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" IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 52
by Euclides - 1871
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pages
...the first line shall be equidistant from the two extremities of the finite line ? 2. If a side of a triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles. State Euclid's corollaries to this proposition. VOLUNTARY PORTION. 1. Given the centre of the circle...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...18th, Book I. The greater side of every triangle is opposite to the greater angle. The 32nd, Book I. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. Reference to Fig. 33 will illustrate the value of the above in triangular...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...PROPOSITION XXVII. THEOREM. If one side of a triangle is produced, the exterior angle tn equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. ^et ABC be any plane triangle, and let the side BC be produced uo D ; then...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...of -0031843449. EUCLID. 1. If a side of a triangle be produced the exterior angle is equal to both the two interior and opposite angles, and the three...every triangle are together equal to two right angles. Hence show that all the exterior angles of any rectilineal figure made by producing the sides successively...
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Return to an Address of the Honourable the House of Commons, Dated 10 ...

Education - 1859
...than the third side. Madras ^e difference of any two sides is always less than the third side. " 4. The three interior angles of every triangle are together equal to two right angles. How many degrees are there in an angle of a regular octagon? 5. In any right angled triangle, tire...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 450 pages
...produced to D; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; also the three interior angles of every triangle are together equal to two right angles. (Euc. I. 32. Simp. I. 9 & 10. Em. H. 1 & 2.) THEOREM V. Parallelograms standing on the same base, and...
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A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service
...less than the other two sides of the triangle, but shall contain a greater angle. PROP. XXXII. — If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. Enunciate and prove the corollaries of the last proposition. PROP. XLIV. — To a given straight line...
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Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860
...less than the other two sides of the triangle, but shall contain a greater angle. 3. PROP. XXXII. — If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. 4. Enunciate and prove the corollaries of the last proposition. 5. PBOP. XLIV. — To a given straight...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...been drawn a straight line EAF parallel to the given straight line BC. QEF PROPOSITION XXXII. THEOREM. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. Let ABCbe a triangle, and let one of its sides UCbe produced to D. Then the exterior angle A CD shall...
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Guide to the three services: civil, naval, and military

John Paxton Hall - 1860
...less than the other two sides of the triangle, but shall contain a greater angle. PROF. XXXII. — If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. Enunciate and prove the corollaries of the last proposition. PROP. XLIV. — To a given straight line...
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