## 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

And since the bases ( and other sides ) coincide the angles at the bases must be

= , and the sides and anglès coinciding and being

triangles must coincide and be = . . PROP . 5 , THEOR . In an isosceles triangle

the ...

And since the bases ( and other sides ) coincide the angles at the bases must be

= , and the sides and anglès coinciding and being

**respectively**= , the wholetriangles must coincide and be = . . PROP . 5 , THEOR . In an isosceles triangle

the ...

Side 12

... shall be

line to one of them and from the extremities of this , draw right lines

to the other two , and with these extremities as centres , and the lines drawn ...

... shall be

**respectively**equal to the three given lines . From any point draw a rightline to one of them and from the extremities of this , draw right lines

**réspectively**=to the other two , and with these extremities as centres , and the lines drawn ...

Side 14

PROP . 26 , THEOR . If two triangles have two angles of the one

equal to two angles of the other , and a side of the one equal to a side of the other

, whether it be adjacent or opposite to these equal angles , the remaining sides

and ...

PROP . 26 , THEOR . If two triangles have two angles of the one

**respectively**equal to two angles of the other , and a side of the one equal to a side of the other

, whether it be adjacent or opposite to these equal angles , the remaining sides

and ...

Side 26

Then in the triangles BAE , CAD , the sides BA and AE are

and AD and the angle A common . . . DC and B ' E are = and the angle ABE is =

to ACD . Then in the triangles DBE , ECD the sides DB , BE are

Then in the triangles BAE , CAD , the sides BA and AE are

**respectively**= to ÇAand AD and the angle A common . . . DC and B ' E are = and the angle ABE is =

to ACD . Then in the triangles DBE , ECD the sides DB , BE are

**respectively**= to ... Side 14

the

proportional " ( alternando and ex æquali ) the sides about the as subtended by

those bases are proportional ; and also the sides which are opposite to = 4s are ...

the

**respectively**= 28 at the bases ( placed in directum ) of the given As , areproportional " ( alternando and ex æquali ) the sides about the as subtended by

those bases are proportional ; and also the sides which are opposite to = 4s 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.