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" Any two sides of a triangle are together greater than the third side. "
Euclid's Elements of Geometry - Page 59
edited by - 1893 - 504 pages
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A School Course of Mathematics

David Mair - Mathematics - 1907 - 412 pages
...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 - Common sense - 1908 - 408 pages
...all 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. 3 Hamilton : Lectures, vol....
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Calendar, for the Year ...

1908 - 274 pages
...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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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...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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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...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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Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - Education - 1909 - 356 pages
...boulders and cobbles in this state? GEOMETRY. 1. Give the points of proof in the following theorems: (a) Any two sides of a triangle are together greater than the third side. (b) The medians of a triangle are concurrent. (c) The angles opposite the equal sides of an isosceles...
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Henley's Encyclopędia of Practical Engineering and Allied Trades: A ...

Joseph Gregory Horner - Engineering - 1909 - 560 pages
...angles. (Prop. 17.) The greater side of every triangle is opposite to the greater angle. (Prop. 18.) Any two sides of a triangle are together greater than the third side. (Prop. 20.) If from the ends of a side of a triangle there be drawn two straight lines to a point within...
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Mathematical Papers for Admission Into the Royal Military Academy and the ...

Royal Military Academy, Woolwich - Mathematics - 1909 - 456 pages
...XYZW have AB = XY, BC= YZ, CD = ZW, B= Y, C = Z. Show that they are equal in every respect. 2. Show that any two sides of a triangle are together greater than the third. Give in substance the enunciation of propositions from which you know that the sum of the squares on...
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Principles of psychology

Herbert Spencer - Philosophy - 1910 - 780 pages
...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 the third side." " Let ABC be a triangle ; any two sides of it are, together, greater than the third side; namely, BA,...
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - Geometry - 1910 - 316 pages
...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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