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" In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Pągina 109
per Euclides - 1821
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811
...equal to the squares of AB, BC,. together with twice the rectangle of AB, BD. c^ ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volum 1

Charles Hutton - 1812
...the squares of AB, BC, together with twice the rectangle of AB, BD. q. B. i>. THEOREM XXXVII. 0, 4^» IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822
...equal to the squares of AB, BC, together with twice the rectangle of AB, BD. u- ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the...
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The First Six Books with Notes

Euclid - 1822 - 179 pągines
...rectangle under DC and CB. PROP. XIII. THEOR. In any triangle (ABC) the square of the side (AB) Fi^. 25. subtending an acute angle is less than the sum of the squares of the sides(AC and CB), containing that angle by twice the rectangle under either of them (AC), and the segment...
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Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 pągines
...twice the rectangle under the base and the distance between the perpendicular and the obtuse angle. In any triangle the square of the side subtending...acute angle is less than the sum of the squares of the two sides containing that angle by twice the rectangle under either of these sides and the distance...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1830 - 316 pągines
...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 from the acute...
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The first six books of the Elements of Euclid: with notes

Euclid, Thomas Elrington - 1833 - 183 pągines
...rectangle under DC and CB. PROP. XIII. THEOPv. In any triangle {ABC) tie square of the side (AB), Fig. 25. subtending an acute angle, is less than the sum of the squares of the sides (AC and CB) containing that angle, by twice the rectangle under either of them (AC) and the segment...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 pągines
...of BC, CA, and twice the rectangle BC.CD. Therefore, in an obtuse-angled triangle, &c. PROP. XIII. THEOR. IN any triangle, the square of the side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 359 pągines
...another place. 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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...opposite angle and the vertex of the obtuse angle. PROP. XIII. THEOR. In any triangle, the square of a side subtending an acute angle is less than the sum...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...
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