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" In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 101
by James Bates Thomson - 1844 - 237 pages
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Short, But Yet Plain Elements of Geometry: Shewing how by a Brief and Easie ...

Ignace Gaston Pardies - Geometry - 1734 - 164 pages
...PROP. II. In an Acute-angled Triangle, the Square of the Side (h) fubtending an Acute Angle, " is lefs than the Sum of the Squares of the other two Sides, by double the Rettangle under the whole Safe, (b + a) and the Segment of the Bafe (a) which is next to...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. ( Let ABC be a triangle, obtuse...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse...
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A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ...

Charles Hutton - Mathematics - 1816
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subren .ing the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rrctungle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle,...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...' j . ,1 ' ' Book III. PROP. V. THEOREM. The square of one of the sides of a triangle is greater or less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and its segment, intercepted between the perpendicular and the angle opposite to that side,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...explained more fully in another place. THEOREM. 191. In any triangle, the square of the side opposite either of the acute angles, is less than the sum of the squares of the sides containing it, by twice the rectangle contained by either of ilie latter sides and the distance...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...rectangle BC, CD. Therefore, in obtuse-angled triangles, &c. Q. . D. PROPOSITION XIII. See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...p!ace. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle ts less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the opposite-...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...GEOMETRY. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the opposite...
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