 | Euclides - 1853 - 176 σελίδες
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose a space. XI. All right... | |
 | Euclid - 1853 - 176 σελίδες
...tho elements, namely, " Magnitudes which are equal coincide with one another when similarly placed." 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. SCHOLIUM. This axiom may bo otherwise expressed, namely, "If two straight lines coincide in two points,... | |
 | Thomas Lund - 1854 - 520 σελίδες
...plain enough, for AB + CD = CD + DE = CE ; and AB taken from CE = CD. The same principle, viz. that ' magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another', leads to the conclusion that, in like manner areas and angles may be added, subtracted, multiplied,... | |
 | Dugald Stewart - 1854 - 452 σελίδες
...place. Ka) TO. tf*(fii%i>rx !«•' aAXnX* tra £xx»x»« Irrl: — thus translated by Dr. Simson ; " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; —... | |
 | Dugald Stewart - 1854 - 454 σελίδες
...K«! ra ifxfpi^nra if «>.?,:,•/.,•/. tvx i\\g>.ti! Irri : — thus translated by Dr. Simson ; " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition . It is the definition of geometrical equality ;... | |
 | John Playfair - 1855 - 340 σελίδες
...are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide with one another, that is,...one another. 9. The whole is greater than its part. 1 0. All right angles are equal to one another. 11." Two straight lines which intersect one another,... | |
 | Euclides - 1855 - 270 σελίδες
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. Dr. Thomson, in his edition of Euclid, has added to this axiom,... | |
 | Robert Rawson - 1856 - 178 σελίδες
...same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vin. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. rx. The whole is greater than its part. X. Two straight lines cannot inclose a space. XI. All right... | |
 | Thomas Cogswell Upham - 1857 - 474 σελίδες
...the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one another (that is,...exactly fill the same space) are equal to one another, &c. It will be admitted (and we shall see it perhaps more clearly when we again have occasion to revert... | |
 | Euclides - 1858 - 248 σελίδες
...one II. The Five Axioms, which apply especially to magnitude, are peculiarly Axioms of Geometry : 8. Magnitudes which coincide with one another, — that...which exactly fill the same space, — are equal. "This Axiom is properly the definition of Geometrical equality." We prove the equality of two straight... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
