## 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 |

### From inside the book

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Page 15

... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ...

... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ...

**remaining angles**of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to ... Page 16

... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from ...

... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from ...

**remaining angles**of the one are equal ( 4. 1. ) to the**remaining angles**of the other , each to each , to which the ... Page 23

... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the

... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the

**remaining angle**ABE is equal ( 3. Ax . ) to the re- ... Page 24

... angle ACD is greater than either of the interior op- posite angles CBA , BAC . join Bisect ( 10. 1. ) AC in BE and ...

... angle ACD is greater than either of the interior op- posite angles CBA , BAC . join Bisect ( 10. 1. ) AC in BE and ...

**remaining angles**, each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ... Page 33

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

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

**remaining angle**AGH is equal to the**remaining angle**GHD ; and they are alternate angles therefore AB is parallel to CD ...### Other editions - View all

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

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore