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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 ... - Side 33
av John Playfair - 1832 - 333 sider
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 sider
...therefore a С is greater than a b. Wherefore the greater angle, &c. QED PROPOSITION XX. — THEOREM. Any two sides of a triangle are together greater than the third side. LET ab С be a triangle ; any two sides of it together are greater than the third side, viz. the sides...
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An introduction to mental philosophy

sir George Ramsay (9th bart.) - 1853 - 282 sider
...14. Alexander conquered Darius. 15. The three angles of a triangle are equal to two right lines. 16. Any two sides of a triangle are together greater than the third side. 17. The French Convention treated Louis XVI. cruelly. 18. The Chamber of Peers condemned Ney to death...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 sider
...AB ; therefore AC is greater than AB. "Wherefore the greater angle, etc. QED PROPOSITION XX. THEOB. Any two sides of a triangle are together greater than the third side. Produce BA to the point D, and make (3. i.) AD equal to AC, and join DC. Because DA is equal to AC,...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 sider
...the point A. B For, if not, let it fall otherwise, if possible, as FGDH, and join AF, AG. And because two sides of a triangle are together greater than the third side, (1. 20.) 1. AG, 6F, are greater than FA; but FA is equal (I. Def. 15.) to FH, both being from the same...
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The popular educator, Volum 4;Volum 7

Popular educator - 1852 - 1272 sider
...D. Therefore, if from a point without a given straight line, &c. QE.D. PROPOSITION XX.— THEOREM. Any two sides of a triangle are together greater than the third side. In fig. 20, let ABO be a triangle; MI. SO. any two of its sides are together greater than the third...
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Sabbath evening readings on the New Testament, Volum 1

John Cumming - 1854 - 496 sider
...are not equally important. Two and two are four, is a truth ; the sun rises and sets, is a truth ; any two sides of a triangle are together greater than the third side, is a truth ; the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 sider
...be drawn to the given straight line, one upon , each side of the shortest line. : PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle : any two of its sides are together greater than the third side ; viz., the sides BA, AC, are greater than the...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J Butler Williams - 1855 - 306 sider
...the true length : this follows from Euclid's 20th proposition of the first book, which proves that any two sides of a triangle are together greater than the third. Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the...
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Essays on the Intellectual Powers of Man

Thomas Reid - 1855 - 528 sider
...this proposition, — Any two sides of a triangle are together equal to the third, — as of this, — Any two sides of a triangle are together greater than the third; yet the first of these is impossible. Perhaps it will be said, that, though you understand the meaning...
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The Elements of Plane and Spherical Trigonometry

John Hind - 1855 - 546 sider
...excluded. The circumstances here pointed out, are nothing more than what have all along been assumed, that any two sides of a triangle are together greater than the third : but it thus appears that the Algebraical Formulae are sufficient of themselves to determine the consistency...
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