Books Books
Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 306
by Euclid - 1835 - 513 pages

## The First Six Books with Notes

Euclid - 1822 - 179 pages
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o Axioms. 1. Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...

## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...But it has been proved dial CA is equal to AB ; therefore CA, CB, are each of diem equal to AB ; but things which are equal to the same are equal to one another (1st Axiom.) tiierefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another j and the...

## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...

## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And things which are equal to the same are equal to one another. Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,...

## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...Euclid had given, has been deceived in applying what is manifest, when understood of magnitudes, unto ratios, viz. that a magnitude cannot be both greater...those things which are equal to the same are equal to'one another, is a most evident axiom when understood of magnitudes; yet Euclid does not make use...

## Outline of a New System of Logic: With a Critical Examination of Dr. Whately ...

George Bentham - Logic - 1827 - 304 pages
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. Things which are equal to the same, are equal to one another. 2. When of two things, one only is equal to a third, and the other is not equal to that third, these...

## Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827 - 638 pages
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the third?" " If equals be added to equals the sums are...

## The London Magazine, Volume 17

English literature - 1827 - 610 pages
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous V " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the thirdV " If equals be added to equals, the sums are...