 | Charles Scott Venable - 1881 - 380 pàgines
...a supposition made either in the enunciation of a proposition, or in the course of a demonstration. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. The whole is greater than its part. 3. The whole is equal to the sum of all its parts. 4. From one... | |
 | Marianne Nops - 1882 - 278 pàgines
...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.'... | |
 | Euclid, Isaac Todhunter - 1883 - 428 pàgines
...produced to any length in a straight line : 3. And that a circle may be described from any centre, at any distance from that centre AXIOMS. 1. Things...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 - 434 pàgines
...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 pàgines
...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 pàgines
...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,... | |
 | Seymour Eaton - 1899 - 362 pàgines
...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 - 1901 - 278 pàgines
...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... | |
 | Joseph Gregory Horner - 1906 - 572 pàgines
...Hundredweight 50802-34 50-8 -0508 1 Ton 1016-0 1-016 Euclid has based the whole of geometry on twelve axioms : — 1. Things which are equal to the same thing are equal to one another. 2. If equals he added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.... | |
 | Euclid - 1908 - 550 pàgines
...less than the two right angles. COMMON NOTIONS. 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. [7] 4. Things which coincide with one another are... | |
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Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... 
