## 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 6

contained angles also = ( by hypoth ) • . the triangles are = , a part to the whole

which is

Elrington . PROP . 7 . THEOR . On the same right line and on the same side of it ...

contained angles also = ( by hypoth ) • . the triangles are = , a part to the whole

which is

**absurd**. · Cor . Hence every equiangular triangle is equilateral ; vide ,Elrington . PROP . 7 . THEOR . On the same right line and on the same side of it ...

Side 10

... acute angle would be greater than a right , which is

perpendiculars cannot be drawn from the same point to the same right line . For

then an external angle would be = to an internal and opposite which is

PROP .

... acute angle would be greater than a right , which is

**absurd**Cor . 2 . Twoperpendiculars cannot be drawn from the same point to the same right line . For

then an external angle would be = to an internal and opposite which is

**absurd**.PROP .

Side 121

1 , ) . . this part is = to the whole line cutting the circles , which is

point is not the centre of both circles , and in the same maoner it can be proved

that no other point is the centre of both . 1 . PROP . 6 , THEOR . If two 121.

1 , ) . . this part is = to the whole line cutting the circles , which is

**absurd**; . . . thispoint is not the centre of both circles , and in the same maoner it can be proved

that no other point is the centre of both . 1 . PROP . 6 , THEOR . If two 121.

Side 127

Then in the triangle formed by the three connecting lines , those drawn from the

centre to this point of contact , are together greater than that joining the centres ,

but they are also = to part of it , which is

THEOR ...

Then in the triangle formed by the three connecting lines , those drawn from the

centre to this point of contact , are together greater than that joining the centres ,

but they are also = to part of it , which is

**absurd**, 6 . & c . & c . . PROP . 13 ,THEOR ...

Side 130

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

the same circle , . o the angles at the points of contact are = , but one of them is a

right augle , which is

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

the same circle , . o the angles at the points of contact are = , but one of them is a

right augle , which is

**absurd**, . . & c . & c . Parr 2 . If possible let a right line be ...### 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.