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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - Liczba stron: 416
...PROP. XIII. THEOR. Iir every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...from the opposite angle and the acute angle.* Let BBC be any triangle, and the angle at B one of its acute angles, and upon BC one of the sides containing...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...XIII. THEOR. In any triangle, the square of a side subtending an acute angle is less than the sum of the squares of the sides containing that angle, by twice the rectangle contained by either of those sides and the part of it intercepted between the perpendicular let fall on it from the opposite...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - Liczba stron: 351
...&c. QED PROP. XIII. THEOR. In every triangle, the square of the side subtending an acute angle, is less than the squares of the sides containing that...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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...сл, by twice the rectangle вc, CD. Therefore, in obtuseangled triangles, &c. QED PROP. XIII. THEOR. the sides containing that angle, by twice the rectangle...acute angle. Let ABC be any triangle, and the angle at в one of its acute angles, and upon в c, one of the sides containing it, let fall the perpendicular...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - Liczba stron: 237
...subtending either of the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these...upon it from the opposite angle, and the acute angle. PROPOSITION XIII. THEOREM. In a triangle ABC, if the angle C is obtuse, the square of the opposite...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...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 Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...THEOR. 13. 2 Ea. In every triangle^ the square of the side sub-tending 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. Prop. 46. Prop. 39. Prop. is. P J, 47 Fig. 1. A BDC 1st. When GEOMETRY. Fig. 2. A Fig. 3. A BC D BC...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...THEOR. 13. 2Eu. In every triangle^ the square of the side sttbtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either oj these sides, and the straight line intercepted between the perpendicular let fall upon it from the...
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The English Journal of Education, Tom 1

1847
...the other part. 2. 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, aud the straight line intercepted between the acute angle and the perpendicular let fall...
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Report of the Committee of Council on Education (England and ..., Wydanie 1

Great Britain. Council on Education - 1848
...the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less than the squares of the sides containing that...upon it from the opposite angle and the acute angle ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose area shall...
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