## 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 13

therefore CA is equal to CB ; wherefore CA , AB ,

and the triangle ABC is therefore equilateral , and it is described upon the

straight line AB . Which was required to be done . PROP . II . PROB . From a

therefore CA is equal to CB ; wherefore CA , AB ,

**BC**are equal to one another ;and the triangle ABC is therefore equilateral , and it is described upon the

**given**straight line AB . Which was required to be done . PROP . II . PROB . From a

**given**... Side 14

Ax . ) BG ; but it has been

are each of them equal to BG ; and things that are equal ... Wherefore from the

Ax . ) BG ; but it has been

**shown**, that**BC**is equal to G , wherefore AL and**BC**are each of them equal to BG ; and things that are equal ... Wherefore from the

**given**point A a straight line AL has been drawn equal to the**given**straight line**BC**. Side 19

the point F. Because

AC shall coincide with ED and DF ; for , if ... to the angle EAF ; wherefore the

be ...

the point F. Because

**BC**is equal to EF ; therefore**BC**coinciding with EF , BA andAC shall coincide with ED and DF ; for , if ... to the angle EAF ; wherefore the

**given**rectilineal angle BAC is bisected by the straight line**B C**AF , which was tobe ...

Side 34

the anK gle GKD ; and it was

; D therefore also AGK is equal to GKD ... Let A be the

the anK gle GKD ; and it was

**shown**that the angle AGK is equal to the angle GHF; D therefore also AGK is equal to GKD ... Let A be the

**given**point , and**BC**the**given**straight line ; it is required to draw a straight line E A F through the point A ... Side 35

Because the straight line AD , which meets the two straight lines

the alternate angles EAD , ADC equal to one another , EF is parallel ( 27. 1. ) to

...

Because the straight line AD , which meets the two straight lines

**BC**, EF , makesthe alternate angles EAD , ADC equal to one another , EF is parallel ( 27. 1. ) to

**BC**. Therefore the straight line EAF is drawn through the**given**point A parallel to...

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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 |

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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