## 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 4

... place of the legitimate one which Euclid had

Book , besides other things , the good Definition which Eudoxus or Euclid had

Definition ...

... place of the legitimate one which Euclid had

**given**; and by taking out of thisBook , besides other things , the good Definition which Eudoxus or Euclid had

**given**of compound**ratio**, and giving an absurd one in place of it in the 5thDefinition ...

Side 173

Next , let it be required to describe upon a

figure similar and similarly situated to the rectilineal figure CDKEF . Join DE ...

Similar triangles are to one another in the duplicate

sides .

Next , let it be required to describe upon a

**given**straight line AB , a rectilinealfigure similar and similarly situated to the rectilineal figure CDKEF . Join DE ...

Similar triangles are to one another in the duplicate

**ratio**of their homologoussides .

Side 186

F TY L C F D B To cut a

the

parallelogram GH equal to 1 db EL and C together , and similar and similarly ...

F TY L C F D B To cut a

**given**straight line in extreme and mean**ratio**. Let AB bethe

**given**straight line ; it is required to cut it in tuated to D : and make ( 25. 6. ) theparallelogram GH equal to 1 db EL and C together , and similar and similarly ...

Side 310

... where mention is made of a

any thing in the proposition relating to a ... ( that he might more fully explain and

embellish his subject ) to

by ...

... where mention is made of a

**given**angle , though there neither is , nor can beany thing in the proposition relating to a ... ( that he might more fully explain and

embellish his subject ) to

**give**a general and summary idea of**ratio**to beginners ,by ...

Side 311

litude of

, but only to

numbers ; though such a definition was as necessary and useful to be

litude of

**ratios**, is of the same kind , and can serve for no purpose in mathematics, but only to

**give**beginners some ... yet without giving any definition of the**ratio**ofnumbers ; though such a definition was as necessary and useful to be

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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