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" If equals be added to 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. "
Elements of Geometry: With Practical Applications ... - Page 12
by George Roberts Perkins - 1847 - 308 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...the remainders are equal. IV. If equals be added to 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. VIII....
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...unequals, the sums are unequals. 5. If equals be taken from unequals, thé remainders are unequals. 6 Things which are double of the same, or equal things, are equal to one another. 7- Things which are halves of the same, or equal things, are equal to one another....
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI....are double of the same, or equal things, are equal to one another. VII. Things which are halves of the same, or equal things, are equal to one another....
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI....are double of the same, or equal things, are equal to one another. VII. Things which are halves of the same, or equal things, are equal to one another....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the remainders are equal. iv. If equals be added to 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. vni. Magnitudes...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...the remainders are equal. IV. If equals be added to 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. VIII....
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...are equal to the same thing, are equal to each other. II. When equals are added to equals, the whole are equal. III. When equals are taken from equals,...coincide, or fill the same space, are identical. X. All right-angles are equal to one another. POSTULATES. I. To draw a straight line from any one point to...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...the remainders are equal. IV. If equals be added to 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. VIII....
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...the remainders are equal. IV. If equals be added to 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. VIII....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...completely determined by the arithmetical method as by the more lengthy method of the Greek geometers. AXIOMS. I. Things which are equal to the same thing,...identical. X. All right angles are equal to one another. XI. A straight line is the shortest distance between two points. XII. Through the same point only one...
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