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" 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 of the base. "
Euclid and His Modern Rivals - Page 203
by Lewis Carroll - 1885 - 275 pages
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...produced. It also bisects the triangle. The sum of the squares on the two sides is equal in area to double the sum of the squares on half the base and on the bisecting line. It is perpendicular to it, And it bisects the opposite angle. It bisects the base,...
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First Lessons in Geometry

Thomas Hill - Geometry - 1855 - 152 pages
...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 ..., Volume 2

William Thomas Brande, George William Cox - Encyclopedias and dictionaries - 1866 - 972 pages
...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...
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An Introduction to Analytical Plane Geometry

William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...Example 8 to prove that in any triangle the squares on two sides are together double of the square on half the base and on the line joining the vertex to the middle point of the base. 10. The axes being inclined at an angle to, and the origin and axis of x being made the origin and...
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An Introduction to Analytical Plane Geometry

W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...Example 8 to prove that in any triangle the squares on two sides are together double of the square on half the base and on the line joining the vertex to the middle point of the base. 10. The axes being inclined at an angle &>, and the origin and axis of x being made the origin and...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...two following theorems. Ex. 1. In any triangle the sum of the squares on any two sides is double of the sum of the squares on half the base and on the line which joins the vertex to the middle point of the base. Let AC, a side of the triangle ABC, be bisected...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...proof. QED Ex. 1. Prove that the sum of the squares on any two sides of a triangle is equal to twice the sum of the squares on half the base and on the line joining the vertical angle with the middle point of the base. To describe a square that shall be equal to a given...
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Elementary statics

James Hamblin Smith - Statics - 1871 - 148 pages
...the triangle is at a distance 2« - aV3 from the centre of the square. 35. The centre of gravity is on the line joining the vertex to the middle point of the base, and at a n distance from the vertex = - ths distance of the middle point. 36. 4 inches. 37. V3 (side...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...proof. QED Ex. 1. Prove that the sum of the squares on any two sides of a triangle is equal to twice the sum of the squares on half the base and on the line joining the vertical angle with the middle point of the base. PROPOSITION XIV. PROBLEM. To describe a square that...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...or deduced from it, thus: -,—I JfC THEOREM (n). The squares on the sides of a triangle are double the squares on half the base and on the line .joining the vertex and the middle point of the base. From the vertex K of A AKH draw KD j. to AH. Bisect AH'm C, and join...
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