| 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.... | |
| 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... | |
| 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.'... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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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