## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 8

... equal to one another ; they shall likewise have their bases , or

... equal to one another ; they shall likewise have their bases , or

**third**sides , equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Page 19

Any two sides of a triangle are together greater than the See N.

Any two sides of a triangle are together greater than the See N.

**third**side . Let ABC be a triangle : any two sides of it together shall be greater than the**third**side , viz . the sides BA , AC greater than the side BC ; and AB ... Page 20

Produce BD to E ; and because two sides of a triangle * are greater than the

Produce BD to E ; and because two sides of a triangle * are greater than the

**third**side , the two sides BA , AE , of the triangle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are greater + than BE ... Page 23

AB to DE , and AC to DF , and the

AB to DE , and AC to DF , and the

**third**angle BAC to the**third**angle EDF . For , if AB be not equal to DE , one of them must be greater than the other . Let AB be the greater of the two , and make BG equalt to DE , and join GC : + 3. Page 24

AB to DE : likewise in this case , the other sides shall be Іi СЕ equal , AC to DF , and BC to EF ; and also the

AB to DE : likewise in this case , the other sides shall be Іi СЕ equal , AC to DF , and BC to EF ; and also the

**third**angle BAC to the**third**angle EDF . For , if BC be not equal to EF , let BC be the greater of them , and make BH equal ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole