## 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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**chord**; and the figure ADF contained by the arc and its**chord**is termed a segment . The space contained by two arcs of circles of different radii is termed a lune , as GHI . B 18. A RECTILINEAL FIGURE is a plane surface , bounded on all ... Page 80

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**chord**is said to be the " arc subtended by that**chord**; " thus the arc ACB is sub- tended by the**chord**AB . 6. Straight lines ( or**chords**) are said to be equally distant from the center of a circle when the per- pendiculars drawn to ... Page 81

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**chord**and its arc . 8. An angle in a segment is the angle contained by the straight lines drawn from any point in the circumference of the segment to the extremities of its**chord**. SCHOLIUM . An angle is said to stand upon the arc ... Page 82

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**chord**AB of the circle ACB perpendicularly ( c ) , it contains the center of the circle ; and because it is bisected in F ( d ) , FE is equal to FC , therefore F is the center of the circle ( e ) . THEOREM . If three points ( A , B ... Page 84

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**chord**of the circle ; The line passes through the center of the circle . The line is perpendicular to the**chord**. The line bisects the**chord**. 2. It is necessary , in the enunciation of the 84 ELEMENTS OF GEOMETRY .### 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