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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 23
by Euclides - 1841 - 351 pages
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Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736
...Triangles the Angles at the Bile are equal ; &?, č 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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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...but it is not ; there\s^~*,J fore the fide AC is not lefs than AB ; and it has been Ihewn 1 i8, *' that it is not equal to AB ; therefore AC is greater...AB. Wherefore the greater angle, &c. Q^ED PROP. XX. THEO R. s« K. A NY two fides of a triangle are together greater than _/JL the third fide. Let ABC...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...angle ACB ; B Book I. but it is not ; therefore the side AC is not less than AB ; and it *"-"V— ^ has been shown that it is not equal to AB ; therefore...Wherefore, the greater angle, &c. QED PROP. XX. THEOR. See N. ANY two sides of a triangle are together greater than the third side. Let ABC be a triangle...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry ...

Sir John Leslie - Geometry, Analytic - 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...less; because then the angle ABC icould be less b than the angle ACB; BC b 18. 1. a 5. l. Jm Book I. but it is not; therefore the side AC is not less than...Wherefore the greater angle, &c. QED PROP. XX. THEOR. See Note. ANY two sides of a triangle are together greater than the third side. Let ABC be a triangle;...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...not less than AB; and it has Booi I. angle ABC would be less b than the angle ACB ; but it is 1811- been shown that it is not equal to AB; therefore AC...Wherefore the greater angle, &c. QED PROP. XX. THEOR. SeeN. ANY two sides of a triangle are together greater than the third side. Let ABC be a triangle;...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...greater angle of every 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
...BC being 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 notes &c ...

Euclides - 1821
...line, of 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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