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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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