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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...
Euclid's plane geometry, practically applied; book i, with explanatory notes ... - Página 17
por Euclides - 1863
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## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 páginas
...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....the remainders are equal. 4. If equals be added to uncquala the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6....
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## First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 páginas
...added to equals, the wholes are equal. 20. (Not given by Euclid, tut assumed by him). If the same thing be added to equals the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 30. (Not given by Euclid, but assumed by him.) If the same thing be taken from equals, the remainders...
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## Class lessons on Euclid

Marianne Nops - 1882 - 278 páginas
...axioms may of course be extended to any multiple or fraction. Axioms 2-5 form a second connected group. 2. ' If equals be added to equals the wholes are equal.'...equals be taken from equals the remainders are equal.' If A=C and B=D, A±B=C±D. 4. ' If equals and unequals be added together, the wholes are unequal.'...
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## Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 páginas
...I. 3 may be omitted. 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....equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are doubles of the...
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## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 páginas
...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....from equals the remainders are equal. 4. If equals bo added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are...
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## An introduction to geometry, consisting of Euclid's Elements, book ..., Volumen1

Euclides - 1884 - 182 páginas
...their minds. AXIOMS 1 — 7, 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....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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## Notes on algebra

Howard Candler - 1885 - 116 páginas
...34, 35, 36, 37-) 1 9. The rules for solving Equations depend on the four fundamental Axioms :-r— a. If equals be added to equals, the wholes are equal....equals be taken from equals, the remainders are equal. y. If equals be multiplied by equals, the products are equal. 0. If equals be divided by equals, the...
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## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...can effect. AXIOMS.1 1. Things which are equal to the Same are Equal to One Another. 2. If equals te Added to equals, the Wholes are equal. 3. If equals be Taken from equals, the Remainders are equai. 4. If equals be Added to unequals, the Wholes are unequai. 5. If equals be Taken from unequals,...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 460 páginas
...definitions. GENERAL 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....equals be added to unequals, the wholes are unequal, the greater sum being that which includes the greater of the unequals. 5. If equals be taken from unequals,...
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## Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 páginas
...general axioms are also employed, viz.: (i.) Things equal to the same thing are equal to each other. (2.) If equals be added to equals, the wholes are...equals be added to unequals, the wholes are unequal in the same order. (5.) If equals be taken from unequals, the remainders are unequal in the same order....
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