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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... "
Elements of Plane Geometry According to Euclid - Σελίδα 1
των Andrew Bell - 1837 - 240 σελίδες
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...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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Charles Hutton - 1816 - 610 σελίδες
...remainders are equal . 4. When equals are added to unequals, the wholes arc Unequal. 5. When equals are taken from unequals, the remainders are unequal. 6 Things which are double of the same thing, or equal things, are equal to each other. 7. Things which arc halves of the same thing, afe...

An Introduction to the Use of the Globes ... 3. Ed. Corr. and Enl

John Greig - 1816 - 224 σελίδες
...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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1819 - 800 σελίδες
...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....

The First Six Books with Notes

Euclid - 1822 - 222 σελίδες
...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,...are unequal. 6. Things which are double of the same or of equals, are equal to one another. 7. Things which are halves of the same or of equals, are equal...

A Course of Mathematics: For the Use of Academies, as Well as Private ...

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...remainders are equal. 4. When equals are added to unequala, the wholes are unequal. 5. When equals are taken from unequals ; the remainders are unequal. 6. Things which are double of the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing, are...

The Youth's instructer [sic] and guardian, Τόμος 14

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...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...

The New Practical Builder and Workman's Companion, Containing a Full Display ...

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...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...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 σελίδες
...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,...

A Course of Mathematics for the Use of Academies: As Well as ..., Τόμος 1

Charles Hutton - 1825 - 608 σελίδες
...are equal. 4. When equals are added to unequals, the wholes are unequal. 5. When equals are taken (ym unequals : the remainders are unequal. 6. Things which are double of the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing, are...




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