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" In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 101
by James Bates Thomson - 1844 - 237 pages
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...other, the base of that which has the greater angle shall be greater than the base of the other. 2. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of those sides...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861 - 572 pages
...a quadrilateral figure are all equal, shew that the diagonals bisect each other at right angles. 8. In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides...
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Responsions

University of Oxford - Education, Higher - 1863 - 328 pages
...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 11. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...Therefore in obtuse-angled triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...Therefore in obtuse-angled triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...twice the rectangle BC, CD. Wherefore, in obtuse-angled triangles, &c. QED PROP. XIII. — THEOREM. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of those sides,...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...XXXVI. 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 perpendicular from the obtuse angle. Let ABC be a triangle obtuse...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...Therefore in obtuse-angled triangles, &c. QED PROPOSITION XIII. THEOREM. Jn every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twicp, the rectangle contained by either of these sides,...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...And 10.5 + ^- = 16 ; then (47. I.) 400 - 256 = 144 ; and *JUi = AD as 31 before. PROP. 13. — THEOB. In every triangle, the square of the side subtending either of the acme angles is less than the squares of the sides containing that acute angle by twice the rectangle...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 580 pages
...is, the square of BA is greater than the squares of BC, CA, by twice the rectangle BC, CD. XIII. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,...
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