## 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 |

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Resultat 1-5 av 7

Side 89

greater equal to the greater , and the less to the less . Let ABC , DEF be equal

circles , and BC , EF equal straight lines in them , which cut off the two greater ...

**THEOR**. In equal circles , equal straight lines cut off equal circumferences , thegreater equal to the greater , and the less to the less . Let ABC , DEF be equal

circles , and BC , EF equal straight lines in them , which cut off the two greater ...

Side 123

fourth ; and if of the first and third there be taken equimultiples , these shall be

equimultiples , the one of the second , and the other of the fourth . Let A the first ,

be ...

**THEOR**. If the first be the same multiple of the second , which the third is of thefourth ; and if of the first and third there be taken equimultiples , these shall be

equimultiples , the one of the second , and the other of the fourth . Let A the first ,

be ...

Side 161

other , and the sides about the equal angles proportionals , the triangles shall be

equiangular , and shall have those angles equal which are opposite to the ...

**THEOR**. Ir two triangles have one angle of the one equal to one angle of theother , and the sides about the equal angles proportionals , the triangles shall be

equiangular , and shall have those angles equal which are opposite to the ...

Side 197

I.

above it . * If it be possible , let AB , part of the straight line ABC , be in the plane ,

and the part BC above it : and since the straight line AB is in the plane , it can be

...

I.

**THEOR**. One part of a straight line cannot be in a plane , and another partabove it . * If it be possible , let AB , part of the straight line ABC , be in the plane ,

and the part BC above it : and since the straight line AB is in the plane , it can be

...

Side 203

line , and not in the same plane with it , are parallel to one another . H Let AB ,

CD be each of them parallel to EF , and not in the same plane with it ; AB shall be

...

**THEOR**. Two straight lines which are each of them parallel to the same straightline , and not in the same plane with it , are parallel to one another . H Let AB ,

CD be each of them parallel to EF , and not in the same plane with it ; AB shall be

...

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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.