| Robert Rawson - 1856 - 200 pages
...unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal, VL Things which are double of the same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vin. Magnitudes which coincide with... | |
| Thomas Cogswell Upham - Ethics - 1857 - 474 pages
...one another ; If equals be added to equals, the "wholes are equal; The whole is greater than a part; Things which are double of the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one... | |
| Euclides - 1858 - 248 pages
...remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be takea from unequals, the remainders are unequal. 6. Things...same, are equal to one another. 7. Things which are another. halves of the same, are equal to one II. The Five Axioms, which apply especially to magnitude,... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another. VEIL Magnitudes which coincide... | |
| Euclides - 1862 - 172 pages
...same parallels EC, AG, therefore the parallelogram FECG is double of the triangle AEC j (1.41) but ' things which are double of the same are equal to one another ' (ax. C) therefore the parallelogram FECG is equal to the triangle ABC, and it has one of its angles... | |
| Euclides - 1863 - 74 pages
...equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. •I. If equals be taken from unequals, the remainders are...are halves of the same, are equal to one another. II. The Five Axioms, which apply especially to magnitude^ are peculiarly AXIOMS OF GEOMETBT: 8. Magnitudes... | |
| Euclides - 1863 - 122 pages
...uuequals, the remainders are unequal. 7. 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... | |
| Euclides - 1864 - 448 pages
...unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vin. Magnitudes which coincide with... | |
| Robert Potts - 1865 - 528 pages
...unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vm. Magnitudes which coincide with... | |
| Euclides - 1865 - 402 pages
...nnequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide... | |
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