| Euclides - 1840 - 192 pages
...doubles 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 with one another (that is to say, which fit together so exactly that every point of the one lies on some point of the other)... | |
| Thomas Cogswell Upham - Intellect - 1841 - 474 pages
...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, which exactly fill the same space) are equal to one another, &c. It will be admitted (and we shall see it perhaps more clearly... | |
| Euclides - Geometry - 1841 - 378 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, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...Things which are double of the same, are equal to one another. 7. Things which are halves of the came, 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. 9. The whole is greater than its part. 10. All right angles are... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...doubles 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...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are... | |
| Chambers W. and R., ltd - 1842 - 744 pages
...fact, merely what a logician would call the converse of it; for in the 8th axiom it is stated, that magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another ; and in this theorem, in order to prove them equal, it is proved... | |
| Euclides - 1842 - 316 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, which exactly fill the same space, are equal to one another. NB. The term ' equivalent' is used in this work to denote equality... | |
| John Playfair - Euclid's Elements - 1844 - 338 pages
...doubles 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...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are... | |
| Scottish school-book assoc - 1845 - 444 pages
...or equal things, are equal to one another. 7- Things which are halves of the same, or equal things, 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. 9. The whole is greater than its part, aud equal to all its parts... | |
| Euclid - Geometry - 1845 - 218 pages
...are equal to one another. vn. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines... | |
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