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

Sir J. Butler Williams - 1846 - 330 σελίδες
...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...

Minutes of the Committee of Council on Education: with appendices ..., Τόμος 1

Great Britain. Committee on Education - 1847
...equal to two right angles, these two straight lines shall be in one and the same straight line. 2. Any two sides of a triangle are together greater than the third side. Section II. 1. To divide a straight line into two such parts that the rectangle of the whole and one...

The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847
...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...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...angle of every triangle is subtended by the greater side, or has the greater side opposite to it. PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. PROP. XXI. THEOREM. If from the ends of a side of a triangle, there be drawn two straight lines to...

General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848
...+P xa~l+P xn-z+ ........ +J» = 0 J * n and in the quadratic equation »* — px + </=0 Geometry. 6. Any two sides of a triangle are together greater than the third side. 7. In a circle, the angle in a semicircle is a right angle, but the angle in a segment greater than...

The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849
...is not equal to AB; therefore AC is greater than AB. Wherefore the 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,...

Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 226 σελίδες
...DF, each to each, and the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any two sides of a triangle are together greater than the third side. For the straight line AB is the shortest path between the points A and B (Def. 3); hence AB is less...

Notes and Queries

1884
...appellation to Euclid, i. 5, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,...

Notes and Queries

1884
...appellation to Euclid, i. 6, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,...

Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850
...sides of a triangle be unequal, the greater side has the greater angle opposite. 8. Prove Euc. 1. '.iO. Any two sides of a triangle are together greater than the third tide. 9. Prove Kuc. I. 48. If the square described upon one side of a triangle be equal to the squares...




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