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" In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Strona 62
autor: John Playfair - 1819 - Liczba stron: 333
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - Liczba stron: 453
...square on a side opposite an acute angle is less than the sum of the squares on the other two sides, by twice the rectangle contained by either of these sides, and the distance from the vertex of the acute angle to the foot of the perpendicular let fall on this side,...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...right angles. 8. In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing that...upon it from the opposite angle and the acute angle. In any triangle shew that the sum of the squares of the two sides is equal to twice the square of half...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...In an acute-angled triangle show that the square of the side subtending one of the acute angles is less than the squares of the sides containing that...angle by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular let fall...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle...line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. (References— Prop. I. 12, 16, 47; II. 3, 7, 12.)...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...the squares of the sides containing that angle, by tenet the rectangle contained by either of those sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite anyle, and the acute angle. (References — Prop. i. 16,47; H. 3, 7, 12.) Let ABC be any triarglp,...
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Responsions

University of Oxford - 1863
...triangle, the square on the side subtending either of the acute angles is less than the squares on the sides containing that angle, by twice the rectangle...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. 3. Describe an equilateral...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864
...1 9. In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle...line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle. Demonstrate the proposition in the case where the...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle,...
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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...XIII. — THEOREM. 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 those sides, and the straight line intercepted between the perpendicular let faU upon it from the opposite...
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