 | Euclides - 1858 - 248 pages
...to one II. The Five Axioms, which apply especially to magnitude, are peculiarly Axioms of Geometry : 8. Magnitudes which coincide with one another, —...which exactly fill the same space, — are equal. "This Axiom is properly the definition of Geometrical equality." We prove the equality of two straight... | |
 | 1858 - 402 pages
...Marvels" is equal to Mrs. Stowe's "Memories," and the total equivalent to a whole calf's head. VIH. Magnitudes which coincide with one another, that is, which exactly fill the same space, are eqnal to one another, thus—two booby lords, or magnitudes, which coincide in the Cabinet, in the... | |
 | Euclides - 1860 - 288 pages
...which are double of the same, are equal. . -,3 7. Things which are halves of the same, are equal. -. , 8. Magnitudes which coincide with one another —...fill the same space — are equal to one another. 'iq 10 9. The whole is greater than its part. . •.: 10. All right angles are equal to one another.... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...In this manner we form our idea of equality, which is thus formally stated in the eighth axiom : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle. With regard to a few more general... | |
 | Euclides - 1862 - 172 pages
...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 inclose a space. XI. All right... | |
 | Euclides - 1862 - 140 pages
...Things which are double of the same are equal to one another. 7. Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, wliich exactly fill the same space, are equal to one another. 9. The whole is greater than its part.... | |
 | Euclides - 1863 - 74 pages
...another. II. The Five Axioms, which apply especially to magnitude^ are peculiarly AXIOMS OF GEOMETBT: 8. Magnitudes which coincide with one another, —...which exactly fill the same space, — are equal. " This Axiom is properly the definition of Geometrical equality." If all the parts and boundaries of... | |
 | Euclides - 1863 - 122 pages
...Things which are halves of the same, are equal to one another. 6. Things which are double of the same, are equal to one another. 8. Magnitudes which coincide with one another, that which is exactly fill the same space, are equal to one another. 9. The whole is greater than its part.... | |
 | Euclides - 1864 - 448 pages
...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. IX. The whole is greater than its part. X. Two straight lines cannot enclose a space. XL All right... | |
 | Robert Potts - 1865 - 528 pages
...In this manner we form our idea of equality, which is thus formally stated in the eighth axiom : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle. With regard to a few more general... | |
| |
Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
