| John Playfair - Mathematics - 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 - 714 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 - 560 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 - 588 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 - Euclid's Elements - 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 - Geometry - 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 - 800 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 - Geometry - 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 - Mathematics - 1825 - 1046 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 - Geometry, Analytic - 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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