## The first and second books of Euclid explained to beginners, by C.P. Mason1872 - Geometry |

### From inside the book

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**lines**,**AB**and CD , of equal length , and that it is requisite for any pur- pose that the one should be supposed to lie upon the other . We may say , " Place the point A upon the point C , and let the**line A B**lie along the line CD ... Page 15

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**A B**be the given finite right**line**. With the centre A , and at the distance**A B**, describe the circle C BE . ( Post . III . ) * By speaking of the**line**as " given , " it is meant that its position is given . By speaking of it as ... Page 16

... lines AC and BC are both equal to the

... lines AC and BC are both equal to the

**line AB**, they are equal to one another ; or , in other words , ACB is an equilateral △ , and is con- structed on the line A B. It would have done equally well if we had taken the point D , and ... Page 20

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**line**and the given point are in different relative positions . By attending to the general directions , all ...**A B**and CD be the two given straight**lines**, of which**A B**is the greater . E A B From the point A draw the straight ... Page 21

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**AB**which was required . For , A E and AF are equal , being radii of the same circle ( Def . XIV . ) ; and as A E and ...**line**A E to be a**line**obtained as the result of all the operations there indicated . Without going through the ...### Other editions - View all

The First and Second Books of Euclid Explained to Beginners, by C.P. Mason Euclides No preview available - 2016 |

### Common terms and phrases

A B and CD A B is equal A C and CB Æneid axiom beginner bisected centre Consequently diagonal draw a straight Edition equal in area equal respectively equal to twice equilateral Euclid exterior exterior angle Fcap figure finite right line follows formed given finite right given line given point given rectilineal given straight line gnomon greater half a right hypotenuse interior and opposite isosceles Join the points join two given Jugurtha Latin length less line A B line CD linear units lines are parallel magnitudes meeting the line opposite sides parallelogram point F proof Prop proposition prove this proposition rectangle contained right angles side A C straight line meets suppose three sides triangle unequal

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Page 144 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Page 149 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...

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Page 152 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

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