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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 ... - Page 22
by John Playfair - 1855 - 318 pages

## Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Electronic book - 1828 - 180 pages
...neither equal nor less than AB, it must be greater than it; as was to be demonstrated. § 19. THEOREM. Two sides of a triangle are together greater than the third side. APPLIC. Let ABC, (fig. 26.) be a triangle, the two sides AC, and CB, taken together, are greater than...

## The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 190 pages
...the side which the sparrow has to fly in proportion to that which it has to fly itself. ART. 43. " Any two sides of a triangle are together greater than the third sidr." As I have observed before, we often, without knowing an angle from a triangle, give an involuntary...

## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...AB; therefore AC is greater than AB. Wherefore, the greater angle &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than...third side. Let ABC be a triangle; any two sides of it are together greater than the third side, namely, the sides BA, AC are greater than the side BC ; and...

## Self-examinations in Euclid

John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...right angles; .-. angles A, ABC are together < than two right angles. PROP. XX. 56. To prove that ' any two sides of a triangle are together greater than the third side,' what is the general construction ? From the point where they meet, produce either of the two sides...

## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 1 0. (Eue. i. 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle...

## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...BE, EC. But AE, EC are equal to AC; therefore BA, AC are together greater than BE, EC. Again, because two sides of a triangle are together greater than the third side, EC and ED are together greater than CD. To each of these add DB; therefore EC, ED, DB are together...

## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...is greater than AB. Wherefore, the greater angle, &c. QED PROPOSITION XX. See N. THEOR — Any Iwo sides of a triangle are together greater than the...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...

## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...is not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 10. (Eue. L 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle...