## 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 6

Side 75

BCD ; it is required to

circle . Find a the centre E of the circle , and join AE ; and from * 1 . 3 . the centre

E , at the distance EA , describe the circle AFG ; from the point D drawb DF at

right ...

BCD ; it is required to

**draw**a straight line from A which Book III . shall touch thecircle . Find a the centre E of the circle , and join AE ; and from * 1 . 3 . the centre

E , at the distance EA , describe the circle AFG ; from the point D drawb DF at

right ...

Side 159

From the point A

take any point D , and take AČ the same multiple of AD , that AB is A of the part

which is to be cut off from it : join BC , and

...

From the point A

**draw**a straight line AC , making any angle with AB ; and in ACtake any point D , and take AČ the same multiple of AD , that AB is A of the part

which is to be cut off from it : join BC , and

**draw**DE parallel to it : Then I AE is the...

Side 198

To

A be the given point above the plane BH ; it is required to

straight line perpendicular to the plane BH . In the plane

To

**draw**a straight line perpendicular to a plane , from a given point above it . LetA be the given point above the plane BH ; it is required to

**draw**from the point A ástraight line perpendicular to the plane BH . In the plane

**draw**any straight line ... Side 334

... within it

DE , DF , equal to one another , upon the opposite sides of the plane , and let G

be any point in EF ; join DA , DB , DC ; EA , EB , EC ; FA , FB , FC ; GA , GB , GC ...

... within it

**draw**a the straight line DE at right angles to the plane ABC ; in DE takeDE , DF , equal to one another , upon the opposite sides of the plane , and let G

be any point in EF ; join DA , DB , DC ; EA , EB , EC ; FA , FB , FC ; GA , GB , GC ...

Side 422

straight line EF given in position and magnitude , and upon it describe the

segment of a circle EGF , containing an angle equal to the given angle BAC ,

EGF is ...

straight line EF given in position and magnitude , and upon it describe the

segment of a circle EGF , containing an angle equal to the given angle BAC ,

**draw**GH bisecting EF at right angles , and join EG , GF : Then , since the angleEGF is ...

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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.