## 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 |

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Resultat 1-5 av 5

Side 122

The remaining part of the

angles with the

through the centre , is greater than one more remote . And more than troo right

lines ...

The remaining part of the

**diameter**is the least . Those lines which make equalangles with the

**diameter**are equal . That line which is nearer to that passingthrough the centre , is greater than one more remote . And more than troo right

lines ...

Side 130

For if it be possible , let there be a right Jine which meets it again and is

perpendicular to the

Then because in the triangle thus formed , two of the sides are = , being radii of

the same ...

For if it be possible , let there be a right Jine which meets it again and is

perpendicular to the

**diameter**, connect the centre and this point of contact . . .Then because in the triangle thus formed , two of the sides are = , being radii of

the same ...

Side 138

Draw a

join the vertex of it with the centre . ' Then this connecting line being s to each part

of the

Draw a

**diameter**connecting the extremities of the sides about the angle , andjoin the vertex of it with the centre . ' Then this connecting line being s to each part

of the

**diameter**at each side of the centre , ( by prop . 5 , b . 1 , ) the sum of the ... Side 29

The extremity of the

subtending side adjacent to the perpendicular , the proof of the similarity of the

right angled As will be the same as when the perpen , falls within the given A .

But if it be ...

The extremity of the

**diameter**being connected with the extremity of thesubtending side adjacent to the perpendicular , the proof of the similarity of the

right angled As will be the same as when the perpen , falls within the given A .

But if it be ...

Side 48

The distance between the centres of the inscribed and circumscribing Os to a A ,

is a mean proportional between the radius of the circumscribing 0 and the

difference between that radius and the

and 4 ...

The distance between the centres of the inscribed and circumscribing Os to a A ,

is a mean proportional between the radius of the circumscribing 0 and the

difference between that radius and the

**diameter**of the inscribed . ( Cor . 6 . 2 ,and 4 ...

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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.