 | Euclides - 1838 - 264 pages
...of the same, are equal to one another. VIII. Magnitudes which coincide, or which may be conceived to coincide with one another, that is, which exactly fill the same space, are equal to one another. This axiom, referring to the most obvious test of geometrical equality, is scarcely comprehensive enough.... | |
 | Thomas Cogswell Upham - Intellect - 1839 - 476 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...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... | |
 | 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,...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 - 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,...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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. "Two straight... | |
 | 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,...exactly fill the same space, are equal to one another. NB. The term ' equivalent' is used in this work to denote equality of magnitude, in surface or volume,... | |
 | William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. Two straight... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...another. This principle of comparison is stated by Euclid in his 8th axiom : " Magnitudes which coincide, that is, which exactly fill the same space, are equal to one another." Relative to this axiom, the utmost diversity of opinion exists : and as it lies at the foundation of... | |
 | Scottish school-book assoc - 1845 - 444 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part, aud equal to all its parts taken together. 10. Two straight... | |
 | 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,...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... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
