 In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it 190 THEOREM XLIX 196.  The Elements of Geometry - Page 146by Webster Wells - 1894 - 378 pagesFull view - About this book
 | Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...of half their difference . . 78 § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the 0 EBD tijstance BE js tne projection of AB on CD. XIV. Theorem. In any triangle, the square of a side opposite an [acute'] angle is equal to the sum of the squares of the other two sides [,£jj twice the rectangle of one of those sides, and the projection... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...same notation, .-. S(PQ.QO) = 0, or PQ and QO are at right angles. 5. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other sides, less or twice the product of the base and the line between the acute angle... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. equals the sum of the squares of the other two sides minus twice the product of one of those sides and the projection of the other upon that side. In the A ABC, let c be an acute Z., and... | |
 | Richard Pears Wright - 1882 - 136 pages
...greater the inclination the less the projection. Rule 1. — In acute-angled triangles the square on the side opposite an acute angle is equal to the sum of the squares on the sides which contain it diminished by twice the product of either of these sides and... | |
 | Simon Newcomb - Logarithms - 1882 - 188 pages
...III. Given the three sides. THEOREM III. In a triangle the square of any side is equal to the sum, of the squares of the other two sides minus twice the product of these two sides into the cosine of the angle included oy them. In symbolic language this theorem is... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...constructed, whose sides shall be 3, 4, and 5 ? Suppose the sides were 6, 9, and 12? THEOREM XII. In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides minus twice the rectangle contained by one of these sides and the projection... | |
 | Euclides - 1884 - 434 pages
...produced, what does the proposition become ? PROPOSITION 13. THEOREM. In every triangle the square on the side opposite an acute angle is equal to the sum of the squares on the other two sides diminished by twice the rectangle contained by either of those sides... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...given straight line, to construct an angle equal to a given angle. 3. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of the base and the distance... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...have, AC : AB : : V2 : 1 ; BOOK IV. Ill PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of the base and the distance... | |
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