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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 16
by Euclides - 1814
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. Any two sides of a triangle are together greater than the third side. 4. The straight lines which join the extremities of two equal and parallel straight lines towards the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. PROP. XX. THEOR. Any two sides of a triangle are together greater than the third suie. Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the...
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Proceedings, Volume 10

Royal Society of Edinburgh - Science - 1880 - 864 pages
...: — That the greater side of every triangle has the greater angl* opposite, and conversely. That any two sides of a triangle are together greater than the third side. Also Euclid I. 21. Euclid I. 24 and 25. Euclid I. 26 (the second part). Also the usual propositions...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...together less than AB, the circles would not intersect, and the construction, would be impossible ; hence any two sides of a triangle are together greater than the third, which is established in a different manner in (Prop. 13.) PROPOSITION V. — THEOREM. If two triangles,...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...pass through the point A, let it fall otherwise, if possible, as FGDH, and join AF, AG. Then, because two sides of a triangle are together greater than the third side, (i. 20.) therefore FG, GA are greater than FA : but FA is equal to FH ; (i. def. 15.) therefore FG,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...not equal to AB : therefore AC is greater than AB. Wherefore, if two angles, &c. PROP. XX. THEOB. — Any two sides of a triangle are together greater than the third side.t * Let the learner compare thia proposition and the following with the 5th and G1h of this book....
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...It has been shown that AC ^ AB, AC > AB. Therefore the greater Z., &c. PROP. XIX. THEOR. 20. 1 Eu. Any two sides of a triangle are together greater than the third side. Let ABC be a <^, then AB + AC> BC, AB+ BOAC, BC + AC> AB. Produce BA to D. Make AD = AC. Prop. s. Join DC. Then...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the triangle, but contain an angle BDC greater than the angle BAC. Produce BD to E : Then, because any two sides of a triangle are together greater than the third side (1. 20), the two sides, BA, AE, of the triangle ABE are greater than BE : To each of these add EC ;...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...the true length : this follows from Euclid's 20th proposition of the first book, which proves that any two sides of a triangle are together greater than the third. Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...is > AC — BC, and AC > BC — AB. Wherefore any side Sec.— QED PROP. XX. THEOR. GEN. ENUN. — Any two sides of a triangle are together greater than the third side. PART. ENUN. — Let ABC be any A. Then the sum of any two of its sides is > the third side, viz., BA...
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