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

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Page 8

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 sides equal to one another ; they shall likewise have their

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 sides equal to one another ; they shall likewise have their

**bases**, or third sides , equal ; and ... Page 9

... and C with F , if the

... and C with F , if the

**base**BC does not coincide with the**base**EF , two straight . lines would inclose a space , which is impossible . * There- * 10 Ax . fore the**base**BC coincides with the**base**EF , and therefore is equal t to it . Page 10

FA G IE * 3 Ax . the two triangles AFC , AGB ; therefore the

FA G IE * 3 Ax . the two triangles AFC , AGB ; therefore the

**base**FC is equal * to the**base**GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal * to the remaining angles of the other , each to ... Page 11

1 . each ; and the angle DBC is equal to the anglet ACB ; + Hyp . therefore the

1 . each ; and the angle DBC is equal to the anglet ACB ; + Hyp . therefore the

**base**DC is equal to the**base**AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater , which is absurd . Page 12

Therefore , upon the same

Therefore , 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 another , and likewise those which are terminated in the ...### 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