## 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 12

... so as to make the two “ interior angles on the same side of it taken together

shall at length meet upon that side on which “ are the angles which are

iwo ...

... so as to make the two “ interior angles on the same side of it taken together

**less**“ than two right angles , these straight lines being continual“ ly produced ,shall at length meet upon that side on which “ are the angles which are

**less**thaniwo ...

Side 14

Wherefore from the given point A a straight line AL has been drawn equal to the

given straight line BC . Which was to be done . PROP . III . PROB . From the

greater of two given straight lines to cut off a part equal to the

be ...

Wherefore from the given point A a straight line AL has been drawn equal to the

given straight line BC . Which was to be done . PROP . III . PROB . From the

greater of two given straight lines to cut off a part equal to the

**less**. Let AB and Cbe ...

Side 17

off DB equal to AC , the

DBC , ACB , DB is equal to AC , and BC common to both , the two D sides DB ,

BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...

off DB equal to AC , the

**less**, and join DC ; therefore , " Α because in the trianglesDBC , ACB , DB is equal to AC , and BC common to both , the two D sides DB ,

BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...

Side 25

to two right angles ; therefore the angles ABC , BCA are

angles . In like manner , it may be demonstrated , that BAC , ACB , as also CAB ,

ABC , are

to two right angles ; therefore the angles ABC , BCA are

**less**than two rightangles . In like manner , it may be demonstrated , that BAC , ACB , as also CAB ,

ABC , are

**less**than two right angles . Therefore any two angles , & c . Q. E. D .. 2 . Side 26

not ; therefore the side AC is not

equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .

Q. E. D. join DC . PROP . XX . THEOR . Any two sides of a triangle are together ...

not ; therefore the side AC is not

**less**than AB ; and it has been shown that it is notequal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .

Q. E. D. join DC . PROP . XX . THEOR . Any two sides of a triangle are together ...

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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