 | Alpheus Crosby - 1847 - 190 ページ
...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 - 1847 - 190 ページ
...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 ページ
...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 ページ
...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... | |
 | Euclides - 1874 - 342 ページ
...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,... | |
 | Francis Cuthbertson - 1874 - 400 ページ
...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... | |
 | James Maurice Wilson - 1878 - 450 ページ
...point to meet a given straight line, the perpendicular is the shortest; and of the others, those making equal angles with the perpendicular are equal ; and...perpendicular is greater than that which makes a less. Part. En. Let O be the given point, and AB the given straight line, and let OP be the perpendicular,... | |
 | 1881 - 504 ページ
...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...the perpendicular are equal ; and that which makes & greater angle with the perpendicular is greater than that which makes a less angle. 3. On a given... | |
 | Mathematical association - 1884 - 146 ページ
...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...perpendicular is greater than that which makes a less angle. Let A be the given point, and BC the given straight line, and let AD be the perpendicular from A to... | |
 | Euclides - 1884 - 182 ページ
...angles of a triangle are together greater than two right angles. 5. Show that only one perpendicular can be drawn to a given straight line from a given point without it. 6. Prove Euclid's Proposition XVII. without producing any side, but using a straight line... | |
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Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest. 
