## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |

### From inside the book

Page iii

And therefore , since true wisdom very much consists in , and is ob tained from , the knowledge of the comparative numbers and

And therefore , since true wisdom very much consists in , and is ob tained from , the knowledge of the comparative numbers and

**magnitudes**of the qualities , powers , efficacies , matter , and motions of sensible objects ... Page xi

... which but lately occurred to me , on the Fifth Definition of the Fifth Book about

... which but lately occurred to me , on the Fifth Definition of the Fifth Book about

**Magnitudes**having the same Ratio , viz . that this Definition does really extend to commensurable**Magnitudes**only , and not to incommensurable ones ... Page xii

“ Multiple of the Fourth , ” cannot exist when the

“ Multiple of the Fourth , ” cannot exist when the

**Magnitudes**are incommensurable ; because when the First and Second , and the Third and Fourthi Terms of Two equal Ratios , or Four Proportionals are incommensurable , no Number of Times ... Page xiii

Sixth Book ; and of Lines , Surfaces , and Solids in the Eleventh and Twelfth Books , being

Sixth Book ; and of Lines , Surfaces , and Solids in the Eleventh and Twelfth Books , being

**Magnitudes**of different kinds . Because I must think all his**Magnitudes**in the Propofitions of the Fifth Book are agreeable to the Fourth ... Page 1

1. 12. for the Angle ADC , r . the Angle ACD . P. 150. 1. 13. for Angle , r . Angles . P. 158. 1. 23 , 24. for opposites , r . opposite . P. 216. 1. 17. the Letter M wants a Stop after it . P. 225. 1. 16. r .

1. 12. for the Angle ADC , r . the Angle ACD . P. 150. 1. 13. for Angle , r . Angles . P. 158. 1. 23 , 24. for opposites , r . opposite . P. 216. 1. 17. the Letter M wants a Stop after it . P. 225. 1. 16. r .

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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |

### Common terms and phrases

A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe

### Popular passages

Page 247 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.

Page 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Page 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.

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