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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. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 105
by Euclides - 1858
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...the given straight line BG. QEF PROPOSITION 32. THEOREM. If a side of any triangle be produced, tJie exterior angle is equal to the two interior and opposite...every triangle are together equal to two right angles. Let ABC be a triangle, and let one of its sides BG be produced to D : the exterior angle A CD shall...
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Annual Report

1886 - 568 pages
...to find x. EUCLID. FIRST DIVISION. 1. Define a right angle, a circle, a square. 2. If one side of a triangle be produced, the exterior angle is equal...opposite angles, and the three interior angles of any triangle are together equal to two right angles. >. 8. To make a parallelogram equal to a given...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...from a given point parallel to a given straight line in either direction. PROPOSITION XXXIL THEOREM. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. In the triangle ABC ; GIVEN that BC is produced to D ; IT is REQUIRED TO PROVE that the angle ACD is...
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Cambridge University Examination Papers

University of Cambridge - 1884 - 624 pages
...condition ? 2. Any two sides of a triangle are together greater than the third side. 3. If a side of a triangle be produced, the exterior angle is equal...and the three interior angles of every triangle are equal to two right angles. 4. If the square described on one of the sides of a triangle be equal to...
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The Practical Teacher, Volume 3

Education - 1884 - 708 pages
...four sides, AE, ED, DB, BA. — QED 2. If a side of any triangle be produced, the exterior angle i* equal to the two interior and opposite angles ; and...every triangle are together equal to two right angles. Prop. 32, Bk. I. 3. To describe a parallelogram that shall be equal to a given triangle, and have one...
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The Civil service year book and official calendar

1884 - 266 pages
...triangle," " parallel straight lines." What is (1) a Postulate, (2) an Axiom ? 2. If any side of a triangle be produced, the exterior angle is equal...opposite angles; and the three interior angles of every triangle'are together equal to two right angles. 3. If a straight line be divided into two equal parts,...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...point A parallel to the given straight line BC. XXXII. — If a side of any triangle be produced, tht exterior angle is equal to the two interior and opposite...and the three interior angles of every triangle are equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the...
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 pages
...perpendicular to a given straight line of unlimited length, from a given point without it. 2. If a side of a triangle be produced, the exterior angle is equal...and opposite angles; and the three interior angles are equal to two right angles. If ABC be any triangle, and through D the middle point of AS, DE is...
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The popular educator, Volume 5

Popular educator - 1884 - 910 pages
...connected with our present subject. Euclid has proved, in the 32nd Proposition of his First Book, that tho three interior angles of every triangle are together equal to two right angles, that is, to 180. Let the reader bear this fact in mind. Hence it follows that if the measure of any...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...of a triangle be produced, the exterior angle is equal to the two opposite interior angles ; and the interior angles of every triangle are together equal to two right angles. Let ABC be a triangle, having one side BC produced to D. Then the exterior angle ACD shall be equal...
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