## 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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**point**C , in which the circles cut one another , draw the straight lines ( 2. Post . ) CA , CB to the**points**A , B ...**F**; from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the cen- tre D , at the ... Page 15

... point C shall coincide with the

... point C shall coincide with the

**point F**, because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B coinciding with E , and C with ... Page 16

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**point F**, and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Α Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the ... Page 18

... F ; there- fore , because AC is equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of ... point B be on E , and the B D G CE F straight line BC upon EF ; the point C shall also coincide with the

... F ; there- fore , because AC is equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of ... point B be on E , and the B D G CE F straight line BC upon EF ; the point C shall also coincide with the

**point F**... Page 19

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**point F**. Because BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have ...### 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