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" If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. "
The first six books of the Elements of Euclid, with numerous exercises - Seite 13
von Euclides - 1853 - 147 Seiten
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Minutes of the General Council of Medical Education & Registration ..., Band 6

General Medical Council (Great Britain) - 1869
...opposite to the equal angles, are equal to one another. 2. To bisect a given rectilineal angle. 3. If one side of a triangle be produced the exterior...greater than either of the interior opposite angles. 4. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...of the octagon, 135°, &c. ; but none of these numbers are measures of 360°. PUOP. 16. — THEOB. If one side of a triangle be produced, the exterior angle is greater tiian eitlier of the interior opposite angles. CONS. — P. 10. To bisect a given st. line. P. 3. From...
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An Elementary Course of Plane Geometry

Richard Wormell - 1870 - 16 Seiten
...equal to the two given sides. Through the extremities draw lines parallel to the sides of the angle. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three angles of a triangle are together equal...
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The Edinburgh university calendar

Edinburgh univ - 1871
...straight line. Show that your construction has given you exactly what your definition required. 2. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. Modify your demonstration so as to bring out distinctly the property of straightness to which you appeal....
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Elements of geometry, containing the first two (third and fourth ..., Teil 1

Euclides - 1871
...hereafter how this definition may be extended, so as to embrace angles greater than two right angles. If one side of -a triangle be produced, the exterior...greater than either of the interior opposite angles. I> Let the side BC of A ABC be produced to D. Then must L ACD be greater than either L CAB or L ABC....
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The National Schoolmaster, Bände 7-8

1877
...rhombus, each of whose sides is equal to that line, by the method employed in the first proposition. z. If one side of a triangle be produced, the exterior angle is greater than either of the interior and opposite angles. Prove this for both the interior angles. Composition. Write notes of a lesson...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 Seiten
...this definition may be extended, so as to embrace angles greater than tico right angles. PBOPOSITION XVI. THEOREM. If one side of a triangle be produced,...greater than either of the interior opposite angles. Let the side BC of A ABC be produced to D. Then must L ACD be greater than either L CAB or L ABC. Bisect...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - 1872
...equal sums, and the remainders will be equal, ie, the /. AE C is equal to the ^ DE B. PEOPOBITION XVI. If one side of a triangle be produced, the exterior...greater than either of the interior opposite* angles. For the construction employed in this proposition we must be able, — * That is, not adjacent to the...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...the point A draw the angle DAE = ADC. Then EA is parallel to g BC, by Prop. 25. Proposition 30. — Theorem. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. If BC be produced to D, the a angle ACD = the two angles...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...one point, are together equal to four right angles. XVI. — If one side of a triangle Reproduced, the exterior angle is greater than either of the interior opposite angles. Let ABC be a triangle, and let its side BC be produced to D, the exterior angle ACD is greater than either...
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