## 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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**triangle ABC**to the tri- angle DEF ; and the other angles , to which the equal sides are op- AA B C E posite , shall be equal , each to each ,. * The three conclusions in this enunciation are more briefly expressed by saying , that the ... Page 24

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**angle ABC**to the angle DEF , and the angle ACB to DFE . For , if the**triangle ABC**be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E ... Page 25

... angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining ... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the

... angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining ... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the

**triangle ABC**: And it ... Page 27

... angle BAC is equal to the angle EDF . For , if the

... angle BAC is equal to the angle EDF . For , if the

**triangle ABC**be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to ... Page 28

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**triangle ABC**, and bisect ( 9. 1. ) the angle ACB by the straight 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 ...### 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