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" AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal.... "
Plane Geometry: A Complete Course in the Elements of the Science - Page 28
by Edward Brooks - 1901 - 266 pages
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The Youth's instructer [sic] and guardian, Volume 14

1854 - 1110 pages
...never fatigue, And pleasures that never decay. Witney, Oxon. WS HOETON. LESSONS. GEOMETRY. — Axtomt. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...axioms, and are to geometry, what the foundations are to a building. Euclid's axioms are the following : 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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A London Encyclopaedia, Or Universal Dictionary of Science, Art ..., Volume 10

Thomas Curtis - Aeronautics - 1829 - 814 pages
...word line occurs, without the addition of either straight or curved, a straight line is always meant. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. When equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1831 - 166 pages
...axioms, and are to Geometry, what the foundations are to a building. Euclid's axioms are the following : 1. Things which are equal to the same thing are equal to one another. 2. If equal sbe added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. THINGs which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...lines, are such as are in the same plane, and which being produced ever so far both ways, do not meet. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes ere equal. 3. If equals be taken from equals, the remainders are equal....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...straight line. • 3. That a circle may be described from any centre, with any interval from that centre. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...of all the other axioms, which, as propounded by Euclid in the first book, are the following : — 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1 . THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal....
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