## 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 127

If troo circles

being produced shall pass • through a point of contact For if possible let the

centres be so situated , that the right line connecting them will not pass through a

point of ...

If troo circles

**touch**one another internally , the right line joining their centresbeing produced shall pass • through a point of contact For if possible let the

centres be so situated , that the right line connecting them will not pass through a

point of ...

Side 182

To describe tron circles , each having a given radius which shall

right line [ DE ] both on the • same side and shall also

. . ANALYSIS . Suppose the circles CI and FI

To describe tron circles , each having a given radius which shall

**touch**a givenright line [ DE ] both on the • same side and shall also

**touch**one another . Fig . 67. . ANALYSIS . Suppose the circles CI and FI

**touch**the given right line DE in C ... Side 46

X . If on three sides of a right angled a semicircles be described , and with the

centres of those described on the sides , Os be described

on the base ; they will also

X . If on three sides of a right angled a semicircles be described , and with the

centres of those described on the sides , Os be described

**touching**that describedon the base ; they will also

**touch**the other semicircles . XI . If two Os**touch**one ... Side 53

If the four Os be described that

the continued product of the four radii ( By Theorem 81 . ) LXXXIII . If semicircles

be described on the segments of the diameter of a semicircle , and a O be ...

If the four Os be described that

**touch**each , three sides of a A , the D of the area =the continued product of the four radii ( By Theorem 81 . ) LXXXIII . If semicircles

be described on the segments of the diameter of a semicircle , and a O be ...

Side 61

To describe a circle through three points . . a circle to

to pass through a point and

To describe a circle through three points . . a circle to

**touch**three given lines . III .to pass through a point and

**touch**two lines . IV . to pass through two points and**touch**a line . to pass through two points and**touch**a circle . to pass through one ...### 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.