## 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 12

Given three right lines of which any troo together are greater than the third to

lines . From any point draw a right line to one of them and from the extremities of

this ...

Given three right lines of which any troo together are greater than the third to

**construct**a triangle , whose sides shall be respectively equal to the three givenlines . From any point draw a right line to one of them and from the extremities of

this ...

Side 22

If the base of the given triangle and the given right line be not in directum ;

produce the given line until the produced part becomes to the base of the triangle

, and on this produced part ,

22 . ) ...

If the base of the given triangle and the given right line be not in directum ;

produce the given line until the produced part becomes to the base of the triangle

, and on this produced part ,

**construct**a triangle = to the given one ; ( cor . prop .22 . ) ...

Side 68

Given the sum of the hypothenuse and one side , and the contained angle of a

right angled trianyle , to

required triangle . Let BA be = to the given sum , and ACD to the given angle ;

join ...

Given the sum of the hypothenuse and one side , and the contained angle of a

right angled trianyle , to

**construct**it . Fig . 42 . ANALYSIS . Suppose DCA is therequired triangle . Let BA be = to the given sum , and ACD to the given angle ;

join ...

Side 93

Gwen the lengths of the three lines which drawn from the angles biseet the

opposite sides to

sides shall be double the given bisectors ; bisect MO in D , join DL , make LI įrds

of LD ...

Gwen the lengths of the three lines which drawn from the angles biseet the

opposite sides to

**construct**the triangle Fig . 57**Construct**a triangle OML whosesides shall be double the given bisectors ; bisect MO in D , join DL , make LI įrds

of LD ...

Side 31

For it is = to the 0 of the mean proportional between them , but the O ' s . of

proportional right lines are themselves proportional , as will be shewn in Prop .

22 . PROP . XVIII . PROB . . On a given right line to

similar to ...

For it is = to the 0 of the mean proportional between them , but the O ' s . of

proportional right lines are themselves proportional , as will be shewn in Prop .

22 . PROP . XVIII . PROB . . On a given right line to

**construct**a rectilineal figuresimilar to ...

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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.