## 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 127

If troo circles touch one another internally , the right line joining their centres

being produced shall pass • through a

centres be so situated , that the right line connecting them will not pass through a

If troo circles touch one another internally , the right line joining their centres

being produced shall pass • through a

**point of contact**For if possible let thecentres be so situated , that the right line connecting them will not pass through a

**point of**... Side 128

joining line to one

the

...

joining line to one

**point of contact**: draw right lines from the centres to the other**point of contact**. Thedi the right lines drawn from the centre of the lesser circle tothe

**points of contact**are = , ( def . 15 , b . 1 , ) add to both the right line joining the...

Side 130

And if any right line be drawn from any point within that perpendicular to the

which meets it again and is perpendicular to the diameter , connect the centre ...

And if any right line be drawn from any point within that perpendicular to the

**point****of contact**, it cuts the circle . Part 1 . For if it be possible , let there be a right Jinewhich meets it again and is perpendicular to the diameter , connect the centre ...

Side 51

In the same construction ; the points of occurse of cd , df , be , with ac , cf , fa ,

respectively , lie in directum . ... If from a point without a O a line pc , through the

centre , and a tangent pt be drawn , and from the

then ...

In the same construction ; the points of occurse of cd , df , be , with ac , cf , fa ,

respectively , lie in directum . ... If from a point without a O a line pc , through the

centre , and a tangent pt be drawn , and from the

**point of contact**a diameter td ,then ...

Side 52

If from a point without a O two tangents be drawn , and also any other right line to

meet it in two points , the lines joining these points and one of the

If from a point without a O two tangents be drawn , and also any other right line to

meet it in two points , the lines joining these points and one of the

**points of****contact**shall cut off = segments from the chord which passes through the other**point**...### Hva folk mener - Skriv en omtale

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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.