## 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 32

sides . 1 Assume on the greater base from either extremity a third proportional to

that base and the homologous side of the other A , and join the extremity of the ...

**Similar**triangles are to one another in the duplicate rutio of their homologoussides . 1 Assume on the greater base from either extremity a third proportional to

that base and the homologous side of the other A , and join the extremity of the ...

Side 33

As adjacent to each of those will also be

excesses of = Zs of the foregoing As above corresponding Ls of the polygons ) ...

**similar**, since those Zs are = and the sides about them proportional ( 6 . 6 ) ; theAs adjacent to each of those will also be

**similar**, having one 2 in each = ( viz . theexcesses of = Zs of the foregoing As above corresponding Ls of the polygons ) ...

Side 34

6 , and let another be described

side ; if it be constructed so that the < s adjacent to this right line shall be = to

those which are adjacent to the side = to this , the polygons shall be = ; but if it be

so ...

6 , and let another be described

**similar**to this , upon a right line = to its greatestside ; if it be constructed so that the < s adjacent to this right line shall be = to

those which are adjacent to the side = to this , the polygons shall be = ; but if it be

so ...

Side 36

And since either of the As into which the diagonal divides the whole

parallelogram is

diagonal , the sides about those equal as are proportional ; . . & c . 33 PROP .

XXV . PROB .

And since either of the As into which the diagonal divides the whole

parallelogram is

**similar**to one of the As into which it divides those about thediagonal , the sides about those equal as are proportional ; . . & c . 33 PROP .

XXV . PROB .

Side 38

If on the sides of a right angled triangle any

described , the figure described on the side subtending the right angle is equal to

the sum of the figures on the other two sides which contain the right angle .

If on the sides of a right angled triangle any

**similar**rectilineal figures be similarlydescribed , the figure described on the side subtending the right angle is equal to

the sum of the figures on the other two sides which contain the right angle .

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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.