## The Elements of Euclid |

### From inside the book

Results 1-5 of 100

Page 34

IF a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be

IF a straight line falling upon two other straight lines make the alternate angles equal to one another , these two straight lines shall be

**parallel**. Let the straight line EF , which falls upon the two straight hnes AB , CD make the ... Page 35

BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is

BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is

**parallel**to CD . Wherefore , if a straight line , & c . Q. E : D . AL PROP . XXIX . TIIEOR . Page 36

STRAIGHT lines which are

STRAIGHT lines which are

**parallel**to the same straigin line are**parallel**to one another . Let AB , CD , be each of them**parallel**to EF ; AB is also**parallel**to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the ... Page 37

EAF is drawn through the given point A

EAF is drawn through the given point A

**parallel**to the given Book I. straight line BC . Which was to be done . PROP . XXXII . THEOR . 3 E . Db 99.1 IF a side of any triangle be produced , the exterior angle is equal to the two interior ... Page 38

Let AB , CD be equal and pa- 1 B rallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and

Let AB , CD be equal and pa- 1 B rallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and

**parallel**. Join BC ; and because AB is**parallel**to CD , and BC meets them , C D the ...### 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: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole