## 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 6-10 of 58

Page 48

...

...

**Bisect**( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23 1. ) the augle CEF equal te D ; and through A draw ( 31. 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel to EF : Therefore ... Page 56

...

...

**bisected**, and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line**bisected**, is equal to the square of the straight line which is ... Page 60

...

...

**bisected**, and of the square of the line made up of the half and the part produced . • Let the straight line AB be**bisected**in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the ... Page 61

...

...

**bisect**( 10. 1. ) AC in E , and join BE ; produce CA to F , and make ( 3. 1. ) EF equal to EB , and upon AF ...**bisected**in E , and produced to the point F , the rectangle CF.FA , together with the square of AE , is equal ( 6. 2 ... Page 63

...

...

**bisect**BF in G : and from the centre G , at the distance GB , or GF , describe the semicircle BHF and produce DE to H , and join GH . Therefore , because the straight line BF is divided into two equal parts in the point G , and into two ...### 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