## 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 311

... of compound ratio , as this was the proper place for it ; duplicate and triplicate

ratio being

Herigon , and Barrow have likewise

they ...

... of compound ratio , as this was the proper place for it ; duplicate and triplicate

ratio being

**species**of compound ratio . ... 23. book 6. and which Clavius ,Herigon , and Barrow have likewise

**given**, but they retain also Theon's , whichthey ...

Side 365

A ratio is said to be given , when a ratio of a given magnitude to a given

magnitude which is the same ratio with it can be found . III . Rectilineal figures are

said to be

ratios of ...

A ratio is said to be given , when a ratio of a given magnitude to a given

magnitude which is the same ratio with it can be found . III . Rectilineal figures are

said to be

**given in species**, which have each of their angles given , and theratios of ...

Side 394

tude ; and the ratio of LM to MN is therefore given ( 1. dat . ) : but as LM to MN , so

is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . If each of

the sides of a triangle be given iu magnitude , the triangle is

tude ; and the ratio of LM to MN is therefore given ( 1. dat . ) : but as LM to MN , so

is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . If each of

the sides of a triangle be given iu magnitude , the triangle is

**given in species**. Side 395

In like manner EF also is given in position ; wherefore the point F is given : and

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

42.

In like manner EF also is given in position ; wherefore the point F is given : and

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

**given in species**(42.

Side 396

If the sides of a triangle have to one another given ratios , the triangle is

AB to BC is given , make the ratio of D to E the same with it ; and D is given ...

If the sides of a triangle have to one another given ratios , the triangle is

**given in****species**. ... Take a straight line D given in magnitude ; and because the ratio ofAB to BC is given , make the ratio of D to E the same with it ; and D is given ...

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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