...Circles cutting each other, the Angles which are oppofite and contrary, are equal to one another. 4. The Sum of any two Sides (of a Triangle) is greater than the third Side. 5. The Sum of the three J jjJJ*^ lis lefs than a J more than i8od. _r6. Any two Sides added together,...

...AB, then, being neither equal to AC, nor less than it, must necessarily be greater. QED i THEOREM X. THE Sum of any Two Sides of a Triangle is Greater than the Third Side. Let ABC be a triangle ; t'jien will the < I) sum of any two of its sides be greater than the third side, as for instance,...

...then, being neither equal to AC, nor less than it, must necessarily be greater, q. ED • THEOREM X. THE Sum of any Two Sides of a Triangle is Greater...Third Side. Let ABC be a triangle ; then will the sun) of any two of its sides be greater than -D the third side, as for instances, AC + CB S greater...

...AB, then, being neither equal to AC, nor less than it, must necessarily be greater. QED THEOREM X. THE Sum of any Two Sides of a Triangle is Greater...Side. Let ABC be a triangle ; then will the sum of any two of its sides be greater than D the third side, as for instances, AC -f- CB S greater than AB....

...AB, then, being neither equal to AC, nor less than it, must necessarily be greater, o.. ED THEOREM X. THE Sum of any Two Sides of a Triangle is Greater...Third Side. Let ABC be a triangle ; then will the . lum of .ny two of its side* be greater than the third side, as for instances, AC -J-cB greater than...

...the greater angle; and, conversely, the greater of any two angles is subtended by the greater side. The sum of any two sides of a triangle is greater than the third side. If one side of any triangle be produced, the external angle is equal to both the internal and opposite...

...equal to AC, nor less than it, must necessarily be greater, a. ED T1IEOBEH X. THE sum of any two sidtes of a triangle is greater than the third side. Let ABC be a triangle ; then will the тч sum of any two of its sides be greater , than the third side, as for instance, ft ^ AC + ев...

...for they may be applied to each other, and the equal parts will mutually coincide. PROPOSITION VII. THEOREM. The sum of any two sides of a triangle, is...triangle : then will the sum of two of its sides, as AC, CB, be greater than the third side AB. For the straight line AB is the shortest distance between...

...respectively equal, namely, the angle D=A, the side ED=BA, and the side DF=AC. PROPOSITION X. THEOREM. The nan of any two sides of a triangle is greater than the...triangle : then will the sum of two of its sides, as AC, CB, be greater than the third side AB. For the straight line AB is the shortest distance between...

...of ж2 =c2 — y1, or in that of the area of the triangle deduced from the expression — . ¿ Since the sum of any two sides of a triangle is greater than the third side, (Eue. i. 20.) half the sum of any two sides is greater than half the third side : therefore, half the...