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" 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. 5. If equals... "
A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI - Page 8
by Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 456 pages
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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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An Introduction to the Use of the Globes ... 3. Ed. Corr. and Enl

John Greig - 1816 - 224 pages
...is frequently called a maxim. 2. If equals be added to equals, the whole are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals be added to unequals, the whole are unequal. 5. If equals be taken from unequals, the remainder are unequal. 6. Things which...
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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 First Six Books with Notes

Euclid - 1822 - 222 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 be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the...
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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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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 be added to unequals, the wholes are unequal. 5. If equals be taken from uncquals, the remainders are unequal. 6. Things which are double of the...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 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 be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the...
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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...equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the...
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