## 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 5

In an

the equal sides be produced the angles below the base shall be also equal .

Assume points on the legs below the base equidistant from the vertex ; and from

...

In an

**isosceles**triangle the angles at the base are equal - to one another ; and ifthe equal sides be produced the angles below the base shall be also equal .

Assume points on the legs below the base equidistant from the vertex ; and from

...

Side 6

If it be possible that there can , Ist , let the vertex of one fall without the other ,

draw a right connecting their vertices , then this connecting line will be the base

of two

they ...

If it be possible that there can , Ist , let the vertex of one fall without the other ,

draw a right connecting their vertices , then this connecting line will be the base

of two

**isosceles**triangles , and the angles at the base must be = : in each , but ifthey ...

Side 49

Describe on AC an

the angles DAC , DCA is half a right angle , and DCA is = to the angles ( ' BD ) ,

DCB , but those angles are = to one another , because CA and CD are = , . . each

...

Describe on AC an

**isosceles**right angled triangle CDA , join DB . Then each ofthe angles DAC , DCA is half a right angle , and DCA is = to the angles ( ' BD ) ,

DCB , but those angles are = to one another , because CA and CD are = , . . each

...

Side 71

In a right angled

hypothenuse and side , to construct ... and since the triarfgle CAD is

the angle CDA is half a right angle , . . . the angle CBD is half the supplement of

half a right ...

In a right angled

**isosceles**triangle , given the difference between thehypothenuse and side , to construct ... and since the triarfgle CAD is

**isosceles**,the angle CDA is half a right angle , . . . the angle CBD is half the supplement of

half a right ...

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 remaining part of the cut is

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 is

**isosceles**, 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.