## 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 11

i the entire angle opposite the greater side is much greater than the angle

opposite the

than an other , the side which is opposite the greater angle is greater than the

side ...

i the entire angle opposite the greater side is much greater than the angle

opposite the

**less**. I PROP . 19 , THEOR . If in any triangle one angle be greaterthan an other , the side which is opposite the greater angle is greater than the

side ...

Side 13

... the exiremity of the side which is not the greater , this connecting line will be =

to the side subtending the lesser angle ( by 4th . ) * But it is

subtending the greater angle , for if you join the extremities of it and the line subt .

nd ...

... the exiremity of the side which is not the greater , this connecting line will be =

to the side subtending the lesser angle ( by 4th . ) * But it is

**less**than the linesubtending the greater angle , for if you join the extremities of it and the line subt .

nd ...

Side 146

CBD is = to the difference between the ' rs of BA , AC , ( cor , prop , 6 , b . l . ) 6 .

The square of the greater of any two lines , is equal to four rectangles under the

CBD is = to the difference between the ' rs of BA , AC , ( cor , prop , 6 , b . l . ) 6 .

The square of the greater of any two lines , is equal to four rectangles under the

**less**and difference , with a square of the difference between the**less**and ... Side 1

A

when the

another when it is contained in it a certain number of times exactly ; for example ,

3 is ...

A

**less**magnitude is said to be an aliquot part or sub - , multiple of a greater ,when the

**less**measures the greater . Note . One magnitude is said to measureanother when it is contained in it a certain number of times exactly ; for example ,

3 is ...

Side 36

If similar and similarly posited parallelograms have a common angle , they are

about the same diagonal . If possible let them not be about the same diagonal ;

then the diagonal of the greater parallelogram will cut a side of the

the ...

If similar and similarly posited parallelograms have a common angle , they are

about the same diagonal . If possible let them not be about the same diagonal ;

then the diagonal of the greater parallelogram will cut a side of the

**less**, not atthe ...

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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.