## 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 17

For if you assume any point within the given

the angles to it , the

and therefore all their angles taken together are = to twice as many right angles

as ...

For if you assume any point within the given

**figure**and draw lines from each ofthe angles to it , the

**figure**will be divided into as many triangles as it has sides ;and therefore all their angles taken together are = to twice as many right angles

as ...

Side 31

On a given right line to construct a rectilineal

similarly posited . Resolve the given

any of it to all other s except those two adjacent to the one from which the lines

are ...

On a given right line to construct a rectilineal

**figure**similar to a given one , andsimilarly posited . Resolve the given

**figure**into As , by drawing right lines fromany of it to all other s except those two adjacent to the one from which the lines

are ...

Side 33

Hence if three right lines be proportional , any rectilineal

similar rectilineal

rectilineal

Hence if three right lines be proportional , any rectilineal

**figure**on the first , is to asimilar rectilineal

**figure**on the second , as the first to the third . Cor . 2 . Hence arectilineal

**figure**may be described which will be to a given rectilineal**figure**in ... Side 36

To construct a rectilinear

any side of the

rectangle = to it ( Cor . 1 . 45 . 1 ) , and to either side of this rectangle , adjacent to

the ...

To construct a rectilinear

**figure**. equal to a given one , and similar to another . Toany side of the

**figure**to which a similar one is to be constructed , apply arectangle = to it ( Cor . 1 . 45 . 1 ) , and to either side of this rectangle , adjacent to

the ...

Side 38

If on the sides of a right angled triangle any similar rectilineal

described , the

the sum of the

If on the sides of a right angled triangle any similar rectilineal

**figures**be similarlydescribed , the

**figure**described on the side subtending the right angle is equal tothe sum of the

**figures**on the other two sides which contain the right angle .### 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.