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

### From inside the book

Results 1-5 of 62

Page

The first Proposition of Book III . has been long known to be imperfectly

The first Proposition of Book III . has been long known to be imperfectly

**demonstrated**; and , as the defect may be supplied by the addition of but two or three lines to the original text , the Editor has not hesitated to introduce the ... Page 11

Which was to be

Which was to be

**demonstrated**. : * PROP . V. THEOR . The angles at the base of an isosceles triangle ure equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Page 12

And , since it has been

And , since it has been

**demonstrated**, that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the 73 Ax . remaining angle ABC is equaltto the remaining angle ACB , which ... Page 13

Again , because CB is equalt to DB , the angle + Hyp BDC is equal * to the angle BCD ) ; but it has * 5.1 been

Again , because CB is equalt to DB , the angle + Hyp BDC is equal * to the angle BCD ) ; but it has * 5.1 been

**demonstrated**to be greater than it ; which is impossible . * 5 . 1 . * с * 5 . 1 . * * * 5 . BOOK I. 13 PROP . VII . Page 17

By help of this problem , it may be

By help of this problem , it may be

**demonstrated**, that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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