The Elements of Euclid |
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Page 27
... ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b 13. 1 . ABC , BCA are ... triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ...
... ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b 13. 1 . ABC , BCA are ... triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ...
Page 28
... triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , GA ...
... triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , GA ...
Page 37
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . ' Let ABC be a triangle , and let one of its sides BC be produ ...
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . ' Let ABC be a triangle , and let one of its sides BC be produ ...
Page 38
... ABC , with its adjacent exterior ABD , is equal to two right an- gles ; therefore all the interior , together with ... triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides ...
... ABC , with its adjacent exterior ABD , is equal to two right an- gles ; therefore all the interior , together with ... triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides ...
Page 40
Euclid Robert Simson. Book I equal to the angle BCD ; therefore the triangle ABC is equal c to the triangle BCD , and the diameter BC divides the paral- lelogram ACDB into two equal parts . Q. E. D. , € 4. 1 . See Note . See the 2d and ...
Euclid Robert Simson. Book I equal to the angle BCD ; therefore the triangle ABC is equal c to the triangle BCD , and the diameter BC divides the paral- lelogram ACDB into two equal parts . Q. E. D. , € 4. 1 . See Note . See the 2d and ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore