## 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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**given**above of such a point would convey no idea . It must not , however , be therefore supposed that the foregoing ...**ANGLE**is a magnitude formed by the inclina- tion ( ie . , opening or divergence ) of two straight lines to one another , ... Page 11

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**given**, the other three can be found and the triangle determined . If , therefore , two triangles are found to agree ...**angle**between them . 4. Two sides and the**angle**opposite to one of them . 5. Two**angles**and the side between them ... Page 13

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**angle**A is common to both ; therefore the base CF is equal to the base BG ...**given**triangle . A COROLLARY . Hence every equilateral triangle is also equi ...**angle**A is the same in both , the side AC must fall on AB ; and because the ... Page 16

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**angle**DEF , so that their bases may coincide , and that the two triangles may lie on opposite sides ; join the ...**given**rectilineal**angle**( BAC ) . SOLUTION . Take any point D in AB , and from AC cut off AE equal to AD ( a ) ; draw DE ... Page 17

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**given angle**, or its division into three equal parts , is a problem that has baffled the attempts of the most able mathematicians , and can only be solved in particular cases . When the**given angle**is a right angle , or such an angle as ...### 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