## 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

THE The first of four magnitudes is said to have the same ratio to the of the first be

equal to that of the second , the

BOOK V. DEFINITIONS . I. A LESS magnitude is said to be a part of a greater ...

THE The first of four magnitudes is said to have the same ratio to the of the first be

equal to that of the second , the

**multiple**of the third ELEMENTS OF EUCLID .BOOK V. DEFINITIONS . I. A LESS magnitude is said to be a part of a greater ...

Side 118

first be greater than that of the second , the

than that of the fourth . VI . Magnitudes which have the same ratio are called

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 greaterthan that of the fourth . VI . Magnitudes which have the same ratio are called

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

expressed ...

Side 121

Wherefore , as many magnitudes AB , CD together equal to E and F together . the

same

E ,

Wherefore , as many magnitudes AB , CD together equal to E and F together . the

same

**multiple**is AB and CD together of Therefore , whatsoever**multiple**AB is ofE ,

**multiples**of as many , each of each , whatsoever**multiple**any Therefore , if ... Side 122

If the first magnitude be the same

fourth , and the fifth the same

then shall the first together with the fifth be the same

the ...

If the first magnitude be the same

**multiple**of the second that the third is of thefourth , 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 , thatthe ...

Side 123

... Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data,

in Like Manner Co Euclid, Robert Simson ! 2 of the second B , which the sixth LH

is of the fourth D ; EF the first together with the fifth , is the same

... Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data,

in Like Manner Co Euclid, Robert Simson ! 2 of the second B , which the sixth LH

is of the fourth D ; EF the first together with the fifth , is the same

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### Andre utgaver - Vis alle

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