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 2
Thus the angle which is contained by the straight lines AB , CB , is named the angle ABC , or CB4 ; that which is ... as the angle at E. ” X. When a straight line standing on another straight line makes the adjacent angles equal to one ...
Thus the angle which is contained by the straight lines AB , CB , is named the angle ABC , or CB4 ; that which is ... as the angle at E. ” X. When a straight line standing on another straight line makes the adjacent angles equal to one ...
Σελίδα 7
the straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . D B C 9 Because the point A is the centre of the circle BCD , ( Definition 15. ) 1 . AC is equal to AB ; and because the point B is the centre of ...
the straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . D B C 9 Because the point A is the centre of the circle BCD , ( Definition 15. ) 1 . AC is equal to AB ; and because the point B is the centre of ...
Σελίδα 9
shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , cach to each , viz . AB to DE , and AC to DF ; and the ...
shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , cach to each , viz . AB to DE , and AC to DF ; and the ...
Σελίδα 10
The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal ...
The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal ...
Σελίδα 11
which are the angles at the base of the triangle ABC . And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c .
which are the angles at the base of the triangle ABC . And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c .
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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