## 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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Page 40

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**meet**on the side of EF on which the two angles are that are less than two right angles . For , if not , KL and CD are either parallel , or they**meet**on the other side of EF ; but they are not parallel ; for the angles KGH , GHC would ... Page 41

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**meets**the two straight lines BC , EF , makes the alternate angles EAD , ADC equal to one another , EF is parallel ( 27. 1. ) to BC . Therefore the straight line EAF is drawn through the given point A parallel to the given straight line ... Page 43

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**meets**them , the alternate angles ABC , BCD are equal ( 29.1 . ) ; and because AB is equal to CD , and BC common to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to the ... Page 49

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**meet**, if produced ; let them**meet**in K , and through K draw KL parallel to EA or FH , and produce HA , GB to the points L , M : Then HLKF is a parallelogram , of which the diame ter is HK , and AG , ME are the parallelograms about ... Page 50

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**meets**the parallels KM , FG , the alternate angles MHG , HGF are equal ( 29. 1. ) ; add to each of these the an- gle HGL ; therefore the angles MHG . HGL , are equal o the angles HGF , HGL : But the angles MHG , HGL , are equal ( 29. 1 ...### 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