals 48, which is less than 64, or the square of 8.] OF EUCLID. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either...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,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...kd PEOPOSITION XII. — THEOREM. In obtuse-angled triangles, if a perpendicular be drawn froni any of the acute angles to the opposite side produced,...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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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853 - 334 pages
...divided in K, as was required. Which was to be done. PEOP. XII. THEOE. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the squares of the sides including the obtuse angle, by twice the rectangle contained by either of those sides, and the straight...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...obtuse-angled triangle if a perpendicular be drawn from the vertex of either of the acute angles upon the opposite side produced, the square of the side subtending the obtuse angle is greater than the sum of the squares of the sides forming the obtuse angle by twice the rectangle contained by the side...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 532 pages
...to be done. PROPOSITION XII.— THEOEEM. In an obtuse-angled triangle (ABC), if a perpendicular (AD) be drawn from either of the acute angles to the opposite side prolonged, the square of the side (AB) subtending thf ebtuse angle is greater than the squares of the...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 336 pages
...the 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,...obtuse angle is greater than the squares, of the sides contammg the obtuse angle, by twice the rectangle contained by the side upon which, when produced,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...catting off from it a part equal to their difference, and so on continually. PROP. XIL THEOREM. In obtuse-angled triangles, if a perpendicular be drawn...the opposite side produced, the square of the side tubtending the obtuse angle, ii greater than the squares of the sides containing the obtuse angle,...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...the square of the straight line, which is made up of the whole line and that part. In obtuse angled triangles, if a perpendicular be drawn from either...of the acute angles to the opposite side produced, tho square of the side subtending the obtuse angle is greater than GEOMETRICAL MEMORANDA. — PERPEls-DICULARS....
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858 - 134 pages
...perpendicular It drawn from cither of tlte acute s to the opposite sidt produced, the square of the fide subtending the obtuse angle is greater than the squares of the sides containing the rib'use angle by tiriee the rect. contained by the side upon which when produced the perp. falh, and...
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