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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 139
by Charles Reiner - 1837 - 215 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...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 bi-twecn the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...the side subtending any of the acute angles, is less than the squares of t 'fie sides containing that angle by twice the rectangle contained by either of...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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...which is opposite to a given angle is greater or less than the squares of the sides containing 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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The Element of Geometry

John Playfair - Geometry - 1836 - 148 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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 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...sides, and the straight line intercepted between the perperdicular, let fall upon it from the opposite angle, and the acute angle. A. If one side of a triangle...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...of the side -btending 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. Fig. 1. Fig. 3. Steps of the Demonstration...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 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...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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...subtending either of the acute angles, is less than the squares of the sides containing that angle, ly twice the rectangle contained by either of these sides,...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 ...

Euclides - Geometry - 1841 - 378 pages
...square of the side subtending an acute angle, 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 acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...вc, CD. Therefore, in obtuseangled triangles, &c. QED PROP. XIII. THEOR. 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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