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 15
... wherefore ( Ax . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Two straight lines cannot have a common segment . PROP . XII . - PROBLEM . To draw a BOOK I. - PROP . XI . 15.
... wherefore ( Ax . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Two straight lines cannot have a common segment . PROP . XII . - PROBLEM . To draw a BOOK I. - PROP . XI . 15.
Σελίδα 18
... less to the greater , which is impossible ; therefore 4. BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the ...
... less to the greater , which is impossible ; therefore 4. BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the ...
Σελίδα 20
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than ...
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than ...
Σελίδα 21
... less ; because then the angle ABC would be less ( I. 18. ) than the angle ACB ; but it is not ; therefore 2 . The side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore 3. AC is greater than AB ...
... less ; because then the angle ABC would be less ( I. 18. ) than the angle ACB ; but it is not ; therefore 2 . The side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore 3. AC is greater than AB ...
Σελίδα 22
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
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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