## 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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**straight line**. Let AB be the given**straight line**; it is required to ...**BC**is equal to BA : but it has been proved that CA is equal to AB ...**BC**are equal to one another ; and the triangle ABC is therefore equilateral , and it is ... Page 14

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**BC**is equal to G , wherefore AL and**BC**are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the**straight line**AL is equal to**BC**. Wherefore from the given point A a**straight line**AL ... Page 15

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**BC**shall be equal to the base EF ; and the triangle ABC to the triangle DEF ...**straight line**AB upon DE ; the point B shall coincide with the point E ...**straight line**AC is equal to DF : but the point B coincides with the point E ... Page 18

... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and the B D G CE F

... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the 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 ... Page 19

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**BC**is equal to EF ; therefore**BC**coin- ciding with EF , BA and AC shall ...**straight line**AF bisects the angle BAC . Because AD is equal to AE , and AF ...**straight line**AF , which was to be done . PROP . X. PROB . B D E C To bisect a ...### 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