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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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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861 - 572 pages
...8. 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...upon it from the opposite angle and the acute angle. In any triangle shew that the sum of the squares of the two sides is equal to twice the square of half...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...acute-angled triangle show that the square of the side subtending one of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular let fall...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle...line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. (References— Prop. I. 12, 16, 47; II. 3, 7, 12.)...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...the squares of the sides containing that angle, by tenet the rectangle contained by either of those sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite anyle, and the acute angle. (References — Prop. i. 16,47; H. 3, 7, 12.) Let ABC be any triarglp,...
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Responsions

University of Oxford - Education, Higher - 1863 - 316 pages
...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...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. 3. Describe an equilateral...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...1 9. In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle...line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle. Demonstrate the proposition in the case where the...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...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...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 school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...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...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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...triangle, the square on the side subtending eitJter of the acate angles, is less than the squares on the sides containing that angle, by twice the rectangle...sides, and the straight line intercepted between the acute angle and the perpendicular let Jail upon it from the opposite angle. Let ABC be any triangle,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...THEOREM. 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 those sides, and the straight line intercepted between the perpendicular let faU upon it from the opposite...
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