 | John Playfair - 1806 - 320 pages
...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 - 734 pages
...Prop. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...upon it from the opposite angle, and the acute angle. Prop. XIV. Prob. To describe a square that shall be equal to a given rectilineal figure. Book III.... | |
 | Euclides - 1814 - 556 pages
...PKOP. XIII. THEOR. IN every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...contained by either of these sides, and the straight line intercopted between the perpendicular let fall upon it from the opposite angle, and the acute angle.... | |
 | Euclides - 1816 - 592 pages
...than the squares of the fides containing that angle, by twice the rectangle contained by either ot these sides, and the straight line intercepted between the perpendicular let fall upon it from ttie opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute... | |
 | Daniel Cresswell - 1817 - 454 pages
...of the base of an isosceles triangle is the double of the rectangle contained by either side, and by the straight line intercepted between the perpendicular,...let fall upon it from the opposite angle, and the extremity of the base. (XIV.) If from any point, in the circumference of the greater of two given concentric... | |
 | Daniel Cresswell - 1819 - 446 pages
...of the base of an isosceles triangle is the double of the rectangle contained by either side, and by the straight line intercepted between the perpendicular,...let fall upon it from the opposite angle, and the extremity of the base. If the vertical angle of the isosceles A be a right angle, the proof of the... | |
 | John Mason Good - 1819 - 714 pages
...Pmp. XIII. Theor. 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 rectangle contained by eithei of these sides, and the straight line ¡ntercepuJ between the perpendicular let fall upon it... | |
 | Euclid, Robert Simson - 1821 - 514 pages
...PROP. XIII. THEOR. IN every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...sides, and the straight line intercepted between the perpendiculai let fall upon it from the opposite angle, and the acute angle.* Let ABC be any triangle,... | |
 | Peter Nicholson - 1825 - 1058 pages
...Proposition XIII. Theorem. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...contained by either of these sides, and the straight line inteicepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.... | |
 | Henry Parr Hamilton - 1826 - 354 pages
...following Proposition : " In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...it from the opposite angle., and the acute angle." (Eve. II. IS). Since the triangle may be either acute angled, or obtuse angled, or right angled, the... | |
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In every triangle, the square on the side subtending either of the acute angles, 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... 
