## 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 |

### Inni boken

Resultat 1-5 av 5

Side 10

nal angle is

opposite side beyond the vertex of this external angle , and

new external angle , thus formed greater than that internal angle : but this ...

nal angle is

**proved**greater than the other internal remote angle by producing theopposite side beyond the vertex of this external angle , and

**proving**as before thenew external angle , thus formed greater than that internal angle : but this ...

Side 6

This definition differs from those following ; in it it is necessary that the quantities

should be of the same kind , but in the others it is not . It is called alternate

proportion , and is

when it ...

This definition differs from those following ; in it it is necessary that the quantities

should be of the same kind , but in the others it is not . It is called alternate

proportion , and is

**proved**by the 35th Prop . of the 5th Book . 15. By invertendo ;when it ...

Side 6

The def . is

concluded , that if there be four magnitudes proportional , the first together with

the second is to the second , as the third together with the fourth is to the fourth .

Note .

The def . is

**proved**by Prop . 20 . Book 5 . 16 . Componendo ; when it isconcluded , that if there be four magnitudes proportional , the first together with

the second is to the second , as the third together with the fourth is to the fourth .

Note .

Side 40

circumference are so . In the proof of that part concerning the sectors , it is

necessary to

equal arcs are = ...

**proved**to be as the arcs on which they stand ; it follows that the < s at thecircumference are so . In the proof of that part concerning the sectors , it is

necessary to

**prove**, that the sectors of the same or equal circles standing onequal arcs are = ...

Side 45

It may be

of the sides of a intersect in one point , hence

perpendiculars from the < s . II . In the same a , the points of occourse of the per -

pendiculars ...

It may be

**proved**by the first Book that the perpendiculars from the middle pointsof the sides of a intersect in one point , hence

**prove**the same of theperpendiculars from the < s . II . In the same a , the points of occourse of the per -

pendiculars ...

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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.