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The locus of points equidistant from two concentric circles is the circle concentric with the given circles and midway between them (Fig. 11-6). The locus of points at a given distance from a given point is a circle whose center is the given point and whose radius is the given distance (Fig. 11-7).

As can be seen above, $1,000 was charged to expense in April and $1,500 in May. The debit to Accrued Salaries Payable of $1,000 in May merely canceled the credit entry made in April, when the liability was set up for the April salaries expense

PRINCIPLE 6:



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Fig. 11-7

PRINCIPLE 7:

Fig. 11-8

range indicates the content contained between two speci ed end points as one contiguous selection A range interface confers the advantage of being able to access and manipulate entire portions of a document tree at a higher-level, rather than requiring that the range be decomposed into a sequence of nodes, each of which must be handled separately See the W3C DOM core for full details A range is comprised of two boundary points representing the start and end of the range The positions of the boundary points in a document (or DocumentFragment) tree consist of a starting node address and an o set (or range of nodes within the DOM s internal tree structure) The starting node address becomes the container for the boundary point and its position in the tree.





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The locus of points at a given distance from a given line is a pair of lines, parallel to the given line and at the given distance from the given line (Fig. 11-8). The locus of points at a given distance from a given circle whose radius is greater than that distance is a pair of concentric circles, one on either side of the given circle and at the given distance from it (Fig. 11-9). The locus of points at a given distance from a given circle whose radius is less than the distance is a circle, outside the given circle and concentric with it (Fig. 11-10). (If r d, the locus also includes the center of the given circle.)

PRINCIPLE 8:

PRINCIPLE 9:

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After the income statement and balance sheet have been prepared, a sum mary account known as Income Summary is set up. Then, by means of closing entries, each expense account is credited so as to produce a zero balance, and the total amount for the closed-out accounts is debited to In come Summary. Similarly, the individual revenue accounts are closed out by debiting them and their total amount is credited to the summary ac count. Thus, the new scal year starts with zero balances in the income and expense accounts, whereas the Income Summary balance gives the net income or the net loss for the old year.

Fig. 11-9

Fig. 11-10

11.1 Determining loci Determine the locus of (a) a runner moving equidistant from the sides of a straight track; (b) a plane flying equidistant from two separated aircraft batteries; (c) a satellite 100 mi above the earth; (d) the furthermost point reached by a gun with a range of 10 mi.

Just for comparison, here are several properties of euclidean geometry: Planes are infinite in area and flat. Lines are infinite in length. The angles of triangles always sum to 180 . There are similar triangles of different sizes. The circumference of a circle with radius r is C The area of a circle with radius r is A pr 2.

The properties of elliptic geometry are Planes are shaped like spheres, finite in area. Lines are great circles, finite in length. The angles of a triangle add up to more than 180 . For an example, take two longitude circles that meet at right angles at the North and South Poles and add the equator. These will cut the globe into 8 triangles where every angle is 90 . Thus, in elliptic geometry it is possible to have a triangle with an angle sum of 270 , as shown in Fig. 19-4. Smaller triangles will have smaller angle sums, but always more than 180 .

Fig. 19-4

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