| Douglas M. Jesseph - Mathematics - 1993 - 322 pages
...that had a long history in geometry and was much discussed in Berkeley's day. According to Euclid, "A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line"** (Elements I, def. 8). This definition covers cases beyond the intersection of two straight lines. In... | |
| John McCleary - Mathematics - 1994 - 308 pages
...arms. The next postulate deals with angles. We first recall a few more of Euclid's definitions: (8) A **plane angle is the inclination to one another of two lines in** the plane that meet one another and do not lie in a straight line. (9) And when the lines containing... | |
| Ronald Calinger - Mathematics - 1996 - 359 pages
...The concept of angle arises with other meanings in Euclid's Elements. Book I, Definition 8, reads: "A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line."** This definition is not operational, that is to say, Euclid does not use it in his proofs. In particular,... | |
| Howard Whitley Eves - Mathematics - 1997 - 344 pages
...are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. 8. A **plane angle is the inclination to one another of two lines in a plane** if the lines meet and do not lie in a straight line. 9. When the lines containing the angle are straight... | |
| Eli Maor - Mathematics - 2002 - 236 pages
...as quoted by Chase, Rhind Mathematical Papyrus, p. 59. 4. Gillings, Mathematics, p. 170. 1 Angles A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line.** — Euclid, The Elements, Definition 8 Geometric entities are of two kinds: those of a strictly qualitative... | |
| Nick Huggett - Science - 1999 - 274 pages
...are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. 8. A **plane angle is the inclination to one another of two...angle are straight, the angle is called rectilineal.** 10. When a straight line set up on a straight line makes the adjacent angles equal to one another,... | |
| Anne Ashley Davenport - Philosophy - 1999 - 438 pages
...define the angle at the point where 77 Euclid defines the plane angle as follows: (definition 8): "A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line."** (definition 9): "And when the lines containing the angle are straight, the angle is called rectilinear."... | |
| Douglas M. Jesseph - Mathematics - 2000 - 419 pages
...six sciences: mechanics, astronomy, optics, geodesy, canonics, and calculation" (Proclus 1970, 31). **in a plane which meet one another and do not lie in a straight line"** (Elements 1, def. 8). Finally, postulates are demands that a certain construction be admitted or effected,... | |
| Judith Cederberg - Mathematics - 2004 - 441 pages
...are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. 8. A **plane angle is the inclination to one another of two...angle are straight, the angle is called rectilineal.** 10. When a straight line set up on a straight line makes the adjacent angles equal to one another,... | |
| Judith Cederberg - Mathematics - 2004 - 441 pages
...are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. 8. A **plane angle is the inclination to one another of two...when the lines containing the angle are straight, the** is called rectilineal. 10. When a straight line set up on a straight line makes the angles equal to... | |
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