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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 28
by Euclid, Robert Simson - 1806 - 518 pages
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Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736
...Triangles the Angles at the Bile are equal ; &?, è contra. -.. .THEOREM VHI. •. • • . • • • Any two Sides of a Triangle, are together greater than the Third Side. N. Б. Thefe Fhre Theorems laft mentioned, are demonftrated after the fame Manner as in Plain Triangles...
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Elements of geometry, geometrical analysis, and plane trigonometry ...

1809 - 524 pages
...being thus neither equal to AB, nor less than it, must therefore be greater than AB. PROP. XVI. THEOR. Two sides of a triangle are together greater than the third side. The two sides AB and BC of the triangle ABC are together greater than the third side AC. For produce...
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Elements of geometry and plane trigonometry: With an appendix, and copious ...

Sir John Leslie - Geometry, Plane - 1817 - 432 pages
...the difference between the sides AB and AC is less than the third side BC. 12. From the property that two sides of a triangle are together greater than the third side, may be derived the generic character of a straight line : The shortest line that can be drawn between...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1819
...triangle is subtended by the greater bide, or has the greater tide opposite to it Prop. XX. Theor. Any two sides of a triangle are together greater than the third side. Prop. XXI. Ihcur. If. from the ends of the side of a triangle, there be drawn two straight lint; to...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ...

Sir John Leslie - Geometry, Plane - 1820 - 465 pages
...thus neither equal to AB, nor less than it, must therefore be greater than AB. % PROP. XIV. THEOR. Any two sides of a triangle are together greater than the third side. The two sides AB and BC of the triangle ABC are together greater than the third side AC. For produce...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Part 3

Euclides - 1821
...which one is perpendicular to it, and the other not, the perpendicular is the least. PROP. 20, THEOR. Any two sides of a triangle are together greater than the third. Bisect the angle contained by the two sides* the bisecting line shall cut the third side into segments...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...QED ' Proportion XX. Tlieurem. Any two sidei of a triangle are together greater than the third lide. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the tides BA, AC, greater than the side BC ; and AB, BC greater than AC : and BC, CA greater than AB. Produce...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1826 - 320 pages
...equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &e. QED f. PROP. XX, THEOR; Any two sides of a triangle are together greater tha.n...ABC be a triangle; any two sides of it together are great?? than the third side, viz. the sides BA, AC greater than the side BC : and AB, BC greater than...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...angle, &c. e. ED PROP. XX. THEOR. Any two sides of a triangle are together greater than the See N. third side. 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 greater...
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Mechanics Magazine, Volume 6

Industrial arts - 1827
...right linr." Again, the first problem which he introduces has, for its object, to establish " that any two sides of a triangle are, together, greater than the third side." He might, \ve think, have taken this for ¡minted with as much safety as that, " when equals are added...
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