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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Page 45
... Join AD ; AD is parallel to BC : For , if , it is not , through A draw ( 31.1 . ) AG parallel to BF , and join GF . The triangle B CE F ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and ...
... Join AD ; AD is parallel to BC : For , if , it is not , through A draw ( 31.1 . ) AG parallel to BF , and join GF . The triangle B CE F ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and ...
Page 47
... Join AD ; AD is parallel to BC : For , if , it is not , through A draw ( 31.1 . ) AG parallel to BF , and join GF . The triangle B A D G CE F ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and ...
... Join AD ; AD is parallel to BC : For , if , it is not , through A draw ( 31.1 . ) AG parallel to BF , and join GF . The triangle B A D G CE F ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and ...
Page 73
... join DE , and produce it to the cir- cumference in F , G ; then FG is a diame . ter of the circle ABC : And because in FG , the diameter of the circle ABC , there is taken the point D which is not the cen- tre , DG is the greatest line ...
... join DE , and produce it to the cir- cumference in F , G ; then FG is a diame . ter of the circle ABC : And because in FG , the diameter of the circle ABC , there is taken the point D which is not the cen- tre , DG is the greatest line ...
Page 74
... joins the points F , G shall pass through the point of contact . For , if not , let it pass otherwise , if possible , as FCDG , and join FA , AG : and because F is the centre of the circle ABC , AF is equal to FC : Also because G is the ...
... joins the points F , G shall pass through the point of contact . For , if not , let it pass otherwise , if possible , as FCDG , and join FA , AG : and because F is the centre of the circle ABC , AF is equal to FC : Also because G is the ...
Page 75
... join AC : Therefore , because the two points A , C are in the circumference of the circle ACK , the straight line AC which joins them shall fall within the circle ACK : And the circle ACK is without the circle ABC ; and therefore the ...
... join AC : Therefore , because the two points A , C are in the circumference of the circle ACK , the straight line AC which joins them shall fall within the circle ACK : And the circle ACK is without the circle ABC ; and therefore the ...
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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 BD THEOR third touches the circle triangle ABC triangle DEF wherefore