## 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 14

Ax . ) BG ; but it has been shown , that BC is equal to G ,

are each of them equal to BG ; and things that are equal to the same are equal to

one another ; therefore the straight line AL is equal to BC .

Ax . ) BG ; but it has been shown , that BC is equal to G ,

**wherefore**AL and BCare each of them equal to BG ; and things that are equal to the same are equal to

one another ; therefore the straight line AL is equal to BC .

**Wherefore**from the ... Side 15

and be equal to it ; and the other angles of the one shall coincide with the

remaining angles of the other , and be equal to them , viz . the angle ABC to the

angle ...

**Wherefore**the whole triangle ABC shall coincide with the whole triangle DEF ,and be equal to it ; and the other angles of the one shall coincide with the

remaining angles of the other , and be equal to them , viz . the angle ABC to the

angle ...

Side 19

to the angle EAF ;

straight line B C AF , which was to be done , PROP . X. PROB . To bisect a given

finite straight line , that is , to divide it into two equal parts . Let AB be the given ...

to the angle EAF ;

**wherefore**the given rectilineal angle BAC is bisected by thestraight line B C AF , which was to be done , PROP . X. PROB . To bisect a given

finite straight line , that is , to divide it into two equal parts . Let AB be the given ...

Side 31

... therefore the angle GCB is equal to the angle DFE ; but DFE is , by the

hypothesis , equal to the angle BCA ;

the angle BCA , the less to the greater , which is impossible ; therefore AB is not

unequal ...

... therefore the angle GCB is equal to the angle DFE ; but DFE is , by the

hypothesis , equal to the angle BCA ;

**wherefore**also the angle BCG is equal tothe angle BCA , the less to the greater , which is impossible ; therefore AB is not

unequal ...

Side 34

lines which are parallel to the same straight line are parallel to one another . Let

AB , CD , be each of them parallel to EF , AB is also parallel to CD . Let the

straight ...

**Wherefore**, if a straight line , & c . Q. E. D. PROP . XXX . THEOR . STRAIGHTlines which are parallel to the same straight line are parallel to one another . Let

AB , CD , be each of them parallel to EF , AB is also parallel to CD . Let the

straight ...

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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