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

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Page 9

... coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one coincide with the

... coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one coincide with the

**remaining**angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Page 10

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

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 16

... ABD : take away the common angle ABČ , and the

... ABD : take away the common angle ABČ , and the

**remaining**angle ABE is equal * to the**remaining**angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . Page 17

... and the

... and the

**remaining**angle CEA is equal * to the**remaining**angle DEB . * 3 Ax . In the same manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. COR . 1. Page 25

AGH , BGH are equal + to the angles BGH , GHD : +1 Ax . take away the common angle BGĦ ; therefore the

AGH , BGH are equal + to the angles BGH , GHD : +1 Ax . take away the common angle BGĦ ; therefore the

**remaining**angle AGH is equalt to the**remaining**angle + 3 Ax . GHD . and they are alternate angles ; therefore AB is parallélt to CD .### 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