## 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 153

If those right angles be bisected , and the subtenses of the halves be drawn , an

octagon will be

angles also an hexagon may be

If those right angles be bisected , and the subtenses of the halves be drawn , an

octagon will be

**inscribed**; and if bisected a duodecagon . By triseoting the rightangles also an hexagon may be

**inscribed**, and also an equilateral triangle . Side 46

... the inner in the points b , b ' , the atb = bt á ( 32 , 3 . Elr . ) XII . The sum of the O '

s of the lines from any point of a O to the xs of the

the O of the radius . And if drawn to the as of the

... the inner in the points b , b ' , the atb = bt á ( 32 , 3 . Elr . ) XII . The sum of the O '

s of the lines from any point of a O to the xs of the

**inscribed**02 is = to eight timesthe O of the radius . And if drawn to the as of the

**inscribed**equilateral A they are ... Side 47

pendiculars be let fall on the three sides of the

perpendiculars lie in directum . XIX . P is a point in the diameter of a 0 , and PB a

perpendicular to the diameter ; draw any chord PA and a tangent AB meeting PB

in B ...

pendiculars be let fall on the three sides of the

**inscribed**A ; the feet of thoseperpendiculars lie in directum . XIX . P is a point in the diameter of a 0 , and PB a

perpendicular to the diameter ; draw any chord PA and a tangent AB meeting PB

in B ...

Side 48

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

centres of their

equilateral A . . XXXII . The distance between the centres of the

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 anequilateral A . . XXXII . The distance between the centres of the

**inscribed**and ... Side 54

Suppose a quadrilateral figure be in scribed in another quadrilateral figure , so

that the perimeter of the

the

Suppose a quadrilateral figure be in scribed in another quadrilateral figure , so

that the perimeter of the

**inscribed**one be a minimum ; then the opposite sides ofthe

**inscribed**figure , when produced , will intersect each other in the diagonals ...### 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.