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 Bøker Bok Let it be granted that a straight line may be drawn from any one point to any other point. The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 8
av Euclid, Robert Simson - 1838 - 416 sider
Uten tilgangsbegrensning - Om denne boken ## The English Journal of Education, Volum 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...
Uten tilgangsbegrensning - Om denne boken ## The Quarterly Review

...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...
Uten tilgangsbegrensning - Om denne boken ## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...other point : n. That a terminated straight line may be produced to any length in a straight line : in. That a circle may be described from any centre, at...which are equal to the same are equal to one another. n. If equals be added to equals, the wholes are equal. in. If equals be taken from equals, the remainders...
Uten tilgangsbegrensning - Om denne boken ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...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,...
Uten tilgangsbegrensning - Om denne boken ## An Historical and Critical View of the Speculative Philosophy of ..., Volum 1

J. D. Morell - 1846
...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,...
Uten tilgangsbegrensning - Om denne boken ## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...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...
Uten tilgangsbegrensning - Om denne boken ## The Biblical review, and Congregational magazine [formerly The ..., Volum 4

1847
...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,...
Uten tilgangsbegrensning - Om denne boken ## The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847
...point : 2. That a terminated straight line may be produced to any length in a straight line : and 3. That a circle may be described from any centre, at any distance from that centre. A postulate (from postulare) is a demand so reasonable that it cannot fail to be granted; or, in other...
Uten tilgangsbegrensning - Om denne boken ## An Historical and Critical View of the Speculative Philosophy of Europe in ...

J. D. Morell - 1847
...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...
Uten tilgangsbegrensning - Om denne boken ## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...other point. II. That a terminated straight line may be produced to any length in a straight line. HI. And that a circle may be described from any centre...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals...
Uten tilgangsbegrensning - Om denne boken