## The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |

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Resultat 1-5 av 5

Side 492

The indices or exponents of a series of ' numbers in geo . inetrical progression ,

proceeding from 1 , are also called the

Thus if a denote any number , and the geometrical series , 1 , a ' , a ' , a ' , at , & c

...

The indices or exponents of a series of ' numbers in geo . inetrical progression ,

proceeding from 1 , are also called the

**logarithms**of the numbers in that series . *Thus if a denote any number , and the geometrical series , 1 , a ' , a ' , a ' , at , & c

...

Side 494

If the

to the

For NSS = - * = l + am - n , by the nature of indices . The addition of

If the

**logarithm**of N be subtracted from the**logarithm**of M , the difference is equalto the

**logarithm**of the quotient which arises from Mitam the division of M by N .For NSS = - * = l + am - n , by the nature of indices . The addition of

**logarithms**... Side 496

The

the addition of lo2n + 1 - 1 . . - . garithms answers to the multiplication of the

numbers to which they belong , the

the ...

The

**logarithm**of " # 1 = 2 x**logarithm**of entit , 2n + 12 the**logarithm**of 2 Ini For asthe addition of lo2n + 1 - 1 . . - . garithms answers to the multiplication of the

numbers to which they belong , the

**logarithm**of the square of any num . ber , isthe ...

Side 498

The hyperbolic

powers of 2 , may be obtained by multiplying the

respectively , as is evident from the properties of

The hyperbolic

**logarithm**of 2 being thus found , that of 4 , 8 , 16 , and all the otherpowers of 2 , may be obtained by multiplying the

**logarithm**of 2 , by 2 , 3 , 4 , & c .respectively , as is evident from the properties of

**logarithms**stated in article 6 . Side 502

If the expeditious methods for calculating hyperbolic

foregoing articles * , had been known to Mr . Briggs , bis trouble would have been

... It has been already determined that the hyperbolic

If the expeditious methods for calculating hyperbolic

**logarithms**explained in theforegoing articles * , had been known to Mr . Briggs , bis trouble would have been

... It has been already determined that the hyperbolic

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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 43 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.

Side 153 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 52 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Side 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.