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In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Schultze and Sevenoak's Plane and Solid Geometry - Page 192
by Arthur Schultze, Frank Louis Sevenoak - 1918 - 457 pages

## A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI ..., Book 1

Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of those sides, and the projection of the other side upon it. The Enunciation of Prop. 12 thus stated should be carefully compared with that of Prop. 13. PROPOSITION...

## Plane and Spherical Trigonometry: An Elementary Text-book

Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1900 - 184 pages
...circumscribed circle. t 41. Law of the cosines. — The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the product of these sides and the cosine of the included angle. Since we are making no use of the directions of the...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...XXXVII. THKOREM 320. In any tnangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice...sides and the projection of the other side upon it- i Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove...

## Plane Geometry

Arthur Schultze - 1901 - 260 pages
...XXXVII. THEOREM 320. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...XXXVII. THEOREM 320. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...XXXVII. THEOREM 320. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove...

## Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...any triangle the square on a side opposite an acute angle is equivalent to the sum of the squares on the other two sides, diminished by twice the product...one of those sides and the projection of the other upon that side. Given. — Let ABC be any triangle, B an acute angle, and BD the projection of BC on...

## Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...THEOREM 659. In any triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides, diminished by twice the product of one of these sides and the projection of the other side upon it. B c Let ABC be a A in which BC lies opposite...