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" 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. "
Elements of geometry, based on Euclid, books i-iii - Page 9
by Edward Atkins - 1876 - 119 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...unequals, the wholes are unequal V. If equals betaken 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...equal to one another. VII. Things which are halves of the same thing, 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. 3 X. All right angles are equal to one another. XI. " Two straight...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1821 - 348 pages
...w*£u'.Ç'*vrî «»' лллих» lea яллялмс tm : — thus translated by Dr. Simson ; " Magnituui's which coincide with one another, that is, which exactly...fill the same " space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the...
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Artis logicæ rudimenta, with illustrative observations [and a transl. By J ...

Henry Aldrich - 1821 - 300 pages
...allowed as soon as perceived : such are axioms ; which neither require nor admit syllogistic proof: as, Things which are double of the same are equal to one another. In the secondary degree, it denotes the certainty of those relations which may be immediately deduced...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...taken from unequals, the remainders are unequal. 6. Things which are double of the same or of equals, are equal to one another. 7. Things which are halves of the same or of equals, are equal to one another. 8. Magnitudes which coincide with one another, are equal to...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...taken from unequals, the remainders will be unequal. 6. Things which 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 with one another, that is, which exactly...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...unequals, the wholes are unequal. 5. If equals be taken from unequal s, the remainders are unequal. 6. Things which are double of the same, are equal to...with one another, that is, which exactly fill the space, are equal to one another. 0. The whole is greater than its part. 10. Twfc«».^^^ lines cannot...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...unequals, the wholes are unequal. 5. If equals be taken from uncquals, the remainders are unequal. 6. Things which are double of the same, are equal to...are halves of the same, are equal to one another. 8. Things which mutually agree with one another, are equal to one another. 9. The whole is greater than...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 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...are halves of the same, are equal to one another. 8. Things which mutually agree with one another, are equal to one another. 0. The whole is greater than...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...which are halves of the same thing, are equal to one another. VIII. — Magnitudes which coincide wiih one another, that is, which exactly fill the same space, are equal to one another. IX. — The whole is greater than its part, and equal to all its parts taken together. X. — All right...
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