## 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 41

Suppose BGC to be the

EC . Therefore if you raise a perpendicular DG from the given point and bisect BC

in E , and subtend the angle BDG with EG drawn from the point of bisection ...

Suppose BGC to be the

**required triangle**. Bisect BC in E , join EG , it is = to EB orEC . Therefore if you raise a perpendicular DG from the given point and bisect BC

in E , and subtend the angle BDG with EG drawn from the point of bisection ...

Side 59

Given in a right angled triangle , one side and the sum of the hypothenuse and

the other side , to conatruct it . Fig . 53 . ANALYSIS . Suppose A BC to be the

BAC ...

Given in a right angled triangle , one side and the sum of the hypothenuse and

the other side , to conatruct it . Fig . 53 . ANALYSIS . Suppose A BC to be the

**required triangle**: AB is = the given side , and AD the given sum ; join DB . SinceBAC ...

Side 65

Given of any triangle the base , the sum and difference - of the angles at the base

to construct it . Fig . 53 ANALYSIS . Suppose ABD to be the

from AD a part AC = to AB ; join BC . Then , because AB is = to AC , it is evident ...

Given of any triangle the base , the sum and difference - of the angles at the base

to construct it . Fig . 53 ANALYSIS . Suppose ABD to be the

**required triangle**, cutfrom AD a part AC = to AB ; join BC . Then , because AB is = to AC , it is evident ...

Side 66

Then at one extremity , G , of the given side , make the angle CGA = to the given

angle , draw EI = to the given perpendicular , join IG , and from I draw a line IA to

IG to meet GĂ , join AC ; AGC is evidently the

Then at one extremity , G , of the given side , make the angle CGA = to the given

angle , draw EI = to the given perpendicular , join IG , and from I draw a line IA to

IG to meet GĂ , join AC ; AGC is evidently the

**required triangle**. PROP . 89 . Side 71

Suppose that ABD is the

given difference , and BAD the given angle ; join BC . Because CD is the

difference between AB and AD , . . AB is = to AC , . . . the angles A BC and ACB

are = , .

Suppose that ABD is the

**required triangle**. Let BD be the given base , CD thegiven difference , and BAD the given angle ; join BC . Because CD is the

difference between AB and AD , . . AB is = to AC , . . . the angles A BC and ACB

are = , .

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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.