## 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]. |

### Inni boken

Side 48

If a straight line be bisected , and

by the whole line thus

square of half the line bisected , is equal ' to the square of the straight line which ...

If a straight line be bisected , and

**produced**to any point : the rectangle containedby the whole line thus

**produced**, and the part of it**produced**, together with thesquare of half the line bisected , is equal ' to the square of the straight line which ...

Side 52

If a straight line be bisected , and

line thus

double of the square of half the line bisected , and of the square of the line made

up of ...

If a straight line be bisected , and

**produced**to any point , the square of the wholeline thus

**produced**, and the square of the part of it**produced**, are togetherdouble of the square of half the line bisected , and of the square of the line made

up of ...

Side 202

For , if it is not , EF , GH , shall meet , if

: First , let them be

Therefore , since EFK is in the plane AB , every point in EFK is in that plane : and

K is a ...

For , if it is not , EF , GH , shall meet , if

**produced**, either on the side of FH , or EG: First , let them be

**produced**on the side of FH , and meet in the point K :Therefore , since EFK is in the plane AB , every point in EFK is in that plane : and

K is a ...

Side 450

If a straight line be drawn within a circle given in magnitude , cutting off a

segment containing a given angle : If the angle adjacent to the angle in the

segment be bisected by a straight line

again , and the ...

If a straight line be drawn within a circle given in magnitude , cutting off a

segment containing a given angle : If the angle adjacent to the angle in the

segment be bisected by a straight line

**produced**till it meet the circumferenceagain , and the ...

Side 492

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

be

logarithms of the first , second , third , and fourth powers of a respeetively .

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

be

**produced**by actual multiplication , then 1 , 2 , 3 , 4 , & c . are called thelogarithms of the first , second , third , and fourth powers of a respeetively .

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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.