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" 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 of these sides, and the straight line intercepted between the perpendicular... "
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 137
by Charles Reiner - 1837 - 215 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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, let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Prop. XIV. Prob. To describe a square...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...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 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...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...straight line intercepted between the perpendicular, let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...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 either...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 - 372 pages
...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 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 - 326 pages
...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 either...straight line intercepted between the perpendicular let fall upon it from the opposite angle., and the acute angle." (Eve. II. IS). Since the triangle...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...subtending either SeeN. of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...which is opposite to any given angle, is greater or less than the squares of the sides contairting that angle, by twice the 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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