Addition of Denominate Numbers. Subtraction of Denominate Numbers .... Applications in Addition and Subtraction.. Multiplication of Denominate Numbers.. Division of Denominate Numbers OF VULGAR OR COMMON FRACTIONS, Definition of, and First Principles :.... Of the Different kinds of Vulgar Fractions Redaction of Denominate Fractions Addition of Vulgar Fractions.. Subtraction of Vulgar Fractions .. To find the area of a Triangle .... To find the area of a Square, Rectangle, &c. To find the area of a Trapezoid.. To find the circumference and diameter of a Circle. To find the area of a Circle...... To find the surface of a Sphere. To find the solidity of a Sphere To find the convex surface of a Prism To find the solid content of a Prism.. To find the convex surface of a Cylinder. To find the solidity of a Cylinder ARITHMETIC. NUMERATION AND NOTATION. 1. A single thing is called One, Two, Three, Four, Four and one more are called Five, Six, Seven, Eight, Eight and one more are called Nine, Ten, &c. Each word, one, two, three, four, five, six, &c., points out how many things are spoken of. These words are called NUMBERS. Hence, NUMBERS are expressions for one or more things of the same kind. 2. The unit of a number is one of the equal things which the number expresses. Thus, if the number express șix apples, one apple is the unit; if it express five pounds of tea, one pound of tea is the unit; if ten feet of length, one foot is the unit; if four hours of time, one hour is the unit. 1. What is a single thing called ? · One and one? Two and one! Three and one ? Four and one ? Five and one ? Six and one? Seven and one ? &c. What are Numbers? 2. What is the unit of a number? What is the unit of the number six apples? Of the number five pounds of tea? Of the number teu feet? Of the number four hours ? 3. ARITHMETIC treats of numbers. Numbers are ex. pressed by certain characters, called figures. There are ten of these characters, and they are the alphabet of the arithmetical language. They are O which is called a cipher, or Naught, One, Two, 3 Three, 4 Four, 5 Five, 6 Six, 7 Seven, 8 Eight, 9 Nine. We see from the language of figures, that 1 expresses a single thing, or a unit of a number. 2 two things of the same kind, or two units. 3 three things or three units. 4 four things or four units. 5 five things or five units. 6 six things or six units. 7 seven things or seven units. 8 eight things or eight units. 9 nine things or nine units.. 4. The character 0 is used to denote the absence of a thing. Thus, to express that there are no apples in a basket, we write, the number of apples is 0. The nine other figures are called, significant figures, or Digits. 5. We have no separate character for the number ten. If we wish to express it by figures, we must combine the characters already known. This we do by writing 0 on the right hand of the 1; thus, 10, which is read len. 3. Of what does arithmetic treat? How are numbers expressed ? How many figures are there ? Name them. What may they be called? How many things does I express? How many things does 2 express? How many units in 3? In 4? In 5? In 6? In 7? In 8? In 9 ? 4. What does 0 express ? What are the other nine figures called ? 5. Have we a separate character for ten? How do we express ten? To how many units 1 is ten equal ? May we consider it a single unit? Of what order ? |