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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 - 1819 - 317 σελίδες
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another .I. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, B are equal to one another ; and the triangle...

The Oedipus Romanus; Or, An Attempt to Prove, from the Principles of ...

George Townsend - 1819 - 147 σελίδες
...circumstance indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as things which are equal to the same, are equal to one another, the Patriarchs are the Caesars, and the Caesars the sons of Jacob, because they are both synonymous...

Artis logicæ rudimenta, with illustrative observations [and a transl. By J ...

Henry Aldrich - 1821
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, Things which are equal to the same are equal to one another ; and, Things of which one is equal and the other not equal to the same, are not equal to one another....

The First Six Books with Notes

Euclid - 1822 - 179 σελίδες
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o Axioms. 1. Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...other point. 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. Thingi which ate equal to the same are equal to one another. 2. If equals be added to equals the...

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

Euclid, John Playfair - 1826 - 320 σελίδες
...from any eentre, at any distanee from that eentre. AXIOMS, I. THlNGS whieh are equal to the same thing are equal to one another, n. If equals be added to equals, the wholes are equal. III. If equals be taken from equal?, the remainders are equal. IV. If equals be added to unequals,...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And things which are equal to the same are equal to one another. Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...other point. If. That a terminated straight line may be produced to any length in a straight line. III. 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...

Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the third?" " If equals be added to equals the sums are...




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