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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, based on Euclid, books i-iii - Page 37
by Edward Atkins - 1876 - 119 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...EAF is drawn through the given point A parallel to the given straight line BC. PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle...sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; and the three interior angles of the triangle,...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...point A parallel to the given straight line BC. Which was to be done. PROPOSITION XXXII. THEOR. — If a side of any triangle be produced, the exterior angle...sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC, and the three interior angles of the triangle,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...line equal to that which is described by eitner extremity of the base.* BOOK I. PKOP. XXXII.— If a side of any triangle be produced, the exterior angle is equal to the two interior and remote angles ; and the three interior angles of every triangle are together equal to two right angles....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...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 angle is equal to the Iwo interior and opposite angles; and Ihe three interior angles of every triangle are together equal...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...Therefore, a str. line has been drawn through A || BC. EF || BC. Pt0ff ^ PROP. XXXI. THEOR. 32. 1 Eu. If a side of any triangle be produced, the exterior angle...and the three interior angles of every triangle are together equal to two right angles. Let ABC be a ^, and the side BC be prod, to D. Then shall the ext....
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
.../. ADC, EF || BC. Prop.2H. PROP. XXXI. THEOR. 32. 1 Eu. If a side of any triangle be produced, t/ie ex-terior angle is equal to the two interior and opposite...and the three interior angles of every triangle are together equal to two riffht angles. Let ABC be a ^\, and the side BC be prod, to D. Then shall the...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...of a triangle be produced, the exterior angle (ACD) is equal to the two interior angles (A and B) ; and the three interior angles of every triangle are equal to two right angles. Argument. Through C draw CE parallel to AB (a). Then because AC meets the parallels AB, CE, the alternate...
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The London University Calendar

London univ - 1846 - 326 pages
...2. Prove that any two sides of a triangle are together greater than a third side. 3. If a side of a triangle be produced, the exterior angle is equal to the two interior opposite angles, and the three interior angles of every triangle are equal to two right angles. Prove...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...angles are also equal. Now, this being demonstrated, it is easy to prove that the three angles of any triangle are equal to two right angles. Let ABC be a triangle right angled at A, draw AD perpendicular to BC. The triangles ABD, ABC have the angles BAC, BDA right...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...base passes through D. Wherefore, of all triangles &c. — QED PROP. XXXII. THEOR. GEN. ENUN. — If a side of any triangle be produced, the exterior angle...the two interior and opposite angles ; and the three inte. rior angles of every triangle are equal to two right angles. PART. ENUN. — Let ABC be a A,...
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