## 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 7

It is evident that the

the triangles themselves , . the . . PROP . 9 , PROB . : To bisect a given rectilineal

angle . On the sides containing the angle assume = portions towards the vertex ...

It is evident that the

**remaining**angles opposite . the = sides are also = and alsothe triangles themselves , . the . . PROP . 9 , PROB . : To bisect a given rectilineal

angle . On the sides containing the angle assume = portions towards the vertex ...

Side 46

DO is = to DO . . the angles DCO , DOC are = , but the angle EDO js = to DOC , .

to DCO ; for the same reason the angle , PEO is = to CAB , . ' . the

angle DOE is to the angle ABC , • , the triangles BAC , OED ale similar , Cor .

DO is = to DO . . the angles DCO , DOC are = , but the angle EDO js = to DOC , .

to DCO ; for the same reason the angle , PEO is = to CAB , . ' . the

**remaining**angle DOE is to the angle ABC , • , the triangles BAC , OED ale similar , Cor .

Side 61

equal , the

in every way . Fig . 55 . Produce AB until BG is = to ED , join GC . . . Then the

triangles BCG and DEF have BG = ED and BC = EF , and the angle CBG = FED ...

equal , the

**remaining**, sides shall be equal , and the tuzo triangles shall be equalin every way . Fig . 55 . Produce AB until BG is = to ED , join GC . . . Then the

triangles BCG and DEF have BG = ED and BC = EF , and the angle CBG = FED ...

Side 122

The

angles with the diameter are equal . That line which is nearer to that passing

through the centre , is greater than one more remote . And more than troo right

lines ...

The

**remaining**part of the diameter is the least . Those lines which make equalangles with the diameter are equal . That line which is nearer to that passing

through the centre , is greater than one more remote . And more than troo right

lines ...

Side 16

Then the line that cuts off this < , also cuts from the given A , a which is

equiangular with the other given one ; and the

isosceles , for two of its sides ( i . e . the cutting line and

cut < ) bear the ...

Then the line that cuts off this < , also cuts from the given A , a which is

equiangular with the other given one ; and the

**remaining**part of the cut isisosceles , for two of its sides ( i . e . the cutting line and

**remaining**side about thecut < ) bear the ...

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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.