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 JMC : Elements of Logic / by Cardinal Mercier

88. I. The Synthetic Method. -- An exact, or deductive science -- such as arithmetic or geometry -- sets out from certain principles in necessary matter and combines them to deduce new relations and to form the definitions of the object with which the science concerns itself. It passes from the simple to the complex, from the more general to the less general. This is the synthetic method. The synthesis which directly forms a definition at the same time effects the division of the defined object and governs all rational demonstrations. Let us suppose, e. g., these theorems established: (1) that the sum of the angles comprising all the space below a straight line is equal to two right angles; (2) that the interior alternate angles are equal; that a straight line can always he drawn parallel to a given straight line. -- The combination of these three propositions under the guidance of the principle of identity gives rise to a new relation: the identity of the three angles of a triangle with two right angles.


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