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" ANY two sides of a triangle are together greater than the third side. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Pāgina 33
per John Playfair - 1832 - 333 pāgines
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Calendar, Part 1

University of Calcutta - 1907
...of a triangle are unequal, the greater side has the greater angle opposite to it ; and the converse. Any two sides of a triangle are together greater than the third. Of all the straight tines that can be drawn to a given straight line from a given point outside it,...
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A School Course of Mathematics

David Mair - 1907 - 379 pāgines
...justify your rule. The rule is important enough to be called a proposition, and may be stated thus: — Any two sides of a triangle are together greater than the third. 5. Points of the Compass. The terms north and east have been used. How do you know which direction...
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The Grammar of Philosophy: A Study of Scientific Method

David Graham - 1908 - 383 pāgines
...time coming ; whilst, on the other hand, a single demonstration of any necessary truth — say that " any two sides of a triangle are together greater than the third side," or the simple proposition that " lying is base," 1 Reid : Works, p. 441. 2 Hamilton : Lectures, vol....
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Calendar, for the Year ...

1908
...asterisk, but such answers are not expected in order to qualify for any of the several classes. 1. Any two sides of a triangle are together greater than the third side. ABO is a triangle, and the vertical angle BAG is bisected by a line which meets BC in X ; show that...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - 1908
...to the first angle shall be greater than the side opposite to the second (Euc. I. 19) 123 T.4. — Any two sides of a triangle are together greater than the third (Euc. I. 2O) 124 T.5. — The shortest line which can be drawn from a given point to a given line is...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 138 pāgines
...greater than AB. QED [For Exercises on Theorems 9 and 10 see page 34.] THEOREM 11. [Euclid I. 20.] Any two sides of a triangle are together greater than the third Let ABC be a triangle. It is required to prove that any two of its sides are together greater than...
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Principles of psychology

Herbert Spencer - 1910
...it falls within or without some other; and the like. Let us take as an example the proposition — " Any two sides of a triangle are together greater than...side." " Let ABC be a triangle ; any two sides of it are, together, greater than the third side; namely, BA, AC, greater than BC; and AB, BC, greater than...
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - 1910 - 302 pāgines
...of the bisectors to the vertex of the third ^ of the A bisects that third Z. INEQUALITIES THEOREM 16 Any two sides of a triangle are together greater than the third side. B DC Hypothesis. — ABC is a A. To prove that AB + AC> BC. Construction. — Bisect ZA and let the...
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Essays on Mathematical Education

George St. Lawrence Carson - 1913 - 139 pāgines
...science may not be a postulate in another. In Euclid's development of geometry, the statement that any two sides of a triangle are together greater than the third side is not a postulate, because it is deduced from other statements (postulates) which are avowedly assumed...
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Review of Reviews and World's Work, Volum 49

Albert Shaw - 1914
...shortest distance from one point to another is as "the crow flies"; and stated his proposition that any two sides of a triangle are together greater than the third. Ask the average boy to prove this as a general theorem: he will draw a perfect figure, measure the...
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