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" Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal. "
Elements of Plane Geometry - Page 5
by William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 263 pages
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...' . 77. A Scholium, is a remark or observation made upon something going before it. -- 9 ' AXIOMS. AXIOMS. 1. THINGS which are equal to the same thing are equal to each other. 2. When equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remains...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...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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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...evident truth. 70. A Postulate is a request to admit the possibility of performing a certain operation. AXIOMS. 1. Things which are equal to the same thing, are equal to each other. 2. When equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825 - 608 pages
...demonstration. 77. A Scholium, is a remark or observation made upon something going before it. AXIOMS. AXIOMS. 1. THINGS which are equal to the same thing are equal to each other. 2. When equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders...
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Mechanics' Magazine, and Journal of the Mechanics' Institute, Volume 4

Industrial arts - 1835 - 398 pages
...truth or demonstration. 77. A Scholium is a remark or observation made upon something going before it. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. When equate 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 - 394 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 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...
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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 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...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...demonstration. An hypothesis is a supposition. A scholium is a remark subjoined to a demonstration. Axioms. 1. Things which are equal to the same thing, are equal to each other. 2. Things which are double, triple, &c. of the same or equal things, are equal to each other. 3. Things...
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Ticknor's Mensuration, Or, Square and Triangle: Being a Practical and ...

Almon Ticknor - Measurement - 1849 - 156 pages
...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 each other. 2. If equals be added to equals, the whole will be equal. 3. If equals be taken from equals, the remainders will...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 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 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...
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