The Elements of Logic in Four Books

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5 according according as they are fpcculative or practical ; (a is it alfo with dcmonjlrable Propofitions. A demonftrable fpeculative Proportion, is by Ma- thematicians called a Theorem. Such is the fa- mous 4jth Proposition of the firft Book of the Elements, known by the Name of the Pythagorick Theorem, from its fuppofed Inventor Pythagoras, "viz. That In every Right-angled Triangle, the Square defcribed upon the Side fubtending the Right /ingle, is equal to both the Squares defcribed upon the
... Sides containing the Right Jingle. On the other hand, a demonftrable practical Propofi- tion is called a Problem ; as where Euclid teaches us to defcribe a Square upon a given Right Line. XI. SINCE I am upon this Sub- 1 Lorollanes an jeer, it may not be amifs to add, obihutDe- that befides the four Kinds of Pro- JSSfeT pofitions already mentioned, Mathe- P r ^"'> maticians have alfo a fifth, known by the Name of Corollaries. Thefe are ufually fubjoined to Theorems^ or Problems, and differ from them only in this ; that they flow from what is there de- monftrated, in fo obvious a Manner as to dif- cover their Dependence upon the Proportion whence they are deduced, almoft as foon as propofed.

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