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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 - Page 86
by Daniel Cresswell - 1819 - 410 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 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 Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 at B one of its acute angles ; and upon BC, one...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 722 pages
...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. Prop. XIV. Prob. To describe a square that shall be equal to a given rectilineal figure....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...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. .' 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 ...

Euclides - 1816 - 528 pages
...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
...sides, which are not parallel, and of twice the rectangle of its parallel sides. • PROP. XIII. (XIII.) The square of the base of an isosceles triangle is...the opposite angle, and the extremity of the base. (XIV.) If from any point, in the circumference of the greater of two given concentric circles, two...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...angle, by twice the rectangle contained by eithei of these sides, and the straight line ”ntercepuJ between the perpendicular let fall upon it from the opposite angle, and the acute angle. Prop. XIV. Prob. To describe a square that shall be equal to a civen rectilineal figure....
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...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. Let ABC be any triangle, and the angle at В one of its acute angles, and upon BC, one...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...equal sides of the triangle. 2. The square of the base of an isosceles triangle, is equal to twice the rectangle contained by either side, and by the...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 of the base will...
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