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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 Seiten
...of straight lines meeting in one point, are together equal to four right angles. PROP. XVI. THEOR. If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles. Let ABC be a triangle, and let its side BC be produced to D, the exterior angle...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 Seiten
...straight lines meeting in one point, are together equal to four right angles-. r PROP. XVI. THEOR. If one side of a triangle be produced, the exterior angle is greater than cither of the interior, and opposite angles. Let ABC be a triangle, and let its side BC be produced...
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Elementary Illustrations of the Celestial Mechanics of Laplace: Part the ...

Pierre Simon marquis de Laplace, Thomas Young - 1821 - 344 Seiten
...(94, 82), subtract ABD, and the remainders, ABC, DBE,' are equal. In the same manner ABD= * CBE. 97. THEOREM. If one side of a triangle be produced, the exterior angle will be greater than either of the interior opposite angles. AE Bisect AB in C, draw DCE; take CE=CD,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 Seiten
...the angles they make at the point where they cut, are together equal to four right angles. Сок. 2. And consequently that all the angles made by any...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 Seiten
...any number of lines meeting in one point, are together equal to four right angles. PROP. XVI. THEOR. If one side of a triangle be produced, the exterior...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 shall be greater than...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 Seiten
...therefore the opposite an•les AEC, BED are equal, and also the opposite angles CEB, ED are equal. QED ED. PROPOSITION XVI. THEOREM.* If one side of a triangle be produced, the exterior angle will be greater than either of the interior and opposite angles. Let ABC 'be a triangle and let one...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 Seiten
...(A} A triangle cannot have more than one right angle, or more than one obtuse angle . . nor. 7 (i) If one side of a triangle be produced, the exterior angle is greater than either uf the interior and opposite . . ._ cor. 7 (i) If one side of a triangle be greater than another, the...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 Seiten
...Which was to be demonstrated. PROPOSITION XVI. THEOREM. — If one side of a triangle be prolonged, the exterior angle is greater than either of the interior opposite angles. Let ABC be a triangle, and let its side BC be prolonged to D. The exterior angle ACD is greater than either...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...point, are together equal to four right angles. PROPOSITION XVI. THEOR — If one side of a triangle he produced, 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 shall be greater than...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...(Л) A triangle cannot have more than one right angle, or more than one obtuse angle . . cor. 7 (¿) If one side of a triangle be produced, the exterior angle is greater than either of the interior and opposite wgles . , . cor, 7 (i) If one side of a Wangle be greater than another, the opposite angle...
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