 | Euclides - 1862 - 140 pages
...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. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight... | |
 | 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 - 1863 - 122 pages
...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. j 11. All right angles are equal to one another. | 10. Two straight lines cannot enclose a space to... | |
 | 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 - 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... | |
 | Euclides - 1865 - 402 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. XL All right angles... | |
 | 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... | |
 | Edward Clarke Lowe - 1866 - 172 pages
...unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to...another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide...another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exag^ly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight Imes cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight... | |
| |
Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
