| G. T. Kneebone
...breadthless length. 3. A straight line is a line which lies evenly with the points on itself. 8. A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line.** 10. When a straight line set up on a straight line makes adjacent angles equal to one another, each... | |
| Audun Holme - Mathematics - 2002 - 378 pages
...and breath only. 6. A plane surface is that which lies evenly with the straight lines on itself. 7. A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line.** 8. And when the lines containing the angle are straight, the angle is caller rectilinear. 9. When a... | |
| Hans Niels Jahnke - Mathematics - 422 pages
...rectilineal angle (Elements I, Def. 2), which can be subsumed under the more general definition: "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). Nevertheless, this special case is that one Euclid considers in his work. In... | |
| Avicenna Study Group. Conference - Philosophy - 2004 - 262 pages
...Euclid's definition of a plane angle, which is the following: "A plane angle is the inclination to one or **another of two lines in a plane which meet one another and do not lie in a straight line** (Elements, def. I, 8)." 7 But there is an essential difference. In their definitions of a plane angle... | |
| 洪萬生 - Mathematics - 2006 - 353 pages
...BC TÎIJ ФЁ ? ' J9fliA ' Г— ^— H r^j ° ^: « ^ift ) Й <HPMJ1IR> 3(1 1X2000): 2-20 Itt : A **plane angle is the inclination to one another of two...meet one another and do not lie in a straight line.** ' "Hne"yFJlí*félL^ ( straight line ) • And when the lines containing the angle are straight, the... | |
| Eli Maor - Mathematics - 2007 - 259 pages
...length"), a straight line ("a line which lies evenly with the points on itself"), and a plane angle **("the inclination to one another of two lines in a...which meet one another and do not lie in a straight** line").2 These are followed by ten statements that Euclid regarded as self-evident, as so clear and... | |
| Euclid, Johan Ludvig Heiberg - Euclid's Elements - 1926
...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,... | |
| ...(cXto-is 8vo ypa/jpuv, the 'inclination of two lines to one another.' We translate therefore: 'A pkne **angle is the inclination to one another of two lines...meet one another and do not lie in a straight line.'** The words TÛV -ypa/x/xûv before кЛип s are unnecessary and should be ignored; they were no doubt... | |
| Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...controversy, rooted in Antiquity, about the nature of such angles. In I.Def. 8 a plane angle is defined as **the inclination to one another of two lines in a plane which meet one another and do not** He in a straight line, and I.Def. 9 calls such an angle "rectilineal" when the lines containing the... | |
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