## 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 58

If a right line drawn through a given point to a right line

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

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 in****position**... Side 62

The area of a rectangle being given to describe it , so that its sides shall pass

through four given points , XV . A Abeing

also given ; it is required to draw lines through those points to intersect one

another ...

The area of a rectangle being given to describe it , so that its sides shall pass

through four given points , XV . A Abeing

**given in position**, and two points beingalso given ; it is required to draw lines through those points to intersect one

another ...

Side 65

From two

Through a

a ...

From two

**given**points A , B to draw two lines AC , BC to meet in a right line DE**given**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 ...

Side 66

AC , BC ,

respectively . LII . To determine the

from three

AC , BC ,

**given**by**position**, shall obtain the ratio of three**given**lines m n and prespectively . LII . To determine the

**position**of a point P , at which , lines drawnfrom three

**given**points A , B , C , shall make**given**as one with another . LIII . Side 67

To describe a trapezium similar to a

placed in four right lines , CN , BM , AL , CBAK ,

O to inscribe a A ; 1o . such , that the three sides of the A shall be parallel to three

...

To describe a trapezium similar to a

**given**one efgh having its angular pointsplaced in four right lines , CN , BM , AL , CBAK ,

**given**by**position**. LXI . In a**given**O to inscribe a A ; 1o . such , that the three sides of the A shall be parallel to three

...

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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.