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AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
A Course of Mathematics: For the Use of Academies, as Well as Private Tuition - Page 257
by Charles Hutton - 1818

Elements of Geometry, Geometrical Analysis, and Plane Trigonometry ...

Sir John Leslie - Geometry, Analytic - 1809 - 524 pages
...sides AB and BC are together greater than the third AC. PROP. XVII. THEOR. The- difference between two sides of a triangle is less than the third side. Let the side AC be greater than AB, and from it cut off a part AE equal to AB ; the remainder EC is less...

A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...distance between two points, is a single right line drawn from the one point to the other. THEOREM XI. THE Difference of any Two Sides of a Triangle, is...two sides, as AB — AC, be less than the third side BC. For, produce the less side AC to D, till AD be equal to the greater side AB, so that CD may be...

Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ...

Sir John Leslie - Geometry, Plane - 1820 - 482 pages
...sides AB and BC are together greater than the third side AC. PROP. XV. THEOR. The difference between any two sides of a triangle is less than the third side. • Let the side AC be greater than AB, and from it cut off a part AE equal to AB ; the remainder EC is less...

A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...it, must necessarily be greater, o.. ED THEOREM X. THE Sum of any Two Sides of a Triangle is Greater than the Third Side. Let ABC be a triangle ; then will the . lum of .ny two of its side* be greater than the third side, as for instances, AC -J-cB greater than...

Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 576 pages
...limitation arises from a known geometrical problem, though it is not found in Muclid's " Elements;" viz. "The difference of any two sides of a triangle is less than the third side." PROS. 4. Giving the hypothenuse of aright-angled triangle, and the side of its inscribed square, to...

The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...KL, FL, FQ. Then, by hypothesis, the angle KML=fML, KM=/M, and LM is common, the base LK is =Li/; but the difference of any two sides of a triangle is less than the third ;* therefore FL — LK, or FL - L/, is less than FK, or F/, or FM -/M, or FQ -/Q. Hence/L is greater...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...and the sides вс, CA, greater than AB. Therefore two sides of every triangle, &c. Deductions. 1. The difference of any two sides of a triangle is less than the third side. 2. Two sides of a triangle are together greater than twice the line from the vertex bisecting the base....

Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...is less than the more remote ; there can be two equal lines, but there cannot be more than two. 5. The difference of any two sides of a triangle is less than the third side. 6. If, from the vertex of a triangle, two straight lines be drawn, one of which is perpendicular to...