## 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 8

connect its vertex with the

given line . For thus there are formed two triangles having the three sides of one

respectively = to those of the other , . . . , & c . Schol . . In the same manner a ...

connect its vertex with the

**given point**; the connecting line is at right angles to thegiven line . For thus there are formed two triangles having the three sides of one

respectively = to those of the other , . . . , & c . Schol . . In the same manner a ...

Side 131

PROB , From a

be a tangent to the circle . From the centre of the given circle as a centre and the

PROB , From a

**given point**without a given circle , to draw a right line which shallbe a tangent to the circle . From the centre of the given circle as a centre and the

**given point**as distance , describe a circle , connect the centre and**given point**... Side 58

If a right line drawn through a

divided in a given ratio , the locus of the point of section is a right line given in

position . XIX . If a right line , drawn from a

position ...

If a right line drawn through a

**given point**to a right line given in position bedivided in a given ratio , the locus of the point of section is a right line given in

position . XIX . If a right line , drawn from a

**given point**to a straight line given inposition ...

Side 63

Let two Os have the same centre , and let A , B , be two

circumference of one of them . ... Any number of points A , B , C , D , & c . being

given in the periphery of a given O , it is required to find another point P ( in the

periphery ) ...

Let two Os have the same centre , and let A , B , be two

**given points**in thecircumference of one of them . ... Any number of points A , B , C , D , & c . being

given in the periphery of a given O , it is required to find another point P ( in the

periphery ) ...

Side 65

From two

given by position ; su that their difference shall be = to a given right line XLIII .

Through a

a ...

From two

**given points**A , B to draw two lines AC , BC to meet in a right line DEgiven by position ; su that their difference shall be = to a given right line XLIII .

Through a

**given point**P , to draw a line GH terminating in a right line AB , and ina ...

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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.