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" 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 contained by either of these sides, and the straight line intercepted between the perpendicular let... "
Gibson's London matriculation guide, by J. Gibson [and others]. - Page 19
1882
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...rectangles under the whole produced line and, side. PROP. 13. THEOR, In any triangle the square of the side subtending an acute angle, is less than the sum of the squares of the sides containing that angle, by twice the rectunyle under either of them and the segment between...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...base and the distance between the perpendicular and the obtuse angle. In any triangle the square of the side subtending an 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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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...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 of the squares of the sides containing that angle, by twice the rectangle contained by either of those sides and the...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...AB and its external segment BD. PROP. XIII. THEOR. In any triangle (ABC) the square of a side (CB) subtending an acute angle, is less than the sum of the squares of the sides (CA, AB) containing that angle, by twice the rectangle contained by either of those sides...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...illustrated by aid of the annexed diagram : n"=9' PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...the annexed diagram : 17 2 =9 2 +10 2+ 2.9X6. PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...to the rectangle under the other side and its produced part. The square on the side subtending that acute angle is less than the sum of the squares on the sides which contain that angle, by double the rectangle under the side to which the perpendicular is drawn,...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...same base and on the same side of it, are between the same parallels. 4. In any triangle the square of the 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 them and the segment...
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