 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 - Page 1by Andrew Bell - 1837 - 240 pagesFull view - About this book
 | Euclides - 1884 - 434 pages
...Euclid's part, are never adhered to in practice.] AXIOMS. 1. Things which are equal to the same thing are equal to 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,... | |
 | Euclid - Geometry - 1892 - 460 pages
...already indicated in the definitions. GENERAL AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals,...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,... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...4. If equals, or the same, be added to unequals, the wholes are unequal. 5. If equals, or the same, be taken from unequals, the remainders are unequal. 6. Things which are doubles of the same, or of equals, are equal to one another. 7. Things which are halves of the same,... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...Common Notions, are known as the Axioms. GENERAL AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals,...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,... | |
 | Nehemiah Hawkins - Steam engineering - 1901 - 354 pages
...the remainders are 4. When equals are added to unequals 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, or of... | |
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