The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second EditionCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 12
... angle ACD is equal to the 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 ...
... angle ACD is equal to the 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 ...
Σελίδα 14
... 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 sides AC , CD are equal to BC , CD ...
... 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 sides AC , CD are equal to BC , CD ...
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
... BCD , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore 3. The angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC , BD , and ...
... BCD , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore 3. The angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC , BD , and ...
Σελίδα 34
... angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter ... BCD , and the diameter BC divides the parallelogram ACDB into two equal parts . Q.E.D. PROP . XXXV . - THEOREM ...
... angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter ... BCD , and the diameter BC divides the parallelogram ACDB into two equal parts . Q.E.D. PROP . XXXV . - THEOREM ...
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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