## 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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... angle ABC to the angle DEF , and the

... 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 CBG . Now , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining

... angle CBG . Now , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining

**angle ACB**, which are the angles at ... Page 26

...

...

**angle**ACD is equal ( 5. 1. ) to the**angle**ADC : But the**angle**ACD is greater than the**angle**BCD ; there- C D fore ...**ACB**; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle F C D ACD , the**angles**ECD ... Page 28

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**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 the two BC , CD , each to each ; but the ... Page 32

... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the

... angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the

**angle ACB**...### 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