| 1829
...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 - 1830 - 272 Seiten
...piece of paper for a plane, with a pen,* a ruler, and a pair of compasses, it 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... | |
| Euclides - 1834
...are in the same plane, and which, being produced ever so far both ways, do not meet. POSTULATES. I. **LET it be granted, that a straight line may be drawn...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.... | |
| 1835
...of paper for a plane, •with a pen,* a ruler, and a pair of compasses, it 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... | |
| John Playfair - 1837 - 318 Seiten
...are in the same plane, and which, being produced ever so far both ways, do not meet. POSTULATES. 1. **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... | |
| Euclid, James Thomson - 1837 - 390 Seiten
...supplementary. So also are two angles which are together equal to two right angles. POSTULATES.* 1. **Let it be granted, that a straight line may be drawn from any one point, to any other point** :.). writers rather improperly use urcb) and chord receive their names from the bow (in Latin arcvs),... | |
| Andrew Bell - 1837 - 240 Seiten
...are in the same plane, and which, being produced eyer i so far both ways, do not meet. POSTULATES. 1. **Let it be granted that a straight- line may be drawn from any one point to any other point.** 3. And that a circle may be described from any centre, and with any radius. AXIOMS. 1. Things which... | |
| Euclides - 1838
...are in the same plane, and which, being produced ever so far both ways, do not meet. V POSTULATES. **LET it be granted, that a straight line may be drawn...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... | |
| Euclid, Robert Simson - 1838 - 416 Seiten
...are in the same plane, and which being produced ever so far both ways, do not meet. POSTULATES. I. **LET it be granted that a straight line may be drawn...terminated straight line may be produced to any length in** at straight line. III. And that a circle may be described from any centre, at any distance from that... | |
| Euclides - 1840
...straight line joining the opposite angles of a quadrilateral figure is called a DIAGONAL.] POSTULATES. 1. **Let it be granted, that a straight line may be drawn from any one point to any other point.** 2. That any terminated straight line may be produced or continued to any length in a straight line.... | |
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