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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... "
Euclid, books i. & ii., with notes, examples, and explanations, by a late ... - Page 6
by Euclides - 1879
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

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...
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Class lessons on Euclid

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.'...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

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....
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Notes on algebra

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...
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The Harpur Euclid: An Edition of Euclid's Elements

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,...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

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...
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Plane Geometry: A Complete Course in the Elements of the Science

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...
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Henley's Encyclopędia of Practical Engineering and Allied Trades: A ...

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....
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Introduction and books 1,2

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...
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