## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

Results 1-5 of 81

Page 17

... stright lines to one another , which

... stright lines to one another , which

**meet**together , but are not in the same straight line . * The definitions marked with inverted commas are different from those of Euclid C A B D E C N. B. When several angles ELEMENTS ... Page 18

...

...

**meet**one another , is put between the other two ' letters , and one of these two is somewhere upon one of those straight ' lines , and the other upon the other line : Thus the angle which ' is contained by the straight lines , AB , CB ... Page 20

... called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not

... called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not

**meet**. POSTULATES . I. LET it be granted that a straight 20 ELEMENTS 00 ... Page 38

...

...

**meet**either towards B , D , or towards A , C ; let them be produced and**meet**towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) 38 ELEMENTS. Page 39

...

...

**meet**towards B , D. In like manner it may be demonstrated that they do not**meet**towards A , C ; but those straight lines . which**meet**neither way , ( 30. Def . ) to one another . fore , if a straight line & c . AE C F B G D though ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore