## The Elements of Euclid |

### From inside the book

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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 ...**magnitude**. " Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be ... Page 226

... the solid LV is greater than the solid NV ; and if less , less : since then there are four

... the solid LV is greater than the solid NV ; and if less , less : since then there are four

**magnitudes**, viz . the ... AT a**given**point in a**given**straight line , to make a solid angle equal to a**given**solid angle contained by three ... Page 315

66 bethis book : the author of it designed to demonstrate , that if four Bok V.

66 bethis book : the author of it designed to demonstrate , that if four Bok V.

**magnitudes**E , G , F , H be ... which we have**given**in its proper place , instead of this corollary ; and another corollary is placed after the ... Page 316

... is demonstrated in the Greek : and it is probable Theon thought it was sufficient to

... is demonstrated in the Greek : and it is probable Theon thought it was sufficient to

**give**this one , since he was to ... That , if four “**magnitudes**be proportionals , the third must necessarily be greater than the fourth , when the ... Page 317

And , indeed , though it is very easy to

And , indeed , though it is very easy to

**give**a right demonstration of it , nobody , as far as I know , has**given**one ... And most of the commentators judge it difficult to prove that four**magnitudes**which are proportionals according 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