## 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 19

Page 74

...

...

**circle**ABC , and G the centre of the**circle**ADE ; the straight line which joins the centres F , G , being pro- duced ...**touches**it on the inside or outside . For , if it be possible , let the**circle**EBF touch the**circle**ABC in ... Page 78

... circle , and therefore the straight line AG cuts the circle . COR . From this it is manifest , that the straight line which is drawn at right an- ⚫ gles to the diameter of a circle from the extremity of it ,

... circle , and therefore the straight line AG cuts the circle . COR . From this it is manifest , that the straight line which is drawn at right an- ⚫ gles to the diameter of a circle from the extremity of it ,

**touches the circle**; and ... Page 79

...

...

**touching the circle**. Let the straight line DE touch the circle ABC in the point C ; take the centre F , and draw the straight line FC : FC is perpendicular to DE . For , if it be not , from the point F draw FBG perpendicular to DE ... Page 87

... Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair ...

... Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair ...

**touches the circle**, shall be equal to the angles in the alter- nate segments of the circle . Let the straight ... Page 88

... Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair ...

... Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair ...

**touches the circle**; and because AB , drawn from the point of contact A , cuts the circle , the angle DAB is ...### 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