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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 - Σελίδα 13
των Euclides - 1853 - 147 σελίδες
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The Civil service year book and official calendar

1884
...direct and an indirect demonstration. Define adjacent angles, opposite angles, and alternate angles. Z. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. Prove, without producing a side, that the three angles of any triangle are equal to two right angles....

Cambridge University Examination Papers

University of Cambridge - 1884
...patronum dixit ad infernas liber iturus aquas. MARTIAL, i. 101. FRIDAY, March 14, 1884. 9—12. 1. IF one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. 2. Write a short essay on Euclid's twelfth axiom, and the principles which may be substituted for it....

Questions and exercises in elementary mathematics

Palaestra Oxoniensis - 1884
...24. What is the least number of sides which a rectilineal figure can have ? Prove your answer. 26. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. By what later proposition in the first book is this superseded ? Shew that this is a necessary step...

The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...bisected, the bisectors and the base form an isosceles triangle. THEOB. 9. If any side of a triangle is produced, the exterior angle is greater than either of the interior opposite angles. Let ABC be a triangle having the side BC produced to D : AF then shall the exterior angle ACD be greater...

The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884
...to one another. Axiom 6. Magnitudes which are double of the same magnitude are equal to one another. PROPOSITION XVI. THEOREM. If one side of a triangle be produced, the exterior angle shall be greater than either of the interior opposite angles. In the triangle ABC; GIVEN that BC is...

Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...meeting in one point, are together equal to four right angles. XVL — If one side of a, triangle lie 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 is greater than either...

The elements of plane geometry, Τόμος 1

Mathematical association - 1884
...bisected, the bisectors and the base form an isosceles triangle. THEOB. 9. If any side of a triangle is produced, the exterior angle is greater than either of the interior opposite angles. Let ABC be a triangle having the side BC produced to D : then shall the exterior angle ACD be greater than...

Annual Report

Canada. Department of the Interior - 1888
...Lake." Class 11.— Euclid. Time, 2 hours. J KEY. D. GIT.LIKS, BA } REV. AB BAIRD, MA, BD , 1. Show that if one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. 2. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever...

Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - 1889 - 1006 σελίδες
...above. IF ¿ II. M. GEOMETRY. Time, l hr. SO. min. fiend this Paper before commenci'iig the work. 1. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. 2. If a straight line, falling upon two other straight lines, make the exterior angle equal to the...

Two Essays

Arthur Schopenhauer - 1889 - 380 σελίδες
...Passing over the intermediate theorems, I take the 16th : " In every triangle in which one side has been produced, the exterior angle is greater than either of the interior opposite angles." Fig.4. This Euclid demonstrates in the following manner (see fig. 4):" Let abc be a triangle ; and...




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