## 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 113

... is evident by taking the rectangle under the segments from the O ' of the greater

segment and the rectangle under given line and lesser . NOTE 1 . Given the

greater segment ( AB ) of a line , eut in extreme and

.

... is evident by taking the rectangle under the segments from the O ' of the greater

segment and the rectangle under given line and lesser . NOTE 1 . Given the

greater segment ( AB ) of a line , eut in extreme and

**mean**ratio , to find the lesser.

Side 22

centre and half sum as radius describe on the sum a semicircle ; from the

common extremity of the parts erect a perpendicular to meet the circumference , it

will be the

...

centre and half sum as radius describe on the sum a semicircle ; from the

common extremity of the parts erect a perpendicular to meet the circumference , it

will be the

**mean**proportional required . For draw chords from the extremity of this...

Side 28

5 is the

can find the fourth . ad Note 2 . Thus also we can apply to a given right line a

rectangle = to a given one ; by finding a fourth proportional to the given line , the

base ...

5 is the

**mean**sought ; in like manner if we are given any other three terms , wecan find the fourth . ad Note 2 . Thus also we can apply to a given right line a

rectangle = to a given one ; by finding a fourth proportional to the given line , the

base ...

Side 30

If three right lines be proportional , the rectangle under the extremes is equal to

the square of the

square of the

...

If three right lines be proportional , the rectangle under the extremes is equal to

the square of the

**mean**. And if the rectangle under the extremes be equal to thesquare of the

**mean**, the three right lines are proportional . Part 1 . Assume a right...

Side 37

To cut a given finite right line in extreme and

ratio is meant , so that the whole line shall be to the greater segment as the

greater segment is to the less ( Def . 4 . B . 6 ) . . . the rectangle under the whole

line ...

To cut a given finite right line in extreme and

**mean**ratio . By extreme and**mean**ratio is meant , so that the whole line shall be to the greater segment as the

greater segment is to the less ( Def . 4 . B . 6 ) . . . the rectangle under the whole

line ...

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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.