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" AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be... "
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Page 5
by John Bonnycastle - 1803 - 279 pages
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The Metaphysics of Aristotle: Translated from the Greek with Copious Notes ...

Aristotle, Thomas Taylor - First philosophy - 1801 - 482 pages
...and at the fame time denied, of the fame : alfo, that which is employed by geometry, viz. that thofe things which are equal to the fame thing are equal to each other; that which the natural philofopher ufes, that nothing can be generated from that which is not; and...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...just proved that AHG=HG D. Consequently FHB=HGD ; each being equal to AHG ; for it is an axiom that things which are equal to the fame thing are equal to each other. 35 . THEOREM. When two parallels are crossed by a straight line, the sum of the two interior angles...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...connexion, their use, their restriction, or their extension. Axioms. I. Things which are equal to the same thing, are equal to each other. 2 If equals be added to equals, the wholes will he equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...may be described from any centre, and with any radius. AXIOMS. 1. Things that are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums are equals. 3. If equals be taken from equals, the remainders are equals. 4. If equals be added...
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Ticknor's Mensuration, Or, Square and Triangle: Being a Practical and ...

Almon Ticknor - Measurement - 1849 - 156 pages
...proposition, or in the course of a demonstration. AXIOMS. — 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the whole will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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A New System of Arithmetic on an Improved Plan

Charles Guilford Burnham - 1850 - 350 pages
...54, or Part I. AXIOMS An axiom is a self-evident proposition. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the wholes will be equal. 8. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...tests of equality between two quantities : 1. Things which are equal to the tame or to equal things, are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be subtracted from equals the remainders will be equal. 4. Like parts...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 368 pages
...— neither admitting nor requiring any demonstration; such as, 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...angles. AXIOMS. 34. An AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles. AXIOMS. 34. An AXIOM is a self-evident trath ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be...
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