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Any two sides of a triangle are together greater than the third side.
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Σελίδα 72
των Thomas Perronet Thompson - 1833 - 150 σελίδες
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## Reports on Elementary schools

...sides of a triangle be unequal, the greater side has the greater angle opposite. 8. Prove Euc. 1. '.iO. Any two sides of a triangle are together greater than the third tide. 9. Prove Kuc. I. 48. If the square described upon one side of a triangle be equal to the squares...

## An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - 1851 - 621 σελίδες
...plane triangle, it will cut the other two sides proportionally, [Eu. vi. 2.] or Theorem D, page 26. Any two sides of a triangle are together greater than the third side [Eu. i. 20.] or Theorem IX. page 19. From this it follows also, that the difference of any two sides...

## The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...another, the side opposite that angle is greater than the side opposite the other.] PROP. XX. THEOR. Any two sides of a triangle are together greater than...third side. Let ABC be a triangle; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,...

## The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...the side is greater than, equal to, or less than the angle opposite to the other. PEOP. XX. ТНЕOB. Any two sides of a triangle are together greater than the third side. In the triangle ABC, the sides л в and в c „ are greater than AC, the sides вc and CA are greater,...

## The New quarterly review, and digest of current literature, Τόμος 7

1858
...an assertion relating to the mind is proved by an induction as wide as that on which we believe that any two sides of a triangle are together greater than the third, we have a right to suppose it true for us ; we feel it to be true by our intuition, our experience...

## The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 σελίδες
...that it is not equal to ab ; 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...

## An introduction to mental philosophy

...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...

## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

...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,...

## The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...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...

## The popular educator, Τόμος 4;Τόμος 7

Popular educator - 1852
...of the least straight line A 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...