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" Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... "
Euclid, books i. & ii., with notes, examples, and explanations, by a late ... - Page 6
by Euclides - 1879
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...any centre, at any distance irom that centre. jtiiams.—l. Things which are equal to the same ore equal to one another. 2. If equals be added to equals, the whiles ari equal. 3. \f equals be taken from equals, «le remainders aro equal. 4. If equals be added...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...that centre. Aihitis. — 1 . Things which are equal to Ihe umc are equal to one another. 2. If equaU be added to equals, the wholes are equal. 3. If equals be taken fi от equals, the remainders are equal. 4. If equals be added to unequal*, the whalM are unequal....
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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...one another. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. This might be...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...the course of a demonstration. 46. AXIOMS. 1. Things which are equal to the same thing, or things, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...described from any centre, at any distance from that centre. AXIOMS. 1. Thingi which ate equal to the same are equal to one another. 2. If equals be added to equals the wholes are equals 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...sections, and are therefore here premised : — • AXIOMS.* • 1. Things, which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders are equal. 4. The doubles of equals are...
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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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...following sections, and are therefore here premised : — AXIOMS.* 1. Things, which are equal to the same, are equal to one another. 2. If equals be added to...be taken from equals, the remainders are equal. 4. The doubles of equals are equal. 5. The halves of equals are equal. 6. The greater of two magnitudes,...
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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...another. 2. If equals be added to equals, the wholes ere equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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