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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. "
A Shorter Geometry - Page xxi
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

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...
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

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...
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Euclid's Elements of geometry, books i. ii. iii. iv

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...
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Solid Geometry and Conic Sections: With Appendices on Transversals, and ...

James Maurice Wilson - Conic sections - 1872 - 162 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...
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Euclidian Geometry

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...
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The Elements of Euclid, containing the first six books, with a selection of ...

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,...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

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...
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The Cambridge Examiner, Volume 1

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...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

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...
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The elements of plane geometry, Volume 1

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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