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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Σελίδα 5
των Euclid, Thomas Tate - 1849 - 108 σελίδες
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Hume

Thomas Henry Huxley - 1879 - 230 σελίδες
...straight and crooked would have no more meaning to him, than red and blue to the blind. The axiom, that things which are equal to the same are equal to one another, is only a particular case of the predication of similarity ; if there were no impressions, it is obvious...

Christian evidence lectures

Christian evidence society - 1879 - 498 σελίδες
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that things which are equal to the same are equal to one another to actual things, we should first have to ascertain the fact that the two things were exactly equal,...

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 σελίδες
...other 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 any distance from that centre. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals...

Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclides, Frederick Burn Harvey - 1880 - 178 σελίδες
...any other point. That a terminated straight line may be produced to any length in a straight line. 3. That a circle may be described from any centre, at any distance from that centre. The Postulates are ' Requests ' that Euclid makes for certain things to be allowed as permissible in...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 σελίδες
...purpose of comparison. See Prop. IV. of this book AXIOMS I. Things which are equal to the ssme thing, are equal to one another . n. If equals be added to...equals be taken from equals, the remainders are equal. IV. If equals be addod to unequals, the wholes are unequal. V. If equals be taken from unequals, the...

Pamphlets, Religious: Miscellaneous, Τόμος 14

1881 - 308 σελίδες
...premises, the science of mathematics is " fundamentally wrong," and that it is an error to believe that things which are equal to the same, are equal to one another, or that the whole is greater than its parts. Accordingly, were it true that Freethinkers differed from...

Macmillan's Magazine, Τόμος 43

1881 - 518 σελίδες
...always begin with an invocation to the Pleiades, thus fixing the original November date of the feast. " Things which are equal to the same are equal to one another." I have already adduced evidence to show that the Serbian Christmas feast is substantially a more primitive...

Works, Τόμος 3

Herbert Spencer - 1881 - 756 σελίδες
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — "Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...

The Intuitions of the Mind Inductively Investigated

James McCosh - 1882 - 472 σελίδες
...that all straight lines drawn from a certain point •within the figure are equal to one another ;" and that " A circle may be described from any centre at any distance from that centre." I shall have occasion, in speaking of the application of the principles laid down in this treatise...

Class lessons on Euclid

Marianne Nops - 1882 - 278 σελίδες
...other.' 2. ' That a terminated straight line may be produced to any length in a straight line.' 3. ' That a circle may be described from any centre at any distance from that centre.' Postulates 4 and 5 refer to simple geometrical truths which are quite evident ; postulate 6 is not...




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