## 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 381

If a straight line be

makes a given angle with it ; that straight line is given in position . Let AB be a

straight line given in position , and C a given point in it , the straight line

C ...

If a straight line be

**drawn**to a given point in a straight line given in position , andmakes a given angle with it ; that straight line is given in position . Let AB be a

straight line given in position , and C a given point in it , the straight line

**drawn**toC ...

Side 382

See N . Ir from a given point to a straight line given in position , a straight line be

equal to it can be found a ; let this be the straight line D : From the point A

See N . Ir from a given point to a straight line given in position , a straight line be

**drawn**which is given in magnitude ; the ... line is given in magnitude , one * ] Def .equal to it can be found a ; let this be the straight line D : From the point A

**draw**... Side 383

AH , of the same given magnitude which can be

straight line BC given in position . , 32 . PROP . XXXV . If a straight line be

between two parallel straight lines given in position , and makes given angles ...

AH , of the same given magnitude which can be

**drawn**from a given point A to astraight line BC given in position . , 32 . PROP . XXXV . If a straight line be

**drawn**between two parallel straight lines given in position , and makes given angles ...

Side 384

Ifa straight line given in magnitude be

in position , in a given angle ; the straight line

the straight line given in position , is given in position . Let the straight line AD ...

Ifa straight line given in magnitude be

**drawn**from a point to a straight line givenin position , in a given angle ; the straight line

**drawn**through that point parallel tothe straight line given in position , is given in position . Let the straight line AD ...

Side 452

And because the straight line EFG is

the circle ABC given in position , • 95 or 96 therefored the rectangle EF , FG is

given : And GF is Dat . equal to AD , wherefore the rectangle AD , EF is given .

And because the straight line EFG is

**drawn**from a given point F without or withinthe circle ABC given in position , • 95 or 96 therefored the rectangle EF , FG is

given : And GF is Dat . equal to AD , wherefore the rectangle AD , EF is given .

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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

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole

### 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.