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 Edition |
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Σελίδα 12
The 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 .
The 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 .
Σελίδα 14
AB is cut into two equal parts in the point D. ) C A. B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . The two sides AC , CD are equal to BC , CD , each to each ; and ( Constr . ) 2 . The angle ACD is ...
AB is cut into two equal parts in the point D. ) C A. B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . The two sides AC , CD are equal to BC , CD , each to each ; and ( Constr . ) 2 . The angle ACD is ...
Σελίδα 22
The angle ADC is equal to ACD ; but 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 ...
The angle ADC is equal to ACD ; but 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 ...
Σελίδα 33
The alternate angles ABC , BCD , are equal . and because AB is equal to CD , and BC common to the two triangles ABC , DCB , the two sides AB , BC , are equal to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore ...
The alternate angles ABC , BCD , are equal . and because AB is equal to CD , and BC common to the two triangles ABC , DCB , the two sides AB , BC , are equal to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore ...
Σελίδα 34
The alternate angles . ABC , BCD , are equal to one another ;, and because AC is parallel to BD , and BC meets them , ( I. 29. ) 2 . The alternate angles ACB , CBD , are equal to one another ; wherefore the two triangles ABC ...
The alternate angles . ABC , BCD , are equal to one another ;, and because AC is parallel to BD , and BC meets them , ( I. 29. ) 2 . The alternate angles ACB , CBD , are equal to one another ; wherefore the two triangles ABC ...
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AB is equal ABC is equal ABCD angle ABC angle ACB angle AGH angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line gnomon greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take touches the circle triangle ABC twice the rectangle wherefore whole