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

John Playfair - 1837 - 318 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 equf.l to one another. 2. If equals be added to equals,...

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

Euclid - 1837 - 390 σελίδες
...the 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.* AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals or the...

Remarks on Mathematical Or Demonstrative Reasoning

Edward Tagart - 1837 - 135 σελίδες
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that things which are equal to the same are equal to one another, or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged...

Parochial lectures

William Josiah Irons - 1837
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' things which are equal to the same are equal to one another,' he would never get any such proof. If he should find by experience that it had been so, in a million...

The Elements of Euclid

Euclid - 1838 - 416 σελίδες
...point. II. That a terminated straight line may be produced to any length in at straight line. III. And that a circle may be described from any centre,...which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equals. m. If equals be taken from enuals, the remainders...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...point. II. That a terminated straight line may be produced to any length in a straight line. III. Anil that a circle may be described from any centre, at any distance from that centre. AXIOMS. THINGS which are equal to the same thing, are equal to one another. II. If equals be added to equals,...

Gradiations in Algebra: In which the First Principles of Analysis are ...

Richard W. Green - 1839 - 148 σελίδες
...dividing the 1st, x= — >£ Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that things which are equal to the same, are equal to one another ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...other point. II. That a terminated straight line may be produced to any length in a straight line. Ill And that a circle may be described from any centre, at any distance from that centre. AXIOMS. L Things which are equal to the same thing, are equal to one another. II. If equals be added to equals,...

Works, Τόμος 3

Francis Bacon - 1841
...similar to that of music termed the declining of a cadence. 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 Dublin Review, Τόμος 11

Nicholas Patrick Wiseman - 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " things which are equal to the same are equal to one another." The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured...




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