Books Books
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

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

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...described from any centre, at any distance from that centre. AXIOMS. 1. Tiiings which are equal to the same thing are equal to one another. 2. If equals...wholes are equal, 3. If equals be taken from equals the remamders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken...

## Induction

Alexander Bain - Logic - 1870 - 478 pages
...unquestionable axioms, conforming to both the criteria. The five succeeding are — AXIOMS OF EDCLID. 209 (3) If equals be taken from equals, the remainders are equal. (4) If equals be added to tmequals, the wholes are unequal. (5) If from unequals, equals be taken, the remainders are unequal....

## Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 4. If to unequals, equals be added, the wholes are unequal. 5. If from unequals, equals...

## The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 238 pages
...polygon with any given number of sides expressed by 2 n -f- 1, provided, 2 n -|- 1 is a prime number. AXIOMS. 1. Things which are equal to the same thing...another. 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to...

## Pure mathematics, Volume 1

Edward Atkins - 1874 - 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...If equals be added to equals the wholes are equal. I 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the...

## The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...a polygon with any given number of sides expressed by 2n + 1, provided, 2n -(- 1 is a prime number. AXIOMS. 1. Things which are equal to the same thing...another. 2. If equals be added to equals the wholes will be equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to...

## Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 pages
...described from any centre, at any distance from that centre. Axioms. 1. Tilings which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. EXPLANATION OF TERMS AND ABBREVIATIONS. 9 3. If equals be taken from equals the remainders are equal....

## The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...straight line ; 3. That a circle may be described from any centre, with a radius equal to any given line. Axioms. 1. Things which are equal to the same thing...added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are...