## 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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Side 13

... connect its extremity with the exiremity of the side which is not the greater , this

connecting line will be = to the side

is less than the line

... connect its extremity with the exiremity of the side which is not the greater , this

connecting line will be = to the side

**subtending**the lesser angle ( by 4th . ) * But itis less than the line

**subtending**the greater angle , for if you join the extremities ... Side 115

THEOR , In an obtuse angled triangle , the square of the side

obtuse angle , exceeds the sum of the squares of the sides which contain the

obtuse angle , by double the rectangle under either of these sides and the

external ...

THEOR , In an obtuse angled triangle , the square of the side

**subtending**the "obtuse angle , exceeds the sum of the squares of the sides which contain the

obtuse angle , by double the rectangle under either of these sides and the

external ...

Side 116

If the triangle be right angled the perpendicular coincides with the side

subtepding the acute angle , and the rectangle under the base and intercept is

the o of the base , but it is evident that in this case the O2 of . the side

the acute ...

If the triangle be right angled the perpendicular coincides with the side

subtepding the acute angle , and the rectangle under the base and intercept is

the o of the base , but it is evident that in this case the O2 of . the side

**subtending**the acute ...

Side 27

Draw a diameter from the vertex of the < from which the perpendicular is let fall ,

and join its other extremity with either extremity of the side

Then the thus formed will be right angled , and will be similar to a A of which the ...

Draw a diameter from the vertex of the < from which the perpendicular is let fall ,

and join its other extremity with either extremity of the side

**subtending**that c .Then the thus formed will be right angled , and will be similar to a A of which the ...

Side 29

The extremity of the diameter being connected with the extremity of the

right angled As will be the same as when the perpen , falls within the given A .

But if it be ...

The extremity of the diameter being connected with the extremity of the

**subtending**side adjacent to the perpendicular , the proof of the similarity of theright angled As will be the same as when the perpen , falls within the given A .

But if it be ...

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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.