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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... "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page xv
by Robert Potts - 1876 - 403 pages
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...Q on AB exceeds the sum of the Ds on AC and CB by twice the rect. AC, C D. PROPOSITION XIII. In any triangle the square on the side subtending an acute angle is less than the sum ot the squares on the sides containing that angle by twice the rectangle contained by either of...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 pages
...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...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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...PROPOSITION 13.— Theorem. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that...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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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...twice the rectangle BC, CD. Therefore, in obtuse-angled triangles, &c. QED Proposition 13.— Theorem. In every triangle, the square on the side subtending an acute angle is less t/ian the squares on the sides containing that angle, by twice the rectangle contained by either of...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...square on the radius. 3. In every triangle, the square on the side subtending either of the acute angles is less than the squares on the sides containing that...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. -, • r, 1. Simplify...
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...straight line which is made up of the half and the part produced. Male Candidates—First Year. 19 2. In every triangle, the square on the side subtending an acute angle is less than the squaies on the sides containing that angle by twice the rectangle contained by either of these sides...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...within any equilateral figure upon its sides is the same, wherever the point be taken. (15). 28. In any triangle, the square on the side subtending an acute...angle by twice the rectangle contained by either of those sides and the straight line intercepted between the perpendicular let fall on it from the opposite...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 126 pages
...half the line. 5. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (Prove this for the case...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...greater than the base of the other. 11. In a triangle in which one angle is obtuse, the square on a side subtending an acute angle is less than the squares...angle, by twice the rectangle contained by either of those sides and the straight line intercepted between the perpendicular let fall on it from the opposite...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...the side subtending either of the acute angles, is less than the squares of the sides contain' ing that angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the acute angle and the perpendicular drawn to it from the opposite angle. Let BCD be a triangle (above...
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