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" In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 287
by Charles Hutton - 1812
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...said hypothenuse and other side (th. 33). Corol. 2. Hence, also, if two right-angled triangles have two sides of the one equal to two corresponding sides...triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...is equal to twice the square of half the base increased by twice the square of the medial line; 2d. The difference of the squares of the two sides is equal to twice the product of the base by the projection of the medial line on the base. In the triangle ABC,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...is equal to twice the square of half the base increased by twice the square of the medial line; 2d. The difference of the squares of the two sides is equal to twice the product of the base by the projection of the medial line on the base. In the triangle ABC,...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...difference of the given squares. Cor. 3. — a. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular. For the square of AB is equal to the squares of BD and DA, and the square...
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Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

Horatio Nelson Robinson - 1875 - 288 pages
...be drawn from the vert1cal angle of any triangle to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. Let ABC be a triangle. From A let fall AD perpendicular on BC, making two right angled triangles ADB,...
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The elementary geometry of the right line and circle

William Alexander Willock - Circle - 1875 - 196 pages
...to the rectangle AP-BP, as stated. Con. 3. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by the perpendicular from the vertical angle upon the base. Let ACB be the triangle and CO the...
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An elementary manual of coordinate geometry and conic sections

James White - Conic sections - 1878 - 160 pages
...point of the base to the foot of the perpendicular on it. For the difference of the squares of the sides is equal to the difference of the squares of the segments of the base made by the perpendicular, and this is equal to the rectangle under the sum and difference of the segments....
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Parliamentary Papers, Volume 22

Great Britain. Parliament. House of Commons - Great Britain - 1879 - 632 pages
...triangle a perpendicular fall upon the base or the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 4. In every triangle the square of the side subtending any of the acute angles is lees than the squares...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 23

1879 - 636 pages
...triangle a perpendicular fall upon the base or the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. In every triangle the square of the side subtending any of the acute angles is less than the squares...
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 23

Great Britain. Civil Service Commission - 1879 - 620 pages
...ti'iangle a perpendicular fall upon the base or the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of tho base. 4. In every triangle the square of the side subtending any of tho acute angles is less than...
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