| Alpheus Crosby - Geometry - 1847 - 190 pages
...side of AD be equal to each other ? Can, then, three equal lines be drawn from A to BC? COR. I. Of **the straight lines that can be drawn to a given straight line from a** point without, — (1.) no three can be equal; and (2.) any two that are equal must be upon opposite... | |
| Alpheus Crosby - Geometry - 1847 - 190 pages
...side of AD be equal to each other ? Can, then, three equal lines be drawn from A to BC ? COR. I. Of **the straight lines that can be drawn to a given straight line** f rum a point without, — (1.) no three can be equal; and (2.) any two that are equal must be upon... | |
| Euclides - 1862 - 140 pages
...bisected, the bisecting lines contain a right angle. Prop. 16 to 26. 13. Prove that only one perpendicular **can be drawn to a given straight line, from a given point,** either within or without it. 14. Prove I. 17, without producing any side. 15. Prove I. 18, by cutting... | |
| James Maurice Wilson - 1872 - 160 pages
...it in the plane AOB1 ; and therefore (by Def. 2) to every straight line in the plane A OB. CoR. 1. **Of all the straight lines that can be drawn to a given** plane from a given point, the shortest is the perpendicular; and of the others those whose extremities... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...and having an angle = a given angle. SUPPLEMENT TO BOOK I. THEOREM (a). Of all straight lines which **can be drawn to a given straight line from a given point** without it, that which is nearer to the perpendicular is less than the more remote; also to every straight... | |
| Euclides - 1874 - 342 pages
...to two right angles, these two straight lines are parallels. 20. Prove that only one perpendicular **can be drawn to a given straight line, from a given point,** either within or without it. 21. From the vertex of a scalene triangle draw a right line to the base,... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...given point outside a given straight line, only one perpendicular can be drawn to that line. THEOR. 19. **Of all the straight lines that can be drawn to a given...point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
| Education, Higher - 1881 - 504 pages
...angles. Determine from the above the size of the angles in a regular pentagon, decagon, and dodecagon. 2. **Of all the straight lines that can be drawn to a given...point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
| Mathematical association - 1883 - 86 pages
...are together less than the two other sides of the triangle, but contain a greater angle. THEOR. 15. **Of all the straight lines that can be drawn to a given...point outside it, the perpendicular is the shortest;** and of the others, those which make equal angles with the perpendicular are equal; and that which makes... | |
| Mathematical association - 1884 - 146 pages
...sum of OA, OB, and OC is less than the perimeter of the triangle. THEOR. 15. Of all the strain-lit **lines that can be drawn to a given straight line from...point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
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