## 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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**segments**. When the point of sec- tion ( C ) lies between the two extremities ( A and B ) of the line , the two portions into which the line is divided ( AC and CB ) are termed internal**segments**. But when that point ( F ) lies in the ... Page 4

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**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 sides by straight lines . SCHOLIUM . The straight lines by which a ... Page 17

... perpendicular to the given line ( e ) . Def . 9 . COROLLARY . By help of this problem it may be demonstrated that " If two lines be straight , they cannot have a common

... perpendicular to the given line ( e ) . Def . 9 . COROLLARY . By help of this problem it may be demonstrated that " If two lines be straight , they cannot have a common

**segment**. " ( a ) I. 11 . ( b ) Def. ELEMENTS OF GEOMETRY . 17. Page 18

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**segment**AB be common to the two straight lines BC and BD . From the point B draw EB perpendicular to AB ( a ) . Then , because BC is the continuation of the straight line AB , the angles ABE and EBC will both be right angles ( 6 ) and ... Page 47

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**segments**Be and eC , and that the square described on either side of the triangle ABC is equal in area to the rectangle under the whole hypotenuse and the seg- ment of the hypotenuse adjacent to the same side . 2. This proposition may ...### 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