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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... "
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 54
by Robert Simson - 1835 - 513 pages
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...triangle, the square of the side which is opposite to any given angle, is greater or less than the squares of the sides containing that angle, by twice...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 Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...XIII. 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...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...In every triangle, the square of the side sub- . tending 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 tides, and the straight line intercepted between the perpendicular, let fall upon it from the opposite...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...Theorem. In every triangle, the square of the side -btending any of the acute angles is less than the squares of the sides containing that angle, by twice...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 A.) 1. Prove...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...is greater than the squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. of these sides, and the straight line intercepted...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 of the sides containing...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...the side subtending any of the acute angles is less than the squares of the sides containing the same angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular, drawn to it from the opposite angle, and the acute angle. SUBSTANCE OF SECTION VII. 1. Squares are...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...THEOR. Iir 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...from the opposite angle and the acute angle.* Let BBC be any triangle, and the angle at B one of its acute angles, and upon BC one of the sides containing...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...THEOR. In any triangle, the square of a side subtending an acute angle is less than the sum of the squares of the sides containing that angle, by twice the rectangle contained by either of those sides and the part of it intercepted between the perpendicular let fall on it from the opposite...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...XIII. THEOR. In every triangle, the square of the side subtending an acute angle, is less than the squares of the sides containing that angle, by twice...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
...сл, by twice the rectangle вc, CD. Therefore, in obtuseangled triangles, &c. QED PROP. XIII. THEOR. the sides containing that angle, by twice the rectangle...acute angle. Let ABC be any triangle, and the angle at в one of its acute angles, and upon в c, one of the sides containing it, let fall the perpendicular...
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