## 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 viii

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**proposition**, " so that we can never make an assertion , or even hazard a conjecture , without expressing one or more**propositions**. Now it will be found that the simplest form in which a**proposition**can exist is the bare statement of ... Page x

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**propositions**employed as premises are not ambiguous , are cor- rectly understood , and are true . ' 66 We have said that every assertion involves a**proposition**, but it is seldom that the**propositions**so involved are explicitly stated ... Page xi

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**proposition**may be more briefly expressed by " X IS Z. "**Propositions**regarded as sentences may be divided according to their grammatical structure into categorical and hypothetical ; a categorical**proposition**makes a simple assertion ... Page xii

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**proposition**must be either affirmative or negative , and also either universal or particular , with the same subject and pre- dicate four different**propositions**may be framed , which , for con- venience , are distinguished by the four ... Page xiii

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**propositions**differ in quality they are called Contraries , as A Every X Is Y. E No X is Y. If two particular**propositions**differ in quality they are called Subcontraries , as JI ...**proposition**is the changing the relative INTRODUCTION .### 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