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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 together equal to two right angles. "
Elements of Geometry and Conic Sections - Page 30
by Elias Loomis - 1857 - 226 pages
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Responsions

University of Oxford - Education, Higher - 1863
...equal to them of the other. 5. 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 together equal to two right angles. 6. Equal triangles on the same base, and on the same side of it,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...QEF PROPOSITION XXXII. THEOREM. 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 together equal to two right angles. Let A BC be a triangle, and let one of its sides B Cbe produced...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...equal to two right angles. Hence the theorem ; the sum of the three angles, etc. THEOREM XII. If any side of a triangle is produced, the exterior angle is equal to the sum of the two interior opposite angles. Let ABC be a triangle. Produce AB to D; and we are to prove that the angle CBD is...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...CQEF PROPOSITION XXXII. THEOREM. lf 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 together equal to two right angles. Let AB C be a triangle, and let one of its sides BC be produced...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...given straight line. Prop. 32. 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 together equal to two right angles. Cor. 1. All the interior angles of any rectilineal figure, together...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...QEF PROPOSITION 32. THEOREM. If a side of any triangle & produced, tlie exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle, are together equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...13), and, consequently, the two lines AB, CD, are parallels (corol., th. 14). QED THEOREM XVII. "When one side of a triangle is produced, the exterior angle is equal to both the interior opposite angles taken together. Let the side AB, of the triangle ABC, be produced...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...27.) PROPOSITION XXXII. THEOREM. If a tide of any triangle be produced, the exterior angle it equal to -the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles. Let A BC be a triangle, and let one of its sides B Cbe produced...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868
...the other. Def. 25. The area of a figure is the space enclosed by the sides of the figure. THEOREM 8. If one side of a triangle is produced, the exterior angle is equal to the two in- *\ terior and opposite angles, a?id the three interior angles of any triangle are together...
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Minutes of the General Council of Medical Education & Registration ..., Volume 6

General Medical Council (Great Britain) - 1869
...Duties ? HIGHER MATHEMATICS. 1. If a side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles. 2. In equal circles equal angles stand upon equal circumferences...
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