## The Elements of Euclid |

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Page v

Peter Ramus * ascribes the

Peter Ramus * ascribes the

**propositions**, as well as their demonstrations , to Theon ; others think the**propositions**to be Euclid's , but that the demonstrations are Theon's ; and others maintain that all the**propositions**and their ... Page vi

Now this

Now this

**proposition**is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and , therefore , though this were a true**proposition**, it ought to have been demonstrated . Page vii

Now , upon the 10th definition of this book depend the 25th and 28th

Now , upon the 10th definition of this book depend the 25th and 28th

**propositions**of it ; and , upon the 25th and ... of the 12th book depends upon the 8th of the same , and this 8th , and the corollary of**proposition**17 , and prop . Page 14

... these straight lines being continually “ produced , shall at length meet upon that side on which are « The angles which are less than two right angles . See the “ notes on prop . 29. of Book I. " . 4

... these straight lines being continually “ produced , shall at length meet upon that side on which are « The angles which are less than two right angles . See the “ notes on prop . 29. of Book I. " . 4

**PROPOSITION**I. PROBLEM . Page 15

**PROPOSITION**I. PROBLEM . Book I. TO describe an equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . с From the centre A , at the ...### 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