## 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 point ; the connecting line is at right angles to the

given line . ... cutting the given line in two points , bisect the intercept and connect

the given point with the extremities of it , and also with the

connect its vertex with the given point ; the connecting line is at right angles to the

given line . ... cutting the given line in two points , bisect the intercept and connect

the given point with the extremities of it , and also with the

**point of bisection**... Side 57

If two sides ( CD , EF ) of a quadrilateral figure be parallel , the triangle ( ICE )

contained by either of theother sides , and the straight lines drawn from its

extremities to the

51 .

If two sides ( CD , EF ) of a quadrilateral figure be parallel , the triangle ( ICE )

contained by either of theother sides , and the straight lines drawn from its

extremities to the

**point of bisection**of the opposite side , , is half the figure . Fig .51 .

Side 119

Draw any right line within the circle , let it be terminated by the circumference ,

bisect it and from the

produce this line to meet the circumference , bisect it ; its

be the ...

Draw any right line within the circle , let it be terminated by the circumference ,

bisect it and from the

**point of bisection**draw a line at right angles to it andproduce this line to meet the circumference , bisect it ; its

**point of bisection**shallbe the ...

Side 120

If any two points be taken in the circumference of a circle , the right line which

joins them falls within the circle . cle with outside right lin For if possible let the ...

8 , 1 , ) the angles at the

If any two points be taken in the circumference of a circle , the right line which

joins them falls within the circle . cle with outside right lin For if possible let the ...

8 , 1 , ) the angles at the

**point of bisection**are = , and are . . . right angles , ( prop . Side 121

internet and also those at the

the centre ( viz . those opposite those angles as being radii of the same circle )

are > , . . the two triangles are = , and their other sides , viz . the parts of the line

not ...

internet and also those at the

**point of bisection**( by constr . ) and the lines fromthe centre ( viz . those opposite those angles as being radii of the same circle )

are > , . . the two triangles are = , and their other sides , viz . the parts of the line

not ...

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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.