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" Any two sides of a triangle are together greater than the third side. "
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... - Side 24
av Euclid, Robert Simson - 1829 - 516 sider
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...side opposite to or subtending the greater angle is greater than the side opposite the less angle. PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side. COR..—Hence the difference between any two sides of a triangle is less than the third side. • '•'.>...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...to AB: neither is it less; because then the angle ABC A would be less* than the angle ACB; but it is not: therefore the side AC is not less than AB; and...Let ABC be a triangle: any two sides of it together shall be greater than the third side, viz. the sides BA, AC greater than the side BC; and AB, BC greater...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...less than AB ; and it has been shewn that *-' it is not equal to AB ; therefore AC is greater than AB. PROP. XX. THEOR. • Any two sides of a triangle are...Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB, . BC greater...
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Chambers's information for the people, ed. by W. and R. Chambers, Volum 2

Chambers W. and R., ltd - 1842
...A proposition is first stated in general terms : take, for instance, the 20th proposition — '• Any two sides of a triangle are together greater than the third side." This is but bare assertion : to advance a step farther, Euclid places the figure referred to, namely,...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 sider
...theorems of Euclid's first Element. I can compel your assent to the truth of the proposition, that " any two sides of a triangle are together greater than the third side ;" and this without requiring from you any notion of a straight line at all. But I must stop here....
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A Course of Mathematics: In Two Volumes. Composed for the Use of ..., Volum 2

Charles Hutton - 1843
...Prove by means of the equations that connect the sides and angles of a spherical triangle, that (1.) Any two sides of a triangle are together greater than the third. (2.) The difference of two sides is less than the third. (3.) If three sides of a triangle be equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 317 sider
...-rT" less than AB; and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. PROP. XX. THEOR. Any two sides of a triangle are together greater than the third suie. Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the...
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The British Annals of Education for ...: Being The Scholastic ..., Volum 1

1844
...sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. Any two sides of a triangle are together greater than the third side. 4. The straight lines which join the extremities of two equal and parallel straight lines towards the...
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Proceedings, Volum 10

Royal Society of Edinburgh - 1880
...: — That the greater side of every triangle has the greater angl* opposite, and conversely. That any two sides of a triangle are together greater than the third side. Also Euclid I. 21. Euclid I. 24 and 25. Euclid I. 26 (the second part). Also the usual propositions...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...together less than AB, the circles would not intersect, and the construction, would be impossible ; hence any two sides of a triangle are together greater than the third, which is established in a different manner in (Prop. 13.) PROPOSITION V. — THEOREM. If two triangles,...
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