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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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## The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 414 sider
...=2BE+2AE. QED 334. Con. Subtracting (2) from (1) in (333), we have AB'-AC'= 2BCXED. Hence, the difference of the squares on two sides of a triangle is equal to twice the product of the third side by the projection of the median upon that side. Let the student prove the...
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## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 sider
...AB2 ~ AP' = BM3 ~ PM2, = (BM + PM) (BM~PM), = BP. CP in both figs. THEOREM (10) — The difference of the squares on two sides of a triangle is equal to twice the rectangle tinder the base and the projection of the median, bisecting the base, on the base. (I) B...
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## Rider Papers on Euclid (books I. and II.)

Rupert Deakin - 1891 - 102 sider
...in AB produced in K. Prove that the rectangle AB, AK is equal to the square ou BK. 5. The difference of the squares on two sides of a triangle is equal to twice the rectangle contained by the base and that part of the base intercepted between the middle point of the...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 460 sider
...by the sum and difference of the hypotenuse and the other side. [i. 47 and n. 5.] 8. The difference of the squares on two sides of a triangle is equal to twice the rectangle contained by the base and the intercept between the middle point of the base and the foot...
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## A Text-book of Geometrical Deductions: Corresponding to Euclid, book ..., Bog 2

James Blaikie - 1892 - 74 sider
...straight lines is equal to the difference between their squares. § 33, Ex. 4. The difference between the squares on two sides of a triangle is equal to twice the rectangle contained by the base and the segment of the base intercepted between its midpoint and the...
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## The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 188 sider
...BC '; prove that if AB is greater than DB then AC is less than DC. 2. If the difference of the areas of the squares on two sides of a triangle is equal to the area of the square on the third side the triangle is right-angled. 3. Part of the locus of a point...
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## Numerical Problems in Plane Geometry with Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 168 sider
...are composed of the same number of similar triangles, similarly placed, the polygons are similar. 4. The sum of the squares on two sides of a triangle...is equal to twice the square on half the third side increased by twice the square on the median to that side. Amherst College, June, 1896. 1. Two triangles...
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## Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 186 sider
...are composed of the same number of similar triangles, similarly placed, the polygons are similar. 4. The sum of the squares on two sides of a triangle...is equal to twice the square on half the third side increased by twice the square on the median to that side. Amherst College, June, 1896. 1. Two triangles...
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## Examination Papers

Queen's University (Kingston, Ont.) - 1896 - 898 sider
...and b stand for line segmenta. (6) Give geometrical constructions for finding (i) and (ii). 12. (a) The sum of the squares on two sides of a triangle is equal to twice the sum of the squares on the median to the third side, and on one-half the third side. (6) ABC is a triangle...
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## The Elements of Geometry

Henry W. Keigwin - 1897 - 254 sider
...the rectangle on one side~~ FIo. isi. and the projection of the other side upon it. 323. COR. 2. If the sum of the squares on two sides of a triangle is equivalent to the square on the third side, the triangle is right-angled. Exs. 1. State §§ 314, 321,...
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