## 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

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 . Wherefore from the ...

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 27

... but it has been

are BA , B С AC greater than BD , DC . Again , because the exterior angle of a

triangle is greater u than the interior and opposite angle , the exterior angle BDC

of ...

... but it has been

**shown**that BA , AC are greater than BE , EC ; much more thenare BA , B С AC greater than BD , DC . Again , because the exterior angle of a

triangle is greater u than the interior and opposite angle , the exterior angle BDC

of ...

Side 30

than the base EF ; but it is not ; therefore B С E F the angle BAC is not less than

the angle EDF ; and it was

BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D.

PROP .

than the base EF ; but it is not ; therefore B С E F the angle BAC is not less than

the angle EDF ; and it was

**shown**that it is not equal to it ; therefore the angleBAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D.

PROP .

Side 34

the anK gle GKD ; and it was

; D therefore also AGK is equal to GKD ; and they are alternate angles ; therefore

AB is parallel ( 27. 1. ) to CD . Wherefore straight lines , & c . Q. E. D. PROP .

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 ; and they are alternate angles ; therefore

AB is parallel ( 27. 1. ) to CD . Wherefore straight lines , & c . Q. E. D. PROP .

Side 35

Again ; because A is parallel to CE , and BD falls upon them , the exterior angle

ECD is equal to the interior and opposite angle ABC ; but the angle ACE was

Again ; because A is parallel to CE , and BD falls upon them , the exterior angle

ECD is equal to the interior and opposite angle ABC ; but the angle ACE was

**shown**to be equal to the angle BAC ; therefore the whole exterior angle ACD is ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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