## 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 12

... them as intervals describe two circles , and from either of their intersections

draw lines to the centres ( or the extremities of the first drawn line ) thus the

triangle is

the two ...

... them as intervals describe two circles , and from either of their intersections

draw lines to the centres ( or the extremities of the first drawn line ) thus the

triangle is

**formed**. · For those lines drawn from intersection are respectively = tothe two ...

Side 19

Parallelograms on the same base and between the same parallels are equal . •

Connect the sides opposite the base , ( if neeessary , ) then there are two

triangles

parallelogram ...

Parallelograms on the same base and between the same parallels are equal . •

Connect the sides opposite the base , ( if neeessary , ) then there are two

triangles

**formed**( viz . the excesses of the quadrilateral figure above eachparallelogram ...

Side 22

line , the side of first parm . adjacent to the given line , then there is

given line a parm , which with the first

about the diagonal of the entire parm , and is . . . I to first parm . ( 43 , 1 , ) and it ...

line , the side of first parm . adjacent to the given line , then there is

**formed**on thegiven line a parm , which with the first

**formed**parm . is complemental of the twoabout the diagonal of the entire parm , and is . . . I to first parm . ( 43 , 1 , ) and it ...

Side 23

Then it is evident that those produced parts intercepted between the <

the extremes and the vertices of the instrument are the required means . Philo ' s

Method . Let the given extremes be placed at right < s to one another , complete ...

Then it is evident that those produced parts intercepted between the <

**formed**bythe extremes and the vertices of the instrument are the required means . Philo ' s

Method . Let the given extremes be placed at right < s to one another , complete ...

Side 51

Euclides James Luby. periphery inscribed in a given A , is that

the feet of the three perpendiculars from the < s . LVIII . In the same construction ;

if de be drawn , the right lines fb , ae and dc , are all three cut harmonically . LIX .

Euclides James Luby. periphery inscribed in a given A , is that

**formed**by joiningthe feet of the three perpendiculars from the < s . LVIII . In the same construction ;

if de be drawn , the right lines fb , ae and dc , are all three cut harmonically . LIX .

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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.