**Points**

- Let a be a point [distinct from . . . ].
- Let a be a point on L [distinct from . . . ].
- Let a be a point on L between b and c [distinct from . . . ].
- Let a be a point on L extending the segment from b to c [with a distinct from. . . ].
- Let a be a point on the same side of L as b [distinct from. . . ].
- Let a be a point on the side of L opposite b [distinct from. . . ].
- Let a be a point on a [distinct from . . . ].
- Let a be a point inside a [distinct from . . . ].
- Let a be a point outside a [distinct from . . . ].

**Lines and Circles**

- Let L be the line through a and b [distinct from . . . ].
- Let a be the circle with center a passing through b [distinct from . . . ].

**Intersections**

- Let a be a point of intersection of L and M [distinct from . . . ].
- Let a be a point of intersection of C and L [distinct from . . . ].
- Let a and b be the two points of intersection of C and L [distinct from . . . ].
- Let a be a point of intersection of L and C between b and c [distinct from . . . ].
- Let a be a point of intersection of L and C extending the segment from c to b [distinct from . . . ].
- Let a be a point of intersection of C and D [distinct from . . . ].
- Let a and b be the two points of intersection of C and D [distinct from . . . ].
- Let a be a point of intersection of C and D on the same side of L as b where L is the line through their centers c and d respectively [distinct from . . . ].
- Let a be a point of intersection of C and D on the side of L opposite b where L is the line through their centers c and d respectively [distinct from . . . ].

I believe that software development is fundamentally about making decisions, and so this is what I write about (mostly).
I've been building software for about 20 years now, as a developer, tech lead, and architect. I have two degrees from Carnegie Mellon University, most recently one in philosophy (thesis here).
I live in Pittsburgh, PA with my wife, 3 energetic boys, and dog.
Subscribe here or write me at ben dot northrop at gmail dot com.