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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. "
The Element of Geometry - Seite 13
von John Playfair - 1836 - 114 Seiten
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 Seiten
...PROPOSITION 32.— THEOREM. If a side of any triangle be produced, the exterior angla in equal to the tiro interior and opposite angles; and the three interior...angles of every triangle are equal to two right angles. (References— Prop. I. 13, 29, 31; ax. 1, 2.) Hypothesis. — Let ABC be a triangle, and let one of...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Band 2

Robert Potts - 1863 - 482 Seiten
...other two, prove that the side AB, is equal to twice the line joining C with the middle point of AB. 2. If a side of any triangle be produced, the exterior...angles of every triangle are equal to two right angles. 3. Triangles upon the same base, and between the same parallels, are equal to one another. If E and...
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Responsions

University of Oxford - 1863 - 316 Seiten
...other, the base of that which has the greater angle shall be greater than the base of the other. 5. If a side of any triangle be produced, the exterior...angle is equal to the two interior and opposite angles j and the three interior angles of every triangle are together equal to two right angles. Add and prove...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 Seiten
...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...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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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 Seiten
...line BC. QEF PROPOSITION XXXII. THEOREM. If a side of any triangle be produced, the exterior angle i* equal to the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles. Let^-BCbeatriangle,andletone of its sides 5 Cbe produced to Z)....
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First Practical Lines of Geometrical Drawing ...

J. F. H. de Rheims - 1865 - 336 Seiten
...interior angles upon the same side together equal to two right angles. Prop. 32. — Theorem. If one side of any triangle be produced, the exterior angle...angles of every triangle are equal to two right angles. Prop. 34. — Theorem. The opposite sides and angles of parallelograms are equal to one another, and...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 Seiten
...drawn a straight line EAF parallel to the given straight line B CQEF PROPOSITION XXXII. THEOREM. lf 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 AB C be a triangle, and let one of its sides BC be produced...
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An Introduction to Plane and Spherical Trigonometry

Alfred Challice Johnson - 1865 - 166 Seiten
...lines, it makes the alternate angles equal to one another. (Eue. I., 29.) 6. If a side of a triangle he produced, the exterior angle is equal to the two interior...and opposite angles; and the three interior angles are equal to two right angles, or 180°. (Eue. L, 32.)* 7. The square upon the hypolheneuse of a right-angled...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 Seiten
...one-third of two right angles, or two thirds of one right angle. PROPOSITION XXXI. THEOR. If one side of a triangle be produced, the exterior angle is equal to the two interior opposite angles. Let BC, one of the sides of the triangle ABC, be produced to D, the exterior angle...
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Half-hour examination papers, for daily use

John Robertson (LL.D., of Upton Park sch.) - 1865 - 106 Seiten
...same, and thence show that two straight lines cannot have a common segment. [ECS] 43. If the 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 together equal to two right angles....
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