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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 geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...straight lines can be drawn to the given straight line, one upon , each side of the shortest line. : PROP. XX. THEOREM. Any two sides of a triangle are together...than the third side. Let ABC be a triangle : any two of its sides are together greater than the third side ; viz., the sides BA, AC, are greater than the...

The elements of plane and spherical trigonometry

John Hind - 1855
...excluded. The circumstances here pointed out, are nothing more than what have all along been assumed, that any two sides of a triangle are together greater than the third : but it thus appears that the Algebraical Formulae are sufficient of themselves to determine the consistency...

Practical geodesy: comprising chain surveying and the use of surveying ...

J. Butler Williams (Sir.) - 1855 - 272 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...

Essays on the Intellectual Powers of Man

Thomas Reid, Sir William Hamilton - 1855 - 492 σελίδες
...this proposition, — Any two sides of a triangle are together equal to the third, — as of this, — Any two sides of a triangle are together greater than the third; yet the first of these is impossible. Perhaps it will be said, that, though you understand the meaning...

The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...opposite the greater of the two AB, AC, or, in other words, AC is greater than A B. XXI.— EUCLID I. 20. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle (Fig. 14), take any side BA and produce it at one extremity to D,- making AD equal to AC the adjacent...

The British and Foreign Evangelical Review and Quarterly Record of Christian ...

James Oswald Dykes, James Stuart Candlish, Hugh Sinclair Paterson, Joseph Samuel Exell - 1856
...of its conclusions. They who can deny them, * Jxdtptndent for June 28, 1855. may as well deny that any two sides of a triangle are together greater than the third side, or the truth of any other demonstrable proposition.* What was the peculiar characteristic nature of...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...angles at the base, prove that the locus of the vertex is a hyperbola, and find its asymptotes. 1. ANY two sides of a triangle are together greater than the third side. If a polygon with only salient angles be situated inside another polygon, the perimeter of the former...

The Popular Educator, Τόμος 1

1856
...restriction is plain, when we consider that he had previously proved in his Prop. XX., Book I. that any two sides of a triangle are together greater than the third. This, however, is manifest without demonstration, if we adopt Archimedes's definición of a straight...

general Report on Public Instruction in the lower Provinces of the Bengal ...

JOHN GRAY - 1857
...each ? 5. If a : b : : c : d show that a + b : J : : c + d : d and that am : b" : : C" : d" EUCLID. 1. Any two sides of a triangle are together greater than the third side. the squares of the sides containing it by twice the rectangle contained by the side upon which, when...

Middle-class education. 2

Middle-class education - 1857
...line. What figure would be formed by placing two equilateral triangles base to base ? 81. Prove that any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle ? Give reasons for your answer. 32. Prove...




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