The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 33
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD , are also equal and parallel . A B D Join BC ; and because AB is parallel to CD , and BC meets ...
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD , are also equal and parallel . A B D Join BC ; and because AB is parallel to CD , and BC meets ...
Σελίδα 34
Euclid, Samuel A. GOOD. Because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC ... parallels , are equal to one another . Let the parallelograms ABCD , EBCF , be upon the same base BC , and between the ...
Euclid, Samuel A. GOOD. Because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC ... parallels , are equal to one another . Let the parallelograms ABCD , EBCF , be upon the same base BC , and between the ...
Σελίδα 35
... parallel straight lines towards the same parts , are themselves equal and parallel ( I. 33. ) ; therefore 2. EB , CH , are both equal and parallel , and ( I. 34. Def . ) 3 . and BOOK I. - PROP . XXXV . XXXVI . 35 336.
... parallel straight lines towards the same parts , are themselves equal and parallel ( I. 33. ) ; therefore 2. EB , CH , are both equal and parallel , and ( I. 34. Def . ) 3 . and BOOK I. - PROP . XXXV . XXXVI . 35 336.
Σελίδα 36
... parallels AD , BC . The triangle ABC is equal to the triangle DBC . E B Produce AD both ways to the points E , F , and through B draw ( I. 31. ) BE parallel to CA ; and through C draw CF parallel to BD . Therefore ( I. 34. Def . ) 1 ...
... parallels AD , BC . The triangle ABC is equal to the triangle DBC . E B Produce AD both ways to the points E , F , and through B draw ( I. 31. ) BE parallel to CA ; and through C draw CF parallel to BD . Therefore ( I. 34. Def . ) 1 ...
Σελίδα 37
... parallels . B Join AD . AD is parallel to BC . For , if it is not , through the point A draw ( I. 31. ) AE parallel to BC , and join EC . Then ( I. 37. ) 1. The triangle ABC is equal to the triangle EBC , because they are upon the same ...
... parallels . B Join AD . AD is parallel to BC . For , if it is not , through the point A draw ( I. 31. ) AE parallel to BC , and join EC . Then ( I. 37. ) 1. The triangle ABC is equal to the triangle EBC , because they are upon the same ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle