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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... "
Euclid's Elements of geometry, books i. ii. iii. iv - Side 66
av Euclides - 1862
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Hermathena, Volum 4

1883 - 548 sider
...the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing it ; (/). In an isosceles triangle whose vertical angle...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 sider
...divided at H, to that the rectangle AB, BH it equal to the square on AH. QEF PROPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute anglet to the opposite side produced, the square on the side subtending the obtuse angle it greater...
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The Practical Teacher, Volum 3

1884 - 708 sider
...the line between the points of section, is equal to the square on half the line. Prop, s, Bk. H. 3. In obtuse-angled triangles, if a perpendicular be...subtending the obtuse angle is greater than the squares containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced,...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 sider
...BD ; and FH is the square of AH ; therefore the rectangle AB, BH is equal to the square of AH. . — 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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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 sider
...that the sum of the triangles APB, PCD is half the parallelogram. 5. In an obtuse-angled triangle, if a perpendicular be drawn from either of the acute angles to the opposite side produced, prove that the square of the side subtending the obtuse angle is greater than the squares of the sides...
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University of Oxford. Examination of women. Examination papers

Oxford univ, local exams - 1885 - 358 sider
...square on the line between the points of section. 7. Describe a square upon a given straight line. 8. In obtuse-angled triangles, if a perpendicular be...than the squares on the sides containing the obtuse augle by twice the rectangle contained by the side on which, when produced, the perpendicular falls...
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The Practical Teacher, Volum 4

1885 - 630 sider
...between the points of section, is equal to the square on half the line. Euclid, Bk. II., Prop. 5. 2. In obtuse-angled triangles, if a perpendicular be...drawn from either of the acute angles to the opposite sideproduced, the square on the side subtending the obtuse angle, is greater than the squares on the...
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Annual Report

Canada. Department of the Interior - 1888 - 756 sider
...squares on half the line and on the line between the points of section. 6. In an obtuse angled triangle the square on the side subtending the obtuse angle is greater than the squares on the other sides by twice the rectangle contained by one ot those sides, and the pai't of it produced, included...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889 - 356 sider
...parts, is invariable, in whatever way the line may be so divided. 5. In an obtuse-angled triangle, if a perpendicular be drawn from either of the acute angles to the opposite side produced, prove that the square of the side subtending the obtuse angle is greater than the squares of the sides...
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Greek Geometry from Thales to Euclid

George Johnston Allman - 1889 - 266 sider
...the sum of the squares on the sides which contain the acute angle ; (e). In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing it ; (/). In an isosceles triangle whose vertical angle...
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