## 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 20

38 ,

equal , Draw through either extremity of each base ( to meet the line par . to the

bases ) lines par . to the sides of the triangles terminating in the other extremity of

...

38 ,

**THEOR**. Triangles on equal bases , and between the same parallels areequal , Draw through either extremity of each base ( to meet the line par . to the

bases ) lines par . to the sides of the triangles terminating in the other extremity of

...

Side 31

6 ,

be drawn through the point of bisectiun ( D ) parallel to the base it kisects the third

side , : Fig . 7 . ANALYSIS , Suppose it to be the case ; connect FB , then since ...

6 ,

**THEOR**. If one side ( AB ) of any triangle be bisected , and a right line ( DF )be drawn through the point of bisectiun ( D ) parallel to the base it kisects the third

side , : Fig . 7 . ANALYSIS , Suppose it to be the case ; connect FB , then since ...

Side 64

84 ,

whose buse ( AB ) is equal to the sum of the parallel sides ( LC , AS ) of the

trapezium , and rohose attitude is equal to that of the trapezium . Fig . 59 . Draw

CT ...

84 ,

**THEOR**. The area of a trapezium ( LS ) is half that of a parallelogram ( LB )whose buse ( AB ) is equal to the sum of the parallel sides ( LC , AS ) of the

trapezium , and rohose attitude is equal to that of the trapezium . Fig . 59 . Draw

CT ...

Side 174

the same side of it , and having the equal vertical angles , the greatest is that (

CDB ) which is isosceles . Fig . 47 . Describe a segt . of a circle on CB to pass ...

**THEOR**. Of all the triangles ( CDB CIB ) standing on the same base ( CB ) , onthe same side of it , and having the equal vertical angles , the greatest is that (

CDB ) which is isosceles . Fig . 47 . Describe a segt . of a circle on CB to pass ...

Side 185

) drawn through the point of contact intercept arches , ( DA FE ) the chords of

which are parallel . Fig . 71 . For by the foregoing proposition the arches ADC

CEF ...

**THEOR**. If two circles ( ACD ECF ) touch one another , troo right lines ( ACF DCE) drawn through the point of contact intercept arches , ( DA FE ) the chords of

which are parallel . Fig . 71 . For by the foregoing proposition the arches ADC

CEF ...

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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.