## 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 120

... the right line which joins them falls within the circle . cle with outside right lin

For if possible let the right line joining them be such that it has a point outside the

circle ; connect the centre of the circle with its

... the right line which joins them falls within the circle . cle with outside right lin

For if possible let the right line joining them be such that it has a point outside the

circle ; connect the centre of the circle with its

**extremities**and with this point . Side 130

If possible let a right line be drawn from a point between a perpendicular and

circumference to the

angle contained by this drawn line and the diameter , must be less than a right ...

If possible let a right line be drawn from a point between a perpendicular and

circumference to the

**extremity**of the diaineter which does not cut the circle . Theangle contained by this drawn line and the diameter , must be less than a right ...

Side 138

Draw a diameter connecting the

join the vertex of it with the centre . ... Draw through the

the given angle , ) of either side about it , a diameter connecting the said

Draw a diameter connecting the

**extremities**of the sides about the angle , andjoin the vertex of it with the centre . ... Draw through the

**extremity**, ( remote fromthe given angle , ) of either side about it , a diameter connecting the said

**extremities**... Side 139

Hence can be derived a method of drawing through the

a perpendicularto it ; take any point without it , and with this point as a centre

describe a circle passing through the

Hence can be derived a method of drawing through the

**extremity**of any right linea perpendicularto it ; take any point without it , and with this point as a centre

describe a circle passing through the

**extremity**and cutting the given live in any ... Side 17

From either

assume on this drawn line from the point of concourse any portion , and also from

the same point another portion , which shall be the same multiple of the first

assumed ...

From either

**extremity**of the given line draw a right line making any with it ;assume on this drawn line from the point of concourse any portion , and also from

the same point another portion , which shall be the same multiple of the first

assumed ...

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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.