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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 Elements of Euclid

Euclid - 1838 - 416 σελίδες
...equal to AB ; 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...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,...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...' Wherefore the greater angle, &c. Q. un PROP. XX. THEOR. Any two sides of a triangle are toget/ier greater than the third side. Let ABC be a triangle : any two sides of it together shall be greater than the third side, viz. the sides BA, AC greater than the side BC ;...

A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - 1838 - 80 σελίδες
...perpendicular to the base. A scalene triangle has all its sides and angles unequal. See fig. 7. Note 1. Any two sides of a triangle are together greater than the third side. 2. The greatest side of every triangle is opposite the greatest angle; and the greatest angle is also...

The Phoenix; or, Lucubrations of the nights of st. John

1839
...day passed on tolerably smoothly with one exception, that when the doctor (arguing very soundly that any two sides of a triangle are together greater than the third side) was taking a shorter cut across a field, his career was stopped about midway by his horse inserting...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...or subtending the greater angle is greater than the side opposite the less angle. PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side. COR..—Hence the difference between any two sides of a triangle is less than the third side. • '•'.>...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...equal to AB; 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...third side. Let ABC be a triangle: any two sides of it together shall be greater than the third side, viz. the sides BA, AC greater than the side BC; and...

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

John Playfair - 1842 - 317 σελίδες
...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 arc greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,...

Chambers's information for the people, ed. by W. and R. Chambers

Chambers W. and R., ltd - 1842
...A proposition is first stated in general terms : take, for instance, the 20th proposition — '• Any two sides of a triangle are together greater than the third side." This is but bare assertion : to advance a step farther, Euclid places the figure referred to, namely,...

Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 σελίδες
...theorems of Euclid's first Element. I can compel your assent to the truth of the proposition, that " any two sides of a triangle are together greater than the third side ;" and this without requiring from you any notion of a straight line at all. But I must stop here....

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...




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