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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 acute... "
Minutes of the Committee of Council on Education: with Appendices - Page cxl
by Great Britain. Committee on Education - 1848
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...t. 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....
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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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...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 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...-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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...QED 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,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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....
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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
...21 (б) In 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...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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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that...of these sides, and the straight line intercepted bi-twecn the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be...
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