## The elements of Euclid, [books I.-VI. XI. XII.] with many additional propositions, and explanatory notes. To which is prefixed an introductory essay on logicJ. Weale, 1853 |

### From inside the book

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Page vii

... premises are not am- biguous , are correctly understood , and are true . 2nd . That the steps by which a conclusion is

... premises are not am- biguous , are correctly understood , and are true . 2nd . That the steps by which a conclusion is

**drawn**from those premises are true . The subject therefore ranges itself properly under two heads ; Page viii

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**drawn**may be as true as the premises . A proposition may be defined to be " An assertion , affirming or denying something " and , as Mills has justly remarked , “ what- ever can be an object of belief , or even of disbelief , must ... Page xvi

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**drawn**. 4. A negative conclusion cannot follow from two affirmative pre- mises . 5. If one of the premises be negative , the conclusion must be nega- tive ; and if one of the premises be particular , the conclusion must be particular ... Page xix

... and EFGH ) are upon equal bases and between the same parallels , CONSEQUENCE . They are equal to one another in area . CONSTRUCTION . -

... and EFGH ) are upon equal bases and between the same parallels , CONSEQUENCE . They are equal to one another in area . CONSTRUCTION . -

**Draw**BE and CH . DEMONSTRATION . Syllogism 1 . Da ( Things which are INTRODUCTION . xix. Page 2

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**drawn**was in reality a solid or magnitude having three dimensions , namely length , breadth , and thickness , the breadth and thickness of the black lead left by the pencil on the surface of the paper , and which constitutes the ...### Other editions - View all

The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides No preview available - 2016 |

### Common terms and phrases

ABCD AC and CB AC is equal angle ABC angle BCD angle equal area to double area to twice bisect CB is equal chord circle ABC circumference Constr CONSTRUCTION COROLLARY DEMONSTRATION diagonal divided double the rectangle draw equal angles equal in area equal to AC Euclid external angle Find the center finite straight line Geometry given angle given line greater Henry Law Hypoth HYPOTHESES intersect join less line BC lines be drawn magnitude major premiss parallel parallelogram perpendicular predicate produced proposition quadratic equation reductio ad absurdum right angles SCHOLIA SCHOLIUM second power segment sides AC sides are equal square on AC square on half squares on AB syllogism termed THEOREM THEOREM.-If triangle ABC twice the rectangle twice the square whole line