## 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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Side 124

If the first of four magnitudes has the same ratio to the second which the third has

to the fourth , then any

same ratio to any

If the first of four magnitudes has the same ratio to the second which the third has

to the fourth , then any

**equimultiples**whatever of the first and third shall have thesame ratio to any

**equimultiples**of the second and fourth , viz . “ the**equimultiple**... Side 125

whatever of the first and third have the same ratio to the second and fourth : and

in like manner , the first and the third have the same ratio to any

whatever of the second and fourth . Let A the first , have to B the second , the

same ...

whatever of the first and third have the same ratio to the second and fourth : and

in like manner , the first and the third have the same ratio to any

**equimultiples**whatever of the second and fourth . Let A the first , have to B the second , the

same ...

Side 133

some

A is greater than the multiple of C , but the multiple of B , is not greater than it : let

them be taken , and let D , E be

some

**equimultiples**of A and B , and some multiple of C such , that the multiple ofA is greater than the multiple of C , but the multiple of B , is not greater than it : let

them be taken , and let D , E be

**equimultiples**of A , B , and F a multiple of C ... Side 135

And G , and G , H , K together are any

because , if there be any number of magnitudes

of each , whatever multiple one of them is of its part , the same multiple is the ...

And G , and G , H , K together are any

**equimultiples**of A , and A , C , E together ;because , if there be any number of magnitudes

**equimultiples**of as many , eachof each , whatever multiple one of them is of its part , the same multiple is the ...

Side 135

And G , and G , H , K together are any

because , if there be any number of magnitudes

of each , whatever multiple one of them is of its part , the same multiple is the ...

And G , and G , H , K together are any

**equimultiples**of A , and A , C , E together ;because , if there be any number of magnitudes

**equimultiples**of as many , eachof each , whatever multiple one of them is of its part , the same multiple is the ...

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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.