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 12
... angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2. The angle ADC is greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB is equal to DB , ( I. 5 ...
... angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2. The angle ADC is greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB is equal to DB , ( I. 5 ...
Σελίδα 14
... triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two equal parts in the point D. C A. D B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two ...
... triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two equal parts in the point D. C A. D B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two ...
Σελίδα 22
... angle BCD is greater than the angle ACD ; therefore 2 . The angle BCD is greater than the angle ADC ; and because the angle BCD of the triangle DCB is greater than its angle BDC , and that the greater ( I. 19. ) side is opposite to the ...
... angle BCD is greater than the angle ACD ; therefore 2 . The angle BCD is greater than the angle ADC ; and because the angle BCD of the triangle DCB is greater than its angle BDC , and that the greater ( I. 19. ) side is opposite to the ...
Σελίδα 33
... angle ABC is equal to the angle BCD ; therefore ( I. 4. ) 2. The base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides are ...
... angle ABC is equal to the angle BCD ; therefore ( I. 4. ) 2. The base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides are ...
Σελίδα 34
... angles BCD , CBD , in the other , each to each , and one side BC common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third ...
... angles BCD , CBD , in the other , each to each , and one side BC common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third ...
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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