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

### From inside the book

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Page 75

If any point be

If any point be

**taken**without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes through ... Page 77

If a point be

If a point be

**taken**within a circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . Let the point D be**taken**within the circle ABC , from which to the ... Page 78

Wherefore , if a point be

Wherefore , if a point be

**taken**, & c . Q.E. D. PROP . X. THEOR . One circumference of a circle cunnot cut another in more than two points . If it be possible , let the circumference FAB cut the circumference DEF in more than B D H two ... Page 105

Let any point D be

Let any point D be

**taken**without the circle ABC , and from it let two straight lines DCA and DB be drawn , of which DCA cuts the circle , and DB meets it ; if the rectangle AD , DC he equal to the square of DB ; DB shall touch the ... Page 127

V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being

V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being

**taken**, and any equimultiples whatsoever of the second and ...### What people are saying - Write a review

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### Other editions - View all

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

### Common terms and phrases

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole