The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |
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Page 17
... greater , and from it cut ( 3. 1. ) off DB equal to AC , the less , and join DC ; therefore , because in the ... greater also than BCD ; much more then is the angle BDC greater than A C D B the angle BCD . Again , because CB is equal to ...
... greater , and from it cut ( 3. 1. ) off DB equal to AC , the less , and join DC ; therefore , because in the ... greater also than BCD ; much more then is the angle BDC greater than A C D B the angle BCD . Again , because CB is equal to ...
Page 24
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be bisected , it may be demonstrat- ed that the angle BCG , that is , ( 15. 1. ) the angle ACD , is great- er than the angle ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be bisected , it may be demonstrat- ed that the angle BCG , that is , ( 15. 1. ) the angle ACD , is great- er than the angle ...
Page 25
... greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 13. 1. ) to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
... greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 13. 1. ) to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
Page 26
... greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any two sides of it together are greater than the third ...
... greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any two sides of it together are greater than the third ...
Page 27
... greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE , EC : again , be- cause the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB ...
... greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE , EC : again , be- cause the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore