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" 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 added to unequals, the sums will be unequal. "
Ticknor's Mensuration, Or, Square and Triangle: Being a Practical and ... - Page 22
by Almon Ticknor - 1849 - 144 pages
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - Euclid's Elements - 1789 - 296 pages
...right lines, may be produced till it meets the other. AXIOMS. 1. Things which are equal to the fame thing are equal to each other, 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders will be equal. 4. If equals...
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A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ...

Charles Hutton - Mathematics - 1816
...demonstration. 77. A Scholium, is a remark or observation made upon something going before it. AXIOMSAXIOMS. 1. THINGS which are equal to the same thing are equal to each other. 2. \Vhnn equals are added to equals, the wholes are equal. 3 When equals are taken from equals, the remainders...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...extracted ; thus V2 means the square-root of 2 ; VA x B means the square-root of the product of A and B. Axioms. • 1. Things which are equal to the same...each other. -2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. . 4. If equals...
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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...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 380 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 be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 264 pages
...Scholium is a remark on one or more preceding propositions. 17. An Axiom is a self evident truth. .. AXIOMS. 1. Things which are equal to the same thing...to each other. 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders will be equal. ClOEST.— 11....
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Elements of Surveying, and Navigation: With a Description of the Instruments ...

Charles Davies - Navigation - 1835 - 359 pages
...supposition, made either in the enunDESCR1PT1ON OF 1NSTRUMENTS. 21 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 be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...circle 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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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...square root of the product of A and B. AXIOMS. 1 . Quantities which are equal to the same quantities, are equal to each other. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...perpendicular to the base. Thus, AB is the base and CD is the altitude of the trapezoid. Of Axioms. AXIOMS. 1 . Things which are equal to the same thing...to each other. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals...
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