## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

### Inni boken

Side 50

From the point B

1. ) to A ; and through K L H Η G

, E , C

From the point B

**draw**( 11. 1. ) BF at right angles to BC , and make BG equal ( 3.1. ) to A ; and through K L H Η G

**draw**( 31. 1. ) GH parallel to BC ; and through D, E , C

**draw**| А ( 31. 1. ) DK , EL , CH parallel to BG : then the rectangle BH is ... Side 81

it is required to

) the centre E of the circle , and join AE ; and from the centre E , at the distance

EA , describe the circle AFG ; from the point D

...

it is required to

**draw**a straight line from A which shall touch the circle . Find ( 1. 3.) the centre E of the circle , and join AE ; and from the centre E , at the distance

EA , describe the circle AFG ; from the point D

**draw**( 11. 1. ) DF at right angles to...

Side 165

From the point A

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

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

part ...

From the point A

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

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

**draw**DE A parallel to it : then AE is thepart ...

Side 204

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

A a straight line perpendicular to the plane BH . In the plane

line BC , and from the point A

be ...

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

**draw**from the pointA a straight line perpendicular to the plane BH . In the plane

**draw**any straightline BC , and from the point A

**draw**( 12. 1. ) AD perpendicular to BC . If then ADbe ...

Side 289

... line AZ consequently greater than the straight line AG . COR . And if in the

lesser sphere there be described a solid polyhedron , by

betwixt the points in which the straight lines from the centre of the sphere drawn ...

... line AZ consequently greater than the straight line AG . COR . And if in the

lesser sphere there be described a solid polyhedron , by

**drawing**straight linesbetwixt the points in which the straight lines from the centre of the sphere drawn ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.