Can someone explain Euclid's Book 1 Definition 7, 8, and 9?
- A plane surface is a surface which lies evenly with the straight lines on itself.
- A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
- And when the lines containing the angle are straight, the angle is called rectilineal.
Also, define rectilineal. If possible provide a picture.
(Mainly 8 and 9). I think 8 is a normal angle and 9 seems like a straight line, but I'm not sure.
- thanks
I found the entire Euclid's Elements on this website. Every topic is a clickable link which provides diagrams.
On the link of definition $8$, the following is made clear. Lines can be straight or curved (e.g., a circular arc). When both the arms of an angle are straight lines, we have a rectilinear angle.
When a curve and a straight line 'contain' an angle e.g., the angle formed between a circle and its tangent at a point, the term horn angle is used.
The phrase rectilinear is used for a figure made of straight lines only. For example, a polygon is rectilinear means it all of its sides are straight lines, none is curved.