## 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 117

Ratio is a mutual relation of two magnitudes of the same kind to one another , in

respect of quantity . ' * IV . Magnitudes are said to have a ratio to one another ,

when the so as to exceed the other . V. second , which the third has to the

Ratio is a mutual relation of two magnitudes of the same kind to one another , in

respect of quantity . ' * IV . Magnitudes are said to have a ratio to one another ,

when the so as to exceed the other . V. second , which the third has to the

**fourth**... Side 118

first be greater than that of the second , the multiple of the third is also greater

than that of the

proportionals . N. B. “ When four magnitudes are proportionals , it is usually

expressed ...

first be greater than that of the second , the multiple of the third is also greater

than that of the

**fourth**. VI . Magnitudes which have the same ratio are calledproportionals . N. B. “ When four magnitudes are proportionals , it is usually

expressed ...

Side 119

Permutando , or alternando , by permutation , or alternately ; this word is used

when there are four proportionals , and it is inferred , that the first has the same

ratio to the third , which the second has to the

, as ...

Permutando , or alternando , by permutation , or alternately ; this word is used

when there are four proportionals , and it is inferred , that the first has the same

ratio to the third , which the second has to the

**fourth**; or that the first is to the third, as ...

Side 120

... 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 Co

Euclid, Robert Simson. second , as the third to its excess above the

... 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 Co

Euclid, Robert Simson. second , as the third to its excess above the

**fourth**. Prop . Side 122

If the first magnitude be the same multiple of the second that the third is of the

then shall the first together with the fifth be the same multiple of the second , that

the ...

If the first magnitude be the same multiple of the second that the third is of the

**fourth**, and the fifth the same multiple of the second that the sixth is of the**fourth**;then shall the first together with the fifth be the same multiple of the second , that

the ...

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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples 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 remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole