## 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 6

mathematical learning , is promoted as far as the limited powers of the mind allow

; and which

many of which geometry is absolutely necessary . This I have endeavoured to do

...

mathematical learning , is promoted as far as the limited powers of the mind allow

; and which

**likewise**is of the greatest use in the arts both of peace and war , tomany of which geometry is absolutely necessary . This I have endeavoured to do

...

Side 14

the circle DEF ; and because A F is the centre of the circle DEF , AE shall be

equal to AD ; but the straight line C is

are each of them equal to AD ; wherefore the straight line AE is equal to ( 1.

the circle DEF ; and because A F is the centre of the circle DEF , AE shall be

equal to AD ; but the straight line C is

**likewise**equal to AD ; whence AE and Care each of them equal to AD ; wherefore the straight line AE is equal to ( 1.

Side 15

Therefore , if two triangles have two sides of the one equal to two sides of the

other , each to each , and have

equal to one another , their bases shall

equal ...

Therefore , if two triangles have two sides of the one equal to two sides of the

other , each to each , and have

**likewise**the angles contained by those sidesequal to one another , their bases shall

**likewise**be equal , and the triangles beequal ...

Side 17

UPON the same base , and on the same side of it , there cannot be two triangles

that have their sides which are terminated in one extremity of the base equal to

one another , and

UPON the same base , and on the same side of it , there cannot be two triangles

that have their sides which are terminated in one extremity of the base equal to

one another , and

**likewise**those which are terminated in the other extremity . Side 18

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

greater than the angle BCD . Again , because CB is equal to DB , the angle BDC

is ...

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

**likewise**D greater than BCD ; much more then is the angle BDCgreater than the angle BCD . Again , because CB is equal to DB , the angle BDC

is ...

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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