Books Books The perpendicular is the shortest line that can be drawn from a point to a straight line. The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 22
by Peter Nicholson - 1823 - 596 pages ## The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...is a str. line. [But one str. line can be drawn between two points.] (Ax. 3) PROP. VII. THEOREM. 46. The perpendicular is the shortest line that can be drawn from a point to a straight line. E \C' Given CD the _L from point C to line AB, and CE any other str. line... ## Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...given point without a plane, one perpendicular to the plane can be drawn, and but one. THEOREM IV. The perpendicular is the shortest line that can be drawn from a point to a plane. THEOREM V. Two oblique straight lines drawn from a point to a plane are equal when,... ## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...(101) But both of the above consequences would contradict the hypothesis. .-. AC>AB. QED 126. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. 12 1. NOTE. — The method used in the above proof is known as the "indirect... ## Plane Geometry

Arthur Schultze - 1901 - 260 pages
...(101) But both of the above consequences would contradict the hypothesis. .'. AC> AB. QED 126. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. 127. NOTR. — The method used in the above proof is known as the "indirect... ## Non-Euclidean Geometry

Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 122 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. The perpendicular is the shortest line that can be drawn from a point to a straight line. 8. Theorem. If oblique lines drawn from a point in a perpendicular to a line... ## Plane Geometry

Edward Brooks - 1901 - 278 pages
...PC is not 1 to AB; and therefore PE is the only _L to AB from the point P. Therefore, etc. COR. — The perpendicular is the shortest line that can be drawn from a point to a straight line. For PP' is less than the broken line PCP'. Ax. 13. SCHOLIUM. — Since a... ## Non-Euclidean Geometry

Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 120 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. The perpendicular is the shortest line that can be drawn from a point to a straight line. Corollary. In a right triangle the hypothenuse is greater than either of... ## Plane and Solid Geometry

Arthur Schultze - 1901 - 392 pages
...(124) (101) But both of the above consequences would contradict the hypothesis. .-. AC> AB. 126. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. 127. NOTE. — The method used in the above proof is known as the "indirect... ## Non-Euclidean Geometry

Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 116 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. The perpendicular is the shortest line that can be drawn from a point to a straight line. 8. Theorem. If oblique lines drawn from a point in a perpendicular to a line... 