## 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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Side 18

Right lines which join the adjacent extremities of equal and parallel right lines are

also themselves equal and parallel , Draw a

formed , haying a given = side , and

Right lines which join the adjacent extremities of equal and parallel right lines are

also themselves equal and parallel , Draw a

**diagonal**, then two triangles areformed , haying a given = side , and

**diagonal**in one respectively = to the other ... Side 30

Suppose it to be done , and that the line CF bisects it , draw the

Then the triangle DBE is half • the parallelogram ( by 31 . 1 . of Elr . ) also the

figure FCBE is half of it . . if you take away the common figure FGBE the triangles

DGF ...

Suppose it to be done , and that the line CF bisects it , draw the

**diagonal**BD ) .Then the triangle DBE is half • the parallelogram ( by 31 . 1 . of Elr . ) also the

figure FCBE is half of it . . if you take away the common figure FGBE the triangles

DGF ...

Side 28

figure , an < = to the less ; that line will divide the

segments , the rect . under either of which and the other

. under the side of the < ( from the vertex of which the line was drawn ) ...

figure , an < = to the less ; that line will divide the

**diagonal**on which it falls intosegments , the rect . under either of which and the other

**diagonal**, is = to the rect. under the side of the < ( from the vertex of which the line was drawn ) ...

Side 36

2. 34. 1. ) with it . And since either of the As into which the

whole parallelogram is similar to one of the As into which it divides those about

the

XXV .

2. 34. 1. ) with it . And since either of the As into which the

**diagonal**divides thewhole parallelogram is similar to one of the As into which it divides those about

the

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

Side 36

And since either of the As into which the

parallelogram is similar to one of the As into which it divides those about the

XXV . PROB .

And since either of the As into which the

**diagonal**divides the wholeparallelogram is similar to one of the As into which it divides those about the

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

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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.