| Charles Scott Venable - 1881 - 380 pages
...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 pages
...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 - Euclid's Elements - 1883 - 428 pages
...point : 2. That a terminated straight line may be produced to any length in a straight line : 3. And **that a circle may be described from any centre, at...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 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,... | |
| 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
...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 - Engineering - 1906 - 572 pages
...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 - Mathematics, Greek - 1908 - 550 pages
...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... | |
| |