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This postulate is the one which establishes that our plane cannot look like a giant sphere.4 a flat plane, On 4 4 given point P not on line AB, only a point C which makes /APC > /PAB will make PC i AB , as shown in Fig. 19-3(a). On a giant sphere, straight lines are great circles which divide the sphere into two equal-sized pieces. Any two such lines will always meet at two spots at opposite points of the sphere (called antipodal points), such as X and Y, as shown in Fig. 19-3(b). Because any two straight lines meet, it is impossible for there to be parallel lines on a sphere.



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Fig. 19-3

1. Another term for an accounting period is an _______. 2. The statement that shows net income for the period is known as the ______ statement. 3. Two groups of items that make up the income statement are _____ and _________. 4. Assets must equal _________. 5. Expense and income must be matched in the same ___________. Answers: 1. accounting statement; 2. income; 3. income, expense; 4. lia bilities and capital; 5. year or period





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<cd> <title>Beautiful Maladies</title> <artist> < rstname>Tom</ rstname> <lastname>Waits</lastname> </artist> <song genre="urban folk" year="1987" length="2:42"> Hang on St. Christopher</song> <song genre="urban folk" year="1987" length="3:51"> Temptation</song> <song genre="urban folk" year="1985" length="3:45"> Clap Hands</song> </cd> Use the DTD created in 2: <!DOCTYPE <!ELEMENT <!ELEMENT <!ELEMENT <!ELEMENT <!ELEMENT <!ELEMENT <!ELEMENT <!ATTLIST <!ATTLIST ]> 4.1 Declare a font color of red and weight of 400 for the title element. 4.2 Declare a font size and weight for the song element. 4.3 Add the notes element and declare the display: block style in the DTD. 4.4 Create a text shadow for the artist element. 4.5 Place all these in a style sheet named cd.css, and link it in the XML document by creating the appropriate PI. title [ CD (title, artist+, song*)> title (#PCDATA)> artist (( rstname*, lastname) | group )> rstname (#PCDATA)> lastname (#PCDATA)> group (#PCDATA)> song (#PCDATA)> song genre CDATA #IMPLIED> song year CDATA #IMPLIED>

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For about 2000 years, certain mathematicians tried to use the first four postulates to prove the fifth. This challenge was called the fifth postulate problem. The first four seem to come straight from the basic tools of geometry: the straight edge (connecting points and extending straight lines), the compass (drawing circles),

and the square (measuring right angles). The fifth, it seemed, was something that ought to be provable. However, no one was able to succeed in proving the fifth postulate without introducing new, equivalent postulates that required belief without proof. (Actually, the fifth postulate stated previously is a simpler alternative to the one Euclid actually used.) If a postulate about parallel lines must be accepted without proof, why must it be the traditional fifth postulate of euclidean geometry

In the 19th century, mathematicians finally established that there are actually three basic types of planar geometry, not one. The traditional one is called euclidean geometry, which is based on the fifth postulate (or one of the many equivalent postulates). However, we could instead believe one of the two alternate fifth postulates:

POSTULATE 5a: POSTULATE 5b:

There are no parallel lines. Through a given point not on a given line, many different lines can be drawn parallel to a given line.

If we believe Postulate 5a (along with Postulates 1 through 4), then we will end up with what is called elliptic geometry. This is the sort of geometry where a plane is actually shaped like the surface of a sphere and lines are great circles. If we believe Postulate 5b, we will end up with an even stranger geometry called hyperbolic geometry.

Solved Problem 4.1 Indicate the name of the account group Income (I), Expense (E), Asset (A), Liability (L), or Capital (C) in which each of the following accounts belong. (a) Accounts payable (b) Accounts receivable (c) Building (d) Supplies (e) Cash (f ) Drawing Solution: (a) L (b) A (c) A (d) A (e) A (f ) C (g) A (h) I (i) E ( j) I (k) L (l) I Solved Problem 4.2 Below is an income statement with some of the in formation missing. Fill in the information needed to complete the income statement. Sales Income Operating Expenses: Wages Expense $16,910 Rent Expense (a) Utilities Expense 3,150 Total Expenses Net Income Solution: (a) 12,090 (b) $73,450 (b) (g) Equipment (h) Fees income (i) Interest expense ( j) Interest income (k) Notes payable (l) Rent income

Fig. 9-21

Fig. 9-22

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