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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 Euclides - 1849
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 σελίδες
...point : f 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. J AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals...

The Quarterly Review

William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray IV, Rowland Edmund Prothero (Baron Ernle) - 1845
...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 English Journal of Education, Τόμος 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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 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'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...

The Biblical review, and Congregational magazine [formerly The ..., Τόμος 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,...

An Historical and Critical View of the Speculative Philosophy of ..., Τόμος 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,...

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

Euclides - 1846
...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...

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...

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...




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