Books Books 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 ... - Page 111
by Euclides - 1821 ## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 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 (AB)... ## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...twice the rectangle BC, CD. Therefore, in obtuse-angled triangles, &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 angle, by twice the rectangle contained by either of these sides,... ## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the square of the side subtending an acute angle is less than the squares of the sides which contain that angle. 21. This will be found to be that particular case of... ## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...The above principle may be illustrated by aid of the annexed diagram : n"=9' PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending...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 from... ## Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...Therefore, by substitution in the last equality but one. AC2 = AB2 + BC2 + 2AB . BD. QED B2 THEOREM XXIX. In any triangle, the square of the side subtending an acute angle is less than the squares of the other two sides, by twice the rectangle of one of the sides containing the acute angle... ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the square of the side subtending an acute angle is less than the squares of the sides which contain that angle. 21. This will be found to be that particular case of... ## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...EF(jH is double of ABCD. 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... ## Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...may be illustrated by aid of the annexed diagram : 17 2 =9 2 +10 2+ 2.9X6. PROPOSITION XI. THEOREM. In any triangle, the square of the side subtending...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 from... ## Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...twice the rectangle BC, CD. 47. PROP. XXV. In every triangle the square of the side opposite to any acute angle is less than the sum of the squares of the aides forming that angle by twice the rectangle contained by either of these sides and that part of... 