This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...9, the surface divides space into two parts which are called, respectively, the inside and the outside of the cylindrical surface. 132. A plane meeting a cylindrical surface meets it in one point at least 12, and the plane either contains the element through this point, or cuts it. If the plane cut that element, it ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...9, the surface divides space into two parts which are called, respectively, the inside and the outside of the cylindrical surface. 132. A plane meeting a cylindrical surface meets it in one point at least 12, and the plane either contains the element through this point, or cuts it. If the plane cut that element, it intersects every other parallel line, and therefore, in particular, it intersects every other element of the cylindrical surface. If a second plane, parallel to this first plane, be taken, it also will intersect every element of the cylindrical surface. 133. The plane curve in which the cylindrical surface meets the cutting plane of the preceding section has a tangent at any point; and this straight line is said to be a tangent to the cylindrical surface. Thus the tangent is a line not an element, which meets the surface, but does not cut through it where it meets it. The point of meeting is called the point of tangency. 134. Any tangent line, with the element through the point of tangency, will determine a plane, which has no part in common with the cylindrical surface except the element thus taken. Such a plane is said to be tangent to the surface. Thus the tangent plane is a plane which contains one element of a cylindrical surface, but does not cut the surface along that element. The single element in which a tangent plane meets the surface is called the element of contact. 135. But, on the other hand, the plane through an element may pass through any other point of the cylindrical surface 15 (3), and will contain the line through this point parallel to the first element; and this parallel line is itself an element 130, def.. Since the surface is convex 131, the cutting plane will not meet the surface except in these two elements. 136. To rec...
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