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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. "
SYLLABUS OF PLANE GEOMETRY - Side 14
1876
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

Alpheus Crosby - 1847 - 164 sider
...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 - 1847 - 164 sider
...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
...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 - 1872 - 136 sider
...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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 sider
...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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Elementary geometry

James Maurice Wilson - 1878
...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,...
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The Cambridge Examiner, Volum 1

1881
...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...
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The elements of plane geometry, Volum 1

Mathematical association - 1884
...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...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

Euclides - 1884
...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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