 | Robert Simson - Trigonometry - 1806 - 546 pages
...triangles, &c. QED PROP. XIII. THEOR. See N. IN every triangle, the square of the side subtending any of the acute angles is less than the squares of the...angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...triangles, &c. QED PROP. XIH. THEOR. Book ii. IN every triangle the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle, by twice the rect. angle contained by either of these sides and the straight line intercepted between the perpendicular,... | |
 | John Mason Good - 1813 - 714 pages
...perpendicular and the obtuse angle. Prop. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the...angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the... | |
 | John Mason Good - 1819 - 800 pages
...аи-I the obtuse angle. Pmp. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the...containing that angle, by twice the rectangle contained by eithei of these sides, and the straight line ¡ntercepuJ between the perpendicular let fall upon it... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...PROP. XIII. THEOR. In every triangle, the square of the side subtending any of the acute angles, i$ less than the squares of the sides containing that...angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular, let fall upon it from the... | |
 | John Playfair - 1819 - 354 pages
...Q,. ED -D PROP. XIII. THEOR. In every triangle, the square of the side subtending any of the aeute angles, is less than the squares of the sides containing that angle, by tvsice tht rectangle contained by cither of these sides, and the straight line intercepted betrvetri... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...triangles, &c. QED Proposition XIII. Theorem. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the...angle by twice the rectangle contained by either of these sides, and the straight line inteicepted between the perpendicular let fall upon it from the... | |
 | Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...algebraically the following Proposition : " In every triangle, the square of the side subtending any of the acute angles is less than the squares of the...angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the... | |
 | Euclides - 1826 - 226 pages
...*• *• PROPOSITION XIII. THEOREM. In acute angled triangles, the square of the side subtending any of the acute angles is less than the squares of the sides containing the acute angle, by twice a rectangle under one of the sides about the acute angle, viz. on which the... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...triangles, &c. QED PROP. XIII. THEOR. In every triangle, the square of the side subtending either SeeN. of the acute angles, is less than the squares of the...angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the... | |
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Therefore, in obtuse-angled triangles, &c. QED PROP. 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 angle, by twice the rectangle contained by either... 
