 | Euclides - 1883 - 176 pages
...then no such restriction is to be read into Post. 3, and Propositions I. 2 and I. 3 may be omitted. Axioms. 1. Things which are equal to the same thing...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 - Euclid's Elements - 1883 - 428 pages
...straight line : 3. And that a circle may be described from any centre, at any distance from that centre AXIOMS. 1. Things which are equal to the same thing...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 pages
...them " common notions," that is, notions which people in general have in their minds. AXIOMS 1 — 7, 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... | |
 | Euclides - 1884 - 434 pages
...ruler and the compasses, somewhat inconsistently on Euclid's part, are never adhered to in practice.] AXIOMS. 1. Things which are equal to the same thing...one another. 2. If equals be added to equals, the sums are equal. 3. If equals be taken from equals, the remainders aro equal. 12 EUCLID'S ELEMENTS.... | |
 | Howard Candler - 1885 - 116 pages
...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 pages
...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,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...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.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...general axioms are also employed, viz. : (1.) 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.... | |
 | Seymour Eaton - 1899 - 362 pages
...was required. The student must construct the figure step by step according to the directions. AXIOMS 2. If equals be added to equals, the wholes are equal....equals be taken from equals, the remainders are equal. PROPOSITION 2. PROBLEM From a given point to draw a straight line equal to a given straight line. Let... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...quantity in general; and, second, those which arise out of the special forms of geometrical quantity. GENERAL AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are... | |
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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... 
