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" The squares on two sides of a triangle are together equal to twice the square on half the third side and twice the square on the median to that side. If ABC be a... "
The American Mathematical Monthly: The Official Journal of the Mathematical ... - Side 52
1920
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First Lessons in Geometry

Thomas Hill - 1855 - 152 sider
...6. This Pythagorean* proposition gives us a good way of trying whether an angle is a right angle. If the sum of the squares on two sides of a triangle is just equal to the square on the third side, we may know that the angle opposite this third side is...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Bind 2

William Thomas Brande, George William Cox - 1866 - 972 sider
...square on one side is equal to the sum of the squares on the other two ; according to the second, if the sum of the squares on two sides of a triangle is equal to the square on the third side, the triangle is right-angled. HYPOTHESIS. In Physics and Natural Science,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 sider
...himself the requisite figures in the cases where they are not given. 1. The tum of the squares on the sides of a triangle •is equal to twice the square on half the base, together with twice the square on the straight line which joins the vertex to the middle point...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 sider
...the requisite figures in the cases where they are not given. 1. Tlie sum 'f fhe squares on the tidei of a triangle is equal to twice the square on half the base, together with twice the square on the straight line which joint the vertex to the middle point...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - 1876 - 66 sider
...is less than, equal to, or greater than, the sum of the squares on the other tsvo sides. THEOR. 12. The sum of the squares on two sides of a triangle is double the sum of the squares on half the base and on the line joining the vertex to the middle point...
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Report of the Secretary for Public Instruction ..., Bind 33

Queensland. Department of Public Instruction - 1909 - 144 sider
...given the base, the vertical angle, and the difference of the sides. 11. Prove that the difference of the squares on two sides of a triangle is equal to twice the rectangle rontainrd by the third side and the distance of its mid-point from the foot of the altitude...
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Exercises on Euclid and in Modern Geometry

James McDowell - 1878 - 310 sider
...AC is equal to twice the rectangle under BC and DE. Q. i '.. I). 41. The sum of the squares on the sides of a triangle is equal to twice the square on half the base, together with twice tlie square on the bisector of base. In the figures to (40), the triangle...
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Elementary Geometry ...

James Maurice Wilson - 1878 - 450 sider
...is less than, equal to, or greater than the sum of the squares on the other two sides. THEOREM 12. The sum of the squares on two sides of a triangle is double the sum of the squares on half the base and on the line joining the vertex to the middle point...
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 396 sider
...triangle, having each of the angles at the base double of the third angle. 9. The sum of the squares on the sides of a triangle is equal to twice the square on half the base, together with twice the square on the straight line which joins the middle point of the base...
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The Competitor, Bind 1–2

1882 - 486 sider
...the fcot of tha perpendicular let fall from the opposite angle. This is Euclid, II. 18. 4. Prove that the sum of the squares on two sides of a triangle is double the sum of the squares on half the base and on the line joining the vertex to the middle point...
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