 | English literature - 1829 - 430 pages
...convenient to substitute for it. How do you reconcile the admission of Euclid's postulate, " that a straight line may be produced to any length in a straight line, 1 ' with the neces-, I. «*_ xy — x + y, II. 3x* — 2xy + y 3 — 4>x — 4y + 3 = 0. III. x>=xy... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the greater of two straight lines, a part may be cut off equal to the less ; and 4thly,... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to...centre, at any distance from that centre. Axioms. iTHINGS which are equal to the same thing are equal to one another. II. If equals be added to equals,... | |
 | Euclides - 1834 - 518 pages
...I. LET it be granted, that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. BOOK I. — AXIOMS. AXIOMS. I. THINGS which are equal to the same thing, are equal to one another.... | |
 | John Claudius Loudon, Edward Charlesworth, John Denson - Natural history - 1834 - 698 pages
...book marks an epoch in the progress of natural history in Britain. One of Euclid's postulates is, " a circle may be described from any centre, at any distance from that centre:" so, in nature, there is not an object which may not become the centre of a thousand associating circumstances.... | |
 | Euclid - 1835 - 540 pages
...POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to...centre. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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,... | |
 | Mathematics - 1835 - 684 pages
...is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the greater of two straight lines, a part may be cut off equal to the less ; and 4thly,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...abbreviated expression, meaning the ^auje as in draw a straight line from one of them to 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.... | |
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LET it be granted that a straight line may be drawn from any one point to any 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... 
