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" Any two sides of a triangle are together greater than the third side. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Σελίδα 72
των Thomas Perronet Thompson - 1833 - 150 σελίδες
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A Course of Mathematics: In Two Volumes. Composed for the Use of ..., Τόμος 2

Charles Hutton - 1843
...Prove by means of the equations that connect the sides and angles of a spherical triangle, that (1.) Any two sides of a triangle are together greater than the third. (2.) The difference of two sides is less than the third. (3.) If three sides of a triangle be equal...

The British Annals of Education for ...: Being The Scholastic ..., Τόμοι 1-2

1844
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 317 σελίδες
...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...

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

Euclid - 1845 - 199 σελίδες
...; 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...third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,...

Proceedings, Τόμος 10

Royal Society of Edinburgh - 1880
...: — 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
...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,...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 σελίδες
...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....

A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 σελίδες
...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...third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...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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