## 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 135

In equal circles , equal angles , whether they be at the centres or circumferences ,

stand upon equal

the extremities of the

In equal circles , equal angles , whether they be at the centres or circumferences ,

stand upon equal

**arches**. First , let the given angles be at the centres , draw fromthe extremities of the

**arches**on which they stand in each , right lines to any ... Side 136

nëcting the extremities of the

( prop . 20 , b . 3 , & ax . 7 , ) . . the segments that contain them are similar , but

they stand on = right lines , . . . those segments are = ; take a way those equals ...

nëcting the extremities of the

**arches**; also the angles at the circumferences are =( prop . 20 , b . 3 , & ax . 7 , ) . . the segments that contain them are similar , but

they stand on = right lines , . . . those segments are = ; take a way those equals ...

Side 137

1 , ) and . . the

those =

THEOR . In equal circles , the right lines which subtend equal

1 , ) and . . the

**arches**on which they stand are = , ( prop . 26 , b . 3 , ) take a waythose =

**arches**from the = circles and the remaining**arches**are = • PROP . 29 ,THEOR . In equal circles , the right lines which subtend equal

**arches**, are equal . Side 153

For suppose the circumference to be 360 degrees , by trisecting the right angles it

is divided into

60 an hexagon will be formed , and the sides of the hexagon are evidently to the

...

For suppose the circumference to be 360 degrees , by trisecting the right angles it

is divided into

**arches**of 60 and 120 , : . by connecting the subtenses of those of60 an hexagon will be formed , and the sides of the hexagon are evidently to the

...

Side 170

If two chords ( AB CD ) cut one another within a given circie , the angle of their

inclination is equal to half the angle at the centre which stands on an

to the sum of the

If two chords ( AB CD ) cut one another within a given circie , the angle of their

inclination is equal to half the angle at the centre which stands on an

**arch**equalto the sum of the

**arches**intercepted between them . And if they cut one another ...### 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.