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" 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 either of these sides, and the straight line intercepted between the perpendicular... "
A Supplement to the Elements of Euclid - Side 104
av Daniel Cresswell - 1819 - 410 sider
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - 1826 - 326 sider
...of the sides containing that angle, by twice the rectangle 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." (Eve. II. IS). Since the triangle may be either acute angled, or obtuse angled, or right...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...of the sides containing that angle, by twice the rectangle 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 at B one of its acute angles, and upon BC, one...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...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 angle, and the given angle : greater, when the given angle is greater than a right angle, and less, when it is less....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...twice the rectangle contained by either 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 any triangle, and the angle at B one of its acute angles ; and upon BC, one...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...of t 'fie sides containing that angle by twice the rectangle 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 at B one of its acute angles, and upon BC, one...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...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 angle, and the acute angle; greater if the given angle is greater than a right angle, and less if it is less . . .22...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...of the sides containing that angle, by twice the rectangle 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 at B one of its acute angles, and upon BC, one...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. 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 he any triangle, and the angle at B one of its acute angles, and upon BC, one...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...of the sides containing that angle, by twice the rectangle 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. Fig. 1. Fig. 3. Steps of the Demonstration to Case 1st. (in which AD falls within the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...of the sides containing that angle, ly twice the rectangle 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 at B one of its acute angles, and upon I3C, one...
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