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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. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 15
by Peter Nicholson - 1823 - 596 pages
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - Euclid's Elements - 1789 - 296 pages
...till it meets the other. AXIOMS. 1. Things which are equal to the fame thing are equal to each other, 2. If equals be added to equals the wholes will be...equals be added to unequals the wholes will be unequal. *k ^* B 3 5. If 5. If equals be taken from unequals the remainders will be unequal. • 6. Things which...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...•i • f • 1 AXIOMS. 1 . Things which are equal to the fame thing are equal to each other. I 5. If equals be added to equals the wholes will be equal....If equals be taken from equals the remainders will berequal. 4. If equals be added to unequals the wholes will be unequal. 5. If equals be taken from...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 722 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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The First Six Books with Notes

Euclid - 1822 - 179 pages
...centre, /&, ff, at any distance from that centre. M o Axioms. 1. Things which are equal to the same 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,...
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The Youth's instructer [sic] and guardian, Volume 14

1854 - 1110 pages
...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 be equal. This might be...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 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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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...this, see Legendre*s Geometry, proposition 1, book i. AXIOMS. 1. Things which are equal to the same 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,...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...side where the angles are less than two right angles. AXIOMS. 1. Things which are equal to the same 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,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...THINGS which are equal to the same thing are equal to one another. Also things which are equal to equal things 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,...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 158 pages
...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. 4. If equals be added to unequals,...
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