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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To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after The Elements of Logic in Four Books?
You can find similar books in the "Read Also" column, or choose other free books by William Duncan to read onlineMoreLess
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