## 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

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**Let**AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A ...**ABC**is an equilateral C D A B E triangle . Because the point A is the centre of the circle BCD , AC is equal ... Page 23

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**Let ABC**, DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz , AB to DE , and AC to DF ; and let the angle BAC be also equal to the angle EDF : then shall the base BC be equal to ... Page 24

... ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that ...

... ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that ...

**Let ABC**be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be ... Page 25

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**Let ABC**be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , one of them is greater than the other : Let AB be the greater , and from it cut ( 3. 1 ... Page 26

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**let**CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian ...**ABC**, DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz ...### 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