## The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 3 |

### Inni boken

Resultat 1-5 av 5

Side 158

Then join the centres F , E ; and on FE describe a semicircle FHE , in it inflect a

right liné FH = to the sum of the

connect their centres , draw a

to the ...

Then join the centres F , E ; and on FE describe a semicircle FHE , in it inflect a

right liné FH = to the sum of the

**radii**FO , LE , join ... If the given circles bé =connect their centres , draw a

**radius**in each on the same side and at right anglesto the ...

Side 161

3 , Elr . ) , the circle described with O as a centre and OK as

through the points of bisection of every right line placed within that circle . PROP .

13 , THEOR . The locus of the centres of any number of circles which shall touch

...

3 , Elr . ) , the circle described with O as a centre and OK as

**radius**shall . passthrough the points of bisection of every right line placed within that circle . PROP .

13 , THEOR . The locus of the centres of any number of circles which shall touch

...

Side 166

Suppose it done , and that CL is the circle required to be described , join D the

centre and point of contact C , CD is to the given

the given line BF . Then inflect between BF and EF a right line CD = to the given ...

Suppose it done , and that CL is the circle required to be described , join D the

centre and point of contact C , CD is to the given

**radius**and is at right angles tothe given line BF . Then inflect between BF and EF a right line CD = to the given ...

Side 47

Prove that if from the extremities of the side of a pentagon inscribed in a straight

lines be drawn to the middle of the arc subtended by the adjacent side , their

difference is = to the

...

Prove that if from the extremities of the side of a pentagon inscribed in a straight

lines be drawn to the middle of the arc subtended by the adjacent side , their

difference is = to the

**radius**; the sum of their O ' s is three times the ? of the**radius**...

Side 48

four times the area , is = to the

XXXI . If equilateral As be described on the three sides of a A , and a , a ' , a ' be

the centres of their inscribed Os , the A a a ' a " formed by joining those points is ...

four times the area , is = to the

**radius**of the circumscribing 0 . ( Cor . 16 . 6 . Elr . )XXXI . If equilateral As be described on the three sides of a A , and a , a ' , a ' be

the centres of their inscribed Os , the A a a ' a " formed by joining those points is ...

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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... Euclides Uten tilgangsbegrensning - 1833 |

### Vanlige uttrykk og setninger

absurd adjacent ANALYSIS arches assumed base centre chord circle circumference common construct describe diagonal diameter difference divided double draw draw a line equal evident external extremity figure formed four fourth given angle given circle given in position given line given point given right line greater half hypothenuse inscribed intercept internal intersect isosceles join less lesser line drawn lines be drawn magnitude mean meet Note O’rs opposite side parallel parallelogram pass perpendicular point of bisection point of contact PROB produced PROP proportional proposition proved radii radius reason rect rectangle remaining required triangle respectively right angled triangle right angles right line segment semicircle side similar square stand subtending Suppose taken tangent THEOR third touch triangle unequal vertex whole line

### Populære avsnitt

Side 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.

Side 28 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.

Side 113 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...

Side 6 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.

Side 98 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 4 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.

Side 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Side 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Side 158 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.

Side 30 - Similar triangles are to one another in the duplicate ratio of their homologous sides.