Proposition 12
Construction
To draw a line perpendicular to a given infinite line from a given point not on it.
Construction Steps
1. Let infinite line AB be given, and let C be the given point not on it.
2. Take a point F on infinite lineAB . Join CF .
3. Construct the circle through the point F centered at C that intersects infinite lineAB at point G.
4. BisectFG at H and join CH . The line CH is perpendicular to infinite line AB from the given point C not on it.
2. Take a point F on infinite line
3. Construct the circle through the point F centered at C that intersects infinite line
4. Bisect
Original statement
ἐπὶ τὴν δοθϵῖσαν ϵὐθϵῖαν ἄπϵιρον ἀπὸ τοῦ δοθέντος σημϵίου, ὃ μή ἐστιν ἐπ᾽ αὐτῆς, κάθϵτον ϵὐθϵῖαν γραμμὴν ἀγαγϵῖν.
English translation
To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line.
