## 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 |

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**line**Let AB be the given straight**line**; it is required to describe an equilateral triangle upon it . From the ...**BC**is equal to AB : But it has been proved that CA is equal to AB ; therefore - CA , CB are each of them equal to AB ... Page 23

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**BC**are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight**line**AL is equal to**BC**. Wherefore , from the given point A , a straight**line**AL has been drawn equal to the ... Page 27

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**line BC**upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD ... Page 28

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**line**CD . AB is cut into two equal parts in the point D. Because AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two**BC**, CD , each to each ; but the angle ACD is also equal to ... Page 30

... line . At the point B in the straight line AB , let the two straight

... line . At the point B in the straight line AB , let the two straight

**lines BC**, BD upon the opposite sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD is in the same straight line with CB ...### 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