## The Elements of Euclid |

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Page vi

stration of the 18th prop . of the 5th book , in place of the legitimate one which Euclid had.

stration of the 18th prop . of the 5th book , in place of the legitimate one which Euclid had.

**given**; and by taking out of this book , besides other things , the good definition which Eudoxus or Erclid had**given**of compound**ratio**... Page 175

Next , Let it be required to describe upon a

Next , Let it be required to describe upon a

**given**straight line AB , a rectilineal figure similar and similarly situated to the rectilineal ... SIMILAR triangles are to one another in the du . plicate**ratio**of their homologous sides . Page 188

TO cut a

TO cut a

**given**straight line in extreme and mean**ratio**, Let AB be the**given**straight line ; it is required to cut it in extreme and mean**ratio**. Upon AB describe a the square BC , and to 188 THE ELEMENTS. Page 189

5 . extreme and mean

5 . extreme and mean

**ratio**in Ef . Which was to be done . f 3. def . 6 . Otherwise , Let AB be the**given**straight line ; it is required to cut it in extreme and mean**ratio**. Divide AB in the point C , so that the rectangle contained by ... Page 312

... of a

... of a

**given**angle , though there neither is , nor can be any thing in the proposition relating to a**given**angle . ... ( that he might more “ fully explain and embellish his subject ) to give a general “ and sumınary idea of**ratio**to ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone 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 prisms produced PROP proportionals proposition pyramid 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