## 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 |

### Inni boken

Resultat 1-5 av 5

Side 5

And since the

= , and the sides and anglès ... In an isosceles triangle the angles at the

equal - to one another ; and if the equal sides be produced the angles below ...

And since the

**bases**( and other sides ) coincide the angles at the**bases**must be= , and the sides and anglès ... In an isosceles triangle the angles at the

**base**areequal - to one another ; and if the equal sides be produced the angles below ...

Side 9

Triangles and parallelograms which have the same altitude , are to one another

as their

parts , and let one of those parts be repeated as often as possible on the ...

Triangles and parallelograms which have the same altitude , are to one another

as their

**bases**. Part 1 . Let the antecedent -**base**be divided into any number of =parts , and let one of those parts be repeated as often as possible on the ...

Side 20

Connect the extremities of those perpendiculars , and produce the connecting

line to meet the line on which the part is assumed . That line will be the

right angled A ; assume on it from the point in which the second perpendicular ...

Connect the extremities of those perpendiculars , and produce the connecting

line to meet the line on which the part is assumed . That line will be the

**base**of aright angled A ; assume on it from the point in which the second perpendicular ...

Side 32

1 Assume on the greater

assumed part with the vertex of the opposite si Then the A standing on the

assumed part ...

1 Assume on the greater

**base**from either extremity a third proportional to that**base**and the homologous side of the other A , and join the extremity of theassumed part with the vertex of the opposite si Then the A standing on the

assumed part ...

Side 56

I . Given the

occurse of the perpendiculars from the s on the sides . 2o . Of the centre of the

circumscribing 0 . 30 . Of the bisectors of the sides . 4° . Of the centre of the

inscribed o ...

I . Given the

**base**and vertical < of a A , required the following loci . 1o . Of theoccurse of the perpendiculars from the s on the sides . 2o . Of the centre of the

circumscribing 0 . 30 . Of the bisectors of the sides . 4° . Of the centre of the

inscribed o ...

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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.