verb (used with object)
to cut or divide by passing through or across: The highway intersects the town.
verb (used without object)
to cross, as lines or wires.
Geometry. to have one or more points in common: intersecting lines.

1605–15; < Latin intersectus past participle of intersecāre to cut through, sever. See inter-, -sect

nonintersecting, adjective
self-intersecting, adjective
unintersected, adjective
unintersecting, adjective Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
intersect (ˌɪntəˈsɛkt)
1.  to divide, cut, or mark off by passing through or across
2.  (esp of roads) to cross (each other)
3.  (often foll by with) maths to have one or more points in common (with another configuration)
[C17: from Latin intersecāre to divide, from inter- + secāre to cut]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1610s, from L. intersectus, pp. of intersecare "intersect, cut asunder," from inter- "between" + secare "to cut" (see section).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Next, they traced a grid with lines intersecting every half-inch or so and
  scanned the model's data set into the computer.
One solution would be to drill a second intersecting borehole before exploiting
  the site.
The layers of intersecting patterns at work in this place were extraordinarily
The fact that two curves are intersecting does not mean that their positions
  may not change in a week.
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