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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 ... - Page 16
by Euclides - 1814
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...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 pages
...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 - Mathematics - 1853 - 400 pages
...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 pages
...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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Sabbath evening readings on the New Testament, Volume 1

John Cumming - Bible - 1854 - 496 pages
...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 popular educator, Volume 4; Volume 7

Popular educator - 1852 - 1272 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 340 pages
...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...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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...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 - Surveying - 1855 - 306 pages
...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 - Intellect - 1855 - 528 pages
...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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