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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 English Journal of Education, Volume 3

1845
...By the whole of any quantity we understand the sum of all its parts ; thus, AB = AD + DC + CB. 70. " Things which are equal to the same are equal to one another " ; that is, if a = m and b = m, a is equal to b. 71. In any arithmetical operation, " quantities which...

The Quarterly Review, Volume 76

...discovery, that both languages admit of the same Erse interpretation, upon the geometrical principle that things which are equal to the same are equal to one another. This argument however depends for its validity on the accuracy of his remaining assumption, that the...

The Biblical review, and Congregational magazine [formerly The ..., Volume 4

1847 - 602 pages
...proved by the use of axioms in the form of propositions, that is not itself evident. The axiom, that things which are equal to the same are equal to one another, is not the proof that A and B, being equal to C, are themselves equal. The latter truth, which is particular,...

Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...3. That a circle can be described 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. 3. If from equals, equals be taken, the...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...But it has been shewn that BC is equal to BG; therefore AL and BC are each of them equal to BG : And things which are equal to the same are equal to one another ; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL...

An Historical and Critical View of the Speculative Philosophy of ..., Volume 1

John Daniel Morell - Philosophy, Modern - 1846 - 536 pages
...judgments, as we have seen in our analysis of Locke, are at first particular and concrete. The axiom, " things which are equal to the same are equal to one another," never suggests itself to a child's mind. and yet as soon as reason is developed enough to observe equality,...

An Historical and Critical View of the Speculative Philosophy of Europe in ...

J. D. Morell - Philosophy, Modern - 1847 - 632 pages
...judgments, as we have seen in our analysis of Locke, are at first particular and concrete. The axiom, " things which are equal to the same are equal to one another," never suggests itself to a child's mind ; and yet as soon as reason is developed enough to observe...

General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848 - 520 pages
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " things which are equal to the same are equal to one another," which can equally well be applied to logic, thereby insinuating that the observations of "philosophia...