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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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The British Annals of Education for ...: Being The Scholastic ..., Τόμος 1

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,Τεύχος 1878

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 ...

Robert Potts - 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 ...

James Thomson - 1845 - 358 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

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 ...

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

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...

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

Euclides - 1846
...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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