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Any two sides of a triangle are together greater than the third side.
Euclid's Elements of Geometry - Page 59
edited by - 1893 - 504 pages

## Proceedings, Volume 10

Royal Society of Edinburgh - Science - 1880 - 864 pages
...space : — 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...

## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 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 the third side. Let ABC be a triangle. Then any two sides of it together shall be greater than the third side, viz....

## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOR. — Any two sides of a triangle are together greater than the third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the sides...

## 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,...

## 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....

## 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...

## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...equal to it ; therefore AC is greater than AB. Wherefore, The greater angle %c. QED PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle : any two sides of it are together greater than the third side, viz. BA, AC greater...

## Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...than 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...