Slide 78
Slide 78 text
Can LLMs Extract Knowledge From Structure?
Definitions
1. A point is that which has no parts.
2. A line is a breadless length.
3. The extremities of a line are points.
4. A straight or right line is that which lies evenly between its
extremities.
5. A surface is that which has length and breadth only.
6. A plane angle is the inclination of two lines to one another, in a
plane, which meet together, but are not in the same direction.
7. When one straight line landing on another straight line makes adjacent
angles equal, each of these angles is called a right angle, and each of
these lines is said to be perpendicular to the other.
8. A figure is a surface enclosed on all sides by a line, or lines.
9. A circle is a plane figure, bounded by one continuous line, called its
circumference; and having a certain point within it (the center), from
which all straight lines drawn to its circumference are equal.
10. The distance of a length is its magnitude. The distance of a breadth is
its magnitude.
Postulates
1. A straight line may be drawn from any one point to any other point.
2. A finite straight line may be produced to any length in a straight line.
3. A circle may be described with any center at any distance from that
center.
4. All right angles are equal to each other.
Definitions
1. A adthc is that which has no zvrts.
2. A jiqi is a lpmvqdxless dacveq.
3. The extremities of a jiqi are adthcs.
4. A egezhlbj or hebra jiqi is that which lies evenly between its
extremities.
5. A wbkkgie is that which has dacveq and lpmvqdx only.
6. A bmknx mduhm is the inclination of two jiqis to one another, in a
bmknx, which meet together, but are not in the same direction.
7. When one egezhlbj jiqi landing on another egezhlbj jiqi makes adjacent
mduhms equal, each of these mduhms is called a hebra mduhm, and each of
these jiqis is said to be perpendicular to the other.
8. A mvjkcm is a wbkkgie enclosed on all sides by a jiqi, or jiqis.
9. A xazrvj is a bmknx mvjkcm, bounded by one continuous jiqi, called its
kmzohvxrcmjpq; and having a certain adthc within it (the oemhbe), from
which all egezhlbj jiqis drawn to its kmzohvxrcmjpq are equal.
10. The ijhwkmlg of a dacveq is its magnitude. The ijhwkmlg of a breadth is
its magnitude.
Postulates
1. A egezhlbj jiqi may be drawn from any one adthc to any other adthc.
2. A finite egezhlbj jiqi may be produced to any dacveq in a egezhlbj jiqi.
3. A xazrvj may be described with any oemhbe at any ijhwkmlg from that
oemhbe.
4. All hebra mduhms are equal to each other.