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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... "
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 54
by Robert Simson - 1835 - 513 pages
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...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...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....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

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...
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A Supplement to the Elements of Euclid

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...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 angle by twice...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....
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...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 angle, by twice...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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...the base of an isosceles triangle, is equal to twice 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. 3. If the vertical angle of a triangle be two-thirds of a right angle, the square...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...triangle the square of the side subtending an acute angle is less than the sum of the squares of the two sides containing that angle, by twice the rectangle contained by either of those sides and the distance between the acute angle and the perpendicular drawn from the opposite...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...every triangle, the square of the side which is opposite to a given angle is greater or less than the squares of the sides containing that angle, by twice...rectangle contained by either of these sides, and that part of it which is intercepted between the perpendicular, let fall upon it from the opposite...
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